%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP721-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Jul 15 06:44:48 AM UTC 2025
% Result : Unsatisfiable 222.71s 222.91s
% Output : CNFRefutation 222.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 8
% Syntax : Number of clauses : 146 ( 146 unt; 0 nHn; 3 RR)
% Number of literals : 146 ( 145 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 312 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
mult(mult(a,a),mult(b,b)) != mult(f(a,b),f(a,b)),
file('theBenchmark.p',goals) ).
cnf(c1,axiom,
mult(X,unit) = X,
file('theBenchmark.p',c01) ).
cnf(c2,axiom,
mult(unit,X) = X,
file('theBenchmark.p',c02) ).
cnf(c3,axiom,
mult(X,Y) = mult(Y,X),
file('theBenchmark.p',c05) ).
cnf(c4,axiom,
ld(X,mult(X,Y)) = Y,
file('theBenchmark.p',c04) ).
cnf(c5,plain,
ld(X,X) = unit,
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c6,plain,
ld(unit,X) = X,
inference(equational,[status(thm)],[c2,c4]) ).
cnf(c7,axiom,
mult(X,ld(X,Y)) = Y,
file('theBenchmark.p',c03) ).
cnf(c8,plain,
ld(X,mult(Y,X)) = Y,
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c9,plain,
ld(ld(X,Y),Y) = X,
inference(equational,[status(thm)],[c7,c8]) ).
cnf(c10,axiom,
f(X,Y) = ld(mult(ld(mult(X,Y),X),ld(mult(X,Y),Y)),unit),
file('theBenchmark.p',c08) ).
cnf(c11,plain,
ld(mult(ld(mult(X,Y),X),ld(mult(X,Y),Y)),unit) = f(X,Y),
inference(equational,[status(thm)],[c10]) ).
cnf(c12,plain,
f(X,unit) = X,
inference(equational,[status(thm)],[c1,c2,c5,c9,c11]) ).
cnf(c13,plain,
f(unit,X) = X,
inference(equational,[status(thm)],[c1,c2,c5,c9,c11]) ).
cnf(c14,plain,
ld(mult(ld(X,Y),ld(X,ld(Y,X))),unit) = f(Y,ld(Y,X)),
inference(equational,[status(thm)],[c7,c11]) ).
cnf(c17,plain,
mult(ld(X,Y),ld(X,ld(Y,X))) = ld(f(Y,ld(Y,X)),unit),
inference(equational,[status(thm)],[c1,c5,c6,c13,c14]) ).
cnf(c18,plain,
ld(f(ld(X,Y),X),unit) = ld(f(X,ld(X,Y)),unit),
inference(equational,[status(thm)],[c3,c9,c17]) ).
cnf(c19,plain,
f(ld(X,Y),X) = f(X,ld(X,Y)),
inference(equational,[status(thm)],[c1,c5,c6,c9,c13,c14,c18]) ).
cnf(c20,plain,
f(X,Y) = f(Y,X),
inference(equational,[status(thm)],[c8,c19]) ).
cnf(c21,plain,
mult(ld(mult(X,Y),X),ld(mult(X,Y),Y)) = ld(f(X,Y),unit),
inference(equational,[status(thm)],[c1,c5,c6,c11,c13,c14]) ).
cnf(c22,plain,
mult(ld(mult(X,Y),Y),ld(mult(X,Y),X)) = ld(f(X,Y),unit),
inference(equational,[status(thm)],[c3,c21]) ).
cnf(c24,plain,
mult(ld(mult(X,Y),X),ld(mult(Y,X),Y)) = ld(f(X,Y),unit),
inference(equational,[status(thm)],[c3,c21]) ).
cnf(c32,plain,
mult(X,ld(ld(X,Y),ld(Y,ld(X,Y)))) = ld(f(Y,ld(Y,ld(X,Y))),unit),
inference(equational,[status(thm)],[c9,c17]) ).
cnf(c34,plain,
ld(f(mult(X,Y),ld(mult(X,Y),X)),unit) = mult(Y,ld(X,ld(mult(X,Y),X))),
inference(equational,[status(thm)],[c4,c17]) ).
cnf(c46,axiom,
ld(mult(X,Y),mult(X,mult(Y,mult(Z,W)))) = mult(ld(mult(X,Y),mult(X,mult(Y,Z))),ld(mult(X,Y),mult(X,mult(Y,W)))),
file('theBenchmark.p',c06) ).
