%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP490-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/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 10:10:48 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 5
% Syntax : Number of clauses : 79 ( 79 unt; 0 nHn; 5 RR)
% Number of literals : 79 ( 78 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 136 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(inverse(a1),a1) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_1) ).
cnf(c2,axiom,
inverse(A) = double_divide(A,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
cnf(c3,plain,
inverse(multiply(inverse(X),X2)) = double_divide(multiply(inverse(X),X2),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
double_divide(identity,inverse(multiply(inverse(X),X2))) = double_divide(identity,double_divide(multiply(inverse(X),X2),identity)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
double_divide(double_divide(identity,X2),double_divide(identity,inverse(multiply(inverse(X),X2)))) = double_divide(double_divide(identity,X2),double_divide(identity,double_divide(multiply(inverse(X),X2),identity))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
identity = double_divide(A2,inverse(A2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
cnf(c7,plain,
identity = double_divide(X,inverse(X)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
double_divide(multiply(inverse(X),X2),identity) = double_divide(multiply(inverse(X),X2),double_divide(X,inverse(X))),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
double_divide(identity,double_divide(multiply(inverse(X),X2),identity)) = double_divide(identity,double_divide(multiply(inverse(X),X2),double_divide(X,inverse(X)))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
double_divide(double_divide(identity,X2),double_divide(identity,double_divide(multiply(inverse(X),X2),identity))) = double_divide(double_divide(identity,X2),double_divide(identity,double_divide(multiply(inverse(X),X2),double_divide(X,inverse(X))))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
inverse(double_divide(X2,X)) = double_divide(double_divide(X2,X),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,axiom,
multiply(A2,B) = double_divide(double_divide(B,A2),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(c13,plain,
multiply(X,X2) = double_divide(double_divide(X2,X),identity),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
double_divide(double_divide(X2,X),identity) = multiply(X,X2),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
inverse(double_divide(X2,X)) = multiply(X,X2),
inference(transitivity,[status(thm)],[c11,c14]) ).
cnf(c16,plain,
multiply(X,X2) = inverse(double_divide(X2,X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
double_divide(multiply(X,X2),double_divide(X3,X)) = double_divide(inverse(double_divide(X2,X)),double_divide(X3,X)),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
double_divide(identity,double_divide(multiply(X2,X3),double_divide(X,X2))) = double_divide(identity,double_divide(inverse(double_divide(X3,X2)),double_divide(X,X2))),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
double_divide(double_divide(identity,X3),double_divide(identity,double_divide(multiply(X2,X3),double_divide(X,X2)))) = double_divide(double_divide(identity,X3),double_divide(identity,double_divide(inverse(double_divide(X3,X2)),double_divide(X,X2)))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
inverse(double_divide(X2,X)) = double_divide(double_divide(X2,X),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c21,plain,
double_divide(inverse(double_divide(X3,X2)),double_divide(X,X2)) = double_divide(double_divide(double_divide(X3,X2),identity),double_divide(X,X2)),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
double_divide(identity,double_divide(inverse(double_divide(X3,X2)),double_divide(X,X2))) = double_divide(identity,double_divide(double_divide(double_divide(X3,X2),identity),double_divide(X,X2))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
double_divide(double_divide(identity,X3),double_divide(identity,double_divide(inverse(double_divide(X3,X2)),double_divide(X,X2)))) = double_divide(double_divide(identity,X3),double_divide(identity,double_divide(double_divide(double_divide(X3,X2),identity),double_divide(X,X2)))),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,axiom,
double_divide(double_divide(identity,A2),double_divide(identity,double_divide(double_divide(double_divide(A2,B2),identity),double_divide(C,B2)))) = C,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(c25,plain,
double_divide(double_divide(identity,X3),double_divide(identity,double_divide(double_divide(double_divide(X3,X2),identity),double_divide(X,X2)))) = X,
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
double_divide(double_divide(identity,X3),double_divide(identity,double_divide(inverse(double_divide(X3,X2)),double_divide(X,X2)))) = X,
inference(transitivity,[status(thm)],[c23,c25]) ).
cnf(c27,plain,
double_divide(double_divide(identity,X3),double_divide(identity,double_divide(multiply(X2,X3),double_divide(X,X2)))) = X,
inference(transitivity,[status(thm)],[c19,c26]) ).
