%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP171-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n006.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 06:43:38 AM UTC 2025
% Result : Unsatisfiable 0.85s 0.99s
% Output : CNFRefutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 6 RR)
% Number of literals : 12 ( 11 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 2 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 : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
least_upper_bound(identity,multiply(a,b)) != multiply(a,b),
file('theBenchmark.p',prove_p04a) ).
cnf(c3,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c4,axiom,
least_upper_bound(identity,a) = a,
file('theBenchmark.p',p04a_1) ).
cnf(c5,axiom,
least_upper_bound(identity,b) = b,
file('theBenchmark.p',p04a_2) ).
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(identity,least_upper_bound(b,X)) = least_upper_bound(b,X),
inference(equational,[status(thm)],[c5,c18]) ).
cnf(c64,axiom,
multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_lub2) ).
cnf(c65,plain,
least_upper_bound(X,multiply(a,X)) = multiply(a,X),
inference(equational,[status(thm)],[c3,c4,c64]) ).
cnf(c71,plain,
least_upper_bound(identity,multiply(a,b)) = multiply(a,b),
inference(equational,[status(thm)],[c23,c65]) ).
cnf(g1,plain,
least_upper_bound(identity,multiply(a,b)) = multiply(a,b),
inference(equational,[status(thm)],[c71]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP171-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.07/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n006.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 08:13:34 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.85/0.99 % SZS status Unsatisfiable
% 0.85/0.99 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------