%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP685-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 10:11:43 AM UTC 2026
% Result : Unsatisfiable 1.63s 0.73s
% Output : CNFRefutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 8
% Syntax : Number of clauses : 135 ( 135 unt; 0 nHn; 3 RR)
% Number of literals : 135 ( 134 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 335 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
rd(mult(x6,ld(x7,x8)),ld(x7,x8)) != rd(mult(x6,x8),x8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(c2,axiom,
mult(rd(A,B),B) = rd(mult(A,B),B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
cnf(c3,plain,
mult(rd(mult(X2,X),X),X) = rd(mult(mult(X2,X),X),X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
rd(mult(mult(A2,B2),rd(C,D)),rd(C,D)) = mult(A2,rd(mult(B2,D),D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
cnf(c5,plain,
rd(mult(mult(X2,X),rd(mult(X3,X3),X3)),rd(mult(X3,X3),X3)) = mult(X2,rd(mult(X,X3),X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
mult(X3,rd(mult(X2,X),X)) = rd(mult(mult(X3,X2),rd(mult(X,X),X)),rd(mult(X,X),X)),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,axiom,
rd(mult(A2,A2),A2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
cnf(c8,plain,
rd(mult(X,X),X) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
mult(mult(X3,X2),rd(mult(X,X),X)) = mult(mult(X3,X2),X),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
rd(mult(mult(X3,X2),rd(mult(X,X),X)),rd(mult(X,X),X)) = rd(mult(mult(X3,X2),X),rd(mult(X,X),X)),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
rd(mult(X,X),X) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c12,plain,
rd(mult(mult(X3,X2),X),rd(mult(X,X),X)) = rd(mult(mult(X3,X2),X),X),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
rd(mult(mult(X3,X2),rd(mult(X,X),X)),rd(mult(X,X),X)) = rd(mult(mult(X3,X2),X),X),
inference(transitivity,[status(thm)],[c10,c12]) ).
cnf(c14,plain,
mult(X3,rd(mult(X2,X),X)) = rd(mult(mult(X3,X2),X),X),
inference(transitivity,[status(thm)],[c6,c13]) ).
cnf(c15,plain,
mult(X2,rd(mult(X,X),X)) = rd(mult(mult(X2,X),X),X),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
rd(mult(mult(X2,X),X),X) = mult(X2,rd(mult(X,X),X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
rd(mult(X,X),X) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c18,plain,
mult(X2,rd(mult(X,X),X)) = mult(X2,X),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
rd(mult(mult(X2,X),X),X) = mult(X2,X),
inference(transitivity,[status(thm)],[c16,c18]) ).
cnf(c20,plain,
mult(rd(mult(X2,X),X),X) = mult(X2,X),
inference(transitivity,[status(thm)],[c3,c19]) ).
cnf(c21,plain,
mult(rd(mult(X2,X),X),X) = mult(X2,X),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
mult(X,X2) = mult(rd(mult(X,X2),X2),X2),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
rd(mult(X3,mult(X,X2)),mult(X,X2)) = rd(mult(X3,mult(X,X2)),mult(rd(mult(X,X2),X2),X2)),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
mult(rd(mult(X,X2),X2),X2) = rd(mult(mult(X,X2),X2),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c25,plain,
rd(mult(X3,mult(X,X2)),mult(rd(mult(X,X2),X2),X2)) = rd(mult(X3,mult(X,X2)),rd(mult(mult(X,X2),X2),X2)),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
mult(rd(mult(X,X2),X2),X2) = mult(X,X2),
inference(substitution,[status(thm)],[c20]) ).
cnf(c27,plain,
mult(X,X2) = mult(rd(mult(X,X2),X2),X2),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
mult(X3,mult(X,X2)) = mult(X3,mult(rd(mult(X,X2),X2),X2)),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
rd(mult(X3,mult(X,X2)),rd(mult(mult(X,X2),X2),X2)) = rd(mult(X3,mult(rd(mult(X,X2),X2),X2)),rd(mult(mult(X,X2),X2),X2)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
mult(rd(mult(X,X2),X2),X2) = rd(mult(mult(X,X2),X2),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c31,plain,
mult(X3,mult(rd(mult(X,X2),X2),X2)) = mult(X3,rd(mult(mult(X,X2),X2),X2)),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
rd(mult(X3,mult(rd(mult(X,X2),X2),X2)),rd(mult(mult(X,X2),X2),X2)) = rd(mult(X3,rd(mult(mult(X,X2),X2),X2)),rd(mult(mult(X,X2),X2),X2)),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,axiom,
ld(A2,mult(A2,A2)) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
cnf(c34,plain,
ld(X,mult(X,X)) = X,
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
X = ld(X,mult(X,X)),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
ld(X,X) = ld(X,ld(X,mult(X,X))),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,axiom,
mult(A2,ld(A2,B2)) = ld(A2,mult(A2,B2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
cnf(c38,plain,
mult(X,ld(X,X)) = ld(X,mult(X,X)),
inference(substitution,[status(thm)],[c37]) ).
