%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP115-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 10:09:17 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 2
% Syntax : Number of clauses : 71 ( 71 unt; 0 nHn; 3 RR)
% Number of literals : 71 ( 70 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 169 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(a,multiply(a,a)) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_order3) ).
cnf(c2,axiom,
multiply(X,multiply(multiply(X,multiply(multiply(X,Y),Z)),multiply(identity,multiply(Z,Z)))) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c3,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,multiply(X4,identity)),X2)),multiply(identity,multiply(X2,X2)))) = multiply(X4,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(X4,identity) = multiply(X3,multiply(multiply(X3,multiply(multiply(X3,multiply(X4,identity)),X2)),multiply(identity,multiply(X2,X2)))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X3),X2)),multiply(identity,multiply(X2,X2)))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
X3 = multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X3),X2)),multiply(identity,multiply(X2,X2)))),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(X3,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2))))) = multiply(multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X3),X2)),multiply(identity,multiply(X2,X2)))),multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2))))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
multiply(X4,multiply(X3,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = multiply(X4,multiply(multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X3),X2)),multiply(identity,multiply(X2,X2)))),multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
multiply(X4,multiply(multiply(X4,multiply(multiply(X4,multiply(multiply(X4,X3),X2)),multiply(identity,multiply(X2,X2)))),multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = multiply(multiply(X4,X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c10,plain,
multiply(X4,multiply(X3,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = multiply(multiply(X4,X3),X2),
inference(transitivity,[status(thm)],[c8,c9]) ).
cnf(c11,plain,
multiply(X4,multiply(multiply(X3,identity),multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = multiply(multiply(X4,multiply(X3,identity)),X2),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(multiply(X4,multiply(X3,identity)),X2) = multiply(X4,multiply(multiply(X3,identity),multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
multiply(X2,multiply(multiply(X2,multiply(multiply(X2,X3),X4)),multiply(identity,multiply(X4,X4)))) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c14,plain,
X4 = multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X4),X2)),multiply(identity,multiply(X2,X2)))),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
multiply(X4,identity) = multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X4),X2)),multiply(identity,multiply(X2,X2)))),identity),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(multiply(X5,identity),X4) = multiply(multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X5),X2)),multiply(identity,multiply(X2,X2)))),identity),X4),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
multiply(multiply(X4,X3),multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = multiply(multiply(multiply(X4,X3),identity),X2),
inference(substitution,[status(thm)],[c10]) ).
cnf(c18,plain,
multiply(multiply(multiply(X4,X3),identity),X2) = multiply(multiply(X4,X3),multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
multiply(X4,multiply(X3,multiply(identity,multiply(multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2))),multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2))))))) = multiply(multiply(X4,X3),multiply(identity,X2)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c20,plain,
multiply(multiply(X4,X3),multiply(identity,X2)) = multiply(X4,multiply(X3,multiply(identity,multiply(multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2))),multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2))))))),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
multiply(identity,multiply(multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2))),multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2))))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c22,plain,
multiply(X3,multiply(identity,multiply(multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2))),multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2)))))) = multiply(X3,X2),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
multiply(X4,multiply(X3,multiply(identity,multiply(multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2))),multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2))))))) = multiply(X4,multiply(X3,X2)),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(multiply(X4,X3),multiply(identity,X2)) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c20,c23]) ).
cnf(c25,plain,
multiply(multiply(X4,X3),multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = multiply(X4,multiply(X3,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))),
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
multiply(multiply(X4,X3),multiply(identity,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = multiply(multiply(X4,X3),X2),
inference(transitivity,[status(thm)],[c25,c10]) ).
cnf(c27,plain,
multiply(multiply(multiply(X4,X3),identity),X2) = multiply(multiply(X4,X3),X2),
inference(transitivity,[status(thm)],[c18,c26]) ).
cnf(c28,plain,
multiply(multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X5),X2)),multiply(identity,multiply(X2,X2)))),identity),X4) = multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X5),X2)),multiply(identity,multiply(X2,X2)))),X4),
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X4),X2)),multiply(identity,multiply(X2,X2)))) = X4,
inference(substitution,[status(thm)],[c2]) ).
cnf(c30,plain,
multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X5),X2)),multiply(identity,multiply(X2,X2)))),X4) = multiply(X5,X4),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
multiply(multiply(multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X5),X2)),multiply(identity,multiply(X2,X2)))),identity),X4) = multiply(X5,X4),
inference(transitivity,[status(thm)],[c28,c30]) ).
cnf(c32,plain,
multiply(multiply(X3,identity),X2) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c16,c31]) ).
cnf(c33,plain,
multiply(multiply(X3,identity),multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2))))) = multiply(X3,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2))))),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
multiply(X4,multiply(multiply(X3,identity),multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = multiply(X4,multiply(X3,multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
multiply(X4,multiply(multiply(X3,identity),multiply(identity,multiply(multiply(identity,multiply(X2,X2)),multiply(identity,multiply(X2,X2)))))) = multiply(multiply(X4,X3),X2),
inference(transitivity,[status(thm)],[c34,c10]) ).
cnf(c36,plain,
multiply(multiply(X4,multiply(X3,identity)),X2) = multiply(multiply(X4,X3),X2),
inference(transitivity,[status(thm)],[c12,c35]) ).
