%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP668-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n001.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 06:44:40 AM UTC 2025
% Result : Unsatisfiable 71.33s 71.44s
% Output : CNFRefutation 71.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of clauses : 109 ( 109 unt; 0 nHn; 3 RR)
% Number of literals : 109 ( 108 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 241 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
mult(mult(a,b),mult(mult(c,b),c)) != mult(mult(a,mult(mult(b,c),b)),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(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,plain,
ld(rd(X,Y),X) = Y,
inference(equational,[status(thm)],[c3,c9]) ).
cnf(c12,plain,
rd(X,ld(Y,X)) = Y,
inference(equational,[status(thm)],[c5,c7]) ).
cnf(c13,axiom,
mult(mult(X,Y),X) = mult(X,mult(Y,X)),
file('theBenchmark.p',c08) ).
cnf(c14,plain,
rd(mult(X,mult(Y,X)),X) = mult(X,Y),
inference(equational,[status(thm)],[c5,c13]) ).
cnf(c15,plain,
mult(X,rd(Y,X)) = rd(mult(X,Y),X),
inference(equational,[status(thm)],[c3,c14]) ).
cnf(c16,plain,
mult(X,mult(ld(X,Y),X)) = mult(Y,X),
inference(equational,[status(thm)],[c7,c13]) ).
cnf(c17,plain,
mult(ld(X,Y),X) = ld(X,mult(Y,X)),
inference(equational,[status(thm)],[c9,c16]) ).
cnf(c18,axiom,
mult(X,mult(Y,mult(Y,Z))) = mult(mult(mult(X,Y),Y),Z),
file('theBenchmark.p',c07) ).
cnf(c19,plain,
mult(mult(mult(X,Y),Y),Z) = mult(X,mult(Y,mult(Y,Z))),
inference(equational,[status(thm)],[c18]) ).
cnf(c20,plain,
mult(mult(X,Y),Y) = mult(X,mult(Y,Y)),
inference(equational,[status(thm)],[c1,c19]) ).
cnf(c21,plain,
mult(mult(X,X),Y) = mult(X,mult(X,Y)),
inference(equational,[status(thm)],[c2,c19]) ).
cnf(c22,plain,
rd(mult(X,mult(X,Y)),Y) = mult(X,X),
inference(equational,[status(thm)],[c5,c21]) ).
cnf(c23,plain,
rd(mult(X,mult(Y,Y)),Y) = mult(X,Y),
inference(equational,[status(thm)],[c5,c20]) ).
cnf(c24,plain,
mult(rd(X,Y),mult(Y,Y)) = mult(X,Y),
inference(equational,[status(thm)],[c3,c20]) ).
cnf(c26,plain,
rd(mult(X,Y),mult(Y,Y)) = rd(X,Y),
inference(equational,[status(thm)],[c5,c24]) ).
cnf(c28,plain,
rd(rd(X,Y),Y) = rd(X,mult(Y,Y)),
inference(equational,[status(thm)],[c3,c26]) ).
cnf(c30,plain,
ld(rd(X,Y),mult(X,Y)) = mult(Y,Y),
inference(equational,[status(thm)],[c9,c24]) ).
cnf(c31,plain,
rd(ld(X,mult(Y,X)),X) = ld(X,Y),
inference(equational,[status(thm)],[c5,c17]) ).
cnf(c32,plain,
rd(unit,X) = ld(X,unit),
inference(equational,[status(thm)],[c2,c10,c31]) ).
cnf(c33,plain,
ld(ld(X,unit),unit) = X,
inference(equational,[status(thm)],[c12,c32]) ).
cnf(c34,plain,
rd(ld(X,Y),X) = ld(X,rd(Y,X)),
inference(equational,[status(thm)],[c3,c31]) ).
cnf(c40,plain,
rd(mult(X,Y),ld(X,Y)) = mult(X,X),
inference(equational,[status(thm)],[c7,c22]) ).
cnf(c41,plain,
mult(rd(X,mult(Y,Y)),Y) = rd(X,Y),
inference(equational,[status(thm)],[c3,c23]) ).
cnf(c47,plain,
mult(mult(X,mult(Y,Y)),Z) = mult(X,mult(Y,mult(Y,Z))),
inference(equational,[status(thm)],[c19,c20]) ).
cnf(c48,plain,
rd(X,ld(Y,ld(Y,X))) = mult(Y,Y),
inference(equational,[status(thm)],[c7,c40]) ).
cnf(c49,plain,
ld(mult(X,X),Y) = ld(X,ld(X,Y)),
inference(equational,[status(thm)],[c11,c48]) ).
cnf(c53,plain,
mult(rd(X,Y),rd(X,Y)) = rd(mult(rd(X,Y),X),Y),
inference(equational,[status(thm)],[c3,c22]) ).
