%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP559-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 10:11:14 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.49s
% Output : CNFRefutation 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 3
% Syntax : Number of clauses : 168 ( 168 unt; 0 nHn; 3 RR)
% Number of literals : 168 ( 167 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 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 : 420 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
cnf(c2,axiom,
divide(A,inverse(divide(divide(B,C),divide(A,C)))) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c3,plain,
divide(X2,inverse(divide(divide(X2,X),divide(X2,X)))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
X2 = divide(X2,inverse(divide(divide(X2,X),divide(X2,X)))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
divide(X2,X3) = divide(divide(X2,inverse(divide(divide(X2,X),divide(X2,X)))),X3),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
inverse(divide(X2,X3)) = inverse(divide(divide(X2,inverse(divide(divide(X2,X),divide(X2,X)))),X3)),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
divide(X3,inverse(divide(X2,X3))) = divide(X3,inverse(divide(divide(X2,inverse(divide(divide(X2,X),divide(X2,X)))),X3))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,axiom,
multiply(A2,B2) = divide(A2,inverse(B2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c9,plain,
multiply(X2,X) = divide(X2,inverse(X)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
divide(divide(X2,inverse(X)),multiply(X3,X)) = divide(divide(X2,inverse(X)),divide(X3,inverse(X))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
inverse(divide(divide(X2,inverse(X)),multiply(X3,X))) = inverse(divide(divide(X2,inverse(X)),divide(X3,inverse(X)))),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
divide(X3,inverse(divide(divide(X2,inverse(X)),multiply(X3,X)))) = divide(X3,inverse(divide(divide(X2,inverse(X)),divide(X3,inverse(X))))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
divide(X3,inverse(divide(divide(X2,inverse(X)),divide(X3,inverse(X))))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c14,plain,
divide(X3,inverse(divide(divide(X2,inverse(X)),multiply(X3,X)))) = X2,
inference(transitivity,[status(thm)],[c12,c13]) ).
cnf(c15,plain,
X2 = divide(X3,inverse(divide(divide(X2,inverse(X)),multiply(X3,X)))),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
divide(X2,X2) = divide(X2,divide(X3,inverse(divide(divide(X2,inverse(X)),multiply(X3,X))))),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
inverse(divide(X2,X2)) = inverse(divide(X2,divide(X3,inverse(divide(divide(X2,inverse(X)),multiply(X3,X)))))),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
divide(X3,inverse(divide(X2,X2))) = divide(X3,inverse(divide(X2,divide(X3,inverse(divide(divide(X2,inverse(X)),multiply(X3,X))))))),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
divide(X3,inverse(divide(divide(X2,inverse(X)),multiply(X3,X)))) = X2,
inference(substitution,[status(thm)],[c14]) ).
cnf(c20,plain,
X3 = divide(X,inverse(divide(divide(X3,inverse(X2)),multiply(X,X2)))),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
divide(X3,divide(X4,inverse(divide(divide(X3,inverse(X2)),multiply(X,X2))))) = divide(divide(X,inverse(divide(divide(X3,inverse(X2)),multiply(X,X2)))),divide(X4,inverse(divide(divide(X3,inverse(X2)),multiply(X,X2))))),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
inverse(divide(X3,divide(X4,inverse(divide(divide(X3,inverse(X2)),multiply(X,X2)))))) = inverse(divide(divide(X,inverse(divide(divide(X3,inverse(X2)),multiply(X,X2)))),divide(X4,inverse(divide(divide(X3,inverse(X2)),multiply(X,X2)))))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
divide(X4,inverse(divide(X3,divide(X4,inverse(divide(divide(X3,inverse(X2)),multiply(X,X2))))))) = divide(X4,inverse(divide(divide(X,inverse(divide(divide(X3,inverse(X2)),multiply(X,X2)))),divide(X4,inverse(divide(divide(X3,inverse(X2)),multiply(X,X2))))))),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
divide(X4,inverse(divide(divide(X,inverse(divide(divide(X3,inverse(X2)),multiply(X,X2)))),divide(X4,inverse(divide(divide(X3,inverse(X2)),multiply(X,X2))))))) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c25,plain,
divide(X4,inverse(divide(X3,divide(X4,inverse(divide(divide(X3,inverse(X2)),multiply(X,X2))))))) = X,
inference(transitivity,[status(thm)],[c23,c24]) ).
