%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP165-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n009.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 0.80s 0.94s
% Output : CNFRefutation 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 5 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; 2 con; 0-2 aty)
% Number of variables : 22 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
greatest_lower_bound(a,multiply(a,a)) != a,
file('theBenchmark.p',prove_lat1b) ).
cnf(c3,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c4,axiom,
greatest_lower_bound(a,identity) = identity,
file('theBenchmark.p',lat1b_1) ).
cnf(c6,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('GRP004-2.ax',symmetry_of_lub) ).
cnf(c7,axiom,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c8,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('GRP004-2.ax',glb_absorbtion) ).
cnf(c9,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('GRP004-2.ax',lub_absorbtion) ).
cnf(c10,plain,
least_upper_bound(a,identity) = a,
inference(equational,[status(thm)],[c4,c9]) ).
cnf(c17,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('GRP004-0.ax',associativity) ).
cnf(c24,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c3,c7,c17]) ).
cnf(c26,plain,
multiply(inverse(inverse(X)),identity) = X,
inference(equational,[status(thm)],[c7,c24]) ).
cnf(c29,plain,
multiply(inverse(inverse(X)),Y) = multiply(X,Y),
inference(equational,[status(thm)],[c24]) ).
cnf(c30,plain,
multiply(X,identity) = X,
inference(equational,[status(thm)],[c26,c29]) ).
cnf(c39,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_lub1) ).
cnf(c40,plain,
least_upper_bound(X,multiply(X,a)) = multiply(X,a),
inference(equational,[status(thm)],[c6,c10,c30,c39]) ).
cnf(c43,plain,
greatest_lower_bound(X,multiply(X,a)) = X,
inference(equational,[status(thm)],[c8,c40]) ).
cnf(g1,plain,
greatest_lower_bound(a,multiply(a,a)) = a,
inference(equational,[status(thm)],[c43]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP165-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n009.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Jul 14 08:12:49 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.80/0.94 % SZS status Unsatisfiable
% 0.80/0.94 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------