%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP186-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 10:09:38 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.51s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 10 RR)
% Number of literals : 25 ( 24 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
least_upper_bound(multiply(a,b),identity) != multiply(a,least_upper_bound(inverse(a),b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p23x) ).
cnf(c2,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).
cnf(c3,plain,
least_upper_bound(multiply(a,b),identity) = least_upper_bound(identity,multiply(a,b)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
least_upper_bound(inverse(X3),X2) = least_upper_bound(X2,inverse(X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c5,plain,
least_upper_bound(X2,inverse(X3)) = least_upper_bound(inverse(X3),X2),
inference(symmetry,[status(thm)],[c4]) ).
cnf(c6,plain,
multiply(X3,least_upper_bound(X2,inverse(X3))) = multiply(X3,least_upper_bound(inverse(X3),X2)),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,axiom,
multiply(X2,least_upper_bound(Y2,Z)) = least_upper_bound(multiply(X2,Y2),multiply(X2,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub1) ).
cnf(c8,plain,
multiply(X3,least_upper_bound(inverse(X3),X2)) = least_upper_bound(multiply(X3,inverse(X3)),multiply(X3,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,axiom,
inverse(inverse(X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c10,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
multiply(X2,inverse(X2)) = multiply(inverse(inverse(X2)),inverse(X2)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,axiom,
multiply(inverse(X2),X2) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
cnf(c13,plain,
multiply(inverse(inverse(X2)),inverse(X2)) = identity,
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
multiply(X2,inverse(X2)) = identity,
inference(transitivity,[status(thm)],[c11,c13]) ).
cnf(c15,plain,
least_upper_bound(multiply(X3,inverse(X3)),multiply(X3,X2)) = least_upper_bound(identity,multiply(X3,X2)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(X3,least_upper_bound(inverse(X3),X2)) = least_upper_bound(identity,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c8,c15]) ).
cnf(c17,plain,
multiply(X3,least_upper_bound(X2,inverse(X3))) = least_upper_bound(identity,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c6,c16]) ).
cnf(c18,plain,
multiply(a,least_upper_bound(b,inverse(a))) = least_upper_bound(identity,multiply(a,b)),
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
least_upper_bound(identity,multiply(a,b)) = multiply(a,least_upper_bound(b,inverse(a))),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
least_upper_bound(inverse(a),b) = least_upper_bound(b,inverse(a)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c21,plain,
least_upper_bound(b,inverse(a)) = least_upper_bound(inverse(a),b),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
multiply(a,least_upper_bound(b,inverse(a))) = multiply(a,least_upper_bound(inverse(a),b)),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
least_upper_bound(identity,multiply(a,b)) = multiply(a,least_upper_bound(inverse(a),b)),
inference(transitivity,[status(thm)],[c19,c22]) ).
cnf(c24,plain,
least_upper_bound(multiply(a,b),identity) = multiply(a,least_upper_bound(inverse(a),b)),
inference(transitivity,[status(thm)],[c3,c23]) ).
cnf(c25,plain,
$false,
inference(resolution,[status(thm)],[c1,c24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP186-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.38 % Computer : n018.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 09:39:08 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.51 Command-line arguments: --no-flatten-goal
% 0.17/0.51
% 0.17/0.51 % SZS status Unsatisfiable
% 0.17/0.51
% 0.17/0.51 % SZS output start CNFRefutation
% See solution above
% 0.17/0.53
% 0.17/0.53 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------