cnf(c26,plain,
divide(X3,inverse(divide(X2,divide(X3,inverse(divide(divide(X2,inverse(X)),multiply(X3,X))))))) = X3,
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
divide(X2,inverse(divide(X,X))) = X2,
inference(transitivity,[status(thm)],[c18,c26]) ).
cnf(c28,plain,
X2 = divide(X2,inverse(divide(X,X))),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
divide(divide(X2,inverse(divide(X,X))),X3) = divide(divide(X2,inverse(divide(X,X))),divide(X3,inverse(divide(X,X)))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
inverse(divide(divide(X2,inverse(divide(X,X))),X3)) = inverse(divide(divide(X2,inverse(divide(X,X))),divide(X3,inverse(divide(X,X))))),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
divide(X3,inverse(divide(divide(X2,inverse(divide(X,X))),X3))) = divide(X3,inverse(divide(divide(X2,inverse(divide(X,X))),divide(X3,inverse(divide(X,X)))))),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
divide(X3,inverse(divide(divide(X2,inverse(divide(X,X))),divide(X3,inverse(divide(X,X)))))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c33,plain,
divide(X3,inverse(divide(divide(X2,inverse(divide(X,X))),X3))) = X2,
inference(transitivity,[status(thm)],[c31,c32]) ).
cnf(c34,plain,
divide(X3,inverse(divide(divide(X2,inverse(divide(divide(X2,X),divide(X2,X)))),X3))) = X2,
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
divide(X2,inverse(divide(X,X2))) = X,
inference(transitivity,[status(thm)],[c7,c34]) ).
cnf(c36,plain,
divide(X,inverse(divide(X2,X))) = X2,
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
X2 = divide(X,inverse(divide(X2,X))),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
divide(X2,divide(X2,X)) = divide(divide(X,inverse(divide(X2,X))),divide(X2,X)),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
divide(X,inverse(divide(divide(X2,X2),X))) = divide(X2,X2),
inference(substitution,[status(thm)],[c35]) ).
cnf(c40,plain,
divide(X2,X2) = divide(X,inverse(divide(divide(X2,X2),X))),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
divide(inverse(divide(divide(X2,X2),X)),inverse(divide(X,X))) = inverse(divide(divide(X2,X2),X)),
inference(substitution,[status(thm)],[c27]) ).
cnf(c42,plain,
inverse(divide(divide(X2,X2),X)) = divide(inverse(divide(divide(X2,X2),X)),inverse(divide(X,X))),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
divide(X,inverse(divide(X2,X))) = X2,
inference(substitution,[status(thm)],[c35]) ).
cnf(c44,plain,
X2 = divide(X,inverse(divide(X2,X))),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
inverse(X2) = inverse(divide(X,inverse(divide(X2,X)))),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
divide(inverse(divide(X2,X)),inverse(X2)) = divide(inverse(divide(X2,X)),inverse(divide(X,inverse(divide(X2,X))))),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
divide(inverse(divide(X2,X)),inverse(divide(X,inverse(divide(X2,X))))) = X,
inference(substitution,[status(thm)],[c35]) ).
cnf(c48,plain,
divide(inverse(divide(X2,X)),inverse(X2)) = X,
inference(transitivity,[status(thm)],[c46,c47]) ).
