%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP731-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 10:11:52 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.51s
% Output : CNFRefutation 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 12
% Syntax : Number of clauses : 154 ( 154 unt; 0 nHn; 3 RR)
% Number of literals : 154 ( 153 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 : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 490 ( 39 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
op_k(asoc(a,b,c),d) != unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c2,axiom,
mult(i(A),mult(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
cnf(c3,plain,
mult(i(asoc(X4,X3,X2)),mult(asoc(X4,X3,X2),op_k(asoc(X4,X3,X2),X))) = op_k(asoc(X4,X3,X2),X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
op_k(asoc(X4,X3,X2),X) = mult(i(asoc(X4,X3,X2)),mult(asoc(X4,X3,X2),op_k(asoc(X4,X3,X2),X))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
mult(i(X),mult(X,mult(asoc(X4,X3,X2),op_k(asoc(X4,X3,X2),X)))) = mult(asoc(X4,X3,X2),op_k(asoc(X4,X3,X2),X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
mult(asoc(X4,X3,X2),op_k(asoc(X4,X3,X2),X)) = mult(i(X),mult(X,mult(asoc(X4,X3,X2),op_k(asoc(X4,X3,X2),X)))),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,axiom,
op_t(A2,B2) = mult(i(B2),mult(A2,B2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c14) ).
cnf(c8,plain,
op_t(X,X2) = mult(i(X2),mult(X,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
mult(X2,op_t(X,X2)) = mult(X2,mult(i(X2),mult(X,X2))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,axiom,
mult(A2,unit) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
cnf(c11,plain,
mult(i(i(X)),unit) = i(i(X)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
i(i(X)) = mult(i(i(X)),unit),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,axiom,
mult(i(A2),A2) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
cnf(c14,plain,
mult(i(X),X) = unit,
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
unit = mult(i(X),X),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
mult(i(i(X)),unit) = mult(i(i(X)),mult(i(X),X)),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
mult(i(i(X)),mult(i(X),X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c18,plain,
mult(i(i(X)),unit) = X,
inference(transitivity,[status(thm)],[c16,c17]) ).
cnf(c19,plain,
i(i(X)) = X,
inference(transitivity,[status(thm)],[c12,c18]) ).
cnf(c20,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
mult(X2,mult(i(X2),X)) = mult(i(i(X2)),mult(i(X2),X)),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
mult(i(i(X2)),mult(i(X2),X)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c23,plain,
mult(X2,mult(i(X2),X)) = X,
inference(transitivity,[status(thm)],[c21,c22]) ).
cnf(c24,plain,
mult(X2,mult(i(X2),mult(X,X2))) = mult(X,X2),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
mult(X2,op_t(X,X2)) = mult(X,X2),
inference(transitivity,[status(thm)],[c9,c24]) ).
cnf(c26,plain,
mult(X,op_t(asoc(X4,X3,X2),X)) = mult(asoc(X4,X3,X2),X),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
mult(asoc(X4,X3,X2),X) = mult(X,op_t(asoc(X4,X3,X2),X)),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c29,plain,
op_t(asoc(X4,X3,X2),X) = op_t(asoc(X4,X3,X2),i(i(X))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,axiom,
i(mult(A2,B2)) = mult(i(A2),i(B2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
cnf(c31,plain,
i(mult(X,X2)) = mult(i(X),i(X2)),
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
mult(i(X),i(X2)) = i(mult(X,X2)),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
mult(X2,mult(i(X),i(X2))) = mult(X2,i(mult(X,X2))),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c35,plain,
mult(X2,i(mult(X,X2))) = mult(i(i(X2)),i(mult(X,X2))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
i(mult(i(X2),mult(X,X2))) = mult(i(i(X2)),i(mult(X,X2))),
inference(substitution,[status(thm)],[c30]) ).
cnf(c37,plain,
mult(i(i(X2)),i(mult(X,X2))) = i(mult(i(X2),mult(X,X2))),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
op_t(X,X2) = mult(i(X2),mult(X,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c39,plain,
mult(i(X2),mult(X,X2)) = op_t(X,X2),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
i(mult(i(X2),mult(X,X2))) = i(op_t(X,X2)),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
mult(i(i(X2)),i(mult(X,X2))) = i(op_t(X,X2)),
inference(transitivity,[status(thm)],[c37,c40]) ).
