%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP409-1 : TPTP v9.3.1. Released v2.6.0.
% 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 10:09:57 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.49s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 2
% Syntax : Number of clauses : 91 ( 91 unt; 0 nHn; 3 RR)
% Number of literals : 91 ( 90 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 15 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 331 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_1) ).
cnf(c2,axiom,
multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))),inverse(multiply(inverse(C),C))) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(c3,plain,
multiply(multiply(inverse(multiply(X,inverse(multiply(X3,X2)))),multiply(X,inverse(X2))),inverse(multiply(inverse(X2),X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
X3 = multiply(multiply(inverse(multiply(X,inverse(multiply(X3,X2)))),multiply(X,inverse(X2))),inverse(multiply(inverse(X2),X2))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
multiply(inverse(X3),X3) = multiply(inverse(X3),multiply(multiply(inverse(multiply(X,inverse(multiply(X3,X2)))),multiply(X,inverse(X2))),inverse(multiply(inverse(X2),X2)))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
multiply(multiply(inverse(multiply(X,inverse(multiply(X3,X2)))),multiply(X,inverse(X2))),inverse(multiply(inverse(X2),X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c7,plain,
X3 = multiply(multiply(inverse(multiply(X2,inverse(multiply(X3,X)))),multiply(X2,inverse(X))),inverse(multiply(inverse(X),X))),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
inverse(X3) = inverse(multiply(multiply(inverse(multiply(X2,inverse(multiply(X3,X)))),multiply(X2,inverse(X))),inverse(multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
multiply(inverse(X4),multiply(multiply(inverse(multiply(X3,inverse(multiply(X4,X2)))),multiply(X3,inverse(X2))),X)) = multiply(inverse(multiply(multiply(inverse(multiply(X3,inverse(multiply(X4,X2)))),multiply(X3,inverse(X2))),inverse(multiply(inverse(X2),X2)))),multiply(multiply(inverse(multiply(X3,inverse(multiply(X4,X2)))),multiply(X3,inverse(X2))),X)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(multiply(inverse(multiply(X,inverse(multiply(X3,X2)))),multiply(X,inverse(X2))),inverse(multiply(inverse(X2),X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c11,plain,
X3 = multiply(multiply(inverse(multiply(X,inverse(multiply(X3,X2)))),multiply(X,inverse(X2))),inverse(multiply(inverse(X2),X2))),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
inverse(X3) = inverse(multiply(multiply(inverse(multiply(X,inverse(multiply(X3,X2)))),multiply(X,inverse(X2))),inverse(multiply(inverse(X2),X2)))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
multiply(X4,inverse(X3)) = multiply(X4,inverse(multiply(multiply(inverse(multiply(X,inverse(multiply(X3,X2)))),multiply(X,inverse(X2))),inverse(multiply(inverse(X2),X2))))),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
inverse(multiply(X4,inverse(X3))) = inverse(multiply(X4,inverse(multiply(multiply(inverse(multiply(X,inverse(multiply(X3,X2)))),multiply(X,inverse(X2))),inverse(multiply(inverse(X2),X2)))))),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
multiply(inverse(multiply(X4,inverse(X3))),multiply(X4,inverse(inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(X4,inverse(multiply(multiply(inverse(multiply(X,inverse(multiply(X3,X2)))),multiply(X,inverse(X2))),inverse(multiply(inverse(X2),X2)))))),multiply(X4,inverse(inverse(multiply(inverse(X2),X2))))),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(multiply(inverse(multiply(X4,inverse(X3))),multiply(X4,inverse(inverse(multiply(inverse(X2),X2))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = multiply(multiply(inverse(multiply(X4,inverse(multiply(multiply(inverse(multiply(X,inverse(multiply(X3,X2)))),multiply(X,inverse(X2))),inverse(multiply(inverse(X2),X2)))))),multiply(X4,inverse(inverse(multiply(inverse(X2),X2))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
multiply(multiply(inverse(multiply(X4,inverse(multiply(multiply(inverse(multiply(X,inverse(multiply(X3,X2)))),multiply(X,inverse(X2))),inverse(multiply(inverse(X2),X2)))))),multiply(X4,inverse(inverse(multiply(inverse(X2),X2))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(X,inverse(multiply(X3,X2)))),multiply(X,inverse(X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c18,plain,
multiply(multiply(inverse(multiply(X4,inverse(X3))),multiply(X4,inverse(inverse(multiply(inverse(X2),X2))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(X,inverse(multiply(X3,X2)))),multiply(X,inverse(X2))),
inference(transitivity,[status(thm)],[c16,c17]) ).
