%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP146-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 10:09:26 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.46s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of clauses : 28 ( 28 unt; 0 nHn; 18 RR)
% Number of literals : 28 ( 27 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
least_upper_bound(least_upper_bound(a,b),c) != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ax_lub1a) ).
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(least_upper_bound(a,b),c) = least_upper_bound(c,least_upper_bound(a,b)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
least_upper_bound(least_upper_bound(X4,X2),X3) = least_upper_bound(X3,least_upper_bound(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c5,plain,
least_upper_bound(X3,least_upper_bound(X4,X2)) = least_upper_bound(least_upper_bound(X4,X2),X3),
inference(symmetry,[status(thm)],[c4]) ).
cnf(c6,axiom,
least_upper_bound(X2,least_upper_bound(Y2,Z)) = least_upper_bound(least_upper_bound(X2,Y2),Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_lub) ).
cnf(c7,plain,
least_upper_bound(X4,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X4,X2),X3),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
least_upper_bound(least_upper_bound(X4,X2),X3) = least_upper_bound(X4,least_upper_bound(X2,X3)),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c10,plain,
least_upper_bound(X4,least_upper_bound(X2,X3)) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
least_upper_bound(least_upper_bound(X4,X2),X3) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c8,c10]) ).
cnf(c12,plain,
least_upper_bound(X3,least_upper_bound(X4,X2)) = least_upper_bound(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c5,c11]) ).
cnf(c13,plain,
least_upper_bound(c,least_upper_bound(a,b)) = least_upper_bound(a,least_upper_bound(c,b)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
least_upper_bound(b,c) = least_upper_bound(c,b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c15,plain,
least_upper_bound(c,b) = least_upper_bound(b,c),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,axiom,
least_upper_bound(b,c) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c17,plain,
least_upper_bound(c,b) = c,
inference(transitivity,[status(thm)],[c15,c16]) ).
cnf(c18,plain,
least_upper_bound(a,least_upper_bound(c,b)) = least_upper_bound(a,c),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
least_upper_bound(a,c) = least_upper_bound(c,a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c20,plain,
least_upper_bound(a,c) = least_upper_bound(c,a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c21,plain,
least_upper_bound(c,a) = least_upper_bound(a,c),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,axiom,
least_upper_bound(a,c) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c23,plain,
least_upper_bound(c,a) = c,
inference(transitivity,[status(thm)],[c21,c22]) ).
cnf(c24,plain,
least_upper_bound(a,c) = c,
inference(transitivity,[status(thm)],[c19,c23]) ).
cnf(c25,plain,
least_upper_bound(a,least_upper_bound(c,b)) = c,
inference(transitivity,[status(thm)],[c18,c24]) ).
cnf(c26,plain,
least_upper_bound(c,least_upper_bound(a,b)) = c,
inference(transitivity,[status(thm)],[c13,c25]) ).
cnf(c27,plain,
least_upper_bound(least_upper_bound(a,b),c) = c,
inference(transitivity,[status(thm)],[c3,c26]) ).
cnf(c28,plain,
$false,
inference(resolution,[status(thm)],[c1,c27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP146-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n010.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 09:34:01 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.46 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.13/0.46
% 0.13/0.46 % SZS status Unsatisfiable
% 0.13/0.46
% 0.13/0.46 % SZS output start CNFRefutation
% See solution above
% 0.13/0.47
% 0.13/0.47 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------