%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP667-10 : TPTP v9.0.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n010.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 98.67s 98.59s
% Output : CNFRefutation 98.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 10
% Syntax : Number of clauses : 127 ( 127 unt; 0 nHn; 3 RR)
% Number of literals : 127 ( 126 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 : 258 ( 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',f05) ).
cnf(c2,axiom,
mult(unit,X) = X,
file('theBenchmark.p',f06) ).
cnf(c4,axiom,
mult(X,ld(X,Y)) = Y,
file('theBenchmark.p',f01) ).
cnf(c6,axiom,
ld(X,mult(X,Y)) = Y,
file('theBenchmark.p',f02) ).
cnf(c7,plain,
ld(X,X) = unit,
inference(equational,[status(thm)],[c1,c6]) ).
cnf(c8,axiom,
mult(rd(X,Y),Y) = X,
file('theBenchmark.p',f03) ).
cnf(c10,axiom,
rd(mult(X,Y),Y) = X,
file('theBenchmark.p',f04) ).
cnf(c11,plain,
rd(X,X) = unit,
inference(equational,[status(thm)],[c2,c10]) ).
cnf(c12,axiom,
mult(f(X),f(X)) = X,
file('theBenchmark.p',f09) ).
cnf(c15,plain,
rd(X,ld(Y,X)) = Y,
inference(equational,[status(thm)],[c4,c10]) ).
cnf(c16,plain,
ld(rd(X,Y),X) = Y,
inference(equational,[status(thm)],[c6,c8]) ).
cnf(c17,axiom,
mult(mult(X,Y),X) = mult(X,mult(Y,X)),
file('theBenchmark.p',f08) ).
cnf(c18,plain,
mult(f(X),X) = mult(X,f(X)),
inference(equational,[status(thm)],[c12,c17]) ).
cnf(c19,plain,
rd(mult(X,f(X)),X) = f(X),
inference(equational,[status(thm)],[c10,c18]) ).
cnf(c20,plain,
rd(mult(X,mult(Y,X)),X) = mult(X,Y),
inference(equational,[status(thm)],[c10,c17]) ).
cnf(c21,plain,
mult(X,rd(Y,X)) = rd(mult(X,Y),X),
inference(equational,[status(thm)],[c8,c20]) ).
cnf(c22,plain,
mult(X,mult(ld(X,Y),X)) = mult(Y,X),
inference(equational,[status(thm)],[c4,c17]) ).
cnf(c23,plain,
mult(ld(X,Y),X) = ld(X,mult(Y,X)),
inference(equational,[status(thm)],[c6,c22]) ).
cnf(c25,plain,
rd(ld(X,mult(Y,X)),X) = ld(X,Y),
inference(equational,[status(thm)],[c10,c23]) ).
cnf(c26,plain,
rd(unit,X) = ld(X,unit),
inference(equational,[status(thm)],[c2,c7,c25]) ).
cnf(c27,plain,
rd(f(X),X) = ld(X,f(X)),
inference(equational,[status(thm)],[c6,c18,c25]) ).
cnf(c28,plain,
ld(ld(X,unit),unit) = X,
inference(equational,[status(thm)],[c15,c26]) ).
cnf(c29,plain,
rd(ld(X,Y),X) = ld(X,rd(Y,X)),
inference(equational,[status(thm)],[c8,c25]) ).
cnf(c36,plain,
ld(ld(X,f(X)),f(X)) = X,
inference(equational,[status(thm)],[c16,c27]) ).
cnf(c38,plain,
mult(rd(X,Y),rd(mult(Y,X),Y)) = mult(X,rd(X,Y)),
inference(equational,[status(thm)],[c8,c17,c21]) ).
cnf(c39,plain,
mult(ld(X,f(X)),f(X)) = mult(f(X),ld(X,f(X))),
inference(equational,[status(thm)],[c19,c27,c38]) ).
cnf(c42,axiom,
mult(mult(X,Y),mult(mult(Z,Y),Z)) = mult(mult(X,mult(mult(Y,Z),Y)),Z),
file('theBenchmark.p',f07) ).
cnf(c43,plain,
mult(mult(X,mult(Y,mult(Z,Y))),Z) = mult(mult(X,Y),mult(Z,mult(Y,Z))),
inference(equational,[status(thm)],[c17,c42]) ).
cnf(c44,plain,
mult(mult(X,Y),Y) = mult(X,mult(Y,Y)),
inference(equational,[status(thm)],[c1,c2,c43]) ).