cnf(c19,plain,
multiply(multiply(inverse(multiply(X,inverse(multiply(X3,inverse(multiply(inverse(X2),X2)))))),multiply(X,inverse(inverse(multiply(inverse(X2),X2))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(X4,inverse(multiply(multiply(X3,inverse(multiply(inverse(X2),X2))),X2)))),multiply(X4,inverse(X2))),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
multiply(inverse(multiply(X4,inverse(multiply(multiply(X3,inverse(multiply(inverse(X2),X2))),X2)))),multiply(X4,inverse(X2))) = multiply(multiply(inverse(multiply(X,inverse(multiply(X3,inverse(multiply(inverse(X2),X2)))))),multiply(X,inverse(inverse(multiply(inverse(X2),X2))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
multiply(multiply(inverse(multiply(X,inverse(multiply(X3,inverse(multiply(inverse(X2),X2)))))),multiply(X,inverse(inverse(multiply(inverse(X2),X2))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c22,plain,
multiply(inverse(multiply(X3,inverse(multiply(multiply(X2,inverse(multiply(inverse(X),X))),X)))),multiply(X3,inverse(X))) = X2,
inference(transitivity,[status(thm)],[c20,c21]) ).
cnf(c23,plain,
multiply(inverse(multiply(X2,inverse(multiply(multiply(X3,inverse(multiply(inverse(X),X))),X)))),multiply(X2,inverse(X))) = X3,
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
X3 = multiply(inverse(multiply(X2,inverse(multiply(multiply(X3,inverse(multiply(inverse(X),X))),X)))),multiply(X2,inverse(X))),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
inverse(X3) = inverse(multiply(inverse(multiply(X2,inverse(multiply(multiply(X3,inverse(multiply(inverse(X),X))),X)))),multiply(X2,inverse(X)))),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
multiply(X4,inverse(X3)) = multiply(X4,inverse(multiply(inverse(multiply(X2,inverse(multiply(multiply(X3,inverse(multiply(inverse(X),X))),X)))),multiply(X2,inverse(X))))),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
inverse(multiply(X4,inverse(X3))) = inverse(multiply(X4,inverse(multiply(inverse(multiply(X2,inverse(multiply(multiply(X3,inverse(multiply(inverse(X),X))),X)))),multiply(X2,inverse(X)))))),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
multiply(inverse(multiply(X4,inverse(X3))),multiply(X4,inverse(multiply(X2,inverse(X))))) = multiply(inverse(multiply(X4,inverse(multiply(inverse(multiply(X2,inverse(multiply(multiply(X3,inverse(multiply(inverse(X),X))),X)))),multiply(X2,inverse(X)))))),multiply(X4,inverse(multiply(X2,inverse(X))))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
multiply(multiply(inverse(multiply(X4,inverse(X3))),multiply(X4,inverse(multiply(X2,inverse(X))))),inverse(multiply(inverse(multiply(X2,inverse(X))),multiply(X2,inverse(X))))) = multiply(multiply(inverse(multiply(X4,inverse(multiply(inverse(multiply(X2,inverse(multiply(multiply(X3,inverse(multiply(inverse(X),X))),X)))),multiply(X2,inverse(X)))))),multiply(X4,inverse(multiply(X2,inverse(X))))),inverse(multiply(inverse(multiply(X2,inverse(X))),multiply(X2,inverse(X))))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
multiply(multiply(inverse(multiply(X4,inverse(multiply(inverse(multiply(X2,inverse(multiply(multiply(X3,inverse(multiply(inverse(X),X))),X)))),multiply(X2,inverse(X)))))),multiply(X4,inverse(multiply(X2,inverse(X))))),inverse(multiply(inverse(multiply(X2,inverse(X))),multiply(X2,inverse(X))))) = inverse(multiply(X2,inverse(multiply(multiply(X3,inverse(multiply(inverse(X),X))),X)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c31,plain,
multiply(multiply(inverse(multiply(X4,inverse(X3))),multiply(X4,inverse(multiply(X2,inverse(X))))),inverse(multiply(inverse(multiply(X2,inverse(X))),multiply(X2,inverse(X))))) = inverse(multiply(X2,inverse(multiply(multiply(X3,inverse(multiply(inverse(X),X))),X)))),
inference(transitivity,[status(thm)],[c29,c30]) ).
