%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP667-2 : 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 06:44:39 AM UTC 2025
% Result : Unsatisfiable 153.84s 153.86s
% Output : CNFRefutation 153.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 10
% Syntax : Number of clauses : 176 ( 176 unt; 0 nHn; 3 RR)
% Number of literals : 176 ( 175 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 390 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c),
file('theBenchmark.p',goals) ).
cnf(c1,axiom,
mult(X,unit) = X,
file('theBenchmark.p',c05) ).
cnf(c2,axiom,
mult(unit,X) = X,
file('theBenchmark.p',c06) ).
cnf(c3,axiom,
mult(rd(X,Y),Y) = X,
file('theBenchmark.p',c03) ).
cnf(c4,plain,
rd(X,unit) = X,
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c5,axiom,
rd(mult(X,Y),Y) = X,
file('theBenchmark.p',c04) ).
cnf(c6,plain,
rd(X,X) = unit,
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c7,axiom,
mult(X,ld(X,Y)) = Y,
file('theBenchmark.p',c01) ).
cnf(c8,plain,
ld(unit,X) = X,
inference(equational,[status(thm)],[c2,c7]) ).
cnf(c9,axiom,
ld(X,mult(X,Y)) = Y,
file('theBenchmark.p',c02) ).
cnf(c10,plain,
ld(X,X) = unit,
inference(equational,[status(thm)],[c1,c9]) ).
cnf(c11,axiom,
mult(f(X),f(X)) = X,
file('theBenchmark.p',c09) ).
cnf(c14,plain,
ld(rd(X,Y),X) = Y,
inference(equational,[status(thm)],[c3,c9]) ).
cnf(c15,plain,
rd(X,ld(Y,X)) = Y,
inference(equational,[status(thm)],[c5,c7]) ).
cnf(c16,axiom,
mult(mult(X,Y),X) = mult(X,mult(Y,X)),
file('theBenchmark.p',c08) ).
cnf(c17,plain,
mult(f(X),X) = mult(X,f(X)),
inference(equational,[status(thm)],[c11,c16]) ).
cnf(c19,plain,
mult(X,mult(ld(X,Y),X)) = mult(Y,X),
inference(equational,[status(thm)],[c7,c16]) ).
cnf(c20,plain,
mult(ld(X,Y),X) = ld(X,mult(Y,X)),
inference(equational,[status(thm)],[c9,c19]) ).
cnf(c21,plain,
rd(mult(X,mult(Y,X)),X) = mult(X,Y),
inference(equational,[status(thm)],[c5,c16]) ).
cnf(c22,plain,
mult(X,rd(Y,X)) = rd(mult(X,Y),X),
inference(equational,[status(thm)],[c3,c21]) ).
cnf(c24,plain,
rd(ld(X,mult(Y,X)),X) = ld(X,Y),
inference(equational,[status(thm)],[c5,c20]) ).
cnf(c25,plain,
rd(unit,X) = ld(X,unit),
inference(equational,[status(thm)],[c2,c10,c24]) ).
cnf(c26,plain,
rd(f(X),X) = ld(X,f(X)),
inference(equational,[status(thm)],[c9,c17,c24]) ).
cnf(c27,plain,
ld(ld(X,unit),unit) = X,
inference(equational,[status(thm)],[c15,c25]) ).
cnf(c28,plain,
rd(ld(X,Y),X) = ld(X,rd(Y,X)),
inference(equational,[status(thm)],[c3,c24]) ).
cnf(c29,plain,
ld(X,rd(mult(X,Y),X)) = rd(Y,X),
inference(equational,[status(thm)],[c9,c22]) ).
cnf(c35,plain,
ld(ld(X,f(X)),f(X)) = X,
inference(equational,[status(thm)],[c14,c26]) ).
cnf(c37,plain,
mult(rd(X,Y),rd(mult(Y,X),Y)) = mult(X,rd(X,Y)),
inference(equational,[status(thm)],[c3,c16,c22]) ).
cnf(c40,plain,
ld(ld(X,Y),ld(X,mult(Y,X))) = X,
inference(equational,[status(thm)],[c9,c20]) ).
