%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP659-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 10:11:36 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.48s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 6
% Syntax : Number of clauses : 139 ( 139 unt; 0 nHn; 2 RR)
% Number of literals : 139 ( 138 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 : 6 ( 6 usr; 0 con; 1-2 aty)
% Number of variables : 278 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
tuple(mult(X0,x1(X0)),mult(x1_2(X0),X0)) != tuple(x1(X0),x1_2(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(c2,axiom,
rd(mult(A,B),B) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
cnf(c3,plain,
rd(mult(ld(ld(X,X),ld(X,X)),X),X) = ld(ld(X,X),ld(X,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
ld(ld(X,X),ld(X,X)) = rd(mult(ld(ld(X,X),ld(X,X)),X),X),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
ld(A2,mult(A2,B2)) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
cnf(c6,plain,
ld(X2,mult(X2,mult(ld(X,X),X))) = mult(ld(X,X),X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
mult(ld(X2,X2),X2) = ld(X,mult(X,mult(ld(X2,X2),X2))),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,axiom,
mult(mult(A2,mult(B2,C)),B2) = mult(mult(A2,B2),mult(C,B2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
cnf(c9,plain,
mult(mult(X2,mult(X,ld(X,X3))),X) = mult(mult(X2,X),mult(ld(X,X3),X)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
mult(mult(X3,X2),mult(ld(X2,X),X2)) = mult(mult(X3,mult(X2,ld(X2,X))),X2),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,axiom,
mult(A2,ld(A2,B2)) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
cnf(c12,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
mult(X3,mult(X2,ld(X2,X))) = mult(X3,X),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
mult(mult(X3,mult(X2,ld(X2,X))),X2) = mult(mult(X3,X),X2),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
mult(mult(X3,X2),mult(ld(X2,X),X2)) = mult(mult(X3,X),X2),
inference(transitivity,[status(thm)],[c10,c14]) ).
cnf(c16,plain,
mult(mult(rd(X3,X2),X2),mult(ld(X2,X),X2)) = mult(mult(rd(X3,X2),X),X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
mult(mult(rd(X3,X2),X),X2) = mult(mult(rd(X3,X2),X2),mult(ld(X2,X),X2)),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,axiom,
mult(rd(A2,B2),B2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
cnf(c19,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
mult(mult(rd(X3,X2),X2),mult(ld(X2,X),X2)) = mult(X3,mult(ld(X2,X),X2)),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
mult(mult(rd(X3,X2),X),X2) = mult(X3,mult(ld(X2,X),X2)),
inference(transitivity,[status(thm)],[c17,c20]) ).
cnf(c22,plain,
mult(mult(rd(X2,X),X),X) = mult(X2,mult(ld(X,X),X)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
mult(X2,mult(ld(X,X),X)) = mult(mult(rd(X2,X),X),X),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c18]) ).
cnf(c25,plain,
mult(mult(rd(X2,X),X),X) = mult(X2,X),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
mult(X2,mult(ld(X,X),X)) = mult(X2,X),
inference(transitivity,[status(thm)],[c23,c25]) ).
cnf(c27,plain,
mult(X,mult(ld(X2,X2),X2)) = mult(X,X2),
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
ld(X,mult(X,mult(ld(X2,X2),X2))) = ld(X,mult(X,X2)),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
ld(X,mult(X,X2)) = X2,
inference(substitution,[status(thm)],[c5]) ).
cnf(c30,plain,
ld(X,mult(X,mult(ld(X2,X2),X2))) = X2,
inference(transitivity,[status(thm)],[c28,c29]) ).
cnf(c31,plain,
mult(ld(X,X),X) = X,
inference(transitivity,[status(thm)],[c7,c30]) ).
cnf(c32,plain,
X = mult(ld(X,X),X),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
rd(X,X) = rd(mult(ld(X,X),X),X),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
rd(mult(ld(X,X),X),X) = ld(X,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c35,plain,
rd(X,X) = ld(X,X),
inference(transitivity,[status(thm)],[c33,c34]) ).