cnf(c49,plain,
divide(inverse(divide(divide(X2,X2),X)),inverse(divide(X2,X2))) = X,
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
X = divide(inverse(divide(divide(X2,X2),X)),inverse(divide(X2,X2))),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
divide(X,X) = divide(X,divide(inverse(divide(divide(X2,X2),X)),inverse(divide(X2,X2)))),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
inverse(divide(X,X)) = inverse(divide(X,divide(inverse(divide(divide(X2,X2),X)),inverse(divide(X2,X2))))),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
divide(inverse(divide(divide(X2,X2),X)),inverse(divide(X,X))) = divide(inverse(divide(divide(X2,X2),X)),inverse(divide(X,divide(inverse(divide(divide(X2,X2),X)),inverse(divide(X2,X2)))))),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
X2 = divide(X2,inverse(divide(X,X))),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c55,plain,
divide(X2,divide(X3,inverse(divide(X,X)))) = divide(divide(X2,inverse(divide(X,X))),divide(X3,inverse(divide(X,X)))),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
inverse(divide(X2,divide(X3,inverse(divide(X,X))))) = inverse(divide(divide(X2,inverse(divide(X,X))),divide(X3,inverse(divide(X,X))))),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
divide(X3,inverse(divide(X2,divide(X3,inverse(divide(X,X)))))) = divide(X3,inverse(divide(divide(X2,inverse(divide(X,X))),divide(X3,inverse(divide(X,X)))))),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
divide(X3,inverse(divide(divide(X2,inverse(divide(X,X))),divide(X3,inverse(divide(X,X)))))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c59,plain,
divide(X3,inverse(divide(X2,divide(X3,inverse(divide(X,X)))))) = X2,
inference(transitivity,[status(thm)],[c57,c58]) ).
cnf(c60,plain,
divide(inverse(divide(divide(X2,X2),X)),inverse(divide(X,divide(inverse(divide(divide(X2,X2),X)),inverse(divide(X2,X2)))))) = X,
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,plain,
divide(inverse(divide(divide(X2,X2),X)),inverse(divide(X,X))) = X,
inference(transitivity,[status(thm)],[c53,c60]) ).
cnf(c62,plain,
inverse(divide(divide(X2,X2),X)) = X,
inference(transitivity,[status(thm)],[c42,c61]) ).
cnf(c63,plain,
divide(X,inverse(divide(divide(X2,X2),X))) = divide(X,X),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
divide(X2,X2) = divide(X,X),
inference(transitivity,[status(thm)],[c40,c63]) ).
cnf(c65,plain,
divide(inverse(X),inverse(X)) = divide(X2,X2),
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,plain,
divide(X2,X2) = divide(inverse(X),inverse(X)),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c67,plain,
divide(divide(X3,X3),inverse(X2)) = divide(divide(inverse(X),inverse(X)),inverse(X2)),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
divide(inverse(X),inverse(divide(inverse(divide(X2,X2)),inverse(X)))) = inverse(divide(X2,X2)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c69,plain,
inverse(divide(X2,X2)) = divide(inverse(X),inverse(divide(inverse(divide(X2,X2)),inverse(X)))),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
divide(X2,inverse(divide(divide(X3,inverse(X)),multiply(X2,X)))) = X3,
inference(substitution,[status(thm)],[c14]) ).
cnf(c71,plain,
X3 = divide(X2,inverse(divide(divide(X3,inverse(X)),multiply(X2,X)))),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c72,plain,
divide(X3,X3) = divide(X3,divide(X2,inverse(divide(divide(X3,inverse(X)),multiply(X2,X))))),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
inverse(divide(X3,X3)) = inverse(divide(X3,divide(X2,inverse(divide(divide(X3,inverse(X)),multiply(X2,X)))))),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
divide(inverse(divide(X3,X3)),inverse(X2)) = divide(inverse(divide(X3,divide(X2,inverse(divide(divide(X3,inverse(X)),multiply(X2,X)))))),inverse(X2)),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
divide(X2,inverse(divide(X3,divide(X2,inverse(divide(divide(X3,inverse(X)),multiply(X2,X))))))) = X2,
inference(substitution,[status(thm)],[c25]) ).
