%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP168-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n002.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 06:43:37 AM UTC 2025
% Result : Unsatisfiable 40.42s 40.57s
% Output : CNFRefutation 40.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 9 unt; 0 nHn; 4 RR)
% Number of literals : 9 ( 8 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 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 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
greatest_lower_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) != multiply(inverse(c),multiply(a,c)),
file('theBenchmark.p',prove_p01b) ).
cnf(c4,axiom,
greatest_lower_bound(a,b) = a,
file('theBenchmark.p',p01b_1) ).
cnf(c5,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('GRP004-2.ax',symmetry_of_glb) ).
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(c50,axiom,
multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_glb2) ).
cnf(c57,plain,
greatest_lower_bound(multiply(b,X),multiply(a,X)) = multiply(a,X),
inference(equational,[status(thm)],[c4,c5,c50]) ).
cnf(c960,plain,
greatest_lower_bound(multiply(X,multiply(b,Y)),multiply(X,multiply(a,Y))) = multiply(X,multiply(a,Y)),
inference(equational,[status(thm)],[c49,c57]) ).
cnf(g1,plain,
greatest_lower_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) = multiply(inverse(c),multiply(a,c)),
inference(equational,[status(thm)],[c5,c960]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP168-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.06/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n002.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 14 08:13:19 EDT 2025
% 0.11/0.32 % CPUTime :
% 40.42/40.57 % SZS status Unsatisfiable
% 40.42/40.57 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------