cnf(c28,plain,
double_divide(double_divide(identity,X2),double_divide(identity,double_divide(multiply(inverse(X),X2),double_divide(X,inverse(X))))) = X,
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
double_divide(double_divide(identity,X2),double_divide(identity,double_divide(multiply(inverse(X),X2),identity))) = X,
inference(transitivity,[status(thm)],[c10,c28]) ).
cnf(c30,plain,
double_divide(double_divide(identity,X2),double_divide(identity,inverse(multiply(inverse(X),X2)))) = X,
inference(transitivity,[status(thm)],[c5,c29]) ).
cnf(c31,plain,
double_divide(double_divide(identity,X),double_divide(identity,inverse(multiply(inverse(multiply(inverse(X2),X2)),X)))) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
multiply(inverse(X2),X2) = double_divide(double_divide(identity,X),double_divide(identity,inverse(multiply(inverse(multiply(inverse(X2),X2)),X)))),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
inverse(multiply(inverse(multiply(inverse(X2),X2)),X)) = double_divide(multiply(inverse(multiply(inverse(X2),X2)),X),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c34,plain,
double_divide(identity,inverse(multiply(inverse(multiply(inverse(X2),X2)),X))) = double_divide(identity,double_divide(multiply(inverse(multiply(inverse(X2),X2)),X),identity)),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
double_divide(double_divide(identity,X),double_divide(identity,inverse(multiply(inverse(multiply(inverse(X2),X2)),X)))) = double_divide(double_divide(identity,X),double_divide(identity,double_divide(multiply(inverse(multiply(inverse(X2),X2)),X),identity))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
inverse(double_divide(X,inverse(X))) = multiply(inverse(X),X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c37,plain,
multiply(inverse(X),X) = inverse(double_divide(X,inverse(X))),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
identity = double_divide(X,inverse(X)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c39,plain,
double_divide(X,inverse(X)) = identity,
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
inverse(double_divide(X,inverse(X))) = inverse(identity),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
multiply(inverse(X),X) = inverse(identity),
inference(transitivity,[status(thm)],[c37,c40]) ).
cnf(c42,plain,
identity = double_divide(X,inverse(X)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c43,plain,
inverse(identity) = inverse(double_divide(X,inverse(X))),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
inverse(double_divide(X,inverse(X))) = multiply(inverse(X),X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c45,plain,
inverse(identity) = multiply(inverse(X),X),
inference(transitivity,[status(thm)],[c43,c44]) ).
cnf(c46,plain,
multiply(inverse(X),X) = multiply(inverse(X2),X2),
inference(transitivity,[status(thm)],[c41,c45]) ).
cnf(c47,plain,
inverse(multiply(inverse(X),X)) = inverse(multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
double_divide(identity,inverse(multiply(inverse(X),X))) = double_divide(identity,inverse(multiply(inverse(X2),X2))),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
double_divide(double_divide(identity,X2),double_divide(identity,inverse(multiply(inverse(X),X)))) = double_divide(double_divide(identity,X2),double_divide(identity,inverse(multiply(inverse(X2),X2)))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
double_divide(double_divide(identity,X),double_divide(identity,inverse(multiply(inverse(X),X)))) = X,
inference(substitution,[status(thm)],[c30]) ).
cnf(c51,plain,
double_divide(double_divide(identity,X2),double_divide(identity,inverse(multiply(inverse(X),X)))) = X2,
inference(transitivity,[status(thm)],[c49,c50]) ).
cnf(c52,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(multiply(inverse(X2),X2)))),double_divide(identity,inverse(multiply(inverse(X),X)))) = double_divide(identity,inverse(multiply(inverse(X2),X2))),
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
double_divide(identity,inverse(multiply(inverse(X2),X2))) = double_divide(double_divide(identity,double_divide(identity,inverse(multiply(inverse(X2),X2)))),double_divide(identity,inverse(multiply(inverse(X),X)))),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
identity = double_divide(identity,inverse(identity)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c55,plain,
double_divide(identity,double_divide(identity,inverse(multiply(inverse(X),X)))) = double_divide(double_divide(identity,inverse(identity)),double_divide(identity,inverse(multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
double_divide(double_divide(identity,inverse(identity)),double_divide(identity,inverse(multiply(inverse(X),X)))) = inverse(identity),
inference(substitution,[status(thm)],[c51]) ).
cnf(c57,plain,
inverse(identity) = multiply(inverse(X),X),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c58,plain,
double_divide(double_divide(identity,inverse(identity)),double_divide(identity,inverse(multiply(inverse(X2),X2)))) = multiply(inverse(X),X),
inference(transitivity,[status(thm)],[c56,c57]) ).