cnf(c42,plain,
mult(X2,i(mult(X,X2))) = i(op_t(X,X2)),
inference(transitivity,[status(thm)],[c35,c41]) ).
cnf(c43,plain,
mult(X2,mult(i(X),i(X2))) = i(op_t(X,X2)),
inference(transitivity,[status(thm)],[c33,c42]) ).
cnf(c44,plain,
mult(i(X),mult(i(X2),i(i(X)))) = i(op_t(X2,i(X))),
inference(substitution,[status(thm)],[c43]) ).
cnf(c45,plain,
i(op_t(X2,i(X))) = mult(i(X),mult(i(X2),i(i(X)))),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,plain,
mult(i(X2),i(i(X))) = mult(i(X2),X),
inference(congruence,[status(thm)],[c19]) ).
cnf(c47,plain,
mult(i(X),mult(i(X2),i(i(X)))) = mult(i(X),mult(i(X2),X)),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
op_t(i(X2),X) = mult(i(X),mult(i(X2),X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c49,plain,
mult(i(X),mult(i(X2),X)) = op_t(i(X2),X),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
mult(i(X),mult(i(X2),i(i(X)))) = op_t(i(X2),X),
inference(transitivity,[status(thm)],[c47,c49]) ).
cnf(c51,plain,
i(op_t(X2,i(X))) = op_t(i(X2),X),
inference(transitivity,[status(thm)],[c45,c50]) ).
cnf(c52,plain,
op_t(i(X2),X) = i(op_t(X2,i(X))),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
i(op_t(i(X2),X)) = i(i(op_t(X2,i(X)))),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
i(i(op_t(X2,i(X)))) = op_t(X2,i(X)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c55,plain,
i(op_t(i(X2),X)) = op_t(X2,i(X)),
inference(transitivity,[status(thm)],[c53,c54]) ).
cnf(c56,plain,
i(op_t(i(asoc(X4,X3,X2)),i(X))) = op_t(asoc(X4,X3,X2),i(i(X))),
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
op_t(asoc(X4,X3,X2),i(i(X))) = i(op_t(i(asoc(X4,X3,X2)),i(X))),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,plain,
mult(i(X),X) = unit,
inference(substitution,[status(thm)],[c13]) ).
cnf(c59,plain,
unit = mult(i(X),X),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
rd(unit,X) = rd(mult(i(X),X),X),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,axiom,
rd(mult(A2,B2),B2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
cnf(c62,plain,
rd(mult(i(X),X),X) = i(X),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
rd(unit,X) = i(X),
inference(transitivity,[status(thm)],[c60,c62]) ).
cnf(c64,plain,
rd(unit,op_t(i(asoc(X4,X3,X2)),i(X))) = i(op_t(i(asoc(X4,X3,X2)),i(X))),
inference(substitution,[status(thm)],[c63]) ).
cnf(c65,plain,
i(op_t(i(asoc(X4,X3,X2)),i(X))) = rd(unit,op_t(i(asoc(X4,X3,X2)),i(X))),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
X = i(i(X)),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c67,plain,
op_t(X2,X) = op_t(X2,i(i(X))),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
i(op_t(X2,X)) = i(op_t(X2,i(i(X)))),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
i(op_t(X2,i(i(X)))) = op_t(i(X2),i(X)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c70,plain,
i(op_t(X2,X)) = op_t(i(X2),i(X)),
inference(transitivity,[status(thm)],[c68,c69]) ).
cnf(c71,plain,
i(op_t(asoc(X4,X3,X2),X)) = op_t(i(asoc(X4,X3,X2)),i(X)),
inference(substitution,[status(thm)],[c70]) ).
cnf(c72,plain,
op_t(i(asoc(X4,X3,X2)),i(X)) = i(op_t(asoc(X4,X3,X2),X)),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
mult(asoc(X4,X3,X2),op_t(i(asoc(X4,X3,X2)),i(X))) = mult(asoc(X4,X3,X2),i(op_t(asoc(X4,X3,X2),X))),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
mult(X,mult(i(asoc(X4,X3,X2)),i(X))) = i(op_t(asoc(X4,X3,X2),X)),
inference(substitution,[status(thm)],[c43]) ).