cnf(c32,plain,
multiply(multiply(inverse(multiply(X,inverse(multiply(X3,multiply(X4,inverse(X2)))))),multiply(X,inverse(multiply(X4,inverse(X2))))),inverse(multiply(inverse(multiply(X4,inverse(X2))),multiply(X4,inverse(X2))))) = inverse(multiply(X4,inverse(multiply(multiply(multiply(X3,multiply(X4,inverse(X2))),inverse(multiply(inverse(X2),X2))),X2)))),
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
inverse(multiply(X4,inverse(multiply(multiply(multiply(X3,multiply(X4,inverse(X2))),inverse(multiply(inverse(X2),X2))),X2)))) = multiply(multiply(inverse(multiply(X,inverse(multiply(X3,multiply(X4,inverse(X2)))))),multiply(X,inverse(multiply(X4,inverse(X2))))),inverse(multiply(inverse(multiply(X4,inverse(X2))),multiply(X4,inverse(X2))))),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
multiply(multiply(inverse(multiply(X,inverse(multiply(X3,multiply(X4,inverse(X2)))))),multiply(X,inverse(multiply(X4,inverse(X2))))),inverse(multiply(inverse(multiply(X4,inverse(X2))),multiply(X4,inverse(X2))))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c35,plain,
inverse(multiply(X3,inverse(multiply(multiply(multiply(X2,multiply(X3,inverse(X))),inverse(multiply(inverse(X),X))),X)))) = X2,
inference(transitivity,[status(thm)],[c33,c34]) ).
cnf(c36,plain,
inverse(multiply(X3,inverse(multiply(multiply(multiply(X2,multiply(X3,inverse(X))),inverse(multiply(inverse(X),X))),X)))) = X2,
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
X3 = inverse(multiply(X2,inverse(multiply(multiply(multiply(X3,multiply(X2,inverse(X))),inverse(multiply(inverse(X),X))),X)))),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
multiply(X3,X4) = multiply(X3,inverse(multiply(X2,inverse(multiply(multiply(multiply(X4,multiply(X2,inverse(X))),inverse(multiply(inverse(X),X))),X))))),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
multiply(inverse(multiply(X3,inverse(X5))),multiply(X3,X4)) = multiply(inverse(multiply(X3,inverse(X5))),multiply(X3,inverse(multiply(X2,inverse(multiply(multiply(multiply(X4,multiply(X2,inverse(X))),inverse(multiply(inverse(X),X))),X)))))),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
multiply(inverse(multiply(X2,inverse(multiply(multiply(X3,inverse(multiply(inverse(X),X))),X)))),multiply(X2,inverse(X))) = X3,
inference(substitution,[status(thm)],[c22]) ).
