%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP660-14 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 10:11:37 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.57s
% Output : CNFRefutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 59
% Number of leaves : 6
% Syntax : Number of clauses : 216 ( 216 unt; 0 nHn; 3 RR)
% Number of literals : 216 ( 215 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 418 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
mult(ld(x1,x1),x0) != x0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
cnf(c2,axiom,
mult(mult(mult(A,B),C),A) = mult(A,mult(B,mult(C,A))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
cnf(c3,plain,
mult(mult(mult(X3,ld(X3,X2)),X),X3) = mult(X3,mult(ld(X3,X2),mult(X,X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
mult(X3,mult(ld(X3,X2),mult(X,X3))) = mult(mult(mult(X3,ld(X3,X2)),X),X3),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
mult(A2,ld(A2,B2)) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
cnf(c6,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
mult(mult(X3,ld(X3,X2)),X) = mult(X2,X),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
mult(mult(mult(X3,ld(X3,X2)),X),X3) = mult(mult(X2,X),X3),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
mult(X3,mult(ld(X3,X2),mult(X,X3))) = mult(mult(X2,X),X3),
inference(transitivity,[status(thm)],[c4,c8]) ).
cnf(c10,plain,
mult(mult(X2,X),X3) = mult(X3,mult(ld(X3,X2),mult(X,X3))),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
ld(X3,mult(mult(X2,X),X3)) = ld(X3,mult(X3,mult(ld(X3,X2),mult(X,X3)))),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,axiom,
ld(A2,mult(A2,B2)) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
cnf(c13,plain,
ld(X3,mult(X3,mult(ld(X3,X2),mult(X,X3)))) = mult(ld(X3,X2),mult(X,X3)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
ld(X3,mult(mult(X2,X),X3)) = mult(ld(X3,X2),mult(X,X3)),
inference(transitivity,[status(thm)],[c11,c13]) ).
cnf(c15,plain,
ld(X2,mult(mult(X,ld(X,X2)),X2)) = mult(ld(X2,X),mult(ld(X,X2),X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
mult(ld(X2,X),mult(ld(X,X2),X2)) = ld(X2,mult(mult(X,ld(X,X2)),X2)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c5]) ).
cnf(c18,plain,
mult(mult(X,ld(X,X2)),X2) = mult(X2,X2),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
ld(X2,mult(mult(X,ld(X,X2)),X2)) = ld(X2,mult(X2,X2)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
ld(X,mult(X,X)) = X,
inference(substitution,[status(thm)],[c12]) ).
cnf(c21,plain,
ld(X2,mult(mult(X,ld(X,X2)),X2)) = X2,
inference(transitivity,[status(thm)],[c19,c20]) ).
cnf(c22,plain,
mult(ld(X2,X),mult(ld(X,X2),X2)) = X2,
inference(transitivity,[status(thm)],[c16,c21]) ).
cnf(c23,plain,
X2 = mult(ld(X2,X),mult(ld(X,X2),X2)),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
ld(ld(X2,X),X2) = ld(ld(X2,X),mult(ld(X2,X),mult(ld(X,X2),X2))),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
ld(ld(X2,X),mult(ld(X2,X),mult(ld(X,X2),X2))) = mult(ld(X,X2),X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c26,plain,
ld(ld(X2,X),X2) = mult(ld(X,X2),X2),
inference(transitivity,[status(thm)],[c24,c25]) ).
cnf(c27,plain,
ld(ld(X,X),X) = mult(ld(X,X),X),
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
mult(ld(X,X),X) = ld(ld(X,X),X),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
mult(mult(ld(X,X),X),mult(ld(X,X),ld(X,X))) = mult(ld(ld(X,X),X),mult(ld(X,X),ld(X,X))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
ld(X3,mult(mult(X2,ld(X2,X)),X3)) = mult(ld(X3,X2),mult(ld(X2,X),X3)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c31,plain,
mult(ld(X3,X2),mult(ld(X2,X),X3)) = ld(X3,mult(mult(X2,ld(X2,X)),X3)),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c33,plain,
mult(mult(X2,ld(X2,X)),X3) = mult(X,X3),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
ld(X3,mult(mult(X2,ld(X2,X)),X3)) = ld(X3,mult(X,X3)),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
mult(ld(X3,X2),mult(ld(X2,X),X3)) = ld(X3,mult(X,X3)),
inference(transitivity,[status(thm)],[c31,c34]) ).
