%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP697-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:11:45 AM UTC 2026
% Result : Unsatisfiable 0.20s 0.60s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 58
% Number of leaves : 12
% Syntax : Number of clauses : 250 ( 250 unt; 0 nHn; 9 RR)
% Number of literals : 250 ( 249 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 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 : 463 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
mult(mult(a,b),mult(b,mult(c,b))) != mult(mult(a,mult(b,mult(b,c))),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c2,axiom,
mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c09) ).
cnf(c3,plain,
mult(mult(X3,mult(X2,mult(X2,X))),X2) = mult(mult(X3,X2),ld(X2,mult(mult(X2,mult(X2,X)),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
ld(A2,mult(A2,B2)) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
cnf(c5,plain,
ld(X,mult(X,i(mult(X2,X)))) = i(mult(X2,X)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
i(mult(X2,X)) = ld(X,mult(X,i(mult(X2,X)))),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,axiom,
mult(A2,i(mult(B2,A2))) = i(B2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).
cnf(c8,plain,
mult(X,i(mult(X2,X))) = i(X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
ld(X,mult(X,i(mult(X2,X)))) = ld(X,i(X2)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
i(mult(X2,X)) = ld(X,i(X2)),
inference(transitivity,[status(thm)],[c6,c9]) ).
cnf(c11,plain,
i(mult(X,X2)) = ld(X2,i(X)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
ld(X2,i(X)) = i(mult(X,X2)),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
i(ld(X2,i(X))) = i(i(mult(X,X2))),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,axiom,
mult(A2,i(A2)) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c11) ).
cnf(c15,plain,
mult(X,i(X)) = unit,
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
unit = mult(X,i(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
ld(X,unit) = ld(X,mult(X,i(X))),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
ld(X,mult(X,i(X))) = i(X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c19,plain,
ld(X,unit) = i(X),
inference(transitivity,[status(thm)],[c17,c18]) ).
cnf(c20,plain,
ld(i(X),unit) = i(i(X)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
i(i(X)) = ld(i(X),unit),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,axiom,
mult(i(A2),A2) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c10) ).
cnf(c23,plain,
mult(i(X),X) = unit,
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
unit = mult(i(X),X),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
ld(i(X),unit) = ld(i(X),mult(i(X),X)),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
ld(i(X),mult(i(X),X)) = X,
inference(substitution,[status(thm)],[c4]) ).
cnf(c27,plain,
ld(i(X),unit) = X,
inference(transitivity,[status(thm)],[c25,c26]) ).
cnf(c28,plain,
i(i(X)) = X,
inference(transitivity,[status(thm)],[c21,c27]) ).
cnf(c29,plain,
i(i(mult(X,X2))) = mult(X,X2),
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
i(ld(X2,i(X))) = mult(X,X2),
inference(transitivity,[status(thm)],[c13,c29]) ).
cnf(c31,plain,
i(ld(X2,i(mult(X2,mult(X2,X))))) = mult(mult(X2,mult(X2,X)),X2),
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
mult(mult(X2,mult(X2,X)),X2) = i(ld(X2,i(mult(X2,mult(X2,X))))),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
mult(X2,i(mult(ld(X2,i(mult(X2,mult(X2,X)))),X2))) = i(ld(X2,i(mult(X2,mult(X2,X))))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c34,plain,
i(ld(X2,i(mult(X2,mult(X2,X))))) = mult(X2,i(mult(ld(X2,i(mult(X2,mult(X2,X)))),X2))),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c36,plain,
ld(X,X2) = ld(X,i(i(X2))),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
ld(X2,ld(X,X2)) = ld(X2,ld(X,i(i(X2)))),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
i(mult(i(X2),X)) = ld(X,i(i(X2))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c39,plain,
ld(X,i(i(X2))) = i(mult(i(X2),X)),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
ld(X2,ld(X,i(i(X2)))) = ld(X2,i(mult(i(X2),X))),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
i(mult(mult(i(X2),X),X2)) = ld(X2,i(mult(i(X2),X))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c42,plain,
ld(X2,i(mult(i(X2),X))) = i(mult(mult(i(X2),X),X2)),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,axiom,
mult(unit,A2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
cnf(c44,plain,
mult(unit,ld(X2,mult(X,X2))) = ld(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c43]) ).
cnf(c45,plain,
ld(X2,mult(X,X2)) = mult(unit,ld(X2,mult(X,X2))),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,plain,
mult(i(X),X) = unit,
inference(substitution,[status(thm)],[c22]) ).