cnf(c41,plain,
X3 = multiply(inverse(multiply(X2,inverse(multiply(multiply(X3,inverse(multiply(inverse(X),X))),X)))),multiply(X2,inverse(X))),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
inverse(X3) = inverse(multiply(inverse(multiply(X2,inverse(multiply(multiply(X3,inverse(multiply(inverse(X),X))),X)))),multiply(X2,inverse(X)))),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
multiply(X,inverse(X4)) = multiply(X,inverse(multiply(inverse(multiply(X3,inverse(multiply(multiply(X4,inverse(multiply(inverse(X2),X2))),X2)))),multiply(X3,inverse(X2))))),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
inverse(multiply(X,inverse(X4))) = inverse(multiply(X,inverse(multiply(inverse(multiply(X3,inverse(multiply(multiply(X4,inverse(multiply(inverse(X2),X2))),X2)))),multiply(X3,inverse(X2)))))),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
multiply(inverse(multiply(X,inverse(X4))),multiply(X,inverse(multiply(X3,inverse(X2))))) = multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(X3,inverse(multiply(multiply(X4,inverse(multiply(inverse(X2),X2))),X2)))),multiply(X3,inverse(X2)))))),multiply(X,inverse(multiply(X3,inverse(X2))))),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
multiply(multiply(inverse(multiply(X,inverse(multiply(multiply(inverse(multiply(X2,inverse(multiply(X4,X3)))),multiply(X2,inverse(X3))),inverse(multiply(inverse(X3),X3)))))),multiply(X,inverse(inverse(multiply(inverse(X3),X3))))),inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(multiply(inverse(X3),X3))))) = multiply(inverse(multiply(X2,inverse(multiply(X4,X3)))),multiply(X2,inverse(X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c47,plain,
multiply(inverse(multiply(X2,inverse(multiply(X4,X3)))),multiply(X2,inverse(X3))) = multiply(multiply(inverse(multiply(X,inverse(multiply(multiply(inverse(multiply(X2,inverse(multiply(X4,X3)))),multiply(X2,inverse(X3))),inverse(multiply(inverse(X3),X3)))))),multiply(X,inverse(inverse(multiply(inverse(X3),X3))))),inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(multiply(inverse(X3),X3))))),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
multiply(multiply(inverse(multiply(X,inverse(multiply(X3,X2)))),multiply(X,inverse(X2))),inverse(multiply(inverse(X2),X2))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c49,plain,
inverse(multiply(multiply(inverse(multiply(X,inverse(multiply(X3,X2)))),multiply(X,inverse(X2))),inverse(multiply(inverse(X2),X2)))) = inverse(X3),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
multiply(X,inverse(multiply(multiply(inverse(multiply(X2,inverse(multiply(X4,X3)))),multiply(X2,inverse(X3))),inverse(multiply(inverse(X3),X3))))) = multiply(X,inverse(X4)),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
inverse(multiply(X,inverse(multiply(multiply(inverse(multiply(X2,inverse(multiply(X4,X3)))),multiply(X2,inverse(X3))),inverse(multiply(inverse(X3),X3)))))) = inverse(multiply(X,inverse(X4))),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
multiply(inverse(multiply(X,inverse(multiply(multiply(inverse(multiply(X2,inverse(multiply(X4,X3)))),multiply(X2,inverse(X3))),inverse(multiply(inverse(X3),X3)))))),multiply(X,inverse(inverse(multiply(inverse(X3),X3))))) = multiply(inverse(multiply(X,inverse(X4))),multiply(X,inverse(inverse(multiply(inverse(X3),X3))))),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
multiply(multiply(inverse(multiply(X,inverse(multiply(multiply(inverse(multiply(X2,inverse(multiply(X4,X3)))),multiply(X2,inverse(X3))),inverse(multiply(inverse(X3),X3)))))),multiply(X,inverse(inverse(multiply(inverse(X3),X3))))),inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(multiply(inverse(X3),X3))))) = multiply(multiply(inverse(multiply(X,inverse(X4))),multiply(X,inverse(inverse(multiply(inverse(X3),X3))))),inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(multiply(inverse(X3),X3))))),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