cnf(c75,plain,
i(op_t(asoc(X4,X3,X2),X)) = mult(X,mult(i(asoc(X4,X3,X2)),i(X))),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
mult(asoc(X4,X3,X2),i(op_t(asoc(X4,X3,X2),X))) = mult(asoc(X4,X3,X2),mult(X,mult(i(asoc(X4,X3,X2)),i(X)))),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
i(mult(asoc(X4,X3,X2),X)) = mult(i(asoc(X4,X3,X2)),i(X)),
inference(substitution,[status(thm)],[c30]) ).
cnf(c78,plain,
mult(i(asoc(X4,X3,X2)),i(X)) = i(mult(asoc(X4,X3,X2),X)),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,plain,
mult(X,mult(i(asoc(X4,X3,X2)),i(X))) = mult(X,i(mult(asoc(X4,X3,X2),X))),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
mult(asoc(X4,X3,X2),mult(X,mult(i(asoc(X4,X3,X2)),i(X)))) = mult(asoc(X4,X3,X2),mult(X,i(mult(asoc(X4,X3,X2),X)))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,axiom,
mult(mult(A2,B2),C) = mult(mult(A2,mult(B2,C)),asoc(A2,B2,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c10) ).
cnf(c82,plain,
mult(mult(asoc(X4,X3,X2),X),X5) = mult(mult(asoc(X4,X3,X2),mult(X,X5)),asoc(asoc(X4,X3,X2),X,X5)),
inference(substitution,[status(thm)],[c81]) ).
cnf(c83,axiom,
asoc(asoc(A2,B2,C2),D,E) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c21) ).
cnf(c84,plain,
asoc(asoc(X5,X4,X3),X2,X) = unit,
inference(substitution,[status(thm)],[c83]) ).
cnf(c85,plain,
mult(mult(asoc(X5,X4,X3),mult(X2,X)),asoc(asoc(X5,X4,X3),X2,X)) = mult(mult(asoc(X5,X4,X3),mult(X2,X)),unit),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
mult(mult(asoc(X5,X4,X3),mult(X2,X)),unit) = mult(asoc(X5,X4,X3),mult(X2,X)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c87,plain,
mult(mult(asoc(X5,X4,X3),mult(X2,X)),asoc(asoc(X5,X4,X3),X2,X)) = mult(asoc(X5,X4,X3),mult(X2,X)),
inference(transitivity,[status(thm)],[c85,c86]) ).
cnf(c88,plain,
mult(mult(asoc(X5,X4,X3),X2),X) = mult(asoc(X5,X4,X3),mult(X2,X)),
inference(transitivity,[status(thm)],[c82,c87]) ).
cnf(c89,plain,
mult(mult(asoc(X4,X3,X2),X),i(mult(asoc(X4,X3,X2),X))) = mult(asoc(X4,X3,X2),mult(X,i(mult(asoc(X4,X3,X2),X)))),
inference(substitution,[status(thm)],[c88]) ).
cnf(c90,plain,
mult(asoc(X4,X3,X2),mult(X,i(mult(asoc(X4,X3,X2),X)))) = mult(mult(asoc(X4,X3,X2),X),i(mult(asoc(X4,X3,X2),X))),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,axiom,
mult(A2,i(A2)) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
cnf(c92,plain,
mult(mult(asoc(X4,X3,X2),X),i(mult(asoc(X4,X3,X2),X))) = unit,
inference(substitution,[status(thm)],[c91]) ).
cnf(c93,plain,
mult(asoc(X4,X3,X2),mult(X,i(mult(asoc(X4,X3,X2),X)))) = unit,
inference(transitivity,[status(thm)],[c90,c92]) ).
cnf(c94,plain,
mult(asoc(X4,X3,X2),mult(X,mult(i(asoc(X4,X3,X2)),i(X)))) = unit,
inference(transitivity,[status(thm)],[c80,c93]) ).
cnf(c95,plain,
mult(asoc(X4,X3,X2),i(op_t(asoc(X4,X3,X2),X))) = unit,
inference(transitivity,[status(thm)],[c76,c94]) ).
cnf(c96,plain,
mult(asoc(X4,X3,X2),op_t(i(asoc(X4,X3,X2)),i(X))) = unit,
inference(transitivity,[status(thm)],[c73,c95]) ).
