%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP186-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 0.45s 0.48s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of clauses : 31 ( 31 unt; 0 nHn; 4 RR)
% Number of literals : 31 ( 30 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 : 54 ( 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,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub1) ).
cnf(c3,plain,
multiply(X4,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X4,X2),multiply(X4,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
least_upper_bound(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,least_upper_bound(X2,X3)),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
least_upper_bound(X2,Y2) = least_upper_bound(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).
cnf(c6,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(X4,least_upper_bound(X2,X3)) = multiply(X4,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
least_upper_bound(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c4,c7]) ).
cnf(c9,plain,
least_upper_bound(multiply(X3,X2),multiply(X3,inverse(X3))) = multiply(X3,least_upper_bound(inverse(X3),X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(X3,least_upper_bound(inverse(X3),X2)) = least_upper_bound(multiply(X3,X2),multiply(X3,inverse(X3))),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,axiom,
multiply(multiply(X2,Y2),Z2) = multiply(X2,multiply(Y2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
cnf(c12,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
multiply(inverse(X3),multiply(X3,X2)) = multiply(multiply(inverse(X3),X3),X2),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,axiom,
multiply(inverse(X2),X2) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c15,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c17,plain,
multiply(multiply(inverse(X3),X3),X2) = X2,
inference(transitivity,[status(thm)],[c15,c16]) ).
cnf(c18,plain,
multiply(inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c13,c17]) ).
cnf(c19,plain,
X2 = multiply(inverse(X3),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
multiply(inverse(inverse(X3)),X2) = multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))) = multiply(X3,X2),
inference(substitution,[status(thm)],[c18]) ).
cnf(c22,plain,
multiply(inverse(inverse(X3)),X2) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c20,c21]) ).
cnf(c23,plain,
multiply(inverse(inverse(X2)),inverse(X2)) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(X2,inverse(X2)) = multiply(inverse(inverse(X2)),inverse(X2)),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
multiply(inverse(inverse(X2)),inverse(X2)) = identity,
inference(substitution,[status(thm)],[c14]) ).
cnf(c26,plain,
multiply(X2,inverse(X2)) = identity,
inference(transitivity,[status(thm)],[c24,c25]) ).
cnf(c27,plain,
least_upper_bound(multiply(X3,X2),multiply(X3,inverse(X3))) = least_upper_bound(multiply(X3,X2),identity),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
multiply(X3,least_upper_bound(inverse(X3),X2)) = least_upper_bound(multiply(X3,X2),identity),
inference(transitivity,[status(thm)],[c10,c27]) ).
cnf(c29,plain,
multiply(a,least_upper_bound(inverse(a),b)) = least_upper_bound(multiply(a,b),identity),
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
least_upper_bound(multiply(a,b),identity) = multiply(a,least_upper_bound(inverse(a),b)),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
$false,
inference(resolution,[status(thm)],[c1,c30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP186-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.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 09:42:45 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.45/0.48 Command-line arguments: --flatten --complete-subsets
% 0.45/0.48
% 0.45/0.48 % SZS status Unsatisfiable
% 0.45/0.48
% 0.45/0.48 % SZS output start CNFRefutation
% See solution above
% 0.45/0.50
% 0.45/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------