cnf(c76,plain,
X2 = divide(X2,inverse(divide(X3,divide(X2,inverse(divide(divide(X3,inverse(X)),multiply(X2,X))))))),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c77,plain,
inverse(X2) = inverse(divide(X2,inverse(divide(X3,divide(X2,inverse(divide(divide(X3,inverse(X)),multiply(X2,X)))))))),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
divide(inverse(divide(X3,divide(X2,inverse(divide(divide(X3,inverse(X)),multiply(X2,X)))))),inverse(X2)) = divide(inverse(divide(X3,divide(X2,inverse(divide(divide(X3,inverse(X)),multiply(X2,X)))))),inverse(divide(X2,inverse(divide(X3,divide(X2,inverse(divide(divide(X3,inverse(X)),multiply(X2,X))))))))),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
divide(inverse(divide(X3,divide(X2,inverse(divide(divide(X3,inverse(X)),multiply(X2,X)))))),inverse(divide(X2,inverse(divide(X3,divide(X2,inverse(divide(divide(X3,inverse(X)),multiply(X2,X))))))))) = X2,
inference(substitution,[status(thm)],[c35]) ).
cnf(c80,plain,
divide(inverse(divide(X3,divide(X2,inverse(divide(divide(X3,inverse(X)),multiply(X2,X)))))),inverse(X2)) = X2,
inference(transitivity,[status(thm)],[c78,c79]) ).
cnf(c81,plain,
divide(inverse(divide(X2,X2)),inverse(X)) = X,
inference(transitivity,[status(thm)],[c74,c80]) ).
cnf(c82,plain,
inverse(divide(inverse(divide(X2,X2)),inverse(X))) = inverse(X),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
divide(inverse(X),inverse(divide(inverse(divide(X2,X2)),inverse(X)))) = divide(inverse(X),inverse(X)),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
inverse(divide(X2,X2)) = divide(inverse(X),inverse(X)),
inference(transitivity,[status(thm)],[c69,c83]) ).
cnf(c85,plain,
inverse(divide(X,X)) = divide(inverse(X2),inverse(X2)),
inference(substitution,[status(thm)],[c84]) ).
cnf(c86,plain,
divide(inverse(X2),inverse(X2)) = inverse(divide(X,X)),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c87,plain,
divide(divide(inverse(X2),inverse(X2)),inverse(X3)) = divide(inverse(divide(X,X)),inverse(X3)),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
X2 = divide(X2,inverse(divide(X,X))),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c89,plain,
inverse(X2) = inverse(divide(X2,inverse(divide(X,X)))),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
divide(inverse(divide(X,X)),inverse(X2)) = divide(inverse(divide(X,X)),inverse(divide(X2,inverse(divide(X,X))))),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
divide(inverse(divide(X,X)),inverse(divide(X2,inverse(divide(X,X))))) = X2,
inference(substitution,[status(thm)],[c35]) ).
cnf(c92,plain,
divide(inverse(divide(X,X)),inverse(X2)) = X2,
inference(transitivity,[status(thm)],[c90,c91]) ).
cnf(c93,plain,
divide(divide(inverse(X),inverse(X)),inverse(X2)) = X2,
inference(transitivity,[status(thm)],[c87,c92]) ).
cnf(c94,plain,
divide(divide(X2,X2),inverse(X)) = X,
inference(transitivity,[status(thm)],[c67,c93]) ).
cnf(c95,plain,
divide(divide(X,X),inverse(divide(divide(X3,inverse(X2)),X2))) = divide(divide(X3,inverse(X2)),X2),
inference(substitution,[status(thm)],[c94]) ).
cnf(c96,plain,
divide(divide(X3,inverse(X2)),X2) = divide(divide(X,X),inverse(divide(divide(X3,inverse(X2)),X2))),
inference(symmetry,[status(thm)],[c95]) ).
cnf(c97,plain,
divide(divide(X,X),inverse(X2)) = X2,
inference(substitution,[status(thm)],[c94]) ).
cnf(c98,plain,
X2 = divide(divide(X,X),inverse(X2)),
inference(symmetry,[status(thm)],[c97]) ).