cnf(c39,plain,
ld(X,mult(X,X)) = mult(X,ld(X,X)),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
ld(X,ld(X,mult(X,X))) = ld(X,mult(X,ld(X,X))),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,axiom,
ld(A2,mult(A2,ld(B2,B2))) = rd(mult(rd(A2,A2),B2),B2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
cnf(c42,plain,
ld(X,mult(X,ld(X,X))) = rd(mult(rd(X,X),X),X),
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
mult(rd(X,X),X) = rd(mult(X,X),X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c44,plain,
rd(mult(rd(X,X),X),X) = rd(rd(mult(X,X),X),X),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
rd(mult(X,X),X) = X,
inference(substitution,[status(thm)],[c7]) ).
cnf(c46,plain,
rd(rd(mult(X,X),X),X) = rd(X,X),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
rd(mult(rd(X,X),X),X) = rd(X,X),
inference(transitivity,[status(thm)],[c44,c46]) ).
cnf(c48,plain,
ld(X,mult(X,ld(X,X))) = rd(X,X),
inference(transitivity,[status(thm)],[c42,c47]) ).
cnf(c49,plain,
ld(X,ld(X,mult(X,X))) = rd(X,X),
inference(transitivity,[status(thm)],[c40,c48]) ).
cnf(c50,plain,
ld(X,X) = rd(X,X),
inference(transitivity,[status(thm)],[c36,c49]) ).
cnf(c51,plain,
rd(X,X) = ld(X,X),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
mult(X,rd(X,X)) = mult(X,ld(X,X)),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
mult(X,ld(X,X)) = ld(X,mult(X,X)),
inference(substitution,[status(thm)],[c37]) ).
cnf(c54,plain,
ld(X,mult(X,X)) = X,
inference(substitution,[status(thm)],[c33]) ).
cnf(c55,plain,
mult(X,ld(X,X)) = X,
inference(transitivity,[status(thm)],[c53,c54]) ).
cnf(c56,plain,
mult(X,rd(X,X)) = X,
inference(transitivity,[status(thm)],[c52,c55]) ).
cnf(c57,plain,
X = mult(X,rd(X,X)),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,plain,
mult(X3,rd(X,X2)) = mult(mult(X3,rd(X3,X3)),rd(X,X2)),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
rd(mult(X3,rd(X,X2)),rd(X,X2)) = rd(mult(mult(X3,rd(X3,X3)),rd(X,X2)),rd(X,X2)),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
rd(mult(mult(X4,X3),rd(X,X2)),rd(X,X2)) = mult(X4,rd(mult(X3,X2),X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c61,plain,
rd(mult(mult(X4,X3),rd(X,X2)),rd(X,X2)) = rd(mult(mult(X4,X3),X2),X2),
inference(transitivity,[status(thm)],[c60,c14]) ).
cnf(c62,plain,
rd(mult(mult(X3,rd(X3,X3)),rd(X,X2)),rd(X,X2)) = rd(mult(mult(X3,rd(X3,X3)),X2),X2),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
mult(mult(X2,rd(X2,X2)),X) = mult(X2,X),
inference(congruence,[status(thm)],[c56]) ).
cnf(c64,plain,
rd(mult(mult(X2,rd(X2,X2)),X),X) = rd(mult(X2,X),X),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
rd(mult(mult(X3,rd(X3,X3)),rd(X,X2)),rd(X,X2)) = rd(mult(X3,X2),X2),
inference(transitivity,[status(thm)],[c62,c64]) ).
cnf(c66,plain,
rd(mult(X3,rd(X,X2)),rd(X,X2)) = rd(mult(X3,X2),X2),
inference(transitivity,[status(thm)],[c59,c65]) ).
cnf(c67,plain,
rd(mult(X3,rd(mult(mult(X,X2),X2),X2)),rd(mult(mult(X,X2),X2),X2)) = rd(mult(X3,X2),X2),
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
rd(mult(X3,rd(X2,X)),rd(X2,X)) = rd(mult(X3,X),X),
inference(substitution,[status(thm)],[c66]) ).