cnf(c36,plain,
mult(ld(ld(X,X),X),mult(ld(X,X),ld(X,X))) = ld(ld(X,X),mult(X,ld(X,X))),
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
mult(X,ld(X,X)) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c38,plain,
ld(ld(X,X),mult(X,ld(X,X))) = ld(ld(X,X),X),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
ld(ld(X,X),X) = mult(ld(X,X),X),
inference(substitution,[status(thm)],[c26]) ).
cnf(c40,plain,
ld(ld(X,X),mult(X,ld(X,X))) = mult(ld(X,X),X),
inference(transitivity,[status(thm)],[c38,c39]) ).
cnf(c41,plain,
mult(ld(ld(X,X),X),mult(ld(X,X),ld(X,X))) = mult(ld(X,X),X),
inference(transitivity,[status(thm)],[c36,c40]) ).
cnf(c42,plain,
mult(mult(ld(X,X),X),mult(ld(X,X),ld(X,X))) = mult(ld(X,X),X),
inference(transitivity,[status(thm)],[c29,c41]) ).
cnf(c43,plain,
mult(ld(X,X),X) = mult(mult(ld(X,X),X),mult(ld(X,X),ld(X,X))),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
ld(mult(ld(X,X),X),mult(ld(X,X),X)) = ld(mult(ld(X,X),X),mult(mult(ld(X,X),X),mult(ld(X,X),ld(X,X)))),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
ld(mult(ld(X,X),X),mult(mult(ld(X,X),X),mult(ld(X,X),ld(X,X)))) = mult(ld(X,X),ld(X,X)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c46,plain,
ld(mult(ld(X,X),X),mult(ld(X,X),X)) = mult(ld(X,X),ld(X,X)),
inference(transitivity,[status(thm)],[c44,c45]) ).
cnf(c47,plain,
mult(ld(X,X),ld(X,X)) = ld(mult(ld(X,X),X),mult(ld(X,X),X)),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
mult(X,ld(X,X2)) = X2,
inference(substitution,[status(thm)],[c5]) ).
cnf(c49,plain,
X2 = mult(X,ld(X,X2)),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
rd(X2,ld(X,X2)) = rd(mult(X,ld(X,X2)),ld(X,X2)),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,axiom,
rd(mult(A2,B2),B2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
cnf(c52,plain,
rd(mult(X,ld(X,X2)),ld(X,X2)) = X,
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
rd(X2,ld(X,X2)) = X,
inference(transitivity,[status(thm)],[c50,c52]) ).
cnf(c54,plain,
rd(ld(X,X),ld(X,ld(X,X))) = X,
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
X = rd(ld(X,X),ld(X,ld(X,X))),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,plain,
mult(ld(X,X),X) = mult(ld(X,X),rd(ld(X,X),ld(X,ld(X,X)))),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
ld(X2,mult(X2,mult(ld(X2,X2),X))) = mult(ld(X2,X2),X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c58,plain,
mult(ld(X2,X2),X) = ld(X2,mult(X2,mult(ld(X2,X2),X))),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,plain,
rd(mult(ld(X2,X2),X),ld(X2,X2)) = rd(ld(X2,mult(X2,mult(ld(X2,X2),X))),ld(X2,X2)),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
mult(X,mult(ld(X,X3),mult(rd(X2,X),X))) = mult(mult(X3,rd(X2,X)),X),
inference(substitution,[status(thm)],[c9]) ).
cnf(c61,plain,
mult(mult(X3,rd(X2,X)),X) = mult(X,mult(ld(X,X3),mult(rd(X2,X),X))),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,axiom,
mult(rd(A2,B2),B2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
cnf(c63,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c62]) ).
cnf(c64,plain,
mult(ld(X,X3),mult(rd(X2,X),X)) = mult(ld(X,X3),X2),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
mult(X,mult(ld(X,X3),mult(rd(X2,X),X))) = mult(X,mult(ld(X,X3),X2)),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
mult(mult(X3,rd(X2,X)),X) = mult(X,mult(ld(X,X3),X2)),
inference(transitivity,[status(thm)],[c61,c65]) ).
cnf(c67,plain,
mult(mult(X2,rd(X,X2)),X2) = mult(X2,mult(ld(X2,X2),X)),
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
mult(X2,mult(ld(X2,X2),X)) = mult(mult(X2,rd(X,X2)),X2),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
ld(X2,mult(X2,mult(ld(X2,X2),X))) = ld(X2,mult(mult(X2,rd(X,X2)),X2)),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
rd(ld(X2,mult(X2,mult(ld(X2,X2),X))),ld(X2,X2)) = rd(ld(X2,mult(mult(X2,rd(X,X2)),X2)),ld(X2,X2)),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
mult(ld(X2,X2),mult(ld(X2,X),X2)) = ld(X2,mult(X,X2)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c72,plain,
ld(X2,mult(X,X2)) = mult(ld(X2,X2),mult(ld(X2,X),X2)),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
rd(ld(X2,mult(X,X2)),ld(X2,X2)) = rd(mult(ld(X2,X2),mult(ld(X2,X),X2)),ld(X2,X2)),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
mult(rd(X,X2),X2) = X,
inference(substitution,[status(thm)],[c62]) ).