cnf(c47,plain,
unit = mult(i(X),X),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
mult(unit,ld(X2,mult(X,X2))) = mult(mult(i(X2),X2),ld(X2,mult(X,X2))),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
mult(mult(i(X2),X),X2) = mult(mult(i(X2),X2),ld(X2,mult(X,X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c50,plain,
mult(mult(i(X2),X2),ld(X2,mult(X,X2))) = mult(mult(i(X2),X),X2),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
mult(unit,ld(X2,mult(X,X2))) = mult(mult(i(X2),X),X2),
inference(transitivity,[status(thm)],[c48,c50]) ).
cnf(c52,plain,
ld(X2,mult(X,X2)) = mult(mult(i(X2),X),X2),
inference(transitivity,[status(thm)],[c45,c51]) ).
cnf(c53,plain,
mult(mult(i(X2),X),X2) = ld(X2,mult(X,X2)),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
i(mult(mult(i(X2),X),X2)) = i(ld(X2,mult(X,X2))),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c56,plain,
ld(X2,X) = ld(X2,i(i(X))),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
i(ld(X2,X)) = i(ld(X2,i(i(X)))),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
i(ld(X2,i(i(X)))) = mult(i(X),X2),
inference(substitution,[status(thm)],[c30]) ).
cnf(c59,plain,
i(ld(X2,X)) = mult(i(X),X2),
inference(transitivity,[status(thm)],[c57,c58]) ).
cnf(c60,plain,
i(ld(X2,mult(X,X2))) = mult(i(mult(X,X2)),X2),
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,plain,
i(mult(X,X2)) = ld(X2,i(X)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c62,plain,
mult(i(mult(X,X2)),X2) = mult(ld(X2,i(X)),X2),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
i(ld(X2,mult(X,X2))) = mult(ld(X2,i(X)),X2),
inference(transitivity,[status(thm)],[c60,c62]) ).
cnf(c64,plain,
i(mult(mult(i(X2),X),X2)) = mult(ld(X2,i(X)),X2),
inference(transitivity,[status(thm)],[c54,c63]) ).
cnf(c65,plain,
ld(X2,i(mult(i(X2),X))) = mult(ld(X2,i(X)),X2),
inference(transitivity,[status(thm)],[c42,c64]) ).
cnf(c66,plain,
ld(X2,ld(X,i(i(X2)))) = mult(ld(X2,i(X)),X2),
inference(transitivity,[status(thm)],[c40,c65]) ).
cnf(c67,plain,
ld(X2,ld(X,X2)) = mult(ld(X2,i(X)),X2),
inference(transitivity,[status(thm)],[c37,c66]) ).
cnf(c68,plain,
ld(X2,ld(mult(X2,mult(X2,X)),X2)) = mult(ld(X2,i(mult(X2,mult(X2,X)))),X2),
inference(substitution,[status(thm)],[c67]) ).
cnf(c69,plain,
mult(ld(X2,i(mult(X2,mult(X2,X)))),X2) = ld(X2,ld(mult(X2,mult(X2,X)),X2)),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c71,plain,
ld(mult(X2,mult(X2,X)),X2) = ld(mult(X2,mult(X2,X)),i(i(X2))),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
ld(X2,ld(mult(X2,mult(X2,X)),X2)) = ld(X2,ld(mult(X2,mult(X2,X)),i(i(X2)))),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
i(mult(i(X2),mult(X2,mult(X2,X)))) = ld(mult(X2,mult(X2,X)),i(i(X2))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c74,plain,
ld(mult(X2,mult(X2,X)),i(i(X2))) = i(mult(i(X2),mult(X2,mult(X2,X)))),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
ld(X2,ld(mult(X2,mult(X2,X)),i(i(X2)))) = ld(X2,i(mult(i(X2),mult(X2,mult(X2,X))))),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c77,plain,
ld(X2,i(mult(i(X2),mult(X2,mult(X2,X))))) = ld(i(i(X2)),i(mult(i(X2),mult(X2,mult(X2,X))))),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
i(i(rd(X2,X))) = rd(X2,X),
inference(substitution,[status(thm)],[c28]) ).
cnf(c79,plain,
rd(X2,X) = i(i(rd(X2,X))),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
mult(X,i(mult(rd(X2,X),X))) = i(rd(X2,X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c81,plain,
i(rd(X2,X)) = mult(X,i(mult(rd(X2,X),X))),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c82,axiom,
mult(rd(A2,B2),B2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
cnf(c83,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c82]) ).
