%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP520-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 10:11:08 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 2
% Syntax : Number of clauses : 46 ( 46 unt; 0 nHn; 3 RR)
% Number of literals : 46 ( 45 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 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 : 147 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_4) ).
cnf(c2,axiom,
multiply(A,multiply(multiply(inverse(multiply(A,B)),C),B)) = C,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c3,plain,
multiply(X4,multiply(multiply(inverse(multiply(X4,X3)),multiply(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),X),X2)),X3)) = multiply(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),X),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),X),X2) = multiply(X4,multiply(multiply(inverse(multiply(X4,X3)),multiply(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),X),X2)),X3)),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
multiply(inverse(multiply(X4,X3)),multiply(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),X),X2)) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
multiply(multiply(inverse(multiply(X4,X3)),multiply(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),X),X2)),X3) = multiply(X,X3),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(X4,multiply(multiply(inverse(multiply(X4,X3)),multiply(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),X),X2)),X3)) = multiply(X4,multiply(X,X3)),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
multiply(multiply(inverse(multiply(inverse(multiply(X4,X3)),X2)),X),X2) = multiply(X4,multiply(X,X3)),
inference(transitivity,[status(thm)],[c4,c7]) ).
cnf(c9,plain,
multiply(multiply(inverse(multiply(inverse(multiply(X4,X3)),X)),X2),X) = multiply(X4,multiply(X2,X3)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(X4,multiply(X2,X3)) = multiply(multiply(inverse(multiply(inverse(multiply(X4,X3)),X)),X2),X),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
multiply(inverse(multiply(X4,X3)),multiply(X4,multiply(X2,X3))) = multiply(inverse(multiply(X4,X3)),multiply(multiply(inverse(multiply(inverse(multiply(X4,X3)),X)),X2),X)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(inverse(multiply(X4,X3)),multiply(multiply(inverse(multiply(inverse(multiply(X4,X3)),X)),X2),X)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c13,plain,
multiply(inverse(multiply(X3,X2)),multiply(X3,multiply(X,X2))) = X,
inference(transitivity,[status(thm)],[c11,c12]) ).
cnf(c14,plain,
multiply(inverse(multiply(X3,X)),multiply(X3,multiply(X2,X))) = X2,
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
X2 = multiply(inverse(multiply(X3,X)),multiply(X3,multiply(X2,X))),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(X2,multiply(X3,X)) = multiply(multiply(inverse(multiply(X3,X)),multiply(X3,multiply(X2,X))),multiply(X3,X)),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
multiply(multiply(inverse(X3),X2),multiply(multiply(inverse(multiply(multiply(inverse(X3),X2),X)),X3),X)) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c18,plain,
X3 = multiply(multiply(inverse(X3),X2),multiply(multiply(inverse(multiply(multiply(inverse(X3),X2),X)),X3),X)),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
multiply(multiply(inverse(X3),X2),X3) = multiply(multiply(inverse(X3),X2),multiply(multiply(inverse(X3),X2),multiply(multiply(inverse(multiply(multiply(inverse(X3),X2),X)),X3),X))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
multiply(X3,multiply(multiply(inverse(multiply(X3,X)),X2),X)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c21,plain,
X2 = multiply(X3,multiply(multiply(inverse(multiply(X3,X)),X2),X)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
inverse(X2) = inverse(multiply(X3,multiply(multiply(inverse(multiply(X3,X)),X2),X))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
multiply(inverse(X3),X2) = multiply(inverse(multiply(X4,multiply(multiply(inverse(multiply(X4,X)),X3),X))),X2),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(multiply(inverse(X3),X2),multiply(multiply(inverse(multiply(X4,X)),X3),X)) = multiply(multiply(inverse(multiply(X4,multiply(multiply(inverse(multiply(X4,X)),X3),X))),X2),multiply(multiply(inverse(multiply(X4,X)),X3),X)),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
multiply(X4,multiply(multiply(inverse(X3),X2),multiply(multiply(inverse(multiply(X4,X)),X3),X))) = multiply(X4,multiply(multiply(inverse(multiply(X4,multiply(multiply(inverse(multiply(X4,X)),X3),X))),X2),multiply(multiply(inverse(multiply(X4,X)),X3),X))),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
multiply(X4,multiply(multiply(inverse(multiply(X4,multiply(multiply(inverse(multiply(X4,X)),X3),X))),X2),multiply(multiply(inverse(multiply(X4,X)),X3),X))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c27,plain,
multiply(X4,multiply(multiply(inverse(X3),X2),multiply(multiply(inverse(multiply(X4,X)),X3),X))) = X2,
inference(transitivity,[status(thm)],[c25,c26]) ).