cnf(c69,plain,
rd(mult(X3,X),X) = rd(mult(X3,rd(X2,X)),rd(X2,X)),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
rd(mult(X4,rd(mult(mult(X,X2),X2),X2)),rd(mult(mult(X,X2),X2),X2)) = rd(mult(X4,rd(X3,X2)),rd(X3,X2)),
inference(transitivity,[status(thm)],[c67,c69]) ).
cnf(c71,plain,
rd(mult(X4,mult(rd(mult(X,X2),X2),X2)),rd(mult(mult(X,X2),X2),X2)) = rd(mult(X4,rd(X3,X2)),rd(X3,X2)),
inference(transitivity,[status(thm)],[c32,c70]) ).
cnf(c72,plain,
rd(mult(X4,mult(X,X2)),rd(mult(mult(X,X2),X2),X2)) = rd(mult(X4,rd(X3,X2)),rd(X3,X2)),
inference(transitivity,[status(thm)],[c29,c71]) ).
cnf(c73,plain,
rd(mult(X4,mult(X,X2)),mult(rd(mult(X,X2),X2),X2)) = rd(mult(X4,rd(X3,X2)),rd(X3,X2)),
inference(transitivity,[status(thm)],[c25,c72]) ).
cnf(c74,plain,
rd(mult(X4,mult(X,X2)),mult(X,X2)) = rd(mult(X4,rd(X3,X2)),rd(X3,X2)),
inference(transitivity,[status(thm)],[c23,c73]) ).
cnf(c75,plain,
rd(mult(X3,mult(X2,X)),mult(X2,X)) = rd(mult(X3,rd(X4,X)),rd(X4,X)),
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,plain,
rd(mult(X4,mult(X3,X2)),mult(X3,X2)) = rd(mult(X4,rd(X,X2)),rd(X,X2)),
inference(substitution,[status(thm)],[c74]) ).
cnf(c77,plain,
rd(mult(X3,mult(X2,X)),mult(X2,X)) = rd(mult(X3,X),X),
inference(transitivity,[status(thm)],[c76,c66]) ).
cnf(c78,plain,
rd(mult(X3,mult(ld(X,X4),X2)),mult(ld(X,X4),X2)) = rd(mult(X3,X2),X2),
inference(substitution,[status(thm)],[c77]) ).
cnf(c79,plain,
rd(mult(X4,X3),X3) = rd(mult(X4,mult(ld(X2,X),X3)),mult(ld(X2,X),X3)),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
X = mult(X,rd(X,X)),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c81,plain,
mult(ld(X3,X),X2) = mult(ld(X3,X),mult(X2,rd(X2,X2))),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
ld(ld(X3,X),mult(ld(X3,X),X2)) = ld(ld(X3,X),mult(ld(X3,X),mult(X2,rd(X2,X2)))),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,axiom,
ld(ld(A2,B2),mult(ld(A2,B2),mult(C2,D2))) = mult(ld(A2,mult(A2,C2)),D2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
cnf(c84,plain,
ld(ld(X4,X),mult(ld(X4,X),mult(X3,X2))) = mult(ld(X4,mult(X4,X3)),X2),
inference(substitution,[status(thm)],[c83]) ).
cnf(c85,plain,
ld(ld(X3,mult(X3,X3)),mult(ld(X3,mult(X3,X3)),mult(X2,X))) = mult(ld(X3,mult(X3,X2)),X),
inference(substitution,[status(thm)],[c83]) ).
cnf(c86,plain,
mult(ld(X3,mult(X3,X2)),X) = ld(ld(X3,mult(X3,X3)),mult(ld(X3,mult(X3,X3)),mult(X2,X))),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c87,plain,
ld(X,mult(X,X)) = X,
inference(substitution,[status(thm)],[c33]) ).
cnf(c88,plain,
ld(ld(X3,mult(X3,X3)),mult(ld(X3,mult(X3,X3)),mult(X2,X))) = ld(X3,mult(ld(X3,mult(X3,X3)),mult(X2,X))),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
ld(X,mult(X,X)) = X,
inference(substitution,[status(thm)],[c33]) ).
cnf(c90,plain,
mult(ld(X3,mult(X3,X3)),mult(X2,X)) = mult(X3,mult(X2,X)),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
ld(X3,mult(ld(X3,mult(X3,X3)),mult(X2,X))) = ld(X3,mult(X3,mult(X2,X))),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
ld(ld(X3,mult(X3,X3)),mult(ld(X3,mult(X3,X3)),mult(X2,X))) = ld(X3,mult(X3,mult(X2,X))),
inference(transitivity,[status(thm)],[c88,c91]) ).