multiply(multiply(inverse(multiply(X3,inverse(multiply(X2,X)))),multiply(X3,inverse(X))),inverse(multiply(inverse(X),X))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c55,plain,
X2 = multiply(multiply(inverse(multiply(X3,inverse(multiply(X2,X)))),multiply(X3,inverse(X))),inverse(multiply(inverse(X),X))),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,plain,
inverse(X2) = inverse(multiply(multiply(inverse(multiply(X3,inverse(multiply(X2,X)))),multiply(X3,inverse(X))),inverse(multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
multiply(X,inverse(X3)) = multiply(X,inverse(multiply(multiply(inverse(multiply(X4,inverse(multiply(X3,X2)))),multiply(X4,inverse(X2))),inverse(multiply(inverse(X2),X2))))),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
inverse(multiply(X,inverse(X3))) = inverse(multiply(X,inverse(multiply(multiply(inverse(multiply(X4,inverse(multiply(X3,X2)))),multiply(X4,inverse(X2))),inverse(multiply(inverse(X2),X2)))))),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
multiply(inverse(multiply(X,inverse(X3))),multiply(X,inverse(inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(X,inverse(multiply(multiply(inverse(multiply(X4,inverse(multiply(X3,X2)))),multiply(X4,inverse(X2))),inverse(multiply(inverse(X2),X2)))))),multiply(X,inverse(inverse(multiply(inverse(X2),X2))))),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
multiply(multiply(inverse(multiply(X,inverse(X3))),multiply(X,inverse(inverse(multiply(inverse(X2),X2))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = multiply(multiply(inverse(multiply(X,inverse(multiply(multiply(inverse(multiply(X4,inverse(multiply(X3,X2)))),multiply(X4,inverse(X2))),inverse(multiply(inverse(X2),X2)))))),multiply(X,inverse(inverse(multiply(inverse(X2),X2))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
multiply(multiply(inverse(multiply(X,inverse(multiply(multiply(inverse(multiply(X4,inverse(multiply(X3,X2)))),multiply(X4,inverse(X2))),inverse(multiply(inverse(X2),X2)))))),multiply(X,inverse(inverse(multiply(inverse(X2),X2))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(X4,inverse(multiply(X3,X2)))),multiply(X4,inverse(X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c62,plain,
multiply(multiply(inverse(multiply(X,inverse(X3))),multiply(X,inverse(inverse(multiply(inverse(X2),X2))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(X4,inverse(multiply(X3,X2)))),multiply(X4,inverse(X2))),
inference(transitivity,[status(thm)],[c60,c61]) ).
cnf(c63,plain,
multiply(multiply(inverse(multiply(X,inverse(multiply(multiply(inverse(multiply(X2,inverse(multiply(X4,X3)))),multiply(X2,inverse(X3))),inverse(multiply(inverse(X3),X3)))))),multiply(X,inverse(inverse(multiply(inverse(X3),X3))))),inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(multiply(inverse(X3),X3))))) = multiply(inverse(multiply(X5,inverse(multiply(X4,X3)))),multiply(X5,inverse(X3))),
inference(transitivity,[status(thm)],[c53,c62]) ).
cnf(c64,plain,
multiply(inverse(multiply(X,inverse(multiply(X3,X2)))),multiply(X,inverse(X2))) = multiply(inverse(multiply(X4,inverse(multiply(X3,X2)))),multiply(X4,inverse(X2))),
inference(transitivity,[status(thm)],[c47,c63]) ).
cnf(c65,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(X3,inverse(multiply(multiply(X4,inverse(multiply(inverse(X2),X2))),X2)))),multiply(X3,inverse(X2)))))),multiply(X,inverse(multiply(X3,inverse(X2))))) = multiply(inverse(multiply(X5,inverse(multiply(inverse(multiply(X3,inverse(multiply(multiply(X4,inverse(multiply(inverse(X2),X2))),X2)))),multiply(X3,inverse(X2)))))),multiply(X5,inverse(multiply(X3,inverse(X2))))),
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,plain,
multiply(inverse(multiply(X2,inverse(multiply(multiply(X3,inverse(multiply(inverse(X),X))),X)))),multiply(X2,inverse(X))) = X3,
inference(substitution,[status(thm)],[c22]) ).
