%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP166-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n003.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 06:43:36 AM UTC 2025
% Result : Unsatisfiable 0.87s 1.03s
% Output : CNFRefutation 0.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 8 ( 8 unt; 0 nHn; 4 RR)
% Number of literals : 8 ( 7 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 : 7 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
least_upper_bound(a,multiply(b,a)) != multiply(b,a),
file('theBenchmark.p',prove_lat3a) ).
cnf(c3,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c5,axiom,
least_upper_bound(b,identity) = b,
file('theBenchmark.p',lat3a_2) ).
cnf(c7,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('GRP004-2.ax',symmetry_of_lub) ).
cnf(c78,axiom,
multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_lub2) ).
cnf(c80,plain,
least_upper_bound(X,multiply(b,X)) = multiply(b,X),
inference(equational,[status(thm)],[c3,c5,c7,c78]) ).
cnf(g1,plain,
least_upper_bound(a,multiply(b,a)) = multiply(b,a),
inference(equational,[status(thm)],[c80]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP166-3 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.00/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n003.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 08:12:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.87/1.03 % SZS status Unsatisfiable
% 0.87/1.03 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------