%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP159-1 : 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 10:09:28 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.47s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of clauses : 24 ( 24 unt; 0 nHn; 11 RR)
% Number of literals : 24 ( 23 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
least_upper_bound(multiply(c,a),multiply(c,b)) != multiply(c,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ax_mono2c) ).
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(X2,least_upper_bound(a,b)) = least_upper_bound(multiply(X2,a),multiply(X2,b)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
least_upper_bound(multiply(X2,a),multiply(X2,b)) = multiply(X2,least_upper_bound(a,b)),
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(b,a) = least_upper_bound(a,b),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
least_upper_bound(a,b) = least_upper_bound(b,a),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,axiom,
greatest_lower_bound(a,b) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c9,plain,
a = greatest_lower_bound(a,b),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
least_upper_bound(b,a) = least_upper_bound(b,greatest_lower_bound(a,b)),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,axiom,
greatest_lower_bound(X2,Y2) = greatest_lower_bound(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
cnf(c12,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
least_upper_bound(X3,greatest_lower_bound(X2,X3)) = least_upper_bound(X3,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,axiom,
least_upper_bound(X2,greatest_lower_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lub_absorbtion) ).
cnf(c16,plain,
least_upper_bound(X3,greatest_lower_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
least_upper_bound(X3,greatest_lower_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c14,c16]) ).
cnf(c18,plain,
least_upper_bound(b,greatest_lower_bound(a,b)) = b,
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
least_upper_bound(b,a) = b,
inference(transitivity,[status(thm)],[c10,c18]) ).
cnf(c20,plain,
least_upper_bound(a,b) = b,
inference(transitivity,[status(thm)],[c7,c19]) ).
cnf(c21,plain,
multiply(X2,least_upper_bound(a,b)) = multiply(X2,b),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
least_upper_bound(multiply(X2,a),multiply(X2,b)) = multiply(X2,b),
inference(transitivity,[status(thm)],[c4,c21]) ).
cnf(c23,plain,
least_upper_bound(multiply(c,a),multiply(c,b)) = multiply(c,b),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
$false,
inference(resolution,[status(thm)],[c1,c23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP159-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:34:31 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.47 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
% 0.19/0.47
% 0.19/0.47 % SZS status Unsatisfiable
% 0.19/0.47
% 0.19/0.47 % SZS output start CNFRefutation
% See solution above
% 0.19/0.48
% 0.19/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------