cnf(c47,plain,
mult(ld(mult(X,Y),mult(X,mult(Y,Z))),ld(mult(X,Y),mult(X,mult(Y,W)))) = ld(mult(X,Y),mult(X,mult(Y,mult(Z,W)))),
inference(equational,[status(thm)],[c46]) ).
cnf(c48,plain,
mult(X,ld(mult(X,X),mult(X,mult(X,Y)))) = ld(mult(X,X),mult(X,mult(X,mult(X,Y)))),
inference(equational,[status(thm)],[c8,c47]) ).
cnf(c49,plain,
mult(X,ld(mult(X,X),mult(X,Y))) = ld(mult(X,X),mult(X,mult(X,Y))),
inference(equational,[status(thm)],[c7,c48]) ).
cnf(c50,plain,
mult(X,ld(mult(X,X),X)) = unit,
inference(equational,[status(thm)],[c1,c5,c49]) ).
cnf(c51,plain,
ld(mult(X,X),X) = ld(X,unit),
inference(equational,[status(thm)],[c1,c5,c6,c13,c34,c50]) ).
cnf(c52,plain,
ld(ld(X,unit),X) = mult(X,X),
inference(equational,[status(thm)],[c9,c51]) ).
cnf(c55,plain,
mult(X,ld(mult(X,X),Y)) = ld(mult(X,X),mult(X,Y)),
inference(equational,[status(thm)],[c7,c49]) ).
cnf(c56,plain,
mult(ld(X,unit),f(X,X)) = X,
inference(equational,[status(thm)],[c1,c9,c11,c51,c55]) ).
cnf(c57,plain,
mult(X,X) = f(X,X),
inference(equational,[status(thm)],[c4,c52,c56]) ).
cnf(c58,plain,
ld(f(X,X),X) = ld(X,unit),
inference(equational,[status(thm)],[c8,c56]) ).
cnf(c61,plain,
mult(X,ld(f(X,X),unit)) = ld(X,unit),
inference(equational,[status(thm)],[c1,c49,c50,c57,c58]) ).
cnf(c62,plain,
ld(f(X,X),unit) = ld(X,ld(X,unit)),
inference(equational,[status(thm)],[c4,c61]) ).
cnf(c66,plain,
f(ld(X,unit),ld(X,unit)) = ld(X,ld(X,unit)),
inference(equational,[status(thm)],[c8,c17,c51,c57,c62]) ).
cnf(c67,plain,
ld(ld(X,ld(X,unit)),unit) = f(X,X),
inference(equational,[status(thm)],[c1,c5,c6,c13,c32,c62]) ).
cnf(c69,plain,
ld(X,ld(f(X,X),mult(X,Y))) = ld(f(X,X),Y),
inference(equational,[status(thm)],[c4,c55,c57]) ).
cnf(c79,plain,
ld(f(X,X),mult(X,mult(Y,f(X,X)))) = mult(X,Y),
inference(equational,[status(thm)],[c8,c55,c57]) ).
cnf(c80,plain,
mult(f(X,X),mult(X,Y)) = mult(X,mult(Y,f(X,X))),
inference(equational,[status(thm)],[c7,c79]) ).
cnf(c84,plain,
mult(X,mult(ld(X,Y),f(X,X))) = mult(f(X,X),Y),
inference(equational,[status(thm)],[c7,c80]) ).
cnf(c85,plain,
mult(ld(X,Y),f(X,X)) = ld(X,mult(f(X,X),Y)),
inference(equational,[status(thm)],[c4,c84]) ).
cnf(c211,plain,
mult(ld(mult(X,Y),mult(X,Z)),ld(mult(X,Y),mult(X,mult(Y,W)))) = ld(mult(X,Y),mult(X,mult(Y,mult(ld(Y,Z),W)))),
inference(equational,[status(thm)],[c7,c47]) ).
cnf(c212,plain,
mult(X,ld(mult(X,Y),mult(X,mult(Y,Z)))) = ld(mult(X,Y),mult(X,mult(Y,mult(X,Z)))),
inference(equational,[status(thm)],[c8,c211]) ).
cnf(c213,plain,
ld(mult(X,Y),mult(X,mult(Y,X))) = X,
inference(equational,[status(thm)],[c1,c5,c212]) ).