cnf(c99,plain,
divide(divide(X3,inverse(X2)),X2) = divide(divide(X3,inverse(X2)),divide(divide(X,X),inverse(X2))),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
inverse(divide(divide(X3,inverse(X2)),X2)) = inverse(divide(divide(X3,inverse(X2)),divide(divide(X,X),inverse(X2)))),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
divide(divide(X,X),inverse(divide(divide(X3,inverse(X2)),X2))) = divide(divide(X,X),inverse(divide(divide(X3,inverse(X2)),divide(divide(X,X),inverse(X2))))),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
divide(divide(X,X),inverse(divide(divide(X3,inverse(X2)),divide(divide(X,X),inverse(X2))))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c103,plain,
divide(divide(X,X),inverse(divide(divide(X3,inverse(X2)),X2))) = X3,
inference(transitivity,[status(thm)],[c101,c102]) ).
cnf(c104,plain,
divide(divide(X2,inverse(X)),X) = X2,
inference(transitivity,[status(thm)],[c96,c103]) ).
cnf(c105,plain,
divide(divide(X,inverse(divide(X2,X))),divide(X2,X)) = X,
inference(substitution,[status(thm)],[c104]) ).
cnf(c106,plain,
divide(X2,divide(X2,X)) = X,
inference(transitivity,[status(thm)],[c38,c105]) ).
cnf(c107,plain,
divide(X3,divide(X3,multiply(multiply(X3,X2),X))) = multiply(multiply(X3,X2),X),
inference(substitution,[status(thm)],[c106]) ).
cnf(c108,plain,
multiply(multiply(X3,X2),X) = divide(X3,divide(X3,multiply(multiply(X3,X2),X))),
inference(symmetry,[status(thm)],[c107]) ).
cnf(c109,plain,
multiply(multiply(X,X3),X2) = divide(multiply(X,X3),inverse(X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c110,plain,
inverse(multiply(multiply(X,X3),X2)) = inverse(divide(multiply(X,X3),inverse(X2))),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
divide(inverse(multiply(X3,X2)),inverse(multiply(multiply(X,X3),X2))) = divide(inverse(multiply(X3,X2)),inverse(divide(multiply(X,X3),inverse(X2)))),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
multiply(X,X2) = divide(X,inverse(X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c113,plain,
inverse(multiply(X,X2)) = inverse(divide(X,inverse(X2))),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
divide(inverse(X2),inverse(multiply(X,X2))) = divide(inverse(X2),inverse(divide(X,inverse(X2)))),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
divide(inverse(X2),inverse(divide(X,inverse(X2)))) = X,
inference(substitution,[status(thm)],[c35]) ).
cnf(c116,plain,
divide(inverse(X2),inverse(multiply(X,X2))) = X,
inference(transitivity,[status(thm)],[c114,c115]) ).
cnf(c117,plain,
divide(inverse(X),inverse(multiply(X2,X))) = X2,
inference(substitution,[status(thm)],[c116]) ).
cnf(c118,plain,
X2 = divide(inverse(X),inverse(multiply(X2,X))),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,plain,
inverse(X2) = inverse(divide(inverse(X),inverse(multiply(X2,X)))),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
divide(inverse(multiply(X2,X)),inverse(X2)) = divide(inverse(multiply(X2,X)),inverse(divide(inverse(X),inverse(multiply(X2,X))))),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
divide(inverse(multiply(X2,X)),inverse(divide(inverse(X),inverse(multiply(X2,X))))) = inverse(X),
inference(substitution,[status(thm)],[c35]) ).
cnf(c122,plain,
divide(inverse(multiply(X2,X)),inverse(X2)) = inverse(X),
inference(transitivity,[status(thm)],[c120,c121]) ).
cnf(c123,plain,
inverse(X) = divide(inverse(multiply(X2,X)),inverse(X2)),
inference(symmetry,[status(thm)],[c122]) ).