cnf(c36,plain,
rd(ld(X,X),ld(X,X)) = ld(ld(X,X),ld(X,X)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
ld(ld(X,X),ld(X,X)) = rd(ld(X,X),ld(X,X)),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
mult(ld(ld(X,X),ld(X,X)),X) = mult(rd(ld(X,X),ld(X,X)),X),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
mult(rd(X2,ld(X,X)),mult(ld(X,X),X)) = mult(rd(X2,ld(X,X)),X),
inference(substitution,[status(thm)],[c26]) ).
cnf(c40,plain,
mult(rd(X2,ld(X,X)),X) = mult(rd(X2,ld(X,X)),mult(ld(X,X),X)),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
mult(mult(X3,mult(X2,X)),X2) = mult(mult(X3,X2),mult(X,X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c42,plain,
mult(mult(X3,X2),mult(X,X2)) = mult(mult(X3,mult(X2,X)),X2),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
rd(mult(mult(X3,X2),mult(X,X2)),X2) = rd(mult(mult(X3,mult(X2,X)),X2),X2),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
rd(mult(mult(X3,mult(X2,X)),X2),X2) = mult(X3,mult(X2,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c45,plain,
rd(mult(mult(X3,X2),mult(X,X2)),X2) = mult(X3,mult(X2,X)),
inference(transitivity,[status(thm)],[c43,c44]) ).
cnf(c46,plain,
rd(mult(mult(rd(X3,X2),X2),mult(X,X2)),X2) = mult(rd(X3,X2),mult(X2,X)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
mult(rd(X3,X2),mult(X2,X)) = rd(mult(mult(rd(X3,X2),X2),mult(X,X2)),X2),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c18]) ).
cnf(c49,plain,
mult(mult(rd(X3,X2),X2),mult(X,X2)) = mult(X3,mult(X,X2)),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
rd(mult(mult(rd(X3,X2),X2),mult(X,X2)),X2) = rd(mult(X3,mult(X,X2)),X2),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
mult(rd(X3,X2),mult(X2,X)) = rd(mult(X3,mult(X,X2)),X2),
inference(transitivity,[status(thm)],[c47,c50]) ).
cnf(c52,plain,
mult(rd(X2,ld(X,X)),mult(ld(X,X),X)) = rd(mult(X2,mult(X,ld(X,X))),ld(X,X)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
mult(X,ld(X,X)) = X,
inference(substitution,[status(thm)],[c11]) ).
cnf(c54,plain,
mult(X2,mult(X,ld(X,X))) = mult(X2,X),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
rd(mult(X2,mult(X,ld(X,X))),ld(X,X)) = rd(mult(X2,X),ld(X,X)),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
mult(rd(X2,ld(X,X)),mult(ld(X,X),X)) = rd(mult(X2,X),ld(X,X)),
inference(transitivity,[status(thm)],[c52,c55]) ).
cnf(c57,plain,
mult(rd(X2,ld(X,X)),X) = rd(mult(X2,X),ld(X,X)),
inference(transitivity,[status(thm)],[c40,c56]) ).
cnf(c58,plain,
mult(rd(ld(X,X),ld(X,X)),X) = rd(mult(ld(X,X),X),ld(X,X)),
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
rd(mult(ld(X,X),X),ld(X,X)) = rd(X,ld(X,X)),
inference(congruence,[status(thm)],[c31]) ).
cnf(c60,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c11]) ).
cnf(c61,plain,
X2 = mult(X,ld(X,X2)),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
rd(X2,ld(X,X2)) = rd(mult(X,ld(X,X2)),ld(X,X2)),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
rd(mult(X,ld(X,X2)),ld(X,X2)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c64,plain,
rd(X2,ld(X,X2)) = X,
inference(transitivity,[status(thm)],[c62,c63]) ).
cnf(c65,plain,
rd(X,ld(X,X)) = X,
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,plain,
rd(mult(ld(X,X),X),ld(X,X)) = X,
inference(transitivity,[status(thm)],[c59,c65]) ).