cnf(c75,plain,
X = mult(rd(X,X2),X2),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
mult(X2,X) = mult(X2,mult(rd(X,X3),X3)),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
mult(X3,mult(X2,X)) = mult(X3,mult(X2,mult(rd(X,X3),X3))),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
rd(mult(X3,mult(X2,X)),X3) = rd(mult(X3,mult(X2,mult(rd(X,X3),X3))),X3),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
mult(mult(mult(X3,X2),X),X3) = mult(X3,mult(X2,mult(X,X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c80,plain,
mult(X3,mult(X2,mult(X,X3))) = mult(mult(mult(X3,X2),X),X3),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
rd(mult(X3,mult(X2,mult(X,X3))),X3) = rd(mult(mult(mult(X3,X2),X),X3),X3),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
rd(mult(mult(mult(X3,X2),X),X3),X3) = mult(mult(X3,X2),X),
inference(substitution,[status(thm)],[c51]) ).
cnf(c83,plain,
rd(mult(X3,mult(X2,mult(X,X3))),X3) = mult(mult(X3,X2),X),
inference(transitivity,[status(thm)],[c81,c82]) ).
cnf(c84,plain,
rd(mult(X3,mult(X2,mult(rd(X,X3),X3))),X3) = mult(mult(X3,X2),rd(X,X3)),
inference(substitution,[status(thm)],[c83]) ).
cnf(c85,plain,
rd(mult(X3,mult(X2,X)),X3) = mult(mult(X3,X2),rd(X,X3)),
inference(transitivity,[status(thm)],[c78,c84]) ).
cnf(c86,plain,
rd(mult(ld(X2,X2),mult(ld(X2,X),X2)),ld(X2,X2)) = mult(mult(ld(X2,X2),ld(X2,X)),rd(X2,ld(X2,X2))),
inference(substitution,[status(thm)],[c85]) ).
cnf(c87,plain,
rd(X,ld(X,X)) = X,
inference(substitution,[status(thm)],[c53]) ).
cnf(c88,plain,
mult(mult(ld(X2,X2),ld(X2,X)),rd(X2,ld(X2,X2))) = mult(mult(ld(X2,X2),ld(X2,X)),X2),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
rd(mult(ld(X2,X2),mult(ld(X2,X),X2)),ld(X2,X2)) = mult(mult(ld(X2,X2),ld(X2,X)),X2),
inference(transitivity,[status(thm)],[c86,c88]) ).
cnf(c90,plain,
rd(ld(X2,mult(X,X2)),ld(X2,X2)) = mult(mult(ld(X2,X2),ld(X2,X)),X2),
inference(transitivity,[status(thm)],[c73,c89]) ).
cnf(c91,plain,
rd(ld(X2,mult(mult(X2,rd(X,X2)),X2)),ld(X2,X2)) = mult(mult(ld(X2,X2),ld(X2,mult(X2,rd(X,X2)))),X2),
inference(substitution,[status(thm)],[c90]) ).
cnf(c92,plain,
ld(X2,mult(X2,rd(X,X2))) = rd(X,X2),
inference(substitution,[status(thm)],[c12]) ).
cnf(c93,plain,
mult(ld(X2,X2),ld(X2,mult(X2,rd(X,X2)))) = mult(ld(X2,X2),rd(X,X2)),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
mult(mult(ld(X2,X2),ld(X2,mult(X2,rd(X,X2)))),X2) = mult(mult(ld(X2,X2),rd(X,X2)),X2),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
mult(mult(ld(X2,X2),rd(X,X2)),X2) = mult(X2,mult(ld(X2,ld(X2,X2)),X)),
inference(substitution,[status(thm)],[c66]) ).
cnf(c96,plain,
mult(mult(ld(X2,X2),ld(X2,mult(X2,rd(X,X2)))),X2) = mult(X2,mult(ld(X2,ld(X2,X2)),X)),
inference(transitivity,[status(thm)],[c94,c95]) ).
cnf(c97,plain,
rd(ld(X2,mult(mult(X2,rd(X,X2)),X2)),ld(X2,X2)) = mult(X2,mult(ld(X2,ld(X2,X2)),X)),
inference(transitivity,[status(thm)],[c91,c96]) ).