cnf(c84,plain,
i(mult(rd(X2,X),X)) = i(X2),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
mult(X,i(mult(rd(X2,X),X))) = mult(X,i(X2)),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
i(rd(X2,X)) = mult(X,i(X2)),
inference(transitivity,[status(thm)],[c81,c85]) ).
cnf(c87,plain,
i(i(rd(X2,X))) = i(mult(X,i(X2))),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
i(mult(X,i(X2))) = ld(i(X2),i(X)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c89,plain,
i(i(rd(X2,X))) = ld(i(X2),i(X)),
inference(transitivity,[status(thm)],[c87,c88]) ).
cnf(c90,plain,
rd(X2,X) = ld(i(X2),i(X)),
inference(transitivity,[status(thm)],[c79,c89]) ).
cnf(c91,plain,
rd(i(X2),mult(i(X2),mult(X2,mult(X2,X)))) = ld(i(i(X2)),i(mult(i(X2),mult(X2,mult(X2,X))))),
inference(substitution,[status(thm)],[c90]) ).
cnf(c92,plain,
ld(i(i(X2)),i(mult(i(X2),mult(X2,mult(X2,X))))) = rd(i(X2),mult(i(X2),mult(X2,mult(X2,X)))),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c93,plain,
ld(i(mult(X2,X)),i(X2)) = ld(ld(X,i(X2)),i(X2)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c94,plain,
i(mult(X,X2)) = ld(X2,i(X)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c95,plain,
ld(X2,i(X)) = i(mult(X,X2)),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,plain,
ld(ld(X2,i(X)),i(X)) = ld(i(mult(X,X2)),i(X)),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
rd(mult(X,X2),X) = ld(i(mult(X,X2)),i(X)),
inference(substitution,[status(thm)],[c90]) ).
cnf(c98,plain,
ld(i(mult(X,X2)),i(X)) = rd(mult(X,X2),X),
inference(symmetry,[status(thm)],[c97]) ).
cnf(c99,axiom,
mult(A2,unit) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
cnf(c100,plain,
mult(rd(mult(X,X2),X),unit) = rd(mult(X,X2),X),
inference(substitution,[status(thm)],[c99]) ).
cnf(c101,plain,
rd(mult(X,X2),X) = mult(rd(mult(X,X2),X),unit),
inference(symmetry,[status(thm)],[c100]) ).
cnf(c102,plain,
mult(X,i(X)) = unit,
inference(substitution,[status(thm)],[c14]) ).
cnf(c103,plain,
unit = mult(X,i(X)),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c104,plain,
mult(rd(mult(X,X2),X),unit) = mult(rd(mult(X,X2),X),mult(X,i(X))),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,axiom,
mult(A2,mult(B2,C2)) = mult(rd(mult(A2,B2),A2),mult(A2,C2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c08) ).
cnf(c106,plain,
mult(X,mult(X2,i(X))) = mult(rd(mult(X,X2),X),mult(X,i(X))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c107,plain,
mult(rd(mult(X,X2),X),mult(X,i(X))) = mult(X,mult(X2,i(X))),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c108,plain,
mult(rd(mult(X,X2),X),unit) = mult(X,mult(X2,i(X))),
inference(transitivity,[status(thm)],[c104,c107]) ).
cnf(c109,plain,
rd(mult(X,X2),X) = mult(X,mult(X2,i(X))),
inference(transitivity,[status(thm)],[c101,c108]) ).
cnf(c110,plain,
ld(i(mult(X,X2)),i(X)) = mult(X,mult(X2,i(X))),
inference(transitivity,[status(thm)],[c98,c109]) ).
cnf(c111,plain,
ld(ld(X2,i(X)),i(X)) = mult(X,mult(X2,i(X))),
inference(transitivity,[status(thm)],[c96,c110]) ).
cnf(c112,plain,
ld(ld(X,i(X2)),i(X2)) = mult(X2,mult(X,i(X2))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c113,plain,
ld(i(mult(X2,X)),i(X2)) = mult(X2,mult(X,i(X2))),
inference(transitivity,[status(thm)],[c93,c112]) ).
cnf(c114,plain,
ld(i(mult(X2,mult(X,X2))),i(X2)) = mult(X2,mult(mult(X,X2),i(X2))),
inference(substitution,[status(thm)],[c113]) ).