cnf(c97,plain,
unit = mult(asoc(X4,X3,X2),op_t(i(asoc(X4,X3,X2)),i(X))),
inference(symmetry,[status(thm)],[c96]) ).
cnf(c98,plain,
rd(unit,op_t(i(asoc(X4,X3,X2)),i(X))) = rd(mult(asoc(X4,X3,X2),op_t(i(asoc(X4,X3,X2)),i(X))),op_t(i(asoc(X4,X3,X2)),i(X))),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
rd(mult(asoc(X4,X3,X2),op_t(i(asoc(X4,X3,X2)),i(X))),op_t(i(asoc(X4,X3,X2)),i(X))) = asoc(X4,X3,X2),
inference(substitution,[status(thm)],[c61]) ).
cnf(c100,plain,
rd(unit,op_t(i(asoc(X4,X3,X2)),i(X))) = asoc(X4,X3,X2),
inference(transitivity,[status(thm)],[c98,c99]) ).
cnf(c101,plain,
i(op_t(i(asoc(X4,X3,X2)),i(X))) = asoc(X4,X3,X2),
inference(transitivity,[status(thm)],[c65,c100]) ).
cnf(c102,plain,
op_t(asoc(X4,X3,X2),i(i(X))) = asoc(X4,X3,X2),
inference(transitivity,[status(thm)],[c57,c101]) ).
cnf(c103,plain,
op_t(asoc(X4,X3,X2),X) = asoc(X4,X3,X2),
inference(transitivity,[status(thm)],[c29,c102]) ).
cnf(c104,plain,
mult(X,op_t(asoc(X4,X3,X2),X)) = mult(X,asoc(X4,X3,X2)),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
mult(asoc(X4,X3,X2),X) = mult(X,asoc(X4,X3,X2)),
inference(transitivity,[status(thm)],[c27,c104]) ).
cnf(c106,plain,
mult(asoc(X3,X2,X),op_k(asoc(X3,X2,X),X4)) = mult(op_k(asoc(X3,X2,X),X4),asoc(X3,X2,X)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c107,plain,
mult(X4,mult(asoc(X3,X2,X),op_k(asoc(X3,X2,X),X4))) = mult(X4,mult(op_k(asoc(X3,X2,X),X4),asoc(X3,X2,X))),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
mult(asoc(X5,X4,X3),mult(X2,X)) = mult(mult(asoc(X5,X4,X3),X2),X),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c109,plain,
mult(mult(asoc(X5,X4,X3),X2),X) = mult(mult(asoc(X5,X4,X3),mult(X2,X)),asoc(asoc(X5,X4,X3),X2,X)),
inference(substitution,[status(thm)],[c81]) ).
cnf(c110,plain,
mult(asoc(X5,X4,X3),mult(X2,X)) = mult(mult(X2,X),asoc(X5,X4,X3)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c111,plain,
mult(mult(asoc(X5,X4,X3),mult(X2,X)),asoc(asoc(X5,X4,X3),X2,X)) = mult(mult(mult(X2,X),asoc(X5,X4,X3)),asoc(asoc(X5,X4,X3),X2,X)),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
mult(mult(X5,X4),asoc(X3,X2,X)) = mult(mult(X5,mult(X4,asoc(X3,X2,X))),asoc(X5,X4,asoc(X3,X2,X))),
inference(substitution,[status(thm)],[c81]) ).
cnf(c113,axiom,
asoc(A2,B2,asoc(C2,D2,E2)) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c22) ).
cnf(c114,plain,
asoc(X5,X4,asoc(X3,X2,X)) = unit,
inference(substitution,[status(thm)],[c113]) ).
cnf(c115,plain,
mult(mult(X5,mult(X4,asoc(X3,X2,X))),asoc(X5,X4,asoc(X3,X2,X))) = mult(mult(X5,mult(X4,asoc(X3,X2,X))),unit),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
mult(mult(X5,mult(X4,asoc(X3,X2,X))),unit) = mult(X5,mult(X4,asoc(X3,X2,X))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c117,plain,
mult(mult(X5,mult(X4,asoc(X3,X2,X))),asoc(X5,X4,asoc(X3,X2,X))) = mult(X5,mult(X4,asoc(X3,X2,X))),
inference(transitivity,[status(thm)],[c115,c116]) ).