cnf(c214,plain,
mult(X,mult(ld(X,unit),mult(X,Y))) = mult(X,mult(X,mult(ld(X,unit),Y))),
inference(equational,[status(thm)],[c6,c7,c50,c57,c58,c212]) ).
cnf(c215,plain,
mult(ld(X,unit),mult(X,Y)) = mult(X,mult(ld(X,unit),Y)),
inference(equational,[status(thm)],[c4,c214]) ).
cnf(c217,plain,
mult(X,mult(ld(X,unit),ld(X,Y))) = mult(ld(X,unit),Y),
inference(equational,[status(thm)],[c7,c215]) ).
cnf(c218,plain,
mult(ld(X,unit),ld(X,Y)) = ld(X,mult(ld(X,unit),Y)),
inference(equational,[status(thm)],[c4,c217]) ).
cnf(c219,plain,
mult(ld(X,Y),ld(X,unit)) = ld(X,mult(ld(X,unit),Y)),
inference(equational,[status(thm)],[c3,c218]) ).
cnf(c220,plain,
mult(X,ld(ld(X,unit),Y)) = ld(ld(X,unit),mult(X,Y)),
inference(equational,[status(thm)],[c9,c218]) ).
cnf(c221,plain,
mult(X,ld(Y,mult(X,mult(ld(X,Y),Z)))) = ld(Y,mult(X,mult(ld(X,Y),mult(X,Z)))),
inference(equational,[status(thm)],[c7,c212]) ).
cnf(c222,plain,
mult(X,ld(mult(Y,X),mult(X,mult(Y,Z)))) = ld(mult(X,Y),mult(X,mult(Y,mult(X,Z)))),
inference(equational,[status(thm)],[c3,c212]) ).
cnf(c223,plain,
mult(X,ld(mult(Y,X),mult(X,Y))) = X,
inference(equational,[status(thm)],[c1,c213,c222]) ).
cnf(c225,plain,
mult(X,ld(mult(X,Y),mult(mult(Y,Z),X))) = ld(mult(X,Y),mult(X,mult(Y,mult(X,Z)))),
inference(equational,[status(thm)],[c3,c212]) ).
cnf(c226,plain,
mult(X,ld(mult(X,Y),mult(Y,X))) = X,
inference(equational,[status(thm)],[c1,c213,c225]) ).
cnf(c227,plain,
mult(ld(X,unit),ld(mult(X,Y),mult(Y,X))) = ld(X,unit),
inference(equational,[status(thm)],[c3,c5,c12,c34,c226]) ).
cnf(c228,plain,
mult(X,ld(mult(X,Y),mult(X,mult(Z,Y)))) = ld(mult(X,Y),mult(X,mult(Y,mult(X,Z)))),
inference(equational,[status(thm)],[c3,c212]) ).
cnf(c233,plain,
mult(X,ld(mult(X,Y),mult(mult(Z,Y),X))) = ld(mult(X,Y),mult(X,mult(Y,mult(X,Z)))),
inference(equational,[status(thm)],[c3,c228]) ).
cnf(c237,plain,
ld(mult(X,Y),mult(X,mult(ld(X,unit),Y))) = ld(X,unit),
inference(equational,[status(thm)],[c8,c215]) ).
cnf(c239,plain,
ld(f(X,ld(mult(X,Y),mult(Y,X))),unit) = ld(X,ld(mult(X,Y),mult(Y,X))),
inference(equational,[status(thm)],[c1,c5,c22,c226]) ).
cnf(c240,plain,
ld(X,ld(mult(X,Y),mult(Y,X))) = ld(X,unit),
inference(equational,[status(thm)],[c3,c5,c12,c239]) ).
cnf(c241,plain,
ld(ld(X,unit),ld(mult(X,Y),mult(Y,X))) = X,
inference(equational,[status(thm)],[c9,c240]) ).
cnf(c243,plain,
ld(ld(X,ld(mult(Y,X),mult(X,Y))),unit) = f(X,ld(mult(Y,X),mult(X,Y))),
inference(equational,[status(thm)],[c2,c5,c11,c223]) ).
cnf(c248,plain,
mult(ld(mult(X,Y),mult(Y,X)),mult(X,Z)) = mult(X,mult(Z,ld(mult(X,Y),mult(Y,X)))),
inference(equational,[status(thm)],[c4,c8,c226,c233]) ).