cnf(c67,plain,
inverse(multiply(inverse(multiply(X2,inverse(multiply(multiply(X3,inverse(multiply(inverse(X),X))),X)))),multiply(X2,inverse(X)))) = inverse(X3),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
multiply(X4,inverse(multiply(inverse(multiply(X2,inverse(multiply(multiply(X3,inverse(multiply(inverse(X),X))),X)))),multiply(X2,inverse(X))))) = multiply(X4,inverse(X3)),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
inverse(multiply(X4,inverse(multiply(inverse(multiply(X2,inverse(multiply(multiply(X3,inverse(multiply(inverse(X),X))),X)))),multiply(X2,inverse(X)))))) = inverse(multiply(X4,inverse(X3))),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
multiply(inverse(multiply(X4,inverse(multiply(inverse(multiply(X2,inverse(multiply(multiply(X3,inverse(multiply(inverse(X),X))),X)))),multiply(X2,inverse(X)))))),multiply(X4,inverse(multiply(X2,inverse(X))))) = multiply(inverse(multiply(X4,inverse(X3))),multiply(X4,inverse(multiply(X2,inverse(X))))),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(X3,inverse(multiply(multiply(X4,inverse(multiply(inverse(X2),X2))),X2)))),multiply(X3,inverse(X2)))))),multiply(X,inverse(multiply(X3,inverse(X2))))) = multiply(inverse(multiply(X5,inverse(X4))),multiply(X5,inverse(multiply(X3,inverse(X2))))),
inference(transitivity,[status(thm)],[c65,c70]) ).
cnf(c72,plain,
multiply(inverse(multiply(X,inverse(X4))),multiply(X,inverse(multiply(X3,inverse(X2))))) = multiply(inverse(multiply(X5,inverse(X4))),multiply(X5,inverse(multiply(X3,inverse(X2))))),
inference(transitivity,[status(thm)],[c45,c71]) ).
cnf(c73,plain,
multiply(inverse(multiply(X3,inverse(X5))),multiply(X3,inverse(multiply(X2,inverse(multiply(multiply(multiply(X4,multiply(X2,inverse(X))),inverse(multiply(inverse(X),X))),X)))))) = multiply(inverse(multiply(X6,inverse(X5))),multiply(X6,inverse(multiply(X2,inverse(multiply(multiply(multiply(X4,multiply(X2,inverse(X))),inverse(multiply(inverse(X),X))),X)))))),
inference(substitution,[status(thm)],[c72]) ).
cnf(c74,plain,
inverse(multiply(X2,inverse(multiply(multiply(multiply(X3,multiply(X2,inverse(X))),inverse(multiply(inverse(X),X))),X)))) = X3,
inference(substitution,[status(thm)],[c35]) ).
cnf(c75,plain,
multiply(X4,inverse(multiply(X2,inverse(multiply(multiply(multiply(X3,multiply(X2,inverse(X))),inverse(multiply(inverse(X),X))),X))))) = multiply(X4,X3),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
multiply(inverse(multiply(X5,inverse(X4))),multiply(X5,inverse(multiply(X2,inverse(multiply(multiply(multiply(X3,multiply(X2,inverse(X))),inverse(multiply(inverse(X),X))),X)))))) = multiply(inverse(multiply(X5,inverse(X4))),multiply(X5,X3)),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
multiply(inverse(multiply(X3,inverse(X5))),multiply(X3,inverse(multiply(X2,inverse(multiply(multiply(multiply(X4,multiply(X2,inverse(X))),inverse(multiply(inverse(X),X))),X)))))) = multiply(inverse(multiply(X6,inverse(X5))),multiply(X6,X4)),
inference(transitivity,[status(thm)],[c73,c76]) ).
cnf(c78,plain,
multiply(inverse(multiply(X,inverse(X3))),multiply(X,X2)) = multiply(inverse(multiply(X4,inverse(X3))),multiply(X4,X2)),
inference(transitivity,[status(thm)],[c39,c77]) ).
cnf(c79,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X3)))),multiply(X,X2)) = multiply(inverse(multiply(multiply(inverse(multiply(X4,inverse(multiply(X5,X3)))),multiply(X4,inverse(X3))),inverse(multiply(inverse(X3),X3)))),multiply(multiply(inverse(multiply(X4,inverse(multiply(X5,X3)))),multiply(X4,inverse(X3))),X2)),
inference(substitution,[status(thm)],[c78]) ).