cnf(c59,plain,
double_divide(identity,double_divide(identity,inverse(multiply(inverse(X2),X2)))) = multiply(inverse(X),X),
inference(transitivity,[status(thm)],[c55,c58]) ).
cnf(c60,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(multiply(inverse(X3),X3)))),double_divide(identity,inverse(multiply(inverse(X2),X2)))) = double_divide(multiply(inverse(X),X),double_divide(identity,inverse(multiply(inverse(X2),X2)))),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
double_divide(multiply(inverse(X2),X2),double_divide(identity,inverse(multiply(inverse(X),X)))) = double_divide(inverse(identity),double_divide(identity,inverse(multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c41]) ).
cnf(c62,plain,
inverse(identity) = double_divide(identity,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c63,plain,
double_divide(inverse(identity),double_divide(identity,inverse(multiply(inverse(X),X)))) = double_divide(double_divide(identity,identity),double_divide(identity,inverse(multiply(inverse(X),X)))),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
double_divide(double_divide(identity,identity),double_divide(identity,inverse(multiply(inverse(X),X)))) = identity,
inference(substitution,[status(thm)],[c51]) ).
cnf(c65,plain,
double_divide(inverse(identity),double_divide(identity,inverse(multiply(inverse(X),X)))) = identity,
inference(transitivity,[status(thm)],[c63,c64]) ).
cnf(c66,plain,
double_divide(multiply(inverse(X2),X2),double_divide(identity,inverse(multiply(inverse(X),X)))) = identity,
inference(transitivity,[status(thm)],[c61,c65]) ).
cnf(c67,plain,
double_divide(multiply(inverse(X),X),double_divide(identity,inverse(multiply(inverse(X2),X2)))) = identity,
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
double_divide(double_divide(identity,double_divide(identity,inverse(multiply(inverse(X2),X2)))),double_divide(identity,inverse(multiply(inverse(X),X)))) = identity,
inference(transitivity,[status(thm)],[c60,c67]) ).
cnf(c69,plain,
double_divide(identity,inverse(multiply(inverse(X),X))) = identity,
inference(transitivity,[status(thm)],[c53,c68]) ).
cnf(c70,plain,
identity = double_divide(identity,inverse(multiply(inverse(X),X))),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c71,plain,
double_divide(multiply(inverse(multiply(inverse(X2),X2)),X),identity) = double_divide(multiply(inverse(multiply(inverse(X2),X2)),X),double_divide(identity,inverse(multiply(inverse(X2),X2)))),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
double_divide(identity,double_divide(multiply(inverse(multiply(inverse(X2),X2)),X),identity)) = double_divide(identity,double_divide(multiply(inverse(multiply(inverse(X2),X2)),X),double_divide(identity,inverse(multiply(inverse(X2),X2))))),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(multiply(inverse(multiply(inverse(X2),X2)),X),identity))) = double_divide(double_divide(identity,X),double_divide(identity,double_divide(multiply(inverse(multiply(inverse(X2),X2)),X),double_divide(identity,inverse(multiply(inverse(X2),X2)))))),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(multiply(inverse(multiply(inverse(X2),X2)),X),double_divide(identity,inverse(multiply(inverse(X2),X2)))))) = identity,
inference(substitution,[status(thm)],[c27]) ).
cnf(c75,plain,
double_divide(double_divide(identity,X),double_divide(identity,double_divide(multiply(inverse(multiply(inverse(X2),X2)),X),identity))) = identity,
inference(transitivity,[status(thm)],[c73,c74]) ).
cnf(c76,plain,
double_divide(double_divide(identity,X),double_divide(identity,inverse(multiply(inverse(multiply(inverse(X2),X2)),X)))) = identity,
inference(transitivity,[status(thm)],[c35,c75]) ).
cnf(c77,plain,
multiply(inverse(X),X) = identity,
inference(transitivity,[status(thm)],[c32,c76]) ).
cnf(c78,plain,
multiply(inverse(a1),a1) = identity,
inference(substitution,[status(thm)],[c77]) ).
cnf(c79,plain,
$false,
inference(resolution,[status(thm)],[c1,c78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP490-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n018.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 10:08:09 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.45 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
% 0.15/0.45
% 0.15/0.45 % SZS status Unsatisfiable
% 0.15/0.45
% 0.15/0.46 % SZS output start CNFRefutation
% See solution above
% 0.15/0.50
% 0.15/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------