%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP421-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 10:10:07 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.45s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 2
% Syntax : Number of clauses : 63 ( 63 unt; 0 nHn; 3 RR)
% Number of literals : 63 ( 62 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 18 ( 4 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 : 234 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
cnf(c2,axiom,
inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),inverse(multiply(inverse(C),C))))))),multiply(A,C))) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c3,plain,
inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
X3 = inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
multiply(X3,multiply(inverse(X4),inverse(multiply(inverse(X4),X4)))) = multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X))),multiply(inverse(X4),inverse(multiply(inverse(X4),X4)))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
inverse(multiply(X4,multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))) = inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X))),multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(X5,inverse(multiply(X4,multiply(inverse(X3),inverse(multiply(inverse(X3),X3)))))) = multiply(X5,inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X))),multiply(inverse(X3),inverse(multiply(inverse(X3),X3)))))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
inverse(multiply(X5,inverse(multiply(X4,multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))) = inverse(multiply(X5,inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X))),multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
multiply(inverse(multiply(X5,inverse(multiply(X4,multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),multiply(X5,X3)) = multiply(inverse(multiply(X5,inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X))),multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),multiply(X5,X3)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
inverse(multiply(inverse(multiply(X5,inverse(multiply(X4,multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),multiply(X5,X3))) = inverse(multiply(inverse(multiply(X5,inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X))),multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),multiply(X5,X3))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
inverse(multiply(inverse(multiply(X5,inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X))),multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),multiply(X5,X3))) = multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,plain,
inverse(multiply(inverse(multiply(X5,inverse(multiply(X4,multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),multiply(X5,X3))) = multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X)),
inference(transitivity,[status(thm)],[c10,c11]) ).
cnf(c13,plain,
inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X))) = multiply(inverse(multiply(X5,inverse(multiply(inverse(inverse(X4)),multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),multiply(X5,X3)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
multiply(inverse(multiply(X5,inverse(multiply(inverse(inverse(X4)),multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),multiply(X5,X3)) = inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X4),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X))),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c16,plain,
multiply(inverse(multiply(X3,inverse(multiply(inverse(inverse(X2)),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X3,X)) = X2,
inference(transitivity,[status(thm)],[c14,c15]) ).
cnf(c17,plain,
multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(X3)),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X)) = X3,
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
X3 = multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(X3)),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X)),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
multiply(inverse(X3),X3) = multiply(inverse(X3),multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(X3)),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c21,plain,
X3 = inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X))),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
multiply(X4,multiply(inverse(multiply(X3,inverse(multiply(inverse(X4),multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))))),X)) = multiply(inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(X4),multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))))),multiply(X3,X2))),multiply(inverse(multiply(X3,inverse(multiply(inverse(X4),multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))))),X)),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(multiply(X2,X4)),multiply(X2,X3))),multiply(inverse(X5),inverse(multiply(inverse(X5),X5))))))),multiply(X,X5))) = multiply(inverse(multiply(X2,X4)),multiply(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c24,plain,
multiply(inverse(multiply(X3,X5)),multiply(X3,X4)) = inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X3,X5)),multiply(X3,X4))),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X))),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
inverse(multiply(inverse(multiply(inverse(X),inverse(multiply(inverse(X2),multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))))))),multiply(inverse(X),inverse(multiply(inverse(X),X))))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c26,plain,
X2 = inverse(multiply(inverse(multiply(inverse(X),inverse(multiply(inverse(X2),multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))))))),multiply(inverse(X),inverse(multiply(inverse(X),X))))),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
multiply(X,X3) = multiply(X,inverse(multiply(inverse(multiply(inverse(X2),inverse(multiply(inverse(X3),multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))))))),multiply(inverse(X2),inverse(multiply(inverse(X2),X2)))))),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
inverse(multiply(X,X3)) = inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(X2),inverse(multiply(inverse(X3),multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))))))),multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))))),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
multiply(inverse(multiply(X,X3)),multiply(X,X2)) = multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(X2),inverse(multiply(inverse(X3),multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))))))),multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))))),multiply(X,X2)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
inverse(multiply(inverse(multiply(X,X3)),multiply(X,X2))) = inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(X2),inverse(multiply(inverse(X3),multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))))))),multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))))),multiply(X,X2))),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(X2),inverse(multiply(inverse(X3),multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))))))),multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))))),multiply(X,X2))) = multiply(inverse(X2),inverse(multiply(inverse(X3),multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2)))))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c32,plain,
inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(X),inverse(multiply(inverse(X2),multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))))))),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X3,X))) = multiply(inverse(X),inverse(multiply(inverse(X2),multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c33,plain,
multiply(inverse(X),inverse(multiply(inverse(X2),multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))))) = inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(X),inverse(multiply(inverse(X2),multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))))))),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X3,X))),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
inverse(multiply(inverse(multiply(inverse(X),inverse(multiply(inverse(X2),multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))))))),multiply(inverse(X),inverse(multiply(inverse(X),X))))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c35,plain,
multiply(X3,inverse(multiply(inverse(multiply(inverse(X),inverse(multiply(inverse(X2),multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))))))),multiply(inverse(X),inverse(multiply(inverse(X),X)))))) = multiply(X3,X2),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(X),inverse(multiply(inverse(X2),multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))))))),multiply(inverse(X),inverse(multiply(inverse(X),X))))))) = inverse(multiply(X3,X2)),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
multiply(inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(X),inverse(multiply(inverse(X2),multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))))))),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X3,X)) = multiply(inverse(multiply(X3,X2)),multiply(X3,X)),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(multiply(inverse(X),inverse(multiply(inverse(X2),multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X))))))))),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X3,X))) = inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,X))),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
multiply(inverse(X),inverse(multiply(inverse(X2),multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(inverse(multiply(inverse(X),X))),inverse(multiply(inverse(X),X)))))))) = inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,X))),
inference(transitivity,[status(thm)],[c33,c38]) ).