cnf(c37,plain,
multiply(multiply(X3,multiply(X4,identity)),X2) = multiply(multiply(X3,X4),X2),
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
multiply(X3,multiply(multiply(X3,multiply(X4,identity)),X2)) = multiply(X3,multiply(multiply(X3,X4),X2)),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
multiply(multiply(X3,multiply(multiply(X3,multiply(X4,identity)),X2)),multiply(identity,multiply(X2,X2))) = multiply(multiply(X3,multiply(multiply(X3,X4),X2)),multiply(identity,multiply(X2,X2))),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,multiply(X4,identity)),X2)),multiply(identity,multiply(X2,X2)))) = multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X4),X2)),multiply(identity,multiply(X2,X2)))),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X4),X2)),multiply(identity,multiply(X2,X2)))) = X4,
inference(substitution,[status(thm)],[c2]) ).
cnf(c42,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,multiply(X4,identity)),X2)),multiply(identity,multiply(X2,X2)))) = X4,
inference(transitivity,[status(thm)],[c40,c41]) ).
cnf(c43,plain,
multiply(X2,identity) = X2,
inference(transitivity,[status(thm)],[c4,c42]) ).
cnf(c44,plain,
X2 = multiply(X2,identity),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
multiply(X2,X2) = multiply(X2,multiply(X2,identity)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
multiply(X2,multiply(X2,X2)) = multiply(X2,multiply(X2,multiply(X2,identity))),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
X2 = multiply(X2,identity),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c48,plain,
multiply(X3,X2) = multiply(X3,multiply(X2,identity)),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
multiply(X3,multiply(X3,X2)) = multiply(X3,multiply(X3,multiply(X2,identity))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
multiply(X3,multiply(X3,multiply(X3,X2))) = multiply(X3,multiply(X3,multiply(X3,multiply(X2,identity)))),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
multiply(multiply(X3,X2),multiply(identity,identity)) = multiply(X3,multiply(X2,identity)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c52,plain,
multiply(X3,multiply(X2,identity)) = multiply(multiply(X3,X2),multiply(identity,identity)),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
multiply(X3,multiply(X3,multiply(X2,identity))) = multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
multiply(X3,multiply(X3,multiply(X3,multiply(X2,identity)))) = multiply(X3,multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity)))),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
multiply(multiply(X3,multiply(X3,X2)),multiply(identity,multiply(identity,identity))) = multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))),
inference(substitution,[status(thm)],[c24]) ).
cnf(c56,plain,
multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity))) = multiply(multiply(X3,multiply(X3,X2)),multiply(identity,multiply(identity,identity))),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
multiply(X3,multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity)))) = multiply(X3,multiply(multiply(X3,multiply(X3,X2)),multiply(identity,multiply(identity,identity)))),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
multiply(multiply(X3,X2),identity) = multiply(X3,X2),
inference(substitution,[status(thm)],[c43]) ).
cnf(c59,plain,
multiply(X3,X2) = multiply(multiply(X3,X2),identity),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
multiply(X3,multiply(X3,X2)) = multiply(X3,multiply(multiply(X3,X2),identity)),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
multiply(multiply(X3,multiply(X3,X2)),multiply(identity,multiply(identity,identity))) = multiply(multiply(X3,multiply(multiply(X3,X2),identity)),multiply(identity,multiply(identity,identity))),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
multiply(X3,multiply(multiply(X3,multiply(X3,X2)),multiply(identity,multiply(identity,identity)))) = multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X2),identity)),multiply(identity,multiply(identity,identity)))),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
multiply(X3,multiply(multiply(X3,multiply(multiply(X3,X2),identity)),multiply(identity,multiply(identity,identity)))) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c64,plain,
multiply(X3,multiply(multiply(X3,multiply(X3,X2)),multiply(identity,multiply(identity,identity)))) = X2,
inference(transitivity,[status(thm)],[c62,c63]) ).
cnf(c65,plain,
multiply(X3,multiply(X3,multiply(multiply(X3,X2),multiply(identity,identity)))) = X2,
inference(transitivity,[status(thm)],[c57,c64]) ).
cnf(c66,plain,
multiply(X3,multiply(X3,multiply(X3,multiply(X2,identity)))) = X2,
inference(transitivity,[status(thm)],[c54,c65]) ).
cnf(c67,plain,
multiply(X3,multiply(X3,multiply(X3,X2))) = X2,
inference(transitivity,[status(thm)],[c50,c66]) ).
cnf(c68,plain,
multiply(X2,multiply(X2,multiply(X2,identity))) = identity,
inference(substitution,[status(thm)],[c67]) ).
cnf(c69,plain,
multiply(X2,multiply(X2,X2)) = identity,
inference(transitivity,[status(thm)],[c46,c68]) ).
cnf(c70,plain,
multiply(a,multiply(a,a)) = identity,
inference(substitution,[status(thm)],[c69]) ).
cnf(c71,plain,
$false,
inference(resolution,[status(thm)],[c1,c70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP115-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n018.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sun Sep 27 09:21:38 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.40 Command-line arguments: --no-flatten-goal
% 0.13/0.40
% 0.13/0.40 % SZS status Unsatisfiable
% 0.13/0.40
% 0.13/0.40 % SZS output start CNFRefutation
% See solution above
% 0.13/0.43
% 0.13/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------