cnf(c67,plain,
mult(rd(ld(X,X),ld(X,X)),X) = X,
inference(transitivity,[status(thm)],[c58,c66]) ).
cnf(c68,plain,
mult(ld(ld(X,X),ld(X,X)),X) = X,
inference(transitivity,[status(thm)],[c38,c67]) ).
cnf(c69,plain,
rd(mult(ld(ld(X,X),ld(X,X)),X),X) = rd(X,X),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
rd(mult(ld(ld(X,X),ld(X,X)),X),X) = ld(X,X),
inference(transitivity,[status(thm)],[c69,c35]) ).
cnf(c71,plain,
ld(ld(X,X),ld(X,X)) = ld(X,X),
inference(transitivity,[status(thm)],[c4,c70]) ).
cnf(c72,plain,
ld(X,X) = ld(ld(X,X),ld(X,X)),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
mult(ld(X2,X2),X) = mult(ld(ld(X2,X2),ld(X2,X2)),X),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c18]) ).
cnf(c75,plain,
X = mult(rd(X,X2),X2),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
ld(X,X) = ld(X,mult(rd(X,X2),X2)),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
mult(X2,ld(X,X)) = mult(X2,ld(X,mult(rd(X,X2),X2))),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c18]) ).
cnf(c79,plain,
X = mult(rd(X,X2),X2),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
ld(X,mult(rd(X,X2),X2)) = ld(mult(rd(X,X2),X2),mult(rd(X,X2),X2)),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
mult(X2,ld(X,mult(rd(X,X2),X2))) = mult(X2,ld(mult(rd(X,X2),X2),mult(rd(X,X2),X2))),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
mult(mult(X3,X),X2) = mult(mult(X3,X2),mult(ld(X2,X),X2)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c83,plain,
ld(mult(X3,X2),mult(mult(X3,X),X2)) = ld(mult(X3,X2),mult(mult(X3,X2),mult(ld(X2,X),X2))),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
ld(mult(X3,X2),mult(mult(X3,X2),mult(ld(X2,X),X2))) = mult(ld(X2,X),X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c85,plain,
ld(mult(X3,X2),mult(mult(X3,X),X2)) = mult(ld(X2,X),X2),
inference(transitivity,[status(thm)],[c83,c84]) ).
cnf(c86,plain,
ld(mult(X2,X3),mult(mult(X2,ld(X2,X)),X3)) = mult(ld(X3,ld(X2,X)),X3),
inference(substitution,[status(thm)],[c85]) ).
cnf(c87,plain,
mult(ld(X3,ld(X2,X)),X3) = ld(mult(X2,X3),mult(mult(X2,ld(X2,X)),X3)),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c88,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c11]) ).
cnf(c89,plain,
mult(mult(X2,ld(X2,X)),X3) = mult(X,X3),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
ld(mult(X2,X3),mult(mult(X2,ld(X2,X)),X3)) = ld(mult(X2,X3),mult(X,X3)),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
mult(ld(X3,ld(X2,X)),X3) = ld(mult(X2,X3),mult(X,X3)),
inference(transitivity,[status(thm)],[c87,c90]) ).
cnf(c92,plain,
mult(ld(X2,ld(X,X)),X2) = ld(mult(X,X2),mult(X,X2)),
inference(substitution,[status(thm)],[c91]) ).
cnf(c93,plain,
ld(mult(X,X2),mult(X,X2)) = mult(ld(X2,ld(X,X)),X2),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
mult(X2,ld(mult(X,X2),mult(X,X2))) = mult(X2,mult(ld(X2,ld(X,X)),X2)),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c11]) ).