cnf(c98,plain,
rd(ld(X2,mult(X2,mult(ld(X2,X2),X))),ld(X2,X2)) = mult(X2,mult(ld(X2,ld(X2,X2)),X)),
inference(transitivity,[status(thm)],[c70,c97]) ).
cnf(c99,plain,
rd(mult(ld(X2,X2),X),ld(X2,X2)) = mult(X2,mult(ld(X2,ld(X2,X2)),X)),
inference(transitivity,[status(thm)],[c59,c98]) ).
cnf(c100,plain,
ld(X2,rd(mult(ld(X2,X2),X),ld(X2,X2))) = ld(X2,mult(X2,mult(ld(X2,ld(X2,X2)),X))),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
ld(X2,mult(X2,mult(ld(X2,ld(X2,X2)),X))) = mult(ld(X2,ld(X2,X2)),X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c102,plain,
ld(X2,rd(mult(ld(X2,X2),X),ld(X2,X2))) = mult(ld(X2,ld(X2,X2)),X),
inference(transitivity,[status(thm)],[c100,c101]) ).
cnf(c103,plain,
ld(X,rd(mult(ld(X,X),ld(X,X)),ld(X,X))) = mult(ld(X,ld(X,X)),ld(X,X)),
inference(substitution,[status(thm)],[c102]) ).
cnf(c104,plain,
mult(ld(X,ld(X,X)),ld(X,X)) = ld(X,rd(mult(ld(X,X),ld(X,X)),ld(X,X))),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,plain,
rd(mult(ld(X,X),ld(X,X)),ld(X,X)) = ld(X,X),
inference(substitution,[status(thm)],[c51]) ).
cnf(c106,plain,
ld(X,rd(mult(ld(X,X),ld(X,X)),ld(X,X))) = ld(X,ld(X,X)),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
mult(ld(X,ld(X,X)),ld(X,X)) = ld(X,ld(X,X)),
inference(transitivity,[status(thm)],[c104,c106]) ).
cnf(c108,plain,
ld(X,ld(X,X)) = mult(ld(X,ld(X,X)),ld(X,X)),
inference(symmetry,[status(thm)],[c107]) ).
cnf(c109,plain,
rd(ld(X,X),ld(X,ld(X,X))) = rd(ld(X,X),mult(ld(X,ld(X,X)),ld(X,X))),
inference(congruence,[status(thm)],[c108]) ).
cnf(c110,plain,
mult(ld(X,X),rd(ld(X,X),ld(X,ld(X,X)))) = mult(ld(X,X),rd(ld(X,X),mult(ld(X,ld(X,X)),ld(X,X)))),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
rd(mult(X3,mult(rd(X2,mult(X,X3)),mult(X,X3))),X3) = mult(mult(X3,rd(X2,mult(X,X3))),X),
inference(substitution,[status(thm)],[c83]) ).
cnf(c112,plain,
mult(mult(X3,rd(X2,mult(X,X3))),X) = rd(mult(X3,mult(rd(X2,mult(X,X3)),mult(X,X3))),X3),
inference(symmetry,[status(thm)],[c111]) ).
cnf(c113,plain,
mult(rd(X2,mult(X,X3)),mult(X,X3)) = X2,
inference(substitution,[status(thm)],[c62]) ).
cnf(c114,plain,
mult(X3,mult(rd(X2,mult(X,X3)),mult(X,X3))) = mult(X3,X2),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
rd(mult(X3,mult(rd(X2,mult(X,X3)),mult(X,X3))),X3) = rd(mult(X3,X2),X3),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
mult(mult(X3,rd(X2,mult(X,X3))),X) = rd(mult(X3,X2),X3),
inference(transitivity,[status(thm)],[c112,c115]) ).
cnf(c117,plain,
rd(mult(X3,X2),X3) = mult(mult(X3,rd(X2,mult(X,X3))),X),
inference(symmetry,[status(thm)],[c116]) ).
cnf(c118,plain,
rd(rd(mult(X3,X2),X3),X) = rd(mult(mult(X3,rd(X2,mult(X,X3))),X),X),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
rd(mult(mult(X3,rd(X2,mult(X,X3))),X),X) = mult(X3,rd(X2,mult(X,X3))),
inference(substitution,[status(thm)],[c51]) ).
cnf(c120,plain,
rd(rd(mult(X3,X2),X3),X) = mult(X3,rd(X2,mult(X,X3))),
inference(transitivity,[status(thm)],[c118,c119]) ).
