%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP147-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n004.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 1.32s 1.45s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 19 ( 19 unt; 0 nHn; 10 RR)
% Number of literals : 19 ( 18 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 : 18 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
greatest_lower_bound(least_upper_bound(a,b),c) != least_upper_bound(a,b),
file('theBenchmark.p',prove_ax_lub1b) ).
cnf(c4,axiom,
greatest_lower_bound(a,c) = a,
file('theBenchmark.p',ax_lub1b_1) ).
cnf(c5,axiom,
greatest_lower_bound(b,c) = b,
file('theBenchmark.p',ax_lub1b_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,
greatest_lower_bound(c,a) = a,
inference(equational,[status(thm)],[c4,c6]) ).
cnf(c9,plain,
greatest_lower_bound(c,b) = b,
inference(equational,[status(thm)],[c5,c6]) ).
cnf(c11,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('GRP004-2.ax',lub_absorbtion) ).
cnf(c12,plain,
least_upper_bound(c,a) = c,
inference(equational,[status(thm)],[c8,c11]) ).
cnf(c13,plain,
least_upper_bound(c,b) = c,
inference(equational,[status(thm)],[c9,c11]) ).
cnf(c14,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('GRP004-2.ax',glb_absorbtion) ).
cnf(c15,plain,
greatest_lower_bound(X,least_upper_bound(Y,X)) = X,
inference(equational,[status(thm)],[c7,c14]) ).
cnf(c19,axiom,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z),
file('GRP004-2.ax',associativity_of_lub) ).
cnf(c20,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c19]) ).
cnf(c59,plain,
least_upper_bound(c,least_upper_bound(b,X)) = least_upper_bound(c,X),
inference(equational,[status(thm)],[c13,c20]) ).
cnf(c205,plain,
greatest_lower_bound(least_upper_bound(c,X),least_upper_bound(b,X)) = least_upper_bound(b,X),
inference(equational,[status(thm)],[c6,c15,c59]) ).
cnf(c206,plain,
greatest_lower_bound(c,least_upper_bound(b,a)) = least_upper_bound(b,a),
inference(equational,[status(thm)],[c12,c205]) ).
cnf(g1,plain,
greatest_lower_bound(least_upper_bound(a,b),c) = least_upper_bound(a,b),
inference(equational,[status(thm)],[c6,c7,c206]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP147-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.03/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n004.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Jul 14 08:12:19 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.32/1.45 % SZS status Unsatisfiable
% 1.32/1.45 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------