cnf(c93,plain,
mult(ld(X3,mult(X3,X2)),X) = ld(X3,mult(X3,mult(X2,X))),
inference(transitivity,[status(thm)],[c86,c92]) ).
cnf(c94,plain,
ld(ld(X4,X),mult(ld(X4,X),mult(X3,X2))) = ld(X4,mult(X4,mult(X3,X2))),
inference(transitivity,[status(thm)],[c84,c93]) ).
cnf(c95,plain,
ld(ld(X3,X),mult(ld(X3,X),mult(X2,rd(X2,X2)))) = ld(X3,mult(X3,mult(X2,rd(X2,X2)))),
inference(substitution,[status(thm)],[c94]) ).
cnf(c96,plain,
mult(X2,mult(X,rd(X,X))) = mult(X2,X),
inference(congruence,[status(thm)],[c56]) ).
cnf(c97,plain,
ld(X2,mult(X2,mult(X,rd(X,X)))) = ld(X2,mult(X2,X)),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
ld(ld(X3,X),mult(ld(X3,X),mult(X2,rd(X2,X2)))) = ld(X3,mult(X3,X2)),
inference(transitivity,[status(thm)],[c95,c97]) ).
cnf(c99,plain,
ld(ld(X3,X),mult(ld(X3,X),X2)) = ld(X3,mult(X3,X2)),
inference(transitivity,[status(thm)],[c82,c98]) ).
cnf(c100,plain,
ld(ld(X3,X2),mult(ld(X3,X2),X)) = ld(X3,mult(X3,X)),
inference(substitution,[status(thm)],[c99]) ).
cnf(c101,plain,
mult(X2,ld(X2,X)) = ld(X2,mult(X2,X)),
inference(substitution,[status(thm)],[c37]) ).
cnf(c102,plain,
ld(X2,mult(X2,X)) = mult(X2,ld(X2,X)),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
ld(ld(X3,X2),mult(ld(X3,X2),X)) = mult(X3,ld(X3,X)),
inference(transitivity,[status(thm)],[c100,c102]) ).
cnf(c104,plain,
mult(X3,ld(X3,X)) = ld(ld(X3,X2),mult(ld(X3,X2),X)),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,plain,
mult(ld(X3,X2),mult(X3,ld(X3,X))) = mult(ld(X3,X2),ld(ld(X3,X2),mult(ld(X3,X2),X))),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
mult(ld(X3,X2),ld(ld(X3,X2),mult(ld(X3,X2),X))) = ld(ld(X3,X2),mult(ld(X3,X2),mult(ld(X3,X2),X))),
inference(substitution,[status(thm)],[c37]) ).
cnf(c107,plain,
mult(ld(X2,mult(X2,X2)),X) = ld(X2,mult(X2,mult(X2,X))),
inference(substitution,[status(thm)],[c93]) ).
cnf(c108,plain,
ld(X2,mult(X2,mult(X2,X))) = mult(ld(X2,mult(X2,X2)),X),
inference(symmetry,[status(thm)],[c107]) ).
cnf(c109,plain,
ld(X,mult(X,X)) = X,
inference(substitution,[status(thm)],[c33]) ).
cnf(c110,plain,
mult(ld(X2,mult(X2,X2)),X) = mult(X2,X),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
ld(X2,mult(X2,mult(X2,X))) = mult(X2,X),
inference(transitivity,[status(thm)],[c108,c110]) ).
cnf(c112,plain,
ld(ld(X3,X2),mult(ld(X3,X2),mult(ld(X3,X2),X))) = mult(ld(X3,X2),X),
inference(substitution,[status(thm)],[c111]) ).
cnf(c113,plain,
mult(ld(X3,X2),ld(ld(X3,X2),mult(ld(X3,X2),X))) = mult(ld(X3,X2),X),
inference(transitivity,[status(thm)],[c106,c112]) ).
cnf(c114,plain,
mult(ld(X3,X2),mult(X3,ld(X3,X))) = mult(ld(X3,X2),X),
inference(transitivity,[status(thm)],[c105,c113]) ).
cnf(c115,plain,
mult(ld(X2,X),mult(X2,ld(X2,X3))) = mult(ld(X2,X),X3),
inference(substitution,[status(thm)],[c114]) ).
cnf(c116,plain,
mult(ld(X2,X),X3) = mult(ld(X2,X),mult(X2,ld(X2,X3))),
inference(symmetry,[status(thm)],[c115]) ).