cnf(c121,plain,
rd(rd(mult(X2,X2),X2),X) = mult(X2,rd(X2,mult(X,X2))),
inference(substitution,[status(thm)],[c120]) ).
cnf(c122,plain,
mult(X2,rd(X2,mult(X,X2))) = rd(rd(mult(X2,X2),X2),X),
inference(symmetry,[status(thm)],[c121]) ).
cnf(c123,plain,
rd(mult(X,X),X) = X,
inference(substitution,[status(thm)],[c51]) ).
cnf(c124,plain,
rd(rd(mult(X2,X2),X2),X) = rd(X2,X),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
mult(X2,rd(X2,mult(X,X2))) = rd(X2,X),
inference(transitivity,[status(thm)],[c122,c124]) ).
cnf(c126,plain,
mult(ld(X,X),rd(ld(X,X),mult(ld(X,ld(X,X)),ld(X,X)))) = rd(ld(X,X),ld(X,ld(X,X))),
inference(substitution,[status(thm)],[c125]) ).
cnf(c127,plain,
rd(ld(X,X),ld(X,ld(X,X))) = X,
inference(substitution,[status(thm)],[c53]) ).
cnf(c128,plain,
mult(ld(X,X),rd(ld(X,X),mult(ld(X,ld(X,X)),ld(X,X)))) = X,
inference(transitivity,[status(thm)],[c126,c127]) ).
cnf(c129,plain,
mult(ld(X,X),rd(ld(X,X),ld(X,ld(X,X)))) = X,
inference(transitivity,[status(thm)],[c110,c128]) ).
cnf(c130,plain,
mult(ld(X,X),X) = X,
inference(transitivity,[status(thm)],[c56,c129]) ).
cnf(c131,plain,
ld(mult(ld(X,X),X),mult(ld(X,X),X)) = ld(X,mult(ld(X,X),X)),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,plain,
ld(X,mult(ld(X,X),X)) = ld(X,X),
inference(congruence,[status(thm)],[c130]) ).
cnf(c133,plain,
ld(mult(ld(X,X),X),mult(ld(X,X),X)) = ld(X,X),
inference(transitivity,[status(thm)],[c131,c132]) ).
cnf(c134,plain,
mult(ld(X,X),ld(X,X)) = ld(X,X),
inference(transitivity,[status(thm)],[c47,c133]) ).
cnf(c135,plain,
ld(X,X) = mult(ld(X,X),ld(X,X)),
inference(symmetry,[status(thm)],[c134]) ).
cnf(c136,plain,
ld(ld(X,X),ld(X,X)) = ld(ld(X,X),mult(ld(X,X),ld(X,X))),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
ld(ld(X,X),mult(ld(X,X),ld(X,X))) = ld(X,X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c138,plain,
ld(ld(X,X),ld(X,X)) = ld(X,X),
inference(transitivity,[status(thm)],[c136,c137]) ).
cnf(c139,plain,
ld(X,X) = ld(ld(X,X),ld(X,X)),
inference(symmetry,[status(thm)],[c138]) ).
cnf(c140,plain,
mult(ld(X2,X2),mult(mult(ld(X2,X2),X),ld(X2,X2))) = mult(ld(ld(X2,X2),ld(X2,X2)),mult(mult(ld(X2,X2),X),ld(X2,X2))),
inference(congruence,[status(thm)],[c139]) ).
cnf(c141,plain,
ld(ld(X2,X2),mult(mult(ld(X2,X2),mult(ld(X2,X2),X)),ld(X2,X2))) = mult(ld(ld(X2,X2),ld(X2,X2)),mult(mult(ld(X2,X2),X),ld(X2,X2))),
inference(substitution,[status(thm)],[c14]) ).
cnf(c142,plain,
mult(ld(ld(X2,X2),ld(X2,X2)),mult(mult(ld(X2,X2),X),ld(X2,X2))) = ld(ld(X2,X2),mult(mult(ld(X2,X2),mult(ld(X2,X2),X)),ld(X2,X2))),
inference(symmetry,[status(thm)],[c141]) ).
cnf(c143,plain,
mult(rd(rd(mult(ld(X2,X2),X),ld(X2,X2)),ld(X2,X2)),ld(X2,X2)) = rd(mult(ld(X2,X2),X),ld(X2,X2)),
inference(substitution,[status(thm)],[c62]) ).
cnf(c144,plain,
rd(mult(ld(X2,X2),X),ld(X2,X2)) = mult(rd(rd(mult(ld(X2,X2),X),ld(X2,X2)),ld(X2,X2)),ld(X2,X2)),
inference(symmetry,[status(thm)],[c143]) ).