cnf(c54,plain,
mult(ld(X,Y),mult(X,X)) = ld(X,mult(Y,mult(X,X))),
inference(equational,[status(thm)],[c17,c20]) ).
cnf(c55,plain,
mult(rd(X,Y),rd(mult(Y,X),Y)) = mult(X,rd(X,Y)),
inference(equational,[status(thm)],[c3,c13,c15]) ).
cnf(c56,plain,
rd(mult(X,mult(Y,mult(Y,Z))),Z) = mult(X,mult(Y,Y)),
inference(equational,[status(thm)],[c5,c19,c20]) ).
cnf(c57,plain,
mult(rd(X,Y),mult(Y,mult(Y,Z))) = mult(mult(X,Y),Z),
inference(equational,[status(thm)],[c3,c19]) ).
cnf(c58,plain,
mult(mult(X,Y),ld(Y,Z)) = mult(rd(X,Y),mult(Y,Z)),
inference(equational,[status(thm)],[c7,c57]) ).
cnf(c59,plain,
mult(ld(X,unit),mult(X,Y)) = Y,
inference(equational,[status(thm)],[c2,c7,c32,c58]) ).
cnf(c60,plain,
rd(X,mult(Y,X)) = ld(Y,unit),
inference(equational,[status(thm)],[c5,c59]) ).
cnf(c61,plain,
ld(ld(X,unit),Y) = mult(X,Y),
inference(equational,[status(thm)],[c9,c59]) ).
cnf(c62,plain,
mult(ld(X,unit),Y) = ld(X,Y),
inference(equational,[status(thm)],[c7,c59]) ).
cnf(c63,plain,
rd(ld(X,Y),Y) = ld(X,unit),
inference(equational,[status(thm)],[c5,c62]) ).
cnf(c64,plain,
ld(rd(X,Y),unit) = rd(Y,X),
inference(equational,[status(thm)],[c3,c60]) ).
cnf(c66,plain,
mult(rd(X,Y),Z) = ld(rd(Y,X),Z),
inference(equational,[status(thm)],[c62,c64]) ).
cnf(c67,plain,
rd(mult(X,X),Y) = rd(X,rd(Y,X)),
inference(equational,[status(thm)],[c28,c64]) ).
cnf(c69,plain,
mult(mult(X,ld(Y,unit)),Y) = X,
inference(equational,[status(thm)],[c1,c3,c33,c58]) ).
cnf(c70,plain,
mult(X,ld(Y,unit)) = rd(X,Y),
inference(equational,[status(thm)],[c5,c69]) ).
cnf(c71,plain,
rd(X,ld(Y,unit)) = mult(X,Y),
inference(equational,[status(thm)],[c3,c69]) ).
cnf(c72,plain,
ld(mult(X,Y),X) = ld(Y,unit),
inference(equational,[status(thm)],[c11,c71]) ).
cnf(c73,plain,
ld(X,rd(X,Y)) = ld(Y,unit),
inference(equational,[status(thm)],[c59,c62,c70]) ).
cnf(c78,plain,
mult(X,ld(Y,X)) = ld(rd(Y,X),X),
inference(equational,[status(thm)],[c13,c62,c66,c70]) ).
cnf(c79,plain,
mult(X,rd(Y,Z)) = rd(X,rd(Z,Y)),
inference(equational,[status(thm)],[c64,c70]) ).
cnf(c80,plain,
rd(ld(rd(X,Y),Y),X) = rd(Y,ld(rd(Y,X),X)),
inference(equational,[status(thm)],[c3,c40,c53,c66]) ).
cnf(c81,plain,
rd(mult(X,Y),mult(X,X)) = rd(X,rd(X,rd(Y,X))),
inference(equational,[status(thm)],[c14,c15,c28,c41,c67,c79]) ).
cnf(c82,plain,
rd(X,rd(X,ld(X,Y))) = rd(Y,X),
inference(equational,[status(thm)],[c16,c17,c26,c31,c81]) ).
cnf(c83,plain,
rd(X,ld(X,Y)) = ld(rd(Y,X),X),
inference(equational,[status(thm)],[c11,c82]) ).
cnf(c87,plain,
mult(ld(X,Y),ld(X,Y)) = ld(X,ld(rd(X,Y),Y)),
inference(equational,[status(thm)],[c12,c30,c78]) ).
cnf(c88,plain,
ld(ld(rd(X,Y),Y),X) = ld(Y,ld(rd(Y,X),X)),
inference(equational,[status(thm)],[c7,c30,c83,c87]) ).
cnf(c90,plain,
rd(ld(X,unit),Y) = ld(X,ld(Y,unit)),
inference(equational,[status(thm)],[c62,c70]) ).