cnf(c46,plain,
rd(mult(X,mult(Y,Y)),Y) = mult(X,Y),
inference(equational,[status(thm)],[c10,c44]) ).
cnf(c47,plain,
rd(mult(X,Y),f(Y)) = mult(X,f(Y)),
inference(equational,[status(thm)],[c12,c46]) ).
cnf(c49,plain,
mult(rd(X,Y),mult(Y,Y)) = mult(X,Y),
inference(equational,[status(thm)],[c8,c44]) ).
cnf(c50,plain,
mult(rd(X,f(Y)),Y) = mult(X,f(Y)),
inference(equational,[status(thm)],[c12,c49]) ).
cnf(c51,plain,
mult(mult(X,mult(Y,X)),Y) = mult(X,mult(Y,mult(X,Y))),
inference(equational,[status(thm)],[c2,c43]) ).
cnf(c52,plain,
rd(mult(X,f(Y)),Y) = rd(X,f(Y)),
inference(equational,[status(thm)],[c10,c50]) ).
cnf(c53,plain,
ld(X,f(X)) = ld(f(X),unit),
inference(equational,[status(thm)],[c2,c26,c27,c52]) ).
cnf(c54,plain,
mult(rd(X,Y),f(Y)) = rd(X,f(Y)),
inference(equational,[status(thm)],[c8,c47]) ).
cnf(c55,plain,
mult(rd(X,mult(Y,Y)),Y) = rd(X,Y),
inference(equational,[status(thm)],[c8,c46]) ).
cnf(c56,plain,
rd(rd(X,Y),Y) = rd(X,mult(Y,Y)),
inference(equational,[status(thm)],[c10,c55]) ).
cnf(c58,plain,
ld(mult(X,X),unit) = ld(X,ld(X,unit)),
inference(equational,[status(thm)],[c26,c29,c56]) ).
cnf(c61,plain,
ld(rd(X,Y),mult(X,Y)) = mult(Y,Y),
inference(equational,[status(thm)],[c6,c49]) ).
cnf(c69,plain,
mult(mult(X,Y),mult(X,X)) = mult(X,mult(Y,mult(X,X))),
inference(equational,[status(thm)],[c17,c44]) ).
cnf(c72,plain,
mult(mult(ld(X,Y),Y),X) = mult(ld(X,Y),mult(Y,X)),
inference(equational,[status(thm)],[c4,c23,c51]) ).
cnf(c88,plain,
rd(rd(X,f(Y)),Y) = rd(rd(X,Y),f(Y)),
inference(equational,[status(thm)],[c12,c52,c55]) ).
cnf(c100,plain,
rd(ld(X,f(X)),f(X)) = ld(f(X),ld(X,f(X))),
inference(equational,[status(thm)],[c6,c25,c39]) ).
cnf(c105,plain,
rd(mult(X,mult(Y,mult(X,Y))),Y) = mult(X,mult(Y,X)),
inference(equational,[status(thm)],[c10,c51]) ).
cnf(c110,plain,
rd(mult(X,mult(Y,mult(X,X))),X) = mult(X,mult(Y,X)),
inference(equational,[status(thm)],[c20,c44]) ).
cnf(c116,plain,
ld(f(X),ld(X,f(X))) = ld(X,unit),
inference(equational,[status(thm)],[c11,c26,c27,c88,c100]) ).
cnf(c127,plain,
mult(mult(X,mult(ld(Y,Z),Z)),Y) = mult(mult(X,ld(Y,Z)),mult(Z,Y)),
inference(equational,[status(thm)],[c4,c23,c43]) ).
cnf(c128,plain,
mult(X,mult(ld(X,Y),mult(Y,X))) = mult(Y,mult(Y,X)),
inference(equational,[status(thm)],[c4,c17,c72,c127]) ).
cnf(c129,plain,
mult(ld(X,Y),mult(Y,X)) = ld(X,mult(Y,mult(Y,X))),
inference(equational,[status(thm)],[c6,c128]) ).
cnf(c157,plain,
rd(ld(X,mult(Y,X)),f(X)) = mult(ld(X,Y),f(X)),
inference(equational,[status(thm)],[c23,c47]) ).
cnf(c160,plain,
ld(X,rd(mult(Y,mult(Y,X)),X)) = mult(ld(X,Y),Y),
inference(equational,[status(thm)],[c4,c22,c29,c105,c129]) ).
cnf(c161,plain,
mult(X,mult(ld(X,Y),Y)) = rd(mult(Y,mult(Y,X)),X),
inference(equational,[status(thm)],[c4,c160]) ).