cnf(c249,plain,
ld(mult(X,Y),mult(Y,X)) = unit,
inference(equational,[status(thm)],[c1,c7,c50,c57,c58,c227,c248]) ).
cnf(c256,plain,
ld(mult(X,Y),mult(Y,mult(ld(Y,unit),X))) = ld(Y,unit),
inference(equational,[status(thm)],[c3,c237]) ).
cnf(c258,plain,
ld(mult(X,Y),mult(X,mult(Y,mult(X,ld(Y,Z))))) = mult(X,ld(mult(X,Y),mult(X,Z))),
inference(equational,[status(thm)],[c7,c212]) ).
cnf(c282,plain,
ld(X,ld(mult(X,Y),mult(X,mult(Y,mult(X,Z))))) = ld(mult(X,Y),mult(X,mult(Y,Z))),
inference(equational,[status(thm)],[c4,c212]) ).
cnf(c283,plain,
ld(mult(X,Y),mult(X,mult(Y,ld(X,Z)))) = ld(X,ld(mult(X,Y),mult(X,mult(Y,Z)))),
inference(equational,[status(thm)],[c7,c282]) ).
cnf(c285,plain,
ld(mult(X,Y),mult(X,mult(ld(X,Z),Y))) = ld(X,ld(mult(X,Y),mult(X,mult(Y,Z)))),
inference(equational,[status(thm)],[c3,c283]) ).
cnf(c286,plain,
ld(X,mult(Y,mult(ld(Y,X),ld(Y,Z)))) = ld(Y,ld(X,mult(Y,mult(ld(Y,X),Z)))),
inference(equational,[status(thm)],[c7,c283]) ).
cnf(c295,plain,
ld(X,ld(Y,mult(X,mult(Z,ld(X,Y))))) = ld(Y,mult(X,mult(ld(X,Y),ld(X,Z)))),
inference(equational,[status(thm)],[c3,c286]) ).
cnf(c312,plain,
mult(mult(X,Y),mult(X,ld(mult(X,Y),mult(X,Z)))) = mult(X,mult(Y,mult(X,ld(Y,Z)))),
inference(equational,[status(thm)],[c7,c258]) ).
cnf(c318,plain,
mult(mult(X,Y),mult(X,ld(mult(X,Y),Z))) = mult(X,mult(Y,mult(X,ld(Y,ld(X,Z))))),
inference(equational,[status(thm)],[c7,c312]) ).
cnf(c322,plain,
mult(mult(X,Y),mult(Y,ld(mult(Y,X),Z))) = mult(Y,mult(X,mult(Y,ld(X,ld(Y,Z))))),
inference(equational,[status(thm)],[c3,c318]) ).
cnf(c329,plain,
mult(ld(X,Y),mult(X,ld(ld(X,Y),unit))) = mult(Y,ld(ld(X,Y),unit)),
inference(equational,[status(thm)],[c3,c9,c217]) ).
cnf(c330,plain,
ld(X,mult(Y,mult(X,ld(ld(Y,X),unit)))) = mult(Y,ld(X,Y)),
inference(equational,[status(thm)],[c1,c7,c258,c329]) ).
cnf(c331,plain,
mult(X,mult(Y,ld(ld(X,Y),unit))) = mult(Y,mult(X,ld(Y,X))),
inference(equational,[status(thm)],[c7,c330]) ).
cnf(c332,plain,
ld(X,mult(Y,mult(X,ld(Y,X)))) = mult(Y,ld(ld(X,Y),unit)),
inference(equational,[status(thm)],[c4,c331]) ).
cnf(c335,plain,
ld(X,mult(Y,mult(ld(Y,Z),ld(Y,X)))) = ld(Y,ld(X,mult(Y,mult(Z,ld(Y,X))))),
inference(equational,[status(thm)],[c3,c295]) ).
cnf(c336,plain,
ld(X,mult(Y,f(ld(Y,X),ld(Y,X)))) = ld(ld(X,Y),unit),
inference(equational,[status(thm)],[c4,c57,c332,c335]) ).
cnf(c337,plain,
ld(X,ld(Y,mult(f(Y,Y),X))) = ld(ld(X,ld(Y,X)),unit),
inference(equational,[status(thm)],[c9,c85,c336]) ).
cnf(c340,plain,
mult(X,f(ld(X,Y),ld(X,Y))) = mult(Y,ld(ld(Y,X),unit)),
inference(equational,[status(thm)],[c7,c336]) ).