cnf(c115,plain,
i(i(mult(X,X2))) = mult(X,X2),
inference(substitution,[status(thm)],[c28]) ).
cnf(c116,plain,
mult(X,X2) = i(i(mult(X,X2))),
inference(symmetry,[status(thm)],[c115]) ).
cnf(c117,plain,
mult(ld(mult(X2,X),X2),mult(X,X2)) = mult(ld(mult(X2,X),X2),i(i(mult(X,X2)))),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c119,plain,
ld(mult(X2,X),X) = ld(mult(X2,X),i(i(X))),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
i(mult(i(X),mult(X2,X))) = ld(mult(X2,X),i(i(X))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c121,plain,
ld(mult(X2,X),i(i(X))) = i(mult(i(X),mult(X2,X))),
inference(symmetry,[status(thm)],[c120]) ).
cnf(c122,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c123,plain,
ld(ld(X2,X),X) = ld(ld(X2,X),i(i(X))),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c125,plain,
ld(X2,X) = ld(X2,i(i(X))),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
ld(ld(X2,X),i(i(X))) = ld(ld(X2,i(i(X))),i(i(X))),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
ld(ld(X2,i(i(X))),i(i(X))) = mult(i(X),mult(X2,i(i(X)))),
inference(substitution,[status(thm)],[c111]) ).
cnf(c128,plain,
mult(X2,i(i(X))) = mult(X2,X),
inference(congruence,[status(thm)],[c28]) ).
cnf(c129,plain,
mult(i(X),mult(X2,i(i(X)))) = mult(i(X),mult(X2,X)),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
ld(ld(X2,i(i(X))),i(i(X))) = mult(i(X),mult(X2,X)),
inference(transitivity,[status(thm)],[c127,c129]) ).
cnf(c131,plain,
ld(ld(X2,X),i(i(X))) = mult(i(X),mult(X2,X)),
inference(transitivity,[status(thm)],[c126,c130]) ).
cnf(c132,plain,
ld(ld(X2,X),X) = mult(i(X),mult(X2,X)),
inference(transitivity,[status(thm)],[c123,c131]) ).
cnf(c133,plain,
mult(i(X),mult(X2,X)) = ld(ld(X2,X),X),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c134,plain,
i(mult(i(X),mult(X2,X))) = i(ld(ld(X2,X),X)),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
i(ld(ld(X2,X),X)) = mult(i(X),ld(X2,X)),
inference(substitution,[status(thm)],[c59]) ).
cnf(c136,plain,
i(mult(i(X),mult(X2,X))) = mult(i(X),ld(X2,X)),
inference(transitivity,[status(thm)],[c134,c135]) ).
cnf(c137,plain,
ld(mult(X2,X),i(i(X))) = mult(i(X),ld(X2,X)),
inference(transitivity,[status(thm)],[c121,c136]) ).
cnf(c138,plain,
ld(mult(X2,X),X) = mult(i(X),ld(X2,X)),
inference(transitivity,[status(thm)],[c119,c137]) ).
cnf(c139,plain,
ld(mult(mult(X2,X),X2),X2) = mult(i(X2),ld(mult(X2,X),X2)),
inference(substitution,[status(thm)],[c138]) ).
cnf(c140,plain,
mult(i(X2),ld(mult(X2,X),X2)) = ld(mult(mult(X2,X),X2),X2),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c141,plain,
mult(mult(X3,i(mult(X2,X))),X2) = mult(mult(X3,X2),ld(X2,mult(i(mult(X2,X)),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c142,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c143,plain,
mult(i(mult(X2,X)),X2) = mult(i(mult(X2,X)),i(i(X2))),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
mult(X,i(mult(X2,X))) = i(X2),
inference(substitution,[status(thm)],[c7]) ).
cnf(c145,plain,
i(X2) = mult(X,i(mult(X2,X))),
inference(symmetry,[status(thm)],[c144]) ).
cnf(c146,plain,
i(i(X2)) = i(mult(X,i(mult(X2,X)))),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
mult(i(mult(X2,X)),i(i(X2))) = mult(i(mult(X2,X)),i(mult(X,i(mult(X2,X))))),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,plain,
mult(i(mult(X2,X)),i(mult(X,i(mult(X2,X))))) = i(X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c149,plain,
mult(i(mult(X2,X)),i(i(X2))) = i(X),
inference(transitivity,[status(thm)],[c147,c148]) ).
cnf(c150,plain,
mult(i(mult(X2,X)),X2) = i(X),
inference(transitivity,[status(thm)],[c143,c149]) ).