cnf(c91,plain,
ld(mult(X,Y),unit) = ld(Y,ld(X,unit)),
inference(equational,[status(thm)],[c64,c71,c90]) ).
cnf(c92,plain,
rd(ld(X,ld(X,Y)),Y) = ld(X,ld(X,unit)),
inference(equational,[status(thm)],[c22,c62]) ).
cnf(c93,plain,
ld(ld(X,Y),unit) = ld(Y,X),
inference(equational,[status(thm)],[c5,c17,c60,c83]) ).
cnf(c94,plain,
mult(ld(X,Y),Z) = ld(ld(Y,X),Z),
inference(equational,[status(thm)],[c62,c93]) ).
cnf(c95,plain,
ld(ld(X,Y),X) = ld(Y,mult(X,X)),
inference(equational,[status(thm)],[c49,c93]) ).
cnf(c96,plain,
mult(X,ld(Y,Z)) = rd(X,ld(Z,Y)),
inference(equational,[status(thm)],[c14,c63,c64,c78,c94]) ).
cnf(c97,plain,
ld(ld(X,Y),Y) = ld(Y,mult(X,Y)),
inference(equational,[status(thm)],[c17,c94]) ).
cnf(c98,plain,
ld(mult(X,Y),Y) = ld(Y,ld(X,Y)),
inference(equational,[status(thm)],[c93,c97]) ).
cnf(c101,plain,
rd(X,mult(X,mult(Y,X))) = ld(Y,ld(X,unit)),
inference(equational,[status(thm)],[c13,c60,c91]) ).
cnf(c105,plain,
ld(X,ld(rd(Y,X),X)) = ld(Y,X),
inference(equational,[status(thm)],[c8,c33,c62,c90,c93,c96,c101]) ).
cnf(c111,plain,
ld(rd(X,Y),mult(mult(X,Y),Z)) = mult(Y,mult(Y,Z)),
inference(equational,[status(thm)],[c9,c57]) ).
cnf(c112,plain,
rd(mult(X,mult(Y,Z)),ld(Y,Z)) = mult(X,mult(Y,Y)),
inference(equational,[status(thm)],[c7,c56]) ).
cnf(c113,plain,
ld(ld(X,ld(Y,X)),ld(X,Y)) = ld(X,mult(Y,Y)),
inference(equational,[status(thm)],[c5,c16,c17,c31,c55,c94,c95,c98]) ).
cnf(c114,plain,
ld(ld(X,Y),ld(Y,unit)) = ld(Y,rd(X,Y)),
inference(equational,[status(thm)],[c11,c53,c66,c73,c80,c93,c113]) ).
cnf(c115,plain,
ld(ld(X,ld(Y,unit)),Y) = mult(Y,mult(X,Y)),
inference(equational,[status(thm)],[c11,c32,c61,c71,c114]) ).
cnf(c124,plain,
ld(ld(X,ld(X,Y)),Z) = ld(Y,mult(X,mult(X,Z))),
inference(equational,[status(thm)],[c47,c49,c62,c94]) ).
cnf(c138,plain,
rd(X,rd(ld(Y,mult(Z,X)),X)) = ld(rd(Z,X),Y),
inference(equational,[status(thm)],[c7,c79,c96,c111]) ).
cnf(c139,plain,
rd(ld(X,mult(Y,Z)),Z) = ld(ld(rd(Y,Z),X),Z),
inference(equational,[status(thm)],[c11,c138]) ).
cnf(c146,plain,
ld(rd(mult(X,Y),Z),mult(X,X)) = rd(Z,ld(X,Y)),
inference(equational,[status(thm)],[c3,c66,c112]) ).
cnf(c147,plain,
rd(X,ld(Y,ld(Y,Z))) = ld(rd(Z,X),mult(Y,Y)),
inference(equational,[status(thm)],[c7,c146]) ).
cnf(c148,plain,
rd(rd(X,ld(Y,Z)),Y) = ld(rd(mult(Y,Z),X),Y),
inference(equational,[status(thm)],[c6,c8,c139,c146]) ).
cnf(c150,plain,
ld(ld(rd(X,Y),Y),mult(Y,X)) = ld(Y,mult(X,X)),
inference(equational,[status(thm)],[c7,c13,c34,c58,c94,c95]) ).
cnf(c152,plain,
ld(rd(X,Y),ld(rd(Y,X),X)) = X,
inference(equational,[status(thm)],[c6,c8,c12,c138,c139,c150]) ).
cnf(c153,plain,
rd(X,ld(rd(X,Y),Y)) = ld(rd(Y,X),rd(X,Y)),
inference(equational,[status(thm)],[c40,c53,c64,c66,c80,c92,c152]) ).