cnf(c41,axiom,
mult(mult(X,Y),mult(mult(Z,Y),Z)) = mult(mult(X,mult(mult(Y,Z),Y)),Z),
file('theBenchmark.p',c07) ).
cnf(c42,plain,
mult(mult(X,mult(Y,mult(Z,Y))),Z) = mult(mult(X,Y),mult(Z,mult(Y,Z))),
inference(equational,[status(thm)],[c16,c41]) ).
cnf(c43,plain,
mult(mult(X,Y),Y) = mult(X,mult(Y,Y)),
inference(equational,[status(thm)],[c1,c2,c42]) ).
cnf(c45,plain,
rd(mult(X,mult(Y,Y)),Y) = mult(X,Y),
inference(equational,[status(thm)],[c5,c43]) ).
cnf(c46,plain,
rd(mult(X,Y),f(Y)) = mult(X,f(Y)),
inference(equational,[status(thm)],[c11,c45]) ).
cnf(c48,plain,
mult(rd(X,Y),mult(Y,Y)) = mult(X,Y),
inference(equational,[status(thm)],[c3,c43]) ).
cnf(c49,plain,
mult(rd(X,f(Y)),Y) = mult(X,f(Y)),
inference(equational,[status(thm)],[c11,c48]) ).
cnf(c50,plain,
mult(mult(X,mult(Y,X)),Y) = mult(X,mult(Y,mult(X,Y))),
inference(equational,[status(thm)],[c2,c42]) ).
cnf(c51,plain,
rd(mult(X,f(Y)),Y) = rd(X,f(Y)),
inference(equational,[status(thm)],[c5,c49]) ).
cnf(c52,plain,
ld(X,f(X)) = ld(f(X),unit),
inference(equational,[status(thm)],[c2,c25,c26,c51]) ).
cnf(c53,plain,
mult(rd(X,Y),f(Y)) = rd(X,f(Y)),
inference(equational,[status(thm)],[c3,c46]) ).
cnf(c54,plain,
mult(rd(X,mult(Y,Y)),Y) = rd(X,Y),
inference(equational,[status(thm)],[c3,c45]) ).
cnf(c55,plain,
rd(rd(X,Y),Y) = rd(X,mult(Y,Y)),
inference(equational,[status(thm)],[c5,c54]) ).
cnf(c57,plain,
ld(mult(X,X),unit) = ld(X,ld(X,unit)),
inference(equational,[status(thm)],[c25,c28,c55]) ).
cnf(c59,plain,
ld(rd(X,Y),mult(X,Y)) = mult(Y,Y),
inference(equational,[status(thm)],[c9,c48]) ).
cnf(c60,plain,
rd(mult(X,Y),mult(Y,Y)) = rd(X,Y),
inference(equational,[status(thm)],[c5,c48]) ).
cnf(c68,plain,
mult(mult(X,Y),mult(X,X)) = mult(X,mult(Y,mult(X,X))),
inference(equational,[status(thm)],[c16,c43]) ).
cnf(c74,plain,
rd(X,f(ld(Y,X))) = mult(Y,f(ld(Y,X))),
inference(equational,[status(thm)],[c7,c46]) ).
cnf(c77,plain,
ld(ld(X,f(X)),unit) = f(X),
inference(equational,[status(thm)],[c2,c10,c40,c52]) ).
cnf(c93,plain,
mult(ld(X,Y),ld(X,Y)) = ld(X,mult(Y,ld(X,Y))),
inference(equational,[status(thm)],[c15,c59]) ).
cnf(c104,plain,
rd(mult(X,mult(Y,mult(X,X))),X) = mult(X,mult(Y,X)),
inference(equational,[status(thm)],[c21,c43]) ).
cnf(c105,plain,
rd(mult(X,mult(Y,mult(X,Y))),Y) = mult(X,mult(Y,X)),
inference(equational,[status(thm)],[c5,c50]) ).
cnf(c107,plain,
ld(rd(X,Y),mult(X,rd(X,Y))) = rd(mult(Y,X),Y),
inference(equational,[status(thm)],[c9,c37]) ).
