%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP168-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 10:09:31 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.46s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of clauses : 14 ( 14 unt; 0 nHn; 12 RR)
% Number of literals : 14 ( 13 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 : 6 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) != multiply(inverse(c),multiply(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p01a) ).
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(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c))) = least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) = multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c))),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(least_upper_bound(Y2,Z2),X2) = least_upper_bound(multiply(Y2,X2),multiply(Z2,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub2) ).
cnf(c6,plain,
multiply(least_upper_bound(a,b),c) = least_upper_bound(multiply(a,c),multiply(b,c)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
least_upper_bound(multiply(a,c),multiply(b,c)) = multiply(least_upper_bound(a,b),c),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c))) = multiply(inverse(c),multiply(least_upper_bound(a,b),c)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,axiom,
least_upper_bound(a,b) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c10,plain,
multiply(least_upper_bound(a,b),c) = multiply(b,c),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
multiply(inverse(c),multiply(least_upper_bound(a,b),c)) = multiply(inverse(c),multiply(b,c)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c))) = multiply(inverse(c),multiply(b,c)),
inference(transitivity,[status(thm)],[c8,c11]) ).
cnf(c13,plain,
least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) = multiply(inverse(c),multiply(b,c)),
inference(transitivity,[status(thm)],[c4,c12]) ).
cnf(c14,plain,
$false,
inference(resolution,[status(thm)],[c1,c13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP168-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 09:39:46 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.46 Command-line arguments: --no-flatten-goal
% 0.11/0.46
% 0.11/0.46 % SZS status Unsatisfiable
% 0.11/0.46
% 0.11/0.46 % SZS output start CNFRefutation
% See solution above
% 0.18/0.47
% 0.18/0.47 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------