cnf(c344,plain,
mult(X,ld(ld(X,ld(Y,X)),unit)) = ld(Y,mult(f(Y,Y),X)),
inference(equational,[status(thm)],[c7,c337]) ).
cnf(c381,plain,
mult(mult(X,Y),ld(mult(Y,X),mult(Y,mult(X,Z)))) = mult(Y,mult(X,Z)),
inference(equational,[status(thm)],[c4,c7,c8,c285,c322]) ).
cnf(c383,plain,
mult(mult(X,Y),ld(mult(Y,X),mult(Y,Z))) = mult(Y,Z),
inference(equational,[status(thm)],[c7,c381]) ).
cnf(c384,plain,
mult(mult(X,Y),ld(mult(Y,X),Z)) = Z,
inference(equational,[status(thm)],[c7,c383]) ).
cnf(c411,plain,
mult(X,mult(ld(X,unit),mult(ld(ld(X,unit),Y),Z))) = mult(mult(X,Y),mult(X,mult(ld(X,unit),Z))),
inference(equational,[status(thm)],[c6,c7,c50,c57,c58,c211]) ).
cnf(c412,plain,
mult(X,mult(Y,ld(ld(Y,ld(X,unit)),unit))) = f(mult(X,Y),mult(X,Y)),
inference(equational,[status(thm)],[c7,c57,c340,c411]) ).
cnf(c413,plain,
ld(X,f(mult(X,Y),mult(X,Y))) = mult(Y,ld(ld(Y,ld(X,unit)),unit)),
inference(equational,[status(thm)],[c4,c412]) ).
cnf(c415,plain,
ld(X,f(mult(Y,X),mult(X,Y))) = mult(Y,ld(ld(Y,ld(X,unit)),unit)),
inference(equational,[status(thm)],[c3,c413]) ).
cnf(c431,plain,
mult(X,mult(Y,ld(ld(Y,ld(X,Y)),unit))) = mult(f(X,X),Y),
inference(equational,[status(thm)],[c7,c344]) ).
cnf(c464,plain,
mult(ld(mult(X,Y),X),ld(mult(X,Y),mult(X,mult(Y,Z)))) = ld(mult(X,Y),mult(X,mult(Y,mult(ld(Y,unit),Z)))),
inference(equational,[status(thm)],[c1,c211]) ).
cnf(c469,plain,
mult(ld(mult(X,Y),X),ld(mult(X,Y),mult(X,Z))) = ld(mult(X,Y),mult(X,mult(ld(Y,unit),Z))),
inference(equational,[status(thm)],[c7,c218,c464]) ).
cnf(c470,plain,
ld(X,mult(Y,mult(ld(ld(Y,X),unit),Z))) = mult(ld(X,Y),ld(X,mult(Y,Z))),
inference(equational,[status(thm)],[c7,c469]) ).
cnf(c471,plain,
mult(X,mult(ld(X,Y),ld(X,mult(Y,Z)))) = mult(Y,mult(ld(ld(Y,X),unit),Z)),
inference(equational,[status(thm)],[c7,c470]) ).
cnf(c472,plain,
mult(X,mult(ld(X,unit),ld(ld(X,Y),unit))) = mult(ld(Y,unit),X),
inference(equational,[status(thm)],[c3,c7,c50,c57,c58,c219,c471]) ).
cnf(c473,plain,
mult(ld(X,unit),ld(ld(X,Y),unit)) = ld(Y,unit),
inference(equational,[status(thm)],[c4,c8,c472]) ).
cnf(c474,plain,
mult(ld(X,unit),ld(Y,unit)) = ld(mult(Y,X),unit),
inference(equational,[status(thm)],[c8,c473]) ).
cnf(c475,plain,
ld(ld(X,unit),ld(Y,unit)) = ld(ld(X,Y),unit),
inference(equational,[status(thm)],[c4,c473]) ).
cnf(c476,plain,
ld(ld(ld(X,unit),Y),unit) = ld(X,ld(Y,unit)),
inference(equational,[status(thm)],[c12,c243,c249,c475]) ).
cnf(c477,plain,
ld(ld(X,ld(Y,unit)),unit) = ld(ld(X,unit),Y),
inference(equational,[status(thm)],[c12,c243,c249,c475]) ).
cnf(c484,plain,
ld(mult(ld(X,ld(X,unit)),Y),unit) = mult(ld(Y,unit),f(X,X)),
inference(equational,[status(thm)],[c67,c474]) ).