cnf(c28,plain,
multiply(multiply(inverse(X3),X2),multiply(multiply(inverse(X3),X2),multiply(multiply(inverse(multiply(multiply(inverse(X3),X2),X)),X3),X))) = X2,
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
multiply(multiply(inverse(X2),X),X2) = X,
inference(transitivity,[status(thm)],[c19,c28]) ).
cnf(c30,plain,
multiply(multiply(inverse(multiply(X3,X)),multiply(X3,multiply(X2,X))),multiply(X3,X)) = multiply(X3,multiply(X2,X)),
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
multiply(X2,multiply(X3,X)) = multiply(X3,multiply(X2,X)),
inference(transitivity,[status(thm)],[c16,c30]) ).
cnf(c32,plain,
multiply(X3,multiply(inverse(multiply(X2,X)),multiply(X2,X))) = multiply(inverse(multiply(X2,X)),multiply(X3,multiply(X2,X))),
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
multiply(X3,multiply(X2,X)) = multiply(X2,multiply(X3,X)),
inference(substitution,[status(thm)],[c31]) ).
cnf(c34,plain,
multiply(inverse(multiply(X2,X)),multiply(X3,multiply(X2,X))) = multiply(inverse(multiply(X2,X)),multiply(X2,multiply(X3,X))),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
multiply(inverse(multiply(X2,X)),multiply(X2,multiply(X3,X))) = X3,
inference(substitution,[status(thm)],[c13]) ).
cnf(c36,plain,
multiply(inverse(multiply(X2,X)),multiply(X3,multiply(X2,X))) = X3,
inference(transitivity,[status(thm)],[c34,c35]) ).
cnf(c37,plain,
multiply(X3,multiply(inverse(multiply(X2,X)),multiply(X2,X))) = X3,
inference(transitivity,[status(thm)],[c32,c36]) ).
cnf(c38,plain,
X3 = multiply(X3,multiply(inverse(multiply(X2,X)),multiply(X2,X))),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
multiply(X3,X4) = multiply(X3,multiply(X4,multiply(inverse(multiply(X2,X)),multiply(X2,X)))),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
multiply(X4,multiply(X3,multiply(inverse(multiply(X2,X)),multiply(X2,X)))) = multiply(X3,multiply(X4,multiply(inverse(multiply(X2,X)),multiply(X2,X)))),
inference(substitution,[status(thm)],[c31]) ).
cnf(c41,plain,
multiply(X3,multiply(X4,multiply(inverse(multiply(X2,X)),multiply(X2,X)))) = multiply(X4,multiply(X3,multiply(inverse(multiply(X2,X)),multiply(X2,X)))),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
multiply(X4,multiply(X3,multiply(inverse(multiply(X2,X)),multiply(X2,X)))) = multiply(X4,X3),
inference(congruence,[status(thm)],[c37]) ).
cnf(c43,plain,
multiply(X3,multiply(X4,multiply(inverse(multiply(X2,X)),multiply(X2,X)))) = multiply(X4,X3),
inference(transitivity,[status(thm)],[c41,c42]) ).
cnf(c44,plain,
multiply(X,X2) = multiply(X2,X),
inference(transitivity,[status(thm)],[c39,c43]) ).
cnf(c45,plain,
multiply(a,b) = multiply(b,a),
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
$false,
inference(resolution,[status(thm)],[c1,c45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP520-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n011.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 10:06:59 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.44 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.14/0.44
% 0.14/0.44 % SZS status Unsatisfiable
% 0.14/0.44
% 0.14/0.44 % SZS output start CNFRefutation
% See solution above
% 0.14/0.49
% 0.14/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------