cnf(c118,plain,
mult(mult(X5,X4),asoc(X3,X2,X)) = mult(X5,mult(X4,asoc(X3,X2,X))),
inference(transitivity,[status(thm)],[c112,c117]) ).
cnf(c119,plain,
mult(mult(X2,X),asoc(X5,X4,X3)) = mult(X2,mult(X,asoc(X5,X4,X3))),
inference(substitution,[status(thm)],[c118]) ).
cnf(c120,plain,
mult(mult(mult(X2,X),asoc(X5,X4,X3)),asoc(asoc(X5,X4,X3),X2,X)) = mult(mult(X2,mult(X,asoc(X5,X4,X3))),asoc(asoc(X5,X4,X3),X2,X)),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
asoc(asoc(X5,X4,X3),X2,X) = unit,
inference(substitution,[status(thm)],[c83]) ).
cnf(c122,plain,
mult(mult(X2,mult(X,asoc(X5,X4,X3))),asoc(asoc(X5,X4,X3),X2,X)) = mult(mult(X2,mult(X,asoc(X5,X4,X3))),unit),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
mult(mult(X2,mult(X,asoc(X5,X4,X3))),unit) = mult(X2,mult(X,asoc(X5,X4,X3))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c124,plain,
mult(mult(X2,mult(X,asoc(X5,X4,X3))),asoc(asoc(X5,X4,X3),X2,X)) = mult(X2,mult(X,asoc(X5,X4,X3))),
inference(transitivity,[status(thm)],[c122,c123]) ).
cnf(c125,plain,
mult(mult(mult(X2,X),asoc(X5,X4,X3)),asoc(asoc(X5,X4,X3),X2,X)) = mult(X2,mult(X,asoc(X5,X4,X3))),
inference(transitivity,[status(thm)],[c120,c124]) ).
cnf(c126,plain,
mult(mult(asoc(X5,X4,X3),mult(X2,X)),asoc(asoc(X5,X4,X3),X2,X)) = mult(X2,mult(X,asoc(X5,X4,X3))),
inference(transitivity,[status(thm)],[c111,c125]) ).
cnf(c127,plain,
mult(mult(asoc(X5,X4,X3),X2),X) = mult(X2,mult(X,asoc(X5,X4,X3))),
inference(transitivity,[status(thm)],[c109,c126]) ).
cnf(c128,plain,
mult(asoc(X5,X4,X3),mult(X2,X)) = mult(X2,mult(X,asoc(X5,X4,X3))),
inference(transitivity,[status(thm)],[c108,c127]) ).
cnf(c129,plain,
mult(asoc(X3,X2,X),mult(X4,op_k(asoc(X3,X2,X),X4))) = mult(X4,mult(op_k(asoc(X3,X2,X),X4),asoc(X3,X2,X))),
inference(substitution,[status(thm)],[c128]) ).
cnf(c130,plain,
mult(X4,mult(op_k(asoc(X3,X2,X),X4),asoc(X3,X2,X))) = mult(asoc(X3,X2,X),mult(X4,op_k(asoc(X3,X2,X),X4))),
inference(symmetry,[status(thm)],[c129]) ).
cnf(c131,plain,
mult(mult(asoc(X3,X2,X),X4),op_k(asoc(X3,X2,X),X4)) = mult(asoc(X3,X2,X),mult(X4,op_k(asoc(X3,X2,X),X4))),
inference(substitution,[status(thm)],[c88]) ).
cnf(c132,plain,
mult(asoc(X3,X2,X),mult(X4,op_k(asoc(X3,X2,X),X4))) = mult(mult(asoc(X3,X2,X),X4),op_k(asoc(X3,X2,X),X4)),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
mult(asoc(X3,X2,X),X4) = mult(X4,asoc(X3,X2,X)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c134,plain,
mult(mult(asoc(X3,X2,X),X4),op_k(asoc(X3,X2,X),X4)) = mult(mult(X4,asoc(X3,X2,X)),op_k(asoc(X3,X2,X),X4)),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,axiom,
mult(A2,B2) = mult(mult(B2,A2),op_k(A2,B2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c11) ).
