%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP159-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n016.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 06:43:35 AM UTC 2025
% Result : Unsatisfiable 0.83s 1.02s
% Output : CNFRefutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 10 ( 10 unt; 0 nHn; 4 RR)
% Number of literals : 10 ( 9 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 : 11 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
least_upper_bound(multiply(c,a),multiply(c,b)) != multiply(c,b),
file('theBenchmark.p',prove_ax_mono2c) ).
cnf(c4,axiom,
greatest_lower_bound(a,b) = a,
file('theBenchmark.p',ax_mono2c_1) ).
cnf(c5,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('GRP004-2.ax',symmetry_of_glb) ).
cnf(c6,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('GRP004-2.ax',symmetry_of_lub) ).
cnf(c10,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('GRP004-2.ax',lub_absorbtion) ).
cnf(c49,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_glb1) ).
cnf(c58,plain,
greatest_lower_bound(multiply(X,b),multiply(X,a)) = multiply(X,a),
inference(equational,[status(thm)],[c4,c5,c49]) ).
cnf(c69,plain,
least_upper_bound(multiply(X,b),multiply(X,a)) = multiply(X,b),
inference(equational,[status(thm)],[c10,c58]) ).
cnf(g1,plain,
least_upper_bound(multiply(c,a),multiply(c,b)) = multiply(c,b),
inference(equational,[status(thm)],[c6,c69]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP159-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n016.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 08:12:49 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.83/1.02 % SZS status Unsatisfiable
% 0.83/1.02 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------