%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP012-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 10:08:53 AM UTC 2026
% Result : Unsatisfiable 0.20s 0.46s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of clauses : 30 ( 30 unt; 0 nHn; 3 RR)
% Number of literals : 30 ( 29 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; 3 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_of_product_is_product_of_inverses) ).
cnf(c2,axiom,
multiply(X,identity) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
cnf(c3,plain,
multiply(inverse(multiply(X3,X2)),identity) = inverse(multiply(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
inverse(multiply(X3,X2)) = multiply(inverse(multiply(X3,X2)),identity),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(multiply(X2,Y),Z) = multiply(X2,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
cnf(c6,plain,
multiply(multiply(X3,X2),multiply(inverse(X2),inverse(X3))) = multiply(X3,multiply(X2,multiply(inverse(X2),inverse(X3)))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(multiply(X3,inverse(X3)),X2) = multiply(X3,multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c8,plain,
multiply(X3,multiply(inverse(X3),X2)) = multiply(multiply(X3,inverse(X3)),X2),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,axiom,
multiply(X2,inverse(X2)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c10,plain,
multiply(multiply(X3,inverse(X3)),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c12,plain,
multiply(multiply(X3,inverse(X3)),X2) = X2,
inference(transitivity,[status(thm)],[c10,c11]) ).
cnf(c13,plain,
multiply(X3,multiply(inverse(X3),X2)) = X2,
inference(transitivity,[status(thm)],[c8,c12]) ).
cnf(c14,plain,
multiply(X2,multiply(inverse(X2),inverse(X3))) = inverse(X3),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
multiply(X3,multiply(X2,multiply(inverse(X2),inverse(X3)))) = multiply(X3,inverse(X3)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(X3,multiply(X2,multiply(inverse(X2),inverse(X3)))) = identity,
inference(transitivity,[status(thm)],[c15,c9]) ).
cnf(c17,plain,
multiply(multiply(X3,X2),multiply(inverse(X2),inverse(X3))) = identity,
inference(transitivity,[status(thm)],[c6,c16]) ).
cnf(c18,plain,
identity = multiply(multiply(X3,X2),multiply(inverse(X2),inverse(X3))),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
multiply(inverse(multiply(X3,X2)),identity) = multiply(inverse(multiply(X3,X2)),multiply(multiply(X3,X2),multiply(inverse(X2),inverse(X3)))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c21,plain,
multiply(inverse(X3),multiply(X3,X2)) = multiply(multiply(inverse(X3),X3),X2),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,axiom,
multiply(inverse(X2),X2) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c23,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(multiply(inverse(X3),X3),X2) = X2,
inference(transitivity,[status(thm)],[c23,c11]) ).
cnf(c25,plain,
multiply(inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c21,c24]) ).
cnf(c26,plain,
multiply(inverse(multiply(X3,X2)),multiply(multiply(X3,X2),multiply(inverse(X2),inverse(X3)))) = multiply(inverse(X2),inverse(X3)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
multiply(inverse(multiply(X3,X2)),identity) = multiply(inverse(X2),inverse(X3)),
inference(transitivity,[status(thm)],[c19,c26]) ).
cnf(c28,plain,
inverse(multiply(X3,X2)) = multiply(inverse(X2),inverse(X3)),
inference(transitivity,[status(thm)],[c4,c27]) ).
cnf(c29,plain,
inverse(multiply(a,b)) = multiply(inverse(b),inverse(a)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
$false,
inference(resolution,[status(thm)],[c1,c29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP012-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.38 % Computer : n015.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 09:16:59 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.46 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.46
% 0.20/0.46 % SZS status Unsatisfiable
% 0.20/0.46
% 0.20/0.46 % SZS output start CNFRefutation
% See solution above
% 0.20/0.47
% 0.20/0.47 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------