%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP022-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 10:09:04 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.44s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 3 RR)
% Number of literals : 18 ( 17 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
inverse(inverse(a)) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_of_inverse_is_original) ).
cnf(c2,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
cnf(c3,plain,
multiply(multiply(X3,inverse(X3)),X2) = multiply(X3,multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(X3,multiply(inverse(X3),X2)) = multiply(multiply(X3,inverse(X3)),X2),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(X2,inverse(X2)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c6,plain,
multiply(multiply(X3,inverse(X3)),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c8,plain,
multiply(multiply(X3,inverse(X3)),X2) = X2,
inference(transitivity,[status(thm)],[c6,c7]) ).
cnf(c9,plain,
multiply(X3,multiply(inverse(X3),X2)) = X2,
inference(transitivity,[status(thm)],[c4,c8]) ).
cnf(c10,plain,
multiply(X2,multiply(inverse(X2),inverse(inverse(X2)))) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
inverse(inverse(X2)) = multiply(X2,multiply(inverse(X2),inverse(inverse(X2)))),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(inverse(X2),inverse(inverse(X2))) = identity,
inference(substitution,[status(thm)],[c5]) ).
cnf(c13,plain,
multiply(X2,multiply(inverse(X2),inverse(inverse(X2)))) = multiply(X2,identity),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,axiom,
multiply(X2,identity) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c15,plain,
multiply(X2,multiply(inverse(X2),inverse(inverse(X2)))) = X2,
inference(transitivity,[status(thm)],[c13,c14]) ).
cnf(c16,plain,
inverse(inverse(X2)) = X2,
inference(transitivity,[status(thm)],[c11,c15]) ).
cnf(c17,plain,
inverse(inverse(a)) = a,
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
$false,
inference(resolution,[status(thm)],[c1,c17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP022-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.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 09:13:21 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.44 Command-line arguments: --no-flatten-goal
% 0.09/0.44
% 0.09/0.44 % SZS status Unsatisfiable
% 0.09/0.44
% 0.09/0.44 % SZS output start CNFRefutation
% See solution above
% 0.09/0.45
% 0.09/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------