cnf(c136,plain,
mult(asoc(X3,X2,X),X4) = mult(mult(X4,asoc(X3,X2,X)),op_k(asoc(X3,X2,X),X4)),
inference(substitution,[status(thm)],[c135]) ).
cnf(c137,plain,
mult(mult(X4,asoc(X3,X2,X)),op_k(asoc(X3,X2,X),X4)) = mult(asoc(X3,X2,X),X4),
inference(symmetry,[status(thm)],[c136]) ).
cnf(c138,plain,
mult(asoc(X3,X2,X),X4) = mult(X4,asoc(X3,X2,X)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c139,plain,
mult(mult(X4,asoc(X3,X2,X)),op_k(asoc(X3,X2,X),X4)) = mult(X4,asoc(X3,X2,X)),
inference(transitivity,[status(thm)],[c137,c138]) ).
cnf(c140,plain,
mult(mult(asoc(X3,X2,X),X4),op_k(asoc(X3,X2,X),X4)) = mult(X4,asoc(X3,X2,X)),
inference(transitivity,[status(thm)],[c134,c139]) ).
cnf(c141,plain,
mult(asoc(X3,X2,X),mult(X4,op_k(asoc(X3,X2,X),X4))) = mult(X4,asoc(X3,X2,X)),
inference(transitivity,[status(thm)],[c132,c140]) ).
cnf(c142,plain,
mult(X4,mult(op_k(asoc(X3,X2,X),X4),asoc(X3,X2,X))) = mult(X4,asoc(X3,X2,X)),
inference(transitivity,[status(thm)],[c130,c141]) ).
cnf(c143,plain,
mult(X4,mult(asoc(X3,X2,X),op_k(asoc(X3,X2,X),X4))) = mult(X4,asoc(X3,X2,X)),
inference(transitivity,[status(thm)],[c107,c142]) ).
cnf(c144,plain,
mult(X,mult(asoc(X4,X3,X2),op_k(asoc(X4,X3,X2),X))) = mult(X,asoc(X4,X3,X2)),
inference(substitution,[status(thm)],[c143]) ).
cnf(c145,plain,
mult(i(X),mult(X,mult(asoc(X4,X3,X2),op_k(asoc(X4,X3,X2),X)))) = mult(i(X),mult(X,asoc(X4,X3,X2))),
inference(congruence,[status(thm)],[c144]) ).
cnf(c146,plain,
mult(i(X),mult(X,asoc(X4,X3,X2))) = asoc(X4,X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c147,plain,
mult(i(X),mult(X,mult(asoc(X4,X3,X2),op_k(asoc(X4,X3,X2),X)))) = asoc(X4,X3,X2),
inference(transitivity,[status(thm)],[c145,c146]) ).
cnf(c148,plain,
mult(asoc(X4,X3,X2),op_k(asoc(X4,X3,X2),X)) = asoc(X4,X3,X2),
inference(transitivity,[status(thm)],[c6,c147]) ).
cnf(c149,plain,
mult(i(asoc(X4,X3,X2)),mult(asoc(X4,X3,X2),op_k(asoc(X4,X3,X2),X))) = mult(i(asoc(X4,X3,X2)),asoc(X4,X3,X2)),
inference(congruence,[status(thm)],[c148]) ).
cnf(c150,plain,
mult(i(asoc(X3,X2,X)),asoc(X3,X2,X)) = unit,
inference(substitution,[status(thm)],[c13]) ).
cnf(c151,plain,
mult(i(asoc(X4,X3,X2)),mult(asoc(X4,X3,X2),op_k(asoc(X4,X3,X2),X))) = unit,
inference(transitivity,[status(thm)],[c149,c150]) ).
cnf(c152,plain,
op_k(asoc(X4,X3,X2),X) = unit,
inference(transitivity,[status(thm)],[c4,c151]) ).
cnf(c153,plain,
op_k(asoc(a,b,c),d) = unit,
inference(substitution,[status(thm)],[c152]) ).
cnf(c154,plain,
$false,
inference(resolution,[status(thm)],[c1,c153]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP731-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 10:41:01 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.51 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.23/0.51
% 0.23/0.51 % SZS status Unsatisfiable
% 0.23/0.51
% 0.23/0.52 % SZS output start CNFRefutation
% See solution above
% 1.10/0.61
% 1.10/0.61 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------