cnf(c162,plain,
rd(mult(rd(X,Y),mult(Y,X)),Y) = mult(X,rd(X,Y)),
inference(equational,[status(thm)],[c8,c21,c38,c105]) ).
cnf(c293,plain,
rd(mult(mult(X,Y),mult(Z,mult(Y,Z))),Z) = mult(X,mult(Y,mult(Z,Y))),
inference(equational,[status(thm)],[c10,c43]) ).
cnf(c295,plain,
rd(mult(X,mult(Y,mult(Z,Y))),Y) = mult(rd(X,Z),mult(Z,mult(Y,Z))),
inference(equational,[status(thm)],[c8,c293]) ).
cnf(c296,plain,
mult(ld(X,unit),mult(X,mult(Y,X))) = mult(Y,X),
inference(equational,[status(thm)],[c2,c20,c26,c295]) ).
cnf(c297,plain,
mult(ld(X,unit),mult(X,Y)) = Y,
inference(equational,[status(thm)],[c8,c296]) ).
cnf(c298,plain,
rd(X,mult(Y,X)) = ld(Y,unit),
inference(equational,[status(thm)],[c10,c297]) ).
cnf(c299,plain,
ld(ld(X,unit),Y) = mult(X,Y),
inference(equational,[status(thm)],[c6,c297]) ).
cnf(c301,plain,
mult(ld(X,unit),Y) = ld(X,Y),
inference(equational,[status(thm)],[c4,c297]) ).
cnf(c302,plain,
rd(ld(X,Y),Y) = ld(X,unit),
inference(equational,[status(thm)],[c10,c301]) ).
cnf(c303,plain,
ld(rd(X,Y),unit) = rd(Y,X),
inference(equational,[status(thm)],[c8,c298]) ).
cnf(c304,plain,
mult(ld(X,Y),Y) = ld(X,mult(Y,Y)),
inference(equational,[status(thm)],[c44,c301]) ).
cnf(c305,plain,
mult(rd(X,Y),Z) = ld(rd(Y,X),Z),
inference(equational,[status(thm)],[c299,c303]) ).
cnf(c306,plain,
rd(mult(X,X),Y) = rd(X,rd(Y,X)),
inference(equational,[status(thm)],[c56,c303]) ).
cnf(c307,plain,
ld(ld(X,f(X)),Y) = mult(f(X),Y),
inference(equational,[status(thm)],[c53,c299]) ).
cnf(c309,plain,
mult(ld(X,f(X)),Y) = ld(f(X),Y),
inference(equational,[status(thm)],[c53,c301]) ).
cnf(c310,plain,
rd(ld(X,Y),f(Y)) = ld(X,f(Y)),
inference(equational,[status(thm)],[c47,c301]) ).
cnf(c312,plain,
mult(X,rd(X,Y)) = rd(X,rd(Y,X)),
inference(equational,[status(thm)],[c61,c162,c305,c306]) ).
cnf(c318,plain,
rd(X,mult(Y,f(X))) = rd(f(X),Y),
inference(equational,[status(thm)],[c52,c303]) ).
cnf(c320,plain,
rd(X,ld(Y,unit)) = mult(X,Y),
inference(equational,[status(thm)],[c15,c302,c312]) ).
cnf(c321,plain,
mult(X,ld(Y,unit)) = rd(X,Y),
inference(equational,[status(thm)],[c10,c298,c312]) ).
cnf(c322,plain,
rd(ld(X,mult(Y,Y)),Y) = ld(X,Y),
inference(equational,[status(thm)],[c46,c301]) ).
cnf(c327,plain,
ld(mult(X,Y),X) = ld(Y,unit),
inference(equational,[status(thm)],[c16,c320]) ).
cnf(c332,plain,
rd(X,mult(X,mult(Y,X))) = ld(mult(X,Y),unit),
inference(equational,[status(thm)],[c17,c298]) ).
cnf(c333,plain,
rd(X,mult(Y,mult(X,X))) = ld(mult(Y,X),unit),
inference(equational,[status(thm)],[c44,c298]) ).
cnf(c334,plain,
rd(X,ld(X,mult(Y,X))) = ld(ld(X,Y),unit),
inference(equational,[status(thm)],[c23,c298]) ).
cnf(c335,plain,
rd(mult(X,ld(Y,X)),X) = rd(X,Y),
inference(equational,[status(thm)],[c20,c301,c321]) ).