cnf(c159,plain,
ld(rd(X,rd(Y,X)),mult(X,Z)) = rd(Y,ld(Z,X)),
inference(equational,[status(thm)],[c3,c28,c58,c66,c67,c96]) ).
cnf(c161,plain,
rd(X,ld(Y,mult(Z,Z))) = ld(rd(Z,rd(X,Z)),Y),
inference(equational,[status(thm)],[c7,c95,c159]) ).
cnf(c162,plain,
rd(X,ld(Y,ld(Z,unit))) = mult(X,mult(Z,Y)),
inference(equational,[status(thm)],[c12,c61,c62,c71,c90,c91,c96,c124,c159]) ).
cnf(c176,plain,
rd(ld(X,mult(Y,Y)),Z) = ld(X,rd(Y,rd(Z,Y))),
inference(equational,[status(thm)],[c64,c93,c161]) ).
cnf(c177,plain,
rd(mult(X,mult(Y,Z)),Z) = ld(rd(rd(Z,Y),X),Z),
inference(equational,[status(thm)],[c8,c96,c148,c162]) ).
cnf(c183,plain,
rd(ld(X,ld(X,Y)),Z) = ld(X,ld(X,rd(Y,Z))),
inference(equational,[status(thm)],[c49,c64,c93,c147]) ).
cnf(c190,plain,
rd(X,ld(Y,mult(Z,X))) = ld(X,ld(rd(Z,X),Y)),
inference(equational,[status(thm)],[c64,c93,c139]) ).
cnf(c201,plain,
rd(rd(X,ld(Y,rd(Z,Y))),Z) = rd(X,ld(rd(Y,Z),rd(Z,Y))),
inference(equational,[status(thm)],[c3,c53,c56,c66,c80,c96,c153]) ).
cnf(c204,plain,
rd(rd(X,ld(Y,Z)),mult(Z,Y)) = rd(X,mult(Z,Z)),
inference(equational,[status(thm)],[c5,c60,c61,c201]) ).
cnf(c209,plain,
ld(X,mult(mult(X,Y),mult(X,Y))) = mult(Y,mult(X,Y)),
inference(equational,[status(thm)],[c9,c72,c113,c115]) ).
cnf(c210,plain,
mult(mult(X,Y),mult(X,Y)) = mult(X,mult(Y,mult(X,Y))),
inference(equational,[status(thm)],[c7,c209]) ).
cnf(c214,plain,
rd(ld(X,ld(Y,unit)),Z) = ld(mult(Y,X),ld(Z,unit)),
inference(equational,[status(thm)],[c64,c91,c162]) ).
cnf(c225,plain,
ld(ld(X,ld(Y,unit)),Z) = mult(mult(Y,X),Z),
inference(equational,[status(thm)],[c61,c94]) ).
cnf(c250,plain,
ld(ld(X,Y),ld(ld(Y,X),Z)) = Z,
inference(equational,[status(thm)],[c59,c93,c94]) ).
cnf(c266,plain,
rd(rd(X,Y),ld(Z,W)) = ld(rd(Y,X),ld(W,Z)),
inference(equational,[status(thm)],[c10,c93,c94,c124,c148,c183,c250]) ).
cnf(c292,plain,
mult(mult(X,mult(Y,mult(Z,Y))),Z) = mult(X,mult(Y,mult(Z,mult(Y,Z)))),
inference(equational,[status(thm)],[c13,c71,c72,c112,c210]) ).
cnf(c342,plain,
rd(X,ld(Y,ld(rd(Y,Z),Z))) = ld(rd(Z,X),ld(rd(Z,Y),Y)),
inference(equational,[status(thm)],[c12,c61,c87,c88,c94,c96,c112,c114,c266]) ).
cnf(c357,plain,
ld(rd(ld(X,Y),Z),ld(Y,X)) = ld(rd(Y,Z),ld(rd(Y,X),X)),
inference(equational,[status(thm)],[c6,c32,c34,c49,c54,c61,c87,c105,c147,c176,c177,c190,c204,c342]) ).
cnf(c469,plain,
mult(mult(X,Y),mult(Z,mult(Y,Z))) = mult(X,mult(Y,mult(Z,mult(Y,Z)))),
inference(equational,[status(thm)],[c13,c20,c61,c90,c210,c214,c225,c357]) ).
cnf(g1,plain,
mult(mult(a,b),mult(mult(c,b),c)) = mult(mult(a,mult(mult(b,c),b)),c),
inference(equational,[status(thm)],[c13,c292,c469]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP668-1 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n001.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 08:50:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 71.33/71.44 % SZS status Unsatisfiable
% 71.33/71.44 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------