cnf(c121,plain,
ld(f(X),ld(f(X),unit)) = ld(X,unit),
inference(equational,[status(thm)],[c11,c57]) ).
cnf(c126,plain,
mult(mult(X,Y),mult(X,mult(Y,X))) = mult(X,mult(Y,mult(X,mult(Y,X)))),
inference(equational,[status(thm)],[c16,c42,c50]) ).
cnf(c128,plain,
mult(X,mult(ld(X,Y),mult(Y,X))) = mult(Y,mult(Y,X)),
inference(equational,[status(thm)],[c7,c20,c126]) ).
cnf(c129,plain,
mult(ld(X,Y),mult(Y,X)) = ld(X,mult(Y,mult(Y,X))),
inference(equational,[status(thm)],[c9,c128]) ).
cnf(c140,plain,
mult(mult(X,mult(ld(Y,Z),Z)),Y) = mult(mult(X,ld(Y,Z)),mult(Z,Y)),
inference(equational,[status(thm)],[c7,c20,c42]) ).
cnf(c155,plain,
rd(ld(X,mult(Y,X)),f(X)) = mult(ld(X,Y),f(X)),
inference(equational,[status(thm)],[c20,c46]) ).
cnf(c160,plain,
ld(X,rd(mult(Y,mult(Y,X)),X)) = mult(ld(X,Y),Y),
inference(equational,[status(thm)],[c7,c19,c28,c105,c129]) ).
cnf(c161,plain,
mult(X,mult(ld(X,Y),Y)) = rd(mult(Y,mult(Y,X)),X),
inference(equational,[status(thm)],[c7,c160]) ).
cnf(c164,plain,
rd(mult(rd(X,Y),mult(Y,X)),Y) = mult(X,rd(X,Y)),
inference(equational,[status(thm)],[c3,c22,c37,c105]) ).
cnf(c222,plain,
ld(X,rd(mult(X,Y),mult(X,X))) = rd(Y,mult(X,X)),
inference(equational,[status(thm)],[c22,c29,c55]) ).
cnf(c224,plain,
rd(mult(X,mult(Y,X)),mult(X,X)) = rd(mult(X,Y),X),
inference(equational,[status(thm)],[c16,c60]) ).
cnf(c246,plain,
ld(f(X),rd(mult(f(X),Y),X)) = rd(Y,X),
inference(equational,[status(thm)],[c11,c222]) ).
cnf(c291,plain,
rd(mult(mult(X,Y),mult(Z,mult(Y,Z))),Z) = mult(X,mult(Y,mult(Z,Y))),
inference(equational,[status(thm)],[c5,c42]) ).
cnf(c293,plain,
rd(mult(X,mult(Y,mult(Z,Y))),Y) = mult(rd(X,Z),mult(Z,mult(Y,Z))),
inference(equational,[status(thm)],[c3,c291]) ).
cnf(c294,plain,
mult(ld(X,unit),mult(X,mult(Y,X))) = mult(Y,X),
inference(equational,[status(thm)],[c2,c21,c25,c293]) ).
cnf(c295,plain,
mult(ld(X,unit),mult(X,Y)) = Y,
inference(equational,[status(thm)],[c3,c294]) ).
cnf(c296,plain,
rd(X,mult(Y,X)) = ld(Y,unit),
inference(equational,[status(thm)],[c5,c295]) ).
cnf(c297,plain,
ld(ld(X,unit),Y) = mult(X,Y),
inference(equational,[status(thm)],[c9,c295]) ).
cnf(c299,plain,
mult(ld(X,unit),Y) = ld(X,Y),
inference(equational,[status(thm)],[c7,c295]) ).
cnf(c300,plain,
rd(ld(X,Y),Y) = ld(X,unit),
inference(equational,[status(thm)],[c5,c299]) ).
cnf(c301,plain,
ld(rd(X,Y),unit) = rd(Y,X),
inference(equational,[status(thm)],[c3,c296]) ).
cnf(c302,plain,
mult(ld(X,Y),Y) = ld(X,mult(Y,Y)),
inference(equational,[status(thm)],[c43,c299]) ).