cnf(c96,plain,
X2 = mult(X,ld(X,X2)),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c97,plain,
mult(X3,mult(X2,ld(X,X3))) = mult(mult(X,ld(X,X3)),mult(X2,ld(X,X3))),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
rd(mult(X3,mult(X2,ld(X,X3))),ld(X,X3)) = rd(mult(mult(X,ld(X,X3)),mult(X2,ld(X,X3))),ld(X,X3)),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
rd(mult(mult(X,ld(X,X3)),mult(X2,ld(X,X3))),ld(X,X3)) = mult(X,mult(ld(X,X3),X2)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c100,plain,
rd(mult(X3,mult(X2,ld(X,X3))),ld(X,X3)) = mult(X,mult(ld(X,X3),X2)),
inference(transitivity,[status(thm)],[c98,c99]) ).
cnf(c101,plain,
rd(mult(X,mult(X2,ld(X2,X))),ld(X2,X)) = mult(X2,mult(ld(X2,X),X2)),
inference(substitution,[status(thm)],[c100]) ).
cnf(c102,plain,
mult(X2,mult(ld(X2,X),X2)) = rd(mult(X,mult(X2,ld(X2,X))),ld(X2,X)),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c11]) ).
cnf(c104,plain,
mult(X,mult(X2,ld(X2,X))) = mult(X,X),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
rd(mult(X,mult(X2,ld(X2,X))),ld(X2,X)) = rd(mult(X,X),ld(X2,X)),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
mult(X2,mult(ld(X2,X),X2)) = rd(mult(X,X),ld(X2,X)),
inference(transitivity,[status(thm)],[c102,c105]) ).
cnf(c107,plain,
mult(X2,mult(ld(X2,ld(X,X)),X2)) = rd(mult(ld(X,X),ld(X,X)),ld(X2,ld(X,X))),
inference(substitution,[status(thm)],[c106]) ).
cnf(c108,plain,
ld(X,X) = ld(ld(X,X),ld(X,X)),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c109,plain,
mult(ld(X,X),ld(X,X)) = mult(ld(X,X),ld(ld(X,X),ld(X,X))),
inference(congruence,[status(thm)],[c108]) ).
cnf(c110,plain,
mult(ld(X,X),ld(ld(X,X),ld(X,X))) = ld(X,X),
inference(substitution,[status(thm)],[c11]) ).
cnf(c111,plain,
mult(ld(X,X),ld(X,X)) = ld(X,X),
inference(transitivity,[status(thm)],[c109,c110]) ).
cnf(c112,plain,
rd(mult(ld(X,X),ld(X,X)),ld(X2,ld(X,X))) = rd(ld(X,X),ld(X2,ld(X,X))),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
rd(ld(X,X),ld(X2,ld(X,X))) = X2,
inference(substitution,[status(thm)],[c64]) ).
cnf(c114,plain,
rd(mult(ld(X,X),ld(X,X)),ld(X2,ld(X,X))) = X2,
inference(transitivity,[status(thm)],[c112,c113]) ).
cnf(c115,plain,
mult(X2,mult(ld(X2,ld(X,X)),X2)) = X2,
inference(transitivity,[status(thm)],[c107,c114]) ).
cnf(c116,plain,
mult(X2,ld(mult(X,X2),mult(X,X2))) = X2,
inference(transitivity,[status(thm)],[c94,c115]) ).
cnf(c117,plain,
mult(X2,ld(mult(rd(X,X2),X2),mult(rd(X,X2),X2))) = X2,
inference(substitution,[status(thm)],[c116]) ).
cnf(c118,plain,
mult(X2,ld(X,mult(rd(X,X2),X2))) = X2,
inference(transitivity,[status(thm)],[c81,c117]) ).
cnf(c119,plain,
mult(X2,ld(X,X)) = X2,
inference(transitivity,[status(thm)],[c77,c118]) ).
cnf(c120,plain,
mult(mult(ld(ld(X2,X2),ld(X2,X2)),X),ld(X2,X2)) = mult(ld(ld(X2,X2),ld(X2,X2)),X),
inference(substitution,[status(thm)],[c119]) ).