cnf(c80,plain,
multiply(inverse(multiply(multiply(inverse(multiply(X4,inverse(multiply(X5,X3)))),multiply(X4,inverse(X3))),inverse(multiply(inverse(X3),X3)))),multiply(multiply(inverse(multiply(X4,inverse(multiply(X5,X3)))),multiply(X4,inverse(X3))),X2)) = multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X3)))),multiply(X,X2)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
multiply(inverse(X5),multiply(multiply(inverse(multiply(X4,inverse(multiply(X5,X3)))),multiply(X4,inverse(X3))),X2)) = multiply(inverse(multiply(X,inverse(multiply(inverse(X3),X3)))),multiply(X,X2)),
inference(transitivity,[status(thm)],[c9,c80]) ).
cnf(c82,plain,
multiply(inverse(X4),multiply(multiply(inverse(multiply(X,inverse(multiply(X4,X3)))),multiply(X,inverse(X3))),inverse(multiply(inverse(X3),X3)))) = multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),X3)))),multiply(X2,inverse(multiply(inverse(X3),X3)))),
inference(substitution,[status(thm)],[c81]) ).
cnf(c83,plain,
multiply(inverse(X4),multiply(multiply(inverse(multiply(X3,inverse(multiply(X4,X2)))),multiply(X3,inverse(X2))),inverse(multiply(inverse(X2),X2)))) = multiply(inverse(multiply(X,inverse(multiply(inverse(X2),X2)))),multiply(X,inverse(multiply(inverse(X2),X2)))),
inference(substitution,[status(thm)],[c81]) ).
cnf(c84,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(X2),X2)))),multiply(X,inverse(multiply(inverse(X2),X2)))) = multiply(inverse(X4),multiply(multiply(inverse(multiply(X3,inverse(multiply(X4,X2)))),multiply(X3,inverse(X2))),inverse(multiply(inverse(X2),X2)))),
inference(symmetry,[status(thm)],[c83]) ).
cnf(c85,plain,
multiply(multiply(inverse(multiply(X2,inverse(multiply(X3,X)))),multiply(X2,inverse(X))),inverse(multiply(inverse(X),X))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c86,plain,
multiply(inverse(X3),multiply(multiply(inverse(multiply(X2,inverse(multiply(X3,X)))),multiply(X2,inverse(X))),inverse(multiply(inverse(X),X)))) = multiply(inverse(X3),X3),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
multiply(inverse(multiply(X,inverse(multiply(inverse(X2),X2)))),multiply(X,inverse(multiply(inverse(X2),X2)))) = multiply(inverse(X3),X3),
inference(transitivity,[status(thm)],[c84,c86]) ).
cnf(c88,plain,
multiply(inverse(X3),multiply(multiply(inverse(multiply(X,inverse(multiply(X3,X2)))),multiply(X,inverse(X2))),inverse(multiply(inverse(X2),X2)))) = multiply(inverse(X4),X4),
inference(transitivity,[status(thm)],[c82,c87]) ).
cnf(c89,plain,
multiply(inverse(X),X) = multiply(inverse(X2),X2),
inference(transitivity,[status(thm)],[c5,c88]) ).
cnf(c90,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(substitution,[status(thm)],[c89]) ).
cnf(c91,plain,
$false,
inference(resolution,[status(thm)],[c1,c90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP409-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.38 % Computer : n001.cluster.edu
% 0.08/0.38 % Model : x86_64 x86_64
% 0.08/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.38 % Memory : 8046.5625MB
% 0.08/0.38 % OS : Linux 6.8.0-71-generic
% 0.08/0.38 % CPULimit : 300
% 0.08/0.38 % WCLimit : 300
% 0.08/0.38 % DateTime : Sun Sep 27 10:09:21 UTC 2026
% 0.08/0.38 % CPUTime :
% 0.08/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.49 Command-line arguments: --no-flatten-goal
% 0.19/0.49
% 0.19/0.49 % SZS status Unsatisfiable
% 0.19/0.49
% 0.19/0.50 % SZS output start CNFRefutation
% See solution above
% 0.19/0.58
% 0.19/0.58 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------