cnf(c151,plain,
ld(X2,mult(i(mult(X2,X)),X2)) = ld(X2,i(X)),
inference(congruence,[status(thm)],[c150]) ).
cnf(c152,plain,
mult(mult(X3,X2),ld(X2,mult(i(mult(X2,X)),X2))) = mult(mult(X3,X2),ld(X2,i(X))),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
i(mult(X,X2)) = ld(X2,i(X)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c154,plain,
ld(X2,i(X)) = i(mult(X,X2)),
inference(symmetry,[status(thm)],[c153]) ).
cnf(c155,plain,
mult(mult(X3,X2),ld(X2,i(X))) = mult(mult(X3,X2),i(mult(X,X2))),
inference(congruence,[status(thm)],[c154]) ).
cnf(c156,plain,
mult(mult(X3,X2),ld(X2,mult(i(mult(X2,X)),X2))) = mult(mult(X3,X2),i(mult(X,X2))),
inference(transitivity,[status(thm)],[c152,c155]) ).
cnf(c157,plain,
mult(mult(X3,i(mult(X2,X))),X2) = mult(mult(X3,X2),i(mult(X,X2))),
inference(transitivity,[status(thm)],[c141,c156]) ).
cnf(c158,plain,
mult(mult(mult(X2,X),i(mult(X2,X))),X2) = mult(mult(mult(X2,X),X2),i(mult(X,X2))),
inference(substitution,[status(thm)],[c157]) ).
cnf(c159,plain,
mult(mult(mult(X2,X),X2),i(mult(X,X2))) = mult(mult(mult(X2,X),i(mult(X2,X))),X2),
inference(symmetry,[status(thm)],[c158]) ).
cnf(c160,plain,
mult(mult(X2,X),i(mult(X2,X))) = unit,
inference(substitution,[status(thm)],[c14]) ).
cnf(c161,plain,
mult(mult(mult(X2,X),i(mult(X2,X))),X2) = mult(unit,X2),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
mult(unit,X) = X,
inference(substitution,[status(thm)],[c43]) ).
cnf(c163,plain,
mult(mult(mult(X2,X),i(mult(X2,X))),X2) = X2,
inference(transitivity,[status(thm)],[c161,c162]) ).
cnf(c164,plain,
mult(mult(mult(X2,X),X2),i(mult(X,X2))) = X2,
inference(transitivity,[status(thm)],[c159,c163]) ).
cnf(c165,plain,
X2 = mult(mult(mult(X2,X),X2),i(mult(X,X2))),
inference(symmetry,[status(thm)],[c164]) ).
cnf(c166,plain,
ld(mult(mult(X2,X),X2),X2) = ld(mult(mult(X2,X),X2),mult(mult(mult(X2,X),X2),i(mult(X,X2)))),
inference(congruence,[status(thm)],[c165]) ).
cnf(c167,plain,
ld(mult(mult(X2,X),X2),mult(mult(mult(X2,X),X2),i(mult(X,X2)))) = i(mult(X,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c168,plain,
ld(mult(mult(X2,X),X2),X2) = i(mult(X,X2)),
inference(transitivity,[status(thm)],[c166,c167]) ).
cnf(c169,plain,
mult(i(X2),ld(mult(X2,X),X2)) = i(mult(X,X2)),
inference(transitivity,[status(thm)],[c140,c168]) ).
cnf(c170,plain,
i(mult(X,X2)) = mult(i(X2),ld(mult(X2,X),X2)),
inference(symmetry,[status(thm)],[c169]) ).
cnf(c171,plain,
i(i(mult(X,X2))) = i(mult(i(X2),ld(mult(X2,X),X2))),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,plain,
mult(ld(mult(X2,X),X2),i(i(mult(X,X2)))) = mult(ld(mult(X2,X),X2),i(mult(i(X2),ld(mult(X2,X),X2)))),
inference(congruence,[status(thm)],[c171]) ).
cnf(c173,plain,
mult(ld(mult(X2,X),X2),i(mult(i(X2),ld(mult(X2,X),X2)))) = i(i(X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c174,plain,
mult(ld(mult(X2,X),X2),i(mult(i(X2),ld(mult(X2,X),X2)))) = X2,
inference(transitivity,[status(thm)],[c173,c28]) ).
cnf(c175,plain,
mult(ld(mult(X2,X),X2),i(i(mult(X,X2)))) = X2,
inference(transitivity,[status(thm)],[c172,c174]) ).
