%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP167-5 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n011.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 1.74s 1.90s
% Output : CNFRefutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 17
% Syntax : Number of clauses : 29 ( 29 unt; 0 nHn; 3 RR)
% Number of literals : 29 ( 28 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 55 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)),
file('theBenchmark.p',prove_lat4) ).
cnf(c2,axiom,
greatest_lower_bound(X,X) = X,
file('GRP004-2.ax',idempotence_of_gld) ).
cnf(c3,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c4,axiom,
positive_part(X) = least_upper_bound(X,identity),
file('theBenchmark.p',lat4_1) ).
cnf(c5,axiom,
negative_part(X) = greatest_lower_bound(X,identity),
file('theBenchmark.p',lat4_2) ).
cnf(c6,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('GRP004-2.ax',symmetry_of_glb) ).
cnf(c7,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('GRP004-2.ax',symmetry_of_lub) ).
cnf(c8,axiom,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c9,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('GRP004-2.ax',lub_absorbtion) ).
cnf(c12,plain,
least_upper_bound(X,greatest_lower_bound(Y,X)) = X,
inference(equational,[status(thm)],[c6,c9]) ).
cnf(c13,axiom,
inverse(least_upper_bound(X,Y)) = greatest_lower_bound(inverse(X),inverse(Y)),
file('theBenchmark.p',p10) ).
cnf(c18,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('GRP004-0.ax',associativity) ).
cnf(c23,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c3,c8,c18]) ).
cnf(c25,plain,
multiply(inverse(inverse(X)),identity) = X,
inference(equational,[status(thm)],[c8,c23]) ).
cnf(c28,plain,
multiply(inverse(inverse(X)),Y) = multiply(X,Y),
inference(equational,[status(thm)],[c23]) ).
cnf(c29,plain,
multiply(X,identity) = X,
inference(equational,[status(thm)],[c25,c28]) ).
cnf(c34,axiom,
least_upper_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(X,Z)),
file('theBenchmark.p',lat4_3) ).
cnf(c35,plain,
greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(X,Z)) = least_upper_bound(X,greatest_lower_bound(Y,Z)),
inference(equational,[status(thm)],[c34]) ).
cnf(c36,axiom,
greatest_lower_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,Z)),
file('theBenchmark.p',lat4_4) ).
cnf(c37,axiom,
multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_glb2) ).
cnf(c38,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_glb1) ).
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,axiom,
multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_lub2) ).
cnf(c47,plain,
least_upper_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,Z)) = greatest_lower_bound(least_upper_bound(Y,Z),X),
inference(equational,[status(thm)],[c6,c36]) ).
cnf(c48,plain,
least_upper_bound(X,greatest_lower_bound(least_upper_bound(Y,X),Z)) = least_upper_bound(X,greatest_lower_bound(Y,Z)),
inference(equational,[status(thm)],[c2,c7,c9,c35,c36,c47]) ).
cnf(c148,plain,
least_upper_bound(X,greatest_lower_bound(multiply(inverse(Y),multiply(Z,X)),multiply(inverse(Z),multiply(Y,X)))) = X,
inference(equational,[status(thm)],[c7,c13,c23,c35,c37,c39,c40]) ).
cnf(c149,plain,
least_upper_bound(X,greatest_lower_bound(identity,multiply(X,X))) = X,
inference(equational,[status(thm)],[c8,c18,c23,c148]) ).
cnf(g1,plain,
a = multiply(positive_part(a),negative_part(a)),
inference(equational,[status(thm)],[c2,c3,c4,c5,c6,c7,c12,c29,c36,c38,c40,c48,c149]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : GRP167-5 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.09/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n011.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 :
% 1.74/1.90 % SZS status Unsatisfiable
% 1.74/1.90 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------