cnf(c303,plain,
mult(rd(X,Y),Z) = ld(rd(Y,X),Z),
inference(equational,[status(thm)],[c299,c301]) ).
cnf(c304,plain,
rd(mult(X,X),Y) = rd(X,rd(Y,X)),
inference(equational,[status(thm)],[c55,c301]) ).
cnf(c305,plain,
ld(ld(X,f(X)),Y) = mult(f(X),Y),
inference(equational,[status(thm)],[c52,c297]) ).
cnf(c307,plain,
mult(ld(X,f(X)),Y) = ld(f(X),Y),
inference(equational,[status(thm)],[c52,c299]) ).
cnf(c308,plain,
rd(ld(X,Y),f(Y)) = ld(X,f(Y)),
inference(equational,[status(thm)],[c46,c299]) ).
cnf(c310,plain,
mult(X,rd(X,Y)) = rd(X,rd(Y,X)),
inference(equational,[status(thm)],[c59,c164,c303,c304]) ).
cnf(c314,plain,
ld(X,f(mult(X,Y))) = rd(Y,f(mult(X,Y))),
inference(equational,[status(thm)],[c74,c297,c299]) ).
cnf(c315,plain,
ld(rd(X,Y),f(X)) = rd(Y,f(X)),
inference(equational,[status(thm)],[c3,c14,c303,c314]) ).
cnf(c316,plain,
rd(X,mult(Y,f(X))) = rd(f(X),Y),
inference(equational,[status(thm)],[c51,c301]) ).
cnf(c319,plain,
mult(X,ld(Y,unit)) = rd(X,Y),
inference(equational,[status(thm)],[c5,c296,c310]) ).
cnf(c320,plain,
rd(X,ld(Y,unit)) = mult(X,Y),
inference(equational,[status(thm)],[c15,c300,c310]) ).
cnf(c326,plain,
ld(X,rd(X,Y)) = ld(Y,unit),
inference(equational,[status(thm)],[c295,c299,c319]) ).
cnf(c327,plain,
ld(mult(X,Y),X) = ld(Y,unit),
inference(equational,[status(thm)],[c14,c320]) ).
cnf(c328,plain,
rd(X,mult(X,mult(Y,X))) = ld(mult(X,Y),unit),
inference(equational,[status(thm)],[c16,c296]) ).
cnf(c330,plain,
rd(mult(X,ld(Y,X)),X) = rd(X,Y),
inference(equational,[status(thm)],[c21,c299,c319]) ).
cnf(c331,plain,
rd(mult(X,Y),X) = rd(X,rd(X,Y)),
inference(equational,[status(thm)],[c14,c330]) ).
cnf(c332,plain,
mult(X,ld(Y,X)) = ld(rd(Y,X),X),
inference(equational,[status(thm)],[c3,c303,c330]) ).
cnf(c333,plain,
rd(rd(X,Y),X) = rd(X,mult(X,Y)),
inference(equational,[status(thm)],[c301,c331]) ).
cnf(c335,plain,
mult(f(X),ld(Y,X)) = ld(rd(Y,f(X)),X),
inference(equational,[status(thm)],[c11,c16,c49,c302,c303,c330]) ).
cnf(c336,plain,
rd(ld(X,unit),Y) = ld(mult(Y,X),unit),
inference(equational,[status(thm)],[c296,c328,c333]) ).
cnf(c337,plain,
rd(X,ld(X,mult(Y,X))) = ld(ld(X,Y),unit),
inference(equational,[status(thm)],[c20,c296]) ).
cnf(c338,plain,
rd(ld(X,Y),mult(Y,Y)) = ld(mult(Y,X),unit),
inference(equational,[status(thm)],[c60,c299,c336]) ).
cnf(c345,plain,
rd(mult(X,mult(X,Y)),Y) = mult(X,X),
inference(equational,[status(thm)],[c7,c161,c302]) ).
cnf(c346,plain,
mult(mult(X,X),Y) = mult(X,mult(X,Y)),
inference(equational,[status(thm)],[c3,c345]) ).
cnf(c347,plain,
ld(ld(X,Y),unit) = ld(Y,X),
inference(equational,[status(thm)],[c299,c320,c336]) ).
