%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP185-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n008.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 06:43:43 AM UTC 2025
% Result : Unsatisfiable 0.89s 1.06s
% Output : CNFRefutation 0.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 4 RR)
% Number of literals : 18 ( 17 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 : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
file('theBenchmark.p',prove_p22a) ).
cnf(c1,axiom,
inverse(identity) = identity,
file('theBenchmark.p',p22a_1) ).
cnf(c2,axiom,
least_upper_bound(X,X) = X,
file('GRP004-2.ax',idempotence_of_lub) ).
cnf(c4,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c5,axiom,
inverse(inverse(X)) = X,
file('theBenchmark.p',p22a_2) ).
cnf(c6,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('GRP004-2.ax',symmetry_of_lub) ).
cnf(c14,axiom,
inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)),
file('theBenchmark.p',p22a_3) ).
cnf(c15,plain,
multiply(inverse(X),identity) = inverse(X),
inference(equational,[status(thm)],[c1,c4,c14]) ).
cnf(c16,plain,
multiply(X,identity) = X,
inference(equational,[status(thm)],[c5,c15]) ).
cnf(c17,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(c18,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c17]) ).
cnf(c23,plain,
least_upper_bound(X,least_upper_bound(X,Y)) = least_upper_bound(X,Y),
inference(equational,[status(thm)],[c2,c18]) ).
cnf(c25,plain,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(Y,least_upper_bound(X,Z)),
inference(equational,[status(thm)],[c6,c18]) ).
cnf(c27,plain,
least_upper_bound(X,least_upper_bound(Y,X)) = least_upper_bound(X,Y),
inference(equational,[status(thm)],[c6,c23]) ).
cnf(c30,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_lub1) ).
cnf(c33,axiom,
multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_lub2) ).
cnf(g1,plain,
least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) = multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
inference(equational,[status(thm)],[c4,c6,c16,c18,c23,c25,c27,c30,c33]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP185-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : run_Leo-III %s %d THM
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Jul 14 08:15:04 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.89/1.06 % SZS status Unsatisfiable
% 0.89/1.06 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------