cnf(c176,plain,
mult(ld(mult(X2,X),X2),mult(X,X2)) = X2,
inference(transitivity,[status(thm)],[c117,c175]) ).
cnf(c177,plain,
X2 = mult(ld(mult(X2,X),X2),mult(X,X2)),
inference(symmetry,[status(thm)],[c176]) ).
cnf(c178,plain,
i(X2) = i(mult(ld(mult(X2,X),X2),mult(X,X2))),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
mult(mult(X,X2),i(X2)) = mult(mult(X,X2),i(mult(ld(mult(X2,X),X2),mult(X,X2)))),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
mult(mult(X,X2),i(mult(ld(mult(X2,X),X2),mult(X,X2)))) = i(ld(mult(X2,X),X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c181,plain,
i(ld(mult(X2,X),X2)) = mult(i(X2),mult(X2,X)),
inference(substitution,[status(thm)],[c59]) ).
cnf(c182,plain,
mult(mult(X,X2),i(mult(ld(mult(X2,X),X2),mult(X,X2)))) = mult(i(X2),mult(X2,X)),
inference(transitivity,[status(thm)],[c180,c181]) ).
cnf(c183,plain,
mult(mult(X,X2),i(X2)) = mult(i(X2),mult(X2,X)),
inference(transitivity,[status(thm)],[c179,c182]) ).
cnf(c184,plain,
mult(X2,mult(mult(X,X2),i(X2))) = mult(X2,mult(i(X2),mult(X2,X))),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
mult(unit,ld(unit,X)) = ld(unit,X),
inference(substitution,[status(thm)],[c43]) ).
cnf(c186,plain,
ld(unit,X) = mult(unit,ld(unit,X)),
inference(symmetry,[status(thm)],[c185]) ).
cnf(c187,axiom,
mult(A2,ld(A2,B2)) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c01) ).
cnf(c188,plain,
mult(unit,ld(unit,X)) = X,
inference(substitution,[status(thm)],[c187]) ).
cnf(c189,plain,
ld(unit,X) = X,
inference(transitivity,[status(thm)],[c186,c188]) ).
cnf(c190,plain,
ld(unit,i(X)) = i(X),
inference(substitution,[status(thm)],[c189]) ).
cnf(c191,plain,
i(X) = ld(unit,i(X)),
inference(symmetry,[status(thm)],[c190]) ).
cnf(c192,plain,
mult(i(X2),mult(X2,X)) = mult(ld(unit,i(X2)),mult(X2,X)),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
mult(unit,i(unit)) = i(unit),
inference(substitution,[status(thm)],[c43]) ).
cnf(c194,plain,
i(unit) = mult(unit,i(unit)),
inference(symmetry,[status(thm)],[c193]) ).
cnf(c195,plain,
mult(unit,i(unit)) = unit,
inference(substitution,[status(thm)],[c14]) ).
cnf(c196,plain,
i(unit) = unit,
inference(transitivity,[status(thm)],[c194,c195]) ).
cnf(c197,plain,
unit = i(unit),
inference(symmetry,[status(thm)],[c196]) ).
cnf(c198,plain,
ld(unit,i(X)) = ld(i(unit),i(X)),
inference(congruence,[status(thm)],[c197]) ).
cnf(c199,plain,
mult(ld(unit,i(X2)),mult(X2,X)) = mult(ld(i(unit),i(X2)),mult(X2,X)),
inference(congruence,[status(thm)],[c198]) ).
cnf(c200,plain,
ld(i(X2),i(X)) = rd(X2,X),
inference(symmetry,[status(thm)],[c90]) ).
cnf(c201,plain,
mult(ld(i(X3),i(X2)),mult(X2,X)) = mult(rd(X3,X2),mult(X2,X)),
inference(congruence,[status(thm)],[c200]) ).
cnf(c202,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c187]) ).
cnf(c203,plain,
X2 = mult(X,ld(X,X2)),
inference(symmetry,[status(thm)],[c202]) ).
cnf(c204,plain,
rd(X2,X) = rd(mult(X,ld(X,X2)),X),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
mult(rd(X3,X2),mult(X2,X)) = mult(rd(mult(X2,ld(X2,X3)),X2),mult(X2,X)),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
mult(X2,mult(ld(X2,X3),X)) = mult(rd(mult(X2,ld(X2,X3)),X2),mult(X2,X)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c207,plain,
mult(rd(mult(X2,ld(X2,X3)),X2),mult(X2,X)) = mult(X2,mult(ld(X2,X3),X)),
inference(symmetry,[status(thm)],[c206]) ).