cnf(c348,plain,
rd(f(X),ld(Y,X)) = ld(f(X),Y),
inference(equational,[status(thm)],[c301,c308,c347]) ).
cnf(c350,plain,
ld(mult(X,Y),mult(X,X)) = ld(Y,X),
inference(equational,[status(thm)],[c3,c299,c338]) ).
cnf(c351,plain,
ld(ld(X,Y),X) = ld(Y,mult(X,X)),
inference(equational,[status(thm)],[c7,c350]) ).
cnf(c356,plain,
ld(ld(X,ld(X,unit)),Y) = mult(X,mult(X,Y)),
inference(equational,[status(thm)],[c57,c297,c346]) ).
cnf(c357,plain,
ld(mult(X,X),Y) = ld(X,ld(X,Y)),
inference(equational,[status(thm)],[c27,c297,c299,c356]) ).
cnf(c364,plain,
rd(f(X),rd(Y,f(X))) = rd(X,Y),
inference(equational,[status(thm)],[c53,c296,c301]) ).
cnf(c365,plain,
mult(f(X),rd(X,Y)) = rd(X,rd(Y,f(X))),
inference(equational,[status(thm)],[c14,c164,c303,c364]) ).
cnf(c366,plain,
ld(f(X),ld(f(X),Y)) = ld(X,Y),
inference(equational,[status(thm)],[c35,c77,c307,c356]) ).
cnf(c369,plain,
mult(f(X),mult(f(X),Y)) = mult(X,Y),
inference(equational,[status(thm)],[c121,c297,c356]) ).
cnf(c372,plain,
mult(X,rd(Y,Z)) = rd(X,rd(Z,Y)),
inference(equational,[status(thm)],[c301,c320]) ).
cnf(c375,plain,
rd(f(X),ld(X,Y)) = ld(rd(Y,f(X)),X),
inference(equational,[status(thm)],[c155,c316,c335,c337,c347,c365]) ).
cnf(c376,plain,
rd(X,ld(X,Y)) = ld(rd(Y,X),X),
inference(equational,[status(thm)],[c11,c55,c310,c335,c364,c375]) ).
cnf(c379,plain,
mult(ld(f(X),Y),Z) = ld(ld(Y,f(X)),Z),
inference(equational,[status(thm)],[c303,c308,c348]) ).
cnf(c380,plain,
mult(ld(X,Y),Z) = ld(ld(Y,X),Z),
inference(equational,[status(thm)],[c11,c351,c366,c379]) ).
cnf(c382,plain,
mult(X,ld(Y,Z)) = rd(X,ld(Z,Y)),
inference(equational,[status(thm)],[c21,c300,c301,c332,c380]) ).
cnf(c384,plain,
rd(mult(f(X),Y),X) = rd(f(X),rd(X,Y)),
inference(equational,[status(thm)],[c11,c22,c55,c315,c330]) ).
cnf(c392,plain,
ld(mult(X,Y),unit) = ld(Y,ld(X,unit)),
inference(equational,[status(thm)],[c299,c319,c336]) ).
cnf(c396,plain,
ld(ld(X,Y),ld(Y,unit)) = ld(Y,rd(X,Y)),
inference(equational,[status(thm)],[c8,c16,c299,c380,c382]) ).
cnf(c433,plain,
ld(mult(X,Y),ld(Y,unit)) = ld(Y,ld(X,ld(Y,unit))),
inference(equational,[status(thm)],[c297,c336,c392,c396]) ).
cnf(c464,plain,
ld(mult(X,Y),mult(X,mult(Y,mult(X,X)))) = mult(X,X),
inference(equational,[status(thm)],[c9,c68]) ).
cnf(c465,plain,
ld(mult(X,Y),rd(X,Y)) = ld(Y,ld(Y,unit)),
inference(equational,[status(thm)],[c2,c93,c224,c294,c297,c299,c301,c326,c331,c382,c464]) ).
cnf(c466,plain,
ld(ld(rd(X,Y),Y),X) = ld(ld(X,Y),ld(Y,X)),
inference(equational,[status(thm)],[c6,c93,c347,c376,c382,c465]) ).