cnf(c336,plain,
rd(mult(X,Y),X) = rd(X,rd(X,Y)),
inference(equational,[status(thm)],[c16,c335]) ).
cnf(c337,plain,
mult(X,ld(Y,X)) = ld(rd(Y,X),X),
inference(equational,[status(thm)],[c8,c305,c335]) ).
cnf(c338,plain,
rd(rd(X,Y),X) = rd(X,mult(X,Y)),
inference(equational,[status(thm)],[c303,c336]) ).
cnf(c340,plain,
mult(f(X),ld(Y,X)) = ld(rd(Y,f(X)),X),
inference(equational,[status(thm)],[c12,c17,c50,c304,c305,c335]) ).
cnf(c341,plain,
rd(ld(X,unit),Y) = ld(mult(Y,X),unit),
inference(equational,[status(thm)],[c298,c332,c338]) ).
cnf(c347,plain,
rd(mult(X,mult(X,Y)),Y) = mult(X,X),
inference(equational,[status(thm)],[c61,c161,c299,c302]) ).
cnf(c348,plain,
mult(mult(X,X),Y) = mult(X,mult(X,Y)),
inference(equational,[status(thm)],[c8,c347]) ).
cnf(c349,plain,
ld(rd(X,Y),mult(X,X)) = mult(Y,X),
inference(equational,[status(thm)],[c16,c304]) ).
cnf(c350,plain,
ld(ld(X,Y),unit) = ld(Y,X),
inference(equational,[status(thm)],[c301,c320,c341]) ).
cnf(c351,plain,
rd(f(X),ld(Y,X)) = ld(f(X),Y),
inference(equational,[status(thm)],[c303,c310,c350]) ).
cnf(c355,plain,
ld(ld(X,ld(X,unit)),Y) = mult(X,mult(X,Y)),
inference(equational,[status(thm)],[c58,c299,c348]) ).
cnf(c356,plain,
ld(mult(X,X),Y) = ld(X,ld(X,Y)),
inference(equational,[status(thm)],[c28,c299,c301,c355]) ).
cnf(c364,plain,
rd(f(X),rd(Y,f(X))) = rd(X,Y),
inference(equational,[status(thm)],[c54,c298,c303]) ).
cnf(c365,plain,
mult(f(X),rd(X,Y)) = rd(X,rd(Y,f(X))),
inference(equational,[status(thm)],[c16,c162,c305,c364]) ).
cnf(c366,plain,
ld(f(X),ld(f(X),Y)) = ld(X,Y),
inference(equational,[status(thm)],[c1,c36,c307,c309,c355]) ).
cnf(c369,plain,
mult(f(X),mult(f(X),Y)) = mult(X,Y),
inference(equational,[status(thm)],[c53,c116,c299,c355]) ).
cnf(c376,plain,
rd(f(X),ld(X,Y)) = ld(rd(Y,f(X)),X),
inference(equational,[status(thm)],[c157,c318,c334,c340,c350,c365]) ).
cnf(c377,plain,
rd(X,ld(X,Y)) = ld(rd(Y,X),X),
inference(equational,[status(thm)],[c12,c56,c312,c340,c364,c376]) ).
cnf(c383,plain,
mult(ld(X,Y),f(Y)) = ld(ld(f(Y),X),Y),
inference(equational,[status(thm)],[c12,c349,c351]) ).
cnf(c384,plain,
ld(ld(X,Y),X) = ld(Y,mult(X,X)),
inference(equational,[status(thm)],[c12,c44,c304,c366,c383]) ).
cnf(c385,plain,
mult(ld(f(X),Y),Z) = ld(ld(Y,f(X)),Z),
inference(equational,[status(thm)],[c305,c310,c351]) ).
cnf(c386,plain,
mult(ld(X,Y),Z) = ld(ld(Y,X),Z),
inference(equational,[status(thm)],[c12,c366,c384,c385]) ).
cnf(c388,plain,
mult(X,ld(Y,Z)) = rd(X,ld(Z,Y)),
inference(equational,[status(thm)],[c20,c302,c303,c337,c386]) ).
cnf(c393,plain,
rd(X,ld(Y,mult(X,X))) = ld(X,Y),
inference(equational,[status(thm)],[c303,c322,c350]) ).
cnf(c394,plain,
ld(mult(X,Y),unit) = ld(Y,ld(X,unit)),
inference(equational,[status(thm)],[c299,c333,c393]) ).
cnf(c401,plain,
ld(X,ld(rd(Y,X),X)) = ld(Y,X),
inference(equational,[status(thm)],[c297,c301,c337]) ).