cnf(c486,plain,
ld(ld(X,unit),ld(Y,ld(Y,unit))) = ld(ld(X,f(Y,Y)),unit),
inference(equational,[status(thm)],[c62,c475]) ).
cnf(c493,plain,
ld(X,f(mult(Y,X),mult(X,Y))) = ld(ld(Y,unit),mult(Y,X)),
inference(equational,[status(thm)],[c220,c415,c477]) ).
cnf(c494,plain,
ld(ld(X,f(Y,Y)),unit) = ld(ld(X,Y),ld(Y,unit)),
inference(equational,[status(thm)],[c7,c9,c66,c473,c474,c486,c493]) ).
cnf(c495,plain,
ld(ld(ld(X,Y),unit),Y) = ld(X,f(Y,Y)),
inference(equational,[status(thm)],[c241,c249,c477,c494]) ).
cnf(c506,plain,
mult(X,mult(ld(X,Y),ld(X,Z))) = mult(Y,mult(ld(ld(Y,X),unit),ld(Y,Z))),
inference(equational,[status(thm)],[c7,c471]) ).
cnf(c520,plain,
f(ld(X,unit),ld(ld(X,Y),unit)) = ld(f(X,ld(X,Y)),unit),
inference(equational,[status(thm)],[c3,c9,c14,c17,c474,c475]) ).
cnf(c521,plain,
f(ld(X,unit),ld(Y,unit)) = ld(f(X,Y),unit),
inference(equational,[status(thm)],[c8,c520]) ).
cnf(c532,plain,
ld(X,ld(Y,mult(X,mult(Z,ld(X,Y))))) = mult(ld(ld(Y,X),unit),ld(Y,Z)),
inference(equational,[status(thm)],[c4,c295,c506]) ).
cnf(c537,plain,
mult(ld(X,ld(Y,unit)),ld(ld(X,Y),unit)) = ld(Y,ld(Y,unit)),
inference(equational,[status(thm)],[c3,c8,c217,c532]) ).
cnf(c540,plain,
ld(X,ld(Y,mult(X,mult(ld(X,Y),Z)))) = mult(ld(ld(Y,X),unit),ld(Y,Z)),
inference(equational,[status(thm)],[c4,c286,c506]) ).
cnf(c545,plain,
ld(X,mult(Y,mult(ld(Y,X),ld(Y,Z)))) = mult(ld(ld(X,Y),unit),ld(X,Z)),
inference(equational,[status(thm)],[c4,c506]) ).
cnf(c549,plain,
mult(X,mult(ld(ld(Y,X),unit),ld(Y,Z))) = ld(Y,mult(X,mult(ld(X,Y),Z))),
inference(equational,[status(thm)],[c4,c7,c221,c506]) ).
cnf(c550,plain,
ld(mult(X,Y),mult(mult(Y,X),Z)) = Z,
inference(equational,[status(thm)],[c2,c6,c249,c384,c549]) ).
cnf(c581,plain,
mult(ld(ld(X,Y),unit),ld(X,ld(Y,X))) = ld(Y,ld(ld(X,Y),unit)),
inference(equational,[status(thm)],[c4,c57,c340,c532]) ).
cnf(c593,plain,
mult(ld(mult(X,Y),X),ld(mult(Y,X),mult(X,Z))) = ld(mult(X,Y),mult(X,mult(ld(Y,unit),Z))),
inference(equational,[status(thm)],[c3,c469]) ).
cnf(c594,plain,
mult(ld(mult(X,Y),X),ld(mult(Y,X),X)) = ld(mult(X,Y),mult(X,ld(Y,unit))),
inference(equational,[status(thm)],[c1,c226,c249,c593]) ).
cnf(c595,plain,
mult(ld(X,unit),ld(Y,ld(mult(X,Y),Y))) = ld(mult(Y,X),ld(X,unit)),
inference(equational,[status(thm)],[c4,c7,c286,c545,c594]) ).
cnf(c605,plain,
ld(ld(X,unit),ld(mult(Y,X),ld(X,unit))) = ld(Y,ld(mult(X,Y),Y)),
inference(equational,[status(thm)],[c4,c595]) ).
cnf(c610,plain,
ld(ld(X,Y),ld(ld(Y,unit),ld(X,Y))) = ld(ld(X,ld(Y,X)),unit),
inference(equational,[status(thm)],[c7,c9,c473,c474,c475,c605]) ).