cnf(c145,plain,
rd(rd(mult(ld(X2,X2),X),ld(X2,X2)),ld(X2,X2)) = mult(ld(X2,X2),rd(X,mult(ld(X2,X2),ld(X2,X2)))),
inference(substitution,[status(thm)],[c120]) ).
cnf(c146,plain,
rd(X,mult(ld(X2,X2),ld(X2,X2))) = rd(X,ld(X2,X2)),
inference(congruence,[status(thm)],[c134]) ).
cnf(c147,plain,
mult(ld(X2,X2),rd(X,mult(ld(X2,X2),ld(X2,X2)))) = mult(ld(X2,X2),rd(X,ld(X2,X2))),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,plain,
rd(rd(mult(ld(X2,X2),X),ld(X2,X2)),ld(X2,X2)) = mult(ld(X2,X2),rd(X,ld(X2,X2))),
inference(transitivity,[status(thm)],[c145,c147]) ).
cnf(c149,plain,
mult(rd(rd(mult(ld(X2,X2),X),ld(X2,X2)),ld(X2,X2)),ld(X2,X2)) = mult(mult(ld(X2,X2),rd(X,ld(X2,X2))),ld(X2,X2)),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
mult(mult(ld(X2,X2),rd(X,ld(X2,X2))),ld(X2,X2)) = mult(ld(X2,X2),mult(ld(ld(X2,X2),ld(X2,X2)),X)),
inference(substitution,[status(thm)],[c66]) ).
cnf(c151,plain,
mult(ld(ld(X2,X2),ld(X2,X2)),X) = mult(ld(X2,X2),X),
inference(congruence,[status(thm)],[c138]) ).
cnf(c152,plain,
mult(ld(X2,X2),mult(ld(ld(X2,X2),ld(X2,X2)),X)) = mult(ld(X2,X2),mult(ld(X2,X2),X)),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
mult(mult(ld(X2,X2),rd(X,ld(X2,X2))),ld(X2,X2)) = mult(ld(X2,X2),mult(ld(X2,X2),X)),
inference(transitivity,[status(thm)],[c150,c152]) ).
cnf(c154,plain,
mult(rd(rd(mult(ld(X2,X2),X),ld(X2,X2)),ld(X2,X2)),ld(X2,X2)) = mult(ld(X2,X2),mult(ld(X2,X2),X)),
inference(transitivity,[status(thm)],[c149,c153]) ).
cnf(c155,plain,
rd(mult(ld(X2,X2),X),ld(X2,X2)) = mult(ld(X2,X2),mult(ld(X2,X2),X)),
inference(transitivity,[status(thm)],[c144,c154]) ).
cnf(c156,plain,
mult(ld(X2,X2),mult(ld(X2,X2),X)) = rd(mult(ld(X2,X2),X),ld(X2,X2)),
inference(symmetry,[status(thm)],[c155]) ).
cnf(c157,plain,
mult(mult(ld(X2,X2),mult(ld(X2,X2),X)),ld(X2,X2)) = mult(rd(mult(ld(X2,X2),X),ld(X2,X2)),ld(X2,X2)),
inference(congruence,[status(thm)],[c156]) ).
cnf(c158,plain,
mult(rd(mult(ld(X2,X2),X),ld(X2,X2)),ld(X2,X2)) = mult(ld(X2,X2),X),
inference(substitution,[status(thm)],[c62]) ).
cnf(c159,plain,
mult(mult(ld(X2,X2),mult(ld(X2,X2),X)),ld(X2,X2)) = mult(ld(X2,X2),X),
inference(transitivity,[status(thm)],[c157,c158]) ).
cnf(c160,plain,
ld(ld(X2,X2),mult(mult(ld(X2,X2),mult(ld(X2,X2),X)),ld(X2,X2))) = ld(ld(X2,X2),mult(ld(X2,X2),X)),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
ld(ld(X2,X2),mult(ld(X2,X2),X)) = X,
inference(substitution,[status(thm)],[c12]) ).
cnf(c162,plain,
ld(ld(X2,X2),mult(mult(ld(X2,X2),mult(ld(X2,X2),X)),ld(X2,X2))) = X,
inference(transitivity,[status(thm)],[c160,c161]) ).
cnf(c163,plain,
mult(ld(ld(X2,X2),ld(X2,X2)),mult(mult(ld(X2,X2),X),ld(X2,X2))) = X,
inference(transitivity,[status(thm)],[c142,c162]) ).
cnf(c164,plain,
mult(ld(X2,X2),mult(mult(ld(X2,X2),X),ld(X2,X2))) = X,
inference(transitivity,[status(thm)],[c140,c163]) ).