cnf(c523,plain,
rd(mult(X,mult(Y,mult(X,X))),mult(X,X)) = mult(X,Y),
inference(equational,[status(thm)],[c10,c69]) ).
cnf(c529,plain,
ld(ld(X,ld(Y,unit)),Z) = mult(mult(Y,X),Z),
inference(equational,[status(thm)],[c110,c305,c306,c332,c394,c523]) ).
cnf(c625,plain,
rd(X,ld(Y,ld(Z,unit))) = mult(X,mult(Z,Y)),
inference(equational,[status(thm)],[c20,c335,c529]) ).
cnf(c659,plain,
rd(ld(rd(ld(X,Y),Z),mult(X,Y)),Y) = rd(Z,ld(X,ld(X,Y))),
inference(equational,[status(thm)],[c4,c22,c293,c305,c356,c384,c386,c388]) ).
cnf(c661,plain,
ld(rd(ld(X,ld(X,Y)),Z),Y) = ld(rd(ld(X,Y),Z),mult(X,Y)),
inference(equational,[status(thm)],[c8,c305,c659]) ).
cnf(c667,plain,
ld(rd(ld(X,Y),Z),mult(X,Y)) = ld(rd(Y,Z),mult(X,mult(X,Y))),
inference(equational,[status(thm)],[c6,c661]) ).
cnf(c675,plain,
ld(rd(ld(X,Y),Z),Y) = ld(rd(Y,Z),mult(X,Y)),
inference(equational,[status(thm)],[c15,c366,c369,c388,c667]) ).
cnf(c695,plain,
rd(ld(rd(X,Y),mult(Z,mult(Z,X))),X) = rd(Y,ld(Z,ld(Z,X))),
inference(equational,[status(thm)],[c10,c127,c305,c356,c384,c386,c388,c667]) ).
cnf(c699,plain,
rd(ld(X,mult(Y,mult(Y,Z))),Z) = rd(ld(X,Z),ld(Y,ld(Y,Z))),
inference(equational,[status(thm)],[c15,c695]) ).
cnf(c716,plain,
rd(ld(X,mult(Y,Z)),Z) = rd(ld(X,Z),ld(Y,Z)),
inference(equational,[status(thm)],[c366,c369,c699]) ).
cnf(c813,plain,
ld(ld(X,mult(Y,Z)),Z) = ld(Z,ld(Y,mult(X,Z))),
inference(equational,[status(thm)],[c15,c401,c675,c716]) ).
cnf(c814,plain,
rd(ld(X,Y),ld(Z,Y)) = rd(Y,ld(Z,mult(X,Y))),
inference(equational,[status(thm)],[c303,c716]) ).
cnf(c1040,plain,
rd(ld(X,Y),ld(X,rd(Z,ld(Y,X)))) = rd(Y,ld(X,mult(Z,Y))),
inference(equational,[status(thm)],[c15,c388,c659,c716,c814]) ).
cnf(c1046,plain,
rd(X,ld(mult(X,Y),mult(Z,X))) = ld(ld(X,Z),Y),
inference(equational,[status(thm)],[c6,c16,c305,c327,c341,c350,c386,c813,c1040]) ).
cnf(c1050,plain,
rd(X,ld(mult(X,Y),Z)) = ld(ld(X,rd(Z,X)),Y),
inference(equational,[status(thm)],[c8,c1046]) ).
cnf(c1051,plain,
ld(mult(X,mult(Y,X)),Z) = ld(X,ld(Y,ld(X,Z))),
inference(equational,[status(thm)],[c299,c301,c320,c341,c350,c386,c1050]) ).
cnf(c1062,plain,
ld(ld(rd(X,Y),Y),Z) = ld(Y,rd(X,ld(Z,Y))),
inference(equational,[status(thm)],[c299,c301,c377,c388,c1051]) ).
cnf(c1115,plain,
mult(mult(X,mult(Y,X)),Z) = mult(X,mult(Y,mult(X,Z))),
inference(equational,[status(thm)],[c299,c320,c529,c625,c1062]) ).
cnf(g1,plain,
mult(a,mult(b,mult(a,c))) = mult(mult(mult(a,b),a),c),
inference(equational,[status(thm)],[c17,c1115]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP667-10 : TPTP v9.0.0. Released v7.5.0.
% 0.10/0.11 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n010.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Jul 14 08:48:49 EDT 2025
% 0.12/0.32 % CPUTime :
% 98.67/98.59 % SZS status Unsatisfiable
% 98.67/98.59 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------