cnf(c467,plain,
ld(ld(X,Y),ld(Y,X)) = ld(Y,ld(rd(Y,X),X)),
inference(equational,[status(thm)],[c7,c347,c376,c465]) ).
cnf(c470,plain,
rd(mult(X,mult(Y,mult(X,X))),mult(X,X)) = mult(X,Y),
inference(equational,[status(thm)],[c5,c68]) ).
cnf(c479,plain,
ld(ld(X,ld(Y,unit)),Z) = mult(mult(Y,X),Z),
inference(equational,[status(thm)],[c104,c303,c304,c328,c392,c470]) ).
cnf(c507,plain,
ld(ld(X,Y),ld(ld(Y,ld(Y,X)),X)) = mult(Y,X),
inference(equational,[status(thm)],[c7,c128,c351,c357,c380]) ).
cnf(c513,plain,
rd(X,ld(Y,ld(rd(Y,X),X))) = ld(rd(X,Y),Y),
inference(equational,[status(thm)],[c14,c297,c303,c326,c382,c466,c467,c507]) ).
cnf(c529,plain,
rd(rd(X,rd(Y,X)),rd(Y,rd(Y,X))) = rd(X,Y),
inference(equational,[status(thm)],[c15,c107,c331,c372]) ).
cnf(c616,plain,
rd(X,ld(Y,ld(Z,unit))) = mult(X,mult(Z,Y)),
inference(equational,[status(thm)],[c21,c330,c479]) ).
cnf(c640,plain,
rd(ld(rd(ld(X,Y),Z),mult(X,Y)),Y) = rd(Z,ld(X,ld(X,Y))),
inference(equational,[status(thm)],[c5,c140,c303,c351,c357,c380,c382]) ).
cnf(c641,plain,
rd(X,ld(Y,ld(Z,ld(Y,unit)))) = mult(X,mult(Y,mult(Z,Y))),
inference(equational,[status(thm)],[c16,c291,c327,c336,c392,c433,c479,c640]) ).
cnf(c642,plain,
ld(rd(ld(X,ld(X,Y)),Z),Y) = ld(rd(ld(X,Y),Z),mult(X,Y)),
inference(equational,[status(thm)],[c3,c303,c640]) ).
cnf(c654,plain,
ld(rd(ld(X,Y),Z),mult(X,Y)) = ld(rd(Y,Z),mult(X,mult(X,Y))),
inference(equational,[status(thm)],[c9,c642]) ).
cnf(c670,plain,
rd(ld(rd(X,Y),mult(Z,mult(Z,X))),X) = rd(Y,ld(Z,ld(Z,X))),
inference(equational,[status(thm)],[c7,c19,c291,c303,c351,c357,c380,c382,c654]) ).
cnf(c674,plain,
rd(ld(X,mult(Y,mult(Y,Z))),Z) = rd(ld(X,Z),ld(Y,ld(Y,Z))),
inference(equational,[status(thm)],[c15,c670]) ).
cnf(c680,plain,
rd(ld(X,ld(Y,Z)),Z) = rd(ld(X,Z),mult(Y,Z)),
inference(equational,[status(thm)],[c305,c307,c366,c369,c674]) ).
cnf(c693,plain,
rd(rd(X,ld(Y,Z)),Y) = rd(mult(X,Y),mult(Z,Y)),
inference(equational,[status(thm)],[c297,c382,c680]) ).
cnf(c694,plain,
rd(mult(X,Y),ld(Z,Y)) = rd(Y,ld(Z,ld(X,Y))),
inference(equational,[status(thm)],[c301,c680]) ).
cnf(c712,plain,
rd(ld(rd(rd(X,Y),Z),mult(X,Y)),X) = rd(Z,rd(X,mult(Y,Y))),
inference(equational,[status(thm)],[c3,c22,c37,c55,c291,c303,c372]) ).
cnf(c713,plain,
rd(ld(rd(X,Y),Z),X) = rd(Y,ld(rd(Z,X),X)),
inference(equational,[status(thm)],[c14,c15,c93,c303,c376,c382,c513,c680,c712]) ).