cnf(c117,plain,
rd(mult(X4,mult(ld(X2,X),X3)),mult(ld(X2,X),X3)) = rd(mult(X4,mult(ld(X2,X),X3)),mult(ld(X2,X),mult(X2,ld(X2,X3)))),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
mult(ld(X2,X),mult(X2,ld(X2,X3))) = mult(ld(X2,X),X3),
inference(substitution,[status(thm)],[c114]) ).
cnf(c119,plain,
mult(ld(X2,X),X3) = mult(ld(X2,X),mult(X2,ld(X2,X3))),
inference(symmetry,[status(thm)],[c118]) ).
cnf(c120,plain,
mult(X4,mult(ld(X2,X),X3)) = mult(X4,mult(ld(X2,X),mult(X2,ld(X2,X3)))),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
rd(mult(X4,mult(ld(X2,X),X3)),mult(ld(X2,X),mult(X2,ld(X2,X3)))) = rd(mult(X4,mult(ld(X2,X),mult(X2,ld(X2,X3)))),mult(ld(X2,X),mult(X2,ld(X2,X3)))),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
rd(mult(X4,mult(ld(X2,X),mult(X2,ld(X2,X3)))),mult(ld(X2,X),mult(X2,ld(X2,X3)))) = rd(mult(X4,mult(X2,ld(X2,X3))),mult(X2,ld(X2,X3))),
inference(substitution,[status(thm)],[c77]) ).
cnf(c123,plain,
rd(mult(X3,mult(X,ld(X,X2))),mult(X,ld(X,X2))) = rd(mult(X3,ld(X,X2)),ld(X,X2)),
inference(substitution,[status(thm)],[c77]) ).
cnf(c124,plain,
rd(mult(X4,mult(ld(X2,X),mult(X2,ld(X2,X3)))),mult(ld(X2,X),mult(X2,ld(X2,X3)))) = rd(mult(X4,ld(X2,X3)),ld(X2,X3)),
inference(transitivity,[status(thm)],[c122,c123]) ).
cnf(c125,plain,
rd(mult(X4,mult(ld(X2,X),X3)),mult(ld(X2,X),mult(X2,ld(X2,X3)))) = rd(mult(X4,ld(X2,X3)),ld(X2,X3)),
inference(transitivity,[status(thm)],[c121,c124]) ).
cnf(c126,plain,
rd(mult(X4,mult(ld(X2,X),X3)),mult(ld(X2,X),X3)) = rd(mult(X4,ld(X2,X3)),ld(X2,X3)),
inference(transitivity,[status(thm)],[c117,c125]) ).
cnf(c127,plain,
rd(mult(X3,X2),X2) = rd(mult(X3,ld(X,X2)),ld(X,X2)),
inference(transitivity,[status(thm)],[c79,c126]) ).
cnf(c128,plain,
rd(mult(X4,rd(X,X3)),rd(X,X3)) = rd(mult(X4,ld(X2,X3)),ld(X2,X3)),
inference(transitivity,[status(thm)],[c66,c127]) ).
cnf(c129,plain,
rd(mult(X4,mult(X3,X2)),mult(X3,X2)) = rd(mult(X4,ld(X,X2)),ld(X,X2)),
inference(transitivity,[status(thm)],[c75,c128]) ).
cnf(c130,plain,
rd(mult(X4,mult(X,X3)),mult(X,X3)) = rd(mult(X4,ld(X2,X3)),ld(X2,X3)),
inference(substitution,[status(thm)],[c129]) ).
cnf(c131,plain,
rd(mult(X4,ld(X2,X3)),ld(X2,X3)) = rd(mult(X4,mult(X,X3)),mult(X,X3)),
inference(symmetry,[status(thm)],[c130]) ).
cnf(c132,plain,
rd(mult(X3,mult(X,X2)),mult(X,X2)) = rd(mult(X3,X2),X2),
inference(substitution,[status(thm)],[c77]) ).
cnf(c133,plain,
rd(mult(X3,ld(X,X2)),ld(X,X2)) = rd(mult(X3,X2),X2),
inference(transitivity,[status(thm)],[c131,c132]) ).
cnf(c134,plain,
rd(mult(x6,ld(x7,x8)),ld(x7,x8)) = rd(mult(x6,x8),x8),
inference(substitution,[status(thm)],[c133]) ).
cnf(c135,plain,
$false,
inference(resolution,[status(thm)],[c1,c134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP685-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n011.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sun Sep 27 10:35:59 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.63/0.73 Command-line arguments: --flatten-regeneralise
% 1.63/0.73
% 1.63/0.73 % SZS status Unsatisfiable
% 1.63/0.73
% 1.63/0.76 % SZS output start CNFRefutation
% See solution above
% 2.41/0.88
% 2.41/0.88 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------