cnf(c121,plain,
mult(ld(ld(X2,X2),ld(X2,X2)),X) = mult(mult(ld(ld(X2,X2),ld(X2,X2)),X),ld(X2,X2)),
inference(symmetry,[status(thm)],[c120]) ).
cnf(c122,plain,
mult(mult(ld(X2,X2),X2),mult(ld(X2,X),X2)) = mult(mult(ld(X2,X2),X),X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c123,plain,
mult(mult(ld(X2,X2),X),X2) = mult(mult(ld(X2,X2),X2),mult(ld(X2,X),X2)),
inference(symmetry,[status(thm)],[c122]) ).
cnf(c124,plain,
mult(mult(ld(X2,X2),X2),mult(ld(X2,X),X2)) = mult(X2,mult(ld(X2,X),X2)),
inference(congruence,[status(thm)],[c31]) ).
cnf(c125,plain,
mult(mult(ld(X2,X2),X),X2) = mult(X2,mult(ld(X2,X),X2)),
inference(transitivity,[status(thm)],[c123,c124]) ).
cnf(c126,plain,
mult(mult(ld(ld(X2,X2),ld(X2,X2)),X),ld(X2,X2)) = mult(ld(X2,X2),mult(ld(ld(X2,X2),X),ld(X2,X2))),
inference(substitution,[status(thm)],[c125]) ).
cnf(c127,plain,
mult(ld(ld(X2,X2),X),ld(X2,X2)) = ld(ld(X2,X2),X),
inference(substitution,[status(thm)],[c119]) ).
cnf(c128,plain,
mult(ld(X2,X2),mult(ld(ld(X2,X2),X),ld(X2,X2))) = mult(ld(X2,X2),ld(ld(X2,X2),X)),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
mult(ld(X2,X2),ld(ld(X2,X2),X)) = X,
inference(substitution,[status(thm)],[c11]) ).
cnf(c130,plain,
mult(ld(X2,X2),mult(ld(ld(X2,X2),X),ld(X2,X2))) = X,
inference(transitivity,[status(thm)],[c128,c129]) ).
cnf(c131,plain,
mult(mult(ld(ld(X2,X2),ld(X2,X2)),X),ld(X2,X2)) = X,
inference(transitivity,[status(thm)],[c126,c130]) ).
cnf(c132,plain,
mult(ld(ld(X2,X2),ld(X2,X2)),X) = X,
inference(transitivity,[status(thm)],[c121,c131]) ).
cnf(c133,plain,
mult(ld(X2,X2),X) = X,
inference(transitivity,[status(thm)],[c73,c132]) ).
cnf(c134,plain,
mult(ld(X,X),x1(ld(X,X))) = x1(ld(X,X)),
inference(substitution,[status(thm)],[c133]) ).
cnf(c135,plain,
tuple(mult(ld(X,X),x1(ld(X,X))),mult(x1_2(ld(X,X)),ld(X,X))) = tuple(x1(ld(X,X)),mult(x1_2(ld(X,X)),ld(X,X))),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
mult(x1_2(ld(X,X)),ld(X,X)) = x1_2(ld(X,X)),
inference(substitution,[status(thm)],[c119]) ).
cnf(c137,plain,
tuple(x1(ld(X,X)),mult(x1_2(ld(X,X)),ld(X,X))) = tuple(x1(ld(X,X)),x1_2(ld(X,X))),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
tuple(mult(ld(X,X),x1(ld(X,X))),mult(x1_2(ld(X,X)),ld(X,X))) = tuple(x1(ld(X,X)),x1_2(ld(X,X))),
inference(transitivity,[status(thm)],[c135,c137]) ).
cnf(c139,plain,
$false,
inference(resolution,[status(thm)],[c1,c138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP659-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 10:32:45 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.48 Command-line arguments: --flatten --complete-subsets
% 0.11/0.48
% 0.11/0.48 % SZS status Unsatisfiable
% 0.11/0.48
% 0.11/0.49 % SZS output start CNFRefutation
% See solution above
% 0.60/0.56
% 0.60/0.56 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------