cnf(c724,plain,
rd(ld(X,Y),ld(rd(Z,Y),Y)) = rd(ld(X,Z),Y),
inference(equational,[status(thm)],[c15,c713]) ).
cnf(c728,plain,
rd(ld(rd(X,Y),Y),Z) = rd(Y,ld(rd(Y,Z),X)),
inference(equational,[status(thm)],[c301,c713]) ).
cnf(c739,plain,
rd(ld(X,mult(Y,mult(Z,Y))),Y) = ld(ld(Y,X),Z),
inference(equational,[status(thm)],[c21,c320,c327,c380,c724]) ).
cnf(c740,plain,
ld(ld(X,Y),ld(Z,unit)) = rd(ld(Y,X),Z),
inference(equational,[status(thm)],[c14,c299,c303,c376,c382,c680,c739]) ).
cnf(c742,plain,
rd(ld(X,mult(Y,Z)),Y) = ld(ld(Y,X),rd(Z,Y)),
inference(equational,[status(thm)],[c3,c739]) ).
cnf(c743,plain,
ld(ld(X,ld(Y,Z)),Y) = ld(Z,mult(Y,mult(X,Y))),
inference(equational,[status(thm)],[c3,c380,c739]) ).
cnf(c744,plain,
ld(rd(X,Y),ld(Z,unit)) = rd(rd(Y,X),Z),
inference(equational,[status(thm)],[c14,c246,c384,c740]) ).
cnf(c745,plain,
rd(ld(mult(X,Y),Z),X) = ld(Y,ld(X,rd(Z,X))),
inference(equational,[status(thm)],[c8,c297,c299,c382,c740,c743]) ).
cnf(c746,plain,
rd(ld(X,Y),ld(Z,W)) = ld(ld(Y,X),ld(W,Z)),
inference(equational,[status(thm)],[c1,c2,c8,c740,c743]) ).
cnf(c747,plain,
ld(rd(X,ld(Y,Z)),Z) = ld(Y,ld(rd(X,Z),Z)),
inference(equational,[status(thm)],[c297,c299,c376,c382,c743]) ).
cnf(c748,plain,
ld(ld(ld(X,Y),Z),X) = ld(mult(X,Z),mult(Y,X)),
inference(equational,[status(thm)],[c297,c299,c320,c380,c742]) ).
cnf(c754,plain,
rd(ld(X,ld(Y,unit)),Z) = ld(mult(Y,X),ld(Z,unit)),
inference(equational,[status(thm)],[c297,c740]) ).
cnf(c759,plain,
ld(rd(ld(X,Y),Z),ld(X,Z)) = ld(rd(Y,Z),Z),
inference(equational,[status(thm)],[c14,c724]) ).
cnf(c760,plain,
ld(rd(mult(X,Y),Z),Z) = ld(rd(Y,Z),ld(X,Z)),
inference(equational,[status(thm)],[c9,c759]) ).
cnf(c761,plain,
ld(rd(ld(X,Y),Z),Z) = ld(rd(Y,Z),mult(X,Z)),
inference(equational,[status(thm)],[c297,c299,c760]) ).
cnf(c772,plain,
rd(rd(X,Y),ld(Z,W)) = ld(rd(Y,X),ld(W,Z)),
inference(equational,[status(thm)],[c1,c4,c744,c761]) ).
cnf(c777,plain,
mult(mult(X,Y),mult(Z,X)) = mult(X,mult(mult(Y,Z),X)),
inference(equational,[status(thm)],[c8,c336,c392,c479,c743,c754,c761]) ).
cnf(c778,plain,
ld(mult(X,Y),rd(Z,Y)) = ld(Y,rd(ld(X,Z),Y)),
inference(equational,[status(thm)],[c8,c28,c320,c382,c744,c746,c761]) ).
cnf(c779,plain,
rd(X,ld(mult(X,Y),Z)) = ld(ld(X,rd(Z,X)),Y),
inference(equational,[status(thm)],[c301,c347,c745]) ).