cnf(c165,plain,
mult(ld(X,X),mult(mult(ld(X,X),X2),ld(X,X))) = X2,
inference(substitution,[status(thm)],[c164]) ).
cnf(c166,plain,
X2 = mult(ld(X,X),mult(mult(ld(X,X),X2),ld(X,X))),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c167,plain,
rd(X2,ld(X,X)) = rd(mult(ld(X,X),mult(mult(ld(X,X),X2),ld(X,X))),ld(X,X)),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,plain,
rd(mult(ld(X,X),mult(mult(ld(X,X),X2),ld(X,X))),ld(X,X)) = mult(mult(ld(X,X),mult(ld(X,X),X2)),rd(ld(X,X),ld(X,X))),
inference(substitution,[status(thm)],[c85]) ).
cnf(c169,plain,
X = mult(ld(X,X),X),
inference(symmetry,[status(thm)],[c130]) ).
cnf(c170,plain,
rd(X,X) = rd(mult(ld(X,X),X),X),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
rd(mult(ld(X,X),X),X) = ld(X,X),
inference(substitution,[status(thm)],[c51]) ).
cnf(c172,plain,
rd(X,X) = ld(X,X),
inference(transitivity,[status(thm)],[c170,c171]) ).
cnf(c173,plain,
ld(X,X) = rd(X,X),
inference(symmetry,[status(thm)],[c172]) ).
cnf(c174,plain,
rd(ld(X,X),ld(X,X)) = rd(ld(X,X),rd(X,X)),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,plain,
rd(mult(X3,mult(X2,ld(X2,X))),X3) = mult(mult(X3,X2),rd(ld(X2,X),X3)),
inference(substitution,[status(thm)],[c85]) ).
cnf(c176,plain,
mult(mult(X3,X2),rd(ld(X2,X),X3)) = rd(mult(X3,mult(X2,ld(X2,X))),X3),
inference(symmetry,[status(thm)],[c175]) ).
cnf(c177,plain,
mult(X2,ld(X2,X)) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c178,plain,
mult(X3,mult(X2,ld(X2,X))) = mult(X3,X),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
rd(mult(X3,mult(X2,ld(X2,X))),X3) = rd(mult(X3,X),X3),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
mult(mult(X3,X2),rd(ld(X2,X),X3)) = rd(mult(X3,X),X3),
inference(transitivity,[status(thm)],[c176,c179]) ).
cnf(c181,plain,
rd(mult(X3,X),X3) = mult(mult(X3,X2),rd(ld(X2,X),X3)),
inference(symmetry,[status(thm)],[c180]) ).
cnf(c182,plain,
ld(mult(X3,X2),rd(mult(X3,X),X3)) = ld(mult(X3,X2),mult(mult(X3,X2),rd(ld(X2,X),X3))),
inference(congruence,[status(thm)],[c181]) ).
cnf(c183,plain,
ld(mult(X3,X2),mult(mult(X3,X2),rd(ld(X2,X),X3))) = rd(ld(X2,X),X3),
inference(substitution,[status(thm)],[c12]) ).
cnf(c184,plain,
ld(mult(X3,X2),rd(mult(X3,X),X3)) = rd(ld(X2,X),X3),
inference(transitivity,[status(thm)],[c182,c183]) ).
cnf(c185,plain,
ld(mult(rd(X2,X),X),rd(mult(rd(X2,X),X),rd(X2,X))) = rd(ld(X,X),rd(X2,X)),
inference(substitution,[status(thm)],[c184]) ).
cnf(c186,plain,
rd(ld(X,X),rd(X2,X)) = ld(mult(rd(X2,X),X),rd(mult(rd(X2,X),X),rd(X2,X))),
inference(symmetry,[status(thm)],[c185]) ).
cnf(c187,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c62]) ).
cnf(c188,plain,
ld(mult(rd(X2,X),X),rd(mult(rd(X2,X),X),rd(X2,X))) = ld(X2,rd(mult(rd(X2,X),X),rd(X2,X))),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
mult(rd(X2,X),X) = X2,
inference(substitution,[status(thm)],[c62]) ).
cnf(c190,plain,
rd(mult(rd(X2,X),X),rd(X2,X)) = rd(X2,rd(X2,X)),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
ld(X2,rd(mult(rd(X2,X),X),rd(X2,X))) = ld(X2,rd(X2,rd(X2,X))),
inference(congruence,[status(thm)],[c190]) ).
