pushreference 1 "(a2 E a1 & P1 & P0) & P0 -> ( An(a1) E a1 & P2 & P0) & P0" "AN"; THEOREMS:=("AN",(termtosequent(parseprop(" (a2 E a1 & P1 & P0) & P0 -> ( An(a1) E a1 & P2 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "AN"; pushreference 2 "P0 -> (Real(a1 + a2) & P3 & P0) & P0" "RPLUS"; THEOREMS:=("RPLUS",(termtosequent(parseprop("P0 -> (Real(a1 + a2) & P3 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "RPLUS"; pushreference 3 "P0 -> (Real(a1 * a2) & P4 & P0) & P0" "RTIMES"; THEOREMS:=("RTIMES",(termtosequent(parseprop("P0 -> (Real(a1 * a2) & P4 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "RTIMES"; pushreference 4 "P0 -> (Real(Minus(a1)) & P5 & P0) & P0" "RMINUS"; THEOREMS:=("RMINUS",(termtosequent(parseprop("P0 -> (Real(Minus(a1)) & P5 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "RMINUS"; pushreference 5 "P0 -> (Real(Inv(a1)) & P6 & P0) & P0" "RINV"; THEOREMS:=("RINV",(termtosequent(parseprop("P0 -> (Real(Inv(a1)) & P6 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "RINV"; pushreference 6 "P0 -> (Real(Sup(a1)) & P7 & P0) & P0" "RSUP"; THEOREMS:=("RSUP",(termtosequent(parseprop("P0 -> (Real(Sup(a1)) & P7 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "RSUP"; pushreference 7 "P0 -> ( a1 + a2 = a2 + a1 & P8 & P0) & P0" "CPLUS"; THEOREMS:=("CPLUS",(termtosequent(parseprop("P0 -> ( a1 + a2 = a2 + a1 & P8 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "CPLUS"; pushreference 8 "P0 -> ( a1 * a2 = a2 * a1 & P9 & P0) & P0" "CTIMES"; THEOREMS:=("CTIMES",(termtosequent(parseprop("P0 -> ( a1 * a2 = a2 * a1 & P9 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "CTIMES"; pushreference 9 "P0 -> ([a1 + a2] + a3 = a1 + a2 + a3 & P10 & P0) & P0" "APLUS"; THEOREMS:=("APLUS",(termtosequent(parseprop(" P0 -> ( [a1 + a2] + a3 = a1 + a2 + a3 & P10 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "APLUS"; pushreference 10 " P0 -> ( [a1 * a2] * a3 = a1 * a2 * a3 & P11 & P0) & P0" "ATIMES"; THEOREMS:=("ATIMES",(termtosequent(parseprop(" P0 -> ( [a1 * a2] * a3 = a1 * a2 * a3 & P11 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "ATIMES"; pushreference 11 " P0 -> (a1 * [a2 + a3] = a1 * a2 + a1 * a3 & P12 & P0) & P0" "DIST"; THEOREMS:=("DIST",(termtosequent(parseprop(" P0 -> (a1 * [a2 + a3] = a1 * a2 + a1 * a3 & P12 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "DIST"; pushreference 12 " P0 -> ( (Real(a1) -> a1 + Zero = a1) & P13 & P0) & P0" "IPLUS"; THEOREMS:=("IPLUS",(termtosequent(parseprop(" P0 -> ( (Real(a1) -> a1 + Zero = a1) & P13 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "IPLUS"; pushreference 13 " P0 -> ( (Real(a1) -> a1 * One = a1) & P14 & P0) & P0" "ITIMES"; THEOREMS:=("ITIMES",(termtosequent(parseprop(" P0 -> ( (Real(a1) -> a1 * One = a1) & P14 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "ITIMES"; pushreference 14 " P0 -> (a1 + Minus(a1) = Zero & P15 & P0) & P0" "MINUS"; THEOREMS:=("MINUS",(termtosequent(parseprop("P0 -> ( a1 + Minus(a1) = Zero & P15 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "MINUS"; pushreference 15 "P0 -> ((a1 Equal Zero v a1 * Inv(a1) = One) & P16 & P0) & P0" "INV"; THEOREMS:=("INV",(termtosequent(parseprop("P0 -> ((a1 Equal Zero v a1 * Inv(a1) = One) & P16 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "INV"; pushreference 16 "P0 -> (~Zero Equal One & P17 & P0) & P0" "NONTRIV"; THEOREMS:=("NONTRIV",(termtosequent(parseprop("P0 -> (~Zero Equal One & P17 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "NONTRIV"; pushreference 17 "P0 -> (~a1 < a1 & P18 & P0) & P0" "IRR"; THEOREMS:=("IRR",(termtosequent(parseprop("P0 -> (~a1 < a1 & P18 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "IRR"; pushreference 18 "P0 -> ( (a1 Equal a2 v a1 < a2 v a2 < a1) & P19 & P0) & P0" "TRI"; THEOREMS:=("TRI",(termtosequent(parseprop("P0 -> ((a1 Equal a2 v a1 < a2 v a2 < a1) & P19 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "TRI"; pushreference 19 "P0 -> (( a1 < a2 & a2 < a3 -> a1 < a3) & P20 & P0) & P0" "TRANS"; THEOREMS:=("TRANS",(termtosequent(parseprop("P0 -> (( a1 < a2 & a2 < a3 -> a1 < a3) & P20 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "TRANS"; pushreference 20 "P0 -> ((a1 < a2 == a1 + a3 < a2 + a3) & P21 & P0) & P0" "MPLUS0"; THEOREMS:=("MPLUS0",(termtosequent(parseprop("P0 -> ((a1 < a2 == a1 + a3 < a2 + a3) & P21 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "MPLUS0"; pushnode 5 " ((a1 < a2 -> a1 + a3 < a2 + a3) & P25 & P24 & P23 & P0) & P0 -> (( a1 < a2 -> a1 + a3 < a2 + a3) & P22 & P0) & P0" 0; pushnode 4 " (((a1 < a2 -> a1 + a3 < a2 + a3) & ( a1 + a3 < a2 + a3 -> a1 < a2)) & P24 & P23 & P0) & P0 -> (( a1 < a2 -> a1 + a3 < a2 + a3) & P22 & P0) & P0" 1; pushnode 3 " ((a1 < a2 == a1 + a3 < a2 + a3) & P23 & P0) & P0 -> ((a1 < a2 -> a1 + a3 < a2 + a3) & P22 & P0) & P0" 1; pushreference 2 "P0 -> ((a1 < a2 == a1 + a3 < a2 + a3) & P23 & P0) & P0" "MPLUS0"; pushnode 1 "P0 -> ((a1 < a2 -> a1 + a3 < a2 + a3) & P22 & P0) & P0" 2; THEOREMS:=("MPLUS",(termtosequent(parseprop("P0 -> ((a1 < a2 -> a1 + a3 < a2 + a3) & P22 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "MPLUS"; pushreference 6 "P0 -> (( Zero < a3 & a1 < a2 -> a1 * a3 < a2 * a3) & P27 & P0) & P0" "MTIMES"; THEOREMS:=("MTIMES",(termtosequent(parseprop("P0 -> (( Zero < a3 & a1 < a2 -> a1 * a3 < a2 * a3) & P27 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "MTIMES"; pushreference 7 "P0 -> (( (Ex1.x1 E a1) & (Ax1.x1 E a1 -> x1 <= a2) -> Sup(a1) <= a2) & P28 & P0) & P0" "SUP1"; THEOREMS:=("SUP1",(termtosequent(parseprop("P0 -> (( (Ex1.x1 E a1) & (Ax1.x1 E a1 -> x1 <= a2) -> Sup(a1) <= a2) & P28 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "SUP1"; pushreference 8 "P0 -> (( (Ax1.x1 E a1 -> x1 <= a2) -> (Ax1.x1 E a1 -> x1 <= Sup(a1))) & P29 & P0) & P0" "SUP2"; THEOREMS:=("SUP2",(termtosequent(parseprop("P0 -> (( (Ax1.x1 E a1 -> x1 <= a2) -> (Ax1.x1 E a1 -> x1 <= Sup(a1))) & P29 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "SUP2"; pushnode 36 " (a1 + Zero = a1 & P72 & P68 & P0) & P0 -> ( a1 + Zero = a1 & P67 & P64 & P37 & P35 & P32 & P30 & P65 & P37 & P35 & P32 & P30 & P0) & P0" 0; pushnode 35 " (Real(a1) & P33 & P31 & P30 & P0) & P0 -> ( Real(a1) & P71 & P68 & P0) & P0" 0; pushnode 33 "((Real(a1) -> a1 + Zero = a1) & P68 & P0) & (Real(a1) & P33 & P31 & P30 & P0) & P0 -> (a1 + Zero = a1 & P67 & P64 & P37 & P35 & P32 & P30 & P65 & P37 & P35 & P32 & P30 & P0) & P0" 2; pushreference 32 "P0 -> ((Real(a1) -> a1 + Zero = a1) & P68 & P0) & P0" "IPLUS"; pushnode 31 "( Real(a1) & P33 & P31 & P30 & P0) & P0 -> (a1 + Zero = a1 & P67 & P64 & P37 & P35 & P32 & P30 & P65 & P37 & P35 & P32 & P30 & P0) & P0" 2; pushnode 30 "( a2 = Zero & P64 & P37 & P35 & P32 & P30 & P0) & ( Real(a1) & P33 & P31 & P30 & P0) & P0 -> (a1 + a2 = a1 & P65 & P37 & P35 & P32 & P30 & P0) & P0" 1; pushnode 6 "( Real(a1) & P33 & P31 & P30 & P0) & P0 -> ((a2 = Zero -> a1 + a2 = a1) & P37 & P35 & P32 & P30 & P0) & P0" 1; pushnode 29 " ( [a2 + a1] + Minus(a1) = a2 & P60 & P58 & P53 & P52 & P45 & P43 & P57 & P55 & P0) & P0 -> ([ a2 + a1] + Minus(a1) = a2 & P63 & P51 & P49 & P59 & P53 & P52 & P45 & P43 & P46 & P0) & P0" 0; pushnode 28 " ( a1 + a2 = a2 + a1 & P51 & P49 & P0) & ([a2 + a1] + Minus(a1) = a2 & P60 & P58 & P53 & P52 & P45 & P43 & P57 & P55 & P0) & P0 -> ([a1 + a2] + Minus(a1) = a2 & P59 & P53 & P52 & P45 & P43 & P46 & P0) & P0" 1; pushnode 27 " ([a2 + a1] + Minus(a1) = a2 + Zero & P58 & P53 & P52 & P45 & P43 & P0) & (a2 + Zero = a2 & P57 & P55 & P0) & (a1 + a2 = a2 + a1 & P51 & P49 & P0) & P0 -> ([ a1 + a2] + Minus(a1) = a2 & P59 & P53 & P52 & P45 & P43 & P46 & P0) & P0" 1; pushnode 26 " ([ a2 + a1] + Minus(a1) = a2 + Zero & P53 & P52 & P45 & P43 & P0) & ( a2 + Zero = a2 & P57 & P55 & P0) & (a1 + a2 = a2 + a1 & P51 & P49 & P0) & P0 -> ( [a1 + a2] + Minus(a1) = a2 & P46 & P0) & P0" 1; pushnode 25 "( Real(a2) & P34 & P31 & P30 & P0) & P0 -> (Real(a2) & P56 & P55 & P0) & P0" 0; pushnode 24 "((Real(a2) -> a2 + Zero = a2) & P55 & P0) & ([a2 + a1] + Minus(a1) = a2 + Zero & P53 & P52 & P45 & P43 & P0) & (Real(a2) & P34 & P31 & P30 & P0) & (a1 + a2 = a2 + a1 & P51 & P49 & P0) & P0 -> ([a1 + a2] + Minus(a1) = a2 & P46 & P0) & P0" 2; pushreference 23 "P0 -> ((Real(a2) -> a2 + Zero = a2) & P55 & P0) & P0" "IPLUS"; pushnode 22 " ([ a2 + a1] + Minus(a1) = a2 + Zero & P53 & P52 & P45 & P43 & P0) & (Real(a2) & P34 & P31 & P30 & P0) & (a1 + a2 = a2 + a1 & P51 & P49 & P0) & P0 -> ([ a1 + a2] + Minus(a1) = a2 & P46 & P0) & P0" 2; pushnode 21 "( [a2 + a1] + Minus(a1) = a2 + a1 + Minus(a1) & P52 & P0) & ( a1 + Minus(a1) = Zero & P45 & P43 & P0) & ( Real(a2) & P34 & P31 & P30 & P0) & ( a1 + a2 = a2 + a1 & P51 & P49 & P0) & P0 -> ([a1 + a2] + Minus(a1) = a2 & P46 & P0) & P0" 1; pushreference 20 "P0 -> ( [a2 + a1] + Minus(a1) = a2 + a1 + Minus(a1) & P52 & P0) & P0" "APLUS"; pushnode 19 "( a1 + a2 = a2 + a1 & P51 & P49 & P0) & (a1 + Minus(a1) = Zero & P45 & P43 & P0) & (Real(a2) & P34 & P31 & P30 & P0) & P0 -> ([ a1 + a2] + Minus(a1) = a2 & P46 & P0) & P0" 2; pushnode 18 " (a1 + a2 = a2 + a1 & P49 & P0) & (a1 + Minus(a1) = Zero & P45 & P43 & P0) & (Real(a2) & P34 & P31 & P30 & P0) & P0 -> ([a1 + a2] + Minus(a1) = a2 & P46 & P0) & P0" 1; pushreference 17 "P0 -> ( a1 + a2 = a2 + a1 & P49 & P0) & P0" "CPLUS"; pushnode 15 "( a1 + Minus(a1) = Zero & P45 & P43 & P0) & ( Real(a2) & P34 & P31 & P30 & P0) & P0 -> ([a1 + a2] + Minus(a1) = a2 & P46 & P0) & P0" 2; pushnode 16 " (a2 = Zero & P47 & P44 & P40 & P43 & P46 & P0) & P0 -> (a2 = Zero & P39 & P36 & P35 & P32 & P30 & P0) & P0" 0; pushnode 14 " ( [a1 + a2] + Minus(a1) = Zero & P44 & P40 & P43 & P0) & ([ a1 + a2] + Minus(a1) = a2 & P46 & P0) & P0 -> (a2 = Zero & P39 & P36 & P35 & P32 & P30 & P0) & P0" 1; pushnode 13 "( [a1 + a2] + Minus(a1) = Zero & P44 & P40 & P43 & P0) & ( a1 + Minus(a1) = Zero & P45 & P43 & P0) & ( Real(a2) & P34 & P31 & P30 & P0) & P0 -> (a2 = Zero & P39 & P36 & P35 & P32 & P30 & P0) & P0" 2; pushnode 12 "([ a1 + a2] + Minus(a1) = a1 + Minus(a1) & P40 & P0) & ( a1 + Minus(a1) = Zero & P43 & P0) & ( Real(a2) & P34 & P31 & P30 & P0) & P0 -> (a2 = Zero & P39 & P36 & P35 & P32 & P30 & P0) & P0" 1; pushreference 11 " P0 -> (a1 + Minus(a1) = Zero & P43 & P0) & P0" "MINUS"; pushnode 9 " ([a1 + a2] + Minus(a1) = a1 + Minus(a1) & P40 & P0) & (Real(a2) & P34 & P31 & P30 & P0) & P0 -> (a2 = Zero & P39 & P36 & P35 & P32 & P30 & P0) & P0" 2; pushnode 10 "P0 -> ( a1 + Minus(a1) = a1 + Minus(a1) & P42 & P38 & P36 & P35 & P32 & P30 & P40 & P0) & P0" 0; pushnode 8 "( a1 + a2 = a1 & P38 & P36 & P35 & P32 & P30 & P0) & P0 -> ([a1 + a2] + Minus(a1) = a1 + Minus(a1) & P40 & P0) & P0" 1; pushnode 7 " (a1 + a2 = a1 & P38 & P36 & P35 & P32 & P30 & P0) & (Real(a2) & P34 & P31 & P30 & P0) & P0 -> ( a2 = Zero & P39 & P36 & P35 & P32 & P30 & P0) & P0" 2; pushnode 5 " (Real(a2) & P34 & P31 & P30 & P0) & P0 -> ((a1 + a2 = a1 -> a2 = Zero) & P36 & P35 & P32 & P30 & P0) & P0" 1; pushnode 4 "( Real(a1) & P33 & P31 & P30 & P0) & ( Real(a2) & P34 & P31 & P30 & P0) & P0 -> ( ((a1 + a2 = a1 -> a2 = Zero) & (a2 = Zero -> a1 + a2 = a1)) & P35 & P32 & P30 & P0) & P0" 2; pushnode 3 " (Real(a1) & P33 & P31 & P30 & P0) & (Real(a2) & P34 & P31 & P30 & P0) & P0 -> ((a1 + a2 = a1 == a2 = Zero) & P32 & P30 & P0) & P0" 1; THEOREMS:=("NULLADD",(termtosequent(parseprop(" (Real(a1) & P33 & P31 & P30 & P0) & (Real(a2) & P34 & P31 & P30 & P0) & P0 -> ((a1 + a2 = a1 == a2 = Zero) & P32 & P30 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "NULLADD"; pushnode 6 " (a1 + Zero = a1 & P78 & P76 & P0) & P0 -> ( a1 + Zero = a1 & P75 & P73 & P0) & P0" 0; pushnode 5 "(Real(a1) & P74 & P73 & P0) & P0 -> (Real(a1) & P77 & P76 & P0) & P0" 0; pushnode 4 "((Real(a1) -> a1 + Zero = a1) & P76 & P0) & (Real(a1) & P74 & P73 & P0) & P0 -> ( a1 + Zero = a1 & P75 & P73 & P0) & P0" 2; pushreference 3 "P0 -> ((Real(a1) -> a1 + Zero = a1) & P76 & P0) & P0" "IPLUS"; pushnode 2 " ( Real(a1) & P74 & P73 & P0) & P0 -> ( a1 + Zero = a1 & P75 & P73 & P0) & P0" 2; THEOREMS:=("IPLUSa",(termtosequent(parseprop("(Real(a1) & P74 & P73 & P0) & P0 -> (a1 + Zero = a1 & P75 & P73 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "IPLUSa"; pushnode 1 "P0 -> (a1 = a1 & P79 & P0) & P0" 0; THEOREMS:=("TRIV",(termtosequent(parseprop(" P0 -> (a1 = a1 & P79 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "TRIV"; pushnode 3 "( P2 & P111 & P108 & P0) & P0 -> (P2 & P109 & P0) & P0" 0; pushnode 2 "( P1 & P107 & P0) & P0 -> (P1 & P110 & P108 & P0) & P0" 0; pushnode 1 " ((P1 -> P2) & P108 & P0) & (P1 & P107 & P0) & P0 -> (P2 & P109 & P0) & P0" 2; THEOREMS:=("MP",(termtosequent(parseprop("(( P1 -> P2) & P108 & P0) & ( P1 & P107 & P0) & P0 -> (P2 & P109 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "MP"; pushreference 4 " P0 -> (Real(U1 + Minus(U1)) & P115 & P113 & P112 & P0) & P0" "RPLUS"; pushnode 3 "( U1 + Minus(U1) = Zero & P113 & P0) & P0 -> (Real(Zero) & P112 & P0) & P0" 1; pushreference 2 "P0 -> ( U1 + Minus(U1) = Zero & P113 & P0) & P0" "MINUS"; pushnode 1 "P0 -> (Real(Zero) & P112 & P0) & P0" 2; THEOREMS:=("RZERO",(termtosequent(parseprop("P0 -> (Real(Zero) & P112 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "RZERO"; pushnode 17 "P0 -> ( a1 * Zero = a1 * Zero & P131 & P129 & P127 & P126 & P124 & P117 & P0) & P0" 0; pushnode 16 "(Zero + Zero = Zero & P129 & P127 & P0) & P0 -> (a1 * [Zero + Zero] = a1 * Zero & P126 & P124 & P117 & P0) & P0" 1; pushreference 15 "P0 -> ( Real(Zero) & P128 & P127 & P0) & P0" "RZERO"; pushnode 14 " ((Real(Zero) -> Zero + Zero = Zero) & P127 & P0) & P0 -> (a1 * [Zero + Zero] = a1 * Zero & P126 & P124 & P117 & P0) & P0" 2; pushreference 13 "P0 -> (( Real(Zero) -> Zero + Zero = Zero) & P127 & P0) & P0" "IPLUS"; pushnode 12 "P0 -> (a1 * [Zero + Zero] = a1 * Zero & P126 & P124 & P117 & P0) & P0" 2; pushnode 11 "( a1 * [Zero + Zero] = a1 * Zero + a1 * Zero & P124 & P0) & P0 -> ( a1 * Zero + a1 * Zero = a1 * Zero & P117 & P0) & P0" 1; pushreference 10 "P0 -> (a1 * [Zero + Zero] = a1 * Zero + a1 * Zero & P124 & P0) & P0" "DIST"; pushnode 3 " P0 -> (a1 * Zero + a1 * Zero = a1 * Zero & P117 & P0) & P0" 2; pushreference 7 " P0 -> (Real(a1 * Zero) & P119 & P0) & P0" "RTIMES"; pushreference 6 "P0 -> (Real(a1 * Zero) & P118 & P0) & P0" "RTIMES"; pushreference 9 " ((a1 * Zero + a1 * Zero = a1 * Zero -> a1 * Zero = Zero) & P122 & P121 & P120 & P0) & (a1 * Zero + a1 * Zero = a1 * Zero & P117 & P0) & P0 -> ( a1 * Zero = Zero & P116 & P0) & P0" "MP"; pushnode 8 " (((a1 * Zero + a1 * Zero = a1 * Zero -> a1 * Zero = Zero) & ( a1 * Zero = Zero -> a1 * Zero + a1 * Zero = a1 * Zero)) & P121 & P120 & P0) & (a1 * Zero + a1 * Zero = a1 * Zero & P117 & P0) & P0 -> ( a1 * Zero = Zero & P116 & P0) & P0" 1; pushnode 5 "((a1 * Zero + a1 * Zero = a1 * Zero == a1 * Zero = Zero) & P120 & P0) & (a1 * Zero + a1 * Zero = a1 * Zero & P117 & P0) & P0 -> ( a1 * Zero = Zero & P116 & P0) & P0" 1; pushreference 4 "(Real(a1 * Zero) & P118 & P0) & ( Real(a1 * Zero) & P119 & P0) & P0 -> ((a1 * Zero + a1 * Zero = a1 * Zero == a1 * Zero = Zero) & P120 & P0) & P0" "NULLADD"; pushnode 2 " (a1 * Zero + a1 * Zero = a1 * Zero & P117 & P0) & P0 -> (a1 * Zero = Zero & P116 & P0) & P0" 4; pushnode 1 "P0 -> (a1 * Zero = Zero & P116 & P0) & P0" 2; THEOREMS:=("MZERO",(termtosequent(parseprop("P0 -> (a1 * Zero = Zero & P116 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "MZERO"; pushnode 28 " (a2 = Minus(a1) & P155 & P151 & P149 & P147 & P141 & P140 & P139 & P136 & P135 & P133 & P132 & P146 & P142 & P145 & P143 & P148 & P150 & P154 & P152 & P0) & ( Minus(a1) + Zero = Minus(a1) & P145 & P143 & P0) & ( a2 + a1 = Zero & P139 & P136 & P135 & P133 & P132 & P0) & ( Zero + Minus(a1) = Minus(a1) & P146 & P142 & P145 & P143 & P0) & ([ a2 + a1] + Minus(a1) = a2 + a1 + Minus(a1) & P148 & P0) & (a1 + Minus(a1) = Zero & P150 & P0) & ( a2 + Zero = a2 & P154 & P152 & P0) & P0 -> (a2 = Minus(a1) & P137 & P135 & P133 & P132 & P0) & P0" 0; pushnode 27 " (a2 + Zero = a2 & P154 & P152 & P0) & (a2 + Zero = Minus(a1) & P151 & P149 & P147 & P141 & P140 & P139 & P136 & P135 & P133 & P132 & P146 & P142 & P145 & P143 & P148 & P150 & P0) & ( Minus(a1) + Zero = Minus(a1) & P145 & P143 & P0) & (a2 + a1 = Zero & P139 & P136 & P135 & P133 & P132 & P0) & ( Zero + Minus(a1) = Minus(a1) & P146 & P142 & P145 & P143 & P0) & ( [a2 + a1] + Minus(a1) = a2 + a1 + Minus(a1) & P148 & P0) & ( a1 + Minus(a1) = Zero & P150 & P0) & P0 -> (a2 = Minus(a1) & P137 & P135 & P133 & P132 & P0) & P0" 1; pushnode 26 " (Real(a2) & P138 & P136 & P135 & P133 & P132 & P0) & P0 -> (Real(a2) & P153 & P152 & P0) & P0" 0; pushnode 25 "((Real(a2) -> a2 + Zero = a2) & P152 & P0) & (a1 + Minus(a1) = Zero & P150 & P0) & ( a2 + Zero = Minus(a1) & P151 & P149 & P147 & P141 & P140 & P139 & P136 & P135 & P133 & P132 & P146 & P142 & P145 & P143 & P148 & P150 & P0) & (Real(a2) & P138 & P136 & P135 & P133 & P132 & P0) & ( Minus(a1) + Zero = Minus(a1) & P145 & P143 & P0) & ( a2 + a1 = Zero & P139 & P136 & P135 & P133 & P132 & P0) & ( Zero + Minus(a1) = Minus(a1) & P146 & P142 & P145 & P143 & P0) & ([ a2 + a1] + Minus(a1) = a2 + a1 + Minus(a1) & P148 & P0) & P0 -> ( a2 = Minus(a1) & P137 & P135 & P133 & P132 & P0) & P0" 2; pushreference 24 " P0 -> ( (Real(a2) -> a2 + Zero = a2) & P152 & P0) & P0" "IPLUS"; pushnode 23 " ( a1 + Minus(a1) = Zero & P150 & P0) & ( a2 + Zero = Minus(a1) & P151 & P149 & P147 & P141 & P140 & P139 & P136 & P135 & P133 & P132 & P146 & P142 & P145 & P143 & P148 & P150 & P0) & (Real(a2) & P138 & P136 & P135 & P133 & P132 & P0) & ( Minus(a1) + Zero = Minus(a1) & P145 & P143 & P0) & ( a2 + a1 = Zero & P139 & P136 & P135 & P133 & P132 & P0) & ( Zero + Minus(a1) = Minus(a1) & P146 & P142 & P145 & P143 & P0) & ([ a2 + a1] + Minus(a1) = a2 + a1 + Minus(a1) & P148 & P0) & P0 -> (a2 = Minus(a1) & P137 & P135 & P133 & P132 & P0) & P0" 2; pushnode 22 "( a1 + Minus(a1) = Zero & P150 & P0) & ( a2 + a1 + Minus(a1) = Minus(a1) & P149 & P147 & P141 & P140 & P139 & P136 & P135 & P133 & P132 & P146 & P142 & P145 & P143 & P148 & P0) & ( Real(a2) & P138 & P136 & P135 & P133 & P132 & P0) & ( Minus(a1) + Zero = Minus(a1) & P145 & P143 & P0) & (a2 + a1 = Zero & P139 & P136 & P135 & P133 & P132 & P0) & ( Zero + Minus(a1) = Minus(a1) & P146 & P142 & P145 & P143 & P0) & ( [a2 + a1] + Minus(a1) = a2 + a1 + Minus(a1) & P148 & P0) & P0 -> ( a2 = Minus(a1) & P137 & P135 & P133 & P132 & P0) & P0" 1; pushreference 21 " P0 -> (a1 + Minus(a1) = Zero & P150 & P0) & P0" "MINUS"; pushnode 20 "( [a2 + a1] + Minus(a1) = a2 + a1 + Minus(a1) & P148 & P0) & ( a2 + a1 + Minus(a1) = Minus(a1) & P149 & P147 & P141 & P140 & P139 & P136 & P135 & P133 & P132 & P146 & P142 & P145 & P143 & P148 & P0) & ( Real(a2) & P138 & P136 & P135 & P133 & P132 & P0) & ( Minus(a1) + Zero = Minus(a1) & P145 & P143 & P0) & (a2 + a1 = Zero & P139 & P136 & P135 & P133 & P132 & P0) & ( Zero + Minus(a1) = Minus(a1) & P146 & P142 & P145 & P143 & P0) & P0 -> (a2 = Minus(a1) & P137 & P135 & P133 & P132 & P0) & P0" 2; pushnode 19 "( [a2 + a1] + Minus(a1) = a2 + a1 + Minus(a1) & P148 & P0) & ([ a2 + a1] + Minus(a1) = Minus(a1) & P147 & P141 & P140 & P139 & P136 & P135 & P133 & P132 & P146 & P142 & P145 & P143 & P0) & (Real(a2) & P138 & P136 & P135 & P133 & P132 & P0) & ( Minus(a1) + Zero = Minus(a1) & P145 & P143 & P0) & (a2 + a1 = Zero & P139 & P136 & P135 & P133 & P132 & P0) & ( Zero + Minus(a1) = Minus(a1) & P146 & P142 & P145 & P143 & P0) & P0 -> ( a2 = Minus(a1) & P137 & P135 & P133 & P132 & P0) & P0" 1; pushreference 18 " P0 -> ( [a2 + a1] + Minus(a1) = a2 + a1 + Minus(a1) & P148 & P0) & P0" "APLUS"; pushnode 17 "( Zero + Minus(a1) = Minus(a1) & P146 & P142 & P145 & P143 & P0) & ([a2 + a1] + Minus(a1) = Minus(a1) & P147 & P141 & P140 & P139 & P136 & P135 & P133 & P132 & P146 & P142 & P145 & P143 & P0) & ( Real(a2) & P138 & P136 & P135 & P133 & P132 & P0) & ( Minus(a1) + Zero = Minus(a1) & P145 & P143 & P0) & (a2 + a1 = Zero & P139 & P136 & P135 & P133 & P132 & P0) & P0 -> ( a2 = Minus(a1) & P137 & P135 & P133 & P132 & P0) & P0" 2; pushnode 16 "( Zero + Minus(a1) = Minus(a1) & P146 & P142 & P145 & P143 & P0) & ([ a2 + a1] + Minus(a1) = Zero + Minus(a1) & P141 & P140 & P139 & P136 & P135 & P133 & P132 & P0) & ( Real(a2) & P138 & P136 & P135 & P133 & P132 & P0) & ( Minus(a1) + Zero = Minus(a1) & P145 & P143 & P0) & (a2 + a1 = Zero & P139 & P136 & P135 & P133 & P132 & P0) & P0 -> ( a2 = Minus(a1) & P137 & P135 & P133 & P132 & P0) & P0" 1; pushnode 15 " ( Minus(a1) + Zero = Minus(a1) & P145 & P143 & P0) & (Zero + Minus(a1) = Minus(a1) + Zero & P142 & P0) & (a2 + a1 = Zero & P139 & P136 & P135 & P133 & P132 & P0) & ([a2 + a1] + Minus(a1) = Zero + Minus(a1) & P141 & P140 & P139 & P136 & P135 & P133 & P132 & P0) & (Real(a2) & P138 & P136 & P135 & P133 & P132 & P0) & P0 -> ( a2 = Minus(a1) & P137 & P135 & P133 & P132 & P0) & P0" 1; pushreference 14 " P0 -> (Real(Minus(a1)) & P144 & P143 & P0) & P0" "RMINUS"; pushnode 13 " ( (Real(Minus(a1)) -> Minus(a1) + Zero = Minus(a1)) & P143 & P0) & ( Zero + Minus(a1) = Minus(a1) + Zero & P142 & P0) & ( a2 + a1 = Zero & P139 & P136 & P135 & P133 & P132 & P0) & ([ a2 + a1] + Minus(a1) = Zero + Minus(a1) & P141 & P140 & P139 & P136 & P135 & P133 & P132 & P0) & ( Real(a2) & P138 & P136 & P135 & P133 & P132 & P0) & P0 -> (a2 = Minus(a1) & P137 & P135 & P133 & P132 & P0) & P0" 2; pushreference 12 "P0 -> ( (Real(Minus(a1)) -> Minus(a1) + Zero = Minus(a1)) & P143 & P0) & P0" "IPLUS"; pushnode 11 " (Zero + Minus(a1) = Minus(a1) + Zero & P142 & P0) & (a2 + a1 = Zero & P139 & P136 & P135 & P133 & P132 & P0) & ([a2 + a1] + Minus(a1) = Zero + Minus(a1) & P141 & P140 & P139 & P136 & P135 & P133 & P132 & P0) & (Real(a2) & P138 & P136 & P135 & P133 & P132 & P0) & P0 -> ( a2 = Minus(a1) & P137 & P135 & P133 & P132 & P0) & P0" 2; pushreference 10 " P0 -> ( Zero + Minus(a1) = Minus(a1) + Zero & P142 & P0) & P0" "CPLUS"; pushnode 9 "( a2 + a1 = Zero & P139 & P136 & P135 & P133 & P132 & P0) & ([ a2 + a1] + Minus(a1) = Zero + Minus(a1) & P141 & P140 & P139 & P136 & P135 & P133 & P132 & P0) & ( Real(a2) & P138 & P136 & P135 & P133 & P132 & P0) & P0 -> ( a2 = Minus(a1) & P137 & P135 & P133 & P132 & P0) & P0" 2; pushnode 8 "( a2 + a1 = Zero & P139 & P136 & P135 & P133 & P132 & P0) & ([ a2 + a1] + Minus(a1) = [a2 + a1] + Minus(a1) & P140 & P0) & ( Real(a2) & P138 & P136 & P135 & P133 & P132 & P0) & P0 -> ( a2 = Minus(a1) & P137 & P135 & P133 & P132 & P0) & P0" 1; pushreference 7 " P0 -> ([a2 + a1] + Minus(a1) = [a2 + a1] + Minus(a1) & P140 & P0) & P0" "TRIV"; pushnode 6 " (Real(a2) & P138 & P136 & P135 & P133 & P132 & P0) & (a2 + a1 = Zero & P139 & P136 & P135 & P133 & P132 & P0) & P0 -> (a2 = Minus(a1) & P137 & P135 & P133 & P132 & P0) & P0" 2; pushnode 5 "((Real(a2) & a2 + a1 = Zero) & P136 & P135 & P133 & P132 & P0) & P0 -> (a2 = Minus(a1) & P137 & P135 & P133 & P132 & P0) & P0" 1; pushnode 4 "P0 -> (( Real(a2) & a2 + a1 = Zero -> a2 = Minus(a1)) & P135 & P133 & P132 & P0) & P0" 1; pushnode 3 "( a1 + a2 = a2 + a1 & P133 & P0) & P0 -> ((Real(a2) & a1 + a2 = Zero -> a2 = Minus(a1)) & P132 & P0) & P0" 1; pushreference 2 "P0 -> ( a1 + a2 = a2 + a1 & P133 & P0) & P0" "CPLUS"; pushnode 1 "P0 -> ((Real(a2) & a1 + a2 = Zero -> a2 = Minus(a1)) & P132 & P0) & P0" 2; THEOREMS:=("UNIQUEINV",(termtosequent(parseprop("P0 -> ((Real(a2) & a1 + a2 = Zero -> a2 = Minus(a1)) & P132 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "UNIQUEINV"; pushnode 5 " (a2 = Minus(a1) & P161 & P159 & P0) & P0 -> ( a2 = Minus(a1) & P158 & P0) & P0" 0; pushnode 7 " (a1 + a2 = Zero & P157 & P0) & P0 -> (a1 + a2 = Zero & P163 & P160 & P159 & P0) & P0" 0; pushnode 6 "(Real(a2) & P156 & P0) & P0 -> ( Real(a2) & P162 & P160 & P159 & P0) & P0" 0; pushnode 4 " (Real(a2) & P156 & P0) & (a1 + a2 = Zero & P157 & P0) & P0 -> ((Real(a2) & a1 + a2 = Zero) & P160 & P159 & P0) & P0" 2; pushnode 3 "((Real(a2) & a1 + a2 = Zero -> a2 = Minus(a1)) & P159 & P0) & ( Real(a2) & P156 & P0) & ( a1 + a2 = Zero & P157 & P0) & P0 -> ( a2 = Minus(a1) & P158 & P0) & P0" 2; pushreference 2 "P0 -> ((Real(a2) & a1 + a2 = Zero -> a2 = Minus(a1)) & P159 & P0) & P0" "UNIQUEINV"; pushnode 1 " (Real(a2) & P156 & P0) & (a1 + a2 = Zero & P157 & P0) & P0 -> ( a2 = Minus(a1) & P158 & P0) & P0" 2; THEOREMS:=("UINV",(termtosequent(parseprop(" (Real(a2) & P156 & P0) & (a1 + a2 = Zero & P157 & P0) & P0 -> ( a2 = Minus(a1) & P158 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "UINV"; pushreference 9 "P0 -> (Real(Zero) & P171 & P0) & P0" "RZERO"; pushnode 8 "(Real(a1) & P165 & P164 & P0) & P0 -> (Real(a1) & P170 & P0) & P0" 0; pushreference 13 "(( Zero = Zero -> a1 + Zero = a1) & P175 & P173 & P172 & P0) & ( Zero = Zero & P176 & P0) & P0 -> ( a1 + Zero = a1 & P169 & P167 & P166 & P164 & P0) & P0" "MP"; pushnode 12 " P0 -> (Zero = Zero & P176 & P0) & P0" 0; pushnode 11 "(( Zero = Zero -> a1 + Zero = a1) & P175 & P173 & P172 & P0) & P0 -> (a1 + Zero = a1 & P169 & P167 & P166 & P164 & P0) & P0" 2; pushnode 10 "( ((a1 + Zero = a1 -> Zero = Zero) & ( Zero = Zero -> a1 + Zero = a1)) & P173 & P172 & P0) & P0 -> (a1 + Zero = a1 & P169 & P167 & P166 & P164 & P0) & P0" 1; pushnode 7 " ((a1 + Zero = a1 == Zero = Zero) & P172 & P0) & P0 -> (a1 + Zero = a1 & P169 & P167 & P166 & P164 & P0) & P0" 1; pushreference 6 " (Real(a1) & P170 & P0) & (Real(Zero) & P171 & P0) & P0 -> ((a1 + Zero = a1 == Zero = Zero) & P172 & P0) & P0" "NULLADD"; pushnode 5 "(Real(a1) & P165 & P164 & P0) & P0 -> (a1 + Zero = a1 & P169 & P167 & P166 & P164 & P0) & P0" 4; pushnode 4 "( Zero + a1 = a1 + Zero & P167 & P0) & ( Real(a1) & P165 & P164 & P0) & P0 -> ( Zero + a1 = a1 & P166 & P164 & P0) & P0" 1; pushreference 3 "P0 -> ( Zero + a1 = a1 + Zero & P167 & P0) & P0" "CPLUS"; pushnode 2 "(Real(a1) & P165 & P164 & P0) & P0 -> (Zero + a1 = a1 & P166 & P164 & P0) & P0" 2; THEOREMS:=("IPLUSb",(termtosequent(parseprop(" (Real(a1) & P165 & P164 & P0) & P0 -> ( Zero + a1 = a1 & P166 & P164 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "IPLUSb"; pushreference 4 "P0 -> ( a1 + Minus(a1) = Zero & P180 & P178 & P177 & P0) & P0" "MINUS"; pushnode 3 "( Minus(a1) + a1 = a1 + Minus(a1) & P178 & P0) & P0 -> ( Minus(a1) + a1 = Zero & P177 & P0) & P0" 1; pushreference 2 " P0 -> ( Minus(a1) + a1 = a1 + Minus(a1) & P178 & P0) & P0" "CPLUS"; pushnode 1 " P0 -> (Minus(a1) + a1 = Zero & P177 & P0) & P0" 2; THEOREMS:=("MINUS2",(termtosequent(parseprop("P0 -> ( Minus(a1) + a1 = Zero & P177 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "MINUS2"; pushnode 62 "P0 -> ( a1 + Zero = a1 + Zero & P235 & P233 & P232 & P230 & P229 & P227 & P213 & P0) & P0" 0; pushnode 61 "( a2 + Minus(a2) = Zero & P233 & P0) & P0 -> (a1 + a2 + Minus(a2) = a1 + Zero & P232 & P230 & P229 & P227 & P213 & P0) & P0" 1; pushreference 60 " P0 -> (a2 + Minus(a2) = Zero & P233 & P0) & P0" "MINUS"; pushnode 59 "P0 -> (a1 + a2 + Minus(a2) = a1 + Zero & P232 & P230 & P229 & P227 & P213 & P0) & P0" 2; pushnode 58 "([ a1 + a2] + Minus(a2) = a1 + a2 + Minus(a2) & P230 & P0) & P0 -> ([ a1 + a2] + Minus(a2) = a1 + Zero & P229 & P227 & P213 & P0) & P0" 1; pushreference 57 "P0 -> ( [a1 + a2] + Minus(a2) = a1 + a2 + Minus(a2) & P230 & P0) & P0" "APLUS"; pushnode 56 "P0 -> ([a1 + a2] + Minus(a2) = a1 + Zero & P229 & P227 & P213 & P0) & P0" 2; pushnode 55 "( Minus(a2) + a1 + a2 = [a1 + a2] + Minus(a2) & P227 & P0) & P0 -> ( Minus(a2) + a1 + a2 = a1 + Zero & P213 & P0) & P0" 1; pushreference 54 "P0 -> ( Minus(a2) + a1 + a2 = [a1 + a2] + Minus(a2) & P227 & P0) & P0" "CPLUS"; pushnode 39 "P0 -> (Minus(a2) + a1 + a2 = a1 + Zero & P213 & P0) & P0" 2; pushreference 53 " P0 -> (Zero + a2 = a2 + Zero & P226 & P224 & P223 & P221 & P215 & P0) & P0" "CPLUS"; pushnode 52 "( Minus(a1) + a1 = Zero & P224 & P0) & P0 -> ([ Minus(a1) + a1] + a2 = a2 + Zero & P223 & P221 & P215 & P0) & P0" 1; pushreference 51 "P0 -> ( Minus(a1) + a1 = Zero & P224 & P0) & P0" "MINUS2"; pushnode 50 " P0 -> ([Minus(a1) + a1] + a2 = a2 + Zero & P223 & P221 & P215 & P0) & P0" 2; pushnode 49 "([ Minus(a1) + a1] + a2 = Minus(a1) + a1 + a2 & P221 & P0) & P0 -> ( Minus(a1) + a1 + a2 = a2 + Zero & P215 & P0) & P0" 1; pushreference 48 "P0 -> ( [Minus(a1) + a1] + a2 = Minus(a1) + a1 + a2 & P221 & P0) & P0" "APLUS"; pushnode 42 " P0 -> ( Minus(a1) + a1 + a2 = a2 + Zero & P215 & P0) & P0" 2; pushreference 47 " (( a1 + Zero < a2 + Zero -> a1 < a2) & P220 & P218 & P217 & P0) & ( a1 + Zero < a2 + Zero & P216 & P214 & P212 & P210 & P213 & P215 & P0) & P0 -> ( a1 < a2 & P209 & P184 & P182 & P181 & P0) & P0" "MP"; pushnode 46 " (((a1 < a2 -> a1 + Zero < a2 + Zero) & ( a1 + Zero < a2 + Zero -> a1 < a2)) & P218 & P217 & P0) & (Minus(a1) + a1 + a2 = a2 + Zero & P215 & P0) & ( a1 + Zero < a2 + Zero & P216 & P214 & P212 & P210 & P213 & P215 & P0) & (Minus(a2) + a1 + a2 = a1 + Zero & P213 & P0) & P0 -> (a1 < a2 & P209 & P184 & P182 & P181 & P0) & P0" 1; pushnode 45 " ((a1 < a2 == a1 + Zero < a2 + Zero) & P217 & P0) & ( Minus(a1) + a1 + a2 = a2 + Zero & P215 & P0) & (a1 + Zero < a2 + Zero & P216 & P214 & P212 & P210 & P213 & P215 & P0) & ( Minus(a2) + a1 + a2 = a1 + Zero & P213 & P0) & P0 -> (a1 < a2 & P209 & P184 & P182 & P181 & P0) & P0" 1; pushreference 44 "P0 -> ((a1 < a2 == a1 + Zero < a2 + Zero) & P217 & P0) & P0" "MPLUS0"; pushnode 43 " (Minus(a1) + a1 + a2 = a2 + Zero & P215 & P0) & ( a1 + Zero < a2 + Zero & P216 & P214 & P212 & P210 & P213 & P215 & P0) & (Minus(a2) + a1 + a2 = a1 + Zero & P213 & P0) & P0 -> ( a1 < a2 & P209 & P184 & P182 & P181 & P0) & P0" 2; pushnode 41 " (Minus(a1) + a1 + a2 = a2 + Zero & P215 & P0) & (a1 + Zero < Minus(a1) + a1 + a2 & P214 & P212 & P210 & P213 & P0) & (Minus(a2) + a1 + a2 = a1 + Zero & P213 & P0) & P0 -> ( a1 < a2 & P209 & P184 & P182 & P181 & P0) & P0" 1; pushnode 40 "(a1 + Zero < Minus(a1) + a1 + a2 & P214 & P212 & P210 & P213 & P0) & (Minus(a2) + a1 + a2 = a1 + Zero & P213 & P0) & P0 -> (a1 < a2 & P209 & P184 & P182 & P181 & P0) & P0" 2; pushnode 38 " (Minus(a2) + a1 + a2 = a1 + Zero & P213 & P0) & (Minus(a2) + a1 + a2 < Minus(a1) + a1 + a2 & P212 & P210 & P0) & P0 -> (a1 < a2 & P209 & P184 & P182 & P181 & P0) & P0" 1; pushnode 37 "( Minus(a2) + a1 + a2 < Minus(a1) + a1 + a2 & P212 & P210 & P0) & P0 -> (a1 < a2 & P209 & P184 & P182 & P181 & P0) & P0" 2; pushnode 36 "(Minus(a2) < Minus(a1) & P208 & P184 & P182 & P181 & P0) & P0 -> (Minus(a2) < Minus(a1) & P211 & P210 & P0) & P0" 0; pushnode 35 " (( Minus(a2) < Minus(a1) -> Minus(a2) + a1 + a2 < Minus(a1) + a1 + a2) & P210 & P0) & ( Minus(a2) < Minus(a1) & P208 & P184 & P182 & P181 & P0) & P0 -> (a1 < a2 & P209 & P184 & P182 & P181 & P0) & P0" 2; pushreference 34 "P0 -> ( (Minus(a2) < Minus(a1) -> Minus(a2) + a1 + a2 < Minus(a1) + a1 + a2) & P210 & P0) & P0" "MPLUS"; pushnode 33 "( Minus(a2) < Minus(a1) & P208 & P184 & P182 & P181 & P0) & P0 -> ( a1 < a2 & P209 & P184 & P182 & P181 & P0) & P0" 2; pushnode 4 "P0 -> ((Minus(a2) < Minus(a1) -> a1 < a2) & P184 & P182 & P181 & P0) & P0" 1; pushreference 18 "P0 -> ( Real(Minus(a2)) & P195 & P0) & P0" "RMINUS"; pushreference 31 "P0 -> (Real(Minus(a1)) & P205 & P0) & P0" "RMINUS"; pushnode 32 "(Minus(a2) < Minus(a1) & P207 & P204 & P202 & P199 & P197 & P194 & P192 & P189 & P185 & P190 & P193 & P196 & P198 & P200 & P203 & P206 & P0) & ( a1 + Minus(a1) = Zero & P193 & P0) & ( Zero + Minus(a2) = Minus(a2) & P196 & P0) & (Minus(a1) + Minus(a2) = Minus(a2) + Minus(a1) & P198 & P0) & (a2 + Minus(a2) = Zero & P203 & P0) & (Zero + Minus(a1) = Minus(a1) & P206 & P0) & P0 -> ( Minus(a2) < Minus(a1) & P187 & P183 & P182 & P181 & P0) & P0" 0; pushnode 30 "( Zero + Minus(a1) = Minus(a1) & P206 & P0) & (Minus(a2) < Zero + Minus(a1) & P204 & P202 & P199 & P197 & P194 & P192 & P189 & P185 & P190 & P193 & P196 & P198 & P200 & P203 & P0) & ( a1 + Minus(a1) = Zero & P193 & P0) & ( Zero + Minus(a2) = Minus(a2) & P196 & P0) & ( Minus(a1) + Minus(a2) = Minus(a2) + Minus(a1) & P198 & P0) & (a2 + Minus(a2) = Zero & P203 & P0) & P0 -> ( Minus(a2) < Minus(a1) & P187 & P183 & P182 & P181 & P0) & P0" 1; pushreference 29 "( Real(Minus(a1)) & P205 & P0) & P0 -> ( Zero + Minus(a1) = Minus(a1) & P206 & P0) & P0" "IPLUSb"; pushnode 28 "( a2 + Minus(a2) = Zero & P203 & P0) & ( Minus(a2) < Zero + Minus(a1) & P204 & P202 & P199 & P197 & P194 & P192 & P189 & P185 & P190 & P193 & P196 & P198 & P200 & P203 & P0) & ( a1 + Minus(a1) = Zero & P193 & P0) & ( Zero + Minus(a2) = Minus(a2) & P196 & P0) & (Minus(a1) + Minus(a2) = Minus(a2) + Minus(a1) & P198 & P0) & P0 -> ( Minus(a2) < Minus(a1) & P187 & P183 & P182 & P181 & P0) & P0" 3; pushnode 27 "( a2 + Minus(a2) = Zero & P203 & P0) & (Minus(a2) < [a2 + Minus(a2)] + Minus(a1) & P202 & P199 & P197 & P194 & P192 & P189 & P185 & P190 & P193 & P196 & P198 & P200 & P0) & (a1 + Minus(a1) = Zero & P193 & P0) & ( Zero + Minus(a2) = Minus(a2) & P196 & P0) & (Minus(a1) + Minus(a2) = Minus(a2) + Minus(a1) & P198 & P0) & P0 -> ( Minus(a2) < Minus(a1) & P187 & P183 & P182 & P181 & P0) & P0" 1; pushreference 26 " P0 -> (a2 + Minus(a2) = Zero & P203 & P0) & P0" "MINUS"; pushnode 25 " (Minus(a2) < [a2 + Minus(a2)] + Minus(a1) & P202 & P199 & P197 & P194 & P192 & P189 & P185 & P190 & P193 & P196 & P198 & P200 & P0) & ( a1 + Minus(a1) = Zero & P193 & P0) & ( Zero + Minus(a2) = Minus(a2) & P196 & P0) & ( Minus(a1) + Minus(a2) = Minus(a2) + Minus(a1) & P198 & P0) & P0 -> (Minus(a2) < Minus(a1) & P187 & P183 & P182 & P181 & P0) & P0" 2; pushnode 24 "([ a2 + Minus(a2)] + Minus(a1) = a2 + Minus(a2) + Minus(a1) & P200 & P0) & ( Minus(a2) < a2 + Minus(a2) + Minus(a1) & P199 & P197 & P194 & P192 & P189 & P185 & P190 & P193 & P196 & P198 & P0) & ( a1 + Minus(a1) = Zero & P193 & P0) & ( Zero + Minus(a2) = Minus(a2) & P196 & P0) & (Minus(a1) + Minus(a2) = Minus(a2) + Minus(a1) & P198 & P0) & P0 -> ( Minus(a2) < Minus(a1) & P187 & P183 & P182 & P181 & P0) & P0" 1; pushreference 23 " P0 -> ( [a2 + Minus(a2)] + Minus(a1) = a2 + Minus(a2) + Minus(a1) & P200 & P0) & P0" "APLUS"; pushnode 22 "( Minus(a1) + Minus(a2) = Minus(a2) + Minus(a1) & P198 & P0) & ( Minus(a2) < a2 + Minus(a2) + Minus(a1) & P199 & P197 & P194 & P192 & P189 & P185 & P190 & P193 & P196 & P198 & P0) & ( a1 + Minus(a1) = Zero & P193 & P0) & ( Zero + Minus(a2) = Minus(a2) & P196 & P0) & P0 -> ( Minus(a2) < Minus(a1) & P187 & P183 & P182 & P181 & P0) & P0" 2; pushnode 21 "( Minus(a1) + Minus(a2) = Minus(a2) + Minus(a1) & P198 & P0) & ( Minus(a2) < a2 + Minus(a1) + Minus(a2) & P197 & P194 & P192 & P189 & P185 & P190 & P193 & P196 & P0) & ( a1 + Minus(a1) = Zero & P193 & P0) & ( Zero + Minus(a2) = Minus(a2) & P196 & P0) & P0 -> ( Minus(a2) < Minus(a1) & P187 & P183 & P182 & P181 & P0) & P0" 1; pushreference 20 " P0 -> ( Minus(a1) + Minus(a2) = Minus(a2) + Minus(a1) & P198 & P0) & P0" "CPLUS"; pushnode 19 "(Minus(a2) < a2 + Minus(a1) + Minus(a2) & P197 & P194 & P192 & P189 & P185 & P190 & P193 & P196 & P0) & ( a1 + Minus(a1) = Zero & P193 & P0) & ( Zero + Minus(a2) = Minus(a2) & P196 & P0) & P0 -> ( Minus(a2) < Minus(a1) & P187 & P183 & P182 & P181 & P0) & P0" 2; pushnode 17 "( Zero + Minus(a2) = Minus(a2) & P196 & P0) & (Zero + Minus(a2) < a2 + Minus(a1) + Minus(a2) & P194 & P192 & P189 & P185 & P190 & P193 & P0) & ( a1 + Minus(a1) = Zero & P193 & P0) & P0 -> ( Minus(a2) < Minus(a1) & P187 & P183 & P182 & P181 & P0) & P0" 1; pushreference 16 "( Real(Minus(a2)) & P195 & P0) & P0 -> ( Zero + Minus(a2) = Minus(a2) & P196 & P0) & P0" "IPLUSb"; pushnode 15 "( a1 + Minus(a1) = Zero & P193 & P0) & ( Zero + Minus(a2) < a2 + Minus(a1) + Minus(a2) & P194 & P192 & P189 & P185 & P190 & P193 & P0) & P0 -> ( Minus(a2) < Minus(a1) & P187 & P183 & P182 & P181 & P0) & P0" 3; pushnode 14 "( a1 + Minus(a1) = Zero & P193 & P0) & ( [a1 + Minus(a1)] + Minus(a2) < a2 + Minus(a1) + Minus(a2) & P192 & P189 & P185 & P190 & P0) & P0 -> ( Minus(a2) < Minus(a1) & P187 & P183 & P182 & P181 & P0) & P0" 1; pushreference 13 " P0 -> (a1 + Minus(a1) = Zero & P193 & P0) & P0" "MINUS"; pushnode 12 "([a1 + Minus(a1)] + Minus(a2) < a2 + Minus(a1) + Minus(a2) & P192 & P189 & P185 & P190 & P0) & P0 -> (Minus(a2) < Minus(a1) & P187 & P183 & P182 & P181 & P0) & P0" 2; pushnode 11 " ([ a1 + Minus(a1)] + Minus(a2) = a1 + Minus(a1) + Minus(a2) & P190 & P0) & (a1 + Minus(a1) + Minus(a2) < a2 + Minus(a1) + Minus(a2) & P189 & P185 & P0) & P0 -> (Minus(a2) < Minus(a1) & P187 & P183 & P182 & P181 & P0) & P0" 1; pushreference 10 "P0 -> ( [a1 + Minus(a1)] + Minus(a2) = a1 + Minus(a1) + Minus(a2) & P190 & P0) & P0" "APLUS"; pushnode 9 " (a1 + Minus(a1) + Minus(a2) < a2 + Minus(a1) + Minus(a2) & P189 & P185 & P0) & P0 -> ( Minus(a2) < Minus(a1) & P187 & P183 & P182 & P181 & P0) & P0" 2; pushnode 8 "( a1 < a2 & P186 & P183 & P182 & P181 & P0) & P0 -> (a1 < a2 & P188 & P185 & P0) & P0" 0; pushnode 7 "( (a1 < a2 -> a1 + Minus(a1) + Minus(a2) < a2 + Minus(a1) + Minus(a2)) & P185 & P0) & ( a1 < a2 & P186 & P183 & P182 & P181 & P0) & P0 -> ( Minus(a2) < Minus(a1) & P187 & P183 & P182 & P181 & P0) & P0" 2; pushnode 6 "( ( a1 < a2 -> a1 + Minus(a1) + Minus(a2) < a2 + Minus(a1) + Minus(a2)) & P185 & P0) & P0 -> ((a1 < a2 -> Minus(a2) < Minus(a1)) & P183 & P182 & P181 & P0) & P0" 1; pushreference 5 " P0 -> ( (a1 < a2 -> a1 + Minus(a1) + Minus(a2) < a2 + Minus(a1) + Minus(a2)) & P185 & P0) & P0" "MPLUS"; pushnode 3 "P0 -> ((a1 < a2 -> Minus(a2) < Minus(a1)) & P183 & P182 & P181 & P0) & P0" 2; pushnode 2 " P0 -> ( ( (a1 < a2 -> Minus(a2) < Minus(a1)) & ( Minus(a2) < Minus(a1) -> a1 < a2)) & P182 & P181 & P0) & P0" 2; pushnode 1 "P0 -> ( (a1 < a2 == Minus(a2) < Minus(a1)) & P181 & P0) & P0" 1; THEOREMS:=("MINUSLESS",(termtosequent(parseprop(" P0 -> ( (a1 < a2 == Minus(a2) < Minus(a1)) & P181 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "MINUSLESS"; pushnode 15 "( a1 = a2 & P251 & P247 & P243 & P242 & P240 & P237 & P236 & P246 & P244 & P250 & P248 & P0) & (a1 + Zero = a1 & P246 & P244 & P0) & ( a2 + Zero = a2 & P250 & P248 & P0) & P0 -> (a1 = a2 & P238 & P236 & P0) & P0" 0; pushnode 14 "( a2 + Zero = a2 & P250 & P248 & P0) & (a1 = a2 + Zero & P247 & P243 & P242 & P240 & P237 & P236 & P246 & P244 & P0) & ( a1 + Zero = a1 & P246 & P244 & P0) & P0 -> (a1 = a2 & P238 & P236 & P0) & P0" 1; pushnode 13 "( Real(a2) & P241 & P240 & P237 & P236 & P0) & P0 -> (Real(a2) & P249 & P248 & P0) & P0" 0; pushnode 12 "((Real(a2) -> a2 + Zero = a2) & P248 & P0) & (a1 + Zero = a1 & P246 & P244 & P0) & (a1 = a2 + Zero & P247 & P243 & P242 & P240 & P237 & P236 & P246 & P244 & P0) & ( Real(a2) & P241 & P240 & P237 & P236 & P0) & P0 -> ( a1 = a2 & P238 & P236 & P0) & P0" 2; pushreference 11 "P0 -> ((Real(a2) -> a2 + Zero = a2) & P248 & P0) & P0" "IPLUS"; pushnode 10 " (a1 + Zero = a1 & P246 & P244 & P0) & (a1 = a2 + Zero & P247 & P243 & P242 & P240 & P237 & P236 & P246 & P244 & P0) & ( Real(a2) & P241 & P240 & P237 & P236 & P0) & P0 -> (a1 = a2 & P238 & P236 & P0) & P0" 2; pushnode 9 "( a1 + Zero = a1 & P246 & P244 & P0) & ( a1 + Zero = a2 + Zero & P243 & P242 & P240 & P237 & P236 & P0) & ( Real(a2) & P241 & P240 & P237 & P236 & P0) & P0 -> (a1 = a2 & P238 & P236 & P0) & P0" 1; pushnode 8 "( Real(a1) & P239 & P237 & P236 & P0) & P0 -> (Real(a1) & P245 & P244 & P0) & P0" 0; pushnode 7 " ((Real(a1) -> a1 + Zero = a1) & P244 & P0) & (a1 + Zero = a2 + Zero & P243 & P242 & P240 & P237 & P236 & P0) & (Real(a1) & P239 & P237 & P236 & P0) & (Real(a2) & P241 & P240 & P237 & P236 & P0) & P0 -> (a1 = a2 & P238 & P236 & P0) & P0" 2; pushreference 6 "P0 -> ((Real(a1) -> a1 + Zero = a1) & P244 & P0) & P0" "IPLUS"; pushnode 5 "( a1 + Zero = a2 + Zero & P243 & P242 & P240 & P237 & P236 & P0) & (Real(a1) & P239 & P237 & P236 & P0) & (Real(a2) & P241 & P240 & P237 & P236 & P0) & P0 -> ( a1 = a2 & P238 & P236 & P0) & P0" 2; pushnode 4 " (a1 Equal a2 & P242 & P240 & P237 & P236 & P0) & (Real(a1) & P239 & P237 & P236 & P0) & (Real(a2) & P241 & P240 & P237 & P236 & P0) & P0 -> (a1 = a2 & P238 & P236 & P0) & P0" 1; THEOREMS:=("EQUALITY",(termtosequent(parseprop(" (a1 Equal a2 & P242 & P240 & P237 & P236 & P0) & (Real(a1) & P239 & P237 & P236 & P0) & (Real(a2) & P241 & P240 & P237 & P236 & P0) & P0 -> (a1 = a2 & P238 & P236 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "EQUALITY"; pushnode 19 " (a1 + Minus(a1) < [a1 + Minus(a1)] + Minus(a1) & P267 & P265 & P0) & P0 -> ( a1 + Minus(a1) < [a1 + Minus(a1)] + Minus(a1) & P258 & P0) & P0" 0; pushnode 20 "( a1 < Zero & P256 & P253 & P252 & P0) & P0 -> (a1 < Zero & P269 & P257 & P266 & P265 & P0) & P0" 0; pushnode 18 "( a1 + Minus(a1) = Zero & P257 & P0) & ( a1 < Zero & P256 & P253 & P252 & P0) & P0 -> ( a1 < a1 + Minus(a1) & P266 & P265 & P0) & P0" 1; pushnode 17 " (( a1 < a1 + Minus(a1) -> a1 + Minus(a1) < [a1 + Minus(a1)] + Minus(a1)) & P265 & P0) & (a1 + Minus(a1) = Zero & P257 & P0) & (a1 < Zero & P256 & P253 & P252 & P0) & P0 -> ( a1 + Minus(a1) < [a1 + Minus(a1)] + Minus(a1) & P258 & P0) & P0" 2; pushreference 16 " P0 -> ( (a1 < a1 + Minus(a1) -> a1 + Minus(a1) < [a1 + Minus(a1)] + Minus(a1)) & P265 & P0) & P0" "MPLUS"; pushnode 7 "( a1 + Minus(a1) = Zero & P257 & P0) & ( a1 < Zero & P256 & P253 & P252 & P0) & P0 -> ( a1 + Minus(a1) < [a1 + Minus(a1)] + Minus(a1) & P258 & P0) & P0" 2; pushreference 14 " P0 -> (Real(Minus(a1)) & P262 & P0) & P0" "RMINUS"; pushnode 15 " ( Zero < Minus(a1) & P264 & P261 & P259 & P258 & P257 & P260 & P263 & P0) & ( a1 + Minus(a1) = Zero & P257 & P0) & ( Zero + Minus(a1) = Minus(a1) + Zero & P260 & P0) & ( Minus(a1) + Zero = Minus(a1) & P263 & P0) & P0 -> (Zero < Minus(a1) & P254 & P252 & P0) & P0" 0; pushnode 13 " ( Minus(a1) + Zero = Minus(a1) & P263 & P0) & (Zero < Minus(a1) + Zero & P261 & P259 & P258 & P257 & P260 & P0) & ( a1 + Minus(a1) = Zero & P257 & P0) & ( Zero + Minus(a1) = Minus(a1) + Zero & P260 & P0) & P0 -> (Zero < Minus(a1) & P254 & P252 & P0) & P0" 1; pushreference 12 "( Real(Minus(a1)) & P262 & P0) & P0 -> ( Minus(a1) + Zero = Minus(a1) & P263 & P0) & P0" "IPLUSa"; pushnode 11 "( Zero + Minus(a1) = Minus(a1) + Zero & P260 & P0) & (Zero < Minus(a1) + Zero & P261 & P259 & P258 & P257 & P260 & P0) & ( a1 + Minus(a1) = Zero & P257 & P0) & P0 -> ( Zero < Minus(a1) & P254 & P252 & P0) & P0" 3; pushnode 10 " (Zero + Minus(a1) = Minus(a1) + Zero & P260 & P0) & ( Zero < Zero + Minus(a1) & P259 & P258 & P257 & P0) & ( a1 + Minus(a1) = Zero & P257 & P0) & P0 -> ( Zero < Minus(a1) & P254 & P252 & P0) & P0" 1; pushreference 9 "P0 -> (Zero + Minus(a1) = Minus(a1) + Zero & P260 & P0) & P0" "CPLUS"; pushnode 8 "( a1 + Minus(a1) = Zero & P257 & P0) & ( Zero < Zero + Minus(a1) & P259 & P258 & P257 & P0) & P0 -> ( Zero < Minus(a1) & P254 & P252 & P0) & P0" 2; pushnode 6 " ( a1 + Minus(a1) = Zero & P257 & P0) & ( a1 + Minus(a1) < [a1 + Minus(a1)] + Minus(a1) & P258 & P0) & P0 -> (Zero < Minus(a1) & P254 & P252 & P0) & P0" 1; pushnode 5 "( a1 + Minus(a1) = Zero & P257 & P0) & ( a1 < Zero & P256 & P253 & P252 & P0) & P0 -> (Zero < Minus(a1) & P254 & P252 & P0) & P0" 2; pushreference 4 "P0 -> (a1 + Minus(a1) = Zero & P257 & P0) & P0" "MINUS"; pushnode 3 "( a1 < Zero & P256 & P253 & P252 & P0) & P0 -> (Zero < Minus(a1) & P254 & P252 & P0) & P0" 2; THEOREMS:=("NEGINEQ",(termtosequent(parseprop("( a1 < Zero & P256 & P253 & P252 & P0) & P0 -> (Zero < Minus(a1) & P254 & P252 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "NEGINEQ"; pushnode 28 "(a1 * Zero = Zero & P295 & P0) & P0 -> ( a1 * Zero = Zero & P294 & P292 & P291 & P289 & P275 & P0) & P0" 0; pushreference 27 "P0 -> ( a1 * Zero = Zero & P295 & P0) & P0" "MZERO"; pushnode 26 "P0 -> (a1 * Zero = Zero & P294 & P292 & P291 & P289 & P275 & P0) & P0" 2; pushnode 25 "( a2 + Minus(a2) = Zero & P292 & P0) & P0 -> ( a1 * [a2 + Minus(a2)] = Zero & P291 & P289 & P275 & P0) & P0" 1; pushreference 24 "P0 -> ( a2 + Minus(a2) = Zero & P292 & P0) & P0" "MINUS"; pushnode 23 "P0 -> (a1 * [a2 + Minus(a2)] = Zero & P291 & P289 & P275 & P0) & P0" 2; pushnode 22 "( a1 * [a2 + Minus(a2)] = a1 * a2 + a1 * Minus(a2) & P289 & P0) & P0 -> ( a1 * a2 + a1 * Minus(a2) = Zero & P275 & P0) & P0" 1; pushreference 21 "P0 -> (a1 * [a2 + Minus(a2)] = a1 * a2 + a1 * Minus(a2) & P289 & P0) & P0" "DIST"; pushnode 5 "P0 -> (a1 * a2 + a1 * Minus(a2) = Zero & P275 & P0) & P0" 2; pushnode 20 " ( a2 + Minus(a2) = Zero & P280 & P0) & ( a1 * Zero = Zero & P282 & P0) & P0 -> (a1 * a2 + a1 * Minus(a2) = a1 * a2 + a1 * Minus(a2) & P288 & P283 & P281 & P278 & P276 & P280 & P282 & P285 & P0) & P0" 0; pushnode 19 "(Zero = a1 * a2 + a1 * Minus(a2) & P283 & P281 & P278 & P276 & P280 & P282 & P0) & ( a2 + Minus(a2) = Zero & P280 & P0) & ( a1 * Zero = Zero & P282 & P0) & P0 -> ( a1 * a2 + a1 * Minus(a2) = Zero & P285 & P0) & P0" 1; pushreference 18 "P0 -> ( Real(a1 * Minus(a2)) & P284 & P0) & P0" "RTIMES"; pushnode 17 "( a1 * Minus(a2) = Minus(a1 * a2) & P286 & P0) & P0 -> ( a1 * Minus(a2) = Minus(a1 * a2) & P272 & P270 & P0) & P0" 0; pushreference 16 "(Real( a1 * Minus(a2)) & P284 & P0) & (a1 * a2 + a1 * Minus(a2) = Zero & P285 & P0) & P0 -> (a1 * Minus(a2) = Minus(a1 * a2) & P286 & P0) & P0" "UINV"; pushnode 15 " (a1 * Zero = Zero & P282 & P0) & ( Zero = a1 * a2 + a1 * Minus(a2) & P283 & P281 & P278 & P276 & P280 & P282 & P0) & ( a2 + Minus(a2) = Zero & P280 & P0) & P0 -> ( a1 * Minus(a2) = Minus(a1 * a2) & P272 & P270 & P0) & P0" 4; pushnode 14 " (a1 * Zero = Zero & P282 & P0) & ( a1 * Zero = a1 * a2 + a1 * Minus(a2) & P281 & P278 & P276 & P280 & P0) & ( a2 + Minus(a2) = Zero & P280 & P0) & P0 -> ( a1 * Minus(a2) = Minus(a1 * a2) & P272 & P270 & P0) & P0" 1; pushreference 13 "P0 -> (a1 * Zero = Zero & P282 & P0) & P0" "MZERO"; pushnode 12 "( a2 + Minus(a2) = Zero & P280 & P0) & ( a1 * Zero = a1 * a2 + a1 * Minus(a2) & P281 & P278 & P276 & P280 & P0) & P0 -> (a1 * Minus(a2) = Minus(a1 * a2) & P272 & P270 & P0) & P0" 2; pushnode 11 " ( a2 + Minus(a2) = Zero & P280 & P0) & ( a1 * [a2 + Minus(a2)] = a1 * a2 + a1 * Minus(a2) & P278 & P276 & P0) & P0 -> ( a1 * Minus(a2) = Minus(a1 * a2) & P272 & P270 & P0) & P0" 1; pushreference 10 "P0 -> ( a2 + Minus(a2) = Zero & P280 & P0) & P0" "MINUS"; pushnode 9 " (a1 * [a2 + Minus(a2)] = a1 * a2 + a1 * Minus(a2) & P278 & P276 & P0) & P0 -> ( a1 * Minus(a2) = Minus(a1 * a2) & P272 & P270 & P0) & P0" 2; pushnode 7 "( a1 * [a2 + Minus(a2)] = a1 * a2 + a1 * Minus(a2) & P276 & P0) & P0 -> ( a1 * Minus(a2) = Minus(a1 * a2) & P272 & P270 & P0) & P0" 1; pushreference 6 " P0 -> ( a1 * [a2 + Minus(a2)] = a1 * a2 + a1 * Minus(a2) & P276 & P0) & P0" "DIST"; pushnode 4 "P0 -> ( a1 * Minus(a2) = Minus(a1 * a2) & P272 & P270 & P0) & P0" 2; pushnode 3 " P0 -> ( a1 * Minus(a2) = Minus(a1 * a2) & P272 & P270 & P0) & P0" 2; THEOREMS:=("NEGCOMM",(termtosequent(parseprop("P0 -> ( a1 * Minus(a2) = Minus(a1 * a2) & P272 & P270 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "NEGCOMM"; pushnode 11 " ( Minus(a1) + a1 = Zero & P301 & P299 & P300 & P0) & ( a1 + Minus(a1) = Minus(a1) + a1 & P300 & P0) & P0 -> ( Minus(a1) + a1 = Zero & P303 & P0) & P0" 0; pushnode 10 "(Real(a1) & P297 & P296 & P0) & P0 -> (Real(a1) & P302 & P0) & P0" 0; pushnode 12 " P0 -> (a1 = a1 & P306 & P304 & P298 & P296 & P0) & P0" 0; pushnode 9 " (a1 = Minus(Minus(a1)) & P304 & P0) & P0 -> (Minus(Minus(a1)) = a1 & P298 & P296 & P0) & P0" 1; pushreference 8 " (Real(a1) & P302 & P0) & ( Minus(a1) + a1 = Zero & P303 & P0) & P0 -> (a1 = Minus(Minus(a1)) & P304 & P0) & P0" "UINV"; pushnode 7 " (a1 + Minus(a1) = Minus(a1) + a1 & P300 & P0) & ( Minus(a1) + a1 = Zero & P301 & P299 & P300 & P0) & (Real(a1) & P297 & P296 & P0) & P0 -> ( Minus(Minus(a1)) = a1 & P298 & P296 & P0) & P0" 4; pushnode 6 "( a1 + Minus(a1) = Minus(a1) + a1 & P300 & P0) & ( a1 + Minus(a1) = Zero & P299 & P0) & ( Real(a1) & P297 & P296 & P0) & P0 -> ( Minus(Minus(a1)) = a1 & P298 & P296 & P0) & P0" 1; pushreference 5 "P0 -> ( a1 + Minus(a1) = Minus(a1) + a1 & P300 & P0) & P0" "CPLUS"; pushnode 4 "( a1 + Minus(a1) = Zero & P299 & P0) & (Real(a1) & P297 & P296 & P0) & P0 -> ( Minus(Minus(a1)) = a1 & P298 & P296 & P0) & P0" 2; pushreference 3 "P0 -> ( a1 + Minus(a1) = Zero & P299 & P0) & P0" "MINUS"; pushnode 2 "(Real(a1) & P297 & P296 & P0) & P0 -> (Minus(Minus(a1)) = a1 & P298 & P296 & P0) & P0" 2; THEOREMS:=("DOUBLENEG",(termtosequent(parseprop(" (Real(a1) & P297 & P296 & P0) & P0 -> ( Minus(Minus(a1)) = a1 & P298 & P296 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "DOUBLENEG"; pushreference 16 "P0 -> (Real(a1 * a2) & P320 & P0) & P0" "RTIMES"; pushnode 15 "( Minus(Minus(a1 * a2)) = a1 * a2 & P321 & P0) & P0 -> (Minus(Minus( a1 * a2)) = a1 * a2 & P319 & P317 & P316 & P314 & P313 & P311 & P310 & P308 & P307 & P0) & P0" 0; pushreference 14 "(Real(a1 * a2) & P320 & P0) & P0 -> ( Minus(Minus(a1 * a2)) = a1 * a2 & P321 & P0) & P0" "DOUBLENEG"; pushnode 13 " P0 -> ( Minus(Minus(a1 * a2)) = a1 * a2 & P319 & P317 & P316 & P314 & P313 & P311 & P310 & P308 & P307 & P0) & P0" 3; pushnode 12 "( a2 * a1 = a1 * a2 & P317 & P0) & P0 -> ( Minus(Minus(a2 * a1)) = a1 * a2 & P316 & P314 & P313 & P311 & P310 & P308 & P307 & P0) & P0" 1; pushreference 11 "P0 -> ( a2 * a1 = a1 * a2 & P317 & P0) & P0" "CTIMES"; pushnode 10 "P0 -> ( Minus(Minus(a2 * a1)) = a1 * a2 & P316 & P314 & P313 & P311 & P310 & P308 & P307 & P0) & P0" 2; pushnode 9 "( a2 * Minus(a1) = Minus(a2 * a1) & P314 & P0) & P0 -> (Minus( a2 * Minus(a1)) = a1 * a2 & P313 & P311 & P310 & P308 & P307 & P0) & P0" 1; pushreference 8 " P0 -> ( a2 * Minus(a1) = Minus(a2 * a1) & P314 & P0) & P0" "NEGCOMM"; pushnode 7 " P0 -> ( Minus(a2 * Minus(a1)) = a1 * a2 & P313 & P311 & P310 & P308 & P307 & P0) & P0" 2; pushnode 6 " (Minus(a1) * a2 = a2 * Minus(a1) & P311 & P0) & P0 -> ( Minus(Minus(a1) * a2) = a1 * a2 & P310 & P308 & P307 & P0) & P0" 1; pushreference 5 "P0 -> ( Minus(a1) * a2 = a2 * Minus(a1) & P311 & P0) & P0" "CTIMES"; pushnode 4 "P0 -> ( Minus(Minus(a1) * a2) = a1 * a2 & P310 & P308 & P307 & P0) & P0" 2; pushnode 3 "( Minus(a1) * Minus(a2) = Minus(Minus(a1) * a2) & P308 & P0) & P0 -> ( Minus(a1) * Minus(a2) = a1 * a2 & P307 & P0) & P0" 1; pushreference 2 "P0 -> (Minus(a1) * Minus(a2) = Minus( Minus(a1) * a2) & P308 & P0) & P0" "NEGCOMM"; pushnode 1 "P0 -> (Minus(a1) * Minus(a2) = a1 * a2 & P307 & P0) & P0" 2; THEOREMS:=("TIMESDOUBNEG",(termtosequent(parseprop(" P0 -> ( Minus(a1) * Minus(a2) = a1 * a2 & P307 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "TIMESDOUBNEG"; pushnode 6 "( a3 < Zero & P325 & P323 & P322 & P0) & P0 -> (a3 < Zero & P327 & P0) & P0" 0; pushnode 28 "( a2 * a3 < a1 * a3 & P347 & P345 & P341 & P339 & P344 & P346 & P0) & ( Minus(a2) * Minus(a3) = a2 * a3 & P344 & P0) & ( Minus(a1) * Minus(a3) = a1 * a3 & P346 & P0) & P0 -> ( a2 * a3 < a1 * a3 & P324 & P322 & P0) & P0" 0; pushnode 27 "( Minus(a1) * Minus(a3) = a1 * a3 & P346 & P0) & (a2 * a3 < Minus(a1) * Minus(a3) & P345 & P341 & P339 & P344 & P0) & ( Minus(a2) * Minus(a3) = a2 * a3 & P344 & P0) & P0 -> ( a2 * a3 < a1 * a3 & P324 & P322 & P0) & P0" 1; pushreference 26 "P0 -> ( Minus(a1) * Minus(a3) = a1 * a3 & P346 & P0) & P0" "TIMESDOUBNEG"; pushnode 25 "( Minus(a2) * Minus(a3) = a2 * a3 & P344 & P0) & (a2 * a3 < Minus(a1) * Minus(a3) & P345 & P341 & P339 & P344 & P0) & P0 -> ( a2 * a3 < a1 * a3 & P324 & P322 & P0) & P0" 2; pushnode 24 " ( Minus(a2) * Minus(a3) = a2 * a3 & P344 & P0) & (Minus(a2) * Minus(a3) < Minus(a1) * Minus(a3) & P341 & P339 & P0) & P0 -> ( a2 * a3 < a1 * a3 & P324 & P322 & P0) & P0" 1; pushreference 23 "P0 -> ( Minus(a2) * Minus(a3) = a2 * a3 & P344 & P0) & P0" "TIMESDOUBNEG"; pushnode 20 " ( Minus(a2) * Minus(a3) < Minus(a1) * Minus(a3) & P341 & P339 & P0) & P0 -> ( a2 * a3 < a1 * a3 & P324 & P322 & P0) & P0" 2; pushnode 22 " (Minus(a2) < Minus(a1) & P334 & P331 & P330 & P329 & P0) & P0 -> ( Minus(a2) < Minus(a1) & P343 & P340 & P339 & P0) & P0" 0; pushnode 21 "( Zero < Minus(a3) & P328 & P0) & P0 -> (Zero < Minus(a3) & P342 & P340 & P339 & P0) & P0" 0; pushnode 19 " ( Zero < Minus(a3) & P328 & P0) & ( Minus(a2) < Minus(a1) & P334 & P331 & P330 & P329 & P0) & P0 -> ((Zero < Minus(a3) & Minus(a2) < Minus(a1)) & P340 & P339 & P0) & P0" 2; pushnode 18 "( ( Zero < Minus(a3) & Minus(a2) < Minus(a1) -> Minus(a2) * Minus(a3) < Minus(a1) * Minus(a3)) & P339 & P0) & ( Zero < Minus(a3) & P328 & P0) & ( Minus(a2) < Minus(a1) & P334 & P331 & P330 & P329 & P0) & P0 -> (a2 * a3 < a1 * a3 & P324 & P322 & P0) & P0" 2; pushreference 17 "P0 -> ( (Zero < Minus(a3) & Minus(a2) < Minus(a1) -> Minus(a2) * Minus(a3) < Minus(a1) * Minus(a3)) & P339 & P0) & P0" "MTIMES"; pushnode 16 " (Zero < Minus(a3) & P328 & P0) & ( Minus(a2) < Minus(a1) & P334 & P331 & P330 & P329 & P0) & P0 -> ( a2 * a3 < a1 * a3 & P324 & P322 & P0) & P0" 2; pushnode 15 " (Minus(a2) < Minus(a1) & P334 & P331 & P330 & P329 & P0) & P0 -> ( Minus(a2) < Minus(a1) & P337 & P332 & P330 & P329 & P0) & P0" 0; pushnode 12 "(( Minus(a2) < Minus(a1) -> a1 < a2) & P332 & P330 & P329 & P0) & ( Zero < Minus(a3) & P328 & P0) & ( Minus(a2) < Minus(a1) & P334 & P331 & P330 & P329 & P0) & P0 -> (a2 * a3 < a1 * a3 & P324 & P322 & P0) & P0" 2; pushnode 14 "(a1 < a2 & P336 & P332 & P330 & P329 & P0) & P0 -> ( a1 < a2 & P333 & P331 & P330 & P329 & P0) & P0" 0; pushnode 13 " (a1 < a2 & P326 & P323 & P322 & P0) & P0 -> ( a1 < a2 & P333 & P331 & P330 & P329 & P0) & P0" 0; pushnode 11 " ((Minus(a2) < Minus(a1) -> a1 < a2) & P332 & P330 & P329 & P0) & (a1 < a2 & P326 & P323 & P322 & P0) & P0 -> ( a1 < a2 & P333 & P331 & P330 & P329 & P0) & P0" 2; pushnode 10 " ((a1 < a2 -> Minus(a2) < Minus(a1)) & P331 & P330 & P329 & P0) & ((Minus(a2) < Minus(a1) -> a1 < a2) & P332 & P330 & P329 & P0) & (Zero < Minus(a3) & P328 & P0) & (a1 < a2 & P326 & P323 & P322 & P0) & P0 -> ( a2 * a3 < a1 * a3 & P324 & P322 & P0) & P0" 2; pushnode 9 "( ( (a1 < a2 -> Minus(a2) < Minus(a1)) & ( Minus(a2) < Minus(a1) -> a1 < a2)) & P330 & P329 & P0) & ( Zero < Minus(a3) & P328 & P0) & ( a1 < a2 & P326 & P323 & P322 & P0) & P0 -> (a2 * a3 < a1 * a3 & P324 & P322 & P0) & P0" 1; pushnode 8 "((a1 < a2 == Minus(a2) < Minus(a1)) & P329 & P0) & ( Zero < Minus(a3) & P328 & P0) & ( a1 < a2 & P326 & P323 & P322 & P0) & P0 -> (a2 * a3 < a1 * a3 & P324 & P322 & P0) & P0" 1; pushreference 7 "P0 -> ((a1 < a2 == Minus(a2) < Minus(a1)) & P329 & P0) & P0" "MINUSLESS"; pushnode 5 " (Zero < Minus(a3) & P328 & P0) & (a1 < a2 & P326 & P323 & P322 & P0) & P0 -> ( a2 * a3 < a1 * a3 & P324 & P322 & P0) & P0" 2; pushreference 4 " (a3 < Zero & P327 & P0) & P0 -> ( Zero < Minus(a3) & P328 & P0) & P0" "NEGINEQ"; pushnode 3 " (a3 < Zero & P325 & P323 & P322 & P0) & (a1 < a2 & P326 & P323 & P322 & P0) & P0 -> ( a2 * a3 < a1 * a3 & P324 & P322 & P0) & P0" 3; THEOREMS:=("MTIMESNEG",(termtosequent(parseprop(" (a3 < Zero & P325 & P323 & P322 & P0) & (a1 < a2 & P326 & P323 & P322 & P0) & P0 -> ( a2 * a3 < a1 * a3 & P324 & P322 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "MTIMESNEG"; pushnode 42 " (Zero < a1 * a1 & P384 & P378 & P376 & P383 & P381 & P382 & P0) & ( a1 * Zero = Zero * a1 & P382 & P0) & (Zero * a1 = Zero & P383 & P381 & P382 & P0) & P0 -> (Zero < a1 * a1 & P353 & P351 & P350 & P348 & P0) & P0" 0; pushnode 41 " (Zero * a1 = Zero & P383 & P381 & P382 & P0) & (Zero * a1 < a1 * a1 & P378 & P376 & P0) & ( a1 * Zero = Zero * a1 & P382 & P0) & P0 -> (Zero < a1 * a1 & P353 & P351 & P350 & P348 & P0) & P0" 1; pushnode 40 "( a1 * Zero = Zero * a1 & P382 & P0) & (a1 * Zero = Zero & P381 & P0) & (Zero * a1 < a1 * a1 & P378 & P376 & P0) & P0 -> ( Zero < a1 * a1 & P353 & P351 & P350 & P348 & P0) & P0" 1; pushreference 39 " P0 -> (a1 * Zero = Zero * a1 & P382 & P0) & P0" "CTIMES"; pushnode 38 "(a1 * Zero = Zero & P381 & P0) & (Zero * a1 < a1 * a1 & P378 & P376 & P0) & P0 -> ( Zero < a1 * a1 & P353 & P351 & P350 & P348 & P0) & P0" 2; pushreference 37 " P0 -> (a1 * Zero = Zero & P381 & P0) & P0" "MZERO"; pushnode 34 "( Zero * a1 < a1 * a1 & P378 & P376 & P0) & P0 -> (Zero < a1 * a1 & P353 & P351 & P350 & P348 & P0) & P0" 2; pushnode 36 "( Zero < a1 & P368 & P356 & P354 & P0) & P0 -> (Zero < a1 & P380 & P377 & P376 & P0) & P0" 0; pushnode 35 "( Zero < a1 & P368 & P356 & P354 & P0) & P0 -> (Zero < a1 & P379 & P377 & P376 & P0) & P0" 0; pushnode 33 "( Zero < a1 & P368 & P356 & P354 & P0) & P0 -> ( (Zero < a1 & Zero < a1) & P377 & P376 & P0) & P0" 2; pushnode 32 "(( Zero < a1 & Zero < a1 -> Zero * a1 < a1 * a1) & P376 & P0) & ( Zero < a1 & P368 & P356 & P354 & P0) & P0 -> ( Zero < a1 * a1 & P353 & P351 & P350 & P348 & P0) & P0" 2; pushreference 31 " P0 -> ( (Zero < a1 & Zero < a1 -> Zero * a1 < a1 * a1) & P376 & P0) & P0" "MTIMES"; pushnode 20 " (Zero < a1 & P368 & P356 & P354 & P0) & P0 -> (Zero < a1 * a1 & P353 & P351 & P350 & P348 & P0) & P0" 2; pushnode 24 " (a1 < Zero & P367 & P356 & P354 & P0) & P0 -> ( a1 < Zero & P370 & P0) & P0" 0; pushnode 23 " (a1 < Zero & P367 & P356 & P354 & P0) & P0 -> ( a1 < Zero & P369 & P0) & P0" 0; pushnode 30 " (Zero < a1 * a1 & P375 & P371 & P374 & P372 & P373 & P0) & ( a1 * Zero = Zero * a1 & P373 & P0) & ( Zero * a1 = Zero & P374 & P372 & P373 & P0) & P0 -> (Zero < a1 * a1 & P353 & P351 & P350 & P348 & P0) & P0" 0; pushnode 29 "(Zero * a1 = Zero & P374 & P372 & P373 & P0) & (Zero * a1 < a1 * a1 & P371 & P0) & (a1 * Zero = Zero * a1 & P373 & P0) & P0 -> (Zero < a1 * a1 & P353 & P351 & P350 & P348 & P0) & P0" 1; pushnode 28 "( a1 * Zero = Zero * a1 & P373 & P0) & ( a1 * Zero = Zero & P372 & P0) & (Zero * a1 < a1 * a1 & P371 & P0) & P0 -> (Zero < a1 * a1 & P353 & P351 & P350 & P348 & P0) & P0" 1; pushreference 27 "P0 -> ( a1 * Zero = Zero * a1 & P373 & P0) & P0" "CTIMES"; pushnode 26 "(a1 * Zero = Zero & P372 & P0) & ( Zero * a1 < a1 * a1 & P371 & P0) & P0 -> ( Zero < a1 * a1 & P353 & P351 & P350 & P348 & P0) & P0" 2; pushreference 25 " P0 -> (a1 * Zero = Zero & P372 & P0) & P0" "MZERO"; pushnode 22 "( Zero * a1 < a1 * a1 & P371 & P0) & P0 -> (Zero < a1 * a1 & P353 & P351 & P350 & P348 & P0) & P0" 2; pushreference 21 "( a1 < Zero & P369 & P0) & ( a1 < Zero & P370 & P0) & P0 -> ( Zero * a1 < a1 * a1 & P371 & P0) & P0" "MTIMESNEG"; pushnode 19 " (a1 < Zero & P367 & P356 & P354 & P0) & P0 -> (Zero < a1 * a1 & P353 & P351 & P350 & P348 & P0) & P0" 4; pushnode 8 "( (a1 < Zero v Zero < a1) & P356 & P354 & P0) & P0 -> (Zero < a1 * a1 & P353 & P351 & P350 & P348 & P0) & P0" 2; pushreference 13 " P0 -> (Real(Zero) & P359 & P0) & P0" "RZERO"; pushnode 12 "( Real(a1) & P349 & P348 & P0) & P0 -> (Real(a1) & P358 & P0) & P0" 0; pushnode 11 "( a1 Equal Zero & P355 & P354 & P0) & P0 -> (a1 Equal Zero & P357 & P0) & P0" 0; pushnode 18 "(Zero Equal Zero & P366 & P355 & P354 & P361 & P360 & P0) & ( a1 = Zero & P361 & P360 & P0) & P0 -> (Zero Equal Zero & P365 & P363 & P362 & P360 & P352 & P351 & P350 & P348 & P0) & P0" 0; pushnode 17 " (a1 = Zero & P361 & P360 & P0) & (a1 Equal Zero & P355 & P354 & P0) & P0 -> ( Zero Equal Zero & P365 & P363 & P362 & P360 & P352 & P351 & P350 & P348 & P0) & P0" 1; pushnode 16 " (Zero * Zero = Zero & P363 & P0) & ( a1 = Zero & P361 & P360 & P0) & ( a1 Equal Zero & P355 & P354 & P0) & P0 -> (Zero Equal Zero * Zero & P362 & P360 & P352 & P351 & P350 & P348 & P0) & P0" 1; pushreference 15 "P0 -> ( Zero * Zero = Zero & P363 & P0) & P0" "MZERO"; pushnode 14 " (a1 = Zero & P361 & P360 & P0) & (a1 Equal Zero & P355 & P354 & P0) & P0 -> (Zero Equal Zero * Zero & P362 & P360 & P352 & P351 & P350 & P348 & P0) & P0" 2; pushnode 10 "( a1 = Zero & P360 & P0) & ( a1 Equal Zero & P355 & P354 & P0) & P0 -> ( Zero Equal a1 * a1 & P352 & P351 & P350 & P348 & P0) & P0" 1; pushreference 9 "( a1 Equal Zero & P357 & P0) & ( Real(a1) & P358 & P0) & ( Real(Zero) & P359 & P0) & P0 -> (a1 = Zero & P360 & P0) & P0" "EQUALITY"; pushnode 7 " (a1 Equal Zero & P355 & P354 & P0) & (Real(a1) & P349 & P348 & P0) & P0 -> ( Zero Equal a1 * a1 & P352 & P351 & P350 & P348 & P0) & P0" 5; pushnode 6 "(( a1 Equal Zero v a1 < Zero v Zero < a1) & P354 & P0) & ( Real(a1) & P349 & P348 & P0) & P0 -> ( Zero Equal a1 * a1 & P352 & P351 & P350 & P348 & P0) & ( Zero < a1 * a1 & P353 & P351 & P350 & P348 & P0) & P0" 2; pushreference 5 "P0 -> ( (a1 Equal Zero v a1 < Zero v Zero < a1) & P354 & P0) & P0" "TRI"; pushnode 4 "(Real(a1) & P349 & P348 & P0) & P0 -> (Zero Equal a1 * a1 & P352 & P351 & P350 & P348 & P0) & (Zero < a1 * a1 & P353 & P351 & P350 & P348 & P0) & P0" 2; pushnode 3 "( Real(a1) & P349 & P348 & P0) & P0 -> ( (Zero Equal a1 * a1 v Zero < a1 * a1) & P351 & P350 & P348 & P0) & P0" 1; pushnode 2 "(Real(a1) & P349 & P348 & P0) & P0 -> (Zero <= a1 * a1 & P350 & P348 & P0) & P0" 1; THEOREMS:=("SQUARENONNEG",(termtosequent(parseprop(" (Real(a1) & P349 & P348 & P0) & P0 -> ( Zero <= a1 * a1 & P350 & P348 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "SQUARENONNEG"; pushreference 4 "P0 -> (a1 * Zero = Zero & P388 & P386 & P385 & P0) & P0" "MZERO"; pushnode 3 "( Zero * a1 = a1 * Zero & P386 & P0) & P0 -> ( Zero * a1 = Zero & P385 & P0) & P0" 1; pushreference 2 " P0 -> (Zero * a1 = a1 * Zero & P386 & P0) & P0" "CTIMES"; pushnode 1 "P0 -> (Zero * a1 = Zero & P385 & P0) & P0" 2; THEOREMS:=("MZERO2",(termtosequent(parseprop("P0 -> (Zero * a1 = Zero & P385 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "MZERO2"; pushnode 5 "P0 -> ( a2 + Zero = a2 + Zero & P395 & P393 & P390 & P389 & P392 & P391 & P389 & P0) & P0" 0; pushnode 4 " ( a1 + Zero = a2 + Zero & P393 & P390 & P389 & P0) & P0 -> (a2 + Zero = a1 + Zero & P392 & P391 & P389 & P0) & P0" 1; pushnode 3 " (a1 Equal a2 & P390 & P389 & P0) & P0 -> ( a2 + Zero = a1 + Zero & P392 & P391 & P389 & P0) & P0" 1; pushnode 2 "( a1 Equal a2 & P390 & P389 & P0) & P0 -> (a2 Equal a1 & P391 & P389 & P0) & P0" 1; THEOREMS:=("EqualSymm",(termtosequent(parseprop("( a1 Equal a2 & P390 & P389 & P0) & P0 -> (a2 Equal a1 & P391 & P389 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "EqualSymm"; pushreference 9 "P0 -> (Real( One * Inv(One)) & P403 & P401 & P397 & P396 & P0) & P0" "RTIMES"; pushnode 8 "( One * Inv(One) = One & P401 & P397 & P0) & P0 -> (Real(One) & P396 & P0) & P0" 1; pushreference 7 "( One Equal Zero & P400 & P397 & P0) & P0 -> (Zero Equal One & P399 & P398 & P0) & P0" "EqualSymm"; pushnode 6 "(( One Equal Zero v One * Inv(One) = One) & P397 & P0) & P0 -> ( Zero Equal One & P399 & P398 & P0) & ( Real(One) & P396 & P0) & P0" 2; pushnode 5 "(~Zero Equal One & P398 & P0) & ( (One Equal Zero v One * Inv(One) = One) & P397 & P0) & P0 -> (Real(One) & P396 & P0) & P0" 1; pushreference 4 "P0 -> (~Zero Equal One & P398 & P0) & P0" "NONTRIV"; pushnode 3 "( (One Equal Zero v One * Inv(One) = One) & P397 & P0) & P0 -> (Real(One) & P396 & P0) & P0" 2; pushreference 2 " P0 -> ((One Equal Zero v One * Inv(One) = One) & P397 & P0) & P0" "INV"; pushnode 1 "P0 -> (Real(One) & P396 & P0) & P0" 2; THEOREMS:=("REALONE",(termtosequent(parseprop("P0 -> (Real(One) & P396 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "REALONE"; pushnode 12 "(a2 < a2 & P410 & P408 & P0) & P0 -> (a2 < a2 & P414 & P413 & P0) & P0" 0; pushnode 11 " (~a2 < a2 & P413 & P0) & (a2 < a2 & P410 & P408 & P0) & P0 -> P0" 1; pushreference 10 "P0 -> (~a2 < a2 & P413 & P0) & P0" "IRR"; pushnode 7 "(a2 < a2 & P410 & P408 & P0) & P0 -> P0" 2; pushnode 9 "(a1 < a2 & P405 & P404 & P0) & P0 -> (a1 < a2 & P412 & P409 & P408 & P0) & P0" 0; pushnode 8 "( a2 < a1 & P407 & P406 & P404 & P0) & P0 -> (a2 < a1 & P411 & P409 & P408 & P0) & P0" 0; pushnode 6 "( a2 < a1 & P407 & P406 & P404 & P0) & ( a1 < a2 & P405 & P404 & P0) & P0 -> ( (a2 < a1 & a1 < a2) & P409 & P408 & P0) & P0" 2; pushnode 5 "(( a2 < a1 & a1 < a2 -> a2 < a2) & P408 & P0) & (a2 < a1 & P407 & P406 & P404 & P0) & (a1 < a2 & P405 & P404 & P0) & P0 -> P0" 2; pushreference 4 "P0 -> (( a2 < a1 & a1 < a2 -> a2 < a2) & P408 & P0) & P0" "TRANS"; pushnode 3 "( a2 < a1 & P407 & P406 & P404 & P0) & ( a1 < a2 & P405 & P404 & P0) & P0 -> P0" 2; THEOREMS:=("NOTBOTH",(termtosequent(parseprop(" (a2 < a1 & P407 & P406 & P404 & P0) & (a1 < a2 & P405 & P404 & P0) & P0 -> P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "NOTBOTH"; pushnode 12 " (a2 + Zero < a2 + Zero & P423 & P422 & P420 & P419 & P416 & P415 & P0) & ( a1 + Zero = a2 + Zero & P419 & P416 & P415 & P0) & P0 -> ( a2 + Zero < a2 + Zero & P425 & P424 & P0) & P0" 0; pushnode 11 "( ~a2 + Zero < a2 + Zero & P424 & P0) & ( a1 + Zero = a2 + Zero & P419 & P416 & P415 & P0) & ( a2 + Zero < a2 + Zero & P423 & P422 & P420 & P419 & P416 & P415 & P0) & P0 -> P0" 1; pushreference 10 "P0 -> (~a2 + Zero < a2 + Zero & P424 & P0) & P0" "IRR"; pushnode 9 "( a1 + Zero = a2 + Zero & P419 & P416 & P415 & P0) & ( a2 + Zero < a2 + Zero & P423 & P422 & P420 & P419 & P416 & P415 & P0) & P0 -> P0" 2; pushnode 8 " (a1 + Zero = a2 + Zero & P419 & P416 & P415 & P0) & ( a1 + Zero < a2 + Zero & P422 & P420 & P0) & P0 -> P0" 1; pushnode 7 " (a1 < a2 & P418 & P417 & P415 & P0) & P0 -> (a1 < a2 & P421 & P420 & P0) & P0" 0; pushnode 6 "((a1 < a2 -> a1 + Zero < a2 + Zero) & P420 & P0) & (a1 + Zero = a2 + Zero & P419 & P416 & P415 & P0) & (a1 < a2 & P418 & P417 & P415 & P0) & P0 -> P0" 2; pushreference 5 "P0 -> ((a1 < a2 -> a1 + Zero < a2 + Zero) & P420 & P0) & P0" "MPLUS"; pushnode 4 " ( a1 + Zero = a2 + Zero & P419 & P416 & P415 & P0) & (a1 < a2 & P418 & P417 & P415 & P0) & P0 -> P0" 2; pushnode 3 "(a1 Equal a2 & P416 & P415 & P0) & ( a1 < a2 & P418 & P417 & P415 & P0) & P0 -> P0" 1; THEOREMS:=("NOTBOTH2",(termtosequent(parseprop(" (a1 Equal a2 & P416 & P415 & P0) & (a1 < a2 & P418 & P417 & P415 & P0) & P0 -> P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "NOTBOTH2"; pushnode 6 "(a1 Equal a2 & P427 & P426 & P0) & P0 -> (a1 Equal a2 & P430 & P0) & P0" 0; pushreference 5 " (a2 Equal a1 & P431 & P0) & (a2 < a1 & P429 & P428 & P426 & P0) & P0 -> P0" "NOTBOTH2"; pushreference 4 " (a1 Equal a2 & P430 & P0) & P0 -> (a2 Equal a1 & P431 & P0) & P0" "EqualSymm"; pushnode 3 " (a2 < a1 & P429 & P428 & P426 & P0) & (a1 Equal a2 & P427 & P426 & P0) & P0 -> P0" 3; THEOREMS:=("NOTBOTH3",(termtosequent(parseprop(" (a2 < a1 & P429 & P428 & P426 & P0) & (a1 Equal a2 & P427 & P426 & P0) & P0 -> P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "NOTBOTH3"; pushreference 4 "P0 -> (Real(One) & P433 & P0) & P0" "REALONE"; pushnode 12 " (Zero < One * One & P442 & P440 & P434 & P0) & P0 -> (Zero < One * One & P439 & P437 & P435 & P432 & P0) & P0" 0; pushnode 16 " (Zero Equal One & P443 & P441 & P440 & P434 & P438 & P437 & P435 & P0) & (One * One = One & P438 & P437 & P435 & P0) & P0 -> (Zero Equal One & P445 & P444 & P0) & P0" 0; pushnode 15 "( ~Zero Equal One & P444 & P0) & ( One * One = One & P438 & P437 & P435 & P0) & (Zero Equal One & P443 & P441 & P440 & P434 & P438 & P437 & P435 & P0) & P0 -> P0" 1; pushreference 14 "P0 -> (~Zero Equal One & P444 & P0) & P0" "NONTRIV"; pushnode 13 " ( One * One = One & P438 & P437 & P435 & P0) & (Zero Equal One & P443 & P441 & P440 & P434 & P438 & P437 & P435 & P0) & P0 -> P0" 2; pushnode 11 "( One * One = One & P438 & P437 & P435 & P0) & (Zero Equal One * One & P441 & P440 & P434 & P0) & P0 -> P0" 1; pushnode 10 " ((Zero Equal One * One v Zero < One * One) & P440 & P434 & P0) & (One * One = One & P438 & P437 & P435 & P0) & P0 -> (Zero < One * One & P439 & P437 & P435 & P432 & P0) & P0" 2; pushnode 9 " (Zero <= One * One & P434 & P0) & (One * One = One & P438 & P437 & P435 & P0) & P0 -> (Zero < One * One & P439 & P437 & P435 & P432 & P0) & P0" 1; pushnode 8 " (One * One = One & P437 & P435 & P0) & (Zero <= One * One & P434 & P0) & P0 -> ( Zero < One & P432 & P0) & P0" 1; pushreference 7 "P0 -> (Real(One) & P436 & P435 & P0) & P0" "REALONE"; pushnode 6 " (( Real(One) -> One * One = One) & P435 & P0) & (Zero <= One * One & P434 & P0) & P0 -> (Zero < One & P432 & P0) & P0" 2; pushreference 5 "P0 -> ((Real(One) -> One * One = One) & P435 & P0) & P0" "ITIMES"; pushnode 3 " (Zero <= One * One & P434 & P0) & P0 -> (Zero < One & P432 & P0) & P0" 2; pushreference 2 "( Real(One) & P433 & P0) & P0 -> (Zero <= One * One & P434 & P0) & P0" "SQUARENONNEG"; pushnode 1 "P0 -> (Zero < One & P432 & P0) & P0" 3; THEOREMS:=("ZEROLESSONE",(termtosequent(parseprop(" P0 -> (Zero < One & P432 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "ZEROLESSONE"; pushreference 17 " P0 -> (a1 * a2 = a2 * a1 & P461 & P459 & P457 & P456 & P454 & P453 & P451 & P450 & P448 & P446 & P0) & P0" "CTIMES"; pushnode 16 "( a2 * a1 + Zero = a2 * a1 & P459 & P457 & P0) & P0 -> ( a1 * a2 = a2 * a1 + Zero & P456 & P454 & P453 & P451 & P450 & P448 & P446 & P0) & P0" 1; pushreference 15 "P0 -> (Real(a2 * a1) & P458 & P457 & P0) & P0" "RTIMES"; pushnode 14 "((Real( a2 * a1) -> a2 * a1 + Zero = a2 * a1) & P457 & P0) & P0 -> ( a1 * a2 = a2 * a1 + Zero & P456 & P454 & P453 & P451 & P450 & P448 & P446 & P0) & P0" 2; pushreference 13 "P0 -> ( (Real(a2 * a1) -> a2 * a1 + Zero = a2 * a1) & P457 & P0) & P0" "IPLUS"; pushnode 12 " P0 -> ( a1 * a2 = a2 * a1 + Zero & P456 & P454 & P453 & P451 & P450 & P448 & P446 & P0) & P0" 2; pushnode 11 "( a2 * Zero = Zero & P454 & P0) & P0 -> (a1 * a2 = a2 * a1 + a2 * Zero & P453 & P451 & P450 & P448 & P446 & P0) & P0" 1; pushreference 10 "P0 -> (a2 * Zero = Zero & P454 & P0) & P0" "MZERO"; pushnode 9 " P0 -> ( a1 * a2 = a2 * a1 + a2 * Zero & P453 & P451 & P450 & P448 & P446 & P0) & P0" 2; pushnode 8 "( a2 * [a1 + Zero] = a2 * a1 + a2 * Zero & P451 & P0) & P0 -> (a1 * a2 = a2 * [a1 + Zero] & P450 & P448 & P446 & P0) & P0" 1; pushreference 7 "P0 -> (a2 * [a1 + Zero] = a2 * a1 + a2 * Zero & P451 & P0) & P0" "DIST"; pushnode 6 "P0 -> (a1 * a2 = a2 * [a1 + Zero] & P450 & P448 & P446 & P0) & P0" 2; pushnode 5 "([a1 + Zero] * a2 = a2 * [a1 + Zero] & P448 & P0) & P0 -> ( a1 * a2 = [a1 + Zero] * a2 & P446 & P0) & P0" 1; pushreference 4 "P0 -> ( [a1 + Zero] * a2 = a2 * [ a1 + Zero] & P448 & P0) & P0" "CTIMES"; pushnode 1 "P0 -> (a1 * a2 = [a1 + Zero] * a2 & P446 & P0) & P0" 2; THEOREMS:=("SubLemma",(termtosequent(parseprop(" P0 -> ( a1 * a2 = [a1 + Zero] * a2 & P446 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "SubLemma"; pushnode 26 "( a1 * a1 < a2 * a2 & P487 & P485 & P0) & P0 -> ( a1 * a1 < a2 * a2 & P472 & P469 & P466 & P465 & P463 & P0) & P0" 0; pushnode 28 "( a1 * a2 < a2 * a2 & P475 & P473 & P0) & P0 -> ( a1 * a2 < a2 * a2 & P489 & P486 & P485 & P0) & P0" 0; pushnode 27 " (a1 * a1 < a1 * a2 & P484 & P480 & P478 & P483 & P0) & (a2 * a1 = a1 * a2 & P483 & P0) & P0 -> ( a1 * a1 < a1 * a2 & P488 & P486 & P485 & P0) & P0" 0; pushnode 25 "(a2 * a1 = a1 * a2 & P483 & P0) & ( a1 * a1 < a1 * a2 & P484 & P480 & P478 & P483 & P0) & ( a1 * a2 < a2 * a2 & P475 & P473 & P0) & P0 -> ((a1 * a1 < a1 * a2 & a1 * a2 < a2 * a2) & P486 & P485 & P0) & P0" 2; pushnode 24 "(( a1 * a1 < a1 * a2 & a1 * a2 < a2 * a2 -> a1 * a1 < a2 * a2) & P485 & P0) & (a2 * a1 = a1 * a2 & P483 & P0) & ( a1 * a1 < a1 * a2 & P484 & P480 & P478 & P483 & P0) & ( a1 * a2 < a2 * a2 & P475 & P473 & P0) & P0 -> ( a1 * a1 < a2 * a2 & P472 & P469 & P466 & P465 & P463 & P0) & P0" 2; pushreference 23 "P0 -> (( a1 * a1 < a1 * a2 & a1 * a2 < a2 * a2 -> a1 * a1 < a2 * a2) & P485 & P0) & P0" "TRANS"; pushnode 22 "( a2 * a1 = a1 * a2 & P483 & P0) & ( a1 * a1 < a1 * a2 & P484 & P480 & P478 & P483 & P0) & ( a1 * a2 < a2 * a2 & P475 & P473 & P0) & P0 -> ( a1 * a1 < a2 * a2 & P472 & P469 & P466 & P465 & P463 & P0) & P0" 2; pushnode 21 "( a2 * a1 = a1 * a2 & P483 & P0) & ( a1 * a1 < a2 * a1 & P480 & P478 & P0) & (a1 * a2 < a2 * a2 & P475 & P473 & P0) & P0 -> (a1 * a1 < a2 * a2 & P472 & P469 & P466 & P465 & P463 & P0) & P0" 1; pushreference 20 "P0 -> ( a2 * a1 = a1 * a2 & P483 & P0) & P0" "CTIMES"; pushnode 17 " ( a1 * a1 < a2 * a1 & P480 & P478 & P0) & ( a1 * a2 < a2 * a2 & P475 & P473 & P0) & P0 -> (a1 * a1 < a2 * a2 & P472 & P469 & P466 & P465 & P463 & P0) & P0" 2; pushnode 19 "( a1 < a2 & P471 & P469 & P466 & P465 & P463 & P0) & P0 -> (a1 < a2 & P482 & P479 & P478 & P0) & P0" 0; pushnode 18 "( Zero < a1 & P467 & P464 & P463 & P0) & P0 -> (Zero < a1 & P481 & P479 & P478 & P0) & P0" 0; pushnode 16 "( a1 < a2 & P471 & P469 & P466 & P465 & P463 & P0) & ( Zero < a1 & P467 & P464 & P463 & P0) & P0 -> ( (Zero < a1 & a1 < a2) & P479 & P478 & P0) & P0" 2; pushnode 15 "(( Zero < a1 & a1 < a2 -> a1 * a1 < a2 * a1) & P478 & P0) & (a1 * a2 < a2 * a2 & P475 & P473 & P0) & ( a1 < a2 & P471 & P469 & P466 & P465 & P463 & P0) & ( Zero < a1 & P467 & P464 & P463 & P0) & P0 -> ( a1 * a1 < a2 * a2 & P472 & P469 & P466 & P465 & P463 & P0) & P0" 2; pushreference 14 "P0 -> (( Zero < a1 & a1 < a2 -> a1 * a1 < a2 * a1) & P478 & P0) & P0" "MTIMES"; pushnode 11 "( a1 * a2 < a2 * a2 & P475 & P473 & P0) & ( a1 < a2 & P471 & P469 & P466 & P465 & P463 & P0) & ( Zero < a1 & P467 & P464 & P463 & P0) & P0 -> (a1 * a1 < a2 * a2 & P472 & P469 & P466 & P465 & P463 & P0) & P0" 2; pushnode 13 " (a1 < a2 & P471 & P469 & P466 & P465 & P463 & P0) & P0 -> (a1 < a2 & P477 & P474 & P473 & P0) & P0" 0; pushnode 12 "( Zero < a2 & P468 & P464 & P463 & P0) & P0 -> (Zero < a2 & P476 & P474 & P473 & P0) & P0" 0; pushnode 10 "( a1 < a2 & P471 & P469 & P466 & P465 & P463 & P0) & ( Zero < a2 & P468 & P464 & P463 & P0) & P0 -> ( (Zero < a2 & a1 < a2) & P474 & P473 & P0) & P0" 2; pushnode 9 "(( Zero < a2 & a1 < a2 -> a1 * a2 < a2 * a2) & P473 & P0) & (a1 < a2 & P471 & P469 & P466 & P465 & P463 & P0) & (Zero < a1 & P467 & P464 & P463 & P0) & (Zero < a2 & P468 & P464 & P463 & P0) & P0 -> ( a1 * a1 < a2 * a2 & P472 & P469 & P466 & P465 & P463 & P0) & P0" 2; pushreference 8 "P0 -> (( Zero < a2 & a1 < a2 -> a1 * a2 < a2 * a2) & P473 & P0) & P0" "MTIMES"; pushnode 7 " (a1 < a2 & P471 & P469 & P466 & P465 & P463 & P0) & (Zero < a1 & P467 & P464 & P463 & P0) & (Zero < a2 & P468 & P464 & P463 & P0) & P0 -> (a1 * a1 < a2 * a2 & P472 & P469 & P466 & P465 & P463 & P0) & P0" 2; THEOREMS:=("SquareOrder1",(termtosequent(parseprop("( a1 < a2 & P471 & P469 & P466 & P465 & P463 & P0) & ( Zero < a1 & P467 & P464 & P463 & P0) & ( Zero < a2 & P468 & P464 & P463 & P0) & P0 -> (a1 * a1 < a2 * a2 & P472 & P469 & P466 & P465 & P463 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "SquareOrder1"; pushnode 67 " (Zero < a1 & P467 & P464 & P463 & P0) & P0 -> ( Zero < a1 & P523 & P0) & P0" 0; pushnode 66 " (Zero < a2 & P468 & P464 & P463 & P0) & P0 -> ( Zero < a2 & P522 & P0) & P0" 0; pushnode 65 " (a2 < a1 & P520 & P494 & P492 & P0) & P0 -> ( a2 < a1 & P521 & P0) & P0" 0; pushreference 64 "( a2 * a2 < a1 * a1 & P524 & P0) & ( a1 * a1 < a2 * a2 & P490 & P470 & P466 & P465 & P463 & P0) & P0 -> P0" "NOTBOTH"; pushreference 63 "(a2 < a1 & P521 & P0) & (Zero < a2 & P522 & P0) & (Zero < a1 & P523 & P0) & P0 -> (a2 * a2 < a1 * a1 & P524 & P0) & P0" "SquareOrder1"; pushnode 62 "( a2 < a1 & P520 & P494 & P492 & P0) & ( a1 * a1 < a2 * a2 & P490 & P470 & P466 & P465 & P463 & P0) & ( Zero < a1 & P467 & P464 & P463 & P0) & ( Zero < a2 & P468 & P464 & P463 & P0) & P0 -> P0" 5; pushnode 61 " (a1 < a2 & P519 & P494 & P492 & P0) & P0 -> ( a1 < a2 & P491 & P470 & P466 & P465 & P463 & P0) & P0" 0; pushnode 33 "( (a1 < a2 v a2 < a1) & P494 & P492 & P0) & ( a1 * a1 < a2 * a2 & P490 & P470 & P466 & P465 & P463 & P0) & ( Zero < a1 & P467 & P464 & P463 & P0) & ( Zero < a2 & P468 & P464 & P463 & P0) & P0 -> ( a1 < a2 & P491 & P470 & P466 & P465 & P463 & P0) & P0" 2; pushnode 60 " ( a2 * a2 < a2 * a2 & P516 & P514 & P510 & P508 & P507 & P505 & P503 & P501 & P499 & P497 & P490 & P470 & P466 & P465 & P463 & P496 & P498 & P500 & P502 & P504 & P506 & P495 & P493 & P492 & P506 & P502 & P498 & P0) & ( a1 * a1 = [a1 + Zero] * a1 & P496 & P0) & ( [a1 + Zero] * a1 = a1 * [a1 + Zero] & P500 & P0) & (a1 * [a1 + Zero] = [a1 + Zero] * [a1 + Zero] & P504 & P0) & (a1 + Zero = a2 + Zero & P495 & P493 & P492 & P0) & P0 -> ( a2 * a2 < a2 * a2 & P518 & P517 & P0) & P0" 0; pushnode 59 "( ~a2 * a2 < a2 * a2 & P517 & P0) & ( a2 * a2 < a2 * a2 & P516 & P514 & P510 & P508 & P507 & P505 & P503 & P501 & P499 & P497 & P490 & P470 & P466 & P465 & P463 & P496 & P498 & P500 & P502 & P504 & P506 & P495 & P493 & P492 & P506 & P502 & P498 & P0) & ( a1 * a1 = [a1 + Zero] * a1 & P496 & P0) & ([a1 + Zero] * a1 = a1 * [a1 + Zero] & P500 & P0) & (a1 * [a1 + Zero] = [a1 + Zero] * [a1 + Zero] & P504 & P0) & (a1 + Zero = a2 + Zero & P495 & P493 & P492 & P0) & P0 -> P0" 1; pushreference 58 "P0 -> (~a2 * a2 < a2 * a2 & P517 & P0) & P0" "IRR"; pushnode 57 " (a2 * a2 < a2 * a2 & P516 & P514 & P510 & P508 & P507 & P505 & P503 & P501 & P499 & P497 & P490 & P470 & P466 & P465 & P463 & P496 & P498 & P500 & P502 & P504 & P506 & P495 & P493 & P492 & P506 & P502 & P498 & P0) & (a1 * a1 = [a1 + Zero] * a1 & P496 & P0) & ( [a1 + Zero] * a1 = a1 * [a1 + Zero] & P500 & P0) & (a1 * [a1 + Zero] = [a1 + Zero] * [a1 + Zero] & P504 & P0) & (a1 + Zero = a2 + Zero & P495 & P493 & P492 & P0) & P0 -> P0" 2; pushnode 56 "( a2 * a2 = [a2 + Zero] * a2 & P498 & P0) & ( [a2 + Zero] * a2 < [a2 + Zero] * a2 & P514 & P510 & P508 & P507 & P505 & P503 & P501 & P499 & P497 & P490 & P470 & P466 & P465 & P463 & P496 & P498 & P500 & P502 & P504 & P506 & P495 & P493 & P492 & P506 & P502 & P0) & ( a1 * a1 = [a1 + Zero] * a1 & P496 & P0) & ([a1 + Zero] * a1 = a1 * [a1 + Zero] & P500 & P0) & (a1 * [a1 + Zero] = [a1 + Zero] * [a1 + Zero] & P504 & P0) & (a1 + Zero = a2 + Zero & P495 & P493 & P492 & P0) & P0 -> P0" 1; pushnode 54 "([a2 + Zero] * a2 = a2 * [a2 + Zero] & P502 & P0) & (a2 * [a2 + Zero] < a2 * [a2 + Zero] & P510 & P508 & P507 & P505 & P503 & P501 & P499 & P497 & P490 & P470 & P466 & P465 & P463 & P496 & P498 & P500 & P502 & P504 & P506 & P495 & P493 & P492 & P506 & P0) & (a1 * a1 = [ a1 + Zero] * a1 & P496 & P0) & (a2 * a2 = [ a2 + Zero] * a2 & P498 & P0) & ([a1 + Zero] * a1 = a1 * [a1 + Zero] & P500 & P0) & (a1 * [a1 + Zero] = [a1 + Zero] * [a1 + Zero] & P504 & P0) & (a1 + Zero = a2 + Zero & P495 & P493 & P492 & P0) & P0 -> P0" 1; pushnode 53 "( a2 * [a2 + Zero] = [a2 + Zero] * [a2 + Zero] & P506 & P0) & ( [a2 + Zero] * [a2 + Zero] < [a2 + Zero] * [a2 + Zero] & P508 & P507 & P505 & P503 & P501 & P499 & P497 & P490 & P470 & P466 & P465 & P463 & P496 & P498 & P500 & P502 & P504 & P506 & P495 & P493 & P492 & P0) & ( a1 * a1 = [a1 + Zero] * a1 & P496 & P0) & (a2 * a2 = [a2 + Zero] * a2 & P498 & P0) & ([a1 + Zero] * a1 = a1 * [a1 + Zero] & P500 & P0) & ( [a2 + Zero] * a2 = a2 * [a2 + Zero] & P502 & P0) & (a1 * [a1 + Zero] = [a1 + Zero] * [a1 + Zero] & P504 & P0) & (a1 + Zero = a2 + Zero & P495 & P493 & P492 & P0) & P0 -> P0" 1; pushnode 52 " (a1 + Zero = a2 + Zero & P495 & P493 & P492 & P0) & ([a1 + Zero] * [a1 + Zero] < [a2 + Zero] * [a2 + Zero] & P507 & P505 & P503 & P501 & P499 & P497 & P490 & P470 & P466 & P465 & P463 & P496 & P498 & P500 & P502 & P504 & P506 & P0) & (a1 * a1 = [a1 + Zero] * a1 & P496 & P0) & (a2 * a2 = [a2 + Zero] * a2 & P498 & P0) & ( [a1 + Zero] * a1 = a1 * [a1 + Zero] & P500 & P0) & ([a2 + Zero] * a2 = a2 * [a2 + Zero] & P502 & P0) & (a1 * [a1 + Zero] = [a1 + Zero] * [a1 + Zero] & P504 & P0) & (a2 * [a2 + Zero] = [a2 + Zero] * [a2 + Zero] & P506 & P0) & P0 -> P0" 1; pushnode 51 "(a2 * [a2 + Zero] = [a2 + Zero] * [a2 + Zero] & P506 & P0) & ( [a1 + Zero] * [a1 + Zero] < a2 * [a2 + Zero] & P505 & P503 & P501 & P499 & P497 & P490 & P470 & P466 & P465 & P463 & P496 & P498 & P500 & P502 & P504 & P0) & ( a1 + Zero = a2 + Zero & P495 & P493 & P492 & P0) & ( a1 * a1 = [a1 + Zero] * a1 & P496 & P0) & (a2 * a2 = [ a2 + Zero] * a2 & P498 & P0) & ([a1 + Zero] * a1 = a1 * [a1 + Zero] & P500 & P0) & ( [a2 + Zero] * a2 = a2 * [a2 + Zero] & P502 & P0) & (a1 * [a1 + Zero] = [a1 + Zero] * [a1 + Zero] & P504 & P0) & P0 -> P0" 1; pushreference 50 "P0 -> ( a2 * [a2 + Zero] = [a2 + Zero] * [a2 + Zero] & P506 & P0) & P0" "SubLemma"; pushnode 49 "( a1 * [a1 + Zero] = [a1 + Zero] * [ a1 + Zero] & P504 & P0) & ( [a1 + Zero] * [a1 + Zero] < a2 * [a2 + Zero] & P505 & P503 & P501 & P499 & P497 & P490 & P470 & P466 & P465 & P463 & P496 & P498 & P500 & P502 & P504 & P0) & ( a1 + Zero = a2 + Zero & P495 & P493 & P492 & P0) & ( a1 * a1 = [a1 + Zero] * a1 & P496 & P0) & (a2 * a2 = [ a2 + Zero] * a2 & P498 & P0) & ([a1 + Zero] * a1 = a1 * [a1 + Zero] & P500 & P0) & ( [a2 + Zero] * a2 = a2 * [a2 + Zero] & P502 & P0) & P0 -> P0" 2; pushnode 48 "(a1 * [a1 + Zero] = [a1 + Zero] * [a1 + Zero] & P504 & P0) & (a1 * [a1 + Zero] < a2 * [a2 + Zero] & P503 & P501 & P499 & P497 & P490 & P470 & P466 & P465 & P463 & P496 & P498 & P500 & P502 & P0) & ( a1 + Zero = a2 + Zero & P495 & P493 & P492 & P0) & ( a1 * a1 = [a1 + Zero] * a1 & P496 & P0) & (a2 * a2 = [a2 + Zero] * a2 & P498 & P0) & ([a1 + Zero] * a1 = a1 * [a1 + Zero] & P500 & P0) & ( [a2 + Zero] * a2 = a2 * [a2 + Zero] & P502 & P0) & P0 -> P0" 1; pushreference 47 "P0 -> (a1 * [ a1 + Zero] = [a1 + Zero] * [ a1 + Zero] & P504 & P0) & P0" "SubLemma"; pushnode 46 "([ a2 + Zero] * a2 = a2 * [a2 + Zero] & P502 & P0) & (a1 * [a1 + Zero] < a2 * [a2 + Zero] & P503 & P501 & P499 & P497 & P490 & P470 & P466 & P465 & P463 & P496 & P498 & P500 & P502 & P0) & ( a1 + Zero = a2 + Zero & P495 & P493 & P492 & P0) & ( a1 * a1 = [a1 + Zero] * a1 & P496 & P0) & (a2 * a2 = [a2 + Zero] * a2 & P498 & P0) & ([a1 + Zero] * a1 = a1 * [a1 + Zero] & P500 & P0) & P0 -> P0" 2; pushnode 45 "([a2 + Zero] * a2 = a2 * [a2 + Zero] & P502 & P0) & (a1 * [a1 + Zero] < [a2 + Zero] * a2 & P501 & P499 & P497 & P490 & P470 & P466 & P465 & P463 & P496 & P498 & P500 & P0) & (a1 + Zero = a2 + Zero & P495 & P493 & P492 & P0) & ( a1 * a1 = [a1 + Zero] * a1 & P496 & P0) & (a2 * a2 = [a2 + Zero] * a2 & P498 & P0) & ([a1 + Zero] * a1 = a1 * [a1 + Zero] & P500 & P0) & P0 -> P0" 1; pushreference 44 "P0 -> ([a2 + Zero] * a2 = a2 * [a2 + Zero] & P502 & P0) & P0" "CTIMES"; pushnode 43 "( [a1 + Zero] * a1 = a1 * [ a1 + Zero] & P500 & P0) & ( a1 * [a1 + Zero] < [a2 + Zero] * a2 & P501 & P499 & P497 & P490 & P470 & P466 & P465 & P463 & P496 & P498 & P500 & P0) & ( a1 + Zero = a2 + Zero & P495 & P493 & P492 & P0) & ( a1 * a1 = [a1 + Zero] * a1 & P496 & P0) & (a2 * a2 = [ a2 + Zero] * a2 & P498 & P0) & P0 -> P0" 2; pushnode 42 "([a1 + Zero] * a1 = a1 * [a1 + Zero] & P500 & P0) & ( [a1 + Zero] * a1 < [a2 + Zero] * a2 & P499 & P497 & P490 & P470 & P466 & P465 & P463 & P496 & P498 & P0) & ( a1 + Zero = a2 + Zero & P495 & P493 & P492 & P0) & ( a1 * a1 = [a1 + Zero] * a1 & P496 & P0) & (a2 * a2 = [a2 + Zero] * a2 & P498 & P0) & P0 -> P0" 1; pushreference 41 "P0 -> ([a1 + Zero] * a1 = a1 * [a1 + Zero] & P500 & P0) & P0" "CTIMES"; pushnode 40 " ( a2 * a2 = [a2 + Zero] * a2 & P498 & P0) & ([a1 + Zero] * a1 < [a2 + Zero] * a2 & P499 & P497 & P490 & P470 & P466 & P465 & P463 & P496 & P498 & P0) & (a1 + Zero = a2 + Zero & P495 & P493 & P492 & P0) & (a1 * a1 = [ a1 + Zero] * a1 & P496 & P0) & P0 -> P0" 2; pushnode 39 " (a2 * a2 = [a2 + Zero] * a2 & P498 & P0) & ( [a1 + Zero] * a1 < a2 * a2 & P497 & P490 & P470 & P466 & P465 & P463 & P496 & P0) & ( a1 + Zero = a2 + Zero & P495 & P493 & P492 & P0) & ( a1 * a1 = [a1 + Zero] * a1 & P496 & P0) & P0 -> P0" 1; pushreference 38 "P0 -> (a2 * a2 = [a2 + Zero] * a2 & P498 & P0) & P0" "SubLemma"; pushnode 37 "( a1 * a1 = [a1 + Zero] * a1 & P496 & P0) & ( [a1 + Zero] * a1 < a2 * a2 & P497 & P490 & P470 & P466 & P465 & P463 & P496 & P0) & ( a1 + Zero = a2 + Zero & P495 & P493 & P492 & P0) & P0 -> P0" 2; pushnode 36 "(a1 * a1 = [a1 + Zero] * a1 & P496 & P0) & (a1 * a1 < a2 * a2 & P490 & P470 & P466 & P465 & P463 & P0) & ( a1 + Zero = a2 + Zero & P495 & P493 & P492 & P0) & P0 -> P0" 1; pushreference 35 "P0 -> (a1 * a1 = [a1 + Zero] * a1 & P496 & P0) & P0" "SubLemma"; pushnode 34 " ( a1 + Zero = a2 + Zero & P495 & P493 & P492 & P0) & (a1 * a1 < a2 * a2 & P490 & P470 & P466 & P465 & P463 & P0) & P0 -> P0" 2; pushnode 32 " (a1 Equal a2 & P493 & P492 & P0) & ( a1 * a1 < a2 * a2 & P490 & P470 & P466 & P465 & P463 & P0) & P0 -> P0" 1; pushnode 31 "( (a1 Equal a2 v a1 < a2 v a2 < a1) & P492 & P0) & ( a1 * a1 < a2 * a2 & P490 & P470 & P466 & P465 & P463 & P0) & ( Zero < a1 & P467 & P464 & P463 & P0) & ( Zero < a2 & P468 & P464 & P463 & P0) & P0 -> ( a1 < a2 & P491 & P470 & P466 & P465 & P463 & P0) & P0" 2; pushreference 30 "P0 -> ((a1 Equal a2 v a1 < a2 v a2 < a1) & P492 & P0) & P0" "TRI"; pushnode 29 "( a1 * a1 < a2 * a2 & P490 & P470 & P466 & P465 & P463 & P0) & ( Zero < a1 & P467 & P464 & P463 & P0) & ( Zero < a2 & P468 & P464 & P463 & P0) & P0 -> (a1 < a2 & P491 & P470 & P466 & P465 & P463 & P0) & P0" 2; pushnode 6 "( Zero < a1 & P467 & P464 & P463 & P0) & ( Zero < a2 & P468 & P464 & P463 & P0) & P0 -> (( a1 * a1 < a2 * a2 -> a1 < a2) & P470 & P466 & P465 & P463 & P0) & P0" 1; pushreference 7 " (a1 < a2 & P471 & P469 & P466 & P465 & P463 & P0) & (Zero < a1 & P467 & P464 & P463 & P0) & (Zero < a2 & P468 & P464 & P463 & P0) & P0 -> (a1 * a1 < a2 * a2 & P472 & P469 & P466 & P465 & P463 & P0) & P0" "SquareOrder1"; pushnode 5 "( Zero < a1 & P467 & P464 & P463 & P0) & ( Zero < a2 & P468 & P464 & P463 & P0) & P0 -> ((a1 < a2 -> a1 * a1 < a2 * a2) & P469 & P466 & P465 & P463 & P0) & P0" 1; pushnode 4 " (Zero < a1 & P467 & P464 & P463 & P0) & (Zero < a2 & P468 & P464 & P463 & P0) & P0 -> ((( a1 < a2 -> a1 * a1 < a2 * a2) & ( a1 * a1 < a2 * a2 -> a1 < a2)) & P466 & P465 & P463 & P0) & P0" 2; pushnode 3 " (( Zero < a1 & Zero < a2) & P464 & P463 & P0) & P0 -> ((( a1 < a2 -> a1 * a1 < a2 * a2) & ( a1 * a1 < a2 * a2 -> a1 < a2)) & P466 & P465 & P463 & P0) & P0" 1; pushnode 2 " (( Zero < a1 & Zero < a2) & P464 & P463 & P0) & P0 -> (( a1 < a2 == a1 * a1 < a2 * a2) & P465 & P463 & P0) & P0" 1; pushnode 1 " P0 -> ( (Zero < a1 & Zero < a2 -> ( a1 < a2 == a1 * a1 < a2 * a2)) & P463 & P0) & P0" 1; THEOREMS:=("SquareOrder",(termtosequent(parseprop(" P0 -> ( (Zero < a1 & Zero < a2 -> ( a1 < a2 == a1 * a1 < a2 * a2)) & P463 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "SquareOrder"; pushnode 5 "( Zero E a1 & P530 & P528 & P527 & P526 & P525 & P0) & P0 -> (Zero E a1 & P529 & P527 & P526 & P525 & P0) & P0" 0; pushnode 4 "( (Zero E a1 & (Ax20.x20 E a1 -> x20 + One E a1)) & P528 & P527 & P526 & P525 & P0) & P0 -> ( Zero E a1 & P529 & P527 & P526 & P525 & P0) & P0" 1; pushnode 3 "P0 -> (( Zero E a1 & (Ax20.x20 E a1 -> x20 + One E a1) -> Zero E a1) & P527 & P526 & P525 & P0) & P0" 1; pushnode 2 "P0 -> ((Ax17. Zero E x17 & (Ax19.x19 E x17 -> x19 + One E x17) -> Zero E x17) & P526 & P525 & P0) & P0" 1; pushnode 1 " P0 -> (Zero E Nat & P525 & P0) & P0" 1; THEOREMS:=("ZeroNat",(termtosequent(parseprop(" P0 -> (Zero E Nat & P525 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "ZeroNat"; pushnode 13 "( a1 + One E a2 & P549 & P546 & P545 & P540 & P537 & P536 & P534 & P532 & P0) & P0 -> (a1 + One E a2 & P541 & P537 & P536 & P534 & P532 & P0) & P0" 0; pushnode 12 "( a1 E a2 & P543 & P538 & P535 & P533 & P532 & P0) & P0 -> (a1 E a2 & P548 & P546 & P545 & P540 & P537 & P536 & P534 & P532 & P0) & P0" 0; pushnode 11 " ((a1 E a2 -> a1 + One E a2) & P546 & P545 & P540 & P537 & P536 & P534 & P532 & P0) & (a1 E a2 & P543 & P538 & P535 & P533 & P532 & P0) & P0 -> ( a1 + One E a2 & P541 & P537 & P536 & P534 & P532 & P0) & P0" 2; pushnode 10 "((Ax20.x20 E a2 -> x20 + One E a2) & P545 & P540 & P537 & P536 & P534 & P532 & P0) & ( a1 E a2 & P543 & P538 & P535 & P533 & P532 & P0) & P0 -> ( a1 + One E a2 & P541 & P537 & P536 & P534 & P532 & P0) & P0" 1; pushnode 9 "( (Zero E a2 & (Ax20.x20 E a2 -> x20 + One E a2)) & P540 & P537 & P536 & P534 & P532 & P0) & ( a1 E a2 & P543 & P538 & P535 & P533 & P532 & P0) & P0 -> ( a1 + One E a2 & P541 & P537 & P536 & P534 & P532 & P0) & P0" 1; pushnode 8 "( (Zero E a2 & (Ax20.x20 E a2 -> x20 + One E a2)) & P540 & P537 & P536 & P534 & P532 & P0) & P0 -> ( (Zero E a2 & (Ax20.x20 E a2 -> x20 + One E a2)) & P542 & P538 & P535 & P533 & P532 & P0) & P0" 0; pushnode 7 "(( Zero E a2 & (Ax20.x20 E a2 -> x20 + One E a2) -> a1 E a2) & P538 & P535 & P533 & P532 & P0) & (( Zero E a2 & (Ax20.x20 E a2 -> x20 + One E a2)) & P540 & P537 & P536 & P534 & P532 & P0) & P0 -> ( a1 + One E a2 & P541 & P537 & P536 & P534 & P532 & P0) & P0" 2; pushnode 6 "(( Zero E a2 & (Ax20.x20 E a2 -> x20 + One E a2) -> a1 E a2) & P538 & P535 & P533 & P532 & P0) & P0 -> (( Zero E a2 & (Ax20.x20 E a2 -> x20 + One E a2) -> a1 + One E a2) & P537 & P536 & P534 & P532 & P0) & P0" 1; pushnode 5 " ((Ax17. Zero E x17 & (Ax19.x19 E x17 -> x19 + One E x17) -> a1 E x17) & P535 & P533 & P532 & P0) & P0 -> (( Zero E a2 & (Ax20.x20 E a2 -> x20 + One E a2) -> a1 + One E a2) & P537 & P536 & P534 & P532 & P0) & P0" 1; pushnode 4 " ((Ax17. Zero E x17 & (Ax19.x19 E x17 -> x19 + One E x17) -> a1 E x17) & P535 & P533 & P532 & P0) & P0 -> ((Ax17. Zero E x17 & (Ax19.x19 E x17 -> x19 + One E x17) -> a1 + One E x17) & P536 & P534 & P532 & P0) & P0" 1; pushnode 3 "((Ax17. Zero E x17 & (Ax19.x19 E x17 -> x19 + One E x17) -> a1 E x17) & P535 & P533 & P532 & P0) & P0 -> ( a1 + One E Nat & P534 & P532 & P0) & P0" 1; pushnode 2 "(a1 E Nat & P533 & P532 & P0) & P0 -> (a1 + One E Nat & P534 & P532 & P0) & P0" 1; THEOREMS:=("NatClosed",(termtosequent(parseprop(" (a1 E Nat & P533 & P532 & P0) & P0 -> ( a1 + One E Nat & P534 & P532 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "NatClosed"; pushnode 14 "(Real(a1) & P566 & P557 & P554 & P553 & P551 & P550 & P0) & P0 -> ( Real(a1) & P552 & P550 & P0) & P0" 0; pushnode 6 " (a1 E {x1|Real(x1)} & P557 & P554 & P553 & P551 & P550 & P0) & P0 -> (Real(a1) & P552 & P550 & P0) & P0" 1; pushreference 13 "P0 -> (Real(a2 + One) & P565 & P563 & P561 & P559 & P556 & P554 & P553 & P551 & P550 & P0) & P0" "RPLUS"; pushnode 12 "P0 -> (a2 + One E {x22|Real(x22)} & P563 & P561 & P559 & P556 & P554 & P553 & P551 & P550 & P0) & P0" 1; pushnode 11 "P0 -> ( a2 + One E {x22|Real(x22)} & P563 & P561 & P559 & P556 & P554 & P553 & P551 & P550 & P0) & P0" 1; pushnode 10 "P0 -> ( (a2 E {x21|Real(x21)} -> a2 + One E {x22|Real(x22)}) & P561 & P559 & P556 & P554 & P553 & P551 & P550 & P0) & P0" 1; pushnode 8 "P0 -> ( (Ax20.x20 E {x1|Real(x1)} -> x20 + One E {x1|Real(x1)}) & P559 & P556 & P554 & P553 & P551 & P550 & P0) & P0" 1; pushreference 9 "P0 -> (Real(Zero) & P560 & P558 & P556 & P554 & P553 & P551 & P550 & P0) & P0" "RZERO"; pushnode 7 " P0 -> (Zero E {x1|Real(x1)} & P558 & P556 & P554 & P553 & P551 & P550 & P0) & P0" 1; pushnode 5 "P0 -> ( (Zero E {x1|Real(x1)} & (Ax20. x20 E {x1|Real(x1)} -> x20 + One E {x1|Real(x1)})) & P556 & P554 & P553 & P551 & P550 & P0) & P0" 2; pushnode 4 "(( Zero E {x1|Real(x1)} & (Ax20. x20 E {x1|Real(x1)} -> x20 + One E {x1|Real(x1)}) -> a1 E {x1|Real(x1)}) & P554 & P553 & P551 & P550 & P0) & P0 -> (Real(a1) & P552 & P550 & P0) & P0" 2; pushnode 3 " ((Ax17. Zero E x17 & (Ax19.x19 E x17 -> x19 + One E x17) -> a1 E x17) & P553 & P551 & P550 & P0) & P0 -> ( Real(a1) & P552 & P550 & P0) & P0" 1; pushnode 2 "(a1 E Nat & P551 & P550 & P0) & P0 -> (Real(a1) & P552 & P550 & P0) & P0" 1; THEOREMS:=("NatReal",(termtosequent(parseprop("(a1 E Nat & P551 & P550 & P0) & P0 -> (Real(a1) & P552 & P550 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "NatReal"; pushnode 11 "(a3 E a2 & P637 & P632 & P630 & P629 & P628 & P627 & P626 & P625 & P0) & P0 -> (a3 E a2 & P634 & P633 & P630 & P629 & P628 & P627 & P626 & P625 & P0) & P0" 0; pushnode 10 "(a3 E a1 & P636 & P632 & P630 & P629 & P628 & P627 & P626 & P625 & P0) & P0 -> (a3 E a1 & P635 & P633 & P630 & P629 & P628 & P627 & P626 & P625 & P0) & P0" 0; pushnode 9 "( (a3 E a1 v a3 E a2) & P632 & P630 & P629 & P628 & P627 & P626 & P625 & P0) & P0 -> ( a3 E a2 & P634 & P633 & P630 & P629 & P628 & P627 & P626 & P625 & P0) & ( a3 E a1 & P635 & P633 & P630 & P629 & P628 & P627 & P626 & P625 & P0) & P0" 2; pushnode 8 "( (a3 E a1 v a3 E a2) & P632 & P630 & P629 & P628 & P627 & P626 & P625 & P0) & P0 -> (( a3 E a2 v a3 E a1) & P633 & P630 & P629 & P628 & P627 & P626 & P625 & P0) & P0" 1; pushnode 6 "P0 -> (( a3 E a1 v a3 E a2 -> a3 E a2 v a3 E a1) & P630 & P629 & P628 & P627 & P626 & P625 & P0) & P0" 1; THEOREMS:=("Symmetric",(termtosequent(parseprop("P0 -> (( a3 E a1 v a3 E a2 -> a3 E a2 v a3 E a1) & P630 & P629 & P628 & P627 & P626 & P625 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "Symmetric"; pushnode 27 " (a3 = a1 & P756 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & P0 -> (a3 = a1 & P772 & P771 & P770 & P768 & P763 & P761 & P759 & P758 & P757 & P745 & P743 & P742 & P741 & P740 & P739 & P760 & P758 & P757 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & P0" 0; pushnode 26 "( a3 = a1 & P756 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & P0 -> (( a3 = a1 v a3 = a2) & P771 & P770 & P768 & P763 & P761 & P759 & P758 & P757 & P745 & P743 & P742 & P741 & P740 & P739 & P760 & P758 & P757 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & P0" 1; pushnode 25 " (a3 = a1 & P756 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & P0 -> (a3 E {x4| x4 = a1 v x4 = a2} & P770 & P768 & P763 & P761 & P759 & P758 & P757 & P745 & P743 & P742 & P741 & P740 & P739 & P760 & P758 & P757 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & P0" 1; pushnode 24 " ( a4 = {x4|x4 = a1 v x4 = a2} & P768 & P763 & P761 & P759 & P758 & P757 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & (a3 = a1 & P756 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & P0 -> (a3 E a4 & P760 & P758 & P757 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & P0" 1; pushnode 20 " (a4 = a1 Couple a2 & P763 & P761 & P759 & P758 & P757 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & (a3 = a1 & P756 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & P0 -> (a3 E a4 & P760 & P758 & P757 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & P0" 1; pushnode 22 "( a3 = a1 & P756 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & P0 -> ( a3 = a1 & P766 & P765 & P762 & P761 & P759 & P758 & P757 & P745 & P743 & P742 & P741 & P740 & P739 & P760 & P758 & P757 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & P0" 0; pushnode 21 " (a3 = a1 & P756 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & P0 -> ( a3 E Sing(a1) & P765 & P762 & P761 & P759 & P758 & P757 & P745 & P743 & P742 & P741 & P740 & P739 & P760 & P758 & P757 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & P0" 1; pushnode 19 " (a4 = Sing(a1) & P762 & P761 & P759 & P758 & P757 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & (a3 = a1 & P756 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & P0 -> (a3 E a4 & P760 & P758 & P757 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & P0" 1; pushnode 18 " ( ( a4 = Sing(a1) v a4 = a1 Couple a2) & P761 & P759 & P758 & P757 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & (a3 = a1 & P756 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & P0 -> (a3 E a4 & P760 & P758 & P757 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & P0" 2; pushnode 17 " (a4 E a1 Kpair a2 & P759 & P758 & P757 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & (a3 = a1 & P756 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & P0 -> (a3 E a4 & P760 & P758 & P757 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & P0" 1; pushnode 16 "( a3 = a1 & P756 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & P0 -> ((a4 E a1 Kpair a2 -> a3 E a4) & P758 & P757 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & P0" 1; pushnode 15 " (a3 = a1 & P756 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & P0 -> ((Ax9. x9 E a1 Kpair a2 -> a3 E x9) & P757 & P745 & P743 & P742 & P741 & P740 & P739 & P0) & P0" 1; pushnode 7 " P0 -> ( (a3 = a1 -> (Ax9.x9 E a1 Kpair a2 -> a3 E x9)) & P745 & P743 & P742 & P741 & P740 & P739 & P0) & P0" 1; pushnode 14 "( a3 = a1 & P755 & P751 & P748 & P746 & P744 & P743 & P742 & P741 & P740 & P739 & P0) & P0 -> ( a3 = a1 & P747 & P744 & P743 & P742 & P741 & P740 & P739 & P0) & P0" 0; pushnode 11 "( a3 E Sing(a1) & P751 & P748 & P746 & P744 & P743 & P742 & P741 & P740 & P739 & P0) & P0 -> ( a3 = a1 & P747 & P744 & P743 & P742 & P741 & P740 & P739 & P0) & P0" 1; pushnode 13 " P0 -> (Sing(a1) = Sing(a1) & P753 & P752 & P750 & P748 & P746 & P744 & P743 & P742 & P741 & P740 & P739 & P0) & P0" 0; pushnode 12 " P0 -> ( (Sing(a1) = Sing(a1) v Sing(a1) = a1 Couple a2) & P752 & P750 & P748 & P746 & P744 & P743 & P742 & P741 & P740 & P739 & P0) & P0" 1; pushnode 10 "P0 -> ( Sing(a1) E a1 Kpair a2 & P750 & P748 & P746 & P744 & P743 & P742 & P741 & P740 & P739 & P0) & P0" 1; pushnode 9 "(( Sing(a1) E a1 Kpair a2 -> a3 E Sing(a1)) & P748 & P746 & P744 & P743 & P742 & P741 & P740 & P739 & P0) & P0 -> (a3 = a1 & P747 & P744 & P743 & P742 & P741 & P740 & P739 & P0) & P0" 2; pushnode 8 " ((Ax9. x9 E a1 Kpair a2 -> a3 E x9) & P746 & P744 & P743 & P742 & P741 & P740 & P739 & P0) & P0 -> ( a3 = a1 & P747 & P744 & P743 & P742 & P741 & P740 & P739 & P0) & P0" 1; pushnode 6 " P0 -> (( (Ax9.x9 E a1 Kpair a2 -> a3 E x9) -> a3 = a1) & P744 & P743 & P742 & P741 & P740 & P739 & P0) & P0" 1; pushnode 5 "P0 -> (( ((Ax9.x9 E a1 Kpair a2 -> a3 E x9) -> a3 = a1) & (a3 = a1 -> (Ax9. x9 E a1 Kpair a2 -> a3 E x9))) & P743 & P742 & P741 & P740 & P739 & P0) & P0" 2; pushnode 4 "P0 -> ( ((Ax9.x9 E a1 Kpair a2 -> a3 E x9) == a3 = a1) & P742 & P741 & P740 & P739 & P0) & P0" 1; pushnode 3 " P0 -> ( (Ax4. (Ax8.x8 E a1 Kpair a2 -> x4 E x8) == x4 = a1) & P741 & P740 & P739 & P0) & P0" 1; pushnode 2 "P0 -> ({x4|(Ax8.x8 E a1 Kpair a2 -> x4 E x8)} = {x3|x3 = a1} & P740 & P739 & P0) & P0" 1; pushnode 1 " P0 -> (Si(a1 Kpair a2) = Sing(a1) & P739 & P0) & P0" 1; THEOREMS:=("PROJ1",(termtosequent(parseprop("P0 -> ( Si(a1 Kpair a2) = Sing(a1) & P739 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "PROJ1"; pushnode 136 " P0 -> ( a1 Couple a2 = a1 Couple a2 & P954 & P932 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P929 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 0; pushnode 120 " (a6 = a1 Couple a2 & P932 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a1 Couple a2 = a6 & P929 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 135 " (a8 = a1 & P949 & P944 & P942 & P941 & P934 & P933 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P939 & P938 & P937 & P936 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P929 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a8 = a1 & P951 & P950 & P944 & P942 & P941 & P934 & P933 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P939 & P938 & P937 & P936 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P929 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 0; pushnode 134 " (a8 = a1 & P949 & P944 & P942 & P941 & P934 & P933 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P939 & P938 & P937 & P936 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P929 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (( a8 = a1 v a8 = a1) & P950 & P944 & P942 & P941 & P934 & P933 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P939 & P938 & P937 & P936 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P929 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 130 " P0 -> ((a8 = a1 -> a8 = a1 v a8 = a1) & P944 & P942 & P941 & P934 & P933 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P939 & P938 & P937 & P936 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P929 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 133 "(a8 = a1 & P948 & P945 & P943 & P942 & P941 & P934 & P933 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P939 & P938 & P937 & P936 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P929 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a8 = a1 & P946 & P943 & P942 & P941 & P934 & P933 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P939 & P938 & P937 & P936 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P929 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 0; pushnode 132 "( a8 = a1 & P947 & P945 & P943 & P942 & P941 & P934 & P933 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P939 & P938 & P937 & P936 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P929 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a8 = a1 & P946 & P943 & P942 & P941 & P934 & P933 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P939 & P938 & P937 & P936 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P929 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 0; pushnode 131 "(( a8 = a1 v a8 = a1) & P945 & P943 & P942 & P941 & P934 & P933 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P939 & P938 & P937 & P936 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P929 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a8 = a1 & P946 & P943 & P942 & P941 & P934 & P933 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P939 & P938 & P937 & P936 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P929 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 2; pushnode 129 "P0 -> (( a8 = a1 v a8 = a1 -> a8 = a1) & P943 & P942 & P941 & P934 & P933 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P939 & P938 & P937 & P936 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P929 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 128 "P0 -> (((a8 = a1 v a8 = a1 -> a8 = a1) & ( a8 = a1 -> a8 = a1 v a8 = a1)) & P942 & P941 & P934 & P933 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P939 & P938 & P937 & P936 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P929 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 2; pushnode 127 "P0 -> (( a8 = a1 v a8 = a1 == a8 = a1) & P941 & P934 & P933 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P939 & P938 & P937 & P936 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P929 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 126 "( a2 = a1 & P934 & P933 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (( a8 = a1 v a8 = a2 == a8 = a1) & P939 & P938 & P937 & P936 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P929 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 125 "(a2 = a1 & P934 & P933 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ((Ax4. x4 = a1 v x4 = a2 == x4 = a1) & P938 & P937 & P936 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P929 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 124 "( a2 = a1 & P934 & P933 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( {x4|x4 = a1 v x4 = a2} = {x3|x3 = a1} & P937 & P936 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P929 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 123 "(a2 = a1 & P934 & P933 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a1 Couple a2 = Sing(a1) & P936 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P929 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 122 "( a6 = Sing(a1) & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & ( a2 = a1 & P934 & P933 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a1 Couple a2 = a6 & P929 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 121 " (a2 E Sing(a1) & P933 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & (a6 = Sing(a1) & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a1 Couple a2 = a6 & P929 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 119 " (a6 = Sing(a1) & P931 & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & (a2 E a6 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a1 Couple a2 = a6 & P929 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 118 " ((a6 = Sing(a1) v a6 = a1 Couple a2) & P930 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & (a2 E a6 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a1 Couple a2 = a6 & P929 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 2; pushnode 117 " (a6 E a1 Kpair a2 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & (a2 E a6 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a1 Couple a2 = a6 & P929 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 95 " (a5 = a1 Couple a2 & P899 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & (a6 E a1 Kpair a2 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & (a2 E a6 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a5 = a6 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 116 "( a7 = a1 & P927 & P924 & P919 & P917 & P916 & P902 & P901 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P914 & P913 & P912 & P911 & P907 & P905 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P904 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a7 = a1 & P925 & P919 & P917 & P916 & P902 & P901 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P914 & P913 & P912 & P911 & P907 & P905 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P904 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 0; pushnode 115 " (a7 = a1 & P926 & P924 & P919 & P917 & P916 & P902 & P901 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P914 & P913 & P912 & P911 & P907 & P905 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P904 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a7 = a1 & P925 & P919 & P917 & P916 & P902 & P901 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P914 & P913 & P912 & P911 & P907 & P905 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P904 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 0; pushnode 114 "( (a7 = a1 v a7 = a1) & P924 & P919 & P917 & P916 & P902 & P901 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P914 & P913 & P912 & P911 & P907 & P905 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P904 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a7 = a1 & P925 & P919 & P917 & P916 & P902 & P901 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P914 & P913 & P912 & P911 & P907 & P905 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P904 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 2; pushnode 111 "P0 -> (( a7 = a1 v a7 = a1 -> a7 = a1) & P919 & P917 & P916 & P902 & P901 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P914 & P913 & P912 & P911 & P907 & P905 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P904 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 113 "(a7 = a1 & P920 & P918 & P917 & P916 & P902 & P901 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P914 & P913 & P912 & P911 & P907 & P905 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P904 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a7 = a1 & P922 & P921 & P918 & P917 & P916 & P902 & P901 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P914 & P913 & P912 & P911 & P907 & P905 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P904 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 0; pushnode 112 "( a7 = a1 & P920 & P918 & P917 & P916 & P902 & P901 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P914 & P913 & P912 & P911 & P907 & P905 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P904 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( (a7 = a1 v a7 = a1) & P921 & P918 & P917 & P916 & P902 & P901 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P914 & P913 & P912 & P911 & P907 & P905 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P904 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 110 "P0 -> ((a7 = a1 -> a7 = a1 v a7 = a1) & P918 & P917 & P916 & P902 & P901 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P914 & P913 & P912 & P911 & P907 & P905 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P904 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 109 "P0 -> (((a7 = a1 -> a7 = a1 v a7 = a1) & ( a7 = a1 v a7 = a1 -> a7 = a1)) & P917 & P916 & P902 & P901 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P914 & P913 & P912 & P911 & P907 & P905 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P904 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 2; pushnode 108 "P0 -> ( ( a7 = a1 == a7 = a1 v a7 = a1) & P916 & P902 & P901 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P914 & P913 & P912 & P911 & P907 & P905 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P904 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 107 "(a2 = a1 & P902 & P901 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( ( a7 = a1 == a7 = a1 v a7 = a2) & P914 & P913 & P912 & P911 & P907 & P905 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P904 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 106 "(a2 = a1 & P902 & P901 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( (Ax3. x3 = a1 == x3 = a1 v x3 = a2) & P913 & P912 & P911 & P907 & P905 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P904 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 105 "(a2 = a1 & P902 & P901 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ({x3|x3 = a1} = {x4| x4 = a1 v x4 = a2} & P912 & P911 & P907 & P905 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P904 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 104 "(a2 = a1 & P902 & P901 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (Sing(a1) = a1 Couple a2 & P911 & P907 & P905 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P904 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 102 " (a6 = a1 Couple a2 & P907 & P905 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & (a2 = a1 & P902 & P901 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (Sing(a1) = a6 & P904 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 103 "P0 -> ( Sing(a1) = Sing(a1) & P909 & P906 & P905 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P904 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 0; pushnode 101 "( a6 = Sing(a1) & P906 & P905 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (Sing(a1) = a6 & P904 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 100 " ((a6 = Sing(a1) v a6 = a1 Couple a2) & P905 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & (a2 = a1 & P902 & P901 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (Sing(a1) = a6 & P904 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 2; pushnode 99 "(a6 E a1 Kpair a2 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & ( a2 = a1 & P902 & P901 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (Sing(a1) = a6 & P904 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 98 "( a5 = Sing(a1) & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & ( a2 = a1 & P902 & P901 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & (a6 E a1 Kpair a2 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a5 = a6 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 97 " (a2 E Sing(a1) & P901 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & (a6 E a1 Kpair a2 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & (a5 = Sing(a1) & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a5 = a6 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 94 "( a5 = Sing(a1) & P898 & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & ( a2 E a5 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & ( a6 E a1 Kpair a2 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a5 = a6 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 93 " ((a5 = Sing(a1) v a5 = a1 Couple a2) & P897 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & (a6 E a1 Kpair a2 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & ( a2 E a5 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & (a2 E a6 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a5 = a6 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 2; pushnode 92 " (a5 E a1 Kpair a2 & P895 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & (a6 E a1 Kpair a2 & P896 & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & ( a2 E a5 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & (a2 E a6 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a5 = a6 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 91 " ((a5 E a1 Kpair a2 & a6 E a1 Kpair a2) & P894 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & (a2 E a5 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & ( a2 E a6 & P893 & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a5 = a6 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 90 " ( (a2 E a6 & a5 E a1 Kpair a2 & a6 E a1 Kpair a2) & P892 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & ( a2 E a5 & P891 & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a5 = a6 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 89 "(( a2 E a5 & a2 E a6 & a5 E a1 Kpair a2 & a6 E a1 Kpair a2) & P889 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a5 = a6 & P890 & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 88 " P0 -> ((a2 E a5 & a2 E a6 & a5 E a1 Kpair a2 & a6 E a1 Kpair a2 -> a5 = a6) & P888 & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 87 "P0 -> ((Ax28.a2 E a5 & a2 E x28 & a5 E a1 Kpair a2 & x28 E a1 Kpair a2 -> a5 = x28) & P887 & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 79 " P0 -> ((Ax25.(Ax27.a2 E x25 & a2 E x27 & x25 E a1 Kpair a2 & x27 E a1 Kpair a2 -> x25 = x27)) & P876 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 86 "P0 -> (a1 Couple a2 = a1 Couple a2 & P886 & P884 & P880 & P877 & P875 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 0; pushnode 85 "P0 -> (( a1 Couple a2 = Sing(a1) v a1 Couple a2 = a1 Couple a2) & P884 & P880 & P877 & P875 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 82 "P0 -> ( a1 Couple a2 E a1 Kpair a2 & P880 & P877 & P875 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 84 "P0 -> (a2 = a2 & P883 & P881 & P879 & P877 & P875 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 0; pushnode 83 "P0 -> ( (a2 = a1 v a2 = a2) & P881 & P879 & P877 & P875 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 81 "P0 -> ( a2 E a1 Couple a2 & P879 & P877 & P875 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 80 "P0 -> ( (a2 E a1 Couple a2 & a1 Couple a2 E a1 Kpair a2) & P877 & P875 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 2; pushnode 78 "P0 -> ((Ex17.a2 E x17 & x17 E a1 Kpair a2) & P875 & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 77 "P0 -> ( ((Ex17.a2 E x17 & x17 E a1 Kpair a2) & (Ax25.(Ax27. a2 E x25 & a2 E x27 & x25 E a1 Kpair a2 & x27 E a1 Kpair a2 -> x25 = x27))) & P874 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 2; pushnode 76 "( a3 = a2 & P871 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (((Ex16. a3 E x16 & x16 E a1 Kpair a2) & (Ax22.(Ax24. a3 E x22 & a3 E x24 & x22 E a1 Kpair a2 & x24 E a1 Kpair a2 -> x22 = x24))) & P872 & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 7 " P0 -> ((a3 = a2 -> (Ex16.a3 E x16 & x16 E a1 Kpair a2) & (Ax22.(Ax24. a3 E x22 & a3 E x24 & x22 E a1 Kpair a2 & x24 E a1 Kpair a2 -> x22 = x24))) & P780 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 49 "(a3 = a2 & P835 & P833 & P832 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a4 = a1 Couple a2 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 0; pushnode 75 "( a3 = a1 & P834 & P833 & P832 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a4 = a1 Couple a2 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a3 = a1 & P870 & P866 & P864 & P862 & P860 & P859 & P858 & P841 & P838 & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 0; pushnode 73 "(a2 = a1 & P866 & P864 & P862 & P860 & P859 & P858 & P841 & P838 & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a4 = a1 Couple a2 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a3 = a1 & P834 & P833 & P832 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 74 " P0 -> (a2 = a2 & P868 & P865 & P864 & P862 & P860 & P859 & P858 & P841 & P838 & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 0; pushnode 72 "P0 -> (( a2 = a1 v a2 = a2) & P865 & P864 & P862 & P860 & P859 & P858 & P841 & P838 & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 71 "(( a2 = a1 v a2 = a2 -> a2 = a1) & P864 & P862 & P860 & P859 & P858 & P841 & P838 & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a4 = a1 Couple a2 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a3 = a1 & P834 & P833 & P832 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 2; pushnode 70 "(( ( a2 = a1 -> a2 = a1 v a2 = a2) & (a2 = a1 v a2 = a2 -> a2 = a1)) & P862 & P860 & P859 & P858 & P841 & P838 & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a4 = a1 Couple a2 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a3 = a1 & P834 & P833 & P832 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 69 "( ( a2 = a1 == a2 = a1 v a2 = a2) & P860 & P859 & P858 & P841 & P838 & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a4 = a1 Couple a2 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a3 = a1 & P834 & P833 & P832 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 68 "( (Ax3. x3 = a1 == x3 = a1 v x3 = a2) & P859 & P858 & P841 & P838 & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a4 = a1 Couple a2 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a3 = a1 & P834 & P833 & P832 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 67 " ({x3|x3 = a1} = {x4| x4 = a1 v x4 = a2} & P858 & P841 & P838 & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a4 = a1 Couple a2 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a3 = a1 & P834 & P833 & P832 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 53 " (Sing(a1) = a1 Couple a2 & P841 & P838 & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a4 = a1 Couple a2 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a3 = a1 & P834 & P833 & P832 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 66 " P0 -> ( a1 Couple a2 = a1 Couple a2 & P857 & P855 & P851 & P846 & P843 & P840 & P838 & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 0; pushnode 65 " P0 -> ( (a1 Couple a2 = Sing(a1) v a1 Couple a2 = a1 Couple a2) & P855 & P851 & P846 & P843 & P840 & P838 & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 62 "P0 -> ( a1 Couple a2 E a1 Kpair a2 & P851 & P846 & P843 & P840 & P838 & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 64 "P0 -> (Sing(a1) = Sing(a1) & P853 & P852 & P850 & P846 & P843 & P840 & P838 & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 0; pushnode 63 "P0 -> ( (Sing(a1) = Sing(a1) v Sing(a1) = a1 Couple a2) & P852 & P850 & P846 & P843 & P840 & P838 & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 61 "P0 -> ( Sing(a1) E a1 Kpair a2 & P850 & P846 & P843 & P840 & P838 & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 58 "P0 -> (( Sing(a1) E a1 Kpair a2 & a1 Couple a2 E a1 Kpair a2) & P846 & P843 & P840 & P838 & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 2; pushnode 60 "( a3 = a1 & P834 & P833 & P832 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a4 = a1 Couple a2 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a3 = a1 & P848 & P847 & P845 & P843 & P840 & P838 & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 0; pushnode 59 " (a4 = a1 Couple a2 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a3 = a1 & P834 & P833 & P832 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( (a3 = a1 v a3 = a2) & P847 & P845 & P843 & P840 & P838 & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 57 " (a4 = a1 Couple a2 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a3 = a1 & P834 & P833 & P832 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a3 E a1 Couple a2 & P845 & P843 & P840 & P838 & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 55 " (a4 = a1 Couple a2 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a3 = a1 & P834 & P833 & P832 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( ( a3 E a1 Couple a2 & Sing(a1) E a1 Kpair a2 & a1 Couple a2 E a1 Kpair a2) & P843 & P840 & P838 & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 2; pushnode 56 "( a3 = a1 & P834 & P833 & P832 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a4 = a1 Couple a2 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a3 = a1 & P844 & P842 & P840 & P838 & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 0; pushnode 54 " (a4 = a1 Couple a2 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a3 = a1 & P834 & P833 & P832 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 E Sing(a1) & P842 & P840 & P838 & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 52 "( a4 = a1 Couple a2 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a3 = a1 & P834 & P833 & P832 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ((a3 E Sing(a1) & a3 E a1 Couple a2 & Sing(a1) E a1 Kpair a2 & a1 Couple a2 E a1 Kpair a2) & P840 & P838 & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 2; pushnode 51 "((a3 E Sing(a1) & a3 E a1 Couple a2 & Sing(a1) E a1 Kpair a2 & a1 Couple a2 E a1 Kpair a2 -> Sing(a1) = a1 Couple a2) & P838 & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a4 = a1 Couple a2 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a3 = a1 & P834 & P833 & P832 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 2; pushnode 50 " ((Ax25. a3 E Sing(a1) & a3 E x25 & Sing(a1) E a1 Kpair a2 & x25 E a1 Kpair a2 -> Sing(a1) = x25) & P836 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a4 = a1 Couple a2 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a3 = a1 & P834 & P833 & P832 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 48 " ((Ax22.(Ax24. a3 E x22 & a3 E x24 & x22 E a1 Kpair a2 & x24 E a1 Kpair a2 -> x22 = x24)) & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a4 = a1 Couple a2 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a3 = a1 & P834 & P833 & P832 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 47 "( (a3 = a1 v a3 = a2) & P833 & P832 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ((Ax22.(Ax24. a3 E x22 & a3 E x24 & x22 E a1 Kpair a2 & x24 E a1 Kpair a2 -> x22 = x24)) & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a4 = a1 Couple a2 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 2; pushnode 46 "(a3 E a1 Couple a2 & P832 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ((Ax22.(Ax24. a3 E x22 & a3 E x24 & x22 E a1 Kpair a2 & x24 E a1 Kpair a2 -> x22 = x24)) & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a4 = a1 Couple a2 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 14 " (a4 = a1 Couple a2 & P790 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a3 E a4 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ((Ax22.(Ax24. a3 E x22 & a3 E x24 & x22 E a1 Kpair a2 & x24 E a1 Kpair a2 -> x22 = x24)) & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 44 "( a3 = a1 & P793 & P792 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a4 = Sing(a1) & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 = a1 & P830 & P826 & P822 & P820 & P818 & P817 & P816 & P799 & P796 & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 0; pushnode 42 "(a2 = a1 & P826 & P822 & P820 & P818 & P817 & P816 & P799 & P796 & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a4 = Sing(a1) & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a3 = a1 & P793 & P792 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 43 " P0 -> (a2 = a2 & P828 & P825 & P822 & P820 & P818 & P817 & P816 & P799 & P796 & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 0; pushnode 41 "P0 -> (( a2 = a1 v a2 = a2) & P825 & P822 & P820 & P818 & P817 & P816 & P799 & P796 & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 39 "(( a2 = a1 v a2 = a2 -> a2 = a1) & P822 & P820 & P818 & P817 & P816 & P799 & P796 & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a4 = Sing(a1) & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a3 = a1 & P793 & P792 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 2; pushnode 38 "(( ( a2 = a1 -> a2 = a1 v a2 = a2) & (a2 = a1 v a2 = a2 -> a2 = a1)) & P820 & P818 & P817 & P816 & P799 & P796 & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a4 = Sing(a1) & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a3 = a1 & P793 & P792 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 37 "( ( a2 = a1 == a2 = a1 v a2 = a2) & P818 & P817 & P816 & P799 & P796 & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a4 = Sing(a1) & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a3 = a1 & P793 & P792 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 36 "( (Ax3. x3 = a1 == x3 = a1 v x3 = a2) & P817 & P816 & P799 & P796 & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a4 = Sing(a1) & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a3 = a1 & P793 & P792 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 35 " ({x3|x3 = a1} = {x4| x4 = a1 v x4 = a2} & P816 & P799 & P796 & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a4 = Sing(a1) & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a3 = a1 & P793 & P792 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 21 " (Sing(a1) = a1 Couple a2 & P799 & P796 & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a4 = Sing(a1) & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a3 = a1 & P793 & P792 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 34 " P0 -> ( a1 Couple a2 = a1 Couple a2 & P815 & P813 & P809 & P804 & P801 & P798 & P796 & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 0; pushnode 33 " P0 -> ( (a1 Couple a2 = Sing(a1) v a1 Couple a2 = a1 Couple a2) & P813 & P809 & P804 & P801 & P798 & P796 & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 30 "P0 -> ( a1 Couple a2 E a1 Kpair a2 & P809 & P804 & P801 & P798 & P796 & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 32 "P0 -> (Sing(a1) = Sing(a1) & P811 & P810 & P808 & P804 & P801 & P798 & P796 & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 0; pushnode 31 "P0 -> ( (Sing(a1) = Sing(a1) v Sing(a1) = a1 Couple a2) & P810 & P808 & P804 & P801 & P798 & P796 & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 29 "P0 -> ( Sing(a1) E a1 Kpair a2 & P808 & P804 & P801 & P798 & P796 & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 26 "P0 -> (( Sing(a1) E a1 Kpair a2 & a1 Couple a2 E a1 Kpair a2) & P804 & P801 & P798 & P796 & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 2; pushnode 28 "( a3 = a1 & P793 & P792 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a4 = Sing(a1) & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 = a1 & P806 & P805 & P803 & P801 & P798 & P796 & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 0; pushnode 27 "( a4 = Sing(a1) & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a3 = a1 & P793 & P792 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( (a3 = a1 v a3 = a2) & P805 & P803 & P801 & P798 & P796 & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 25 " (a4 = Sing(a1) & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a3 = a1 & P793 & P792 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a3 E a1 Couple a2 & P803 & P801 & P798 & P796 & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 23 " (a4 = Sing(a1) & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a3 = a1 & P793 & P792 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( ( a3 E a1 Couple a2 & Sing(a1) E a1 Kpair a2 & a1 Couple a2 E a1 Kpair a2) & P801 & P798 & P796 & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 2; pushnode 24 "( a3 = a1 & P793 & P792 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a4 = Sing(a1) & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 = a1 & P802 & P800 & P798 & P796 & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 0; pushnode 22 " (a4 = Sing(a1) & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a3 = a1 & P793 & P792 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 E Sing(a1) & P800 & P798 & P796 & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 20 " (a4 = Sing(a1) & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a3 = a1 & P793 & P792 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ((a3 E Sing(a1) & a3 E a1 Couple a2 & Sing(a1) E a1 Kpair a2 & a1 Couple a2 E a1 Kpair a2) & P798 & P796 & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 2; pushnode 19 "((a3 E Sing(a1) & a3 E a1 Couple a2 & Sing(a1) E a1 Kpair a2 & a1 Couple a2 E a1 Kpair a2 -> Sing(a1) = a1 Couple a2) & P796 & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a4 = Sing(a1) & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a3 = a1 & P793 & P792 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 2; pushnode 18 " ((Ax25. a3 E Sing(a1) & a3 E x25 & Sing(a1) E a1 Kpair a2 & x25 E a1 Kpair a2 -> Sing(a1) = x25) & P794 & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a4 = Sing(a1) & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & (a3 = a1 & P793 & P792 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 17 "((Ax22.(Ax24. a3 E x22 & a3 E x24 & x22 E a1 Kpair a2 & x24 E a1 Kpair a2 -> x22 = x24)) & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a4 = Sing(a1) & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a3 = a1 & P793 & P792 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 16 "( a3 E Sing(a1) & P792 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ((Ax22.(Ax24. a3 E x22 & a3 E x24 & x22 E a1 Kpair a2 & x24 E a1 Kpair a2 -> x22 = x24)) & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a4 = Sing(a1) & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 13 "( a4 = Sing(a1) & P789 & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a3 E a4 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ((Ax22.(Ax24. a3 E x22 & a3 E x24 & x22 E a1 Kpair a2 & x24 E a1 Kpair a2 -> x22 = x24)) & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 12 "( ( a4 = Sing(a1) v a4 = a1 Couple a2) & P788 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ((Ax22.(Ax24. a3 E x22 & a3 E x24 & x22 E a1 Kpair a2 & x24 E a1 Kpair a2 -> x22 = x24)) & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a3 E a4 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 2; pushnode 11 "(a4 E a1 Kpair a2 & P787 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ((Ax22.(Ax24. a3 E x22 & a3 E x24 & x22 E a1 Kpair a2 & x24 E a1 Kpair a2 -> x22 = x24)) & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ( a3 E a4 & P786 & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 10 " (( a3 E a4 & a4 E a1 Kpair a2) & P785 & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ((Ax22.(Ax24.a3 E x22 & a3 E x24 & x22 E a1 Kpair a2 & x24 E a1 Kpair a2 -> x22 = x24)) & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 9 "((Ex16. a3 E x16 & x16 E a1 Kpair a2) & P783 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & ((Ax22.(Ax24. a3 E x22 & a3 E x24 & x22 E a1 Kpair a2 & x24 E a1 Kpair a2 -> x22 = x24)) & P784 & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> (a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 8 " (((Ex16. a3 E x16 & x16 E a1 Kpair a2) & (Ax22.(Ax24. a3 E x22 & a3 E x24 & x22 E a1 Kpair a2 & x24 E a1 Kpair a2 -> x22 = x24))) & P781 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0 -> ( a3 = a2 & P782 & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 6 " P0 -> (( (Ex16.a3 E x16 & x16 E a1 Kpair a2) & (Ax22.(Ax24.a3 E x22 & a3 E x24 & x22 E a1 Kpair a2 & x24 E a1 Kpair a2 -> x22 = x24)) -> a3 = a2) & P779 & P778 & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 5 "P0 -> ((( (Ex16.a3 E x16 & x16 E a1 Kpair a2) & (Ax22.(Ax24. a3 E x22 & a3 E x24 & x22 E a1 Kpair a2 & x24 E a1 Kpair a2 -> x22 = x24)) -> a3 = a2) & ( a3 = a2 -> (Ex16.a3 E x16 & x16 E a1 Kpair a2) & (Ax22.(Ax24. a3 E x22 & a3 E x24 & x22 E a1 Kpair a2 & x24 E a1 Kpair a2 -> x22 = x24)))) & P778 & P777 & P776 & P775 & P774 & P0) & P0" 2; pushnode 4 " P0 -> (( (Ex16.a3 E x16 & x16 E a1 Kpair a2) & (Ax22.(Ax24.a3 E x22 & a3 E x24 & x22 E a1 Kpair a2 & x24 E a1 Kpair a2 -> x22 = x24)) == a3 = a2) & P777 & P776 & P775 & P774 & P0) & P0" 1; pushnode 3 " P0 -> ((Ax5. (Ex15.x5 E x15 & x15 E a1 Kpair a2) & (Ax17.(Ax21.x5 E x17 & x5 E x21 & x17 E a1 Kpair a2 & x21 E a1 Kpair a2 -> x17 = x21)) == x5 = a2) & P776 & P775 & P774 & P0) & P0" 1; pushnode 2 "P0 -> ({x5|(Ex15. x5 E x15 & x15 E a1 Kpair a2) & (Ax17.(Ax21. x5 E x17 & x5 E x21 & x17 E a1 Kpair a2 & x21 E a1 Kpair a2 -> x17 = x21))} = {x3|x3 = a2} & P775 & P774 & P0) & P0" 1; pushnode 1 " P0 -> (Projtwo(a1 Kpair a2) = Sing(a2) & P774 & P0) & P0" 1; THEOREMS:=("PROJ2",(termtosequent(parseprop("P0 -> (Projtwo(a1 Kpair a2) = Sing(a2) & P774 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "PROJ2"; pushnode 37 "P0 -> ( a3 Kpair a4 = a3 Kpair a4 & P996 & P992 & P989 & P958 & P956 & P955 & P994 & P991 & P989 & P958 & P956 & P955 & P990 & P958 & P956 & P955 & P0) & P0" 0; pushnode 36 " (a2 = a4 & P992 & P989 & P958 & P956 & P955 & P0) & P0 -> ( a3 Kpair a2 = a3 Kpair a4 & P994 & P991 & P989 & P958 & P956 & P955 & P990 & P958 & P956 & P955 & P0) & P0" 1; pushnode 35 "( a1 = a3 & P991 & P989 & P958 & P956 & P955 & P0) & ( a2 = a4 & P992 & P989 & P958 & P956 & P955 & P0) & P0 -> (a1 Kpair a2 = a3 Kpair a4 & P990 & P958 & P956 & P955 & P0) & P0" 1; pushnode 34 "( (a1 = a3 & a2 = a4) & P989 & P958 & P956 & P955 & P0) & P0 -> ( a1 Kpair a2 = a3 Kpair a4 & P990 & P958 & P956 & P955 & P0) & P0" 1; pushnode 4 "P0 -> (( a1 = a3 & a2 = a4 -> a1 Kpair a2 = a3 Kpair a4) & P958 & P956 & P955 & P0) & P0" 1; pushnode 33 "(a2 = a4 & P988 & P986 & P984 & P982 & P981 & P980 & P979 & P977 & P976 & P959 & P957 & P956 & P955 & P978 & P0) & ( a1 Kpair a2 = a3 Kpair a4 & P959 & P957 & P956 & P955 & P0) & (Projtwo( a3 Kpair a4) = Sing(a4) & P978 & P0) & P0 -> (a2 = a4 & P962 & P960 & P957 & P956 & P955 & P0) & P0" 0; pushnode 32 " ( a1 Kpair a2 = a3 Kpair a4 & P959 & P957 & P956 & P955 & P0) & (Projtwo( a3 Kpair a4) = Sing(a4) & P978 & P0) & P0 -> (a2 = a2 & P987 & P986 & P984 & P982 & P981 & P980 & P979 & P977 & P976 & P959 & P957 & P956 & P955 & P978 & P0) & P0" 0; pushnode 31 "( (a2 = a2 -> a2 = a4) & P986 & P984 & P982 & P981 & P980 & P979 & P977 & P976 & P959 & P957 & P956 & P955 & P978 & P0) & ( a1 Kpair a2 = a3 Kpair a4 & P959 & P957 & P956 & P955 & P0) & (Projtwo( a3 Kpair a4) = Sing(a4) & P978 & P0) & P0 -> (a2 = a4 & P962 & P960 & P957 & P956 & P955 & P0) & P0" 2; pushnode 30 " ((( a2 = a4 -> a2 = a2) & ( a2 = a2 -> a2 = a4)) & P984 & P982 & P981 & P980 & P979 & P977 & P976 & P959 & P957 & P956 & P955 & P978 & P0) & ( a1 Kpair a2 = a3 Kpair a4 & P959 & P957 & P956 & P955 & P0) & ( Projtwo(a3 Kpair a4) = Sing(a4) & P978 & P0) & P0 -> ( a2 = a4 & P962 & P960 & P957 & P956 & P955 & P0) & P0" 1; pushnode 29 "( (a2 = a4 == a2 = a2) & P982 & P981 & P980 & P979 & P977 & P976 & P959 & P957 & P956 & P955 & P978 & P0) & ( a1 Kpair a2 = a3 Kpair a4 & P959 & P957 & P956 & P955 & P0) & (Projtwo( a3 Kpair a4) = Sing(a4) & P978 & P0) & P0 -> (a2 = a4 & P962 & P960 & P957 & P956 & P955 & P0) & P0" 1; pushnode 28 "((Ax3. x3 = a4 == x3 = a2) & P981 & P980 & P979 & P977 & P976 & P959 & P957 & P956 & P955 & P978 & P0) & (a1 Kpair a2 = a3 Kpair a4 & P959 & P957 & P956 & P955 & P0) & ( Projtwo(a3 Kpair a4) = Sing(a4) & P978 & P0) & P0 -> ( a2 = a4 & P962 & P960 & P957 & P956 & P955 & P0) & P0" 1; pushnode 27 " ({x3|x3 = a4} = {x3|x3 = a2} & P980 & P979 & P977 & P976 & P959 & P957 & P956 & P955 & P978 & P0) & ( a1 Kpair a2 = a3 Kpair a4 & P959 & P957 & P956 & P955 & P0) & ( Projtwo(a3 Kpair a4) = Sing(a4) & P978 & P0) & P0 -> ( a2 = a4 & P962 & P960 & P957 & P956 & P955 & P0) & P0" 1; pushnode 26 "(Sing(a4) = Sing(a2) & P979 & P977 & P976 & P959 & P957 & P956 & P955 & P978 & P0) & ( a1 Kpair a2 = a3 Kpair a4 & P959 & P957 & P956 & P955 & P0) & (Projtwo( a3 Kpair a4) = Sing(a4) & P978 & P0) & P0 -> (a2 = a4 & P962 & P960 & P957 & P956 & P955 & P0) & P0" 1; pushnode 25 "(Projtwo( a3 Kpair a4) = Sing(a4) & P978 & P0) & ( Projtwo(a3 Kpair a4) = Sing(a2) & P977 & P976 & P959 & P957 & P956 & P955 & P0) & ( a1 Kpair a2 = a3 Kpair a4 & P959 & P957 & P956 & P955 & P0) & P0 -> (a2 = a4 & P962 & P960 & P957 & P956 & P955 & P0) & P0" 1; pushreference 24 " P0 -> (Projtwo(a3 Kpair a4) = Sing(a4) & P978 & P0) & P0" "PROJ2"; pushnode 23 "(a1 Kpair a2 = a3 Kpair a4 & P959 & P957 & P956 & P955 & P0) & (Projtwo( a3 Kpair a4) = Sing(a2) & P977 & P976 & P959 & P957 & P956 & P955 & P0) & P0 -> (a2 = a4 & P962 & P960 & P957 & P956 & P955 & P0) & P0" 2; pushnode 22 " ( a1 Kpair a2 = a3 Kpair a4 & P959 & P957 & P956 & P955 & P0) & ( Projtwo(a1 Kpair a2) = Sing(a2) & P976 & P0) & P0 -> (a2 = a4 & P962 & P960 & P957 & P956 & P955 & P0) & P0" 1; pushreference 21 "P0 -> ( Projtwo(a1 Kpair a2) = Sing(a2) & P976 & P0) & P0" "PROJ2"; pushnode 7 "( a1 Kpair a2 = a3 Kpair a4 & P959 & P957 & P956 & P955 & P0) & P0 -> (a2 = a4 & P962 & P960 & P957 & P956 & P955 & P0) & P0" 2; pushnode 20 "(a1 = a3 & P975 & P973 & P971 & P969 & P968 & P967 & P966 & P964 & P963 & P959 & P957 & P956 & P955 & P965 & P0) & (a1 Kpair a2 = a3 Kpair a4 & P959 & P957 & P956 & P955 & P0) & (Si( a3 Kpair a4) = Sing(a3) & P965 & P0) & P0 -> (a1 = a3 & P961 & P960 & P957 & P956 & P955 & P0) & P0" 0; pushnode 19 " ( a1 Kpair a2 = a3 Kpair a4 & P959 & P957 & P956 & P955 & P0) & (Si( a3 Kpair a4) = Sing(a3) & P965 & P0) & P0 -> (a1 = a1 & P974 & P973 & P971 & P969 & P968 & P967 & P966 & P964 & P963 & P959 & P957 & P956 & P955 & P965 & P0) & P0" 0; pushnode 18 "( (a1 = a1 -> a1 = a3) & P973 & P971 & P969 & P968 & P967 & P966 & P964 & P963 & P959 & P957 & P956 & P955 & P965 & P0) & ( a1 Kpair a2 = a3 Kpair a4 & P959 & P957 & P956 & P955 & P0) & (Si( a3 Kpair a4) = Sing(a3) & P965 & P0) & P0 -> (a1 = a3 & P961 & P960 & P957 & P956 & P955 & P0) & P0" 2; pushnode 17 " ((( a1 = a3 -> a1 = a1) & ( a1 = a1 -> a1 = a3)) & P971 & P969 & P968 & P967 & P966 & P964 & P963 & P959 & P957 & P956 & P955 & P965 & P0) & ( a1 Kpair a2 = a3 Kpair a4 & P959 & P957 & P956 & P955 & P0) & ( Si(a3 Kpair a4) = Sing(a3) & P965 & P0) & P0 -> ( a1 = a3 & P961 & P960 & P957 & P956 & P955 & P0) & P0" 1; pushnode 16 "( (a1 = a3 == a1 = a1) & P969 & P968 & P967 & P966 & P964 & P963 & P959 & P957 & P956 & P955 & P965 & P0) & ( a1 Kpair a2 = a3 Kpair a4 & P959 & P957 & P956 & P955 & P0) & (Si( a3 Kpair a4) = Sing(a3) & P965 & P0) & P0 -> (a1 = a3 & P961 & P960 & P957 & P956 & P955 & P0) & P0" 1; pushnode 15 "((Ax3. x3 = a3 == x3 = a1) & P968 & P967 & P966 & P964 & P963 & P959 & P957 & P956 & P955 & P965 & P0) & (a1 Kpair a2 = a3 Kpair a4 & P959 & P957 & P956 & P955 & P0) & ( Si(a3 Kpair a4) = Sing(a3) & P965 & P0) & P0 -> ( a1 = a3 & P961 & P960 & P957 & P956 & P955 & P0) & P0" 1; pushnode 14 " ({x3|x3 = a3} = {x3|x3 = a1} & P967 & P966 & P964 & P963 & P959 & P957 & P956 & P955 & P965 & P0) & ( a1 Kpair a2 = a3 Kpair a4 & P959 & P957 & P956 & P955 & P0) & ( Si(a3 Kpair a4) = Sing(a3) & P965 & P0) & P0 -> ( a1 = a3 & P961 & P960 & P957 & P956 & P955 & P0) & P0" 1; pushnode 13 "(Sing(a3) = Sing(a1) & P966 & P964 & P963 & P959 & P957 & P956 & P955 & P965 & P0) & ( a1 Kpair a2 = a3 Kpair a4 & P959 & P957 & P956 & P955 & P0) & (Si( a3 Kpair a4) = Sing(a3) & P965 & P0) & P0 -> (a1 = a3 & P961 & P960 & P957 & P956 & P955 & P0) & P0" 1; pushnode 12 "(Si( a3 Kpair a4) = Sing(a3) & P965 & P0) & ( Si(a3 Kpair a4) = Sing(a1) & P964 & P963 & P959 & P957 & P956 & P955 & P0) & ( a1 Kpair a2 = a3 Kpair a4 & P959 & P957 & P956 & P955 & P0) & P0 -> (a1 = a3 & P961 & P960 & P957 & P956 & P955 & P0) & P0" 1; pushreference 11 " P0 -> (Si(a3 Kpair a4) = Sing(a3) & P965 & P0) & P0" "PROJ1"; pushnode 10 "(a1 Kpair a2 = a3 Kpair a4 & P959 & P957 & P956 & P955 & P0) & ( Si(a3 Kpair a4) = Sing(a1) & P964 & P963 & P959 & P957 & P956 & P955 & P0) & P0 -> (a1 = a3 & P961 & P960 & P957 & P956 & P955 & P0) & P0" 2; pushnode 9 " ( a1 Kpair a2 = a3 Kpair a4 & P959 & P957 & P956 & P955 & P0) & ( Si(a1 Kpair a2) = Sing(a1) & P963 & P0) & P0 -> (a1 = a3 & P961 & P960 & P957 & P956 & P955 & P0) & P0" 1; pushreference 8 "P0 -> ( Si(a1 Kpair a2) = Sing(a1) & P963 & P0) & P0" "PROJ1"; pushnode 6 "( a1 Kpair a2 = a3 Kpair a4 & P959 & P957 & P956 & P955 & P0) & P0 -> (a1 = a3 & P961 & P960 & P957 & P956 & P955 & P0) & P0" 2; pushnode 5 " (a1 Kpair a2 = a3 Kpair a4 & P959 & P957 & P956 & P955 & P0) & P0 -> ( (a1 = a3 & a2 = a4) & P960 & P957 & P956 & P955 & P0) & P0" 2; pushnode 3 " P0 -> (( a1 Kpair a2 = a3 Kpair a4 -> a1 = a3 & a2 = a4) & P957 & P956 & P955 & P0) & P0" 1; pushnode 2 "P0 -> ((( a1 Kpair a2 = a3 Kpair a4 -> a1 = a3 & a2 = a4) & ( a1 = a3 & a2 = a4 -> a1 Kpair a2 = a3 Kpair a4)) & P956 & P955 & P0) & P0" 2; pushnode 1 " P0 -> (( a1 Kpair a2 = a3 Kpair a4 == a1 = a3 & a2 = a4) & P955 & P0) & P0" 1; THEOREMS:=("KPAIR",(termtosequent(parseprop("P0 -> (( a1 Kpair a2 = a3 Kpair a4 == a1 = a3 & a2 = a4) & P955 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "KPAIR"; pushnode 94 " (a5 = a4 & P1189 & P1184 & P1177 & P1175 & P1174 & P1173 & P1172 & P1171 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0 -> ( a5 = a4 & P1186 & P1185 & P1177 & P1175 & P1174 & P1173 & P1172 & P1171 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0" 0; pushnode 93 "(a5 = a3 & P1188 & P1184 & P1177 & P1175 & P1174 & P1173 & P1172 & P1171 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0 -> (a5 = a3 & P1187 & P1185 & P1177 & P1175 & P1174 & P1173 & P1172 & P1171 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0" 0; pushnode 92 "(( a5 = a3 v a5 = a4) & P1184 & P1177 & P1175 & P1174 & P1173 & P1172 & P1171 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0 -> (a5 = a4 & P1186 & P1185 & P1177 & P1175 & P1174 & P1173 & P1172 & P1171 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & (a5 = a3 & P1187 & P1185 & P1177 & P1175 & P1174 & P1173 & P1172 & P1171 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0" 2; pushnode 91 "( (a5 = a3 v a5 = a4) & P1184 & P1177 & P1175 & P1174 & P1173 & P1172 & P1171 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0 -> (( a5 = a4 v a5 = a3) & P1185 & P1177 & P1175 & P1174 & P1173 & P1172 & P1171 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0" 1; pushnode 86 "P0 -> (( a5 = a3 v a5 = a4 -> a5 = a4 v a5 = a3) & P1177 & P1175 & P1174 & P1173 & P1172 & P1171 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0" 1; pushnode 90 "( a5 = a3 & P1183 & P1178 & P1176 & P1175 & P1174 & P1173 & P1172 & P1171 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0 -> ( a5 = a3 & P1180 & P1179 & P1176 & P1175 & P1174 & P1173 & P1172 & P1171 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0" 0; pushnode 89 "(a5 = a4 & P1182 & P1178 & P1176 & P1175 & P1174 & P1173 & P1172 & P1171 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0 -> (a5 = a4 & P1181 & P1179 & P1176 & P1175 & P1174 & P1173 & P1172 & P1171 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0" 0; pushnode 88 "(( a5 = a4 v a5 = a3) & P1178 & P1176 & P1175 & P1174 & P1173 & P1172 & P1171 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0 -> (a5 = a3 & P1180 & P1179 & P1176 & P1175 & P1174 & P1173 & P1172 & P1171 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & (a5 = a4 & P1181 & P1179 & P1176 & P1175 & P1174 & P1173 & P1172 & P1171 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0" 2; pushnode 87 "( (a5 = a4 v a5 = a3) & P1178 & P1176 & P1175 & P1174 & P1173 & P1172 & P1171 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0 -> (( a5 = a3 v a5 = a4) & P1179 & P1176 & P1175 & P1174 & P1173 & P1172 & P1171 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0" 1; pushnode 85 "P0 -> (( a5 = a4 v a5 = a3 -> a5 = a3 v a5 = a4) & P1176 & P1175 & P1174 & P1173 & P1172 & P1171 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0" 1; pushnode 84 " P0 -> (( (a5 = a4 v a5 = a3 -> a5 = a3 v a5 = a4) & (a5 = a3 v a5 = a4 -> a5 = a4 v a5 = a3)) & P1175 & P1174 & P1173 & P1172 & P1171 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0" 2; pushnode 83 "P0 -> (( a5 = a4 v a5 = a3 == a5 = a3 v a5 = a4) & P1174 & P1173 & P1172 & P1171 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0" 1; pushnode 82 " P0 -> ( (Ax4.x4 = a4 v x4 = a3 == x4 = a3 v x4 = a4) & P1173 & P1172 & P1171 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0" 1; pushnode 81 "P0 -> ( {x4|x4 = a4 v x4 = a3} = {x4|x4 = a3 v x4 = a4} & P1172 & P1171 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0" 1; pushnode 80 " P0 -> ( a4 Couple a3 = a3 Couple a4 & P1171 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0" 1; pushnode 79 " (a2 = a3 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P0) & P0 -> ( a4 Couple a2 = a3 Couple a4 & P1169 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0" 1; pushnode 78 "( a1 = a4 & P1166 & P1159 & P1156 & P1060 & P1058 & P1057 & P0) & ( a2 = a3 & P1167 & P1159 & P1156 & P1060 & P1058 & P1057 & P0) & P0 -> (a1 Couple a2 = a3 Couple a4 & P1157 & P1060 & P1058 & P1057 & P0) & P0" 1; pushnode 74 "( (a1 = a4 & a2 = a3) & P1159 & P1156 & P1060 & P1058 & P1057 & P0) & P0 -> ( a1 Couple a2 = a3 Couple a4 & P1157 & P1060 & P1058 & P1057 & P0) & P0" 1; pushnode 77 "P0 -> ( a3 Couple a4 = a3 Couple a4 & P1165 & P1161 & P1158 & P1156 & P1060 & P1058 & P1057 & P1163 & P1160 & P1158 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0" 0; pushnode 76 " (a2 = a4 & P1161 & P1158 & P1156 & P1060 & P1058 & P1057 & P0) & P0 -> ( a3 Couple a2 = a3 Couple a4 & P1163 & P1160 & P1158 & P1156 & P1060 & P1058 & P1057 & P1157 & P1060 & P1058 & P1057 & P0) & P0" 1; pushnode 75 "( a1 = a3 & P1160 & P1158 & P1156 & P1060 & P1058 & P1057 & P0) & ( a2 = a4 & P1161 & P1158 & P1156 & P1060 & P1058 & P1057 & P0) & P0 -> (a1 Couple a2 = a3 Couple a4 & P1157 & P1060 & P1058 & P1057 & P0) & P0" 1; pushnode 73 "( (a1 = a3 & a2 = a4) & P1158 & P1156 & P1060 & P1058 & P1057 & P0) & P0 -> ( a1 Couple a2 = a3 Couple a4 & P1157 & P1060 & P1058 & P1057 & P0) & P0" 1; pushnode 72 "(( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1156 & P1060 & P1058 & P1057 & P0) & P0 -> ( a1 Couple a2 = a3 Couple a4 & P1157 & P1060 & P1058 & P1057 & P0) & P0" 2; pushnode 4 "P0 -> ( ( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3 -> a1 Couple a2 = a3 Couple a4) & P1060 & P1058 & P1057 & P0) & P0" 1; pushnode 71 "P0 -> ( a2 = a2 & P1155 & P1153 & P1151 & P1141 & P1137 & P1135 & P1133 & P1131 & P1117 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P1062 & P1059 & P1058 & P1057 & P0) & P0" 0; pushnode 70 " (a1 = a4 & P1075 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> ( a1 = a4 & P1154 & P1153 & P1151 & P1141 & P1137 & P1135 & P1133 & P1131 & P1117 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P1062 & P1059 & P1058 & P1057 & P0) & P0" 0; pushnode 69 " (a1 = a4 & P1075 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a4 & a2 = a2) & P1153 & P1151 & P1141 & P1137 & P1135 & P1133 & P1131 & P1117 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P1062 & P1059 & P1058 & P1057 & P0) & P0" 2; pushnode 68 " (a1 = a4 & P1075 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a2 & a2 = a4 v a1 = a4 & a2 = a2) & P1151 & P1141 & P1137 & P1135 & P1133 & P1131 & P1117 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 62 " (a3 = a2 & P1141 & P1137 & P1135 & P1133 & P1131 & P1117 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a1 = a4 & P1075 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 67 "(a2 = a4 & P1126 & P1122 & P1119 & P1118 & P1116 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> ( a2 = a4 & P1149 & P1146 & P1145 & P1075 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P1143 & P1140 & P1137 & P1135 & P1133 & P1131 & P1117 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P1062 & P1059 & P1058 & P1057 & P0) & P0" 0; pushnode 66 " P0 -> (a4 = a4 & P1148 & P1146 & P1145 & P1075 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P1143 & P1140 & P1137 & P1135 & P1133 & P1131 & P1117 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P1062 & P1059 & P1058 & P1057 & P0) & P0" 0; pushnode 65 " (a2 = a4 & P1126 & P1122 & P1119 & P1118 & P1116 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> ( (a4 = a4 & a2 = a4) & P1146 & P1145 & P1075 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P1143 & P1140 & P1137 & P1135 & P1133 & P1131 & P1117 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P1062 & P1059 & P1058 & P1057 & P0) & P0" 2; pushnode 64 "(a2 = a4 & P1126 & P1122 & P1119 & P1118 & P1116 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a4 = a4 & a2 = a4 v a4 = a4 & a2 = a4) & P1145 & P1075 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P1143 & P1140 & P1137 & P1135 & P1133 & P1131 & P1117 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 63 " (a1 = a4 & P1075 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a2 = a4 & P1126 & P1122 & P1119 & P1118 & P1116 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a1 & a2 = a4 v a1 = a4 & a2 = a1) & P1143 & P1140 & P1137 & P1135 & P1133 & P1131 & P1117 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 61 " (a3 = a1 & P1140 & P1137 & P1135 & P1133 & P1131 & P1117 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a1 = a4 & P1075 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a2 = a4 & P1126 & P1122 & P1119 & P1118 & P1116 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 59 "( (a3 = a1 v a3 = a2) & P1137 & P1135 & P1133 & P1131 & P1117 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a1 = a4 & P1075 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a2 = a4 & P1126 & P1122 & P1119 & P1118 & P1116 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 2; pushnode 60 "P0 -> (a3 = a3 & P1138 & P1136 & P1135 & P1133 & P1131 & P1117 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0" 0; pushnode 58 "P0 -> (( a3 = a3 v a3 = a4) & P1136 & P1135 & P1133 & P1131 & P1117 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 57 " (( a3 = a3 v a3 = a4 -> a3 = a1 v a3 = a2) & P1135 & P1133 & P1131 & P1117 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a1 = a4 & P1075 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a2 = a4 & P1126 & P1122 & P1119 & P1118 & P1116 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 2; pushnode 56 "( (( a3 = a1 v a3 = a2 -> a3 = a3 v a3 = a4) & ( a3 = a3 v a3 = a4 -> a3 = a1 v a3 = a2)) & P1133 & P1131 & P1117 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ( a1 = a4 & P1075 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a2 = a4 & P1126 & P1122 & P1119 & P1118 & P1116 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 55 "(( a3 = a1 v a3 = a2 == a3 = a3 v a3 = a4) & P1131 & P1117 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ( a1 = a4 & P1075 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a2 = a4 & P1126 & P1122 & P1119 & P1118 & P1116 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 51 " ((Ax4. x4 = a1 v x4 = a2 == x4 = a3 v x4 = a4) & P1117 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ( a1 = a4 & P1075 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a2 = a4 & P1126 & P1122 & P1119 & P1118 & P1116 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> ( (a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 54 "(a2 = a3 & P1125 & P1122 & P1119 & P1118 & P1116 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> ( a2 = a3 & P1130 & P1128 & P1062 & P1059 & P1058 & P1057 & P0) & P0" 0; pushnode 53 " (a1 = a4 & P1075 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> ( a1 = a4 & P1129 & P1128 & P1062 & P1059 & P1058 & P1057 & P0) & P0" 0; pushnode 52 "(a2 = a3 & P1125 & P1122 & P1119 & P1118 & P1116 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a1 = a4 & P1075 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a4 & a2 = a3) & P1128 & P1062 & P1059 & P1058 & P1057 & P0) & P0" 2; pushnode 50 " ( a2 = a3 & P1125 & P1122 & P1119 & P1118 & P1116 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ( a1 = a4 & P1075 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 48 "( (a2 = a3 v a2 = a4) & P1122 & P1119 & P1118 & P1116 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ((Ax4. x4 = a1 v x4 = a2 == x4 = a3 v x4 = a4) & P1117 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ( a1 = a4 & P1075 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 2; pushnode 49 "P0 -> (a2 = a2 & P1124 & P1121 & P1119 & P1118 & P1116 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0" 0; pushnode 47 "P0 -> ( (a2 = a1 v a2 = a2) & P1121 & P1119 & P1118 & P1116 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 46 "(( a2 = a1 v a2 = a2 -> a2 = a3 v a2 = a4) & P1119 & P1118 & P1116 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ((Ax4. x4 = a1 v x4 = a2 == x4 = a3 v x4 = a4) & P1117 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ( a1 = a4 & P1075 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 2; pushnode 45 " ( (( a2 = a1 v a2 = a2 -> a2 = a3 v a2 = a4) & ( a2 = a3 v a2 = a4 -> a2 = a1 v a2 = a2)) & P1118 & P1116 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ((Ax4. x4 = a1 v x4 = a2 == x4 = a3 v x4 = a4) & P1117 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ( a1 = a4 & P1075 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 44 "(( a2 = a1 v a2 = a2 == a2 = a3 v a2 = a4) & P1116 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ((Ax4. x4 = a1 v x4 = a2 == x4 = a3 v x4 = a4) & P1117 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ( a1 = a4 & P1075 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 15 " ((Ax4. x4 = a1 v x4 = a2 == x4 = a3 v x4 = a4) & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a1 = a4 & P1075 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 43 "(a2 = a4 & P1086 & P1082 & P1079 & P1078 & P1076 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> ( a2 = a4 & P1115 & P1112 & P1062 & P1059 & P1058 & P1057 & P0) & P0" 0; pushnode 42 " (a1 = a3 & P1074 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> ( a1 = a3 & P1114 & P1112 & P1062 & P1059 & P1058 & P1057 & P0) & P0" 0; pushnode 41 "(a2 = a4 & P1086 & P1082 & P1079 & P1078 & P1076 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a1 = a3 & P1074 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4) & P1112 & P1062 & P1059 & P1058 & P1057 & P0) & P0" 2; pushnode 23 " ( a2 = a4 & P1086 & P1082 & P1079 & P1078 & P1076 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ( a1 = a3 & P1074 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 40 "P0 -> (a2 = a2 & P1111 & P1108 & P1107 & P1097 & P1093 & P1091 & P1089 & P1087 & P1077 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P1062 & P1059 & P1058 & P1057 & P0) & P0" 0; pushnode 39 " ( a1 = a3 & P1074 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> ( a1 = a3 & P1110 & P1108 & P1107 & P1097 & P1093 & P1091 & P1089 & P1087 & P1077 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P1062 & P1059 & P1058 & P1057 & P0) & P0" 0; pushnode 38 " (a1 = a3 & P1074 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a2) & P1108 & P1107 & P1097 & P1093 & P1091 & P1089 & P1087 & P1077 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P1062 & P1059 & P1058 & P1057 & P0) & P0" 2; pushnode 37 " (a1 = a3 & P1074 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a2 v a1 = a2 & a2 = a3) & P1107 & P1097 & P1093 & P1091 & P1089 & P1087 & P1077 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 31 " (a4 = a2 & P1097 & P1093 & P1091 & P1089 & P1087 & P1077 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a1 = a3 & P1074 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 36 "(a2 = a3 & P1085 & P1082 & P1079 & P1078 & P1076 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> ( a2 = a3 & P1105 & P1074 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P1103 & P1100 & P1099 & P1096 & P1093 & P1091 & P1089 & P1087 & P1077 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P1062 & P1059 & P1058 & P1057 & P0) & P0" 0; pushnode 35 " ( a1 = a3 & P1074 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a2 = a3 & P1085 & P1082 & P1079 & P1078 & P1076 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> ( a2 = a1 & P1103 & P1100 & P1099 & P1096 & P1093 & P1091 & P1089 & P1087 & P1077 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 34 " (a1 = a3 & P1074 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> ( a1 = a3 & P1102 & P1100 & P1099 & P1096 & P1093 & P1091 & P1089 & P1087 & P1077 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P1062 & P1059 & P1058 & P1057 & P0) & P0" 0; pushnode 33 " (a1 = a3 & P1074 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a2 = a3 & P1085 & P1082 & P1079 & P1078 & P1076 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a1) & P1100 & P1099 & P1096 & P1093 & P1091 & P1089 & P1087 & P1077 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P1062 & P1059 & P1058 & P1057 & P0) & P0" 2; pushnode 32 " (a1 = a3 & P1074 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a2 = a3 & P1085 & P1082 & P1079 & P1078 & P1076 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a1 v a1 = a1 & a2 = a3) & P1099 & P1096 & P1093 & P1091 & P1089 & P1087 & P1077 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 30 " (a4 = a1 & P1096 & P1093 & P1091 & P1089 & P1087 & P1077 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a1 = a3 & P1074 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a2 = a3 & P1085 & P1082 & P1079 & P1078 & P1076 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 28 "( (a4 = a1 v a4 = a2) & P1093 & P1091 & P1089 & P1087 & P1077 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a1 = a3 & P1074 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a2 = a3 & P1085 & P1082 & P1079 & P1078 & P1076 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 2; pushnode 29 "P0 -> (a4 = a4 & P1095 & P1092 & P1091 & P1089 & P1087 & P1077 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0" 0; pushnode 27 "P0 -> (( a4 = a3 v a4 = a4) & P1092 & P1091 & P1089 & P1087 & P1077 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 26 " (( a4 = a3 v a4 = a4 -> a4 = a1 v a4 = a2) & P1091 & P1089 & P1087 & P1077 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a1 = a3 & P1074 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a2 = a3 & P1085 & P1082 & P1079 & P1078 & P1076 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 2; pushnode 25 "( (( a4 = a1 v a4 = a2 -> a4 = a3 v a4 = a4) & ( a4 = a3 v a4 = a4 -> a4 = a1 v a4 = a2)) & P1089 & P1087 & P1077 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ( a1 = a3 & P1074 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a2 = a3 & P1085 & P1082 & P1079 & P1078 & P1076 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 24 "(( a4 = a1 v a4 = a2 == a4 = a3 v a4 = a4) & P1087 & P1077 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ( a1 = a3 & P1074 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a2 = a3 & P1085 & P1082 & P1079 & P1078 & P1076 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 22 " ((Ax4. x4 = a1 v x4 = a2 == x4 = a3 v x4 = a4) & P1077 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ( a1 = a3 & P1074 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a2 = a3 & P1085 & P1082 & P1079 & P1078 & P1076 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> ( (a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 20 "( (a2 = a3 v a2 = a4) & P1082 & P1079 & P1078 & P1076 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ((Ax4. x4 = a1 v x4 = a2 == x4 = a3 v x4 = a4) & P1077 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ( a1 = a3 & P1074 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 2; pushnode 21 "P0 -> (a2 = a2 & P1084 & P1081 & P1079 & P1078 & P1076 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0" 0; pushnode 19 "P0 -> ( (a2 = a1 v a2 = a2) & P1081 & P1079 & P1078 & P1076 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 18 "(( a2 = a1 v a2 = a2 -> a2 = a3 v a2 = a4) & P1079 & P1078 & P1076 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ((Ax4. x4 = a1 v x4 = a2 == x4 = a3 v x4 = a4) & P1077 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ( a1 = a3 & P1074 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 2; pushnode 17 " ( (( a2 = a1 v a2 = a2 -> a2 = a3 v a2 = a4) & ( a2 = a3 v a2 = a4 -> a2 = a1 v a2 = a2)) & P1078 & P1076 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ((Ax4. x4 = a1 v x4 = a2 == x4 = a3 v x4 = a4) & P1077 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ( a1 = a3 & P1074 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 16 "(( a2 = a1 v a2 = a2 == a2 = a3 v a2 = a4) & P1076 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ((Ax4. x4 = a1 v x4 = a2 == x4 = a3 v x4 = a4) & P1077 & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ( a1 = a3 & P1074 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 14 " ((Ax4. x4 = a1 v x4 = a2 == x4 = a3 v x4 = a4) & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & (a1 = a3 & P1074 & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 12 "( (a1 = a3 v a1 = a4) & P1071 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ((Ax4. x4 = a1 v x4 = a2 == x4 = a3 v x4 = a4) & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 2; pushnode 13 "P0 -> (a1 = a1 & P1072 & P1070 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0" 0; pushnode 11 "P0 -> (( a1 = a1 v a1 = a2) & P1070 & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 10 " ((a1 = a1 v a1 = a2 -> a1 = a3 v a1 = a4) & P1068 & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ((Ax4. x4 = a1 v x4 = a2 == x4 = a3 v x4 = a4) & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 2; pushnode 9 "( (( a1 = a1 v a1 = a2 -> a1 = a3 v a1 = a4) & ( a1 = a3 v a1 = a4 -> a1 = a1 v a1 = a2)) & P1067 & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ((Ax4. x4 = a1 v x4 = a2 == x4 = a3 v x4 = a4) & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 8 " (( a1 = a1 v a1 = a2 == a1 = a3 v a1 = a4) & P1065 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & ((Ax4. x4 = a1 v x4 = a2 == x4 = a3 v x4 = a4) & P1066 & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 7 "((Ax4. x4 = a1 v x4 = a2 == x4 = a3 v x4 = a4) & P1064 & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 6 "( {x4|x4 = a1 v x4 = a2} = {x4|x4 = a3 v x4 = a4} & P1063 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 5 "( a1 Couple a2 = a3 Couple a4 & P1061 & P1059 & P1058 & P1057 & P0) & P0 -> (( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1062 & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 3 "P0 -> ( ( a1 Couple a2 = a3 Couple a4 -> a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1059 & P1058 & P1057 & P0) & P0" 1; pushnode 2 " P0 -> (( ( a1 Couple a2 = a3 Couple a4 -> a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & ( a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3 -> a1 Couple a2 = a3 Couple a4)) & P1058 & P1057 & P0) & P0" 2; pushnode 1 " P0 -> ( ( a1 Couple a2 = a3 Couple a4 == a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1057 & P0) & P0" 1; THEOREMS:=("CoupleEq",(termtosequent(parseprop("P0 -> ( ( a1 Couple a2 = a3 Couple a4 == a1 = a3 & a2 = a4 v a1 = a4 & a2 = a3) & P1057 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "CoupleEq"; pushnode 23 "P0 -> (a1 = a1 & P1221 & P1217 & P1215 & P1213 & P1211 & P1210 & P1209 & P1191 & P1190 & P1194 & P1192 & P1190 & P0) & P0" 0; pushnode 21 "(a3 = a1 & P1217 & P1215 & P1213 & P1211 & P1210 & P1209 & P1191 & P1190 & P0) & P0 -> (a1 = a3 & P1194 & P1192 & P1190 & P0) & P0" 1; pushnode 22 "P0 -> (a3 = a3 & P1219 & P1216 & P1215 & P1213 & P1211 & P1210 & P1209 & P1191 & P1190 & P0) & P0" 0; pushnode 20 "P0 -> (( a3 = a2 v a3 = a3) & P1216 & P1215 & P1213 & P1211 & P1210 & P1209 & P1191 & P1190 & P0) & P0" 1; pushnode 19 " (( a3 = a2 v a3 = a3 -> a3 = a1) & P1215 & P1213 & P1211 & P1210 & P1209 & P1191 & P1190 & P0) & P0 -> ( a1 = a3 & P1194 & P1192 & P1190 & P0) & P0" 2; pushnode 18 "(( ( a3 = a1 -> a3 = a2 v a3 = a3) & (a3 = a2 v a3 = a3 -> a3 = a1)) & P1213 & P1211 & P1210 & P1209 & P1191 & P1190 & P0) & P0 -> (a1 = a3 & P1194 & P1192 & P1190 & P0) & P0" 1; pushnode 17 " ((a3 = a1 == a3 = a2 v a3 = a3) & P1211 & P1210 & P1209 & P1191 & P1190 & P0) & P0 -> ( a1 = a3 & P1194 & P1192 & P1190 & P0) & P0" 1; pushnode 16 "( (Ax3. x3 = a1 == x3 = a2 v x3 = a3) & P1210 & P1209 & P1191 & P1190 & P0) & P0 -> (a1 = a3 & P1194 & P1192 & P1190 & P0) & P0" 1; pushnode 15 "( {x3|x3 = a1} = {x4|x4 = a2 v x4 = a3} & P1209 & P1191 & P1190 & P0) & P0 -> (a1 = a3 & P1194 & P1192 & P1190 & P0) & P0" 1; pushnode 4 "( Sing(a1) = a2 Couple a3 & P1191 & P1190 & P0) & P0 -> (a1 = a3 & P1194 & P1192 & P1190 & P0) & P0" 1; THEOREMS:=("SCLEMMA2",(termtosequent(parseprop("( Sing(a1) = a2 Couple a3 & P1191 & P1190 & P0) & P0 -> (a1 = a3 & P1194 & P1192 & P1190 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "SCLEMMA2"; pushnode 14 "P0 -> (a1 = a1 & P1208 & P1204 & P1202 & P1200 & P1198 & P1197 & P1196 & P1191 & P1190 & P1193 & P1192 & P1190 & P0) & P0" 0; pushnode 12 "(a2 = a1 & P1204 & P1202 & P1200 & P1198 & P1197 & P1196 & P1191 & P1190 & P0) & P0 -> ( a1 = a2 & P1193 & P1192 & P1190 & P0) & P0" 1; pushnode 13 " P0 -> (a2 = a2 & P1205 & P1203 & P1202 & P1200 & P1198 & P1197 & P1196 & P1191 & P1190 & P0) & P0" 0; pushnode 11 "P0 -> ( (a2 = a2 v a2 = a3) & P1203 & P1202 & P1200 & P1198 & P1197 & P1196 & P1191 & P1190 & P0) & P0" 1; pushnode 10 " (( a2 = a2 v a2 = a3 -> a2 = a1) & P1202 & P1200 & P1198 & P1197 & P1196 & P1191 & P1190 & P0) & P0 -> ( a1 = a2 & P1193 & P1192 & P1190 & P0) & P0" 2; pushnode 9 "(( ( a2 = a1 -> a2 = a2 v a2 = a3) & (a2 = a2 v a2 = a3 -> a2 = a1)) & P1200 & P1198 & P1197 & P1196 & P1191 & P1190 & P0) & P0 -> (a1 = a2 & P1193 & P1192 & P1190 & P0) & P0" 1; pushnode 8 " ((a2 = a1 == a2 = a2 v a2 = a3) & P1198 & P1197 & P1196 & P1191 & P1190 & P0) & P0 -> ( a1 = a2 & P1193 & P1192 & P1190 & P0) & P0" 1; pushnode 7 "( (Ax3. x3 = a1 == x3 = a2 v x3 = a3) & P1197 & P1196 & P1191 & P1190 & P0) & P0 -> (a1 = a2 & P1193 & P1192 & P1190 & P0) & P0" 1; pushnode 6 "( {x3|x3 = a1} = {x4|x4 = a2 v x4 = a3} & P1196 & P1191 & P1190 & P0) & P0 -> (a1 = a2 & P1193 & P1192 & P1190 & P0) & P0" 1; pushnode 3 "( Sing(a1) = a2 Couple a3 & P1191 & P1190 & P0) & P0 -> (a1 = a2 & P1193 & P1192 & P1190 & P0) & P0" 1; THEOREMS:=("SCLEMMA1",(termtosequent(parseprop("( Sing(a1) = a2 Couple a3 & P1191 & P1190 & P0) & P0 -> (a1 = a2 & P1193 & P1192 & P1190 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "SCLEMMA1"; pushnode 15 "(a3 = a1 & P1240 & P1235 & P1228 & P1226 & P1225 & P1224 & P1223 & P1222 & P0) & P0 -> (a3 = a1 & P1237 & P1236 & P1228 & P1226 & P1225 & P1224 & P1223 & P1222 & P0) & P0" 0; pushnode 14 "(a3 = a2 & P1239 & P1235 & P1228 & P1226 & P1225 & P1224 & P1223 & P1222 & P0) & P0 -> (a3 = a2 & P1238 & P1236 & P1228 & P1226 & P1225 & P1224 & P1223 & P1222 & P0) & P0" 0; pushnode 13 "( (a3 = a2 v a3 = a1) & P1235 & P1228 & P1226 & P1225 & P1224 & P1223 & P1222 & P0) & P0 -> (a3 = a1 & P1237 & P1236 & P1228 & P1226 & P1225 & P1224 & P1223 & P1222 & P0) & ( a3 = a2 & P1238 & P1236 & P1228 & P1226 & P1225 & P1224 & P1223 & P1222 & P0) & P0" 2; pushnode 12 "( (a3 = a2 v a3 = a1) & P1235 & P1228 & P1226 & P1225 & P1224 & P1223 & P1222 & P0) & P0 -> ( (a3 = a1 v a3 = a2) & P1236 & P1228 & P1226 & P1225 & P1224 & P1223 & P1222 & P0) & P0" 1; pushnode 7 "P0 -> (( a3 = a2 v a3 = a1 -> a3 = a1 v a3 = a2) & P1228 & P1226 & P1225 & P1224 & P1223 & P1222 & P0) & P0" 1; pushnode 11 "(a3 = a2 & P1234 & P1229 & P1227 & P1226 & P1225 & P1224 & P1223 & P1222 & P0) & P0 -> (a3 = a2 & P1231 & P1230 & P1227 & P1226 & P1225 & P1224 & P1223 & P1222 & P0) & P0" 0; pushnode 10 "(a3 = a1 & P1233 & P1229 & P1227 & P1226 & P1225 & P1224 & P1223 & P1222 & P0) & P0 -> (a3 = a1 & P1232 & P1230 & P1227 & P1226 & P1225 & P1224 & P1223 & P1222 & P0) & P0" 0; pushnode 9 "( (a3 = a1 v a3 = a2) & P1229 & P1227 & P1226 & P1225 & P1224 & P1223 & P1222 & P0) & P0 -> (a3 = a2 & P1231 & P1230 & P1227 & P1226 & P1225 & P1224 & P1223 & P1222 & P0) & ( a3 = a1 & P1232 & P1230 & P1227 & P1226 & P1225 & P1224 & P1223 & P1222 & P0) & P0" 2; pushnode 8 "( (a3 = a1 v a3 = a2) & P1229 & P1227 & P1226 & P1225 & P1224 & P1223 & P1222 & P0) & P0 -> ( (a3 = a2 v a3 = a1) & P1230 & P1227 & P1226 & P1225 & P1224 & P1223 & P1222 & P0) & P0" 1; pushnode 6 "P0 -> (( a3 = a1 v a3 = a2 -> a3 = a2 v a3 = a1) & P1227 & P1226 & P1225 & P1224 & P1223 & P1222 & P0) & P0" 1; pushnode 5 "P0 -> ( (( a3 = a1 v a3 = a2 -> a3 = a2 v a3 = a1) & ( a3 = a2 v a3 = a1 -> a3 = a1 v a3 = a2)) & P1226 & P1225 & P1224 & P1223 & P1222 & P0) & P0" 2; pushnode 4 "P0 -> (( a3 = a1 v a3 = a2 == a3 = a2 v a3 = a1) & P1225 & P1224 & P1223 & P1222 & P0) & P0" 1; pushnode 3 "P0 -> ((Ax4. x4 = a1 v x4 = a2 == x4 = a2 v x4 = a1) & P1224 & P1223 & P1222 & P0) & P0" 1; pushnode 2 " P0 -> ( {x4|x4 = a1 v x4 = a2} = {x4|x4 = a2 v x4 = a1} & P1223 & P1222 & P0) & P0" 1; pushnode 1 " P0 -> ( a1 Couple a2 = a2 Couple a1 & P1222 & P0) & P0" 1; THEOREMS:=("CoupleComm",(termtosequent(parseprop(" P0 -> ( a1 Couple a2 = a2 Couple a1 & P1222 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "CoupleComm"; pushnode 5 "(Sing(a1) = a2 Couple a3 & P1242 & P1241 & P0) & P0 -> ( Sing(a1) = a2 Couple a3 & P1244 & P0) & P0" 0; pushnode 8 "(Sing(a1) = a2 Couple a3 & P1242 & P1241 & P0) & P0 -> ( Sing(a1) = a2 Couple a3 & P1246 & P0) & P0" 0; pushnode 10 " P0 -> (a2 = a2 & P1251 & P1245 & P1249 & P1247 & P1243 & P1241 & P0) & P0" 0; pushnode 9 "( a1 = a2 & P1245 & P0) & P0 -> (a2 = a1 & P1249 & P1247 & P1243 & P1241 & P0) & P0" 1; pushnode 7 " (a1 = a3 & P1247 & P0) & (a1 = a2 & P1245 & P0) & P0 -> ( a2 = a3 & P1243 & P1241 & P0) & P0" 1; pushreference 6 "( Sing(a1) = a2 Couple a3 & P1246 & P0) & P0 -> ( a1 = a3 & P1247 & P0) & P0" "SCLEMMA2"; pushnode 4 " (a1 = a2 & P1245 & P0) & ( Sing(a1) = a2 Couple a3 & P1242 & P1241 & P0) & P0 -> (a2 = a3 & P1243 & P1241 & P0) & P0" 3; pushreference 3 "( Sing(a1) = a2 Couple a3 & P1244 & P0) & P0 -> ( a1 = a2 & P1245 & P0) & P0" "SCLEMMA1"; pushnode 2 "( Sing(a1) = a2 Couple a3 & P1242 & P1241 & P0) & P0 -> (a2 = a3 & P1243 & P1241 & P0) & P0" 3; THEOREMS:=("SCLEMMA3",(termtosequent(parseprop("(Sing(a1) = a2 Couple a3 & P1242 & P1241 & P0) & P0 -> (a2 = a3 & P1243 & P1241 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "SCLEMMA3"; pushnode 34 "P0 -> ( a1 = a1 & P1406 & P1402 & P1400 & P1398 & P1396 & P1395 & P1394 & P1384 & P1380 & P1377 & P1376 & P1374 & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P1369 & P1368 & P1365 & P1364 & P1363 & P0) & P0" 0; pushnode 32 "(a3 = a1 & P1402 & P1400 & P1398 & P1396 & P1395 & P1394 & P1384 & P1380 & P1377 & P1376 & P1374 & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P0) & P0 -> (a1 = a3 & P1369 & P1368 & P1365 & P1364 & P1363 & P0) & P0" 1; pushnode 33 "P0 -> ( a3 = a3 & P1403 & P1401 & P1400 & P1398 & P1396 & P1395 & P1394 & P1384 & P1380 & P1377 & P1376 & P1374 & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P0) & P0" 0; pushnode 31 " P0 -> ((a3 = a3 v a3 = a4) & P1401 & P1400 & P1398 & P1396 & P1395 & P1394 & P1384 & P1380 & P1377 & P1376 & P1374 & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P0) & P0" 1; pushnode 30 " (( a3 = a3 v a3 = a4 -> a3 = a1) & P1400 & P1398 & P1396 & P1395 & P1394 & P1384 & P1380 & P1377 & P1376 & P1374 & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P0) & P0 -> ( a1 = a3 & P1369 & P1368 & P1365 & P1364 & P1363 & P0) & P0" 2; pushnode 29 " (( ( a3 = a1 -> a3 = a3 v a3 = a4) & (a3 = a3 v a3 = a4 -> a3 = a1)) & P1398 & P1396 & P1395 & P1394 & P1384 & P1380 & P1377 & P1376 & P1374 & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P0) & P0 -> ( a1 = a3 & P1369 & P1368 & P1365 & P1364 & P1363 & P0) & P0" 1; pushnode 28 " ( ( a3 = a1 == a3 = a3 v a3 = a4) & P1396 & P1395 & P1394 & P1384 & P1380 & P1377 & P1376 & P1374 & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P0) & P0 -> ( a1 = a3 & P1369 & P1368 & P1365 & P1364 & P1363 & P0) & P0" 1; pushnode 27 "( (Ax3. x3 = a1 == x3 = a3 v x3 = a4) & P1395 & P1394 & P1384 & P1380 & P1377 & P1376 & P1374 & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P0) & P0 -> (a1 = a3 & P1369 & P1368 & P1365 & P1364 & P1363 & P0) & P0" 1; pushnode 26 " ({x3|x3 = a1} = {x4|x4 = a3 v x4 = a4} & P1394 & P1384 & P1380 & P1377 & P1376 & P1374 & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P0) & P0 -> (a1 = a3 & P1369 & P1368 & P1365 & P1364 & P1363 & P0) & P0" 1; pushnode 18 " (Sing(a1) = a3 Couple a4 & P1384 & P1380 & P1377 & P1376 & P1374 & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P0) & P0 -> (a1 = a3 & P1369 & P1368 & P1365 & P1364 & P1363 & P0) & P0" 1; pushnode 25 " (a1 = a3 & P1393 & P1390 & P1389 & P1387 & P1386 & P1385 & P1383 & P1380 & P1377 & P1376 & P1374 & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P0) & P0 -> ( a1 = a3 & P1369 & P1368 & P1365 & P1364 & P1363 & P0) & P0" 0; pushnode 24 " P0 -> (a1 = a1 & P1392 & P1390 & P1389 & P1387 & P1386 & P1385 & P1383 & P1380 & P1377 & P1376 & P1374 & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P0) & P0" 0; pushnode 23 " ( (a1 = a1 -> a1 = a3) & P1390 & P1389 & P1387 & P1386 & P1385 & P1383 & P1380 & P1377 & P1376 & P1374 & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P0) & P0 -> ( a1 = a3 & P1369 & P1368 & P1365 & P1364 & P1363 & P0) & P0" 2; pushnode 22 " ((( a1 = a1 -> a1 = a3) & ( a1 = a3 -> a1 = a1)) & P1389 & P1387 & P1386 & P1385 & P1383 & P1380 & P1377 & P1376 & P1374 & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P0) & P0 -> ( a1 = a3 & P1369 & P1368 & P1365 & P1364 & P1363 & P0) & P0" 1; pushnode 21 "(( a1 = a1 == a1 = a3) & P1387 & P1386 & P1385 & P1383 & P1380 & P1377 & P1376 & P1374 & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P0) & P0 -> (a1 = a3 & P1369 & P1368 & P1365 & P1364 & P1363 & P0) & P0" 1; pushnode 20 "((Ax3.x3 = a1 == x3 = a3) & P1386 & P1385 & P1383 & P1380 & P1377 & P1376 & P1374 & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P0) & P0 -> (a1 = a3 & P1369 & P1368 & P1365 & P1364 & P1363 & P0) & P0" 1; pushnode 19 "( {x3|x3 = a1} = {x3|x3 = a3} & P1385 & P1383 & P1380 & P1377 & P1376 & P1374 & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P0) & P0 -> (a1 = a3 & P1369 & P1368 & P1365 & P1364 & P1363 & P0) & P0" 1; pushnode 17 "( Sing(a1) = Sing(a3) & P1383 & P1380 & P1377 & P1376 & P1374 & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P0) & P0 -> ( a1 = a3 & P1369 & P1368 & P1365 & P1364 & P1363 & P0) & P0" 1; pushnode 15 " (( Sing(a1) = Sing(a3) v Sing(a1) = a3 Couple a4) & P1380 & P1377 & P1376 & P1374 & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P0) & P0 -> ( a1 = a3 & P1369 & P1368 & P1365 & P1364 & P1363 & P0) & P0" 2; pushnode 16 " P0 -> (Sing(a1) = Sing(a1) & P1381 & P1379 & P1377 & P1376 & P1374 & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P0) & P0" 0; pushnode 14 "P0 -> ( (Sing(a1) = Sing(a1) v Sing(a1) = a1 Couple a2) & P1379 & P1377 & P1376 & P1374 & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P0) & P0" 1; pushnode 13 "( ( Sing(a1) = Sing(a1) v Sing(a1) = a1 Couple a2 -> Sing(a1) = Sing(a3) v Sing(a1) = a3 Couple a4) & P1377 & P1376 & P1374 & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P0) & P0 -> ( a1 = a3 & P1369 & P1368 & P1365 & P1364 & P1363 & P0) & P0" 2; pushnode 12 "(( ( Sing(a1) = Sing(a1) v Sing(a1) = a1 Couple a2 -> Sing(a1) = Sing(a3) v Sing(a1) = a3 Couple a4) & ( Sing(a1) = Sing(a3) v Sing(a1) = a3 Couple a4 -> Sing(a1) = Sing(a1) v Sing(a1) = a1 Couple a2)) & P1376 & P1374 & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P0) & P0 -> (a1 = a3 & P1369 & P1368 & P1365 & P1364 & P1363 & P0) & P0" 1; pushnode 11 "( ( Sing(a1) = Sing(a1) v Sing(a1) = a1 Couple a2 == Sing(a1) = Sing(a3) v Sing(a1) = a3 Couple a4) & P1374 & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P0) & P0 -> (a1 = a3 & P1369 & P1368 & P1365 & P1364 & P1363 & P0) & P0" 1; pushnode 10 " ((Ax4. x4 = Sing(a1) v x4 = a1 Couple a2 == x4 = Sing(a3) v x4 = a3 Couple a4) & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P0) & P0 -> ( a1 = a3 & P1369 & P1368 & P1365 & P1364 & P1363 & P0) & P0" 1; THEOREMS:=("COORDONE",(termtosequent(parseprop(" ((Ax4. x4 = Sing(a1) v x4 = a1 Couple a2 == x4 = Sing(a3) v x4 = a3 Couple a4) & P1373 & P1372 & P1371 & P1367 & P1365 & P1364 & P1363 & P0) & P0 -> ( a1 = a3 & P1369 & P1368 & P1365 & P1364 & P1363 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "COORDONE"; pushnode 6 " P0 -> (a1 = a1 & P1542 & P1539 & P0) & P0" 0; pushnode 4 "P0 -> (a1 E Sing(a1) & P1539 & P0) & P0" 1; pushnode 5 " (An(Sing(a1)) = a1 & P1541 & P1540 & P0) & P0 -> ( An(Sing(a1)) = a1 & P1538 & P0) & P0" 0; pushnode 3 " (An(Sing(a1)) E Sing(a1) & P1540 & P0) & P0 -> (An(Sing(a1)) = a1 & P1538 & P0) & P0" 1; pushreference 2 "( a1 E Sing(a1) & P1539 & P0) & P0 -> (An(Sing(a1)) E Sing(a1) & P1540 & P0) & P0" "AN"; pushnode 1 "P0 -> ( An(Sing(a1)) = a1 & P1538 & P0) & P0" 3; THEOREMS:=("THE",(termtosequent(parseprop("P0 -> (An(Sing(a1)) = a1 & P1538 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "THE"; pushreference 19 " ( a2 + Zero < a1 + Zero & P1562 & P1560 & P0) & ( a1 + Zero < a2 + Zero & P1558 & P1543 & P0) & P0 -> P0" "NOTBOTH"; pushnode 18 "(a2 < a1 & P1555 & P1546 & P1544 & P0) & P0 -> (a2 < a1 & P1561 & P1560 & P0) & P0" 0; pushnode 17 "(( a2 < a1 -> a2 + Zero < a1 + Zero) & P1560 & P0) & (a1 + Zero < a2 + Zero & P1558 & P1543 & P0) & ( a2 < a1 & P1555 & P1546 & P1544 & P0) & P0 -> P0" 2; pushreference 16 "P0 -> ((a2 < a1 -> a2 + Zero < a1 + Zero) & P1560 & P0) & P0" "MPLUS"; pushnode 15 " ( a1 + Zero < a2 + Zero & P1558 & P1543 & P0) & ( a2 < a1 & P1555 & P1546 & P1544 & P0) & P0 -> P0" 2; pushnode 13 "(a2 < a1 & P1555 & P1546 & P1544 & P0) & P0 -> (( a1 + Zero < a2 + Zero -> a1 < a2) & P1543 & P0) & P0" 1; pushnode 14 "(a1 < a2 & P1554 & P1546 & P1544 & P0) & P0 -> ( a1 < a2 & P1557 & P1543 & P0) & P0" 0; pushnode 12 "(a1 < a2 & P1554 & P1546 & P1544 & P0) & P0 -> (( a1 + Zero < a2 + Zero -> a1 < a2) & P1543 & P0) & P0" 1; pushnode 5 "(( a1 < a2 v a2 < a1) & P1546 & P1544 & P0) & P0 -> (( a1 + Zero < a2 + Zero -> a1 < a2) & P1543 & P0) & P0" 2; pushnode 11 "( a2 + Zero < a2 + Zero & P1550 & P1549 & P1547 & P1545 & P1544 & P1543 & P0) & P0 -> ( a2 + Zero < a2 + Zero & P1553 & P1552 & P0) & P0" 0; pushnode 10 " ( ~a2 + Zero < a2 + Zero & P1552 & P0) & (a2 + Zero < a2 + Zero & P1550 & P1549 & P1547 & P1545 & P1544 & P1543 & P0) & P0 -> P0" 1; pushreference 9 "P0 -> (~a2 + Zero < a2 + Zero & P1552 & P0) & P0" "IRR"; pushnode 8 "( a2 + Zero < a2 + Zero & P1550 & P1549 & P1547 & P1545 & P1544 & P1543 & P0) & P0 -> P0" 2; pushnode 7 "P0 -> (( a2 + Zero < a2 + Zero -> a1 < a2) & P1549 & P1547 & P1545 & P1544 & P1543 & P0) & P0" 1; pushnode 6 " ( a1 + Zero = a2 + Zero & P1547 & P1545 & P1544 & P0) & P0 -> (( a1 + Zero < a2 + Zero -> a1 < a2) & P1543 & P0) & P0" 1; pushnode 4 "( a1 Equal a2 & P1545 & P1544 & P0) & P0 -> (( a1 + Zero < a2 + Zero -> a1 < a2) & P1543 & P0) & P0" 1; pushnode 3 "((a1 Equal a2 v a1 < a2 v a2 < a1) & P1544 & P0) & P0 -> (( a1 + Zero < a2 + Zero -> a1 < a2) & P1543 & P0) & P0" 2; pushreference 2 "P0 -> ((a1 Equal a2 v a1 < a2 v a2 < a1) & P1544 & P0) & P0" "TRI"; pushnode 1 "P0 -> (( a1 + Zero < a2 + Zero -> a1 < a2) & P1543 & P0) & P0" 2; THEOREMS:=("LESSTYPE",(termtosequent(parseprop("P0 -> (( a1 + Zero < a2 + Zero -> a1 < a2) & P1543 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "LESSTYPE"; pushnode 5 " (a1 < a2 & P1567 & P1565 & P0) & P0 -> ( a1 < a2 & P1564 & P0) & P0" 0; pushnode 4 "( a1 + Zero < a2 + Zero & P1563 & P0) & P0 -> ( a1 + Zero < a2 + Zero & P1566 & P1565 & P0) & P0" 0; pushnode 3 " (( a1 + Zero < a2 + Zero -> a1 < a2) & P1565 & P0) & (a1 + Zero < a2 + Zero & P1563 & P0) & P0 -> (a1 < a2 & P1564 & P0) & P0" 2; pushreference 2 " P0 -> ((a1 + Zero < a2 + Zero -> a1 < a2) & P1565 & P0) & P0" "LESSTYPE"; pushnode 1 "( a1 + Zero < a2 + Zero & P1563 & P0) & P0 -> (a1 < a2 & P1564 & P0) & P0" 2; THEOREMS:=("LESSTYPEa",(termtosequent(parseprop("( a1 + Zero < a2 + Zero & P1563 & P0) & P0 -> (a1 < a2 & P1564 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "LESSTYPEa"; pushreference 4 " P0 -> (Real(a1 + Zero) & P1569 & P0) & P0" "RPLUS"; pushnode 5 "P0 -> ( a1 + Zero = a1 + Zero & P1572 & P1570 & P1568 & P0) & P0" 0; pushnode 3 "([ a1 + Zero] + Zero = a1 + Zero & P1570 & P0) & P0 -> ([a1 + Zero] + Zero = a1 + Zero & P1568 & P0) & P0" 1; pushreference 2 "(Real( a1 + Zero) & P1569 & P0) & P0 -> ([ a1 + Zero] + Zero = a1 + Zero & P1570 & P0) & P0" "IPLUSa"; pushnode 1 "P0 -> ([a1 + Zero] + Zero = a1 + Zero & P1568 & P0) & P0" 3; THEOREMS:=("RETRACT",(termtosequent(parseprop("P0 -> ([a1 + Zero] + Zero = a1 + Zero & P1568 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "RETRACT"; pushnode 13 "P0 -> ( a1 * a3 + a2 * a3 = a1 * a3 + a2 * a3 & P1585 & P1583 & P1582 & P1580 & P1579 & P1577 & P1576 & P1574 & P1573 & P0) & P0" 0; pushnode 12 "( a3 * a2 = a2 * a3 & P1583 & P0) & P0 -> ( a1 * a3 + a3 * a2 = a1 * a3 + a2 * a3 & P1582 & P1580 & P1579 & P1577 & P1576 & P1574 & P1573 & P0) & P0" 1; pushreference 11 "P0 -> ( a3 * a2 = a2 * a3 & P1583 & P0) & P0" "CTIMES"; pushnode 10 " P0 -> (a1 * a3 + a3 * a2 = a1 * a3 + a2 * a3 & P1582 & P1580 & P1579 & P1577 & P1576 & P1574 & P1573 & P0) & P0" 2; pushnode 9 "(a3 * a1 = a1 * a3 & P1580 & P0) & P0 -> ( a3 * a1 + a3 * a2 = a1 * a3 + a2 * a3 & P1579 & P1577 & P1576 & P1574 & P1573 & P0) & P0" 1; pushreference 8 " P0 -> (a3 * a1 = a1 * a3 & P1580 & P0) & P0" "CTIMES"; pushnode 7 "P0 -> ( a3 * a1 + a3 * a2 = a1 * a3 + a2 * a3 & P1579 & P1577 & P1576 & P1574 & P1573 & P0) & P0" 2; pushnode 6 "(a3 * [a1 + a2] = a3 * a1 + a3 * a2 & P1577 & P0) & P0 -> (a3 * [a1 + a2] = a1 * a3 + a2 * a3 & P1576 & P1574 & P1573 & P0) & P0" 1; pushreference 5 " P0 -> (a3 * [a1 + a2] = a3 * a1 + a3 * a2 & P1577 & P0) & P0" "DIST"; pushnode 4 "P0 -> ( a3 * [a1 + a2] = a1 * a3 + a2 * a3 & P1576 & P1574 & P1573 & P0) & P0" 2; pushnode 3 "([ a1 + a2] * a3 = a3 * [a1 + a2] & P1574 & P0) & P0 -> ([ a1 + a2] * a3 = a1 * a3 + a2 * a3 & P1573 & P0) & P0" 1; pushreference 2 " P0 -> ( [a1 + a2] * a3 = a3 * [a1 + a2] & P1574 & P0) & P0" "CTIMES"; pushnode 1 " P0 -> ([a1 + a2] * a3 = a1 * a3 + a2 * a3 & P1573 & P0) & P0" 2; THEOREMS:=("DIST2",(termtosequent(parseprop("P0 -> ( [a1 + a2] * a3 = a1 * a3 + a2 * a3 & P1573 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "DIST2"; pushreference 62 "P0 -> (Real(a1 * One) & P1631 & P0) & P0" "RTIMES"; pushnode 66 " ( a1 * One < a1 * One & P1633 & P1630 & P1628 & P1624 & P1620 & P1618 & P1623 & P1627 & P1625 & P1629 & P1632 & P0) & ([ a1 + Zero] * One = a1 * One + Zero * One & P1623 & P0) & ([a1 * One] * One = a1 * One & P1627 & P1625 & P0) & ( Zero * One = Zero & P1629 & P0) & ( a1 * One + Zero = a1 * One & P1632 & P0) & P0 -> (a1 * One < a1 * One & P1635 & P1634 & P0) & P0" 0; pushnode 65 " (~a1 * One < a1 * One & P1634 & P0) & (a1 * One + Zero = a1 * One & P1632 & P0) & ( a1 * One < a1 * One & P1633 & P1630 & P1628 & P1624 & P1620 & P1618 & P1623 & P1627 & P1625 & P1629 & P1632 & P0) & ([ a1 + Zero] * One = a1 * One + Zero * One & P1623 & P0) & ([a1 * One] * One = a1 * One & P1627 & P1625 & P0) & ( Zero * One = Zero & P1629 & P0) & P0 -> P0" 1; pushreference 64 "P0 -> ( ~a1 * One < a1 * One & P1634 & P0) & P0" "IRR"; pushnode 63 " (a1 * One + Zero = a1 * One & P1632 & P0) & ( a1 * One < a1 * One & P1633 & P1630 & P1628 & P1624 & P1620 & P1618 & P1623 & P1627 & P1625 & P1629 & P1632 & P0) & ([ a1 + Zero] * One = a1 * One + Zero * One & P1623 & P0) & ([a1 * One] * One = a1 * One & P1627 & P1625 & P0) & ( Zero * One = Zero & P1629 & P0) & P0 -> P0" 2; pushnode 61 " ( a1 * One + Zero = a1 * One & P1632 & P0) & ( a1 * One + Zero < a1 * One & P1630 & P1628 & P1624 & P1620 & P1618 & P1623 & P1627 & P1625 & P1629 & P0) & ([ a1 + Zero] * One = a1 * One + Zero * One & P1623 & P0) & ([a1 * One] * One = a1 * One & P1627 & P1625 & P0) & ( Zero * One = Zero & P1629 & P0) & P0 -> P0" 1; pushreference 60 " (Real(a1 * One) & P1631 & P0) & P0 -> (a1 * One + Zero = a1 * One & P1632 & P0) & P0" "IPLUSa"; pushnode 59 " ( Zero * One = Zero & P1629 & P0) & ( a1 * One + Zero < a1 * One & P1630 & P1628 & P1624 & P1620 & P1618 & P1623 & P1627 & P1625 & P1629 & P0) & ([ a1 + Zero] * One = a1 * One + Zero * One & P1623 & P0) & ([a1 * One] * One = a1 * One & P1627 & P1625 & P0) & P0 -> P0" 3; pushnode 58 " ( Zero * One = Zero & P1629 & P0) & ( a1 * One + Zero * One < a1 * One & P1628 & P1624 & P1620 & P1618 & P1623 & P1627 & P1625 & P0) & ( [a1 + Zero] * One = a1 * One + Zero * One & P1623 & P0) & ( [a1 * One] * One = a1 * One & P1627 & P1625 & P0) & P0 -> P0" 1; pushreference 57 "P0 -> ( Zero * One = Zero & P1629 & P0) & P0" "MZERO2"; pushnode 56 "([a1 * One] * One = a1 * One & P1627 & P1625 & P0) & ( a1 * One + Zero * One < a1 * One & P1628 & P1624 & P1620 & P1618 & P1623 & P1627 & P1625 & P0) & ( [a1 + Zero] * One = a1 * One + Zero * One & P1623 & P0) & P0 -> P0" 2; pushnode 55 "( [a1 * One] * One = a1 * One & P1627 & P1625 & P0) & ( a1 * One + Zero * One < [ a1 * One] * One & P1624 & P1620 & P1618 & P1623 & P0) & ([ a1 + Zero] * One = a1 * One + Zero * One & P1623 & P0) & P0 -> P0" 1; pushreference 54 "P0 -> (Real(a1 * One) & P1626 & P1625 & P0) & P0" "RTIMES"; pushnode 53 "( (Real(a1 * One) -> [a1 * One] * One = a1 * One) & P1625 & P0) & ( [a1 + Zero] * One = a1 * One + Zero * One & P1623 & P0) & ( a1 * One + Zero * One < [a1 * One] * One & P1624 & P1620 & P1618 & P1623 & P0) & P0 -> P0" 2; pushreference 52 "P0 -> ((Real(a1 * One) -> [a1 * One] * One = a1 * One) & P1625 & P0) & P0" "ITIMES"; pushnode 51 "( [a1 + Zero] * One = a1 * One + Zero * One & P1623 & P0) & ( a1 * One + Zero * One < [ a1 * One] * One & P1624 & P1620 & P1618 & P1623 & P0) & P0 -> P0" 2; pushnode 50 " ( [a1 + Zero] * One = a1 * One + Zero * One & P1623 & P0) & ( [a1 + Zero] * One < [a1 * One] * One & P1620 & P1618 & P0) & P0 -> P0" 1; pushreference 49 "P0 -> ( [a1 + Zero] * One = a1 * One + Zero * One & P1623 & P0) & P0" "DIST2"; pushnode 46 "([ a1 + Zero] * One < [a1 * One] * One & P1620 & P1618 & P0) & P0 -> P0" 2; pushnode 48 "( a1 + Zero < a1 * One & P1598 & P1589 & P1587 & P0) & P0 -> ( a1 + Zero < a1 * One & P1622 & P1619 & P1618 & P0) & P0" 0; pushreference 47 " P0 -> (Zero < One & P1621 & P1619 & P1618 & P0) & P0" "ZEROLESSONE"; pushnode 45 " ( a1 + Zero < a1 * One & P1598 & P1589 & P1587 & P0) & P0 -> (( Zero < One & a1 + Zero < a1 * One) & P1619 & P1618 & P0) & P0" 2; pushnode 44 "(( Zero < One & a1 + Zero < a1 * One -> [ a1 + Zero] * One < [a1 * One] * One) & P1618 & P0) & (a1 + Zero < a1 * One & P1598 & P1589 & P1587 & P0) & P0 -> P0" 2; pushreference 43 "P0 -> (( Zero < One & a1 + Zero < a1 * One -> [a1 + Zero] * One < [ a1 * One] * One) & P1618 & P0) & P0" "MTIMES"; pushnode 16 " ( a1 + Zero < a1 * One & P1598 & P1589 & P1587 & P0) & P0 -> P0" 2; pushreference 36 "P0 -> (Real(a1 * One) & P1612 & P0) & P0" "RTIMES"; pushnode 40 " ( a1 * One < a1 * One & P1614 & P1611 & P1609 & P1605 & P1601 & P1599 & P1604 & P1608 & P1606 & P1610 & P1613 & P0) & ([ a1 + Zero] * One = a1 * One + Zero * One & P1604 & P0) & ([a1 * One] * One = a1 * One & P1608 & P1606 & P0) & ( Zero * One = Zero & P1610 & P0) & ( a1 * One + Zero = a1 * One & P1613 & P0) & P0 -> (a1 * One < a1 * One & P1616 & P1615 & P0) & P0" 0; pushnode 39 " (~a1 * One < a1 * One & P1615 & P0) & (a1 * One + Zero = a1 * One & P1613 & P0) & ( a1 * One < a1 * One & P1614 & P1611 & P1609 & P1605 & P1601 & P1599 & P1604 & P1608 & P1606 & P1610 & P1613 & P0) & ([ a1 + Zero] * One = a1 * One + Zero * One & P1604 & P0) & ([a1 * One] * One = a1 * One & P1608 & P1606 & P0) & ( Zero * One = Zero & P1610 & P0) & P0 -> P0" 1; pushreference 38 "P0 -> ( ~a1 * One < a1 * One & P1615 & P0) & P0" "IRR"; pushnode 37 " (a1 * One + Zero = a1 * One & P1613 & P0) & ( a1 * One < a1 * One & P1614 & P1611 & P1609 & P1605 & P1601 & P1599 & P1604 & P1608 & P1606 & P1610 & P1613 & P0) & ([ a1 + Zero] * One = a1 * One + Zero * One & P1604 & P0) & ([a1 * One] * One = a1 * One & P1608 & P1606 & P0) & ( Zero * One = Zero & P1610 & P0) & P0 -> P0" 2; pushnode 35 " ( a1 * One + Zero = a1 * One & P1613 & P0) & (a1 * One < a1 * One + Zero & P1611 & P1609 & P1605 & P1601 & P1599 & P1604 & P1608 & P1606 & P1610 & P0) & ( [a1 + Zero] * One = a1 * One + Zero * One & P1604 & P0) & ([ a1 * One] * One = a1 * One & P1608 & P1606 & P0) & ( Zero * One = Zero & P1610 & P0) & P0 -> P0" 1; pushreference 34 " (Real(a1 * One) & P1612 & P0) & P0 -> (a1 * One + Zero = a1 * One & P1613 & P0) & P0" "IPLUSa"; pushnode 33 " ( Zero * One = Zero & P1610 & P0) & (a1 * One < a1 * One + Zero & P1611 & P1609 & P1605 & P1601 & P1599 & P1604 & P1608 & P1606 & P1610 & P0) & ( [a1 + Zero] * One = a1 * One + Zero * One & P1604 & P0) & ([ a1 * One] * One = a1 * One & P1608 & P1606 & P0) & P0 -> P0" 3; pushnode 32 " ( Zero * One = Zero & P1610 & P0) & ( a1 * One < a1 * One + Zero * One & P1609 & P1605 & P1601 & P1599 & P1604 & P1608 & P1606 & P0) & ( [a1 + Zero] * One = a1 * One + Zero * One & P1604 & P0) & ( [a1 * One] * One = a1 * One & P1608 & P1606 & P0) & P0 -> P0" 1; pushreference 31 "P0 -> ( Zero * One = Zero & P1610 & P0) & P0" "MZERO2"; pushnode 30 "([a1 * One] * One = a1 * One & P1608 & P1606 & P0) & ( a1 * One < a1 * One + Zero * One & P1609 & P1605 & P1601 & P1599 & P1604 & P1608 & P1606 & P0) & ( [a1 + Zero] * One = a1 * One + Zero * One & P1604 & P0) & P0 -> P0" 2; pushnode 29 "( [a1 * One] * One = a1 * One & P1608 & P1606 & P0) & ([ a1 * One] * One < a1 * One + Zero * One & P1605 & P1601 & P1599 & P1604 & P0) & ([ a1 + Zero] * One = a1 * One + Zero * One & P1604 & P0) & P0 -> P0" 1; pushreference 28 "P0 -> (Real(a1 * One) & P1607 & P1606 & P0) & P0" "RTIMES"; pushnode 27 "( (Real(a1 * One) -> [a1 * One] * One = a1 * One) & P1606 & P0) & ( [a1 + Zero] * One = a1 * One + Zero * One & P1604 & P0) & ( [a1 * One] * One < a1 * One + Zero * One & P1605 & P1601 & P1599 & P1604 & P0) & P0 -> P0" 2; pushreference 26 "P0 -> ((Real(a1 * One) -> [a1 * One] * One = a1 * One) & P1606 & P0) & P0" "ITIMES"; pushnode 25 "( [a1 + Zero] * One = a1 * One + Zero * One & P1604 & P0) & ([ a1 * One] * One < a1 * One + Zero * One & P1605 & P1601 & P1599 & P1604 & P0) & P0 -> P0" 2; pushnode 24 " ( [a1 + Zero] * One = a1 * One + Zero * One & P1604 & P0) & ( [a1 * One] * One < [a1 + Zero] * One & P1601 & P1599 & P0) & P0 -> P0" 1; pushreference 23 "P0 -> ( [a1 + Zero] * One = a1 * One + Zero * One & P1604 & P0) & P0" "DIST2"; pushnode 20 "([ a1 * One] * One < [a1 + Zero] * One & P1601 & P1599 & P0) & P0 -> P0" 2; pushnode 22 "( a1 * One < a1 + Zero & P1597 & P1589 & P1587 & P0) & P0 -> ( a1 * One < a1 + Zero & P1603 & P1600 & P1599 & P0) & P0" 0; pushreference 21 " P0 -> (Zero < One & P1602 & P1600 & P1599 & P0) & P0" "ZEROLESSONE"; pushnode 19 " ( a1 * One < a1 + Zero & P1597 & P1589 & P1587 & P0) & P0 -> (( Zero < One & a1 * One < a1 + Zero) & P1600 & P1599 & P0) & P0" 2; pushnode 18 "(( Zero < One & a1 * One < a1 + Zero -> [ a1 * One] * One < [a1 + Zero] * One) & P1599 & P0) & (a1 * One < a1 + Zero & P1597 & P1589 & P1587 & P0) & P0 -> P0" 2; pushreference 17 "P0 -> (( Zero < One & a1 * One < a1 + Zero -> [a1 * One] * One < [a1 + Zero] * One) & P1599 & P0) & P0" "MTIMES"; pushnode 15 " ( a1 * One < a1 + Zero & P1597 & P1589 & P1587 & P0) & P0 -> P0" 2; pushnode 5 "( (a1 * One < a1 + Zero v a1 + Zero < a1 * One) & P1589 & P1587 & P0) & P0 -> P0" 2; pushreference 9 "P0 -> (Real(a1 * One) & P1591 & P0) & P0" "RTIMES"; pushreference 13 "P0 -> (Real(a1 + Zero) & P1594 & P0) & P0" "RPLUS"; pushnode 14 "( a1 * One = a1 + Zero & P1596 & P1593 & P1590 & P1588 & P1587 & P1592 & P1595 & P0) & (a1 * One + Zero = a1 * One & P1592 & P0) & ([a1 + Zero] + Zero = a1 + Zero & P1595 & P0) & P0 -> (a1 * One = a1 + Zero & P1586 & P0) & P0" 0; pushnode 12 "([ a1 + Zero] + Zero = a1 + Zero & P1595 & P0) & (a1 * One = [a1 + Zero] + Zero & P1593 & P1590 & P1588 & P1587 & P1592 & P0) & (a1 * One + Zero = a1 * One & P1592 & P0) & P0 -> ( a1 * One = a1 + Zero & P1586 & P0) & P0" 1; pushreference 11 " (Real(a1 + Zero) & P1594 & P0) & P0 -> ([a1 + Zero] + Zero = a1 + Zero & P1595 & P0) & P0" "IPLUSa"; pushnode 10 " ( a1 * One + Zero = a1 * One & P1592 & P0) & (a1 * One = [a1 + Zero] + Zero & P1593 & P1590 & P1588 & P1587 & P1592 & P0) & P0 -> ( a1 * One = a1 + Zero & P1586 & P0) & P0" 3; pushnode 8 " (a1 * One + Zero = a1 * One & P1592 & P0) & ( a1 * One + Zero = [a1 + Zero] + Zero & P1590 & P1588 & P1587 & P0) & P0 -> ( a1 * One = a1 + Zero & P1586 & P0) & P0" 1; pushreference 7 " (Real(a1 * One) & P1591 & P0) & P0 -> ( a1 * One + Zero = a1 * One & P1592 & P0) & P0" "IPLUSa"; pushnode 6 " ( a1 * One + Zero = [a1 + Zero] + Zero & P1590 & P1588 & P1587 & P0) & P0 -> ( a1 * One = a1 + Zero & P1586 & P0) & P0" 3; pushnode 4 "( a1 * One Equal a1 + Zero & P1588 & P1587 & P0) & P0 -> ( a1 * One = a1 + Zero & P1586 & P0) & P0" 1; pushnode 3 "( ( a1 * One Equal a1 + Zero v a1 * One < a1 + Zero v a1 + Zero < a1 * One) & P1587 & P0) & P0 -> ( a1 * One = a1 + Zero & P1586 & P0) & P0" 2; pushreference 2 "P0 -> ( ( a1 * One Equal a1 + Zero v a1 * One < a1 + Zero v a1 + Zero < a1 * One) & P1587 & P0) & P0" "TRI"; pushnode 1 " P0 -> (a1 * One = a1 + Zero & P1586 & P0) & P0" 2; THEOREMS:=("TYPECONVERT",(termtosequent(parseprop("P0 -> ( a1 * One = a1 + Zero & P1586 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "TYPECONVERT"; pushnode 21 " ( a1 + Zero < a2 + Zero & P1650 & P1648 & P1646 & P1644 & P1642 & P1640 & P1643 & P1645 & P1647 & P1649 & P0) & ( [a1 + a3] + Minus(a3) = a1 + a3 + Minus(a3) & P1643 & P0) & ( [a2 + a3] + Minus(a3) = a2 + a3 + Minus(a3) & P1645 & P0) & (a3 + Minus(a3) = Zero & P1647 & P0) & ( a3 + Minus(a3) = Zero & P1649 & P0) & P0 -> (a1 + Zero < a2 + Zero & P1651 & P0) & P0" 0; pushnode 20 "(a1 < a2 & P1652 & P0) & P0 -> (a1 < a2 & P1639 & P1637 & P0) & P0" 0; pushreference 19 "(a1 + Zero < a2 + Zero & P1651 & P0) & P0 -> ( a1 < a2 & P1652 & P0) & P0" "LESSTYPEa"; pushnode 18 "( a3 + Minus(a3) = Zero & P1649 & P0) & ( a1 + Zero < a2 + Zero & P1650 & P1648 & P1646 & P1644 & P1642 & P1640 & P1643 & P1645 & P1647 & P1649 & P0) & ([a1 + a3] + Minus(a3) = a1 + a3 + Minus(a3) & P1643 & P0) & ( [a2 + a3] + Minus(a3) = a2 + a3 + Minus(a3) & P1645 & P0) & (a3 + Minus(a3) = Zero & P1647 & P0) & P0 -> ( a1 < a2 & P1639 & P1637 & P0) & P0" 3; pushnode 17 " ( a3 + Minus(a3) = Zero & P1649 & P0) & ( a1 + Zero < a2 + a3 + Minus(a3) & P1648 & P1646 & P1644 & P1642 & P1640 & P1643 & P1645 & P1647 & P0) & ([ a1 + a3] + Minus(a3) = a1 + a3 + Minus(a3) & P1643 & P0) & ([a2 + a3] + Minus(a3) = a2 + a3 + Minus(a3) & P1645 & P0) & ( a3 + Minus(a3) = Zero & P1647 & P0) & P0 -> (a1 < a2 & P1639 & P1637 & P0) & P0" 1; pushreference 16 "P0 -> ( a3 + Minus(a3) = Zero & P1649 & P0) & P0" "MINUS"; pushnode 15 "( a3 + Minus(a3) = Zero & P1647 & P0) & ( a1 + Zero < a2 + a3 + Minus(a3) & P1648 & P1646 & P1644 & P1642 & P1640 & P1643 & P1645 & P1647 & P0) & ([ a1 + a3] + Minus(a3) = a1 + a3 + Minus(a3) & P1643 & P0) & ([a2 + a3] + Minus(a3) = a2 + a3 + Minus(a3) & P1645 & P0) & P0 -> ( a1 < a2 & P1639 & P1637 & P0) & P0" 2; pushnode 14 "( a3 + Minus(a3) = Zero & P1647 & P0) & ( a1 + a3 + Minus(a3) < a2 + a3 + Minus(a3) & P1646 & P1644 & P1642 & P1640 & P1643 & P1645 & P0) & ([ a1 + a3] + Minus(a3) = a1 + a3 + Minus(a3) & P1643 & P0) & ([a2 + a3] + Minus(a3) = a2 + a3 + Minus(a3) & P1645 & P0) & P0 -> ( a1 < a2 & P1639 & P1637 & P0) & P0" 1; pushreference 13 "P0 -> ( a3 + Minus(a3) = Zero & P1647 & P0) & P0" "MINUS"; pushnode 12 "( [a2 + a3] + Minus(a3) = a2 + a3 + Minus(a3) & P1645 & P0) & ( a1 + a3 + Minus(a3) < a2 + a3 + Minus(a3) & P1646 & P1644 & P1642 & P1640 & P1643 & P1645 & P0) & ([ a1 + a3] + Minus(a3) = a1 + a3 + Minus(a3) & P1643 & P0) & P0 -> (a1 < a2 & P1639 & P1637 & P0) & P0" 2; pushnode 11 "([ a2 + a3] + Minus(a3) = a2 + a3 + Minus(a3) & P1645 & P0) & (a1 + a3 + Minus(a3) < [a2 + a3] + Minus(a3) & P1644 & P1642 & P1640 & P1643 & P0) & ([a1 + a3] + Minus(a3) = a1 + a3 + Minus(a3) & P1643 & P0) & P0 -> (a1 < a2 & P1639 & P1637 & P0) & P0" 1; pushreference 10 "P0 -> ( [a2 + a3] + Minus(a3) = a2 + a3 + Minus(a3) & P1645 & P0) & P0" "APLUS"; pushnode 9 "([ a1 + a3] + Minus(a3) = a1 + a3 + Minus(a3) & P1643 & P0) & (a1 + a3 + Minus(a3) < [a2 + a3] + Minus(a3) & P1644 & P1642 & P1640 & P1643 & P0) & P0 -> (a1 < a2 & P1639 & P1637 & P0) & P0" 2; pushnode 8 "( [a1 + a3] + Minus(a3) = a1 + a3 + Minus(a3) & P1643 & P0) & ( [a1 + a3] + Minus(a3) < [a2 + a3] + Minus(a3) & P1642 & P1640 & P0) & P0 -> (a1 < a2 & P1639 & P1637 & P0) & P0" 1; pushreference 7 "P0 -> ( [a1 + a3] + Minus(a3) = a1 + a3 + Minus(a3) & P1643 & P0) & P0" "APLUS"; pushnode 6 " ([ a1 + a3] + Minus(a3) < [a2 + a3] + Minus(a3) & P1642 & P1640 & P0) & P0 -> ( a1 < a2 & P1639 & P1637 & P0) & P0" 2; pushnode 5 "( a1 + a3 < a2 + a3 & P1638 & P1637 & P0) & P0 -> ( a1 + a3 < a2 + a3 & P1641 & P1640 & P0) & P0" 0; pushnode 4 "(( a1 + a3 < a2 + a3 -> [a1 + a3] + Minus(a3) < [ a2 + a3] + Minus(a3)) & P1640 & P0) & (a1 + a3 < a2 + a3 & P1638 & P1637 & P0) & P0 -> (a1 < a2 & P1639 & P1637 & P0) & P0" 2; pushreference 3 "P0 -> (( a1 + a3 < a2 + a3 -> [a1 + a3] + Minus(a3) < [ a2 + a3] + Minus(a3)) & P1640 & P0) & P0" "MPLUS"; pushnode 2 "( a1 + a3 < a2 + a3 & P1638 & P1637 & P0) & P0 -> (a1 < a2 & P1639 & P1637 & P0) & P0" 2; THEOREMS:=("MPLUSCONV",(termtosequent(parseprop("(a1 + a3 < a2 + a3 & P1638 & P1637 & P0) & P0 -> ( a1 < a2 & P1639 & P1637 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "MPLUSCONV"; pushreference 27 "(Zero < One & P1674 & P0) & (One < Zero & P1673 & P1671 & P1663 & P1661 & P1670 & P1668 & P1666 & P1669 & P1672 & P0) & P0 -> P0" "NOTBOTH"; pushreference 26 "P0 -> (Zero < One & P1674 & P0) & P0" "ZEROLESSONE"; pushnode 25 "( One < Zero & P1673 & P1671 & P1663 & P1661 & P1670 & P1668 & P1666 & P1669 & P1672 & P0) & P0 -> P0" 2; pushnode 24 " ( Zero * a1 = Zero & P1672 & P0) & (One < Zero * a1 & P1671 & P1663 & P1661 & P1670 & P1668 & P1666 & P1669 & P0) & P0 -> P0" 1; pushreference 23 "P0 -> ( Zero * a1 = Zero & P1672 & P0) & P0" "MZERO2"; pushnode 22 " (One < Zero * a1 & P1671 & P1663 & P1661 & P1670 & P1668 & P1666 & P1669 & P0) & P0 -> P0" 2; pushnode 21 " (Inv(a1) * a1 = One & P1670 & P1668 & P1666 & P1669 & P0) & ( Inv(a1) * a1 < Zero * a1 & P1663 & P1661 & P0) & P0 -> P0" 1; pushnode 20 "(a1 * Inv(a1) = Inv(a1) * a1 & P1669 & P0) & ( a1 * Inv(a1) = One & P1668 & P1666 & P0) & ( Inv(a1) * a1 < Zero * a1 & P1663 & P1661 & P0) & P0 -> P0" 1; pushreference 19 "P0 -> ( a1 * Inv(a1) = Inv(a1) * a1 & P1669 & P0) & P0" "CTIMES"; pushnode 18 "( a1 * Inv(a1) = One & P1668 & P1666 & P0) & (Inv(a1) * a1 < Zero * a1 & P1663 & P1661 & P0) & P0 -> P0" 2; pushreference 17 "(Zero < a1 & P1654 & P1653 & P0) & ( a1 Equal Zero & P1667 & P1666 & P0) & P0 -> P0" "NOTBOTH3"; pushnode 16 "( (a1 Equal Zero v a1 * Inv(a1) = One) & P1666 & P0) & ( Inv(a1) * a1 < Zero * a1 & P1663 & P1661 & P0) & (Zero < a1 & P1654 & P1653 & P0) & P0 -> P0" 2; pushreference 15 "P0 -> ((a1 Equal Zero v a1 * Inv(a1) = One) & P1666 & P0) & P0" "INV"; pushnode 12 "( Inv(a1) * a1 < Zero * a1 & P1663 & P1661 & P0) & ( Zero < a1 & P1654 & P1653 & P0) & P0 -> P0" 2; pushnode 14 " (Inv(a1) < Zero & P1660 & P1658 & P1656 & P0) & P0 -> ( Inv(a1) < Zero & P1665 & P1662 & P1661 & P0) & P0" 0; pushnode 13 "( Zero < a1 & P1654 & P1653 & P0) & P0 -> (Zero < a1 & P1664 & P1662 & P1661 & P0) & P0" 0; pushnode 11 "(Inv(a1) < Zero & P1660 & P1658 & P1656 & P0) & (Zero < a1 & P1654 & P1653 & P0) & P0 -> (( Zero < a1 & Inv(a1) < Zero) & P1662 & P1661 & P0) & P0" 2; pushnode 10 "( ( Zero < a1 & Inv(a1) < Zero -> Inv(a1) * a1 < Zero * a1) & P1661 & P0) & ( Inv(a1) < Zero & P1660 & P1658 & P1656 & P0) & (Zero < a1 & P1654 & P1653 & P0) & P0 -> P0" 2; pushreference 9 "P0 -> (( Zero < a1 & Inv(a1) < Zero -> Inv(a1) * a1 < Zero * a1) & P1661 & P0) & P0" "MTIMES"; pushnode 8 " ( Inv(a1) < Zero & P1660 & P1658 & P1656 & P0) & (Zero < a1 & P1654 & P1653 & P0) & P0 -> P0" 2; pushnode 7 " (Zero < Inv(a1) & P1659 & P1658 & P1656 & P0) & P0 -> ( Zero < Inv(a1) & P1655 & P1653 & P0) & P0" 0; pushnode 6 " ((Zero < Inv(a1) v Inv(a1) < Zero) & P1658 & P1656 & P0) & (Zero < a1 & P1654 & P1653 & P0) & P0 -> ( Zero < Inv(a1) & P1655 & P1653 & P0) & P0" 2; pushreference 36 "P0 -> (Real(Inv(a1)) & P1680 & P0) & P0" "RINV"; pushreference 35 "P0 -> (Real(Zero) & P1679 & P0) & P0" "RZERO"; pushnode 34 " (Zero Equal Inv(a1) & P1657 & P1656 & P0) & P0 -> ( Zero Equal Inv(a1) & P1678 & P0) & P0" 0; pushnode 46 "(One < One & P1687 & P1686 & P1685 & P1683 & P1677 & P1675 & P1681 & P1684 & P0) & ( Zero = One & P1685 & P1683 & P1677 & P1675 & P1681 & P1684 & P0) & P0 -> (One < One & P1689 & P1688 & P0) & P0" 0; pushnode 45 "(~One < One & P1688 & P0) & (Zero = One & P1685 & P1683 & P1677 & P1675 & P1681 & P1684 & P0) & ( One < One & P1687 & P1686 & P1685 & P1683 & P1677 & P1675 & P1681 & P1684 & P0) & P0 -> P0" 1; pushreference 44 "P0 -> ( ~One < One & P1688 & P0) & P0" "IRR"; pushnode 43 " (Zero = One & P1685 & P1683 & P1677 & P1675 & P1681 & P1684 & P0) & (One < One & P1687 & P1686 & P1685 & P1683 & P1677 & P1675 & P1681 & P1684 & P0) & P0 -> P0" 2; pushnode 42 "(Zero = One & P1685 & P1683 & P1677 & P1675 & P1681 & P1684 & P0) & ( Zero < One & P1686 & P0) & P0 -> P0" 1; pushreference 41 "P0 -> (Zero < One & P1686 & P0) & P0" "ZEROLESSONE"; pushnode 40 " (Zero = One & P1685 & P1683 & P1677 & P1675 & P1681 & P1684 & P0) & P0 -> P0" 2; pushnode 39 "(a1 * Zero = Zero & P1684 & P0) & ( a1 * Zero = One & P1683 & P1677 & P1675 & P1681 & P0) & P0 -> P0" 1; pushreference 38 "P0 -> ( a1 * Zero = Zero & P1684 & P0) & P0" "MZERO"; pushnode 37 "(a1 * Zero = One & P1683 & P1677 & P1675 & P1681 & P0) & P0 -> P0" 2; pushnode 33 "(Zero = Inv(a1) & P1681 & P0) & ( a1 * Inv(a1) = One & P1677 & P1675 & P0) & P0 -> P0" 1; pushreference 32 "( Zero Equal Inv(a1) & P1678 & P0) & ( Real(Zero) & P1679 & P0) & ( Real(Inv(a1)) & P1680 & P0) & P0 -> ( Zero = Inv(a1) & P1681 & P0) & P0" "EQUALITY"; pushnode 31 " (Zero Equal Inv(a1) & P1657 & P1656 & P0) & (a1 * Inv(a1) = One & P1677 & P1675 & P0) & P0 -> P0" 5; pushreference 30 "(Zero < a1 & P1654 & P1653 & P0) & ( a1 Equal Zero & P1676 & P1675 & P0) & P0 -> P0" "NOTBOTH3"; pushnode 29 "( (a1 Equal Zero v a1 * Inv(a1) = One) & P1675 & P0) & ( Zero Equal Inv(a1) & P1657 & P1656 & P0) & ( Zero < a1 & P1654 & P1653 & P0) & P0 -> P0" 2; pushreference 28 "P0 -> (( a1 Equal Zero v a1 * Inv(a1) = One) & P1675 & P0) & P0" "INV"; pushnode 5 " (Zero Equal Inv(a1) & P1657 & P1656 & P0) & (Zero < a1 & P1654 & P1653 & P0) & P0 -> P0" 2; pushnode 4 "(( Zero Equal Inv(a1) v Zero < Inv(a1) v Inv(a1) < Zero) & P1656 & P0) & ( Zero < a1 & P1654 & P1653 & P0) & P0 -> (Zero < Inv(a1) & P1655 & P1653 & P0) & P0" 2; pushreference 3 "P0 -> (( Zero Equal Inv(a1) v Zero < Inv(a1) v Inv(a1) < Zero) & P1656 & P0) & P0" "TRI"; pushnode 2 " (Zero < a1 & P1654 & P1653 & P0) & P0 -> ( Zero < Inv(a1) & P1655 & P1653 & P0) & P0" 2; THEOREMS:=("POSINV",(termtosequent(parseprop(" (Zero < a1 & P1654 & P1653 & P0) & P0 -> ( Zero < Inv(a1) & P1655 & P1653 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "POSINV"; pushnode 25 "( [a1 + Minus(One)] + Zero < a1 + Zero & P1707 & P1705 & P1703 & P1701 & P1698 & P1696 & P1694 & P1697 & P1699 & P1702 & P1704 & P1706 & P0) & ( a1 + Minus(One) = Minus(One) + a1 & P1697 & P0) & (One + Minus(One) = Zero & P1702 & P0) & (Zero + a1 + Minus(One) = [a1 + Minus(One)] + Zero & P1704 & P0) & (Zero + a1 = a1 + Zero & P1706 & P0) & P0 -> ([ a1 + Minus(One)] + Zero < a1 + Zero & P1708 & P0) & P0" 0; pushnode 24 "( a1 + Minus(One) < a1 & P1709 & P0) & P0 -> ( a1 + Minus(One) < a1 & P1692 & P0) & P0" 0; pushreference 23 "( [a1 + Minus(One)] + Zero < a1 + Zero & P1708 & P0) & P0 -> ( a1 + Minus(One) < a1 & P1709 & P0) & P0" "LESSTYPEa"; pushnode 22 " ( Zero + a1 = a1 + Zero & P1706 & P0) & ([ a1 + Minus(One)] + Zero < a1 + Zero & P1707 & P1705 & P1703 & P1701 & P1698 & P1696 & P1694 & P1697 & P1699 & P1702 & P1704 & P1706 & P0) & (a1 + Minus(One) = Minus(One) + a1 & P1697 & P0) & (One + Minus(One) = Zero & P1702 & P0) & (Zero + a1 + Minus(One) = [a1 + Minus(One)] + Zero & P1704 & P0) & P0 -> (a1 + Minus(One) < a1 & P1692 & P0) & P0" 3; pushnode 21 " ( Zero + a1 = a1 + Zero & P1706 & P0) & ([ a1 + Minus(One)] + Zero < Zero + a1 & P1705 & P1703 & P1701 & P1698 & P1696 & P1694 & P1697 & P1699 & P1702 & P1704 & P0) & (a1 + Minus(One) = Minus(One) + a1 & P1697 & P0) & (One + Minus(One) = Zero & P1702 & P0) & (Zero + a1 + Minus(One) = [a1 + Minus(One)] + Zero & P1704 & P0) & P0 -> (a1 + Minus(One) < a1 & P1692 & P0) & P0" 1; pushreference 20 "P0 -> ( Zero + a1 = a1 + Zero & P1706 & P0) & P0" "CPLUS"; pushnode 19 "(Zero + a1 + Minus(One) = [a1 + Minus(One)] + Zero & P1704 & P0) & ([a1 + Minus(One)] + Zero < Zero + a1 & P1705 & P1703 & P1701 & P1698 & P1696 & P1694 & P1697 & P1699 & P1702 & P1704 & P0) & ( a1 + Minus(One) = Minus(One) + a1 & P1697 & P0) & (One + Minus(One) = Zero & P1702 & P0) & P0 -> (a1 + Minus(One) < a1 & P1692 & P0) & P0" 2; pushnode 18 "( Zero + a1 + Minus(One) = [a1 + Minus(One)] + Zero & P1704 & P0) & ( Zero + a1 + Minus(One) < Zero + a1 & P1703 & P1701 & P1698 & P1696 & P1694 & P1697 & P1699 & P1702 & P0) & ( a1 + Minus(One) = Minus(One) + a1 & P1697 & P0) & (One + Minus(One) = Zero & P1702 & P0) & P0 -> (a1 + Minus(One) < a1 & P1692 & P0) & P0" 1; pushreference 17 " P0 -> ( Zero + a1 + Minus(One) = [a1 + Minus(One)] + Zero & P1704 & P0) & P0" "CPLUS"; pushnode 16 "( One + Minus(One) = Zero & P1702 & P0) & ( Zero + a1 + Minus(One) < Zero + a1 & P1703 & P1701 & P1698 & P1696 & P1694 & P1697 & P1699 & P1702 & P0) & ( a1 + Minus(One) = Minus(One) + a1 & P1697 & P0) & P0 -> (a1 + Minus(One) < a1 & P1692 & P0) & P0" 2; pushnode 15 "( One + Minus(One) = Zero & P1702 & P0) & (Zero + a1 + Minus(One) < [One + Minus(One)] + a1 & P1701 & P1698 & P1696 & P1694 & P1697 & P1699 & P0) & ( a1 + Minus(One) = Minus(One) + a1 & P1697 & P0) & P0 -> (a1 + Minus(One) < a1 & P1692 & P0) & P0" 1; pushreference 14 " P0 -> (One + Minus(One) = Zero & P1702 & P0) & P0" "MINUS"; pushnode 13 "( Zero + a1 + Minus(One) < [One + Minus(One)] + a1 & P1701 & P1698 & P1696 & P1694 & P1697 & P1699 & P0) & (a1 + Minus(One) = Minus(One) + a1 & P1697 & P0) & P0 -> (a1 + Minus(One) < a1 & P1692 & P0) & P0" 2; pushnode 12 "([ One + Minus(One)] + a1 = One + Minus(One) + a1 & P1699 & P0) & (Zero + a1 + Minus(One) < One + Minus(One) + a1 & P1698 & P1696 & P1694 & P1697 & P0) & ( a1 + Minus(One) = Minus(One) + a1 & P1697 & P0) & P0 -> (a1 + Minus(One) < a1 & P1692 & P0) & P0" 1; pushreference 11 " P0 -> ( [One + Minus(One)] + a1 = One + Minus(One) + a1 & P1699 & P0) & P0" "APLUS"; pushnode 10 " ( a1 + Minus(One) = Minus(One) + a1 & P1697 & P0) & (Zero + a1 + Minus(One) < One + Minus(One) + a1 & P1698 & P1696 & P1694 & P1697 & P0) & P0 -> ( a1 + Minus(One) < a1 & P1692 & P0) & P0" 2; pushnode 9 " ( a1 + Minus(One) = Minus(One) + a1 & P1697 & P0) & (Zero + a1 + Minus(One) < One + a1 + Minus(One) & P1696 & P1694 & P0) & P0 -> ( a1 + Minus(One) < a1 & P1692 & P0) & P0" 1; pushreference 8 "P0 -> (a1 + Minus(One) = Minus(One) + a1 & P1697 & P0) & P0" "CPLUS"; pushnode 7 " ( Zero + a1 + Minus(One) < One + a1 + Minus(One) & P1696 & P1694 & P0) & P0 -> ( a1 + Minus(One) < a1 & P1692 & P0) & P0" 2; pushnode 6 "( Zero < One & P1693 & P0) & P0 -> (Zero < One & P1695 & P1694 & P0) & P0" 0; pushnode 5 "(( Zero < One -> Zero + a1 + Minus(One) < One + a1 + Minus(One)) & P1694 & P0) & ( Zero < One & P1693 & P0) & P0 -> ( a1 + Minus(One) < a1 & P1692 & P0) & P0" 2; pushreference 4 "P0 -> ( (Zero < One -> Zero + a1 + Minus(One) < One + a1 + Minus(One)) & P1694 & P0) & P0" "MPLUS"; pushnode 3 " (Zero < One & P1693 & P0) & P0 -> ( a1 + Minus(One) < a1 & P1692 & P0) & P0" 2; pushreference 2 "P0 -> (Zero < One & P1693 & P0) & P0" "ZEROLESSONE"; pushnode 1 "P0 -> ( a1 + Minus(One) < a1 & P1692 & P0) & P0" 2; THEOREMS:=("SomethingLess",(termtosequent(parseprop("P0 -> ( a1 + Minus(One) < a1 & P1692 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "SomethingLess"; pushreference 13 "P0 -> (Real(a1 + One) & P1725 & P0) & P0" "RPLUS"; pushreference 17 "( a1 + Zero < [a1 + One] + Zero & P1730 & P1728 & P1724 & P1722 & P1720 & P1723 & P1726 & P1729 & P0) & P0 -> (a1 < a1 + One & P1718 & P0) & P0" "LESSTYPEa"; pushnode 16 "( Zero + a1 = a1 + Zero & P1729 & P0) & ( Zero + a1 < [a1 + One] + Zero & P1728 & P1724 & P1722 & P1720 & P1723 & P1726 & P0) & ( One + a1 = a1 + One & P1723 & P0) & P0 -> ( a1 < a1 + One & P1718 & P0) & P0" 1; pushreference 15 "P0 -> ( Zero + a1 = a1 + Zero & P1729 & P0) & P0" "CPLUS"; pushnode 14 "(Zero + a1 < [a1 + One] + Zero & P1728 & P1724 & P1722 & P1720 & P1723 & P1726 & P0) & ( One + a1 = a1 + One & P1723 & P0) & P0 -> ( a1 < a1 + One & P1718 & P0) & P0" 2; pushnode 12 " ([a1 + One] + Zero = a1 + One & P1726 & P0) & ( Zero + a1 < a1 + One & P1724 & P1722 & P1720 & P1723 & P0) & ( One + a1 = a1 + One & P1723 & P0) & P0 -> ( a1 < a1 + One & P1718 & P0) & P0" 1; pushreference 11 " (Real(a1 + One) & P1725 & P0) & P0 -> ( [a1 + One] + Zero = a1 + One & P1726 & P0) & P0" "IPLUSa"; pushnode 10 "( One + a1 = a1 + One & P1723 & P0) & ( Zero + a1 < a1 + One & P1724 & P1722 & P1720 & P1723 & P0) & P0 -> ( a1 < a1 + One & P1718 & P0) & P0" 3; pushnode 9 " ( One + a1 = a1 + One & P1723 & P0) & ( Zero + a1 < One + a1 & P1722 & P1720 & P0) & P0 -> (a1 < a1 + One & P1718 & P0) & P0" 1; pushreference 8 "P0 -> ( One + a1 = a1 + One & P1723 & P0) & P0" "CPLUS"; pushnode 7 "( Zero + a1 < One + a1 & P1722 & P1720 & P0) & P0 -> (a1 < a1 + One & P1718 & P0) & P0" 2; pushnode 6 " (Zero < One & P1719 & P0) & P0 -> ( Zero < One & P1721 & P1720 & P0) & P0" 0; pushnode 5 "((Zero < One -> Zero + a1 < One + a1) & P1720 & P0) & ( Zero < One & P1719 & P0) & P0 -> ( a1 < a1 + One & P1718 & P0) & P0" 2; pushreference 4 "P0 -> ((Zero < One -> Zero + a1 < One + a1) & P1720 & P0) & P0" "MPLUS"; pushnode 3 " (Zero < One & P1719 & P0) & P0 -> (a1 < a1 + One & P1718 & P0) & P0" 2; pushreference 2 "P0 -> (Zero < One & P1719 & P0) & P0" "ZEROLESSONE"; pushnode 1 "P0 -> (a1 < a1 + One & P1718 & P0) & P0" 2; THEOREMS:=("SOMETHINGBIGGER",(termtosequent(parseprop("P0 -> (a1 < a1 + One & P1718 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "SOMETHINGBIGGER"; pushnode 5 "P0 -> ( One + One = One + One & P1735 & P1732 & P0) & P0" 0; pushnode 3 "P0 -> (One + One = Two & P1732 & P0) & P0" 1; pushreference 4 "P0 -> (Real(One + One) & P1734 & P1732 & P1731 & P0) & P0" "RPLUS"; pushnode 2 "( One + One = Two & P1732 & P0) & P0 -> ( Real(Two) & P1731 & P0) & P0" 1; pushnode 1 "P0 -> (Real(Two) & P1731 & P0) & P0" 2; THEOREMS:=("RTWO",(termtosequent(parseprop("P0 -> (Real(Two) & P1731 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "RTWO"; pushnode 5 "P0 -> (Inv(Two) = Inv(Two) & P1740 & P1737 & P0) & P0" 0; pushnode 3 "P0 -> ( Half = Inv(Two) & P1737 & P0) & P0" 1; pushreference 4 "P0 -> (Real(Inv(Two)) & P1739 & P1737 & P1736 & P0) & P0" "RINV"; pushnode 2 " (Half = Inv(Two) & P1737 & P0) & P0 -> (Real(Half) & P1736 & P0) & P0" 1; pushnode 1 "P0 -> (Real(Half) & P1736 & P0) & P0" 2; THEOREMS:=("RHALF",(termtosequent(parseprop("P0 -> (Real(Half) & P1736 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "RHALF"; pushnode 17 "P0 -> ( One + One = One + One & P1753 & P1750 & P0) & P0" 0; pushnode 15 "P0 -> (One + One = Two & P1750 & P0) & P0" 1; pushnode 16 " (Zero < One + One & P1747 & P1745 & P0) & P0 -> (Zero < One + One & P1752 & P1750 & P1741 & P0) & P0" 0; pushnode 14 "(One + One = Two & P1750 & P0) & (Zero < One + One & P1747 & P1745 & P0) & P0 -> (Zero < Two & P1741 & P0) & P0" 1; pushnode 11 " (Zero < One + One & P1747 & P1745 & P0) & P0 -> ( Zero < Two & P1741 & P0) & P0" 2; pushnode 13 " (One < One + One & P1744 & P0) & P0 -> (One < One + One & P1749 & P1746 & P1745 & P0) & P0" 0; pushnode 12 " (Zero < One & P1742 & P0) & P0 -> (Zero < One & P1748 & P1746 & P1745 & P0) & P0" 0; pushnode 10 " (One < One + One & P1744 & P0) & (Zero < One & P1742 & P0) & P0 -> (( Zero < One & One < One + One) & P1746 & P1745 & P0) & P0" 2; pushnode 9 "(( Zero < One & One < One + One -> Zero < One + One) & P1745 & P0) & ( One < One + One & P1744 & P0) & ( Zero < One & P1742 & P0) & P0 -> (Zero < Two & P1741 & P0) & P0" 2; pushreference 8 "P0 -> ((Zero < One & One < One + One -> Zero < One + One) & P1745 & P0) & P0" "TRANS"; pushnode 7 "(One < One + One & P1744 & P0) & ( Zero < One & P1742 & P0) & P0 -> (Zero < Two & P1741 & P0) & P0" 2; pushreference 6 "P0 -> (One < One + One & P1744 & P0) & P0" "SOMETHINGBIGGER"; pushnode 3 " (Zero < One & P1742 & P0) & P0 -> (Zero < Two & P1741 & P0) & P0" 2; pushreference 2 "P0 -> (Zero < One & P1742 & P0) & P0" "ZEROLESSONE"; pushnode 1 "P0 -> (Zero < Two & P1741 & P0) & P0" 2; THEOREMS:=("TWOPOS",(termtosequent(parseprop("P0 -> (Zero < Two & P1741 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "TWOPOS"; pushnode 6 " (Zero < Two & P1755 & P0) & P0 -> (Zero < Two & P1756 & P0) & P0" 0; pushnode 10 "P0 -> (Inv(Two) = Inv(Two) & P1760 & P1758 & P0) & P0" 0; pushnode 8 "P0 -> ( Inv(Two) = Half & P1758 & P0) & P0" 1; pushnode 9 "(Zero < Half & P1759 & P1757 & P1758 & P0) & (Inv(Two) = Half & P1758 & P0) & P0 -> ( Zero < Half & P1754 & P0) & P0" 0; pushnode 7 "(Inv(Two) = Half & P1758 & P0) & ( Zero < Inv(Two) & P1757 & P0) & P0 -> (Zero < Half & P1754 & P0) & P0" 1; pushnode 5 " (Zero < Inv(Two) & P1757 & P0) & P0 -> (Zero < Half & P1754 & P0) & P0" 2; pushreference 4 " (Zero < Two & P1756 & P0) & P0 -> (Zero < Inv(Two) & P1757 & P0) & P0" "POSINV"; pushnode 3 " (Zero < Two & P1755 & P0) & P0 -> (Zero < Half & P1754 & P0) & P0" 3; pushreference 2 "P0 -> (Zero < Two & P1755 & P0) & P0" "TWOPOS"; pushnode 1 "P0 -> (Zero < Half & P1754 & P0) & P0" 2; THEOREMS:=("HALFPOS",(termtosequent(parseprop("P0 -> (Zero < Half & P1754 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "HALFPOS"; pushnode 27 "P0 -> ( One + One = One + One & P1785 & P1771 & P0) & P0" 0; pushnode 12 "P0 -> (One + One = Two & P1771 & P0) & P0" 1; pushnode 26 "P0 -> (Inv(Two) = Inv(Two) & P1784 & P1774 & P0) & P0" 0; pushnode 15 "P0 -> ( Half = Inv(Two) & P1774 & P0) & P0" 1; pushnode 23 "( Two * Inv(Two) = One & P1782 & P1780 & P0) & P0 -> ( Two * Inv(Two) = One & P1779 & P1777 & P1776 & P1774 & P1773 & P1771 & P1769 & P1767 & P1766 & P1764 & P1762 & P1761 & P0) & P0" 0; pushreference 25 "( Zero < Two & P1783 & P0) & ( Two Equal Zero & P1781 & P1780 & P0) & P0 -> P0" "NOTBOTH3"; pushreference 24 "P0 -> (Zero < Two & P1783 & P0) & P0" "TWOPOS"; pushnode 22 " (Two Equal Zero & P1781 & P1780 & P0) & P0 -> P0" 2; pushnode 21 "((Two Equal Zero v Two * Inv(Two) = One) & P1780 & P0) & P0 -> ( Two * Inv(Two) = One & P1779 & P1777 & P1776 & P1774 & P1773 & P1771 & P1769 & P1767 & P1766 & P1764 & P1762 & P1761 & P0) & P0" 2; pushreference 20 " P0 -> ((Two Equal Zero v Two * Inv(Two) = One) & P1780 & P0) & P0" "INV"; pushnode 19 "P0 -> ( Two * Inv(Two) = One & P1779 & P1777 & P1776 & P1774 & P1773 & P1771 & P1769 & P1767 & P1766 & P1764 & P1762 & P1761 & P0) & P0" 2; pushnode 18 "( Inv(Two) * Two = Two * Inv(Two) & P1777 & P0) & P0 -> ( Inv(Two) * Two = One & P1776 & P1774 & P1773 & P1771 & P1769 & P1767 & P1766 & P1764 & P1762 & P1761 & P0) & P0" 1; pushreference 17 "P0 -> ( Inv(Two) * Two = Two * Inv(Two) & P1777 & P0) & P0" "CTIMES"; pushnode 16 " P0 -> (Inv(Two) * Two = One & P1776 & P1774 & P1773 & P1771 & P1769 & P1767 & P1766 & P1764 & P1762 & P1761 & P0) & P0" 2; pushnode 14 " (Half = Inv(Two) & P1774 & P0) & P0 -> (Half * Two = One & P1773 & P1771 & P1769 & P1767 & P1766 & P1764 & P1762 & P1761 & P0) & P0" 1; pushnode 13 "P0 -> ( Half * Two = One & P1773 & P1771 & P1769 & P1767 & P1766 & P1764 & P1762 & P1761 & P0) & P0" 2; pushnode 11 "( One + One = Two & P1771 & P0) & P0 -> ( Half * [One + One] = One & P1769 & P1767 & P1766 & P1764 & P1762 & P1761 & P0) & P0" 1; pushnode 9 "P0 -> ( Half * [One + One] = One & P1769 & P1767 & P1766 & P1764 & P1762 & P1761 & P0) & P0" 2; pushnode 8 " (Half * [One + One] = Half * One + Half * One & P1767 & P0) & P0 -> (Half * One + Half * One = One & P1766 & P1764 & P1762 & P1761 & P0) & P0" 1; pushreference 7 " P0 -> ( Half * [One + One] = Half * One + Half * One & P1767 & P0) & P0" "DIST"; pushnode 6 " P0 -> ( Half * One + Half * One = One & P1766 & P1764 & P1762 & P1761 & P0) & P0" 2; pushnode 5 " (Half * One = Half & P1764 & P1762 & P0) & P0 -> ( Half + Half = One & P1761 & P0) & P0" 1; pushreference 4 " P0 -> (Real(Half) & P1763 & P1762 & P0) & P0" "RHALF"; pushnode 3 "((Real(Half) -> Half * One = Half) & P1762 & P0) & P0 -> (Half + Half = One & P1761 & P0) & P0" 2; pushreference 2 "P0 -> (( Real(Half) -> Half * One = Half) & P1762 & P0) & P0" "ITIMES"; pushnode 1 "P0 -> (Half + Half = One & P1761 & P0) & P0" 2; THEOREMS:=("TWOHALVES",(termtosequent(parseprop("P0 -> (Half + Half = One & P1761 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "TWOHALVES"; pushnode 14 " (Zero < Half * a1 & P1797 & P1795 & P1791 & P1789 & P1794 & P1796 & P0) & (Zero * Half = Zero & P1794 & P0) & ( a1 * Half = Half * a1 & P1796 & P0) & P0 -> ( Zero < Half * a1 & P1788 & P1786 & P0) & P0" 0; pushnode 13 "( a1 * Half = Half * a1 & P1796 & P0) & (Zero < a1 * Half & P1795 & P1791 & P1789 & P1794 & P0) & ( Zero * Half = Zero & P1794 & P0) & P0 -> ( Zero < Half * a1 & P1788 & P1786 & P0) & P0" 1; pushreference 12 "P0 -> ( a1 * Half = Half * a1 & P1796 & P0) & P0" "CTIMES"; pushnode 11 " (Zero * Half = Zero & P1794 & P0) & (Zero < a1 * Half & P1795 & P1791 & P1789 & P1794 & P0) & P0 -> ( Zero < Half * a1 & P1788 & P1786 & P0) & P0" 2; pushnode 10 " (Zero * Half = Zero & P1794 & P0) & ( Zero * Half < a1 * Half & P1791 & P1789 & P0) & P0 -> ( Zero < Half * a1 & P1788 & P1786 & P0) & P0" 1; pushreference 9 "P0 -> ( Zero * Half = Zero & P1794 & P0) & P0" "MZERO2"; pushnode 6 "( Zero * Half < a1 * Half & P1791 & P1789 & P0) & P0 -> (Zero < Half * a1 & P1788 & P1786 & P0) & P0" 2; pushnode 8 "( Zero < a1 & P1787 & P1786 & P0) & P0 -> (Zero < a1 & P1793 & P1790 & P1789 & P0) & P0" 0; pushreference 7 "P0 -> (Zero < Half & P1792 & P1790 & P1789 & P0) & P0" "HALFPOS"; pushnode 5 " (Zero < a1 & P1787 & P1786 & P0) & P0 -> (( Zero < Half & Zero < a1) & P1790 & P1789 & P0) & P0" 2; pushnode 4 " ( ( Zero < Half & Zero < a1 -> Zero * Half < a1 * Half) & P1789 & P0) & (Zero < a1 & P1787 & P1786 & P0) & P0 -> ( Zero < Half * a1 & P1788 & P1786 & P0) & P0" 2; pushreference 3 "P0 -> (( Zero < Half & Zero < a1 -> Zero * Half < a1 * Half) & P1789 & P0) & P0" "MTIMES"; pushnode 2 " (Zero < a1 & P1787 & P1786 & P0) & P0 -> (Zero < Half * a1 & P1788 & P1786 & P0) & P0" 2; THEOREMS:=("MHALFPOS",(termtosequent(parseprop(" (Zero < a1 & P1787 & P1786 & P0) & P0 -> (Zero < Half * a1 & P1788 & P1786 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "MHALFPOS"; pushreference 5 " (Zero < a1 & P1801 & P1799 & P1798 & P0) & P0 -> (Zero < Half * a1 & P1803 & P0) & P0" "MHALFPOS"; pushreference 12 "P0 -> (Real(Half * a1) & P1807 & P0) & P0" "RTIMES"; pushnode 30 " (Half * a1 < a1 & P1822 & P1816 & P1814 & P1811 & P1806 & P1804 & P1810 & P1808 & P1809 & P1812 & P1815 & P1821 & P1819 & P1817 & P1820 & P0) & (Half * a1 + Zero = Zero + Half * a1 & P1809 & P0) & (Zero + Half * a1 = Half * a1 & P1810 & P1808 & P1809 & P0) & ( a1 * One = One * a1 & P1820 & P0) & ( Half + Half = One & P1815 & P0) & ( One * a1 = a1 & P1821 & P1819 & P1817 & P1820 & P0) & P0 -> (Half * a1 < a1 & P1800 & P1798 & P0) & P0" 0; pushnode 29 "( One * a1 = a1 & P1821 & P1819 & P1817 & P1820 & P0) & ( Half * a1 < One * a1 & P1816 & P1814 & P1811 & P1806 & P1804 & P1810 & P1808 & P1809 & P1812 & P1815 & P0) & (Half * a1 + Zero = Zero + Half * a1 & P1809 & P0) & (Zero + Half * a1 = Half * a1 & P1810 & P1808 & P1809 & P0) & ( a1 * One = One * a1 & P1820 & P0) & ( Half + Half = One & P1815 & P0) & P0 -> ( Half * a1 < a1 & P1800 & P1798 & P0) & P0" 1; pushnode 28 "( a1 * One = One * a1 & P1820 & P0) & ( a1 * One = a1 & P1819 & P1817 & P0) & ( Half + Half = One & P1815 & P0) & (Half * a1 < One * a1 & P1816 & P1814 & P1811 & P1806 & P1804 & P1810 & P1808 & P1809 & P1812 & P1815 & P0) & ( Half * a1 + Zero = Zero + Half * a1 & P1809 & P0) & (Zero + Half * a1 = Half * a1 & P1810 & P1808 & P1809 & P0) & P0 -> ( Half * a1 < a1 & P1800 & P1798 & P0) & P0" 1; pushreference 27 "P0 -> ( a1 * One = One * a1 & P1820 & P0) & P0" "CTIMES"; pushnode 26 " (a1 * One = a1 & P1819 & P1817 & P0) & (Half + Half = One & P1815 & P0) & ( Half * a1 < One * a1 & P1816 & P1814 & P1811 & P1806 & P1804 & P1810 & P1808 & P1809 & P1812 & P1815 & P0) & ( Half * a1 + Zero = Zero + Half * a1 & P1809 & P0) & (Zero + Half * a1 = Half * a1 & P1810 & P1808 & P1809 & P0) & P0 -> ( Half * a1 < a1 & P1800 & P1798 & P0) & P0" 2; pushnode 25 " (Real(a1) & P1802 & P1799 & P1798 & P0) & P0 -> (Real(a1) & P1818 & P1817 & P0) & P0" 0; pushnode 24 " (( Real(a1) -> a1 * One = a1) & P1817 & P0) & (Half + Half = One & P1815 & P0) & (Half * a1 < One * a1 & P1816 & P1814 & P1811 & P1806 & P1804 & P1810 & P1808 & P1809 & P1812 & P1815 & P0) & ( Real(a1) & P1802 & P1799 & P1798 & P0) & (Half * a1 + Zero = Zero + Half * a1 & P1809 & P0) & (Zero + Half * a1 = Half * a1 & P1810 & P1808 & P1809 & P0) & P0 -> ( Half * a1 < a1 & P1800 & P1798 & P0) & P0" 2; pushreference 23 "P0 -> ((Real(a1) -> a1 * One = a1) & P1817 & P0) & P0" "ITIMES"; pushnode 22 "( Half + Half = One & P1815 & P0) & (Half * a1 < One * a1 & P1816 & P1814 & P1811 & P1806 & P1804 & P1810 & P1808 & P1809 & P1812 & P1815 & P0) & ( Real(a1) & P1802 & P1799 & P1798 & P0) & (Half * a1 + Zero = Zero + Half * a1 & P1809 & P0) & (Zero + Half * a1 = Half * a1 & P1810 & P1808 & P1809 & P0) & P0 -> ( Half * a1 < a1 & P1800 & P1798 & P0) & P0" 2; pushnode 21 " (Half + Half = One & P1815 & P0) & (Half * a1 < [Half + Half] * a1 & P1814 & P1811 & P1806 & P1804 & P1810 & P1808 & P1809 & P1812 & P0) & (Real(a1) & P1802 & P1799 & P1798 & P0) & ( Half * a1 + Zero = Zero + Half * a1 & P1809 & P0) & ( Zero + Half * a1 = Half * a1 & P1810 & P1808 & P1809 & P0) & P0 -> ( Half * a1 < a1 & P1800 & P1798 & P0) & P0" 1; pushreference 20 "P0 -> (Half + Half = One & P1815 & P0) & P0" "TWOHALVES"; pushnode 19 " (Half * a1 < [Half + Half] * a1 & P1814 & P1811 & P1806 & P1804 & P1810 & P1808 & P1809 & P1812 & P0) & ( Real(a1) & P1802 & P1799 & P1798 & P0) & (Half * a1 + Zero = Zero + Half * a1 & P1809 & P0) & (Zero + Half * a1 = Half * a1 & P1810 & P1808 & P1809 & P0) & P0 -> ( Half * a1 < a1 & P1800 & P1798 & P0) & P0" 2; pushnode 18 "( [Half + Half] * a1 = Half * a1 + Half * a1 & P1812 & P0) & ( Half * a1 < Half * a1 + Half * a1 & P1811 & P1806 & P1804 & P1810 & P1808 & P1809 & P0) & ( Real(a1) & P1802 & P1799 & P1798 & P0) & (Half * a1 + Zero = Zero + Half * a1 & P1809 & P0) & (Zero + Half * a1 = Half * a1 & P1810 & P1808 & P1809 & P0) & P0 -> ( Half * a1 < a1 & P1800 & P1798 & P0) & P0" 1; pushreference 17 "P0 -> ( [Half + Half] * a1 = Half * a1 + Half * a1 & P1812 & P0) & P0" "DIST2"; pushnode 16 " ( Zero + Half * a1 = Half * a1 & P1810 & P1808 & P1809 & P0) & (Half * a1 < Half * a1 + Half * a1 & P1811 & P1806 & P1804 & P1810 & P1808 & P1809 & P0) & ( Real(a1) & P1802 & P1799 & P1798 & P0) & (Half * a1 + Zero = Zero + Half * a1 & P1809 & P0) & P0 -> ( Half * a1 < a1 & P1800 & P1798 & P0) & P0" 2; pushnode 15 " (Zero + Half * a1 = Half * a1 & P1810 & P1808 & P1809 & P0) & (Zero + Half * a1 < Half * a1 + Half * a1 & P1806 & P1804 & P0) & ( Real(a1) & P1802 & P1799 & P1798 & P0) & (Half * a1 + Zero = Zero + Half * a1 & P1809 & P0) & P0 -> (Half * a1 < a1 & P1800 & P1798 & P0) & P0" 1; pushnode 14 " ( Half * a1 + Zero = Zero + Half * a1 & P1809 & P0) & ( Half * a1 + Zero = Half * a1 & P1808 & P0) & (Zero + Half * a1 < Half * a1 + Half * a1 & P1806 & P1804 & P0) & ( Real(a1) & P1802 & P1799 & P1798 & P0) & P0 -> ( Half * a1 < a1 & P1800 & P1798 & P0) & P0" 1; pushreference 13 "P0 -> (Half * a1 + Zero = Zero + Half * a1 & P1809 & P0) & P0" "CPLUS"; pushnode 11 " (Half * a1 + Zero = Half * a1 & P1808 & P0) & ( Zero + Half * a1 < Half * a1 + Half * a1 & P1806 & P1804 & P0) & ( Real(a1) & P1802 & P1799 & P1798 & P0) & P0 -> ( Half * a1 < a1 & P1800 & P1798 & P0) & P0" 2; pushreference 10 " (Real(Half * a1) & P1807 & P0) & P0 -> ( Half * a1 + Zero = Half * a1 & P1808 & P0) & P0" "IPLUSa"; pushnode 9 " ( Zero + Half * a1 < Half * a1 + Half * a1 & P1806 & P1804 & P0) & ( Real(a1) & P1802 & P1799 & P1798 & P0) & P0 -> ( Half * a1 < a1 & P1800 & P1798 & P0) & P0" 3; pushnode 8 " (Zero < Half * a1 & P1803 & P0) & P0 -> (Zero < Half * a1 & P1805 & P1804 & P0) & P0" 0; pushnode 7 "((Zero < Half * a1 -> Zero + Half * a1 < Half * a1 + Half * a1) & P1804 & P0) & ( Zero < Half * a1 & P1803 & P0) & ( Real(a1) & P1802 & P1799 & P1798 & P0) & P0 -> ( Half * a1 < a1 & P1800 & P1798 & P0) & P0" 2; pushreference 6 "P0 -> ( (Zero < Half * a1 -> Zero + Half * a1 < Half * a1 + Half * a1) & P1804 & P0) & P0" "MPLUS"; pushnode 4 " (Zero < Half * a1 & P1803 & P0) & (Real(a1) & P1802 & P1799 & P1798 & P0) & P0 -> (Half * a1 < a1 & P1800 & P1798 & P0) & P0" 2; pushnode 3 " ( Zero < a1 & P1801 & P1799 & P1798 & P0) & (Real(a1) & P1802 & P1799 & P1798 & P0) & P0 -> ( Half * a1 < a1 & P1800 & P1798 & P0) & P0" 2; THEOREMS:=("HalfLess",(termtosequent(parseprop("(Zero < a1 & P1801 & P1799 & P1798 & P0) & (Real(a1) & P1802 & P1799 & P1798 & P0) & P0 -> ( Half * a1 < a1 & P1800 & P1798 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "HalfLess"; pushnode 11 " (Zero < a1 * a1 & P1832 & P1828 & P1826 & P1831 & P0) & ( Zero * a1 = Zero & P1831 & P0) & P0 -> (Zero < a1 * a1 & P1825 & P1823 & P0) & P0" 0; pushnode 10 " (Zero * a1 = Zero & P1831 & P0) & ( Zero * a1 < a1 * a1 & P1828 & P1826 & P0) & P0 -> ( Zero < a1 * a1 & P1825 & P1823 & P0) & P0" 1; pushreference 9 "P0 -> (Zero * a1 = Zero & P1831 & P0) & P0" "MZERO2"; pushnode 6 "( Zero * a1 < a1 * a1 & P1828 & P1826 & P0) & P0 -> (Zero < a1 * a1 & P1825 & P1823 & P0) & P0" 2; pushnode 8 "( Zero < a1 & P1824 & P1823 & P0) & P0 -> (Zero < a1 & P1830 & P1827 & P1826 & P0) & P0" 0; pushnode 7 " (Zero < a1 & P1824 & P1823 & P0) & P0 -> ( Zero < a1 & P1829 & P1827 & P1826 & P0) & P0" 0; pushnode 5 "( Zero < a1 & P1824 & P1823 & P0) & P0 -> ( (Zero < a1 & Zero < a1) & P1827 & P1826 & P0) & P0" 2; pushnode 4 "(( Zero < a1 & Zero < a1 -> Zero * a1 < a1 * a1) & P1826 & P0) & ( Zero < a1 & P1824 & P1823 & P0) & P0 -> ( Zero < a1 * a1 & P1825 & P1823 & P0) & P0" 2; pushreference 3 "P0 -> (( Zero < a1 & Zero < a1 -> Zero * a1 < a1 * a1) & P1826 & P0) & P0" "MTIMES"; pushnode 2 " (Zero < a1 & P1824 & P1823 & P0) & P0 -> (Zero < a1 * a1 & P1825 & P1823 & P0) & P0" 2; THEOREMS:=("SQPOS",(termtosequent(parseprop(" (Zero < a1 & P1824 & P1823 & P0) & P0 -> (Zero < a1 * a1 & P1825 & P1823 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "SQPOS"; pushnode 66 " (Zero < a1 & P1837 & P1834 & P1833 & P0) & P0 -> (Zero < a1 & P1891 & P0) & P0" 0; pushnode 65 "(Zero < a2 & P1838 & P1834 & P1833 & P0) & P0 -> ( Zero < a2 & P1890 & P0) & P0" 0; pushnode 64 "(a2 < a1 & P1888 & P1864 & P1862 & P0) & P0 -> ( a2 < a1 & P1889 & P0) & P0" 0; pushreference 63 " ( a2 * a2 < a1 * a1 & P1892 & P0) & ( a1 * a1 < a2 * a2 & P1860 & P1840 & P1836 & P1835 & P1833 & P0) & P0 -> P0" "NOTBOTH"; pushreference 62 "(a2 < a1 & P1889 & P0) & (Zero < a2 & P1890 & P0) & (Zero < a1 & P1891 & P0) & P0 -> (a2 * a2 < a1 * a1 & P1892 & P0) & P0" "SquareOrder1"; pushnode 61 " ( a2 < a1 & P1888 & P1864 & P1862 & P0) & ( a1 * a1 < a2 * a2 & P1860 & P1840 & P1836 & P1835 & P1833 & P0) & (Zero < a1 & P1837 & P1834 & P1833 & P0) & (Zero < a2 & P1838 & P1834 & P1833 & P0) & P0 -> P0" 5; pushnode 60 "(a1 < a2 & P1887 & P1864 & P1862 & P0) & P0 -> ( a1 < a2 & P1861 & P1840 & P1836 & P1835 & P1833 & P0) & P0" 0; pushnode 33 "(( a1 < a2 v a2 < a1) & P1864 & P1862 & P0) & ( a1 * a1 < a2 * a2 & P1860 & P1840 & P1836 & P1835 & P1833 & P0) & (Zero < a1 & P1837 & P1834 & P1833 & P0) & (Zero < a2 & P1838 & P1834 & P1833 & P0) & P0 -> ( a1 < a2 & P1861 & P1840 & P1836 & P1835 & P1833 & P0) & P0" 2; pushnode 59 " ( a2 * a2 < a2 * a2 & P1884 & P1882 & P1880 & P1878 & P1877 & P1875 & P1873 & P1871 & P1869 & P1867 & P1860 & P1840 & P1836 & P1835 & P1833 & P1866 & P1868 & P1870 & P1872 & P1874 & P1876 & P1865 & P1863 & P1862 & P1876 & P1872 & P1868 & P0) & (a1 * a1 = [a1 + Zero] * a1 & P1866 & P0) & ([a1 + Zero] * a1 = a1 * [a1 + Zero] & P1870 & P0) & (a1 * [a1 + Zero] = [a1 + Zero] * [a1 + Zero] & P1874 & P0) & (a1 + Zero = a2 + Zero & P1865 & P1863 & P1862 & P0) & P0 -> ( a2 * a2 < a2 * a2 & P1886 & P1885 & P0) & P0" 0; pushnode 58 "( ~a2 * a2 < a2 * a2 & P1885 & P0) & ( a2 * a2 < a2 * a2 & P1884 & P1882 & P1880 & P1878 & P1877 & P1875 & P1873 & P1871 & P1869 & P1867 & P1860 & P1840 & P1836 & P1835 & P1833 & P1866 & P1868 & P1870 & P1872 & P1874 & P1876 & P1865 & P1863 & P1862 & P1876 & P1872 & P1868 & P0) & (a1 * a1 = [a1 + Zero] * a1 & P1866 & P0) & ([a1 + Zero] * a1 = a1 * [a1 + Zero] & P1870 & P0) & (a1 * [a1 + Zero] = [a1 + Zero] * [a1 + Zero] & P1874 & P0) & (a1 + Zero = a2 + Zero & P1865 & P1863 & P1862 & P0) & P0 -> P0" 1; pushreference 57 "P0 -> (~a2 * a2 < a2 * a2 & P1885 & P0) & P0" "IRR"; pushnode 56 " (a2 * a2 < a2 * a2 & P1884 & P1882 & P1880 & P1878 & P1877 & P1875 & P1873 & P1871 & P1869 & P1867 & P1860 & P1840 & P1836 & P1835 & P1833 & P1866 & P1868 & P1870 & P1872 & P1874 & P1876 & P1865 & P1863 & P1862 & P1876 & P1872 & P1868 & P0) & (a1 * a1 = [a1 + Zero] * a1 & P1866 & P0) & ( [a1 + Zero] * a1 = a1 * [a1 + Zero] & P1870 & P0) & (a1 * [a1 + Zero] = [a1 + Zero] * [a1 + Zero] & P1874 & P0) & (a1 + Zero = a2 + Zero & P1865 & P1863 & P1862 & P0) & P0 -> P0" 2; pushnode 55 "(a2 * a2 = [a2 + Zero] * a2 & P1868 & P0) & ( [a2 + Zero] * a2 < [a2 + Zero] * a2 & P1882 & P1880 & P1878 & P1877 & P1875 & P1873 & P1871 & P1869 & P1867 & P1860 & P1840 & P1836 & P1835 & P1833 & P1866 & P1868 & P1870 & P1872 & P1874 & P1876 & P1865 & P1863 & P1862 & P1876 & P1872 & P0) & (a1 * a1 = [a1 + Zero] * a1 & P1866 & P0) & ([a1 + Zero] * a1 = a1 * [a1 + Zero] & P1870 & P0) & (a1 * [a1 + Zero] = [a1 + Zero] * [a1 + Zero] & P1874 & P0) & (a1 + Zero = a2 + Zero & P1865 & P1863 & P1862 & P0) & P0 -> P0" 1; pushnode 54 " ([a2 + Zero] * a2 = a2 * [a2 + Zero] & P1872 & P0) & (a2 * [a2 + Zero] < a2 * [a2 + Zero] & P1880 & P1878 & P1877 & P1875 & P1873 & P1871 & P1869 & P1867 & P1860 & P1840 & P1836 & P1835 & P1833 & P1866 & P1868 & P1870 & P1872 & P1874 & P1876 & P1865 & P1863 & P1862 & P1876 & P0) & (a1 * a1 = [a1 + Zero] * a1 & P1866 & P0) & (a2 * a2 = [a2 + Zero] * a2 & P1868 & P0) & ( [a1 + Zero] * a1 = a1 * [a1 + Zero] & P1870 & P0) & (a1 * [a1 + Zero] = [a1 + Zero] * [a1 + Zero] & P1874 & P0) & (a1 + Zero = a2 + Zero & P1865 & P1863 & P1862 & P0) & P0 -> P0" 1; pushnode 53 "(a2 * [a2 + Zero] = [a2 + Zero] * [a2 + Zero] & P1876 & P0) & ( [a2 + Zero] * [a2 + Zero] < [a2 + Zero] * [a2 + Zero] & P1878 & P1877 & P1875 & P1873 & P1871 & P1869 & P1867 & P1860 & P1840 & P1836 & P1835 & P1833 & P1866 & P1868 & P1870 & P1872 & P1874 & P1876 & P1865 & P1863 & P1862 & P0) & (a1 * a1 = [a1 + Zero] * a1 & P1866 & P0) & (a2 * a2 = [a2 + Zero] * a2 & P1868 & P0) & ( [a1 + Zero] * a1 = a1 * [a1 + Zero] & P1870 & P0) & ([a2 + Zero] * a2 = a2 * [a2 + Zero] & P1872 & P0) & (a1 * [a1 + Zero] = [a1 + Zero] * [a1 + Zero] & P1874 & P0) & (a1 + Zero = a2 + Zero & P1865 & P1863 & P1862 & P0) & P0 -> P0" 1; pushnode 52 " (a1 + Zero = a2 + Zero & P1865 & P1863 & P1862 & P0) & ([a1 + Zero] * [a1 + Zero] < [a2 + Zero] * [a2 + Zero] & P1877 & P1875 & P1873 & P1871 & P1869 & P1867 & P1860 & P1840 & P1836 & P1835 & P1833 & P1866 & P1868 & P1870 & P1872 & P1874 & P1876 & P0) & (a1 * a1 = [a1 + Zero] * a1 & P1866 & P0) & (a2 * a2 = [a2 + Zero] * a2 & P1868 & P0) & ([a1 + Zero] * a1 = a1 * [a1 + Zero] & P1870 & P0) & ( [a2 + Zero] * a2 = a2 * [a2 + Zero] & P1872 & P0) & (a1 * [a1 + Zero] = [a1 + Zero] * [a1 + Zero] & P1874 & P0) & (a2 * [a2 + Zero] = [a2 + Zero] * [a2 + Zero] & P1876 & P0) & P0 -> P0" 1; pushnode 51 "( a2 * [a2 + Zero] = [a2 + Zero] * [a2 + Zero] & P1876 & P0) & ( [a1 + Zero] * [a1 + Zero] < a2 * [a2 + Zero] & P1875 & P1873 & P1871 & P1869 & P1867 & P1860 & P1840 & P1836 & P1835 & P1833 & P1866 & P1868 & P1870 & P1872 & P1874 & P0) & ( a1 + Zero = a2 + Zero & P1865 & P1863 & P1862 & P0) & (a1 * a1 = [a1 + Zero] * a1 & P1866 & P0) & (a2 * a2 = [a2 + Zero] * a2 & P1868 & P0) & ([a1 + Zero] * a1 = a1 * [a1 + Zero] & P1870 & P0) & ( [a2 + Zero] * a2 = a2 * [a2 + Zero] & P1872 & P0) & (a1 * [a1 + Zero] = [a1 + Zero] * [a1 + Zero] & P1874 & P0) & P0 -> P0" 1; pushreference 50 "P0 -> ( a2 * [a2 + Zero] = [a2 + Zero] * [a2 + Zero] & P1876 & P0) & P0" "SubLemma"; pushnode 49 "( a1 * [a1 + Zero] = [a1 + Zero] * [ a1 + Zero] & P1874 & P0) & ( [a1 + Zero] * [a1 + Zero] < a2 * [a2 + Zero] & P1875 & P1873 & P1871 & P1869 & P1867 & P1860 & P1840 & P1836 & P1835 & P1833 & P1866 & P1868 & P1870 & P1872 & P1874 & P0) & ( a1 + Zero = a2 + Zero & P1865 & P1863 & P1862 & P0) & (a1 * a1 = [a1 + Zero] * a1 & P1866 & P0) & (a2 * a2 = [a2 + Zero] * a2 & P1868 & P0) & ([a1 + Zero] * a1 = a1 * [a1 + Zero] & P1870 & P0) & ( [a2 + Zero] * a2 = a2 * [a2 + Zero] & P1872 & P0) & P0 -> P0" 2; pushnode 48 "(a1 * [a1 + Zero] = [a1 + Zero] * [a1 + Zero] & P1874 & P0) & (a1 * [a1 + Zero] < a2 * [a2 + Zero] & P1873 & P1871 & P1869 & P1867 & P1860 & P1840 & P1836 & P1835 & P1833 & P1866 & P1868 & P1870 & P1872 & P0) & ( a1 + Zero = a2 + Zero & P1865 & P1863 & P1862 & P0) & (a1 * a1 = [a1 + Zero] * a1 & P1866 & P0) & (a2 * a2 = [a2 + Zero] * a2 & P1868 & P0) & ([a1 + Zero] * a1 = a1 * [a1 + Zero] & P1870 & P0) & ( [a2 + Zero] * a2 = a2 * [a2 + Zero] & P1872 & P0) & P0 -> P0" 1; pushreference 47 "P0 -> (a1 * [ a1 + Zero] = [a1 + Zero] * [ a1 + Zero] & P1874 & P0) & P0" "SubLemma"; pushnode 46 "([ a2 + Zero] * a2 = a2 * [a2 + Zero] & P1872 & P0) & (a1 * [a1 + Zero] < a2 * [a2 + Zero] & P1873 & P1871 & P1869 & P1867 & P1860 & P1840 & P1836 & P1835 & P1833 & P1866 & P1868 & P1870 & P1872 & P0) & ( a1 + Zero = a2 + Zero & P1865 & P1863 & P1862 & P0) & (a1 * a1 = [a1 + Zero] * a1 & P1866 & P0) & (a2 * a2 = [a2 + Zero] * a2 & P1868 & P0) & ([a1 + Zero] * a1 = a1 * [a1 + Zero] & P1870 & P0) & P0 -> P0" 2; pushnode 45 " ([a2 + Zero] * a2 = a2 * [a2 + Zero] & P1872 & P0) & (a1 * [a1 + Zero] < [a2 + Zero] * a2 & P1871 & P1869 & P1867 & P1860 & P1840 & P1836 & P1835 & P1833 & P1866 & P1868 & P1870 & P0) & ( a1 + Zero = a2 + Zero & P1865 & P1863 & P1862 & P0) & (a1 * a1 = [a1 + Zero] * a1 & P1866 & P0) & (a2 * a2 = [a2 + Zero] * a2 & P1868 & P0) & ([a1 + Zero] * a1 = a1 * [a1 + Zero] & P1870 & P0) & P0 -> P0" 1; pushreference 44 "P0 -> ( [a2 + Zero] * a2 = a2 * [a2 + Zero] & P1872 & P0) & P0" "CTIMES"; pushnode 43 " ( [a1 + Zero] * a1 = a1 * [a1 + Zero] & P1870 & P0) & ( a1 * [a1 + Zero] < [a2 + Zero] * a2 & P1871 & P1869 & P1867 & P1860 & P1840 & P1836 & P1835 & P1833 & P1866 & P1868 & P1870 & P0) & ( a1 + Zero = a2 + Zero & P1865 & P1863 & P1862 & P0) & (a1 * a1 = [a1 + Zero] * a1 & P1866 & P0) & (a2 * a2 = [a2 + Zero] * a2 & P1868 & P0) & P0 -> P0" 2; pushnode 42 " ( [a1 + Zero] * a1 = a1 * [a1 + Zero] & P1870 & P0) & ([ a1 + Zero] * a1 < [a2 + Zero] * a2 & P1869 & P1867 & P1860 & P1840 & P1836 & P1835 & P1833 & P1866 & P1868 & P0) & ( a1 + Zero = a2 + Zero & P1865 & P1863 & P1862 & P0) & (a1 * a1 = [a1 + Zero] * a1 & P1866 & P0) & (a2 * a2 = [a2 + Zero] * a2 & P1868 & P0) & P0 -> P0" 1; pushreference 41 "P0 -> ( [a1 + Zero] * a1 = a1 * [a1 + Zero] & P1870 & P0) & P0" "CTIMES"; pushnode 40 " (a2 * a2 = [a2 + Zero] * a2 & P1868 & P0) & ( [a1 + Zero] * a1 < [ a2 + Zero] * a2 & P1869 & P1867 & P1860 & P1840 & P1836 & P1835 & P1833 & P1866 & P1868 & P0) & ( a1 + Zero = a2 + Zero & P1865 & P1863 & P1862 & P0) & (a1 * a1 = [a1 + Zero] * a1 & P1866 & P0) & P0 -> P0" 2; pushnode 39 "( a2 * a2 = [a2 + Zero] * a2 & P1868 & P0) & ( [a1 + Zero] * a1 < a2 * a2 & P1867 & P1860 & P1840 & P1836 & P1835 & P1833 & P1866 & P0) & ( a1 + Zero = a2 + Zero & P1865 & P1863 & P1862 & P0) & (a1 * a1 = [a1 + Zero] * a1 & P1866 & P0) & P0 -> P0" 1; pushreference 38 "P0 -> ( a2 * a2 = [a2 + Zero] * a2 & P1868 & P0) & P0" "SubLemma"; pushnode 37 "( a1 * a1 = [a1 + Zero] * a1 & P1866 & P0) & ([a1 + Zero] * a1 < a2 * a2 & P1867 & P1860 & P1840 & P1836 & P1835 & P1833 & P1866 & P0) & ( a1 + Zero = a2 + Zero & P1865 & P1863 & P1862 & P0) & P0 -> P0" 2; pushnode 36 "( a1 * a1 = [a1 + Zero] * a1 & P1866 & P0) & (a1 * a1 < a2 * a2 & P1860 & P1840 & P1836 & P1835 & P1833 & P0) & (a1 + Zero = a2 + Zero & P1865 & P1863 & P1862 & P0) & P0 -> P0" 1; pushreference 35 "P0 -> ( a1 * a1 = [a1 + Zero] * a1 & P1866 & P0) & P0" "SubLemma"; pushnode 34 " ( a1 + Zero = a2 + Zero & P1865 & P1863 & P1862 & P0) & ( a1 * a1 < a2 * a2 & P1860 & P1840 & P1836 & P1835 & P1833 & P0) & P0 -> P0" 2; pushnode 32 " (a1 Equal a2 & P1863 & P1862 & P0) & (a1 * a1 < a2 * a2 & P1860 & P1840 & P1836 & P1835 & P1833 & P0) & P0 -> P0" 1; pushnode 31 "( (a1 Equal a2 v a1 < a2 v a2 < a1) & P1862 & P0) & ( a1 * a1 < a2 * a2 & P1860 & P1840 & P1836 & P1835 & P1833 & P0) & (Zero < a1 & P1837 & P1834 & P1833 & P0) & (Zero < a2 & P1838 & P1834 & P1833 & P0) & P0 -> ( a1 < a2 & P1861 & P1840 & P1836 & P1835 & P1833 & P0) & P0" 2; pushreference 30 " P0 -> ((a1 Equal a2 v a1 < a2 v a2 < a1) & P1862 & P0) & P0" "TRI"; pushnode 29 "( a1 * a1 < a2 * a2 & P1860 & P1840 & P1836 & P1835 & P1833 & P0) & (Zero < a1 & P1837 & P1834 & P1833 & P0) & (Zero < a2 & P1838 & P1834 & P1833 & P0) & P0 -> (a1 < a2 & P1861 & P1840 & P1836 & P1835 & P1833 & P0) & P0" 2; THEOREMS:=("SquareOrder2",(termtosequent(parseprop(" ( a1 * a1 < a2 * a2 & P1860 & P1840 & P1836 & P1835 & P1833 & P0) & (Zero < a1 & P1837 & P1834 & P1833 & P0) & (Zero < a2 & P1838 & P1834 & P1833 & P0) & P0 -> (a1 < a2 & P1861 & P1840 & P1836 & P1835 & P1833 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "SquareOrder2"; pushnode 19 " P0 -> (Inv(Two) = Inv(Two) & P1910 & P1897 & P0) & P0" 0; pushnode 6 "P0 -> ( Half = Inv(Two) & P1897 & P0) & P0" 1; pushnode 16 "P0 -> (One = One & P1908 & P1904 & P1902 & P1900 & P1903 & P1906 & P1903 & P1899 & P1897 & P1894 & P0) & P0" 0; pushnode 15 "( Inv(Two) * Two = One & P1904 & P1902 & P1900 & P1903 & P0) & P0 -> ( One = Inv(Two) * Two & P1906 & P1903 & P1899 & P1897 & P1894 & P0) & P0" 1; pushnode 14 " ( Two * Inv(Two) = Inv(Two) * Two & P1903 & P0) & (Inv(Two) * Two = One & P1904 & P1902 & P1900 & P1903 & P0) & P0 -> (One = Two * Inv(Two) & P1899 & P1897 & P1894 & P0) & P0" 1; pushnode 13 "( Two * Inv(Two) = Inv(Two) * Two & P1903 & P0) & (Two * Inv(Two) = One & P1902 & P1900 & P0) & P0 -> ( One = Two * Inv(Two) & P1899 & P1897 & P1894 & P0) & P0" 1; pushreference 12 " P0 -> ( Two * Inv(Two) = Inv(Two) * Two & P1903 & P0) & P0" "CTIMES"; pushnode 11 "( Two * Inv(Two) = One & P1902 & P1900 & P0) & P0 -> ( One = Two * Inv(Two) & P1899 & P1897 & P1894 & P0) & P0" 2; pushreference 18 "( Zero < Two & P1909 & P0) & ( Two Equal Zero & P1901 & P1900 & P0) & P0 -> P0" "NOTBOTH3"; pushreference 17 "P0 -> (Zero < Two & P1909 & P0) & P0" "TWOPOS"; pushnode 10 " (Two Equal Zero & P1901 & P1900 & P0) & P0 -> P0" 2; pushnode 9 "((Two Equal Zero v Two * Inv(Two) = One) & P1900 & P0) & P0 -> ( One = Two * Inv(Two) & P1899 & P1897 & P1894 & P0) & P0" 2; pushreference 8 " P0 -> ((Two Equal Zero v Two * Inv(Two) = One) & P1900 & P0) & P0" "INV"; pushnode 7 "P0 -> ( One = Two * Inv(Two) & P1899 & P1897 & P1894 & P0) & P0" 2; pushnode 5 "( Half = Inv(Two) & P1897 & P0) & P0 -> (One = Two * Half & P1894 & P0) & P0" 1; pushnode 3 "P0 -> (One = Two * Half & P1894 & P0) & P0" 2; pushreference 4 "P0 -> (Real(Two * Half) & P1896 & P1894 & P1893 & P0) & P0" "RTIMES"; pushnode 2 "(One = Two * Half & P1894 & P0) & P0 -> ( Real(One) & P1893 & P0) & P0" 1; pushnode 1 "P0 -> (Real(One) & P1893 & P0) & P0" 2; THEOREMS:=("RONE",(termtosequent(parseprop("P0 -> (Real(One) & P1893 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "RONE"; pushreference 10 "P0 -> (Real(One) & P1919 & P0) & P0" "RONE"; pushnode 46 " (a1 < [a1 + One] * [a1 + One] & P1948 & P1946 & P0) & P0 -> (a1 < [a1 + One] * [a1 + One] & P1913 & P1911 & P0) & P0" 0; pushnode 48 "( [a1 + One] * a1 < [a1 + One] * [a1 + One] & P1945 & P1936 & P1934 & P1944 & P0) & P0 -> ([ a1 + One] * a1 < [a1 + One] * [ a1 + One] & P1950 & P1947 & P1946 & P0) & P0" 0; pushnode 47 "( a1 < [a1 + One] * a1 & P1932 & P1924 & P1922 & P1931 & P1929 & P1927 & P1930 & P0) & P0 -> ( a1 < [a1 + One] * a1 & P1949 & P1947 & P1946 & P0) & P0" 0; pushnode 45 "([ a1 + One] * a1 < [a1 + One] * [ a1 + One] & P1945 & P1936 & P1934 & P1944 & P0) & (a1 < [ a1 + One] * a1 & P1932 & P1924 & P1922 & P1931 & P1929 & P1927 & P1930 & P0) & P0 -> ((a1 < [ a1 + One] * a1 & [ a1 + One] * a1 < [a1 + One] * [ a1 + One]) & P1947 & P1946 & P0) & P0" 2; pushnode 44 "((a1 < [ a1 + One] * a1 & [ a1 + One] * a1 < [a1 + One] * [ a1 + One] -> a1 < [ a1 + One] * [a1 + One]) & P1946 & P0) & ([a1 + One] * a1 < [a1 + One] * [a1 + One] & P1945 & P1936 & P1934 & P1944 & P0) & (a1 < [a1 + One] * a1 & P1932 & P1924 & P1922 & P1931 & P1929 & P1927 & P1930 & P0) & P0 -> ( a1 < [a1 + One] * [a1 + One] & P1913 & P1911 & P0) & P0" 2; pushreference 43 "P0 -> (( a1 < [a1 + One] * a1 & [a1 + One] * a1 < [a1 + One] * [a1 + One] -> a1 < [ a1 + One] * [a1 + One]) & P1946 & P0) & P0" "TRANS"; pushnode 42 "( [a1 + One] * a1 < [a1 + One] * [a1 + One] & P1945 & P1936 & P1934 & P1944 & P0) & (a1 < [ a1 + One] * a1 & P1932 & P1924 & P1922 & P1931 & P1929 & P1927 & P1930 & P0) & P0 -> ( a1 < [ a1 + One] * [a1 + One] & P1913 & P1911 & P0) & P0" 2; pushnode 41 " (a1 * [a1 + One] = [a1 + One] * a1 & P1944 & P0) & (a1 * [a1 + One] < [a1 + One] * [a1 + One] & P1936 & P1934 & P0) & (a1 < [a1 + One] * a1 & P1932 & P1924 & P1922 & P1931 & P1929 & P1927 & P1930 & P0) & P0 -> (a1 < [a1 + One] * [ a1 + One] & P1913 & P1911 & P0) & P0" 1; pushreference 40 "P0 -> ( a1 * [a1 + One] = [a1 + One] * a1 & P1944 & P0) & P0" "CTIMES"; pushnode 31 "( a1 * [a1 + One] < [a1 + One] * [a1 + One] & P1936 & P1934 & P0) & (a1 < [ a1 + One] * a1 & P1932 & P1924 & P1922 & P1931 & P1929 & P1927 & P1930 & P0) & P0 -> ( a1 < [ a1 + One] * [a1 + One] & P1913 & P1911 & P0) & P0" 2; pushnode 33 " (a1 < a1 + One & P1933 & P0) & P0 -> (a1 < a1 + One & P1938 & P1935 & P1934 & P0) & P0" 0; pushnode 37 " (Zero < a1 + One & P1941 & P1939 & P0) & P0 -> ( Zero < a1 + One & P1937 & P1935 & P1934 & P0) & P0" 0; pushnode 39 " (a1 < a1 + One & P1933 & P0) & P0 -> (a1 < a1 + One & P1943 & P1940 & P1939 & P0) & P0" 0; pushnode 38 "(Zero < a1 & P1914 & P1912 & P1911 & P0) & P0 -> ( Zero < a1 & P1942 & P1940 & P1939 & P0) & P0" 0; pushnode 36 " (a1 < a1 + One & P1933 & P0) & (Zero < a1 & P1914 & P1912 & P1911 & P0) & P0 -> ((Zero < a1 & a1 < a1 + One) & P1940 & P1939 & P0) & P0" 2; pushnode 35 "(( Zero < a1 & a1 < a1 + One -> Zero < a1 + One) & P1939 & P0) & ( a1 < a1 + One & P1933 & P0) & ( Zero < a1 & P1914 & P1912 & P1911 & P0) & P0 -> (Zero < a1 + One & P1937 & P1935 & P1934 & P0) & P0" 2; pushreference 34 "P0 -> ((Zero < a1 & a1 < a1 + One -> Zero < a1 + One) & P1939 & P0) & P0" "TRANS"; pushnode 32 " (a1 < a1 + One & P1933 & P0) & (Zero < a1 & P1914 & P1912 & P1911 & P0) & P0 -> (Zero < a1 + One & P1937 & P1935 & P1934 & P0) & P0" 2; pushnode 30 " (a1 < a1 + One & P1933 & P0) & (Zero < a1 & P1914 & P1912 & P1911 & P0) & P0 -> ((Zero < a1 + One & a1 < a1 + One) & P1935 & P1934 & P0) & P0" 2; pushnode 29 " (( Zero < a1 + One & a1 < a1 + One -> a1 * [a1 + One] < [ a1 + One] * [a1 + One]) & P1934 & P0) & (a1 < a1 + One & P1933 & P0) & ( a1 < [a1 + One] * a1 & P1932 & P1924 & P1922 & P1931 & P1929 & P1927 & P1930 & P0) & ( Zero < a1 & P1914 & P1912 & P1911 & P0) & P0 -> (a1 < [a1 + One] * [ a1 + One] & P1913 & P1911 & P0) & P0" 2; pushreference 28 "P0 -> (( Zero < a1 + One & a1 < a1 + One -> a1 * [a1 + One] < [ a1 + One] * [a1 + One]) & P1934 & P0) & P0" "MTIMES"; pushnode 27 " (a1 < a1 + One & P1933 & P0) & (a1 < [a1 + One] * a1 & P1932 & P1924 & P1922 & P1931 & P1929 & P1927 & P1930 & P0) & ( Zero < a1 & P1914 & P1912 & P1911 & P0) & P0 -> (a1 < [a1 + One] * [ a1 + One] & P1913 & P1911 & P0) & P0" 2; pushreference 26 "P0 -> (a1 < a1 + One & P1933 & P0) & P0" "SOMETHINGBIGGER"; pushnode 25 " (a1 < [ a1 + One] * a1 & P1932 & P1924 & P1922 & P1931 & P1929 & P1927 & P1930 & P0) & (Zero < a1 & P1914 & P1912 & P1911 & P0) & P0 -> ( a1 < [a1 + One] * [a1 + One] & P1913 & P1911 & P0) & P0" 2; pushnode 24 " (One * a1 = a1 & P1931 & P1929 & P1927 & P1930 & P0) & ( One * a1 < [a1 + One] * a1 & P1924 & P1922 & P0) & (Zero < a1 & P1914 & P1912 & P1911 & P0) & P0 -> (a1 < [a1 + One] * [a1 + One] & P1913 & P1911 & P0) & P0" 1; pushnode 23 "( a1 * One = One * a1 & P1930 & P0) & ( a1 * One = a1 & P1929 & P1927 & P0) & ( One * a1 < [a1 + One] * a1 & P1924 & P1922 & P0) & (Zero < a1 & P1914 & P1912 & P1911 & P0) & P0 -> (a1 < [a1 + One] * [ a1 + One] & P1913 & P1911 & P0) & P0" 1; pushreference 22 "P0 -> (a1 * One = One * a1 & P1930 & P0) & P0" "CTIMES"; pushnode 21 " ( a1 * One = a1 & P1929 & P1927 & P0) & ( One * a1 < [a1 + One] * a1 & P1924 & P1922 & P0) & (Zero < a1 & P1914 & P1912 & P1911 & P0) & P0 -> (a1 < [a1 + One] * [a1 + One] & P1913 & P1911 & P0) & P0" 2; pushnode 20 " (Real(a1) & P1915 & P1912 & P1911 & P0) & P0 -> (Real(a1) & P1928 & P1927 & P0) & P0" 0; pushnode 19 "(( Real(a1) -> a1 * One = a1) & P1927 & P0) & (One * a1 < [a1 + One] * a1 & P1924 & P1922 & P0) & (Zero < a1 & P1914 & P1912 & P1911 & P0) & (Real(a1) & P1915 & P1912 & P1911 & P0) & P0 -> ( a1 < [a1 + One] * [a1 + One] & P1913 & P1911 & P0) & P0" 2; pushreference 18 "P0 -> ((Real(a1) -> a1 * One = a1) & P1927 & P0) & P0" "ITIMES"; pushnode 15 " ( One * a1 < [a1 + One] * a1 & P1924 & P1922 & P0) & (Zero < a1 & P1914 & P1912 & P1911 & P0) & (Real(a1) & P1915 & P1912 & P1911 & P0) & P0 -> ( a1 < [ a1 + One] * [a1 + One] & P1913 & P1911 & P0) & P0" 2; pushnode 17 "(One < a1 + One & P1921 & P1918 & P1916 & P1920 & P0) & P0 -> (One < a1 + One & P1926 & P1923 & P1922 & P0) & P0" 0; pushnode 16 " (Zero < a1 & P1914 & P1912 & P1911 & P0) & P0 -> (Zero < a1 & P1925 & P1923 & P1922 & P0) & P0" 0; pushnode 14 " ( One < a1 + One & P1921 & P1918 & P1916 & P1920 & P0) & ( Zero < a1 & P1914 & P1912 & P1911 & P0) & P0 -> ((Zero < a1 & One < a1 + One) & P1923 & P1922 & P0) & P0" 2; pushnode 13 "( ( Zero < a1 & One < a1 + One -> One * a1 < [a1 + One] * a1) & P1922 & P0) & ( One < a1 + One & P1921 & P1918 & P1916 & P1920 & P0) & ( Zero < a1 & P1914 & P1912 & P1911 & P0) & (Real(a1) & P1915 & P1912 & P1911 & P0) & P0 -> (a1 < [a1 + One] * [ a1 + One] & P1913 & P1911 & P0) & P0" 2; pushreference 12 "P0 -> ( ( Zero < a1 & One < a1 + One -> One * a1 < [a1 + One] * a1) & P1922 & P0) & P0" "MTIMES"; pushnode 11 "(One < a1 + One & P1921 & P1918 & P1916 & P1920 & P0) & (Zero < a1 & P1914 & P1912 & P1911 & P0) & (Real(a1) & P1915 & P1912 & P1911 & P0) & P0 -> (a1 < [a1 + One] * [a1 + One] & P1913 & P1911 & P0) & P0" 2; pushnode 9 "( Zero + One = One & P1920 & P0) & (Zero + One < a1 + One & P1918 & P1916 & P0) & ( Zero < a1 & P1914 & P1912 & P1911 & P0) & (Real(a1) & P1915 & P1912 & P1911 & P0) & P0 -> (a1 < [a1 + One] * [ a1 + One] & P1913 & P1911 & P0) & P0" 1; pushreference 8 "( Real(One) & P1919 & P0) & P0 -> (Zero + One = One & P1920 & P0) & P0" "IPLUSb"; pushnode 7 " ( Zero + One < a1 + One & P1918 & P1916 & P0) & ( Zero < a1 & P1914 & P1912 & P1911 & P0) & (Real(a1) & P1915 & P1912 & P1911 & P0) & P0 -> (a1 < [a1 + One] * [a1 + One] & P1913 & P1911 & P0) & P0" 3; pushnode 6 " (Zero < a1 & P1914 & P1912 & P1911 & P0) & P0 -> (Zero < a1 & P1917 & P1916 & P0) & P0" 0; pushnode 5 " (( Zero < a1 -> Zero + One < a1 + One) & P1916 & P0) & ( Zero < a1 & P1914 & P1912 & P1911 & P0) & (Real(a1) & P1915 & P1912 & P1911 & P0) & P0 -> (a1 < [a1 + One] * [a1 + One] & P1913 & P1911 & P0) & P0" 2; pushreference 4 "P0 -> ((Zero < a1 -> Zero + One < a1 + One) & P1916 & P0) & P0" "MPLUS"; pushnode 3 "(Zero < a1 & P1914 & P1912 & P1911 & P0) & (Real(a1) & P1915 & P1912 & P1911 & P0) & P0 -> (a1 < [a1 + One] * [a1 + One] & P1913 & P1911 & P0) & P0" 2; THEOREMS:=("SqLemma",(termtosequent(parseprop(" ( Zero < a1 & P1914 & P1912 & P1911 & P0) & (Real(a1) & P1915 & P1912 & P1911 & P0) & P0 -> ( a1 < [ a1 + One] * [a1 + One] & P1913 & P1911 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "SqLemma"; pushnode 71 " (Real(a1) & P1956 & P1955 & P1952 & P1951 & P0) & P0 -> (Real(a1) & P2019 & P0) & P0" 0; pushnode 70 "( Zero < a1 & P1964 & P1962 & P1954 & P1952 & P1951 & P0) & P0 -> ( Zero < a1 & P2018 & P0) & P0" 0; pushreference 69 "(Half * a1 < a1 & P2020 & P0) & ( a1 < Half * a1 & P2014 & P2012 & P1972 & P1969 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> P0" "NOTBOTH"; pushreference 68 "(Zero < a1 & P2018 & P0) & (Real(a1) & P2019 & P0) & P0 -> ( Half * a1 < a1 & P2020 & P0) & P0" "HalfLess"; pushnode 63 "(a1 < Half * a1 & P2014 & P2012 & P1972 & P1969 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & (Zero < a1 & P1964 & P1962 & P1954 & P1952 & P1951 & P0) & (Real(a1) & P1956 & P1955 & P1952 & P1951 & P0) & P0 -> P0" 4; pushnode 67 "( Real(a1) & P1956 & P1955 & P1952 & P1951 & P0) & P0 -> (Real(a1) & P2016 & P0) & P0" 0; pushnode 66 "(Zero < a1 & P1964 & P1962 & P1954 & P1952 & P1951 & P0) & P0 -> (Zero < a1 & P2015 & P0) & P0" 0; pushreference 65 "(Half * a1 < a1 & P2017 & P0) & (a1 Equal Half * a1 & P2013 & P2012 & P1972 & P1969 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> P0" "NOTBOTH3"; pushreference 64 "(Zero < a1 & P2015 & P0) & (Real(a1) & P2016 & P0) & P0 -> ( Half * a1 < a1 & P2017 & P0) & P0" "HalfLess"; pushnode 62 "(a1 Equal Half * a1 & P2013 & P2012 & P1972 & P1969 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & (Zero < a1 & P1964 & P1962 & P1954 & P1952 & P1951 & P0) & (Real(a1) & P1956 & P1955 & P1952 & P1951 & P0) & P0 -> P0" 4; pushnode 61 " ( (a1 Equal Half * a1 v a1 < Half * a1) & P2012 & P1972 & P1969 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & (Zero < a1 & P1964 & P1962 & P1954 & P1952 & P1951 & P0) & (Real(a1) & P1956 & P1955 & P1952 & P1951 & P0) & P0 -> P0" 2; pushnode 17 " (a1 <= Half * a1 & P1972 & P1969 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & (Zero < a1 & P1964 & P1962 & P1954 & P1952 & P1951 & P0) & ( Real(a1) & P1956 & P1955 & P1952 & P1951 & P0) & P0 -> P0" 1; pushnode 54 "( Real(a2) & P1960 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> (Real(a2) & P2005 & P0) & P0" 0; pushnode 53 "(Zero < a2 & P1958 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> (Zero < a2 & P2004 & P0) & P0" 0; pushnode 58 " (a1 < a2 & P2009 & P2007 & P0) & P0 -> ( a1 < a2 & P1977 & P0) & P0" 0; pushnode 60 " (Half * a2 < a2 & P2006 & P0) & P0 -> (Half * a2 < a2 & P2011 & P2008 & P2007 & P0) & P0" 0; pushnode 59 " (a1 < Half * a2 & P1996 & P1994 & P1989 & P1986 & P1970 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> (a1 < Half * a2 & P2010 & P2008 & P2007 & P0) & P0" 0; pushnode 57 " (Half * a2 < a2 & P2006 & P0) & (a1 < Half * a2 & P1996 & P1994 & P1989 & P1986 & P1970 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> (( a1 < Half * a2 & Half * a2 < a2) & P2008 & P2007 & P0) & P0" 2; pushnode 56 "((a1 < Half * a2 & Half * a2 < a2 -> a1 < a2) & P2007 & P0) & ( Half * a2 < a2 & P2006 & P0) & (a1 < Half * a2 & P1996 & P1994 & P1989 & P1986 & P1970 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> (a1 < a2 & P1977 & P0) & P0" 2; pushreference 55 "P0 -> ((a1 < Half * a2 & Half * a2 < a2 -> a1 < a2) & P2007 & P0) & P0" "TRANS"; pushnode 52 " (Half * a2 < a2 & P2006 & P0) & (a1 < Half * a2 & P1996 & P1994 & P1989 & P1986 & P1970 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> (a1 < a2 & P1977 & P0) & P0" 2; pushreference 51 "(Zero < a2 & P2004 & P0) & (Real(a2) & P2005 & P0) & P0 -> ( Half * a2 < a2 & P2006 & P0) & P0" "HalfLess"; pushnode 43 " (a1 < Half * a2 & P1996 & P1994 & P1989 & P1986 & P1970 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & (Zero < a2 & P1958 & P1957 & P1955 & P1952 & P1951 & P0) & (Real(a2) & P1960 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> (a1 < a2 & P1977 & P0) & P0" 4; pushreference 48 " P0 -> (Real(Half * a2) & P1999 & P0) & P0" "RTIMES"; pushnode 47 "(Real(a1) & P1956 & P1955 & P1952 & P1951 & P0) & P0 -> (Real(a1) & P1998 & P0) & P0" 0; pushnode 46 "( a1 Equal Half * a2 & P1995 & P1994 & P1989 & P1986 & P1970 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> (a1 Equal Half * a2 & P1997 & P0) & P0" 0; pushreference 50 "( Zero < a2 & P1958 & P1957 & P1955 & P1952 & P1951 & P0) & (Real(a2) & P1960 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> ( Half * a2 < a2 & P2003 & P2000 & P1977 & P0) & P0" "HalfLess"; pushnode 45 "(a1 = Half * a2 & P2000 & P0) & (Zero < a2 & P1958 & P1957 & P1955 & P1952 & P1951 & P0) & (Real(a2) & P1960 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> (a1 < a2 & P1977 & P0) & P0" 1; pushreference 44 " (a1 Equal Half * a2 & P1997 & P0) & (Real(a1) & P1998 & P0) & ( Real(Half * a2) & P1999 & P0) & P0 -> ( a1 = Half * a2 & P2000 & P0) & P0" "EQUALITY"; pushnode 42 " (a1 Equal Half * a2 & P1995 & P1994 & P1989 & P1986 & P1970 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & (Real(a1) & P1956 & P1955 & P1952 & P1951 & P0) & ( Zero < a2 & P1958 & P1957 & P1955 & P1952 & P1951 & P0) & (Real(a2) & P1960 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> ( a1 < a2 & P1977 & P0) & P0" 5; pushnode 41 "( (a1 Equal Half * a2 v a1 < Half * a2) & P1994 & P1989 & P1986 & P1970 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & ( Real(a1) & P1956 & P1955 & P1952 & P1951 & P0) & ( Zero < a2 & P1958 & P1957 & P1955 & P1952 & P1951 & P0) & (Real(a2) & P1960 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> ( a1 < a2 & P1977 & P0) & P0" 2; pushnode 36 " (a1 <= Half * a2 & P1989 & P1986 & P1970 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & (Real(a1) & P1956 & P1955 & P1952 & P1951 & P0) & (Zero < a2 & P1958 & P1957 & P1955 & P1952 & P1951 & P0) & (Real(a2) & P1960 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> ( a1 < a2 & P1977 & P0) & P0" 1; pushreference 40 " (Zero < a2 & P1958 & P1957 & P1955 & P1952 & P1951 & P0) & (Real(a2) & P1960 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> (Half * a2 < a2 & P1993 & P1991 & P1988 & P1986 & P1970 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0" "HalfLess"; pushreference 39 "( Zero < a2 & P1958 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> (Zero < Half * a2 & P1992 & P1991 & P1988 & P1986 & P1970 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0" "MHALFPOS"; pushnode 38 " (Zero < a2 & P1958 & P1957 & P1955 & P1952 & P1951 & P0) & (Real(a2) & P1960 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> ((Zero < Half * a2 & Half * a2 < a2) & P1991 & P1988 & P1986 & P1970 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0" 2; pushreference 37 "P0 -> (Real(Half * a2) & P1990 & P1988 & P1986 & P1970 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0" "RTIMES"; pushnode 35 "( Zero < a2 & P1958 & P1957 & P1955 & P1952 & P1951 & P0) & (Real(a2) & P1960 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> (( Real(Half * a2) & Zero < Half * a2 & Half * a2 < a2) & P1988 & P1986 & P1970 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0" 2; pushnode 34 " ((Real(Half * a2) & Zero < Half * a2 & Half * a2 < a2 -> a1 <= Half * a2) & P1986 & P1970 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & (Real(a1) & P1956 & P1955 & P1952 & P1951 & P0) & ( Zero < a2 & P1958 & P1957 & P1955 & P1952 & P1951 & P0) & (Real(a2) & P1960 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> (a1 < a2 & P1977 & P0) & P0" 2; pushnode 23 " ((Ax1. Real(x1) & Zero < x1 & x1 < a2 -> a1 <= x1) & P1970 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & (Real(a1) & P1956 & P1955 & P1952 & P1951 & P0) & ( Zero < a2 & P1958 & P1957 & P1955 & P1952 & P1951 & P0) & (Real(a2) & P1960 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> ( a1 < a2 & P1977 & P0) & P0" 1; pushnode 27 " (Real(a1) & P1956 & P1955 & P1952 & P1951 & P0) & P0 -> (Real(a1) & P1979 & P0) & P0" 0; pushnode 26 "( Zero < a1 & P1964 & P1962 & P1954 & P1952 & P1951 & P0) & P0 -> ( Zero < a1 & P1978 & P0) & P0" 0; pushnode 31 " (Half * a1 < a2 & P1983 & P1981 & P0) & P0 -> (Half * a1 < a2 & P1976 & P1974 & P1971 & P1969 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0" 0; pushnode 33 " (a1 < a2 & P1977 & P0) & P0 -> ( a1 < a2 & P1985 & P1982 & P1981 & P0) & P0" 0; pushnode 32 "( Half * a1 < a1 & P1980 & P0) & P0 -> ( Half * a1 < a1 & P1984 & P1982 & P1981 & P0) & P0" 0; pushnode 30 " (Half * a1 < a1 & P1980 & P0) & (a1 < a2 & P1977 & P0) & P0 -> (( Half * a1 < a1 & a1 < a2) & P1982 & P1981 & P0) & P0" 2; pushnode 29 "(( Half * a1 < a1 & a1 < a2 -> Half * a1 < a2) & P1981 & P0) & (Half * a1 < a1 & P1980 & P0) & (a1 < a2 & P1977 & P0) & P0 -> ( Half * a1 < a2 & P1976 & P1974 & P1971 & P1969 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0" 2; pushreference 28 " P0 -> (( Half * a1 < a1 & a1 < a2 -> Half * a1 < a2) & P1981 & P0) & P0" "TRANS"; pushnode 25 "(Half * a1 < a1 & P1980 & P0) & (a1 < a2 & P1977 & P0) & P0 -> ( Half * a1 < a2 & P1976 & P1974 & P1971 & P1969 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0" 2; pushreference 24 "( Zero < a1 & P1978 & P0) & ( Real(a1) & P1979 & P0) & P0 -> ( Half * a1 < a1 & P1980 & P0) & P0" "HalfLess"; pushnode 22 " (a1 < a2 & P1977 & P0) & (Zero < a1 & P1964 & P1962 & P1954 & P1952 & P1951 & P0) & (Real(a1) & P1956 & P1955 & P1952 & P1951 & P0) & P0 -> ( Half * a1 < a2 & P1976 & P1974 & P1971 & P1969 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0" 4; pushnode 21 " ((Ax1.Real(x1) & Zero < x1 & x1 < a2 -> a1 <= x1) & P1970 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & (Zero < a1 & P1964 & P1962 & P1954 & P1952 & P1951 & P0) & (Real(a1) & P1956 & P1955 & P1952 & P1951 & P0) & ( Zero < a2 & P1958 & P1957 & P1955 & P1952 & P1951 & P0) & (Real(a2) & P1960 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> ( Half * a1 < a2 & P1976 & P1974 & P1971 & P1969 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0" 2; pushreference 20 "( Zero < a1 & P1964 & P1962 & P1954 & P1952 & P1951 & P0) & P0 -> (Zero < Half * a1 & P1975 & P1974 & P1971 & P1969 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0" "MHALFPOS"; pushnode 19 " ((Ax1.Real(x1) & Zero < x1 & x1 < a2 -> a1 <= x1) & P1970 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & (Zero < a1 & P1964 & P1962 & P1954 & P1952 & P1951 & P0) & (Real(a1) & P1956 & P1955 & P1952 & P1951 & P0) & ( Zero < a2 & P1958 & P1957 & P1955 & P1952 & P1951 & P0) & (Real(a2) & P1960 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> ((Zero < Half * a1 & Half * a1 < a2) & P1974 & P1971 & P1969 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0" 2; pushreference 18 "P0 -> (Real( Half * a1) & P1973 & P1971 & P1969 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0" "RTIMES"; pushnode 16 " ((Ax1. Real(x1) & Zero < x1 & x1 < a2 -> a1 <= x1) & P1970 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & (Zero < a1 & P1964 & P1962 & P1954 & P1952 & P1951 & P0) & (Real(a1) & P1956 & P1955 & P1952 & P1951 & P0) & ( Zero < a2 & P1958 & P1957 & P1955 & P1952 & P1951 & P0) & (Real(a2) & P1960 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> ( (Real( Half * a1) & Zero < Half * a1 & Half * a1 < a2) & P1971 & P1969 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0" 2; pushnode 15 " (( Real( Half * a1) & Zero < Half * a1 & Half * a1 < a2 -> a1 <= Half * a1) & P1969 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & ((Ax1.Real(x1) & Zero < x1 & x1 < a2 -> a1 <= x1) & P1970 & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & (Zero < a1 & P1964 & P1962 & P1954 & P1952 & P1951 & P0) & (Real(a1) & P1956 & P1955 & P1952 & P1951 & P0) & ( Zero < a2 & P1958 & P1957 & P1955 & P1952 & P1951 & P0) & (Real(a2) & P1960 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> P0" 2; pushnode 9 " ((Ax1.Real(x1) & Zero < x1 & x1 < a2 -> a1 <= x1) & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & (Zero < a1 & P1964 & P1962 & P1954 & P1952 & P1951 & P0) & (Real(a1) & P1956 & P1955 & P1952 & P1951 & P0) & ( Zero < a2 & P1958 & P1957 & P1955 & P1952 & P1951 & P0) & (Real(a2) & P1960 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> P0" 1; pushnode 14 " (Real(a1) & P1956 & P1955 & P1952 & P1951 & P0) & P0 -> ( Real(a1) & P1967 & P0) & P0" 0; pushreference 13 "P0 -> (Real(Zero) & P1966 & P0) & P0" "RZERO"; pushnode 12 " (Zero Equal a1 & P1963 & P1962 & P1954 & P1952 & P1951 & P0) & P0 -> ( Zero Equal a1 & P1965 & P0) & P0" 0; pushnode 11 " (Zero = a1 & P1968 & P0) & P0 -> (Zero = a1 & P1953 & P1951 & P0) & P0" 0; pushreference 10 "( Zero Equal a1 & P1965 & P0) & ( Real(Zero) & P1966 & P0) & ( Real(a1) & P1967 & P0) & P0 -> (Zero = a1 & P1968 & P0) & P0" "EQUALITY"; pushnode 8 "(Zero Equal a1 & P1963 & P1962 & P1954 & P1952 & P1951 & P0) & ( Real(a1) & P1956 & P1955 & P1952 & P1951 & P0) & P0 -> (Zero = a1 & P1953 & P1951 & P0) & P0" 5; pushnode 7 " ((Zero Equal a1 v Zero < a1) & P1962 & P1954 & P1952 & P1951 & P0) & ( Real(a1) & P1956 & P1955 & P1952 & P1951 & P0) & ( Zero < a2 & P1958 & P1957 & P1955 & P1952 & P1951 & P0) & (Real(a2) & P1960 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & ((Ax1. Real(x1) & Zero < x1 & x1 < a2 -> a1 <= x1) & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> (Zero = a1 & P1953 & P1951 & P0) & P0" 2; pushnode 6 "(Zero <= a1 & P1954 & P1952 & P1951 & P0) & (Real(a1) & P1956 & P1955 & P1952 & P1951 & P0) & ( Zero < a2 & P1958 & P1957 & P1955 & P1952 & P1951 & P0) & (Real(a2) & P1960 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & ((Ax1. Real(x1) & Zero < x1 & x1 < a2 -> a1 <= x1) & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> (Zero = a1 & P1953 & P1951 & P0) & P0" 1; THEOREMS:=("EPSLEMMA",(termtosequent(parseprop(" ( Zero <= a1 & P1954 & P1952 & P1951 & P0) & (Real(a1) & P1956 & P1955 & P1952 & P1951 & P0) & ( Zero < a2 & P1958 & P1957 & P1955 & P1952 & P1951 & P0) & (Real(a2) & P1960 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & ((Ax1. Real(x1) & Zero < x1 & x1 < a2 -> a1 <= x1) & P1961 & P1959 & P1957 & P1955 & P1952 & P1951 & P0) & P0 -> (Zero = a1 & P1953 & P1951 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "EPSLEMMA"; pushnode 36 "P0 -> ( One + One = One + One & P2055 & P2043 & P0) & P0" 0; pushnode 24 " P0 -> (Two = One + One & P2043 & P0) & P0" 1; pushnode 37 "P0 -> ( a1 * a2 + a1 * a2 = a1 * a2 + a1 * a2 & P2057 & P2054 & P2052 & P2051 & P2049 & P2048 & P2046 & P2045 & P2043 & P2022 & P0) & P0" 0; pushnode 35 " ([ a1 * a2] * One = a1 * a2 & P2054 & P2052 & P0) & P0 -> ([ a1 * a2] * One + [ a1 * a2] * One = a1 * a2 + a1 * a2 & P2051 & P2049 & P2048 & P2046 & P2045 & P2043 & P2022 & P0) & P0" 1; pushreference 34 "P0 -> (Real( a1 * a2) & P2053 & P2052 & P0) & P0" "RTIMES"; pushnode 33 "( (Real(a1 * a2) -> [a1 * a2] * One = a1 * a2) & P2052 & P0) & P0 -> ([ a1 * a2] * One + [ a1 * a2] * One = a1 * a2 + a1 * a2 & P2051 & P2049 & P2048 & P2046 & P2045 & P2043 & P2022 & P0) & P0" 2; pushreference 32 "P0 -> ((Real( a1 * a2) -> [a1 * a2] * One = a1 * a2) & P2052 & P0) & P0" "ITIMES"; pushnode 31 "P0 -> ( [a1 * a2] * One + [a1 * a2] * One = a1 * a2 + a1 * a2 & P2051 & P2049 & P2048 & P2046 & P2045 & P2043 & P2022 & P0) & P0" 2; pushnode 30 "( One * a1 * a2 = [a1 * a2] * One & P2049 & P0) & P0 -> ( One * a1 * a2 + One * a1 * a2 = a1 * a2 + a1 * a2 & P2048 & P2046 & P2045 & P2043 & P2022 & P0) & P0" 1; pushreference 29 "P0 -> (One * a1 * a2 = [a1 * a2] * One & P2049 & P0) & P0" "CTIMES"; pushnode 28 "P0 -> ( One * a1 * a2 + One * a1 * a2 = a1 * a2 + a1 * a2 & P2048 & P2046 & P2045 & P2043 & P2022 & P0) & P0" 2; pushnode 27 "( [One + One] * a1 * a2 = One * a1 * a2 + One * a1 * a2 & P2046 & P0) & P0 -> ( [One + One] * a1 * a2 = a1 * a2 + a1 * a2 & P2045 & P2043 & P2022 & P0) & P0" 1; pushreference 26 "P0 -> ([One + One] * a1 * a2 = One * a1 * a2 + One * a1 * a2 & P2046 & P0) & P0" "DIST2"; pushnode 25 " P0 -> ( [One + One] * a1 * a2 = a1 * a2 + a1 * a2 & P2045 & P2043 & P2022 & P0) & P0" 2; pushnode 23 "(Two = One + One & P2043 & P0) & P0 -> ( Two * a1 * a2 = a1 * a2 + a1 * a2 & P2022 & P0) & P0" 1; pushnode 3 " P0 -> (Two * a1 * a2 = a1 * a2 + a1 * a2 & P2022 & P0) & P0" 2; pushnode 22 "P0 -> ([a1 + a2] * [a1 + a2] = [a1 + a2] * [a1 + a2] & P2042 & P2040 & P2039 & P2037 & P2036 & P2034 & P2033 & P2031 & P2030 & P2028 & P2027 & P2025 & P2024 & P2022 & P2021 & P0) & P0" 0; pushnode 21 "([ a1 + a2] * [a1 + a2] = [a1 + a2] * a1 + [a1 + a2] * a2 & P2040 & P0) & P0 -> ([a1 + a2] * [a1 + a2] = [a1 + a2] * a1 + [a1 + a2] * a2 & P2039 & P2037 & P2036 & P2034 & P2033 & P2031 & P2030 & P2028 & P2027 & P2025 & P2024 & P2022 & P2021 & P0) & P0" 1; pushreference 20 " P0 -> ( [a1 + a2] * [a1 + a2] = [a1 + a2] * a1 + [a1 + a2] * a2 & P2040 & P0) & P0" "DIST"; pushnode 19 "P0 -> ([a1 + a2] * [a1 + a2] = [a1 + a2] * a1 + [a1 + a2] * a2 & P2039 & P2037 & P2036 & P2034 & P2033 & P2031 & P2030 & P2028 & P2027 & P2025 & P2024 & P2022 & P2021 & P0) & P0" 2; pushnode 18 "( a1 * [a1 + a2] = [a1 + a2] * a1 & P2037 & P0) & P0 -> ([a1 + a2] * [a1 + a2] = a1 * [a1 + a2] + [a1 + a2] * a2 & P2036 & P2034 & P2033 & P2031 & P2030 & P2028 & P2027 & P2025 & P2024 & P2022 & P2021 & P0) & P0" 1; pushreference 17 "P0 -> (a1 * [a1 + a2] = [a1 + a2] * a1 & P2037 & P0) & P0" "CTIMES"; pushnode 16 "P0 -> ([a1 + a2] * [a1 + a2] = a1 * [a1 + a2] + [a1 + a2] * a2 & P2036 & P2034 & P2033 & P2031 & P2030 & P2028 & P2027 & P2025 & P2024 & P2022 & P2021 & P0) & P0" 2; pushnode 15 "( [a1 + a2] * a2 = a1 * a2 + a2 * a2 & P2034 & P0) & P0 -> ([a1 + a2] * [a1 + a2] = a1 * [a1 + a2] + a1 * a2 + a2 * a2 & P2033 & P2031 & P2030 & P2028 & P2027 & P2025 & P2024 & P2022 & P2021 & P0) & P0" 1; pushreference 14 "P0 -> ([a1 + a2] * a2 = a1 * a2 + a2 * a2 & P2034 & P0) & P0" "DIST2"; pushnode 13 "P0 -> ([a1 + a2] * [a1 + a2] = a1 * [a1 + a2] + a1 * a2 + a2 * a2 & P2033 & P2031 & P2030 & P2028 & P2027 & P2025 & P2024 & P2022 & P2021 & P0) & P0" 2; pushnode 12 "(a1 * [a1 + a2] = a1 * a1 + a1 * a2 & P2031 & P0) & P0 -> ([a1 + a2] * [a1 + a2] = [a1 * a1 + a1 * a2] + a1 * a2 + a2 * a2 & P2030 & P2028 & P2027 & P2025 & P2024 & P2022 & P2021 & P0) & P0" 1; pushreference 11 "P0 -> ( a1 * [a1 + a2] = a1 * a1 + a1 * a2 & P2031 & P0) & P0" "DIST"; pushnode 10 " P0 -> ( [a1 + a2] * [a1 + a2] = [ a1 * a1 + a1 * a2] + a1 * a2 + a2 * a2 & P2030 & P2028 & P2027 & P2025 & P2024 & P2022 & P2021 & P0) & P0" 2; pushnode 9 "( [a1 * a1 + a1 * a2] + a1 * a2 + a2 * a2 = a1 * a1 + a1 * a2 + a1 * a2 + a2 * a2 & P2028 & P0) & P0 -> ([a1 + a2] * [a1 + a2] = a1 * a1 + a1 * a2 + a1 * a2 + a2 * a2 & P2027 & P2025 & P2024 & P2022 & P2021 & P0) & P0" 1; pushreference 8 " P0 -> ( [a1 * a1 + a1 * a2] + a1 * a2 + a2 * a2 = a1 * a1 + a1 * a2 + a1 * a2 + a2 * a2 & P2028 & P0) & P0" "APLUS"; pushnode 7 "P0 -> ([a1 + a2] * [a1 + a2] = a1 * a1 + a1 * a2 + a1 * a2 + a2 * a2 & P2027 & P2025 & P2024 & P2022 & P2021 & P0) & P0" 2; pushnode 6 "( [ a1 * a2 + a1 * a2] + a2 * a2 = a1 * a2 + a1 * a2 + a2 * a2 & P2025 & P0) & P0 -> ([a1 + a2] * [a1 + a2] = a1 * a1 + [a1 * a2 + a1 * a2] + a2 * a2 & P2024 & P2022 & P2021 & P0) & P0" 1; pushreference 5 "P0 -> ([a1 * a2 + a1 * a2] + a2 * a2 = a1 * a2 + a1 * a2 + a2 * a2 & P2025 & P0) & P0" "APLUS"; pushnode 4 " P0 -> ( [a1 + a2] * [a1 + a2] = a1 * a1 + [a1 * a2 + a1 * a2] + a2 * a2 & P2024 & P2022 & P2021 & P0) & P0" 2; pushnode 2 " (Two * a1 * a2 = a1 * a2 + a1 * a2 & P2022 & P0) & P0 -> ([a1 + a2] * [a1 + a2] = a1 * a1 + Two * a1 * a2 + a2 * a2 & P2021 & P0) & P0" 1; pushnode 1 "P0 -> ([a1 + a2] * [a1 + a2] = a1 * a1 + Two * a1 * a2 + a2 * a2 & P2021 & P0) & P0" 2; THEOREMS:=("FOIL",(termtosequent(parseprop("P0 -> ([a1 + a2] * [a1 + a2] = a1 * a1 + Two * a1 * a2 + a2 * a2 & P2021 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "FOIL"; pushnode 144 " (One < a1 & P2122 & P2065 & P2063 & P0) & P0 -> (One < a1 & P2183 & P2181 & P2179 & P2178 & P2176 & P2174 & P2060 & P2058 & P0) & P0" 0; pushnode 143 " (One * One = One & P2181 & P2179 & P0) & (One < a1 & P2122 & P2065 & P2063 & P0) & P0 -> ( One * One < a1 & P2178 & P2176 & P2174 & P2060 & P2058 & P0) & P0" 1; pushreference 142 "P0 -> (Real(One) & P2180 & P2179 & P0) & P0" "RONE"; pushnode 141 " (( Real(One) -> One * One = One) & P2179 & P0) & ( One < a1 & P2122 & P2065 & P2063 & P0) & P0 -> ( One * One < a1 & P2178 & P2176 & P2174 & P2060 & P2058 & P0) & P0" 2; pushreference 140 " P0 -> ( (Real(One) -> One * One = One) & P2179 & P0) & P0" "ITIMES"; pushnode 139 " ( One < a1 & P2122 & P2065 & P2063 & P0) & P0 -> ( One * One < a1 & P2178 & P2176 & P2174 & P2060 & P2058 & P0) & P0" 2; pushreference 138 "P0 -> (Zero < One & P2177 & P2176 & P2174 & P2060 & P2058 & P0) & P0" "ZEROLESSONE"; pushnode 137 " (One < a1 & P2122 & P2065 & P2063 & P0) & P0 -> ((Zero < One & One * One < a1) & P2176 & P2174 & P2060 & P2058 & P0) & P0" 2; pushnode 136 " (One < a1 & P2122 & P2065 & P2063 & P0) & P0 -> (One E {x4|Zero < x4 & x4 * x4 < a1} & P2174 & P2060 & P2058 & P0) & P0" 1; pushnode 73 " (One < a1 & P2122 & P2065 & P2063 & P0) & P0 -> ((Ex2.x2 E {x3|Zero < x3 & x3 * x3 < a1}) & P2060 & P2058 & P0) & P0" 1; pushreference 93 "P0 -> ( Zero < Half & P2139 & P0) & P0" "HALFPOS"; pushreference 135 "(Zero < a1 & P2062 & P2059 & P2058 & P0) & (Real(a1) & P2061 & P2059 & P2058 & P0) & P0 -> ( Half * a1 < a1 & P2173 & P2171 & P2145 & P0) & P0" "HalfLess"; pushnode 134 "( a1 * Half = Half * a1 & P2171 & P0) & ( Real(a1) & P2061 & P2059 & P2058 & P0) & (Zero < a1 & P2062 & P2059 & P2058 & P0) & P0 -> (a1 * Half < a1 & P2145 & P0) & P0" 1; pushreference 133 " P0 -> (a1 * Half = Half * a1 & P2171 & P0) & P0" "CTIMES"; pushnode 101 " (Real(a1) & P2061 & P2059 & P2058 & P0) & (Zero < a1 & P2062 & P2059 & P2058 & P0) & P0 -> (a1 * Half < a1 & P2145 & P0) & P0" 2; pushnode 132 " (Half * a1 * Half * a1 < a1 & P2167 & P2164 & P2162 & P2158 & P2156 & P2161 & P2163 & P2165 & P0) & ([[ a1 * a1] * Half] * Half = Half * [a1 * a1] * Half & P2161 & P0) & ([a1 * a1] * Half = a1 * a1 * Half & P2163 & P0) & (a1 * Half = Half * a1 & P2165 & P0) & P0 -> (Half * a1 * Half * a1 < a1 & P2170 & P2168 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 0; pushnode 131 "([ Half * a1] * Half * a1 = Half * a1 * Half * a1 & P2168 & P0) & (a1 * Half = Half * a1 & P2165 & P0) & (Half * a1 * Half * a1 < a1 & P2167 & P2164 & P2162 & P2158 & P2156 & P2161 & P2163 & P2165 & P0) & ([[ a1 * a1] * Half] * Half = Half * [a1 * a1] * Half & P2161 & P0) & ([a1 * a1] * Half = a1 * a1 * Half & P2163 & P0) & P0 -> ( [ Half * a1] * Half * a1 < a1 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 1; pushreference 130 "P0 -> ([Half * a1] * Half * a1 = Half * a1 * Half * a1 & P2168 & P0) & P0" "ATIMES"; pushnode 129 "( a1 * Half = Half * a1 & P2165 & P0) & ( Half * a1 * Half * a1 < a1 & P2167 & P2164 & P2162 & P2158 & P2156 & P2161 & P2163 & P2165 & P0) & ([[ a1 * a1] * Half] * Half = Half * [a1 * a1] * Half & P2161 & P0) & ([a1 * a1] * Half = a1 * a1 * Half & P2163 & P0) & P0 -> ( [ Half * a1] * Half * a1 < a1 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 2; pushnode 127 "( a1 * Half = Half * a1 & P2165 & P0) & ( Half * a1 * a1 * Half < a1 & P2164 & P2162 & P2158 & P2156 & P2161 & P2163 & P0) & ([[ a1 * a1] * Half] * Half = Half * [a1 * a1] * Half & P2161 & P0) & ([a1 * a1] * Half = a1 * a1 * Half & P2163 & P0) & P0 -> ( [ Half * a1] * Half * a1 < a1 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 1; pushreference 126 "P0 -> ( a1 * Half = Half * a1 & P2165 & P0) & P0" "CTIMES"; pushnode 125 " ([a1 * a1] * Half = a1 * a1 * Half & P2163 & P0) & (Half * a1 * a1 * Half < a1 & P2164 & P2162 & P2158 & P2156 & P2161 & P2163 & P0) & ( [[a1 * a1] * Half] * Half = Half * [a1 * a1] * Half & P2161 & P0) & P0 -> ([Half * a1] * Half * a1 < a1 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 2; pushnode 124 " ([a1 * a1] * Half = a1 * a1 * Half & P2163 & P0) & (Half * [a1 * a1] * Half < a1 & P2162 & P2158 & P2156 & P2161 & P0) & ([[ a1 * a1] * Half] * Half = Half * [a1 * a1] * Half & P2161 & P0) & P0 -> ([Half * a1] * Half * a1 < a1 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 1; pushreference 123 " P0 -> ([a1 * a1] * Half = a1 * a1 * Half & P2163 & P0) & P0" "ATIMES"; pushnode 122 "( [[a1 * a1] * Half] * Half = Half * [a1 * a1] * Half & P2161 & P0) & (Half * [a1 * a1] * Half < a1 & P2162 & P2158 & P2156 & P2161 & P0) & P0 -> ([Half * a1] * Half * a1 < a1 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 2; pushnode 121 "([[ a1 * a1] * Half] * Half = Half * [a1 * a1] * Half & P2161 & P0) & ([[a1 * a1] * Half] * Half < a1 & P2158 & P2156 & P0) & P0 -> ([Half * a1] * Half * a1 < a1 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 1; pushreference 120 " P0 -> ([[a1 * a1] * Half] * Half = Half * [a1 * a1] * Half & P2161 & P0) & P0" "CTIMES"; pushnode 117 " ( [[a1 * a1] * Half] * Half < a1 & P2158 & P2156 & P0) & P0 -> ( [ Half * a1] * Half * a1 < a1 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 2; pushnode 119 " (a1 * Half < a1 & P2145 & P0) & P0 -> (a1 * Half < a1 & P2160 & P2157 & P2156 & P0) & P0" 0; pushnode 118 " ( [[a1 * a1] * Half] * Half < a1 * Half & P2153 & P2151 & P0) & P0 -> ([[ a1 * a1] * Half] * Half < a1 * Half & P2159 & P2157 & P2156 & P0) & P0" 0; pushnode 116 " ( [[a1 * a1] * Half] * Half < a1 * Half & P2153 & P2151 & P0) & (a1 * Half < a1 & P2145 & P0) & P0 -> (( [[a1 * a1] * Half] * Half < a1 * Half & a1 * Half < a1) & P2157 & P2156 & P0) & P0" 2; pushnode 115 "(( [[a1 * a1] * Half] * Half < a1 * Half & a1 * Half < a1 -> [[ a1 * a1] * Half] * Half < a1) & P2156 & P0) & ([[a1 * a1] * Half] * Half < a1 * Half & P2153 & P2151 & P0) & ( a1 * Half < a1 & P2145 & P0) & P0 -> ( [ Half * a1] * Half * a1 < a1 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 2; pushreference 114 "P0 -> (( [[a1 * a1] * Half] * Half < a1 * Half & a1 * Half < a1 -> [[ a1 * a1] * Half] * Half < a1) & P2156 & P0) & P0" "TRANS"; pushnode 111 " ( [[a1 * a1] * Half] * Half < a1 * Half & P2153 & P2151 & P0) & (a1 * Half < a1 & P2145 & P0) & P0 -> ([Half * a1] * Half * a1 < a1 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 2; pushnode 113 " ([ a1 * a1] * Half < a1 & P2148 & P2146 & P0) & P0 -> ([ a1 * a1] * Half < a1 & P2155 & P2152 & P2151 & P0) & P0" 0; pushnode 112 "( Zero < Half & P2139 & P0) & P0 -> (Zero < Half & P2154 & P2152 & P2151 & P0) & P0" 0; pushnode 110 " ( [a1 * a1] * Half < a1 & P2148 & P2146 & P0) & (Zero < Half & P2139 & P0) & P0 -> (( Zero < Half & [a1 * a1] * Half < a1) & P2152 & P2151 & P0) & P0" 2; pushnode 109 "(( Zero < Half & [a1 * a1] * Half < a1 -> [[ a1 * a1] * Half] * Half < a1 * Half) & P2151 & P0) & ([a1 * a1] * Half < a1 & P2148 & P2146 & P0) & (a1 * Half < a1 & P2145 & P0) & ( Zero < Half & P2139 & P0) & P0 -> ( [ Half * a1] * Half * a1 < a1 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 2; pushreference 108 "P0 -> ( ( Zero < Half & [a1 * a1] * Half < a1 -> [[a1 * a1] * Half] * Half < a1 * Half) & P2151 & P0) & P0" "MTIMES"; pushnode 105 " ([ a1 * a1] * Half < a1 & P2148 & P2146 & P0) & (a1 * Half < a1 & P2145 & P0) & ( Zero < Half & P2139 & P0) & P0 -> ( [Half * a1] * Half * a1 < a1 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 2; pushnode 107 "( a1 * Half < a1 & P2145 & P0) & P0 -> ( a1 * Half < a1 & P2150 & P2147 & P2146 & P0) & P0" 0; pushnode 106 " ( [a1 * a1] * Half < a1 * Half & P2142 & P2140 & P0) & P0 -> ([ a1 * a1] * Half < a1 * Half & P2149 & P2147 & P2146 & P0) & P0" 0; pushnode 104 " ( a1 * Half < a1 & P2145 & P0) & ( [a1 * a1] * Half < a1 * Half & P2142 & P2140 & P0) & P0 -> (([a1 * a1] * Half < a1 * Half & a1 * Half < a1) & P2147 & P2146 & P0) & P0" 2; pushnode 103 "( ([ a1 * a1] * Half < a1 * Half & a1 * Half < a1 -> [ a1 * a1] * Half < a1) & P2146 & P0) & ( a1 * Half < a1 & P2145 & P0) & ( [a1 * a1] * Half < a1 * Half & P2142 & P2140 & P0) & (Zero < Half & P2139 & P0) & P0 -> ( [ Half * a1] * Half * a1 < a1 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 2; pushreference 102 "P0 -> (( [a1 * a1] * Half < a1 * Half & a1 * Half < a1 -> [a1 * a1] * Half < a1) & P2146 & P0) & P0" "TRANS"; pushnode 100 " (a1 * Half < a1 & P2145 & P0) & ([a1 * a1] * Half < a1 * Half & P2142 & P2140 & P0) & (Zero < Half & P2139 & P0) & P0 -> ( [Half * a1] * Half * a1 < a1 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 2; pushnode 97 " ([ a1 * a1] * Half < a1 * Half & P2142 & P2140 & P0) & (Zero < Half & P2139 & P0) & (Real(a1) & P2061 & P2059 & P2058 & P0) & ( Zero < a1 & P2062 & P2059 & P2058 & P0) & P0 -> ( [Half * a1] * Half * a1 < a1 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 2; pushnode 99 " ( a1 * a1 < a1 & P2138 & P2130 & P2128 & P2137 & P2135 & P2133 & P2136 & P0) & ( a1 * One = One * a1 & P2136 & P0) & ( One * a1 = a1 & P2137 & P2135 & P2133 & P2136 & P0) & P0 -> ( a1 * a1 < a1 & P2144 & P2141 & P2140 & P0) & P0" 0; pushnode 98 "( Zero < Half & P2139 & P0) & P0 -> (Zero < Half & P2143 & P2141 & P2140 & P0) & P0" 0; pushnode 96 "( Zero < Half & P2139 & P0) & ( One * a1 = a1 & P2137 & P2135 & P2133 & P2136 & P0) & (a1 * a1 < a1 & P2138 & P2130 & P2128 & P2137 & P2135 & P2133 & P2136 & P0) & (a1 * One = One * a1 & P2136 & P0) & P0 -> (( Zero < Half & a1 * a1 < a1) & P2141 & P2140 & P0) & P0" 2; pushnode 95 "( ( Zero < Half & a1 * a1 < a1 -> [ a1 * a1] * Half < a1 * Half) & P2140 & P0) & (Zero < Half & P2139 & P0) & (One * a1 = a1 & P2137 & P2135 & P2133 & P2136 & P0) & ( a1 * a1 < a1 & P2138 & P2130 & P2128 & P2137 & P2135 & P2133 & P2136 & P0) & (Real(a1) & P2061 & P2059 & P2058 & P0) & (Zero < a1 & P2062 & P2059 & P2058 & P0) & (a1 * One = One * a1 & P2136 & P0) & P0 -> ( [ Half * a1] * Half * a1 < a1 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 2; pushreference 94 "P0 -> ( (Zero < Half & a1 * a1 < a1 -> [a1 * a1] * Half < a1 * Half) & P2140 & P0) & P0" "MTIMES"; pushnode 92 "( Zero < Half & P2139 & P0) & ( One * a1 = a1 & P2137 & P2135 & P2133 & P2136 & P0) & (a1 * a1 < a1 & P2138 & P2130 & P2128 & P2137 & P2135 & P2133 & P2136 & P0) & ( Real(a1) & P2061 & P2059 & P2058 & P0) & (Zero < a1 & P2062 & P2059 & P2058 & P0) & ( a1 * One = One * a1 & P2136 & P0) & P0 -> ([Half * a1] * Half * a1 < a1 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 2; pushnode 91 " ( One * a1 = a1 & P2137 & P2135 & P2133 & P2136 & P0) & (a1 * a1 < a1 & P2138 & P2130 & P2128 & P2137 & P2135 & P2133 & P2136 & P0) & ( Real(a1) & P2061 & P2059 & P2058 & P0) & (Zero < a1 & P2062 & P2059 & P2058 & P0) & ( a1 * One = One * a1 & P2136 & P0) & P0 -> ([Half * a1] * Half * a1 < a1 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 2; pushnode 90 " ( One * a1 = a1 & P2137 & P2135 & P2133 & P2136 & P0) & (a1 * a1 < One * a1 & P2130 & P2128 & P0) & (Real(a1) & P2061 & P2059 & P2058 & P0) & (Zero < a1 & P2062 & P2059 & P2058 & P0) & ( a1 * One = One * a1 & P2136 & P0) & P0 -> ([Half * a1] * Half * a1 < a1 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 1; pushnode 89 " ( a1 * One = One * a1 & P2136 & P0) & ( a1 * One = a1 & P2135 & P2133 & P0) & ( a1 * a1 < One * a1 & P2130 & P2128 & P0) & ( Real(a1) & P2061 & P2059 & P2058 & P0) & (Zero < a1 & P2062 & P2059 & P2058 & P0) & P0 -> ([Half * a1] * Half * a1 < a1 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 1; pushreference 88 " P0 -> (a1 * One = One * a1 & P2136 & P0) & P0" "CTIMES"; pushnode 87 " (a1 * One = a1 & P2135 & P2133 & P0) & (a1 * a1 < One * a1 & P2130 & P2128 & P0) & (Real(a1) & P2061 & P2059 & P2058 & P0) & (Zero < a1 & P2062 & P2059 & P2058 & P0) & P0 -> ( [Half * a1] * Half * a1 < a1 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 2; pushnode 86 " ( Real(a1) & P2061 & P2059 & P2058 & P0) & P0 -> ( Real(a1) & P2134 & P2133 & P0) & P0" 0; pushnode 85 " ((Real(a1) -> a1 * One = a1) & P2133 & P0) & ( a1 * a1 < One * a1 & P2130 & P2128 & P0) & ( Real(a1) & P2061 & P2059 & P2058 & P0) & (Zero < a1 & P2062 & P2059 & P2058 & P0) & P0 -> ([Half * a1] * Half * a1 < a1 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 2; pushreference 84 " P0 -> ( (Real(a1) -> a1 * One = a1) & P2133 & P0) & P0" "ITIMES"; pushnode 81 "( a1 * a1 < One * a1 & P2130 & P2128 & P0) & ( Real(a1) & P2061 & P2059 & P2058 & P0) & (Zero < a1 & P2062 & P2059 & P2058 & P0) & P0 -> ([Half * a1] * Half * a1 < a1 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 2; pushnode 83 " ( a1 < One & P2121 & P2065 & P2063 & P0) & P0 -> ( a1 < One & P2132 & P2129 & P2128 & P0) & P0" 0; pushnode 82 " ( Zero < a1 & P2062 & P2059 & P2058 & P0) & P0 -> ( Zero < a1 & P2131 & P2129 & P2128 & P0) & P0" 0; pushnode 80 " ( a1 < One & P2121 & P2065 & P2063 & P0) & (Zero < a1 & P2062 & P2059 & P2058 & P0) & P0 -> ( (Zero < a1 & a1 < One) & P2129 & P2128 & P0) & P0" 2; pushnode 79 "(( Zero < a1 & a1 < One -> a1 * a1 < One * a1) & P2128 & P0) & ( a1 < One & P2121 & P2065 & P2063 & P0) & (Real(a1) & P2061 & P2059 & P2058 & P0) & (Zero < a1 & P2062 & P2059 & P2058 & P0) & P0 -> ( [ Half * a1] * Half * a1 < a1 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 2; pushreference 78 "P0 -> (( Zero < a1 & a1 < One -> a1 * a1 < One * a1) & P2128 & P0) & P0" "MTIMES"; pushnode 77 "(a1 < One & P2121 & P2065 & P2063 & P0) & (Real(a1) & P2061 & P2059 & P2058 & P0) & ( Zero < a1 & P2062 & P2059 & P2058 & P0) & P0 -> ( [ Half * a1] * Half * a1 < a1 & P2127 & P2125 & P2123 & P2060 & P2058 & P0) & P0" 2; pushreference 76 " (Zero < a1 & P2062 & P2059 & P2058 & P0) & P0 -> (Zero < Half * a1 & P2126 & P2125 & P2123 & P2060 & P2058 & P0) & P0" "MHALFPOS"; pushnode 75 " ( a1 < One & P2121 & P2065 & P2063 & P0) & (Real(a1) & P2061 & P2059 & P2058 & P0) & (Zero < a1 & P2062 & P2059 & P2058 & P0) & P0 -> ( (Zero < Half * a1 & [Half * a1] * Half * a1 < a1) & P2125 & P2123 & P2060 & P2058 & P0) & P0" 2; pushnode 74 "(a1 < One & P2121 & P2065 & P2063 & P0) & (Real(a1) & P2061 & P2059 & P2058 & P0) & ( Zero < a1 & P2062 & P2059 & P2058 & P0) & P0 -> ( Half * a1 E {x4|Zero < x4 & x4 * x4 < a1} & P2123 & P2060 & P2058 & P0) & P0" 1; pushnode 72 " ( a1 < One & P2121 & P2065 & P2063 & P0) & (Real(a1) & P2061 & P2059 & P2058 & P0) & (Zero < a1 & P2062 & P2059 & P2058 & P0) & P0 -> ((Ex2.x2 E {x3| Zero < x3 & x3 * x3 < a1}) & P2060 & P2058 & P0) & P0" 1; pushnode 7 " (( a1 < One v One < a1) & P2065 & P2063 & P0) & (Real(a1) & P2061 & P2059 & P2058 & P0) & (Zero < a1 & P2062 & P2059 & P2058 & P0) & P0 -> ((Ex2.x2 E {x3| Zero < x3 & x3 * x3 < a1}) & P2060 & P2058 & P0) & P0" 2; pushreference 12 " P0 -> (Real(One) & P2068 & P0) & P0" "RONE"; pushnode 11 " ( Real(a1) & P2061 & P2059 & P2058 & P0) & P0 -> ( Real(a1) & P2067 & P0) & P0" 0; pushnode 10 " (a1 Equal One & P2064 & P2063 & P0) & P0 -> ( a1 Equal One & P2066 & P0) & P0" 0; pushreference 48 "P0 -> (Real(One) & P2102 & P0) & P0" "RONE"; pushreference 47 "P0 -> (Zero < One & P2101 & P0) & P0" "ZEROLESSONE"; pushreference 66 "P0 -> (Real(One) & P2115 & P0) & P0" "RONE"; pushnode 71 "P0 -> ( One + One = One + One & P2120 & P2118 & P0) & P0" 0; pushnode 69 "P0 -> (One + One = Two & P2118 & P0) & P0" 1; pushnode 70 " (One < Two & P2119 & P2117 & P2114 & P2112 & P2116 & P2118 & P0) & (Zero + One = One & P2116 & P0) & (One + One = Two & P2118 & P0) & P0 -> ( One < Two & P2105 & P0) & P0" 0; pushnode 68 "(One + One = Two & P2118 & P0) & ( One < One + One & P2117 & P2114 & P2112 & P2116 & P0) & ( Zero + One = One & P2116 & P0) & P0 -> ( One < Two & P2105 & P0) & P0" 1; pushnode 67 "(Zero + One = One & P2116 & P0) & (One < One + One & P2117 & P2114 & P2112 & P2116 & P0) & P0 -> (One < Two & P2105 & P0) & P0" 2; pushnode 65 "(Zero + One = One & P2116 & P0) & (Zero + One < One + One & P2114 & P2112 & P0) & P0 -> (One < Two & P2105 & P0) & P0" 1; pushreference 64 " (Real(One) & P2115 & P0) & P0 -> (Zero + One = One & P2116 & P0) & P0" "IPLUSb"; pushnode 63 "( Zero + One < One + One & P2114 & P2112 & P0) & P0 -> (One < Two & P2105 & P0) & P0" 3; pushnode 62 " (Zero < One & P2111 & P0) & P0 -> (Zero < One & P2113 & P2112 & P0) & P0" 0; pushnode 61 "(( Zero < One -> Zero + One < One + One) & P2112 & P0) & ( Zero < One & P2111 & P0) & P0 -> (One < Two & P2105 & P0) & P0" 2; pushreference 60 "P0 -> ( (Zero < One -> Zero + One < One + One) & P2112 & P0) & P0" "MPLUS"; pushnode 59 " (Zero < One & P2111 & P0) & P0 -> (One < Two & P2105 & P0) & P0" 2; pushreference 58 "P0 -> (Zero < One & P2111 & P0) & P0" "ZEROLESSONE"; pushnode 51 "P0 -> (One < Two & P2105 & P0) & P0" 2; pushnode 55 " (Half < Two & P2108 & P2106 & P0) & P0 -> ( Half < Two & P2082 & P0) & P0" 0; pushnode 57 " (One < Two & P2105 & P0) & P0 -> (One < Two & P2110 & P2107 & P2106 & P0) & P0" 0; pushnode 56 " ( Half < One & P2104 & P2103 & P2080 & P2079 & P2077 & P0) & ( Half * One = Half & P2080 & P2079 & P2077 & P0) & P0 -> (Half < One & P2109 & P2107 & P2106 & P0) & P0" 0; pushnode 54 "( One < Two & P2105 & P0) & ( Half * One = Half & P2080 & P2079 & P2077 & P0) & (Half < One & P2104 & P2103 & P2080 & P2079 & P2077 & P0) & P0 -> (( Half < One & One < Two) & P2107 & P2106 & P0) & P0" 2; pushnode 53 " (( Half < One & One < Two -> Half < Two) & P2106 & P0) & (One < Two & P2105 & P0) & (Half * One = Half & P2080 & P2079 & P2077 & P0) & (Half < One & P2104 & P2103 & P2080 & P2079 & P2077 & P0) & P0 -> (Half < Two & P2082 & P0) & P0" 2; pushreference 52 "P0 -> (( Half < One & One < Two -> Half < Two) & P2106 & P0) & P0" "TRANS"; pushnode 50 "(One < Two & P2105 & P0) & ( Half * One = Half & P2080 & P2079 & P2077 & P0) & (Half < One & P2104 & P2103 & P2080 & P2079 & P2077 & P0) & P0 -> ( Half < Two & P2082 & P0) & P0" 2; pushnode 49 " (Half * One = Half & P2080 & P2079 & P2077 & P0) & (Half < One & P2104 & P2103 & P2080 & P2079 & P2077 & P0) & P0 -> (Half < Two & P2082 & P0) & P0" 2; pushnode 46 " (Half * One = Half & P2080 & P2079 & P2077 & P0) & ( Half * One < One & P2103 & P0) & P0 -> (Half < Two & P2082 & P0) & P0" 1; pushreference 45 "(Zero < One & P2101 & P0) & (Real(One) & P2102 & P0) & P0 -> ( Half * One < One & P2103 & P0) & P0" "HalfLess"; pushnode 24 " (Half * One = Half & P2080 & P2079 & P2077 & P0) & P0 -> ( Half < Two & P2082 & P0) & P0" 4; pushnode 41 "P0 -> (Inv(Two) = Inv(Two) & P2097 & P2091 & P0) & P0" 0; pushnode 35 "P0 -> ( Half = Inv(Two) & P2091 & P0) & P0" 1; pushnode 42 "P0 -> (One = One & P2099 & P2096 & P2094 & P2093 & P2091 & P2088 & P0) & P0" 0; pushnode 40 "( Two * Inv(Two) = One & P2096 & P2094 & P0) & P0 -> ( Two * Inv(Two) = One & P2093 & P2091 & P2088 & P0) & P0" 1; pushreference 44 "( Zero < Two & P2100 & P0) & ( Two Equal Zero & P2095 & P2094 & P0) & P0 -> P0" "NOTBOTH3"; pushreference 43 "P0 -> (Zero < Two & P2100 & P0) & P0" "TWOPOS"; pushnode 39 " (Two Equal Zero & P2095 & P2094 & P0) & P0 -> P0" 2; pushnode 38 "((Two Equal Zero v Two * Inv(Two) = One) & P2094 & P0) & P0 -> ( Two * Inv(Two) = One & P2093 & P2091 & P2088 & P0) & P0" 2; pushreference 37 " P0 -> ((Two Equal Zero v Two * Inv(Two) = One) & P2094 & P0) & P0" "INV"; pushnode 36 "P0 -> ( Two * Inv(Two) = One & P2093 & P2091 & P2088 & P0) & P0" 2; pushnode 34 "( Half = Inv(Two) & P2091 & P0) & P0 -> (Two * Half = One & P2088 & P0) & P0" 1; pushnode 32 "P0 -> (Two * Half = One & P2088 & P0) & P0" 2; pushnode 33 "( Half * Half < Two * Half & P2085 & P2083 & P0) & P0 -> ( Half * Half < Two * Half & P2090 & P2088 & P2081 & P2079 & P2077 & P2076 & P2069 & P2074 & P2072 & P2070 & P2060 & P2058 & P0) & P0" 0; pushnode 31 "( Two * Half = One & P2088 & P0) & (Half * Half < Two * Half & P2085 & P2083 & P0) & P0 -> ( Half * Half < One & P2081 & P2079 & P2077 & P2076 & P2069 & P2074 & P2072 & P2070 & P2060 & P2058 & P0) & P0" 1; pushnode 28 " ( Half * Half < Two * Half & P2085 & P2083 & P0) & P0 -> ( Half * Half < One & P2081 & P2079 & P2077 & P2076 & P2069 & P2074 & P2072 & P2070 & P2060 & P2058 & P0) & P0" 2; pushnode 30 "( Half < Two & P2082 & P0) & P0 -> (Half < Two & P2087 & P2084 & P2083 & P0) & P0" 0; pushreference 29 "P0 -> (Zero < Half & P2086 & P2084 & P2083 & P0) & P0" "HALFPOS"; pushnode 27 " (Half < Two & P2082 & P0) & P0 -> ( (Zero < Half & Half < Two) & P2084 & P2083 & P0) & P0" 2; pushnode 26 "(( Zero < Half & Half < Two -> Half * Half < Two * Half) & P2083 & P0) & ( Half < Two & P2082 & P0) & P0 -> ( Half * Half < One & P2081 & P2079 & P2077 & P2076 & P2069 & P2074 & P2072 & P2070 & P2060 & P2058 & P0) & P0" 2; pushreference 25 "P0 -> (( Zero < Half & Half < Two -> Half * Half < Two * Half) & P2083 & P0) & P0" "MTIMES"; pushnode 23 " (Half < Two & P2082 & P0) & P0 -> ( Half * Half < One & P2081 & P2079 & P2077 & P2076 & P2069 & P2074 & P2072 & P2070 & P2060 & P2058 & P0) & P0" 2; pushnode 22 " (Half * One = Half & P2080 & P2079 & P2077 & P0) & P0 -> ( Half * Half < One & P2081 & P2079 & P2077 & P2076 & P2069 & P2074 & P2072 & P2070 & P2060 & P2058 & P0) & P0" 2; pushnode 21 "( Half * One = Half & P2079 & P2077 & P0) & P0 -> ([ Half * One] * Half * One < One & P2076 & P2069 & P2074 & P2072 & P2070 & P2060 & P2058 & P0) & P0" 1; pushreference 20 "P0 -> ( Real(Half) & P2078 & P2077 & P0) & P0" "RHALF"; pushnode 19 "((Real(Half) -> Half * One = Half) & P2077 & P0) & P0 -> ([Half * One] * Half * One < One & P2076 & P2069 & P2074 & P2072 & P2070 & P2060 & P2058 & P0) & P0" 2; pushreference 18 " P0 -> ( (Real(Half) -> Half * One = Half) & P2077 & P0) & P0" "ITIMES"; pushnode 17 " P0 -> ([Half * One] * Half * One < One & P2076 & P2069 & P2074 & P2072 & P2070 & P2060 & P2058 & P0) & P0" 2; pushnode 16 "( a1 = One & P2069 & P0) & P0 -> ([Half * a1] * Half * a1 < a1 & P2074 & P2072 & P2070 & P2060 & P2058 & P0) & P0" 1; pushreference 15 " ( Zero < a1 & P2062 & P2059 & P2058 & P0) & P0 -> (Zero < Half * a1 & P2073 & P2072 & P2070 & P2060 & P2058 & P0) & P0" "MHALFPOS"; pushnode 14 " (a1 = One & P2069 & P0) & ( Zero < a1 & P2062 & P2059 & P2058 & P0) & P0 -> (( Zero < Half * a1 & [Half * a1] * Half * a1 < a1) & P2072 & P2070 & P2060 & P2058 & P0) & P0" 2; pushnode 13 " (a1 = One & P2069 & P0) & (Zero < a1 & P2062 & P2059 & P2058 & P0) & P0 -> ( Half * a1 E {x4|Zero < x4 & x4 * x4 < a1} & P2070 & P2060 & P2058 & P0) & P0" 1; pushnode 9 " ( a1 = One & P2069 & P0) & ( Zero < a1 & P2062 & P2059 & P2058 & P0) & P0 -> ((Ex2.x2 E {x3|Zero < x3 & x3 * x3 < a1}) & P2060 & P2058 & P0) & P0" 1; pushreference 8 "( a1 Equal One & P2066 & P0) & ( Real(a1) & P2067 & P0) & ( Real(One) & P2068 & P0) & P0 -> (a1 = One & P2069 & P0) & P0" "EQUALITY"; pushnode 6 " (a1 Equal One & P2064 & P2063 & P0) & (Real(a1) & P2061 & P2059 & P2058 & P0) & (Zero < a1 & P2062 & P2059 & P2058 & P0) & P0 -> ((Ex2.x2 E {x3| Zero < x3 & x3 * x3 < a1}) & P2060 & P2058 & P0) & P0" 5; pushnode 5 "(( a1 Equal One v a1 < One v One < a1) & P2063 & P0) & ( Real(a1) & P2061 & P2059 & P2058 & P0) & (Zero < a1 & P2062 & P2059 & P2058 & P0) & P0 -> ((Ex2.x2 E {x3| Zero < x3 & x3 * x3 < a1}) & P2060 & P2058 & P0) & P0" 2; pushreference 4 " P0 -> ((a1 Equal One v a1 < One v One < a1) & P2063 & P0) & P0" "TRI"; pushnode 3 " (Real(a1) & P2061 & P2059 & P2058 & P0) & (Zero < a1 & P2062 & P2059 & P2058 & P0) & P0 -> ((Ex2.x2 E {x3|Zero < x3 & x3 * x3 < a1}) & P2060 & P2058 & P0) & P0" 2; THEOREMS:=("SupLemma",(termtosequent(parseprop(" (Real(a1) & P2061 & P2059 & P2058 & P0) & (Zero < a1 & P2062 & P2059 & P2058 & P0) & P0 -> ((Ex2.x2 E {x3|Zero < x3 & x3 * x3 < a1}) & P2060 & P2058 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "SupLemma"; pushnode 14 "P0 -> ( Inv(Two) = Inv(Two) & P2195 & P2185 & P0) & P0" 0; pushnode 3 "P0 -> (Half = Inv(Two) & P2185 & P0) & P0" 1; pushnode 11 "( Two * Inv(Two) = One & P2193 & P2191 & P0) & P0 -> ( Two * Inv(Two) = One & P2190 & P2188 & P2187 & P2185 & P2184 & P0) & P0" 0; pushreference 13 " (Zero < Two & P2194 & P0) & (Two Equal Zero & P2192 & P2191 & P0) & P0 -> P0" "NOTBOTH3"; pushreference 12 "P0 -> (Zero < Two & P2194 & P0) & P0" "TWOPOS"; pushnode 10 "( Two Equal Zero & P2192 & P2191 & P0) & P0 -> P0" 2; pushnode 9 "( (Two Equal Zero v Two * Inv(Two) = One) & P2191 & P0) & P0 -> ( Two * Inv(Two) = One & P2190 & P2188 & P2187 & P2185 & P2184 & P0) & P0" 2; pushreference 8 "P0 -> ((Two Equal Zero v Two * Inv(Two) = One) & P2191 & P0) & P0" "INV"; pushnode 7 "P0 -> ( Two * Inv(Two) = One & P2190 & P2188 & P2187 & P2185 & P2184 & P0) & P0" 2; pushnode 6 "( Inv(Two) * Two = Two * Inv(Two) & P2188 & P0) & P0 -> ( Inv(Two) * Two = One & P2187 & P2185 & P2184 & P0) & P0" 1; pushreference 5 "P0 -> ( Inv(Two) * Two = Two * Inv(Two) & P2188 & P0) & P0" "CTIMES"; pushnode 4 " P0 -> (Inv(Two) * Two = One & P2187 & P2185 & P2184 & P0) & P0" 2; pushnode 2 " (Half = Inv(Two) & P2185 & P0) & P0 -> (Half * Two = One & P2184 & P0) & P0" 1; pushnode 1 "P0 -> (Half * Two = One & P2184 & P0) & P0" 2; THEOREMS:=("HALFTWO",(termtosequent(parseprop("P0 -> (Half * Two = One & P2184 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "HALFTWO"; pushnode 17 " (a1 * a1 + Two * a1 * a2 + a2 * a2 < a1 * a2 + Two * a1 * a2 + a2 * a2 & P2211 & P2208 & P2206 & P2209 & P0) & ( a2 * a1 = a1 * a2 & P2209 & P0) & P0 -> ( a1 * a1 + Two * a1 * a2 + a2 * a2 < a1 * a2 + Two * a1 * a2 + a2 * a2 & P2198 & P2196 & P0) & P0" 0; pushnode 15 "( a2 * a1 = a1 * a2 & P2209 & P0) & ( a1 * a1 + Two * a1 * a2 + a2 * a2 < a2 * a1 + Two * a1 * a2 + a2 * a2 & P2208 & P2206 & P0) & P0 -> (a1 * a1 + Two * a1 * a2 + a2 * a2 < a1 * a2 + Two * a1 * a2 + a2 * a2 & P2198 & P2196 & P0) & P0" 1; pushreference 14 " P0 -> (a2 * a1 = a1 * a2 & P2209 & P0) & P0" "CTIMES"; pushnode 13 " (a1 * a1 + Two * a1 * a2 + a2 * a2 < a2 * a1 + Two * a1 * a2 + a2 * a2 & P2208 & P2206 & P0) & P0 -> ( a1 * a1 + Two * a1 * a2 + a2 * a2 < a1 * a2 + Two * a1 * a2 + a2 * a2 & P2198 & P2196 & P0) & P0" 2; pushnode 12 "( a1 * a1 < a2 * a1 & P2203 & P2201 & P0) & P0 -> ( a1 * a1 < a2 * a1 & P2207 & P2206 & P0) & P0" 0; pushnode 11 "( ( a1 * a1 < a2 * a1 -> a1 * a1 + Two * a1 * a2 + a2 * a2 < a2 * a1 + Two * a1 * a2 + a2 * a2) & P2206 & P0) & ( a1 * a1 < a2 * a1 & P2203 & P2201 & P0) & P0 -> (a1 * a1 + Two * a1 * a2 + a2 * a2 < a1 * a2 + Two * a1 * a2 + a2 * a2 & P2198 & P2196 & P0) & P0" 2; pushreference 10 " P0 -> ( (a1 * a1 < a2 * a1 -> a1 * a1 + Two * a1 * a2 + a2 * a2 < a2 * a1 + Two * a1 * a2 + a2 * a2) & P2206 & P0) & P0" "MPLUS"; pushnode 7 "( a1 * a1 < a2 * a1 & P2203 & P2201 & P0) & P0 -> (a1 * a1 + Two * a1 * a2 + a2 * a2 < a1 * a2 + Two * a1 * a2 + a2 * a2 & P2198 & P2196 & P0) & P0" 2; pushnode 9 " ( a1 < a2 & P2200 & P2197 & P2196 & P0) & P0 -> ( a1 < a2 & P2205 & P2202 & P2201 & P0) & P0" 0; pushnode 8 " ( Zero < a1 & P2199 & P2197 & P2196 & P0) & P0 -> ( Zero < a1 & P2204 & P2202 & P2201 & P0) & P0" 0; pushnode 6 " ( Zero < a1 & P2199 & P2197 & P2196 & P0) & (a1 < a2 & P2200 & P2197 & P2196 & P0) & P0 -> (( Zero < a1 & a1 < a2) & P2202 & P2201 & P0) & P0" 2; pushnode 5 " (( Zero < a1 & a1 < a2 -> a1 * a1 < a2 * a1) & P2201 & P0) & ( Zero < a1 & P2199 & P2197 & P2196 & P0) & (a1 < a2 & P2200 & P2197 & P2196 & P0) & P0 -> ( a1 * a1 + Two * a1 * a2 + a2 * a2 < a1 * a2 + Two * a1 * a2 + a2 * a2 & P2198 & P2196 & P0) & P0" 2; pushreference 4 "P0 -> (( Zero < a1 & a1 < a2 -> a1 * a1 < a2 * a1) & P2201 & P0) & P0" "MTIMES"; pushnode 3 "(Zero < a1 & P2199 & P2197 & P2196 & P0) & (a1 < a2 & P2200 & P2197 & P2196 & P0) & P0 -> (a1 * a1 + Two * a1 * a2 + a2 * a2 < a1 * a2 + Two * a1 * a2 + a2 * a2 & P2198 & P2196 & P0) & P0" 2; THEOREMS:=("ORDERLEMMA1",(termtosequent(parseprop(" ( Zero < a1 & P2199 & P2197 & P2196 & P0) & (a1 < a2 & P2200 & P2197 & P2196 & P0) & P0 -> ( a1 * a1 + Two * a1 * a2 + a2 * a2 < a1 * a2 + Two * a1 * a2 + a2 * a2 & P2198 & P2196 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "ORDERLEMMA1"; pushreference 10 "P0 -> (Real(One) & P2217 & P0) & P0" "RONE"; pushreference 24 "P0 -> (Real(One) & P2228 & P0) & P0" "RONE"; pushnode 39 "P0 -> (One + One + One = One + One + One & P2242 & P2238 & P0) & P0" 0; pushnode 36 " P0 -> ( Three = One + One + One & P2238 & P0) & P0" 1; pushnode 38 " (Zero < One + One + One & P2237 & P2233 & P2231 & P2236 & P0) & ([ One + One] + One = One + One + One & P2236 & P0) & P0 -> ( Zero < One + One + One & P2241 & P2238 & P2212 & P0) & P0" 0; pushnode 35 "(Three = One + One + One & P2238 & P0) & ([One + One] + One = One + One + One & P2236 & P0) & (Zero < One + One + One & P2237 & P2233 & P2231 & P2236 & P0) & P0 -> ( Zero < Three & P2212 & P0) & P0" 1; pushnode 34 "( [One + One] + One = One + One + One & P2236 & P0) & (Zero < One + One + One & P2237 & P2233 & P2231 & P2236 & P0) & P0 -> (Zero < Three & P2212 & P0) & P0" 2; pushnode 33 " ( [One + One] + One = One + One + One & P2236 & P0) & (Zero < [ One + One] + One & P2233 & P2231 & P0) & P0 -> (Zero < Three & P2212 & P0) & P0" 1; pushreference 32 "P0 -> ( [One + One] + One = One + One + One & P2236 & P0) & P0" "APLUS"; pushnode 29 "( Zero < [One + One] + One & P2233 & P2231 & P0) & P0 -> (Zero < Three & P2212 & P0) & P0" 2; pushnode 31 "( One < [One + One] + One & P2230 & P2227 & P2225 & P2229 & P0) & ( Zero + One = One & P2229 & P0) & P0 -> (One < [One + One] + One & P2235 & P2232 & P2231 & P0) & P0" 0; pushnode 30 " (Zero < One & P2213 & P0) & P0 -> (Zero < One & P2234 & P2232 & P2231 & P0) & P0" 0; pushnode 28 "(Zero + One = One & P2229 & P0) & (One < [One + One] + One & P2230 & P2227 & P2225 & P2229 & P0) & ( Zero < One & P2213 & P0) & P0 -> ( (Zero < One & One < [ One + One] + One) & P2232 & P2231 & P0) & P0" 2; pushnode 27 "(( Zero < One & One < [One + One] + One -> Zero < [One + One] + One) & P2231 & P0) & (Zero + One = One & P2229 & P0) & (One < [One + One] + One & P2230 & P2227 & P2225 & P2229 & P0) & ( Zero < One & P2213 & P0) & P0 -> ( Zero < Three & P2212 & P0) & P0" 2; pushreference 26 "P0 -> (( Zero < One & One < [One + One] + One -> Zero < [One + One] + One) & P2231 & P0) & P0" "TRANS"; pushnode 25 "(Zero + One = One & P2229 & P0) & (One < [One + One] + One & P2230 & P2227 & P2225 & P2229 & P0) & ( Zero < One & P2213 & P0) & P0 -> ( Zero < Three & P2212 & P0) & P0" 2; pushnode 23 " (Zero + One = One & P2229 & P0) & (Zero + One < [One + One] + One & P2227 & P2225 & P0) & (Zero < One & P2213 & P0) & P0 -> (Zero < Three & P2212 & P0) & P0" 1; pushreference 22 " (Real(One) & P2228 & P0) & P0 -> (Zero + One = One & P2229 & P0) & P0" "IPLUSb"; pushnode 21 " (Zero + One < [One + One] + One & P2227 & P2225 & P0) & (Zero < One & P2213 & P0) & P0 -> ( Zero < Three & P2212 & P0) & P0" 3; pushnode 20 " (Zero < One + One & P2222 & P2220 & P0) & P0 -> (Zero < One + One & P2226 & P2225 & P0) & P0" 0; pushnode 19 "( (Zero < One + One -> Zero + One < [One + One] + One) & P2225 & P0) & ( Zero < One + One & P2222 & P2220 & P0) & ( Zero < One & P2213 & P0) & P0 -> ( Zero < Three & P2212 & P0) & P0" 2; pushreference 18 "P0 -> ( (Zero < One + One -> Zero + One < [One + One] + One) & P2225 & P0) & P0" "MPLUS"; pushnode 15 "(Zero < One + One & P2222 & P2220 & P0) & ( Zero < One & P2213 & P0) & P0 -> (Zero < Three & P2212 & P0) & P0" 2; pushnode 17 " (One < One + One & P2219 & P2216 & P2214 & P2218 & P0) & (Zero + One = One & P2218 & P0) & P0 -> ( One < One + One & P2224 & P2221 & P2220 & P0) & P0" 0; pushnode 16 "( Zero < One & P2213 & P0) & P0 -> (Zero < One & P2223 & P2221 & P2220 & P0) & P0" 0; pushnode 14 "(Zero + One = One & P2218 & P0) & (One < One + One & P2219 & P2216 & P2214 & P2218 & P0) & ( Zero < One & P2213 & P0) & P0 -> ((Zero < One & One < One + One) & P2221 & P2220 & P0) & P0" 2; pushnode 13 "(( Zero < One & One < One + One -> Zero < One + One) & P2220 & P0) & ( Zero + One = One & P2218 & P0) & (One < One + One & P2219 & P2216 & P2214 & P2218 & P0) & (Zero < One & P2213 & P0) & P0 -> ( Zero < Three & P2212 & P0) & P0" 2; pushreference 12 "P0 -> ((Zero < One & One < One + One -> Zero < One + One) & P2220 & P0) & P0" "TRANS"; pushnode 11 "(Zero + One = One & P2218 & P0) & (One < One + One & P2219 & P2216 & P2214 & P2218 & P0) & ( Zero < One & P2213 & P0) & P0 -> ( Zero < Three & P2212 & P0) & P0" 2; pushnode 9 "(Zero + One = One & P2218 & P0) & (Zero + One < One + One & P2216 & P2214 & P0) & ( Zero < One & P2213 & P0) & P0 -> ( Zero < Three & P2212 & P0) & P0" 1; pushreference 8 " (Real(One) & P2217 & P0) & P0 -> (Zero + One = One & P2218 & P0) & P0" "IPLUSb"; pushnode 7 "( Zero + One < One + One & P2216 & P2214 & P0) & ( Zero < One & P2213 & P0) & P0 -> (Zero < Three & P2212 & P0) & P0" 3; pushnode 6 " (Zero < One & P2213 & P0) & P0 -> ( Zero < One & P2215 & P2214 & P0) & P0" 0; pushnode 5 "((Zero < One -> Zero + One < One + One) & P2214 & P0) & ( Zero < One & P2213 & P0) & P0 -> (Zero < Three & P2212 & P0) & P0" 2; pushreference 4 "P0 -> ((Zero < One -> Zero + One < One + One) & P2214 & P0) & P0" "MPLUS"; pushnode 3 " (Zero < One & P2213 & P0) & P0 -> (Zero < Three & P2212 & P0) & P0" 2; pushreference 2 "P0 -> (Zero < One & P2213 & P0) & P0" "ZEROLESSONE"; pushnode 1 "P0 -> (Zero < Three & P2212 & P0) & P0" 2; THEOREMS:=("THREEPOS",(termtosequent(parseprop("P0 -> (Zero < Three & P2212 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "THREEPOS"; pushnode 15 "(Zero < a1 * a2 & P2256 & P2254 & P2250 & P2248 & P2253 & P2255 & P0) & ( Zero * a1 = Zero & P2253 & P0) & (a2 * a1 = a1 * a2 & P2255 & P0) & P0 -> (Zero < a1 * a2 & P2245 & P2243 & P0) & P0" 0; pushnode 14 "( a2 * a1 = a1 * a2 & P2255 & P0) & (Zero < a2 * a1 & P2254 & P2250 & P2248 & P2253 & P0) & ( Zero * a1 = Zero & P2253 & P0) & P0 -> (Zero < a1 * a2 & P2245 & P2243 & P0) & P0" 1; pushreference 13 "P0 -> ( a2 * a1 = a1 * a2 & P2255 & P0) & P0" "CTIMES"; pushnode 12 "(Zero * a1 = Zero & P2253 & P0) & ( Zero < a2 * a1 & P2254 & P2250 & P2248 & P2253 & P0) & P0 -> ( Zero < a1 * a2 & P2245 & P2243 & P0) & P0" 2; pushnode 11 "(Zero * a1 = Zero & P2253 & P0) & ( Zero * a1 < a2 * a1 & P2250 & P2248 & P0) & P0 -> ( Zero < a1 * a2 & P2245 & P2243 & P0) & P0" 1; pushreference 10 "P0 -> (Zero * a1 = Zero & P2253 & P0) & P0" "MZERO2"; pushnode 7 "( Zero * a1 < a2 * a1 & P2250 & P2248 & P0) & P0 -> (Zero < a1 * a2 & P2245 & P2243 & P0) & P0" 2; pushnode 9 " ( Zero < a2 & P2247 & P2244 & P2243 & P0) & P0 -> ( Zero < a2 & P2252 & P2249 & P2248 & P0) & P0" 0; pushnode 8 " ( Zero < a1 & P2246 & P2244 & P2243 & P0) & P0 -> ( Zero < a1 & P2251 & P2249 & P2248 & P0) & P0" 0; pushnode 6 " ( Zero < a1 & P2246 & P2244 & P2243 & P0) & (Zero < a2 & P2247 & P2244 & P2243 & P0) & P0 -> ( (Zero < a1 & Zero < a2) & P2249 & P2248 & P0) & P0" 2; pushnode 5 "(( Zero < a1 & Zero < a2 -> Zero * a1 < a2 * a1) & P2248 & P0) & ( Zero < a1 & P2246 & P2244 & P2243 & P0) & (Zero < a2 & P2247 & P2244 & P2243 & P0) & P0 -> ( Zero < a1 * a2 & P2245 & P2243 & P0) & P0" 2; pushreference 4 "P0 -> (( Zero < a1 & Zero < a2 -> Zero * a1 < a2 * a1) & P2248 & P0) & P0" "MTIMES"; pushnode 3 " (Zero < a1 & P2246 & P2244 & P2243 & P0) & (Zero < a2 & P2247 & P2244 & P2243 & P0) & P0 -> ( Zero < a1 * a2 & P2245 & P2243 & P0) & P0" 2; THEOREMS:=("TIMESPOS",(termtosequent(parseprop(" (Zero < a1 & P2246 & P2244 & P2243 & P0) & (Zero < a2 & P2247 & P2244 & P2243 & P0) & P0 -> ( Zero < a1 * a2 & P2245 & P2243 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "TIMESPOS"; pushnode 21 "P0 -> ( One + One = One + One & P2278 & P2271 & P0) & P0" 0; pushnode 15 "P0 -> (Two = One + One & P2271 & P0) & P0" 1; pushnode 20 "P0 -> ( One + One + One = One + One + One & P2277 & P2274 & P0) & P0" 0; pushnode 18 "P0 -> ( Three = One + One + One & P2274 & P0) & P0" 1; pushnode 19 " P0 -> (Three * a1 = Three * a1 & P2276 & P2274 & P2273 & P2271 & P2270 & P2268 & P2267 & P2265 & P2264 & P2262 & P2260 & P2259 & P2257 & P0) & P0" 0; pushnode 17 "(Three = One + One + One & P2274 & P0) & P0 -> ( [One + One + One] * a1 = Three * a1 & P2273 & P2271 & P2270 & P2268 & P2267 & P2265 & P2264 & P2262 & P2260 & P2259 & P2257 & P0) & P0" 1; pushnode 16 " P0 -> ([One + One + One] * a1 = Three * a1 & P2273 & P2271 & P2270 & P2268 & P2267 & P2265 & P2264 & P2262 & P2260 & P2259 & P2257 & P0) & P0" 2; pushnode 14 " (Two = One + One & P2271 & P0) & P0 -> ([ One + Two] * a1 = Three * a1 & P2270 & P2268 & P2267 & P2265 & P2264 & P2262 & P2260 & P2259 & P2257 & P0) & P0" 1; pushnode 13 "P0 -> ([One + Two] * a1 = Three * a1 & P2270 & P2268 & P2267 & P2265 & P2264 & P2262 & P2260 & P2259 & P2257 & P0) & P0" 2; pushnode 12 "([ One + Two] * a1 = One * a1 + Two * a1 & P2268 & P0) & P0 -> ( One * a1 + Two * a1 = Three * a1 & P2267 & P2265 & P2264 & P2262 & P2260 & P2259 & P2257 & P0) & P0" 1; pushreference 11 "P0 -> ( [One + Two] * a1 = One * a1 + Two * a1 & P2268 & P0) & P0" "DIST2"; pushnode 10 "P0 -> (One * a1 + Two * a1 = Three * a1 & P2267 & P2265 & P2264 & P2262 & P2260 & P2259 & P2257 & P0) & P0" 2; pushnode 9 "(a1 * One = One * a1 & P2265 & P0) & P0 -> ( a1 * One + Two * a1 = Three * a1 & P2264 & P2262 & P2260 & P2259 & P2257 & P0) & P0" 1; pushreference 8 " P0 -> (a1 * One = One * a1 & P2265 & P0) & P0" "CTIMES"; pushnode 7 "P0 -> (a1 * One + Two * a1 = Three * a1 & P2264 & P2262 & P2260 & P2259 & P2257 & P0) & P0" 2; pushnode 6 "( a1 * One = a1 & P2262 & P2260 & P0) & P0 -> (a1 + Two * a1 = Three * a1 & P2259 & P2257 & P0) & P0" 1; pushnode 5 " (Real(a1) & P2258 & P2257 & P0) & P0 -> ( Real(a1) & P2261 & P2260 & P0) & P0" 0; pushnode 4 "((Real(a1) -> a1 * One = a1) & P2260 & P0) & (Real(a1) & P2258 & P2257 & P0) & P0 -> (a1 + Two * a1 = Three * a1 & P2259 & P2257 & P0) & P0" 2; pushreference 3 " P0 -> ( (Real(a1) -> a1 * One = a1) & P2260 & P0) & P0" "ITIMES"; pushnode 2 "( Real(a1) & P2258 & P2257 & P0) & P0 -> (a1 + Two * a1 = Three * a1 & P2259 & P2257 & P0) & P0" 2; THEOREMS:=("LIKETERMS1",(termtosequent(parseprop(" (Real(a1) & P2258 & P2257 & P0) & P0 -> (a1 + Two * a1 = Three * a1 & P2259 & P2257 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "LIKETERMS1"; pushnode 30 "( Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & P0 -> (Real(a1) & P2309 & P0) & P0" 0; pushnode 29 "(Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & P0 -> (Zero < a1 & P2308 & P0) & P0" 0; pushnode 44 "(Zero < a8 & P2303 & P2302 & P2300 & P2299 & P2297 & P2296 & P0) & P0 -> (Zero < a8 & P2320 & P0) & P0" 0; pushnode 56 " (Zero < a1 + One & P2330 & P2328 & P0) & P0 -> (Zero < a1 + One & P2318 & P0) & P0" 0; pushnode 58 " (a1 < a1 + One & P2327 & P0) & P0 -> (a1 < a1 + One & P2332 & P2329 & P2328 & P0) & P0" 0; pushnode 57 " (Zero < a1 & P2324 & P2322 & P0) & P0 -> ( Zero < a1 & P2331 & P2329 & P2328 & P0) & P0" 0; pushnode 55 " (a1 < a1 + One & P2327 & P0) & (Zero < a1 & P2324 & P2322 & P0) & P0 -> (( Zero < a1 & a1 < a1 + One) & P2329 & P2328 & P0) & P0" 2; pushnode 54 "(( Zero < a1 & a1 < a1 + One -> Zero < a1 + One) & P2328 & P0) & ( a1 < a1 + One & P2327 & P0) & ( Zero < a1 & P2324 & P2322 & P0) & P0 -> ( Zero < a1 + One & P2318 & P0) & P0" 2; pushreference 53 "P0 -> ((Zero < a1 & a1 < a1 + One -> Zero < a1 + One) & P2328 & P0) & P0" "TRANS"; pushnode 52 " (a1 < a1 + One & P2327 & P0) & (Zero < a1 & P2324 & P2322 & P0) & P0 -> (Zero < a1 + One & P2318 & P0) & P0" 2; pushreference 51 "P0 -> (a1 < a1 + One & P2327 & P0) & P0" "SOMETHINGBIGGER"; pushnode 48 " (Zero < a1 & P2324 & P2322 & P0) & P0 -> (Zero < a1 + One & P2318 & P0) & P0" 2; pushnode 50 "( a8 * a8 < a1 & P2304 & P2302 & P2300 & P2299 & P2297 & P2296 & P0) & P0 -> (a8 * a8 < a1 & P2326 & P2323 & P2322 & P0) & P0" 0; pushnode 49 " (Zero < a8 * a8 & P2321 & P0) & P0 -> (Zero < a8 * a8 & P2325 & P2323 & P2322 & P0) & P0" 0; pushnode 47 " (Zero < a8 * a8 & P2321 & P0) & (a8 * a8 < a1 & P2304 & P2302 & P2300 & P2299 & P2297 & P2296 & P0) & P0 -> ((Zero < a8 * a8 & a8 * a8 < a1) & P2323 & P2322 & P0) & P0" 2; pushnode 46 "(( Zero < a8 * a8 & a8 * a8 < a1 -> Zero < a1) & P2322 & P0) & ( Zero < a8 * a8 & P2321 & P0) & ( a8 * a8 < a1 & P2304 & P2302 & P2300 & P2299 & P2297 & P2296 & P0) & P0 -> ( Zero < a1 + One & P2318 & P0) & P0" 2; pushreference 45 "P0 -> ((Zero < a8 * a8 & a8 * a8 < a1 -> Zero < a1) & P2322 & P0) & P0" "TRANS"; pushnode 43 " (Zero < a8 * a8 & P2321 & P0) & (a8 * a8 < a1 & P2304 & P2302 & P2300 & P2299 & P2297 & P2296 & P0) & P0 -> (Zero < a1 + One & P2318 & P0) & P0" 2; pushreference 42 " (Zero < a8 & P2320 & P0) & P0 -> (Zero < a8 * a8 & P2321 & P0) & P0" "SQPOS"; pushnode 41 " (Zero < a8 & P2303 & P2302 & P2300 & P2299 & P2297 & P2296 & P0) & (a8 * a8 < a1 & P2304 & P2302 & P2300 & P2299 & P2297 & P2296 & P0) & P0 -> (Zero < a1 + One & P2318 & P0) & P0" 3; pushnode 40 " (Zero < a8 & P2303 & P2302 & P2300 & P2299 & P2297 & P2296 & P0) & P0 -> ( Zero < a8 & P2317 & P0) & P0" 0; pushnode 39 " (a8 * a8 < [a1 + One] * [a1 + One] & P2313 & P2311 & P0) & P0 -> ( a8 * a8 < [a1 + One] * [a1 + One] & P2316 & P0) & P0" 0; pushnode 38 " (a8 < a1 + One & P2319 & P0) & P0 -> (a8 < a1 + One & P2307 & P2305 & P2301 & P2299 & P2297 & P2296 & P0) & P0" 0; pushreference 37 "( a8 * a8 < [a1 + One] * [a1 + One] & P2316 & P0) & (Zero < a8 & P2317 & P0) & (Zero < a1 + One & P2318 & P0) & P0 -> (a8 < a1 + One & P2319 & P0) & P0" "SquareOrder2"; pushnode 34 "( a8 * a8 < [a1 + One] * [a1 + One] & P2313 & P2311 & P0) & (Zero < a8 & P2303 & P2302 & P2300 & P2299 & P2297 & P2296 & P0) & ( a8 * a8 < a1 & P2304 & P2302 & P2300 & P2299 & P2297 & P2296 & P0) & P0 -> ( a8 < a1 + One & P2307 & P2305 & P2301 & P2299 & P2297 & P2296 & P0) & P0" 5; pushnode 36 "(a1 < [a1 + One] * [a1 + One] & P2310 & P0) & P0 -> (a1 < [a1 + One] * [a1 + One] & P2315 & P2312 & P2311 & P0) & P0" 0; pushnode 35 "(a8 * a8 < a1 & P2304 & P2302 & P2300 & P2299 & P2297 & P2296 & P0) & P0 -> (a8 * a8 < a1 & P2314 & P2312 & P2311 & P0) & P0" 0; pushnode 33 " (a1 < [a1 + One] * [a1 + One] & P2310 & P0) & ( a8 * a8 < a1 & P2304 & P2302 & P2300 & P2299 & P2297 & P2296 & P0) & P0 -> ( (a8 * a8 < a1 & a1 < [a1 + One] * [a1 + One]) & P2312 & P2311 & P0) & P0" 2; pushnode 32 "( ( a8 * a8 < a1 & a1 < [a1 + One] * [a1 + One] -> a8 * a8 < [a1 + One] * [a1 + One]) & P2311 & P0) & (a1 < [a1 + One] * [a1 + One] & P2310 & P0) & ( Zero < a8 & P2303 & P2302 & P2300 & P2299 & P2297 & P2296 & P0) & ( a8 * a8 < a1 & P2304 & P2302 & P2300 & P2299 & P2297 & P2296 & P0) & P0 -> (a8 < a1 + One & P2307 & P2305 & P2301 & P2299 & P2297 & P2296 & P0) & P0" 2; pushreference 31 " P0 -> (( a8 * a8 < a1 & a1 < [a1 + One] * [a1 + One] -> a8 * a8 < [a1 + One] * [a1 + One]) & P2311 & P0) & P0" "TRANS"; pushnode 28 "(a1 < [a1 + One] * [a1 + One] & P2310 & P0) & (Zero < a8 & P2303 & P2302 & P2300 & P2299 & P2297 & P2296 & P0) & ( a8 * a8 < a1 & P2304 & P2302 & P2300 & P2299 & P2297 & P2296 & P0) & P0 -> ( a8 < a1 + One & P2307 & P2305 & P2301 & P2299 & P2297 & P2296 & P0) & P0" 2; pushreference 27 "( Zero < a1 & P2308 & P0) & ( Real(a1) & P2309 & P0) & P0 -> (a1 < [a1 + One] * [a1 + One] & P2310 & P0) & P0" "SqLemma"; pushnode 26 "(Zero < a8 & P2303 & P2302 & P2300 & P2299 & P2297 & P2296 & P0) & ( a8 * a8 < a1 & P2304 & P2302 & P2300 & P2299 & P2297 & P2296 & P0) & ( Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & P0 -> (a8 < a1 + One & P2307 & P2305 & P2301 & P2299 & P2297 & P2296 & P0) & P0" 4; pushnode 25 "( Zero < a8 & P2303 & P2302 & P2300 & P2299 & P2297 & P2296 & P0) & ( a8 * a8 < a1 & P2304 & P2302 & P2300 & P2299 & P2297 & P2296 & P0) & ( Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & P0 -> ( (a8 Equal a1 + One v a8 < a1 + One) & P2305 & P2301 & P2299 & P2297 & P2296 & P0) & P0" 1; pushnode 24 " (Zero < a8 & P2303 & P2302 & P2300 & P2299 & P2297 & P2296 & P0) & (a8 * a8 < a1 & P2304 & P2302 & P2300 & P2299 & P2297 & P2296 & P0) & ( Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & P0 -> (a8 <= a1 + One & P2301 & P2299 & P2297 & P2296 & P0) & P0" 1; pushnode 23 " (( Zero < a8 & a8 * a8 < a1) & P2302 & P2300 & P2299 & P2297 & P2296 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & P0 -> ( a8 <= a1 + One & P2301 & P2299 & P2297 & P2296 & P0) & P0" 1; pushnode 22 "(a8 E {x3|Zero < x3 & x3 * x3 < a1} & P2300 & P2299 & P2297 & P2296 & P0) & ( Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & P0 -> ( a8 <= a1 + One & P2301 & P2299 & P2297 & P2296 & P0) & P0" 1; pushnode 21 " (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & (Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & P0 -> ((a8 E {x4|Zero < x4 & x4 * x4 < a1} -> a8 <= a1 + One) & P2299 & P2297 & P2296 & P0) & P0" 1; pushnode 19 "( Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & P0 -> ((Ax5.x5 E {x7|Zero < x7 & x7 * x7 < a1} -> x5 <= a1 + One) & P2297 & P2296 & P0) & P0" 1; THEOREMS:=("BDED",(termtosequent(parseprop("( Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & P0 -> ((Ax5.x5 E {x7|Zero < x7 & x7 * x7 < a1} -> x5 <= a1 + One) & P2297 & P2296 & P0) & P0")),hd(!PROOFSTACK)))::(!THEOREMS); PROOFSTACK:=nil; td "BDED"; pushreference 6 " P0 -> ( ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) Equal a1 v Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < a1 v a1 < Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1})) & P2287 & P0) & P0" "TRI"; pushnode 14 "( Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & P0 -> (Real(a1) & P2292 & P0) & P0" 0; pushreference 13 "P0 -> ( Real(Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1})) & P2291 & P0) & P0" "RTIMES"; pushnode 12 "( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) Equal a1 & P2288 & P2287 & P0) & P0 -> ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) Equal a1 & P2290 & P0) & P0" 0; pushnode 11 "( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2293 & P0) & P0 -> ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & P0" 0; pushreference 10 "( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) Equal a1 & P2290 & P0) & ( Real(Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1})) & P2291 & P0) & (Real(a1) & P2292 & P0) & P0 -> ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2293 & P0) & P0" "EQUALITY"; pushnode 8 "( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) Equal a1 & P2288 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & P0 -> ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & P0" 5; pushgoal 16 "( a1 < Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) & P2295 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & (Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & P0 -> ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0"; pushreference 17 "P0 -> (((Ax5. x5 E {x7|Zero < x7 & x7 * x7 < a1} -> x5 <= a1 + One) -> (Ax8. x8 E {x10| Zero < x10 & x10 * x10 < a1} -> x8 <= Sup({x11|Zero < x11 & x11 * x11 < a1}))) & P2296 & P0) & P0" "SUP2"; pushreference 19 " (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & (Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & P0 -> ((Ax5.x5 E {x7|Zero < x7 & x7 * x7 < a1} -> x5 <= a1 + One) & P2297 & P2296 & P0) & P0" "BDED"; pushreference 65 " P0 -> ((Zero < a23 -> Zero + Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x3| Zero < x3 & x3 * x3 < a1})) & P2341 & P0) & P0" "MPLUS"; pushnode 67 "(Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & (Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & (a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & P0 -> (Zero < a23 & P2342 & P2341 & P0) & ( [a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv(Three * Sup({x73| Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushreference 69 "(Real(Sup({x3| Zero < x3 & x3 * x3 < a1})) & P2344 & P0) & P0 -> ( Zero + Sup({x3|Zero < x3 & x3 * x3 < a1}) = Sup({x3| Zero < x3 & x3 * x3 < a1}) & P2345 & P0) & P0" "IPLUSb"; pushreference 71 " P0 -> ( Real(Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2344 & P0) & P0" "RSUP"; pushreference 73 " (Sup({x3| Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x6|Zero < x6 & x6 * x6 < a1}) & P2347 & P0) & ( Zero < Sup({x3| Zero < x3 & x3 * x3 < a1}) & P2348 & P0) & (Zero < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2349 & P0) & P0 -> ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & P0" "SquareOrder1"; pushreference 84 " P0 -> (( Zero < a23 & a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) -> Zero < Sup({x4| Zero < x4 & x4 * x4 < a1})) & P2356 & P0) & P0" "TRANS"; pushnode 88 "(Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & P0 -> (Zero < a23 & P2359 & P2357 & P2356 & P0) & ( Zero < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2349 & P0) & ( [ a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv(Three * Sup({x73| Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushnode 89 " ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & (Sup({x3| Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & P0 -> (a23 < Sup({x4| Zero < x4 & x4 * x4 < a1}) & P2360 & P2357 & P2356 & P0) & ( Zero < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2349 & P0) & ( [ a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv(Three * Sup({x73| Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushnode 86 "( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5| Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ((Zero < a23 & a23 < Sup({x4| Zero < x4 & x4 * x4 < a1})) & P2357 & P2356 & P0) & ( Zero < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2349 & P0) & ( [ a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv(Three * Sup({x73| Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushreference 90 "P0 -> (( Zero < Sup({x6|Zero < x6 & x6 * x6 < a1}) & Sup({x7| Zero < x7 & x7 * x7 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) -> Zero < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2361 & P0) & P0" "TRANS"; pushnode 94 "( Zero < Sup({x4| Zero < x4 & x4 * x4 < a1}) & P2358 & P2356 & P0) & (Sup({x3| Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( Zero < Sup({x5| Zero < x5 & x5 * x5 < a1}) & P2364 & P2362 & P2361 & P0) & ( Zero < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2349 & P0) & ( [ a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv(Three * Sup({x73| Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushnode 95 " ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5| Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & ( Zero < Sup({x4| Zero < x4 & x4 * x4 < a1}) & P2358 & P2356 & P0) & P0 -> ( Sup({x6|Zero < x6 & x6 * x6 < a1}) < a23 + Sup({x5| Zero < x5 & x5 * x5 < a1}) & P2365 & P2362 & P2361 & P0) & ( Zero < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2349 & P0) & ( [ a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv(Three * Sup({x73| Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushnode 92 " ( Zero < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2358 & P2356 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> (( Zero < Sup({x6| Zero < x6 & x6 * x6 < a1}) & Sup({x7|Zero < x7 & x7 * x7 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2362 & P2361 & P0) & (Zero < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2349 & P0) & ([a1 + Minus(Sup({x71| Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 93 " ( Zero < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2363 & P2361 & P0) & ( Zero < Sup({x4| Zero < x4 & x4 * x4 < a1}) & P2358 & P2356 & P0) & (Sup({x3| Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( Zero < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2349 & P0) & ([a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72|Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushnode 91 " (( Zero < Sup({x6| Zero < x6 & x6 * x6 < a1}) & Sup({x7|Zero < x7 & x7 * x7 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) -> Zero < a23 + Sup({x5| Zero < x5 & x5 * x5 < a1})) & P2361 & P0) & ( Zero < Sup({x4| Zero < x4 & x4 * x4 < a1}) & P2358 & P2356 & P0) & (Sup({x3| Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( Zero < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2349 & P0) & ([a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72|Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 87 "( Zero < Sup({x4| Zero < x4 & x4 * x4 < a1}) & P2358 & P2356 & P0) & (Sup({x3| Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> (Zero < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2349 & P0) & ([a1 + Minus(Sup({x71| Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 85 "(( Zero < a23 & a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) -> Zero < Sup({x4| Zero < x4 & x4 * x4 < a1})) & P2356 & P0) & (Sup({x3| Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> (Zero < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2349 & P0) & ([a1 + Minus(Sup({x71| Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 77 "(Sup({x3| Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( Zero < a23 + Sup({x5| Zero < x5 & x5 * x5 < a1}) & P2349 & P0) & ([a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72|Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushreference 78 "P0 -> (( Zero < a23 & a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) -> Zero < Sup({x4| Zero < x4 & x4 * x4 < a1})) & P2351 & P0) & P0" "TRANS"; pushnode 82 "(Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & P0 -> (Zero < a23 & P2354 & P2352 & P2351 & P0) & (Zero < Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2348 & P0) & ([a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72|Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushnode 83 " (a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & (Sup({x3| Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & P0 -> (a23 < Sup({x4| Zero < x4 & x4 * x4 < a1}) & P2355 & P2352 & P2351 & P0) & (Zero < Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2348 & P0) & ([a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72|Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushnode 80 "( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ((Zero < a23 & a23 < Sup({x4| Zero < x4 & x4 * x4 < a1})) & P2352 & P2351 & P0) & (Zero < Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2348 & P0) & ([a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72|Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 81 " (Zero < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2353 & P2351 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5| Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( Zero < Sup({x3| Zero < x3 & x3 * x3 < a1}) & P2348 & P0) & ([a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72|Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushnode 79 "(( Zero < a23 & a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) -> Zero < Sup({x4| Zero < x4 & x4 * x4 < a1})) & P2351 & P0) & (Sup({x3| Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( Zero < Sup({x3| Zero < x3 & x3 * x3 < a1}) & P2348 & P0) & ([a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72|Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 76 "(Sup({x3| Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( Zero < Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2348 & P0) & ( [ a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv(Three * Sup({x73| Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 75 "(Sup({x3| Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x6|Zero < x6 & x6 * x6 < a1}) & P2347 & P0) & ( [ a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv(Three * Sup({x73| Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushreference 96 "P0 -> (( a1 Equal [ a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [ a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] v a1 < [a23 + Sup({x3| Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] v [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] < a1) & P2366 & P0) & P0" "TRI"; pushreference 130 "(a1 Equal [a23 + Sup({x4|Zero < x4 & x4 * x4 < a1})] * [a23 + Sup({x5|Zero < x5 & x5 * x5 < a1})] & P2398 & P0) & ( Real(a1) & P2399 & P0) & ( Real([ a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [ a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})]) & P2400 & P0) & P0 -> (a1 = [a23 + Sup({x4|Zero < x4 & x4 * x4 < a1})] * [a23 + Sup({x5|Zero < x5 & x5 * x5 < a1})] & P2401 & P0) & P0" "EQUALITY"; pushreference 134 "P0 -> (Real( [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})]) & P2400 & P0) & P0" "RTIMES"; pushnode 133 " (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & (Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & (Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & (a1 Equal [a23 + Sup({x3| Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & P0 -> (Real(a1) & P2399 & P0) & ([a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72|Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushnode 132 " ( a1 Equal [ a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [ a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( a1 Equal [a23 + Sup({x4|Zero < x4 & x4 * x4 < a1})] * [ a23 + Sup({x5|Zero < x5 & x5 * x5 < a1})] & P2398 & P0) & ([a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72|Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushreference 135 "P0 -> ([ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] = a23 * a23 + Two * a23 * Sup({x8|Zero < x8 & x8 * x8 < a1}) + Sup({x9| Zero < x9 & x9 * x9 < a1}) * Sup({x10| Zero < x10 & x10 * x10 < a1}) & P2402 & P0) & P0" "FOIL"; pushreference 138 "(Zero < a23 & P2404 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2405 & P0) & P0 -> ( a23 * a23 + Two * a23 * Sup({x4|Zero < x4 & x4 * x4 < a1}) + Sup({x4| Zero < x4 & x4 * x4 < a1}) * Sup({x4| Zero < x4 & x4 * x4 < a1}) < a23 * Sup({x4|Zero < x4 & x4 * x4 < a1}) + Two * a23 * Sup({x4|Zero < x4 & x4 * x4 < a1}) + Sup({x4| Zero < x4 & x4 * x4 < a1}) * Sup({x4| Zero < x4 & x4 * x4 < a1}) & P2406 & P0) & P0" "ORDERLEMMA1"; pushnode 141 " (a23 < Sup({x4| Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & ( a1 = a23 * a23 + Two * a23 * Sup({x6|Zero < x6 & x6 * x6 < a1}) + Sup({x7| Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2403 & P2401 & P2402 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & P0 -> (a23 < Sup({x4| Zero < x4 & x4 * x4 < a1}) & P2405 & P0) & ([a1 + Minus(Sup({x71| Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushnode 140 "(Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & ( a1 = a23 * a23 + Two * a23 * Sup({x6|Zero < x6 & x6 * x6 < a1}) + Sup({x7| Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2403 & P2401 & P2402 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & P0 -> (Zero < a23 & P2404 & P0) & ([a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72|Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushreference 143 "P0 -> ( ( Sup({x4| Zero < x4 & x4 * x4 < a1}) * Sup({x5| Zero < x5 & x5 * x5 < a1}) < a1 -> Sup({x6|Zero < x6 & x6 * x6 < a1}) * Sup({x7| Zero < x7 & x7 * x7 < a1}) + Minus(Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1})) < a1 + Minus(Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}))) & P2409 & P0) & P0" "MPLUS"; pushnode 145 "( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & (Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & ( a1 = a23 * a23 + Two * a23 * Sup({x6|Zero < x6 & x6 * x6 < a1}) + Sup({x7| Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2407 & P2403 & P2401 & P2402 & P0) & ( a1 < a23 * Sup({x5| Zero < x5 & x5 * x5 < a1}) + Two * a23 * Sup({x6|Zero < x6 & x6 * x6 < a1}) + Sup({x7|Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2408 & P2406 & P2403 & P2401 & P2402 & P0) & (a1 Equal [a23 + Sup({x3| Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & P0 -> ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < a1 & P2410 & P2409 & P0) & ([a1 + Minus(Sup({x71| Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushreference 147 "P0 -> ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) + Minus(Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1})) = Zero & P2412 & P0) & P0" "MINUS"; pushreference 150 "P0 -> ( (a1 < a23 * Sup({x7|Zero < x7 & x7 * x7 < a1}) + Two * a23 * Sup({x8|Zero < x8 & x8 * x8 < a1}) + Sup({x9| Zero < x9 & x9 * x9 < a1}) * Sup({x10| Zero < x10 & x10 * x10 < a1}) -> a1 + Minus( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1})) < [ a23 * Sup({x11|Zero < x11 & x11 * x11 < a1}) + Two * a23 * Sup({x12|Zero < x12 & x12 * x12 < a1}) + Sup({x13| Zero < x13 & x13 * x13 < a1}) * Sup({x14| Zero < x14 & x14 * x14 < a1})] + Minus(Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}))) & P2414 & P0) & P0" "MPLUS"; pushnode 152 "( a1 < a23 * Sup({x5|Zero < x5 & x5 * x5 < a1}) + Two * a23 * Sup({x6|Zero < x6 & x6 * x6 < a1}) + Sup({x7| Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2408 & P2406 & P2403 & P2401 & P2402 & P0) & (a1 Equal [a23 + Sup({x3| Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & ( a1 = a23 * a23 + Two * a23 * Sup({x6| Zero < x6 & x6 * x6 < a1}) + Sup({x7| Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2407 & P2403 & P2401 & P2402 & P0) & P0 -> ( a1 < a23 * Sup({x6| Zero < x6 & x6 * x6 < a1}) + Two * a23 * Sup({x7|Zero < x7 & x7 * x7 < a1}) + Sup({x8|Zero < x8 & x8 * x8 < a1}) * Sup({x9| Zero < x9 & x9 * x9 < a1}) & P2415 & P2414 & P0) & ( [ a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv(Three * Sup({x73| Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushreference 154 "P0 -> ( [ a23 * Sup({x7|Zero < x7 & x7 * x7 < a1}) + Two * a23 * Sup({x9|Zero < x9 & x9 * x9 < a1}) + Sup({x10| Zero < x10 & x10 * x10 < a1}) * Sup({x11| Zero < x11 & x11 * x11 < a1})] + Minus(Sup({x12| Zero < x12 & x12 * x12 < a1}) * Sup({x13| Zero < x13 & x13 * x13 < a1})) = a23 * Sup({x7|Zero < x7 & x7 * x7 < a1}) + [Two * a23 * Sup({x14|Zero < x14 & x14 * x14 < a1}) + Sup({x15| Zero < x15 & x15 * x15 < a1}) * Sup({x16| Zero < x16 & x16 * x16 < a1})] + Minus( Sup({x17|Zero < x17 & x17 * x17 < a1}) * Sup({x18|Zero < x18 & x18 * x18 < a1})) & P2417 & P0) & P0" "APLUS"; pushreference 157 "P0 -> ( [Two * a23 * Sup({x14|Zero < x14 & x14 * x14 < a1}) + Sup({x16| Zero < x16 & x16 * x16 < a1}) * Sup({x17| Zero < x17 & x17 * x17 < a1})] + Minus( Sup({x19|Zero < x19 & x19 * x19 < a1}) * Sup({x20|Zero < x20 & x20 * x20 < a1})) = Two * a23 * Sup({x14|Zero < x14 & x14 * x14 < a1}) + Sup({x21| Zero < x21 & x21 * x21 < a1}) * Sup({x22| Zero < x22 & x22 * x22 < a1}) + Minus(Sup({x23| Zero < x23 & x23 * x23 < a1}) * Sup({x24| Zero < x24 & x24 * x24 < a1})) & P2419 & P0) & P0" "APLUS"; pushreference 160 " P0 -> ( Sup({x26|Zero < x26 & x26 * x26 < a1}) * Sup({x27| Zero < x27 & x27 * x27 < a1}) + Minus(Sup({x26| Zero < x26 & x26 * x26 < a1}) * Sup({x27| Zero < x27 & x27 * x27 < a1})) = Zero & P2421 & P0) & P0" "MINUS"; pushreference 163 "(Real(Two * a23 * Sup({x25|Zero < x25 & x25 * x25 < a1})) & P2423 & P0) & P0 -> (Two * a23 * Sup({x25|Zero < x25 & x25 * x25 < a1}) + Zero = Two * a23 * Sup({x25|Zero < x25 & x25 * x25 < a1}) & P2424 & P0) & P0" "IPLUSa"; pushreference 165 "P0 -> (Real(Two * a23 * Sup({x25|Zero < x25 & x25 * x25 < a1})) & P2423 & P0) & P0" "RTIMES"; pushreference 167 "( Real(a23 * Sup({x25|Zero < x25 & x25 * x25 < a1})) & P2426 & P0) & P0 -> ( a23 * Sup({x25|Zero < x25 & x25 * x25 < a1}) + Two * a23 * Sup({x25|Zero < x25 & x25 * x25 < a1}) = Three * a23 * Sup({x25|Zero < x25 & x25 * x25 < a1}) & P2427 & P0) & P0" "LIKETERMS1"; pushreference 169 "P0 -> ( Real(a23 * Sup({x25|Zero < x25 & x25 * x25 < a1})) & P2426 & P0) & P0" "RTIMES"; pushreference 171 "P0 -> (a23 * Sup({x26|Zero < x26 & x26 * x26 < a1}) = Sup({x27| Zero < x27 & x27 * x27 < a1}) * a23 & P2429 & P0) & P0" "CTIMES"; pushreference 174 " P0 -> (( Zero < Inv(Three * Sup({x35|Zero < x35 & x35 * x35 < a1})) & a1 + Minus(Sup({x31| Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x36|Zero < x36 & x36 * x36 < a1}) * a23 -> [ a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1}))] * Inv(Three * Sup({x37| Zero < x37 & x37 * x37 < a1})) < [ Three * Sup({x38|Zero < x38 & x38 * x38 < a1}) * a23] * Inv( Three * Sup({x39|Zero < x39 & x39 * x39 < a1}))) & P2431 & P0) & P0" "MTIMES"; pushreference 180 "( Zero < Three * Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2436 & P0) & P0 -> ( Zero < Inv(Three * Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2434 & P2432 & P2431 & P0) & P0" "POSINV"; pushreference 182 " P0 -> (Zero < Three & P2437 & P0) & P0" "THREEPOS"; pushreference 184 " ( Zero < Three & P2437 & P0) & ( Zero < Sup({x3| Zero < x3 & x3 * x3 < a1}) & P2438 & P0) & P0 -> ( Zero < Three * Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2436 & P0) & P0" "TIMESPOS"; pushreference 186 "P0 -> (( Zero < a23 & a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) -> Zero < Sup({x4|Zero < x4 & x4 * x4 < a1})) & P2439 & P0) & P0" "TRANS"; pushnode 190 "(Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & (a23 * Sup({x26|Zero < x26 & x26 * x26 < a1}) = Sup({x27|Zero < x27 & x27 * x27 < a1}) * a23 & P2429 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & ( a1 = a23 * a23 + Two * a23 * Sup({x6| Zero < x6 & x6 * x6 < a1}) + Sup({x7| Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2407 & P2403 & P2401 & P2402 & P0) & ( a1 < a23 * Sup({x5| Zero < x5 & x5 * x5 < a1}) + Two * a23 * Sup({x6|Zero < x6 & x6 * x6 < a1}) + Sup({x7|Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2408 & P2406 & P2403 & P2401 & P2402 & P0) & (a1 Equal [a23 + Sup({x3| Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & P0 -> (Zero < a23 & P2442 & P2440 & P2439 & P0) & ( Zero < Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2438 & P0) & (Zero < Three * Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2436 & P0) & ( Zero < Inv( Three * Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2434 & P2432 & P2431 & P0) & ([a1 + Minus(Sup({x71| Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushnode 191 " (a23 < Sup({x4| Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & ( a23 * Sup({x26|Zero < x26 & x26 * x26 < a1}) = Sup({x27| Zero < x27 & x27 * x27 < a1}) * a23 & P2429 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & ( a1 = a23 * a23 + Two * a23 * Sup({x6| Zero < x6 & x6 * x6 < a1}) + Sup({x7| Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2407 & P2403 & P2401 & P2402 & P0) & ( a1 < a23 * Sup({x5| Zero < x5 & x5 * x5 < a1}) + Two * a23 * Sup({x6|Zero < x6 & x6 * x6 < a1}) + Sup({x7|Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2408 & P2406 & P2403 & P2401 & P2402 & P0) & (a1 Equal [a23 + Sup({x3| Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & P0 -> (a23 < Sup({x4| Zero < x4 & x4 * x4 < a1}) & P2443 & P2440 & P2439 & P0) & (Zero < Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2438 & P0) & ( Zero < Three * Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2436 & P0) & ( Zero < Inv( Three * Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2434 & P2432 & P2431 & P0) & ([a1 + Minus(Sup({x71| Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushnode 188 " ( a23 * Sup({x26|Zero < x26 & x26 * x26 < a1}) = Sup({x27| Zero < x27 & x27 * x27 < a1}) * a23 & P2429 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & ( a1 = a23 * a23 + Two * a23 * Sup({x6| Zero < x6 & x6 * x6 < a1}) + Sup({x7| Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2407 & P2403 & P2401 & P2402 & P0) & ( a1 < a23 * Sup({x5| Zero < x5 & x5 * x5 < a1}) + Two * a23 * Sup({x6|Zero < x6 & x6 * x6 < a1}) + Sup({x7|Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2408 & P2406 & P2403 & P2401 & P2402 & P0) & (a1 Equal [a23 + Sup({x3| Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( (Zero < a23 & a23 < Sup({x4|Zero < x4 & x4 * x4 < a1})) & P2440 & P2439 & P0) & ( Zero < Sup({x3| Zero < x3 & x3 * x3 < a1}) & P2438 & P0) & ( Zero < Three * Sup({x3| Zero < x3 & x3 * x3 < a1}) & P2436 & P0) & ( Zero < Inv(Three * Sup({x3| Zero < x3 & x3 * x3 < a1})) & P2434 & P2432 & P2431 & P0) & ([a1 + Minus(Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 189 "( Zero < Sup({x4| Zero < x4 & x4 * x4 < a1}) & P2441 & P2439 & P0) & ( a23 * Sup({x26|Zero < x26 & x26 * x26 < a1}) = Sup({x27| Zero < x27 & x27 * x27 < a1}) * a23 & P2429 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & ( a1 = a23 * a23 + Two * a23 * Sup({x6| Zero < x6 & x6 * x6 < a1}) + Sup({x7| Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2407 & P2403 & P2401 & P2402 & P0) & ( a1 < a23 * Sup({x5| Zero < x5 & x5 * x5 < a1}) + Two * a23 * Sup({x6|Zero < x6 & x6 * x6 < a1}) + Sup({x7|Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2408 & P2406 & P2403 & P2401 & P2402 & P0) & (a1 Equal [a23 + Sup({x3| Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> (Zero < Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2438 & P0) & ( Zero < Three * Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2436 & P0) & ( Zero < Inv( Three * Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2434 & P2432 & P2431 & P0) & ([a1 + Minus(Sup({x71| Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushnode 187 "((Zero < a23 & a23 < Sup({x4| Zero < x4 & x4 * x4 < a1}) -> Zero < Sup({x4| Zero < x4 & x4 * x4 < a1})) & P2439 & P0) & (a23 * Sup({x26| Zero < x26 & x26 * x26 < a1}) = Sup({x27|Zero < x27 & x27 * x27 < a1}) * a23 & P2429 & P0) & ( a1 + Minus(Sup({x31| Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & ( a1 = a23 * a23 + Two * a23 * Sup({x6| Zero < x6 & x6 * x6 < a1}) + Sup({x7| Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2407 & P2403 & P2401 & P2402 & P0) & ( a1 < a23 * Sup({x5| Zero < x5 & x5 * x5 < a1}) + Two * a23 * Sup({x6|Zero < x6 & x6 * x6 < a1}) + Sup({x7|Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2408 & P2406 & P2403 & P2401 & P2402 & P0) & (a1 Equal [a23 + Sup({x3| Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> (Zero < Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2438 & P0) & ( Zero < Three * Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2436 & P0) & ( Zero < Inv( Three * Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2434 & P2432 & P2431 & P0) & ([a1 + Minus(Sup({x71| Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 185 " (a23 * Sup({x26|Zero < x26 & x26 * x26 < a1}) = Sup({x27|Zero < x27 & x27 * x27 < a1}) * a23 & P2429 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & ( a1 = a23 * a23 + Two * a23 * Sup({x6| Zero < x6 & x6 * x6 < a1}) + Sup({x7| Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2407 & P2403 & P2401 & P2402 & P0) & ( a1 < a23 * Sup({x5| Zero < x5 & x5 * x5 < a1}) + Two * a23 * Sup({x6|Zero < x6 & x6 * x6 < a1}) + Sup({x7|Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2408 & P2406 & P2403 & P2401 & P2402 & P0) & (a1 Equal [a23 + Sup({x3| Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( Zero < Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2438 & P0) & (Zero < Three * Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2436 & P0) & ( Zero < Inv( Three * Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2434 & P2432 & P2431 & P0) & ([a1 + Minus(Sup({x71| Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 183 "(Zero < Three & P2437 & P0) & (a23 * Sup({x26|Zero < x26 & x26 * x26 < a1}) = Sup({x27|Zero < x27 & x27 * x27 < a1}) * a23 & P2429 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & ( a1 = a23 * a23 + Two * a23 * Sup({x6| Zero < x6 & x6 * x6 < a1}) + Sup({x7| Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2407 & P2403 & P2401 & P2402 & P0) & ( a1 < a23 * Sup({x5| Zero < x5 & x5 * x5 < a1}) + Two * a23 * Sup({x6|Zero < x6 & x6 * x6 < a1}) + Sup({x7|Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2408 & P2406 & P2403 & P2401 & P2402 & P0) & (a1 Equal [a23 + Sup({x3| Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( Zero < Three * Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2436 & P0) & ( Zero < Inv( Three * Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2434 & P2432 & P2431 & P0) & ([a1 + Minus(Sup({x71| Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 181 " (a23 * Sup({x26|Zero < x26 & x26 * x26 < a1}) = Sup({x27| Zero < x27 & x27 * x27 < a1}) * a23 & P2429 & P0) & ( a1 + Minus(Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & ( a1 = a23 * a23 + Two * a23 * Sup({x6| Zero < x6 & x6 * x6 < a1}) + Sup({x7| Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2407 & P2403 & P2401 & P2402 & P0) & ( a1 < a23 * Sup({x5| Zero < x5 & x5 * x5 < a1}) + Two * a23 * Sup({x6|Zero < x6 & x6 * x6 < a1}) + Sup({x7|Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2408 & P2406 & P2403 & P2401 & P2402 & P0) & (a1 Equal [a23 + Sup({x3| Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> (Zero < Three * Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2436 & P0) & ( Zero < Inv( Three * Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2434 & P2432 & P2431 & P0) & ([a1 + Minus(Sup({x71| Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 178 " (a23 * Sup({x26|Zero < x26 & x26 * x26 < a1}) = Sup({x27| Zero < x27 & x27 * x27 < a1}) * a23 & P2429 & P0) & ( a1 + Minus(Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & ( a1 = a23 * a23 + Two * a23 * Sup({x6| Zero < x6 & x6 * x6 < a1}) + Sup({x7| Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2407 & P2403 & P2401 & P2402 & P0) & ( a1 < a23 * Sup({x5| Zero < x5 & x5 * x5 < a1}) + Two * a23 * Sup({x6|Zero < x6 & x6 * x6 < a1}) + Sup({x7|Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2408 & P2406 & P2403 & P2401 & P2402 & P0) & (a1 Equal [a23 + Sup({x3| Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( Zero < Inv( Three * Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2434 & P2432 & P2431 & P0) & ([a1 + Minus(Sup({x71| Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 179 "( a1 + Minus(Sup({x31| Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & ( a1 = a23 * a23 + Two * a23 * Sup({x6| Zero < x6 & x6 * x6 < a1}) + Sup({x7| Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2407 & P2403 & P2401 & P2402 & P0) & ( a1 < a23 * Sup({x5| Zero < x5 & x5 * x5 < a1}) + Two * a23 * Sup({x6|Zero < x6 & x6 * x6 < a1}) + Sup({x7|Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2408 & P2406 & P2403 & P2401 & P2402 & P0) & (a1 Equal [a23 + Sup({x3| Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & ( a23 * Sup({x26|Zero < x26 & x26 * x26 < a1}) = Sup({x27| Zero < x27 & x27 * x27 < a1}) * a23 & P2429 & P0) & P0 -> ( a1 + Minus(Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x34|Zero < x34 & x34 * x34 < a1}) * a23 & P2435 & P2432 & P2431 & P0) & ([a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72|Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushnode 176 " ( a23 * Sup({x26|Zero < x26 & x26 * x26 < a1}) = Sup({x27| Zero < x27 & x27 * x27 < a1}) * a23 & P2429 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & ( a1 = a23 * a23 + Two * a23 * Sup({x6| Zero < x6 & x6 * x6 < a1}) + Sup({x7| Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2407 & P2403 & P2401 & P2402 & P0) & ( a1 < a23 * Sup({x5| Zero < x5 & x5 * x5 < a1}) + Two * a23 * Sup({x6|Zero < x6 & x6 * x6 < a1}) + Sup({x7|Zero < x7 & x7 * x7 < a1}) * Sup({x8| Zero < x8 & x8 * x8 < a1}) & P2408 & P2406 & P2403 & P2401 & P2402 & P0) & (a1 Equal [a23 + Sup({x3| Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> (( Zero < Inv(Three * Sup({x35|Zero < x35 & x35 * x35 < a1})) & a1 + Minus(Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x36|Zero < x36 & x36 * x36 < a1}) * a23) & P2432 & P2431 & P0) & ([a1 + Minus(Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushreference 192 "P0 -> ([ Three * Sup({x39|Zero < x39 & x39 * x39 < a1}) * a23] * Inv( Three * Sup({x41|Zero < x41 & x41 * x41 < a1})) = Three * [ Sup({x42|Zero < x42 & x42 * x42 < a1}) * a23] * Inv( Three * Sup({x43|Zero < x43 & x43 * x43 < a1})) & P2444 & P0) & P0" "ATIMES"; pushreference 197 "P0 -> ( [Sup({x45|Zero < x45 & x45 * x45 < a1}) * a23] * Inv(Three * Sup({x48|Zero < x48 & x48 * x48 < a1})) = Sup({x45|Zero < x45 & x45 * x45 < a1}) * a23 * Inv( Three * Sup({x49|Zero < x49 & x49 * x49 < a1})) & P2448 & P0) & P0" "ATIMES"; pushreference 200 "P0 -> (a23 * Inv(Three * Sup({x53|Zero < x53 & x53 * x53 < a1})) = Inv(Three * Sup({x54|Zero < x54 & x54 * x54 < a1})) * a23 & P2450 & P0) & P0" "CTIMES"; pushreference 203 "P0 -> ( [Three * Sup({x58|Zero < x58 & x58 * x58 < a1})] * Inv(Three * Sup({x60|Zero < x60 & x60 * x60 < a1})) * a23 = Three * Sup({x61|Zero < x61 & x61 * x61 < a1}) * Inv(Three * Sup({x62| Zero < x62 & x62 * x62 < a1})) * a23 & P2452 & P0) & P0" "ATIMES"; pushreference 206 " P0 -> ( [ [Three * Sup({x64|Zero < x64 & x64 * x64 < a1})] * Inv( Three * Sup({x66|Zero < x66 & x66 * x66 < a1}))] * a23 = [Three * Sup({x64|Zero < x64 & x64 * x64 < a1})] * Inv(Three * Sup({x67|Zero < x67 & x67 * x67 < a1})) * a23 & P2455 & P0) & P0" "ATIMES"; pushreference 209 " P0 -> ( ( Three * Sup({x70|Zero < x70 & x70 * x70 < a1}) Equal Zero v [ Three * Sup({x70|Zero < x70 & x70 * x70 < a1})] * Inv( Three * Sup({x70|Zero < x70 & x70 * x70 < a1})) = One) & P2458 & P0) & P0" "INV"; pushreference 214 "P0 -> ((Real(a23) -> a23 * One = a23) & P2462 & P0) & P0" "ITIMES"; pushreference 218 "P0 -> ( a23 * One = One * a23 & P2465 & P0) & P0" "CTIMES"; pushreference 222 "P0 -> (( Zero < Inv(Three * Sup({x7|Zero < x7 & x7 * x7 < a1})) & Zero < a1 + Minus(Sup({x8|Zero < x8 & x8 * x8 < a1}) * Sup({x9| Zero < x9 & x9 * x9 < a1})) -> Zero * Inv(Three * Sup({x10| Zero < x10 & x10 * x10 < a1})) < [ a1 + Minus( Sup({x11|Zero < x11 & x11 * x11 < a1}) * Sup({x12| Zero < x12 & x12 * x12 < a1}))] * Inv(Three * Sup({x13| Zero < x13 & x13 * x13 < a1}))) & P2468 & P0) & P0" "MTIMES"; pushnode 228 "( Zero < Inv(Three * Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2473 & P0) & ( [ a1 + Minus( Sup({x70|Zero < x70 & x70 * x70 < a1}) * Sup({x71| Zero < x71 & x71 * x71 < a1}))] * Inv(Three * Sup({x72| Zero < x72 & x72 * x72 < a1})) < a23 & P2467 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P2466 & P2464 & P2462 & P2465 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( Zero < Inv( Three * Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2471 & P2469 & P2468 & P0) & ([a1 + Minus(Sup({x71| Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushreference 230 "(Zero < Three * Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2474 & P0) & P0 -> ( Zero < Inv(Three * Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2473 & P0) & P0" "POSINV"; pushreference 232 "P0 -> (Zero < Three & P2475 & P0) & P0" "THREEPOS"; pushreference 234 "(Zero < Three & P2475 & P0) & ( Zero < Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2476 & P0) & P0 -> ( Zero < Three * Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2474 & P0) & P0" "TIMESPOS"; pushreference 236 "P0 -> (( Zero < a23 & a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) -> Zero < Sup({x4|Zero < x4 & x4 * x4 < a1})) & P2477 & P0) & P0" "TRANS"; pushnode 240 "(Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & ([a1 + Minus( Sup({x70|Zero < x70 & x70 * x70 < a1}) * Sup({x71|Zero < x71 & x71 * x71 < a1}))] * Inv( Three * Sup({x72|Zero < x72 & x72 * x72 < a1})) < a23 & P2467 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P2466 & P2464 & P2462 & P2465 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & P0 -> (Zero < a23 & P2480 & P2478 & P2477 & P0) & (Zero < Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2476 & P0) & ( Zero < Three * Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2474 & P0) & ( Zero < Inv( Three * Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2473 & P0) & ( Zero < Inv(Three * Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2471 & P2469 & P2468 & P0) & ([a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72|Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushnode 241 " (a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & ( [ a1 + Minus( Sup({x70|Zero < x70 & x70 * x70 < a1}) * Sup({x71| Zero < x71 & x71 * x71 < a1}))] * Inv(Three * Sup({x72| Zero < x72 & x72 * x72 < a1})) < a23 & P2467 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P2466 & P2464 & P2462 & P2465 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & P0 -> (a23 < Sup({x4| Zero < x4 & x4 * x4 < a1}) & P2481 & P2478 & P2477 & P0) & (Zero < Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2476 & P0) & ( Zero < Three * Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2474 & P0) & ( Zero < Inv( Three * Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2473 & P0) & ( Zero < Inv(Three * Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2471 & P2469 & P2468 & P0) & ([a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72|Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushnode 238 "([a1 + Minus( Sup({x70|Zero < x70 & x70 * x70 < a1}) * Sup({x71|Zero < x71 & x71 * x71 < a1}))] * Inv( Three * Sup({x72|Zero < x72 & x72 * x72 < a1})) < a23 & P2467 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P2466 & P2464 & P2462 & P2465 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ((Zero < a23 & a23 < Sup({x4| Zero < x4 & x4 * x4 < a1})) & P2478 & P2477 & P0) & (Zero < Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2476 & P0) & ( Zero < Three * Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2474 & P0) & ( Zero < Inv( Three * Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2473 & P0) & ( Zero < Inv(Three * Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2471 & P2469 & P2468 & P0) & ([a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72|Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 239 " (Zero < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2479 & P2477 & P0) & ([a1 + Minus(Sup({x70|Zero < x70 & x70 * x70 < a1}) * Sup({x71| Zero < x71 & x71 * x71 < a1}))] * Inv( Three * Sup({x72|Zero < x72 & x72 * x72 < a1})) < a23 & P2467 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P2466 & P2464 & P2462 & P2465 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( Zero < Sup({x3| Zero < x3 & x3 * x3 < a1}) & P2476 & P0) & ( Zero < Three * Sup({x3| Zero < x3 & x3 * x3 < a1}) & P2474 & P0) & ( Zero < Inv(Three * Sup({x3| Zero < x3 & x3 * x3 < a1})) & P2473 & P0) & ( Zero < Inv(Three * Sup({x3| Zero < x3 & x3 * x3 < a1})) & P2471 & P2469 & P2468 & P0) & ([a1 + Minus(Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushnode 237 "(( Zero < a23 & a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) -> Zero < Sup({x4| Zero < x4 & x4 * x4 < a1})) & P2477 & P0) & ([a1 + Minus(Sup({x70| Zero < x70 & x70 * x70 < a1}) * Sup({x71| Zero < x71 & x71 * x71 < a1}))] * Inv( Three * Sup({x72|Zero < x72 & x72 * x72 < a1})) < a23 & P2467 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P2466 & P2464 & P2462 & P2465 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( Zero < Sup({x3| Zero < x3 & x3 * x3 < a1}) & P2476 & P0) & ( Zero < Three * Sup({x3| Zero < x3 & x3 * x3 < a1}) & P2474 & P0) & ( Zero < Inv(Three * Sup({x3| Zero < x3 & x3 * x3 < a1})) & P2473 & P0) & ( Zero < Inv(Three * Sup({x3| Zero < x3 & x3 * x3 < a1})) & P2471 & P2469 & P2468 & P0) & ([a1 + Minus(Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 235 "([a1 + Minus(Sup({x70| Zero < x70 & x70 * x70 < a1}) * Sup({x71| Zero < x71 & x71 * x71 < a1}))] * Inv( Three * Sup({x72|Zero < x72 & x72 * x72 < a1})) < a23 & P2467 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P2466 & P2464 & P2462 & P2465 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( Zero < Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2476 & P0) & (Zero < Three * Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2474 & P0) & ( Zero < Inv( Three * Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2473 & P0) & ( Zero < Inv(Three * Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2471 & P2469 & P2468 & P0) & ([a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72|Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 233 "( Zero < Three & P2475 & P0) & ( [ a1 + Minus( Sup({x70|Zero < x70 & x70 * x70 < a1}) * Sup({x71| Zero < x71 & x71 * x71 < a1}))] * Inv(Three * Sup({x72| Zero < x72 & x72 * x72 < a1})) < a23 & P2467 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P2466 & P2464 & P2462 & P2465 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> (Zero < Three * Sup({x3|Zero < x3 & x3 * x3 < a1}) & P2474 & P0) & ( Zero < Inv( Three * Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2473 & P0) & ( Zero < Inv(Three * Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2471 & P2469 & P2468 & P0) & ([a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72|Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 231 "([a1 + Minus( Sup({x70|Zero < x70 & x70 * x70 < a1}) * Sup({x71|Zero < x71 & x71 * x71 < a1}))] * Inv( Three * Sup({x72|Zero < x72 & x72 * x72 < a1})) < a23 & P2467 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P2466 & P2464 & P2462 & P2465 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( Zero < Three * Sup({x3| Zero < x3 & x3 * x3 < a1}) & P2474 & P0) & ( Zero < Inv(Three * Sup({x3| Zero < x3 & x3 * x3 < a1})) & P2473 & P0) & ( Zero < Inv(Three * Sup({x3| Zero < x3 & x3 * x3 < a1})) & P2471 & P2469 & P2468 & P0) & ([a1 + Minus(Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 229 "([a1 + Minus( Sup({x70|Zero < x70 & x70 * x70 < a1}) * Sup({x71|Zero < x71 & x71 * x71 < a1}))] * Inv( Three * Sup({x72|Zero < x72 & x72 * x72 < a1})) < a23 & P2467 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P2466 & P2464 & P2462 & P2465 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( Zero < Inv(Three * Sup({x3| Zero < x3 & x3 * x3 < a1})) & P2473 & P0) & ( Zero < Inv(Three * Sup({x3| Zero < x3 & x3 * x3 < a1})) & P2471 & P2469 & P2468 & P0) & ([a1 + Minus(Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 226 "([a1 + Minus(Sup({x70|Zero < x70 & x70 * x70 < a1}) * Sup({x71| Zero < x71 & x71 * x71 < a1}))] * Inv( Three * Sup({x72|Zero < x72 & x72 * x72 < a1})) < a23 & P2467 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P2466 & P2464 & P2462 & P2465 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( Zero < Inv(Three * Sup({x3| Zero < x3 & x3 * x3 < a1})) & P2471 & P2469 & P2468 & P0) & ([a1 + Minus(Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 227 "(Zero < a1 + Minus(Sup({x4| Zero < x4 & x4 * x4 < a1}) * Sup({x5| Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & ( a1 Equal [ a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [ a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & ( [ a1 + Minus( Sup({x70|Zero < x70 & x70 * x70 < a1}) * Sup({x71| Zero < x71 & x71 * x71 < a1}))] * Inv(Three * Sup({x72| Zero < x72 & x72 * x72 < a1})) < a23 & P2467 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P2466 & P2464 & P2462 & P2465 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & P0 -> (Zero < a1 + Minus(Sup({x5| Zero < x5 & x5 * x5 < a1}) * Sup({x6| Zero < x6 & x6 * x6 < a1})) & P2472 & P2469 & P2468 & P0) & ([a1 + Minus(Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushnode 224 "([a1 + Minus(Sup({x70| Zero < x70 & x70 * x70 < a1}) * Sup({x71| Zero < x71 & x71 * x71 < a1}))] * Inv( Three * Sup({x72|Zero < x72 & x72 * x72 < a1})) < a23 & P2467 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P2466 & P2464 & P2462 & P2465 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( ( Zero < Inv(Three * Sup({x7| Zero < x7 & x7 * x7 < a1})) & Zero < a1 + Minus(Sup({x8|Zero < x8 & x8 * x8 < a1}) * Sup({x9| Zero < x9 & x9 * x9 < a1}))) & P2469 & P2468 & P0) & ( [ a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv(Three * Sup({x73| Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushreference 242 "P0 -> ( Zero * Inv(Three * Sup({x7|Zero < x7 & x7 * x7 < a1})) = Zero & P2482 & P0) & P0" "MZERO2"; pushnode 246 " ([a1 + Minus(Sup({x70|Zero < x70 & x70 * x70 < a1}) * Sup({x71| Zero < x71 & x71 * x71 < a1}))] * Inv( Three * Sup({x72|Zero < x72 & x72 * x72 < a1})) < a23 & P2467 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P2466 & P2464 & P2462 & P2465 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & ( Zero < [ a1 + Minus( Sup({x9|Zero < x9 & x9 * x9 < a1}) * Sup({x10|Zero < x10 & x10 * x10 < a1}))] * Inv( Three * Sup({x11|Zero < x11 & x11 * x11 < a1})) & P2483 & P2470 & P2468 & P2482 & P0) & P0 -> ( [a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv(Three * Sup({x73| Zero < x73 & x73 * x73 < a1})) < a23 & P2486 & P2484 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & ([a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72|Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) Equal a23 & P2485 & P2484 & P2336 & P2334 & P2333 & P0) & P0" 0; pushnode 245 "( Zero < [a1 + Minus(Sup({x9|Zero < x9 & x9 * x9 < a1}) * Sup({x10| Zero < x10 & x10 * x10 < a1}))] * Inv( Three * Sup({x11|Zero < x11 & x11 * x11 < a1})) & P2483 & P2470 & P2468 & P2482 & P0) & ( [ a1 + Minus( Sup({x70|Zero < x70 & x70 * x70 < a1}) * Sup({x71| Zero < x71 & x71 * x71 < a1}))] * Inv(Three * Sup({x72| Zero < x72 & x72 * x72 < a1})) < a23 & P2467 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P2466 & P2464 & P2462 & P2465 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( ( [ a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv(Three * Sup({x73| Zero < x73 & x73 * x73 < a1})) Equal a23 v [a1 + Minus(Sup({x71| Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) < a23) & P2484 & P2336 & P2334 & P2333 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 1; pushnode 244 "( Zero < [a1 + Minus(Sup({x9|Zero < x9 & x9 * x9 < a1}) * Sup({x10| Zero < x10 & x10 * x10 < a1}))] * Inv( Three * Sup({x11|Zero < x11 & x11 * x11 < a1})) & P2483 & P2470 & P2468 & P2482 & P0) & ( [ a1 + Minus( Sup({x70|Zero < x70 & x70 * x70 < a1}) * Sup({x71| Zero < x71 & x71 * x71 < a1}))] * Inv(Three * Sup({x72| Zero < x72 & x72 * x72 < a1})) < a23 & P2467 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P2466 & P2464 & P2462 & P2465 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( [ a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv(Three * Sup({x73| Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 1; pushnode 243 " ( Zero * Inv(Three * Sup({x7|Zero < x7 & x7 * x7 < a1})) = Zero & P2482 & P0) & ( Zero * Inv(Three * Sup({x7| Zero < x7 & x7 * x7 < a1})) < [a1 + Minus(Sup({x8|Zero < x8 & x8 * x8 < a1}) * Sup({x9| Zero < x9 & x9 * x9 < a1}))] * Inv( Three * Sup({x10|Zero < x10 & x10 * x10 < a1})) & P2470 & P2468 & P0) & ([a1 + Minus(Sup({x70|Zero < x70 & x70 * x70 < a1}) * Sup({x71| Zero < x71 & x71 * x71 < a1}))] * Inv( Three * Sup({x72|Zero < x72 & x72 * x72 < a1})) < a23 & P2467 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P2466 & P2464 & P2462 & P2465 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( [ a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv(Three * Sup({x73| Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 1; pushnode 225 " ( Zero * Inv(Three * Sup({x7|Zero < x7 & x7 * x7 < a1})) < [a1 + Minus(Sup({x8|Zero < x8 & x8 * x8 < a1}) * Sup({x9| Zero < x9 & x9 * x9 < a1}))] * Inv( Three * Sup({x10|Zero < x10 & x10 * x10 < a1})) & P2470 & P2468 & P0) & ([a1 + Minus(Sup({x70|Zero < x70 & x70 * x70 < a1}) * Sup({x71| Zero < x71 & x71 * x71 < a1}))] * Inv( Three * Sup({x72|Zero < x72 & x72 * x72 < a1})) < a23 & P2467 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P2466 & P2464 & P2462 & P2465 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( [ a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv(Three * Sup({x73| Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 223 "(( Zero < Inv(Three * Sup({x7|Zero < x7 & x7 * x7 < a1})) & Zero < a1 + Minus(Sup({x8|Zero < x8 & x8 * x8 < a1}) * Sup({x9| Zero < x9 & x9 * x9 < a1})) -> Zero * Inv(Three * Sup({x10| Zero < x10 & x10 * x10 < a1})) < [ a1 + Minus( Sup({x11|Zero < x11 & x11 * x11 < a1}) * Sup({x12| Zero < x12 & x12 * x12 < a1}))] * Inv(Three * Sup({x13| Zero < x13 & x13 * x13 < a1}))) & P2468 & P0) & ([a1 + Minus(Sup({x70| Zero < x70 & x70 * x70 < a1}) * Sup({x71| Zero < x71 & x71 * x71 < a1}))] * Inv( Three * Sup({x72|Zero < x72 & x72 * x72 < a1})) < a23 & P2467 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P2466 & P2464 & P2462 & P2465 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( [ a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv(Three * Sup({x73| Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 221 "([a1 + Minus( Sup({x70|Zero < x70 & x70 * x70 < a1}) * Sup({x71|Zero < x71 & x71 * x71 < a1}))] * Inv( Three * Sup({x72|Zero < x72 & x72 * x72 < a1})) < a23 & P2467 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P2466 & P2464 & P2462 & P2465 & P0) & ( a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ([a1 + Minus(Sup({x71| Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 220 "( One * a23 = a23 & P2466 & P2464 & P2462 & P2465 & P0) & ( [ a1 + Minus( Sup({x68|Zero < x68 & x68 * x68 < a1}) * Sup({x69| Zero < x69 & x69 * x69 < a1}))] * Inv(Three * Sup({x70| Zero < x70 & x70 * x70 < a1})) < One * a23 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P0) & (a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32|Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus(Sup({x4| Zero < x4 & x4 * x4 < a1}) * Sup({x5| Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & ( a1 Equal [ a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [ a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & ( a23 * One = One * a23 & P2465 & P0) & P0 -> ([a1 + Minus(Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 1; pushnode 219 " ( a23 * One = One * a23 & P2465 & P0) & ( a23 * One = a23 & P2464 & P2462 & P0) & ( [ a1 + Minus( Sup({x68|Zero < x68 & x68 * x68 < a1}) * Sup({x69| Zero < x69 & x69 * x69 < a1}))] * Inv(Three * Sup({x70| Zero < x70 & x70 * x70 < a1})) < One * a23 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P0) & (a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32|Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus(Sup({x4| Zero < x4 & x4 * x4 < a1}) * Sup({x5| Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & ( a1 Equal [ a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [ a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( [a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv(Three * Sup({x73| Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 1; pushnode 217 "( a23 * One = a23 & P2464 & P2462 & P0) & ( [ a1 + Minus( Sup({x68|Zero < x68 & x68 * x68 < a1}) * Sup({x69| Zero < x69 & x69 * x69 < a1}))] * Inv(Three * Sup({x70| Zero < x70 & x70 * x70 < a1})) < One * a23 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P0) & (a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32|Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus(Sup({x4| Zero < x4 & x4 * x4 < a1}) * Sup({x5| Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & ( a1 Equal [ a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [ a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( [ a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv(Three * Sup({x73| Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 216 " (Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & (a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & ( [ a1 + Minus( Sup({x68|Zero < x68 & x68 * x68 < a1}) * Sup({x69| Zero < x69 & x69 * x69 < a1}))] * Inv(Three * Sup({x70| Zero < x70 & x70 * x70 < a1})) < One * a23 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P0) & (a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32|Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus(Sup({x4| Zero < x4 & x4 * x4 < a1}) * Sup({x5| Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & ( a1 Equal [ a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [ a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & P0 -> ( Real(a23) & P2463 & P2462 & P0) & ( [ a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv(Three * Sup({x73| Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushnode 215 "(( Real(a23) -> a23 * One = a23) & P2462 & P0) & ([a1 + Minus(Sup({x68| Zero < x68 & x68 * x68 < a1}) * Sup({x69| Zero < x69 & x69 * x69 < a1}))] * Inv( Three * Sup({x70|Zero < x70 & x70 * x70 < a1})) < One * a23 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P0) & ( a1 + Minus(Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( [ a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv(Three * Sup({x73| Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 213 " ([a1 + Minus( Sup({x68|Zero < x68 & x68 * x68 < a1}) * Sup({x69|Zero < x69 & x69 * x69 < a1}))] * Inv( Three * Sup({x70|Zero < x70 & x70 * x70 < a1})) < One * a23 & P2461 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P2460 & P2458 & P0) & ( a1 + Minus(Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ([a1 + Minus(Sup({x71| Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 212 "( [Three * Sup({x70|Zero < x70 & x70 * x70 < a1})] * Inv(Three * Sup({x70| Zero < x70 & x70 * x70 < a1})) = One & P2460 & P2458 & P0) & ( [ a1 + Minus( Sup({x67|Zero < x67 & x67 * x67 < a1}) * Sup({x68| Zero < x68 & x68 * x68 < a1}))] * Inv(Three * Sup({x69| Zero < x69 & x69 * x69 < a1})) < [[ Three * Sup({x64|Zero < x64 & x64 * x64 < a1})] * Inv( Three * Sup({x70|Zero < x70 & x70 * x70 < a1}))] * a23 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P0) & ( a1 + Minus(Sup({x31| Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( [ a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv(Three * Sup({x73| Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 1; pushreference 247 "(Three * Sup({x70|Zero < x70 & x70 * x70 < a1}) Equal Zero & P2487 & P0) & ( Real( Three * Sup({x70|Zero < x70 & x70 * x70 < a1})) & P2488 & P0) & ( Real(Zero) & P2489 & P0) & P0 -> (Three * Sup({x70| Zero < x70 & x70 * x70 < a1}) = Zero & P2490 & P0) & P0" "EQUALITY"; pushreference 251 "P0 -> (Real(Zero) & P2489 & P0) & P0" "RZERO"; pushreference 250 "P0 -> ( Real(Three * Sup({x70|Zero < x70 & x70 * x70 < a1})) & P2488 & P0) & P0" "RTIMES"; pushnode 249 "( Three * Sup({x70|Zero < x70 & x70 * x70 < a1}) Equal Zero & P2459 & P2458 & P0) & ( [ a1 + Minus( Sup({x67|Zero < x67 & x67 * x67 < a1}) * Sup({x68| Zero < x68 & x68 * x68 < a1}))] * Inv(Three * Sup({x69| Zero < x69 & x69 * x69 < a1})) < [[ Three * Sup({x64|Zero < x64 & x64 * x64 < a1})] * Inv( Three * Sup({x70|Zero < x70 & x70 * x70 < a1}))] * a23 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P0) & ( a1 + Minus(Sup({x31| Zero < x31 & x31 * x31 < a1}) * Sup({x32| Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & P0 -> ( Three * Sup({x70|Zero < x70 & x70 * x70 < a1}) Equal Zero & P2487 & P0) & ([a1 + Minus(Sup({x71| Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 0; pushreference 253 "P0 -> ([ Three * Sup({x35|Zero < x35 & x35 * x35 < a1})] * a23 = Three * Sup({x36|Zero < x36 & x36 * x36 < a1}) * a23 & P2492 & P0) & P0" "ATIMES"; pushreference 257 " P0 -> (Zero * a23 = Zero & P2496 & P0) & P0" "MZERO2"; pushreference 259 " (a1 + Minus(Sup({x38|Zero < x38 & x38 * x38 < a1}) * Sup({x39| Zero < x39 & x39 * x39 < a1})) < Zero & P2497 & P2495 & P2494 & P2491 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P2490 & P2492 & P2490 & P2496 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & P0 -> P0" "NOTBOTH"; pushnode 258 "( Zero * a23 = Zero & P2496 & P0) & ( a1 + Minus( Sup({x37|Zero < x37 & x37 * x37 < a1}) * Sup({x38| Zero < x38 & x38 * x38 < a1})) < Zero * a23 & P2495 & P2494 & P2491 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P2490 & P2492 & P2490 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & ( Three * Sup({x70|Zero < x70 & x70 * x70 < a1}) Equal Zero & P2459 & P2458 & P0) & ([a1 + Minus(Sup({x67|Zero < x67 & x67 * x67 < a1}) * Sup({x68| Zero < x68 & x68 * x68 < a1}))] * Inv( Three * Sup({x69|Zero < x69 & x69 * x69 < a1})) < [[ Three * Sup({x64|Zero < x64 & x64 * x64 < a1})] * Inv( Three * Sup({x70|Zero < x70 & x70 * x70 < a1}))] * a23 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P0) & ([ Three * Sup({x35|Zero < x35 & x35 * x35 < a1})] * a23 = Three * Sup({x36|Zero < x36 & x36 * x36 < a1}) * a23 & P2493 & P2492 & P0) & ( Three * Sup({x70|Zero < x70 & x70 * x70 < a1}) = Zero & P2490 & P0) & P0 -> ([a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72|Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 1; pushnode 256 "(Three * Sup({x70|Zero < x70 & x70 * x70 < a1}) = Zero & P2490 & P0) & (a1 + Minus( Sup({x37|Zero < x37 & x37 * x37 < a1}) * Sup({x38|Zero < x38 & x38 * x38 < a1})) < Zero * a23 & P2495 & P2494 & P2491 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P2490 & P2492 & P2490 & P0) & (Zero < a1 + Minus(Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5| Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & ( a1 Equal [ a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [ a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & ( Three * Sup({x70|Zero < x70 & x70 * x70 < a1}) Equal Zero & P2459 & P2458 & P0) & ([a1 + Minus(Sup({x67|Zero < x67 & x67 * x67 < a1}) * Sup({x68| Zero < x68 & x68 * x68 < a1}))] * Inv( Three * Sup({x69|Zero < x69 & x69 * x69 < a1})) < [[ Three * Sup({x64|Zero < x64 & x64 * x64 < a1})] * Inv( Three * Sup({x70|Zero < x70 & x70 * x70 < a1}))] * a23 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P0) & ([ Three * Sup({x35|Zero < x35 & x35 * x35 < a1})] * a23 = Three * Sup({x36|Zero < x36 & x36 * x36 < a1}) * a23 & P2493 & P2492 & P0) & P0 -> ([a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72|Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 255 "(Three * Sup({x70|Zero < x70 & x70 * x70 < a1}) = Zero & P2490 & P0) & (a1 + Minus( Sup({x36|Zero < x36 & x36 * x36 < a1}) * Sup({x37|Zero < x37 & x37 * x37 < a1})) < [Three * Sup({x38|Zero < x38 & x38 * x38 < a1})] * a23 & P2494 & P2491 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P2490 & P2492 & P0) & (Zero < a1 + Minus(Sup({x4| Zero < x4 & x4 * x4 < a1}) * Sup({x5| Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & ( a1 Equal [ a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [ a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & ( Three * Sup({x70|Zero < x70 & x70 * x70 < a1}) Equal Zero & P2459 & P2458 & P0) & ([a1 + Minus(Sup({x67|Zero < x67 & x67 * x67 < a1}) * Sup({x68| Zero < x68 & x68 * x68 < a1}))] * Inv( Three * Sup({x69|Zero < x69 & x69 * x69 < a1})) < [[ Three * Sup({x64|Zero < x64 & x64 * x64 < a1})] * Inv( Three * Sup({x70|Zero < x70 & x70 * x70 < a1}))] * a23 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P0) & ([ Three * Sup({x35|Zero < x35 & x35 * x35 < a1})] * a23 = Three * Sup({x36|Zero < x36 & x36 * x36 < a1}) * a23 & P2493 & P2492 & P0) & P0 -> ([a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72|Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 1; pushnode 254 "([Three * Sup({x35|Zero < x35 & x35 * x35 < a1})] * a23 = Three * Sup({x36| Zero < x36 & x36 * x36 < a1}) * a23 & P2492 & P0) & (a1 + Minus( Sup({x32|Zero < x32 & x32 * x32 < a1}) * Sup({x33|Zero < x33 & x33 * x33 < a1})) < Three * Sup({x34|Zero < x34 & x34 * x34 < a1}) * a23 & P2491 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P2490 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & ( Three * Sup({x70|Zero < x70 & x70 * x70 < a1}) Equal Zero & P2459 & P2458 & P0) & ([a1 + Minus(Sup({x67|Zero < x67 & x67 * x67 < a1}) * Sup({x68| Zero < x68 & x68 * x68 < a1}))] * Inv( Three * Sup({x69|Zero < x69 & x69 * x69 < a1})) < [[ Three * Sup({x64|Zero < x64 & x64 * x64 < a1})] * Inv( Three * Sup({x70|Zero < x70 & x70 * x70 < a1}))] * a23 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P0) & ( Three * Sup({x70|Zero < x70 & x70 * x70 < a1}) = Zero & P2490 & P0) & P0 -> ([a1 + Minus(Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv( Three * Sup({x73|Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 1; pushnode 252 " (Three * Sup({x70|Zero < x70 & x70 * x70 < a1}) = Zero & P2490 & P0) & (a1 + Minus( Sup({x32|Zero < x32 & x32 * x32 < a1}) * Sup({x33|Zero < x33 & x33 * x33 < a1})) < Three * Sup({x34|Zero < x34 & x34 * x34 < a1}) * a23 & P2491 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P2490 & P0) & (Zero < a1 + Minus( Sup({x4|Zero < x4 & x4 * x4 < a1}) * Sup({x5|Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & (a1 Equal [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] * [a23 + Sup({x3|Zero < x3 & x3 * x3 < a1})] & P2367 & P2366 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) < [ a23 + Sup({x6|Zero < x6 & x6 * x6 < a1})] * [ a23 + Sup({x7|Zero < x7 & x7 * x7 < a1})] & P2350 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) < a23 + Sup({x5|Zero < x5 & x5 * x5 < a1}) & P2346 & P2343 & P2341 & P2345 & P0) & ( Real(a23) & P2339 & P2338 & P2335 & P2334 & P2333 & P0) & ( a23 < Sup({x4|Zero < x4 & x4 * x4 < a1}) & P2340 & P2338 & P2335 & P2334 & P2333 & P0) & ((Ax4.x4 E {x3|Zero < x3 & x3 * x3 < a1} -> x4 <= Sup({x3|Zero < x3 & x3 * x3 < a1})) & P2298 & P2296 & P0) & ( Sup({x3|Zero < x3 & x3 * x3 < a1}) * Sup({x3|Zero < x3 & x3 * x3 < a1}) < a1 & P2294 & P2289 & P2287 & P0) & (Real(a1) & P2283 & P2281 & P2280 & P2279 & P0) & ( Zero < a1 & P2284 & P2281 & P2280 & P2279 & P0) & ( Zero < a23 & P2337 & P2335 & P2334 & P2333 & P0) & ( Three * Sup({x70|Zero < x70 & x70 * x70 < a1}) Equal Zero & P2459 & P2458 & P0) & ([a1 + Minus(Sup({x67|Zero < x67 & x67 * x67 < a1}) * Sup({x68| Zero < x68 & x68 * x68 < a1}))] * Inv( Three * Sup({x69|Zero < x69 & x69 * x69 < a1})) < [[ Three * Sup({x64|Zero < x64 & x64 * x64 < a1})] * Inv( Three * Sup({x70|Zero < x70 & x70 * x70 < a1}))] * a23 & P2457 & P2454 & P2451 & P2449 & P2447 & P2446 & P2445 & P2433 & P2431 & P2444 & P2444 & P2444 & P2448 & P2450 & P2452 & P2455 & P0) & P0 -> ( [a1 + Minus( Sup({x71|Zero < x71 & x71 * x71 < a1}) * Sup({x72| Zero < x72 & x72 * x72 < a1}))] * Inv(Three * Sup({x73| Zero < x73 & x73 * x73 < a1})) <= a23 & P2336 & P2334 & P2333 & P0) & ( Sup({x3| Zero < x3 & x3 * x3 < a1}) * Sup({x3| Zero < x3 & x3 * x3 < a1}) = a1 & P2285 & P2282 & P2280 & P2279 & P0) & ((Ex3. x3 * x3 = a1) & P2286 & P2282 & P2280 & P2279 & P0) & P0" 2; pushnode 248 " (Three * Sup({x70|Zero < x70 & x70 * x70 < a1}) = Zero & P2490 & P0) & (a1 + Minus( Sup({x31|Zero < x31 & x31 * x31 < a1}) * Sup({x32|Zero < x32 & x32 * x32 < a1})) < Three * Sup({x33|Zero < x33 & x33 * x33 < a1}) * a23 & P2430 & P2428 & P2425 & P2422 & P2420 & P2418 & P2416 & P2414 & P2417 & P2419 & P2421 & P2424 & P2427 & P2429 & P0) & (Zero < a1 + Minus(Sup({x4| Zero < x4 & x4 * x4 < a1}) * Sup({x5| Zero < x5 & x5 * x5 < a1})) & P2413 & P2411 & P2409 & P2412 & P0) & ( a1 Equal [ a23 + Sup(