%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP141-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Jul 15 06:43:33 AM UTC 2025
% Result : Unsatisfiable 0.83s 1.00s
% Output : CNFRefutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 16 ( 16 unt; 0 nHn; 9 RR)
% Number of literals : 16 ( 15 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
greatest_lower_bound(greatest_lower_bound(a,b),c) != c,
file('theBenchmark.p',prove_ax_glb1d) ).
cnf(c4,axiom,
least_upper_bound(a,c) = a,
file('theBenchmark.p',ax_glb1d_1) ).
cnf(c5,axiom,
least_upper_bound(b,c) = b,
file('theBenchmark.p',ax_glb1d_2) ).
cnf(c6,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('GRP004-2.ax',symmetry_of_glb) ).
cnf(c7,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('GRP004-2.ax',symmetry_of_lub) ).
cnf(c8,plain,
least_upper_bound(c,a) = a,
inference(equational,[status(thm)],[c4,c7]) ).
cnf(c9,plain,
least_upper_bound(c,b) = b,
inference(equational,[status(thm)],[c5,c7]) ).
cnf(c12,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('GRP004-2.ax',glb_absorbtion) ).
cnf(c13,plain,
greatest_lower_bound(c,a) = c,
inference(equational,[status(thm)],[c8,c12]) ).
cnf(c14,plain,
greatest_lower_bound(c,b) = c,
inference(equational,[status(thm)],[c9,c12]) ).
cnf(c17,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z),
file('GRP004-2.ax',associativity_of_glb) ).
cnf(c18,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(equational,[status(thm)],[c17]) ).
cnf(c30,plain,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(Y,greatest_lower_bound(X,Z)),
inference(equational,[status(thm)],[c6,c18]) ).
cnf(c60,plain,
greatest_lower_bound(c,greatest_lower_bound(X,a)) = greatest_lower_bound(X,c),
inference(equational,[status(thm)],[c13,c30]) ).
cnf(g1,plain,
greatest_lower_bound(greatest_lower_bound(a,b),c) = c,
inference(equational,[status(thm)],[c6,c14,c60]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP141-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 14 08:12:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.83/1.00 % SZS status Unsatisfiable
% 0.83/1.00 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------