cnf(c644,plain,
mult(ld(X,Y),ld(ld(X,ld(Y,X)),unit)) = ld(ld(Y,unit),ld(X,Y)),
inference(equational,[status(thm)],[c7,c610]) ).
cnf(c648,plain,
mult(ld(X,ld(Y,X)),ld(ld(X,Y),unit)) = ld(Y,ld(ld(X,Y),unit)),
inference(equational,[status(thm)],[c3,c581]) ).
cnf(c668,plain,
mult(ld(X,ld(X,unit)),ld(Y,X)) = ld(mult(X,f(X,ld(X,Y))),unit),
inference(equational,[status(thm)],[c3,c9,c17,c62,c431,c474,c521,c610]) ).
cnf(c674,plain,
mult(ld(ld(X,Y),unit),ld(X,ld(Y,Z))) = ld(Y,mult(ld(ld(X,Y),unit),ld(X,Z))),
inference(equational,[status(thm)],[c540,c545]) ).
cnf(c698,plain,
mult(ld(ld(X,Y),unit),f(Y,Y)) = mult(Y,f(Y,ld(Y,X))),
inference(equational,[status(thm)],[c9,c484,c668]) ).
cnf(c735,plain,
ld(ld(mult(X,Y),unit),mult(ld(mult(Y,X),unit),Z)) = Z,
inference(equational,[status(thm)],[c474,c550]) ).
cnf(c736,plain,
ld(f(X,Y),mult(f(Y,X),Z)) = Z,
inference(equational,[status(thm)],[c9,c24,c735]) ).
cnf(c737,plain,
ld(f(X,Y),f(Y,X)) = unit,
inference(equational,[status(thm)],[c1,c736]) ).
cnf(c741,plain,
mult(f(X,Y),ld(f(Y,X),Z)) = Z,
inference(equational,[status(thm)],[c2,c6,c549,c736,c737]) ).
cnf(c754,plain,
ld(ld(mult(X,Y),unit),mult(X,ld(mult(Y,X),unit))) = X,
inference(equational,[status(thm)],[c9,c215,c256,c474]) ).
cnf(c755,plain,
ld(f(X,X),mult(X,f(X,ld(X,Y)))) = ld(ld(Y,X),unit),
inference(equational,[status(thm)],[c7,c52,c57,c474,c477,c537,c674,c698,c754]) ).
cnf(c756,plain,
ld(f(X,X),f(X,ld(X,Y))) = ld(X,ld(ld(Y,X),unit)),
inference(equational,[status(thm)],[c69,c755]) ).
cnf(c759,plain,
ld(X,ld(ld(mult(Y,X),X),unit)) = ld(f(X,X),f(X,Y)),
inference(equational,[status(thm)],[c8,c756]) ).
cnf(c760,plain,
ld(X,ld(ld(mult(X,Y),X),unit)) = ld(f(X,X),f(X,Y)),
inference(equational,[status(thm)],[c4,c756]) ).
cnf(c778,plain,
ld(ld(X,Y),ld(ld(Y,ld(X,Y)),unit)) = ld(ld(X,unit),ld(Y,X)),
inference(equational,[status(thm)],[c9,c644,c648]) ).
cnf(c779,plain,
ld(f(X,X),f(X,Y)) = ld(ld(Y,unit),ld(mult(X,Y),Y)),
inference(equational,[status(thm)],[c8,c760,c778]) ).
cnf(c783,plain,
ld(f(X,X),f(Y,X)) = ld(ld(Y,unit),ld(mult(X,Y),Y)),
inference(equational,[status(thm)],[c20,c779]) ).
cnf(c1026,plain,
ld(f(X,X),f(f(Y,X),f(Y,X))) = f(Y,Y),
inference(equational,[status(thm)],[c9,c476,c495,c759,c783]) ).
cnf(c1027,plain,
mult(f(X,X),f(Y,Y)) = f(f(Y,X),f(Y,X)),
inference(equational,[status(thm)],[c741,c1026]) ).
cnf(g1,plain,
mult(mult(a,a),mult(b,b)) = mult(f(a,b),f(a,b)),
inference(equational,[status(thm)],[c20,c57,c1027]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP721-1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 08:56:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 222.71/222.91 % SZS status Unsatisfiable
% 222.71/222.91 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------