%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP496-1 : 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 10:10:49 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.43s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of clauses : 40 ( 40 unt; 0 nHn; 7 RR)
% Number of literals : 40 ( 39 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(inverse(a1),a1) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
cnf(c2,axiom,
inverse(A) = double_divide(A,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(c3,plain,
inverse(double_divide(X2,X)) = double_divide(double_divide(X2,X),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
multiply(A2,B) = double_divide(double_divide(B,A2),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c5,plain,
multiply(X,X2) = double_divide(double_divide(X2,X),identity),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
double_divide(double_divide(X2,X),identity) = multiply(X,X2),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
inverse(double_divide(X2,X)) = multiply(X,X2),
inference(transitivity,[status(thm)],[c3,c6]) ).
cnf(c8,plain,
inverse(double_divide(X,inverse(X))) = multiply(inverse(X),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
multiply(inverse(X),X) = inverse(double_divide(X,inverse(X))),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,axiom,
identity = double_divide(A2,inverse(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
cnf(c11,plain,
identity = double_divide(X,inverse(X)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
double_divide(X,inverse(X)) = identity,
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
inverse(double_divide(X,inverse(X))) = inverse(identity),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
multiply(inverse(X),X) = inverse(identity),
inference(transitivity,[status(thm)],[c9,c13]) ).
cnf(c15,plain,
inverse(double_divide(X,double_divide(X3,X2))) = multiply(double_divide(X3,X2),X),
inference(substitution,[status(thm)],[c7]) ).
cnf(c16,plain,
multiply(double_divide(X,X3),X2) = inverse(double_divide(X2,double_divide(X,X3))),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
double_divide(double_divide(identity,double_divide(X3,inverse(X2))),multiply(double_divide(X,X3),X2)) = double_divide(double_divide(identity,double_divide(X3,inverse(X2))),inverse(double_divide(X2,double_divide(X,X3)))),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
inverse(double_divide(X2,double_divide(X,X3))) = double_divide(double_divide(X2,double_divide(X,X3)),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c19,plain,
double_divide(double_divide(identity,double_divide(X3,inverse(X2))),inverse(double_divide(X2,double_divide(X,X3)))) = double_divide(double_divide(identity,double_divide(X3,inverse(X2))),double_divide(double_divide(X2,double_divide(X,X3)),identity)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
inverse(X) = double_divide(X,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c21,plain,
double_divide(X2,inverse(X)) = double_divide(X2,double_divide(X,identity)),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
double_divide(identity,double_divide(X2,inverse(X))) = double_divide(identity,double_divide(X2,double_divide(X,identity))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
double_divide(double_divide(identity,double_divide(X3,inverse(X2))),double_divide(double_divide(X2,double_divide(X,X3)),identity)) = double_divide(double_divide(identity,double_divide(X3,double_divide(X2,identity))),double_divide(double_divide(X2,double_divide(X,X3)),identity)),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,axiom,
double_divide(double_divide(identity,double_divide(A2,double_divide(B2,identity))),double_divide(double_divide(B2,double_divide(C,A2)),identity)) = C,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(c25,plain,
double_divide(double_divide(identity,double_divide(X3,double_divide(X2,identity))),double_divide(double_divide(X2,double_divide(X,X3)),identity)) = X,
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
double_divide(double_divide(identity,double_divide(X3,inverse(X2))),double_divide(double_divide(X2,double_divide(X,X3)),identity)) = X,
inference(transitivity,[status(thm)],[c23,c25]) ).
cnf(c27,plain,
double_divide(double_divide(identity,double_divide(X3,inverse(X2))),inverse(double_divide(X2,double_divide(X,X3)))) = X,
inference(transitivity,[status(thm)],[c19,c26]) ).
cnf(c28,plain,
double_divide(double_divide(identity,double_divide(X3,inverse(X2))),multiply(double_divide(X,X3),X2)) = X,
inference(transitivity,[status(thm)],[c17,c27]) ).
cnf(c29,plain,
double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity)) = inverse(identity),
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
inverse(identity) = double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity)),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
multiply(X,X2) = inverse(double_divide(X2,X)),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c32,plain,
double_divide(double_divide(X2,X),multiply(X,X2)) = double_divide(double_divide(X2,X),inverse(double_divide(X2,X))),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
identity = double_divide(double_divide(X2,X),inverse(double_divide(X2,X))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c34,plain,
double_divide(double_divide(X2,X),inverse(double_divide(X2,X))) = identity,
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
double_divide(double_divide(X2,X),multiply(X,X2)) = identity,
inference(transitivity,[status(thm)],[c32,c34]) ).
cnf(c36,plain,
double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),multiply(double_divide(inverse(identity),inverse(identity)),identity)) = identity,
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
inverse(identity) = identity,
inference(transitivity,[status(thm)],[c30,c36]) ).
cnf(c38,plain,
multiply(inverse(X),X) = identity,
inference(transitivity,[status(thm)],[c14,c37]) ).
cnf(c39,plain,
multiply(inverse(a1),a1) = identity,
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
$false,
inference(resolution,[status(thm)],[c1,c39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP496-1 : 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 10:05:47 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.43 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.10/0.43
% 0.10/0.43 % SZS status Unsatisfiable
% 0.10/0.43
% 0.10/0.43 % SZS output start CNFRefutation
% See solution above
% 0.10/0.44
% 0.10/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------