cnf(c208,plain,
mult(rd(X3,X2),mult(X2,X)) = mult(X2,mult(ld(X2,X3),X)),
inference(transitivity,[status(thm)],[c205,c207]) ).
cnf(c209,plain,
mult(ld(i(X3),i(X2)),mult(X2,X)) = mult(X2,mult(ld(X2,X3),X)),
inference(transitivity,[status(thm)],[c201,c208]) ).
cnf(c210,plain,
mult(ld(i(unit),i(X2)),mult(X2,X)) = mult(X2,mult(ld(X2,unit),X)),
inference(substitution,[status(thm)],[c209]) ).
cnf(c211,plain,
mult(ld(X2,unit),X) = mult(i(X2),X),
inference(congruence,[status(thm)],[c19]) ).
cnf(c212,plain,
mult(X2,mult(ld(X2,unit),X)) = mult(X2,mult(i(X2),X)),
inference(congruence,[status(thm)],[c211]) ).
cnf(c213,plain,
mult(ld(i(unit),i(X2)),mult(X2,X)) = mult(X2,mult(i(X2),X)),
inference(transitivity,[status(thm)],[c210,c212]) ).
cnf(c214,plain,
mult(ld(unit,i(X2)),mult(X2,X)) = mult(X2,mult(i(X2),X)),
inference(transitivity,[status(thm)],[c199,c213]) ).
cnf(c215,plain,
mult(i(X2),mult(X2,X)) = mult(X2,mult(i(X2),X)),
inference(transitivity,[status(thm)],[c192,c214]) ).
cnf(c216,plain,
mult(i(X2),mult(X2,mult(X2,X))) = mult(X2,mult(i(X2),mult(X2,X))),
inference(substitution,[status(thm)],[c215]) ).
cnf(c217,plain,
mult(X2,mult(i(X2),mult(X2,X))) = mult(i(X2),mult(X2,mult(X2,X))),
inference(symmetry,[status(thm)],[c216]) ).
cnf(c218,plain,
mult(X2,mult(mult(X,X2),i(X2))) = mult(i(X2),mult(X2,mult(X2,X))),
inference(transitivity,[status(thm)],[c184,c217]) ).
cnf(c219,plain,
ld(i(mult(X2,mult(X,X2))),i(X2)) = mult(i(X2),mult(X2,mult(X2,X))),
inference(transitivity,[status(thm)],[c114,c218]) ).
cnf(c220,plain,
mult(i(X2),mult(X2,mult(X2,X))) = ld(i(mult(X2,mult(X,X2))),i(X2)),
inference(symmetry,[status(thm)],[c219]) ).
cnf(c221,plain,
rd(i(X2),mult(i(X2),mult(X2,mult(X2,X)))) = rd(i(X2),ld(i(mult(X2,mult(X,X2))),i(X2))),
inference(congruence,[status(thm)],[c220]) ).
cnf(c222,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c187]) ).
cnf(c223,plain,
X2 = mult(X,ld(X,X2)),
inference(symmetry,[status(thm)],[c222]) ).
cnf(c224,plain,
rd(X2,ld(X,X2)) = rd(mult(X,ld(X,X2)),ld(X,X2)),
inference(congruence,[status(thm)],[c223]) ).
cnf(c225,axiom,
rd(mult(A2,B2),B2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
cnf(c226,plain,
rd(mult(X,ld(X,X2)),ld(X,X2)) = X,
inference(substitution,[status(thm)],[c225]) ).
cnf(c227,plain,
rd(X2,ld(X,X2)) = X,
inference(transitivity,[status(thm)],[c224,c226]) ).
cnf(c228,plain,
rd(i(X2),ld(i(mult(X2,mult(X,X2))),i(X2))) = i(mult(X2,mult(X,X2))),
inference(substitution,[status(thm)],[c227]) ).
cnf(c229,plain,
rd(i(X2),mult(i(X2),mult(X2,mult(X2,X)))) = i(mult(X2,mult(X,X2))),
inference(transitivity,[status(thm)],[c221,c228]) ).
cnf(c230,plain,
ld(i(i(X2)),i(mult(i(X2),mult(X2,mult(X2,X))))) = i(mult(X2,mult(X,X2))),
inference(transitivity,[status(thm)],[c92,c229]) ).