cnf(c124,plain,
divide(multiply(X,X3),inverse(X2)) = divide(multiply(X,X3),divide(inverse(multiply(X3,X2)),inverse(X3))),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
inverse(divide(multiply(X,X3),inverse(X2))) = inverse(divide(multiply(X,X3),divide(inverse(multiply(X3,X2)),inverse(X3)))),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
divide(inverse(multiply(X3,X2)),inverse(divide(multiply(X,X3),inverse(X2)))) = divide(inverse(multiply(X3,X2)),inverse(divide(multiply(X,X3),divide(inverse(multiply(X3,X2)),inverse(X3))))),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
multiply(X2,X) = divide(X2,inverse(X)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c128,plain,
divide(multiply(X2,X),divide(X3,inverse(X))) = divide(divide(X2,inverse(X)),divide(X3,inverse(X))),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
inverse(divide(multiply(X2,X),divide(X3,inverse(X)))) = inverse(divide(divide(X2,inverse(X)),divide(X3,inverse(X)))),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
divide(X3,inverse(divide(multiply(X2,X),divide(X3,inverse(X))))) = divide(X3,inverse(divide(divide(X2,inverse(X)),divide(X3,inverse(X))))),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
divide(X3,inverse(divide(divide(X2,inverse(X)),divide(X3,inverse(X))))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c132,plain,
divide(X3,inverse(divide(multiply(X2,X),divide(X3,inverse(X))))) = X2,
inference(transitivity,[status(thm)],[c130,c131]) ).
cnf(c133,plain,
divide(inverse(multiply(X3,X2)),inverse(divide(multiply(X,X3),divide(inverse(multiply(X3,X2)),inverse(X3))))) = X,
inference(substitution,[status(thm)],[c132]) ).
cnf(c134,plain,
divide(inverse(multiply(X3,X2)),inverse(divide(multiply(X,X3),inverse(X2)))) = X,
inference(transitivity,[status(thm)],[c126,c133]) ).
cnf(c135,plain,
divide(inverse(multiply(X3,X2)),inverse(multiply(multiply(X,X3),X2))) = X,
inference(transitivity,[status(thm)],[c111,c134]) ).
cnf(c136,plain,
divide(inverse(multiply(X2,X)),inverse(multiply(multiply(X3,X2),X))) = X3,
inference(substitution,[status(thm)],[c135]) ).
cnf(c137,plain,
X3 = divide(inverse(multiply(X2,X)),inverse(multiply(multiply(X3,X2),X))),
inference(symmetry,[status(thm)],[c136]) ).
cnf(c138,plain,
divide(X3,multiply(multiply(X3,X2),X)) = divide(divide(inverse(multiply(X2,X)),inverse(multiply(multiply(X3,X2),X))),multiply(multiply(X3,X2),X)),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
divide(divide(inverse(multiply(X2,X)),inverse(multiply(multiply(X3,X2),X))),multiply(multiply(X3,X2),X)) = inverse(multiply(X2,X)),
inference(substitution,[status(thm)],[c104]) ).
cnf(c140,plain,
divide(X3,multiply(multiply(X3,X2),X)) = inverse(multiply(X2,X)),
inference(transitivity,[status(thm)],[c138,c139]) ).
cnf(c141,plain,
divide(X3,divide(X3,multiply(multiply(X3,X2),X))) = divide(X3,inverse(multiply(X2,X))),
inference(congruence,[status(thm)],[c140]) ).
cnf(c142,plain,
divide(X,inverse(divide(divide(X2,inverse(X)),X))) = divide(X2,inverse(X)),
inference(substitution,[status(thm)],[c35]) ).
cnf(c143,plain,
divide(X2,inverse(X)) = divide(X,inverse(divide(divide(X2,inverse(X)),X))),
inference(symmetry,[status(thm)],[c142]) ).
cnf(c144,plain,
inverse(divide(divide(X2,inverse(X)),X)) = inverse(X2),
inference(congruence,[status(thm)],[c104]) ).
cnf(c145,plain,
divide(X,inverse(divide(divide(X2,inverse(X)),X))) = divide(X,inverse(X2)),
inference(congruence,[status(thm)],[c144]) ).
cnf(c146,plain,
divide(X2,inverse(X)) = divide(X,inverse(X2)),
inference(transitivity,[status(thm)],[c143,c145]) ).