cnf(c192,plain,
ld(mult(rd(X2,X),X),rd(mult(rd(X2,X),X),rd(X2,X))) = ld(X2,rd(X2,rd(X2,X))),
inference(transitivity,[status(thm)],[c188,c191]) ).
cnf(c193,plain,
rd(ld(X,X),rd(X2,X)) = ld(X2,rd(X2,rd(X2,X))),
inference(transitivity,[status(thm)],[c186,c192]) ).
cnf(c194,plain,
rd(ld(X,X),rd(X,X)) = ld(X,rd(X,rd(X,X))),
inference(substitution,[status(thm)],[c193]) ).
cnf(c195,plain,
rd(X,rd(X,X)) = rd(X,ld(X,X)),
inference(congruence,[status(thm)],[c172]) ).
cnf(c196,plain,
ld(X,rd(X,rd(X,X))) = ld(X,rd(X,ld(X,X))),
inference(congruence,[status(thm)],[c195]) ).
cnf(c197,plain,
rd(X,ld(X,X)) = X,
inference(substitution,[status(thm)],[c53]) ).
cnf(c198,plain,
ld(X,rd(X,ld(X,X))) = ld(X,X),
inference(congruence,[status(thm)],[c197]) ).
cnf(c199,plain,
ld(X,rd(X,rd(X,X))) = ld(X,X),
inference(transitivity,[status(thm)],[c196,c198]) ).
cnf(c200,plain,
rd(ld(X,X),rd(X,X)) = ld(X,X),
inference(transitivity,[status(thm)],[c194,c199]) ).
cnf(c201,plain,
rd(ld(X,X),ld(X,X)) = ld(X,X),
inference(transitivity,[status(thm)],[c174,c200]) ).
cnf(c202,plain,
mult(mult(ld(X,X),mult(ld(X,X),X2)),rd(ld(X,X),ld(X,X))) = mult(mult(ld(X,X),mult(ld(X,X),X2)),ld(X,X)),
inference(congruence,[status(thm)],[c201]) ).
cnf(c203,plain,
mult(mult(ld(X,X),mult(ld(X,X),X2)),ld(X,X)) = mult(ld(X,X),X2),
inference(substitution,[status(thm)],[c159]) ).
cnf(c204,plain,
mult(mult(ld(X,X),mult(ld(X,X),X2)),rd(ld(X,X),ld(X,X))) = mult(ld(X,X),X2),
inference(transitivity,[status(thm)],[c202,c203]) ).
cnf(c205,plain,
rd(mult(ld(X,X),mult(mult(ld(X,X),X2),ld(X,X))),ld(X,X)) = mult(ld(X,X),X2),
inference(transitivity,[status(thm)],[c168,c204]) ).
cnf(c206,plain,
rd(X2,ld(X,X)) = mult(ld(X,X),X2),
inference(transitivity,[status(thm)],[c167,c205]) ).
cnf(c207,plain,
rd(X,ld(X2,X2)) = mult(ld(X2,X2),X),
inference(substitution,[status(thm)],[c206]) ).
cnf(c208,plain,
mult(ld(X2,X2),X) = rd(X,ld(X2,X2)),
inference(symmetry,[status(thm)],[c207]) ).
cnf(c209,plain,
mult(mult(ld(X2,X2),X),ld(X2,X2)) = mult(rd(X,ld(X2,X2)),ld(X2,X2)),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
mult(rd(X,ld(X2,X2)),ld(X2,X2)) = X,
inference(substitution,[status(thm)],[c62]) ).
cnf(c211,plain,
mult(mult(ld(X2,X2),X),ld(X2,X2)) = X,
inference(transitivity,[status(thm)],[c209,c210]) ).
cnf(c212,plain,
X = mult(mult(ld(X2,X2),X),ld(X2,X2)),
inference(symmetry,[status(thm)],[c211]) ).
cnf(c213,plain,
mult(ld(X2,X2),X) = mult(ld(X2,X2),mult(mult(ld(X2,X2),X),ld(X2,X2))),
inference(congruence,[status(thm)],[c212]) ).
cnf(c214,plain,
mult(ld(X2,X2),X) = X,
inference(transitivity,[status(thm)],[c213,c164]) ).
cnf(c215,plain,
mult(ld(x1,x1),x0) = x0,
inference(substitution,[status(thm)],[c214]) ).
cnf(c216,plain,
$false,
inference(resolution,[status(thm)],[c1,c215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP660-14 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 10:38:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.57 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.17/0.57
% 0.17/0.57 % SZS status Unsatisfiable
% 0.17/0.57
% 0.17/0.59 % SZS output start CNFRefutation
% See solution above
% 2.14/0.76
% 2.14/0.76 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------