cnf(c231,plain,
ld(X2,i(mult(i(X2),mult(X2,mult(X2,X))))) = i(mult(X2,mult(X,X2))),
inference(transitivity,[status(thm)],[c77,c230]) ).
cnf(c232,plain,
ld(X2,ld(mult(X2,mult(X2,X)),i(i(X2)))) = i(mult(X2,mult(X,X2))),
inference(transitivity,[status(thm)],[c75,c231]) ).
cnf(c233,plain,
ld(X2,ld(mult(X2,mult(X2,X)),X2)) = i(mult(X2,mult(X,X2))),
inference(transitivity,[status(thm)],[c72,c232]) ).
cnf(c234,plain,
mult(ld(X2,i(mult(X2,mult(X2,X)))),X2) = i(mult(X2,mult(X,X2))),
inference(transitivity,[status(thm)],[c69,c233]) ).
cnf(c235,plain,
i(mult(ld(X2,i(mult(X2,mult(X2,X)))),X2)) = i(i(mult(X2,mult(X,X2)))),
inference(congruence,[status(thm)],[c234]) ).
cnf(c236,plain,
mult(X2,i(mult(ld(X2,i(mult(X2,mult(X2,X)))),X2))) = mult(X2,i(i(mult(X2,mult(X,X2))))),
inference(congruence,[status(thm)],[c235]) ).
cnf(c237,plain,
i(i(mult(X2,mult(X,X2)))) = mult(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c238,plain,
mult(X2,i(i(mult(X2,mult(X,X2))))) = mult(X2,mult(X2,mult(X,X2))),
inference(congruence,[status(thm)],[c237]) ).
cnf(c239,plain,
mult(X2,i(mult(ld(X2,i(mult(X2,mult(X2,X)))),X2))) = mult(X2,mult(X2,mult(X,X2))),
inference(transitivity,[status(thm)],[c236,c238]) ).
cnf(c240,plain,
i(ld(X2,i(mult(X2,mult(X2,X))))) = mult(X2,mult(X2,mult(X,X2))),
inference(transitivity,[status(thm)],[c34,c239]) ).
cnf(c241,plain,
mult(mult(X2,mult(X2,X)),X2) = mult(X2,mult(X2,mult(X,X2))),
inference(transitivity,[status(thm)],[c32,c240]) ).
cnf(c242,plain,
ld(X2,mult(mult(X2,mult(X2,X)),X2)) = ld(X2,mult(X2,mult(X2,mult(X,X2)))),
inference(congruence,[status(thm)],[c241]) ).
cnf(c243,plain,
mult(mult(X3,X2),ld(X2,mult(mult(X2,mult(X2,X)),X2))) = mult(mult(X3,X2),ld(X2,mult(X2,mult(X2,mult(X,X2))))),
inference(congruence,[status(thm)],[c242]) ).
cnf(c244,plain,
ld(X2,mult(X2,mult(X2,mult(X,X2)))) = mult(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c245,plain,
mult(mult(X3,X2),ld(X2,mult(X2,mult(X2,mult(X,X2))))) = mult(mult(X3,X2),mult(X2,mult(X,X2))),
inference(congruence,[status(thm)],[c244]) ).
cnf(c246,plain,
mult(mult(X3,X2),ld(X2,mult(mult(X2,mult(X2,X)),X2))) = mult(mult(X3,X2),mult(X2,mult(X,X2))),
inference(transitivity,[status(thm)],[c243,c245]) ).
cnf(c247,plain,
mult(mult(X3,mult(X2,mult(X2,X))),X2) = mult(mult(X3,X2),mult(X2,mult(X,X2))),
inference(transitivity,[status(thm)],[c3,c246]) ).
cnf(c248,plain,
mult(mult(a,mult(b,mult(b,c))),b) = mult(mult(a,b),mult(b,mult(c,b))),
inference(substitution,[status(thm)],[c247]) ).
cnf(c249,plain,
mult(mult(a,b),mult(b,mult(c,b))) = mult(mult(a,mult(b,mult(b,c))),b),
inference(symmetry,[status(thm)],[c248]) ).
cnf(c250,plain,
$false,
inference(resolution,[status(thm)],[c1,c249]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP697-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n013.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 10:35:51 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.60 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.60
% 0.20/0.60 % SZS status Unsatisfiable
% 0.20/0.60
% 0.20/0.61 % SZS output start CNFRefutation
% See solution above
% 1.66/0.70
% 1.66/0.70 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------