cnf(c147,plain,
divide(X3,inverse(multiply(X2,X))) = divide(multiply(X2,X),inverse(X3)),
inference(substitution,[status(thm)],[c146]) ).
cnf(c148,plain,
divide(X2,inverse(divide(multiply(X,X2),X2))) = multiply(X,X2),
inference(substitution,[status(thm)],[c35]) ).
cnf(c149,plain,
multiply(X,X2) = divide(X2,inverse(divide(multiply(X,X2),X2))),
inference(symmetry,[status(thm)],[c148]) ).
cnf(c150,plain,
divide(divide(X,X),inverse(X2)) = X2,
inference(substitution,[status(thm)],[c94]) ).
cnf(c151,plain,
X2 = divide(divide(X,X),inverse(X2)),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
divide(multiply(X3,X2),X2) = divide(multiply(X3,X2),divide(divide(X,X),inverse(X2))),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
divide(divide(X,X),inverse(divide(multiply(X3,X2),divide(divide(X,X),inverse(X2))))) = divide(multiply(X3,X2),divide(divide(X,X),inverse(X2))),
inference(substitution,[status(thm)],[c94]) ).
cnf(c154,plain,
divide(multiply(X3,X2),divide(divide(X,X),inverse(X2))) = divide(divide(X,X),inverse(divide(multiply(X3,X2),divide(divide(X,X),inverse(X2))))),
inference(symmetry,[status(thm)],[c153]) ).
cnf(c155,plain,
divide(divide(X,X),inverse(divide(multiply(X3,X2),divide(divide(X,X),inverse(X2))))) = X3,
inference(substitution,[status(thm)],[c132]) ).
cnf(c156,plain,
divide(multiply(X3,X2),divide(divide(X,X),inverse(X2))) = X3,
inference(transitivity,[status(thm)],[c154,c155]) ).
cnf(c157,plain,
divide(multiply(X2,X),X) = X2,
inference(transitivity,[status(thm)],[c152,c156]) ).
cnf(c158,plain,
divide(multiply(X,X2),X2) = X,
inference(substitution,[status(thm)],[c157]) ).
cnf(c159,plain,
inverse(divide(multiply(X,X2),X2)) = inverse(X),
inference(congruence,[status(thm)],[c158]) ).
cnf(c160,plain,
divide(X2,inverse(divide(multiply(X,X2),X2))) = divide(X2,inverse(X)),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
multiply(X,X2) = divide(X2,inverse(X)),
inference(transitivity,[status(thm)],[c149,c160]) ).
cnf(c162,plain,
multiply(X3,multiply(X2,X)) = divide(multiply(X2,X),inverse(X3)),
inference(substitution,[status(thm)],[c161]) ).
cnf(c163,plain,
divide(multiply(X2,X),inverse(X3)) = multiply(X3,multiply(X2,X)),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c164,plain,
divide(X3,inverse(multiply(X2,X))) = multiply(X3,multiply(X2,X)),
inference(transitivity,[status(thm)],[c147,c163]) ).
cnf(c165,plain,
divide(X3,divide(X3,multiply(multiply(X3,X2),X))) = multiply(X3,multiply(X2,X)),
inference(transitivity,[status(thm)],[c141,c164]) ).
cnf(c166,plain,
multiply(multiply(X3,X2),X) = multiply(X3,multiply(X2,X)),
inference(transitivity,[status(thm)],[c108,c165]) ).
cnf(c167,plain,
multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)),
inference(substitution,[status(thm)],[c166]) ).
cnf(c168,plain,
$false,
inference(resolution,[status(thm)],[c1,c167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP559-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n002.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sun Sep 27 10:10:21 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.49 Command-line arguments: --flatten --complete-subsets
% 0.14/0.49
% 0.14/0.49 % SZS status Unsatisfiable
% 0.14/0.49
% 0.14/0.49 % SZS output start CNFRefutation
% See solution above
% 0.73/0.55
% 0.73/0.55 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------