cnf(c780,plain,
rd(rd(rd(X,Y),Z),Y) = rd(X,mult(Y,mult(Z,Y))),
inference(equational,[status(thm)],[c8,c336,c392,c713,c743,c744]) ).
cnf(c781,plain,
rd(X,ld(Y,rd(Z,Y))) = ld(rd(Z,mult(X,Y)),Y),
inference(equational,[status(thm)],[c297,c382,c747]) ).
cnf(c800,plain,
rd(X,ld(rd(Y,X),ld(Z,X))) = rd(mult(Z,Y),X),
inference(equational,[status(thm)],[c296,c297,c694,c713]) ).
cnf(c801,plain,
rd(mult(X,Y),mult(Z,Y)) = rd(Y,rd(Z,ld(Y,X))),
inference(equational,[status(thm)],[c297,c300,c382,c693,c800]) ).
cnf(c804,plain,
rd(ld(X,Y),mult(Z,Y)) = rd(Y,mult(Z,mult(X,Y))),
inference(equational,[status(thm)],[c299,c616,c801]) ).
cnf(c882,plain,
rd(mult(X,Y),ld(X,Z)) = ld(rd(rd(Z,Y),X),X),
inference(equational,[status(thm)],[c8,c299,c303,c376,c382,c777]) ).
cnf(c890,plain,
ld(mult(X,mult(Y,X)),Z) = ld(X,ld(Y,ld(X,Z))),
inference(equational,[status(thm)],[c8,c297,c299,c320,c746,c779]) ).
cnf(c891,plain,
rd(ld(X,rd(Y,X)),Z) = ld(X,rd(Y,mult(Z,X))),
inference(equational,[status(thm)],[c301,c347,c781]) ).
cnf(c892,plain,
rd(mult(X,mult(Y,X)),Z) = rd(X,rd(rd(Z,X),Y)),
inference(equational,[status(thm)],[c301,c780]) ).
cnf(c1330,plain,
rd(ld(X,Y),mult(X,Z)) = ld(X,rd(rd(Y,Z),X)),
inference(equational,[status(thm)],[c8,c28,c297,c299,c740,c772,c882]) ).
cnf(c1404,plain,
ld(ld(X,rd(rd(Y,Z),X)),Z) = ld(rd(Y,mult(X,Z)),mult(X,Z)),
inference(equational,[status(thm)],[c9,c759,c1330]) ).
cnf(c1449,plain,
rd(X,ld(rd(Y,ld(Z,X)),ld(Z,X))) = ld(rd(rd(X,Y),Z),Z),
inference(equational,[status(thm)],[c5,c7,c291,c376,c380,c382,c728,c761,c778,c781,c882,c1330,c1404]) ).
cnf(c1453,plain,
rd(X,ld(rd(X,Y),mult(Z,Y))) = ld(rd(Z,rd(X,Y)),rd(X,Y)),
inference(equational,[status(thm)],[c15,c303,c713,c724,c761,c800,c1449]) ).
cnf(c1457,plain,
rd(X,mult(Y,mult(Z,mult(Y,X)))) = ld(Y,ld(Z,ld(Y,unit))),
inference(equational,[status(thm)],[c296,c297,c320,c433,c1453]) ).
cnf(c1460,plain,
rd(mult(X,mult(Y,mult(X,Z))),Z) = mult(X,mult(Y,X)),
inference(equational,[status(thm)],[c9,c25,c296,c336,c380,c382,c392,c479,c529,c616,c641,c693,c743,c745,c748,c754,c804,c882,c890,c891,c892,c1330,c1457]) ).
cnf(c1461,plain,
mult(mult(X,mult(Y,X)),Z) = mult(X,mult(Y,mult(X,Z))),
inference(equational,[status(thm)],[c3,c1460]) ).
cnf(g1,plain,
mult(a,mult(b,mult(a,c))) = mult(mult(mult(a,b),a),c),
inference(equational,[status(thm)],[c16,c1461]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : GRP667-2 : TPTP v9.0.0. Released v4.0.0.
% 0.02/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n012.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 08:48:49 EDT 2025
% 0.11/0.32 % CPUTime :
% 153.84/153.86 % SZS status Unsatisfiable
% 153.84/153.86 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------