cnf(c40,plain,
inverse(multiply(inverse(multiply(X,inverse(multiply(inverse(multiply(inverse(X2),inverse(multiply(inverse(X3),multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))))))),multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))))),multiply(X,X2))) = inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,X2))),
inference(transitivity,[status(thm)],[c31,c39]) ).
cnf(c41,plain,
inverse(multiply(inverse(multiply(X,X3)),multiply(X,X2))) = inverse(multiply(inverse(multiply(X4,X3)),multiply(X4,X2))),
inference(transitivity,[status(thm)],[c30,c40]) ).
cnf(c42,plain,
multiply(inverse(multiply(inverse(multiply(X2,X4)),multiply(X2,X3))),multiply(inverse(X),inverse(multiply(inverse(X),X)))) = multiply(inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,X3))),multiply(inverse(X),inverse(multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X2,X4)),multiply(X2,X3))),multiply(inverse(X),inverse(multiply(inverse(X),X))))) = inverse(multiply(inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,X3))),multiply(inverse(X),inverse(multiply(inverse(X),X))))),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X3,X5)),multiply(X3,X4))),multiply(inverse(X),inverse(multiply(inverse(X),X)))))) = multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X6,X5)),multiply(X6,X4))),multiply(inverse(X),inverse(multiply(inverse(X),X)))))),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X3,X5)),multiply(X3,X4))),multiply(inverse(X),inverse(multiply(inverse(X),X))))))) = inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X6,X5)),multiply(X6,X4))),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X3,X5)),multiply(X3,X4))),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X)) = multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X6,X5)),multiply(X6,X4))),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X)),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X3,X5)),multiply(X3,X4))),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X))) = inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X6,X5)),multiply(X6,X4))),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X))),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X5,X4)),multiply(X5,X3))),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X))) = multiply(inverse(multiply(X5,X4)),multiply(X5,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c49,plain,
inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(multiply(X3,X5)),multiply(X3,X4))),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X))) = multiply(inverse(multiply(X6,X5)),multiply(X6,X4)),
inference(transitivity,[status(thm)],[c47,c48]) ).
cnf(c50,plain,
multiply(inverse(multiply(X,X3)),multiply(X,X2)) = multiply(inverse(multiply(X4,X3)),multiply(X4,X2)),
inference(transitivity,[status(thm)],[c24,c49]) ).
cnf(c51,plain,
multiply(inverse(multiply(X,multiply(X4,X3))),multiply(X,X2)) = multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(X5),multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),multiply(X4,X3))),multiply(inverse(multiply(X4,inverse(multiply(inverse(X5),multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),X2)),
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(X5),multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),multiply(X4,X3))),multiply(inverse(multiply(X4,inverse(multiply(inverse(X5),multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),X2)) = multiply(inverse(multiply(X,multiply(X4,X3))),multiply(X,X2)),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
multiply(X5,multiply(inverse(multiply(X4,inverse(multiply(inverse(X5),multiply(inverse(X3),inverse(multiply(inverse(X3),X3))))))),X2)) = multiply(inverse(multiply(X,multiply(X4,X3))),multiply(X,X2)),
inference(transitivity,[status(thm)],[c22,c52]) ).
cnf(c54,plain,
multiply(inverse(X4),multiply(inverse(multiply(X3,inverse(multiply(inverse(inverse(X4)),multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))))),multiply(X3,X2))) = multiply(inverse(multiply(X,multiply(X3,X2))),multiply(X,multiply(X3,X2))),
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
multiply(inverse(X4),multiply(inverse(multiply(X3,inverse(multiply(inverse(inverse(X4)),multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))))),multiply(X3,X2))) = multiply(inverse(multiply(X,multiply(X3,X2))),multiply(X,multiply(X3,X2))),
inference(substitution,[status(thm)],[c53]) ).
cnf(c56,plain,
multiply(inverse(multiply(X,multiply(X3,X2))),multiply(X,multiply(X3,X2))) = multiply(inverse(X4),multiply(inverse(multiply(X3,inverse(multiply(inverse(inverse(X4)),multiply(inverse(X2),inverse(multiply(inverse(X2),X2))))))),multiply(X3,X2))),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(X3)),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X)) = X3,
inference(substitution,[status(thm)],[c16]) ).
cnf(c58,plain,
multiply(inverse(X3),multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(X3)),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X))) = multiply(inverse(X3),X3),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
multiply(inverse(multiply(X,multiply(X3,X2))),multiply(X,multiply(X3,X2))) = multiply(inverse(X4),X4),
inference(transitivity,[status(thm)],[c56,c58]) ).
cnf(c60,plain,
multiply(inverse(X3),multiply(inverse(multiply(X2,inverse(multiply(inverse(inverse(X3)),multiply(inverse(X),inverse(multiply(inverse(X),X))))))),multiply(X2,X))) = multiply(inverse(X4),X4),
inference(transitivity,[status(thm)],[c54,c59]) ).
cnf(c61,plain,
multiply(inverse(X),X) = multiply(inverse(X2),X2),
inference(transitivity,[status(thm)],[c19,c60]) ).
cnf(c62,plain,
multiply(inverse(a1),a1) = multiply(inverse(b1),b1),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
$false,
inference(resolution,[status(thm)],[c1,c62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP421-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 10:03:46 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.45 Command-line arguments: --no-flatten-goal
% 0.12/0.45
% 0.12/0.45 % SZS status Unsatisfiable
% 0.12/0.45
% 0.12/0.46 % SZS output start CNFRefutation
% See solution above
% 0.59/0.53
% 0.59/0.53 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------