%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP173-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n007.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 06:43:39 AM UTC 2025
% Result : Unsatisfiable 0.90s 1.04s
% Output : CNFRefutation 0.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 12 RR)
% Number of literals : 26 ( 25 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 : 23 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
identity != a,
file('theBenchmark.p',prove_p05a) ).
cnf(c3,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c4,axiom,
least_upper_bound(identity,a) = identity,
file('theBenchmark.p',p05a_1) ).
cnf(c5,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('GRP004-2.ax',symmetry_of_glb) ).
cnf(c6,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('GRP004-2.ax',symmetry_of_lub) ).
cnf(c7,plain,
least_upper_bound(a,identity) = identity,
inference(equational,[status(thm)],[c4,c6]) ).
cnf(c8,axiom,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c9,axiom,
least_upper_bound(identity,inverse(a)) = identity,
file('theBenchmark.p',p05a_2) ).
cnf(c10,plain,
least_upper_bound(inverse(a),identity) = identity,
inference(equational,[status(thm)],[c6,c9]) ).
cnf(c12,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('GRP004-2.ax',glb_absorbtion) ).
cnf(c13,plain,
greatest_lower_bound(a,identity) = a,
inference(equational,[status(thm)],[c7,c12]) ).
cnf(c14,plain,
greatest_lower_bound(inverse(a),identity) = inverse(a),
inference(equational,[status(thm)],[c10,c12]) ).
cnf(c19,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('GRP004-0.ax',associativity) ).
cnf(c29,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c3,c8,c19]) ).
cnf(c31,plain,
multiply(inverse(inverse(X)),identity) = X,
inference(equational,[status(thm)],[c8,c29]) ).
cnf(c34,plain,
multiply(inverse(inverse(X)),Y) = multiply(X,Y),
inference(equational,[status(thm)],[c29]) ).
cnf(c35,plain,
multiply(X,identity) = X,
inference(equational,[status(thm)],[c31,c34]) ).
cnf(c36,plain,
inverse(identity) = identity,
inference(equational,[status(thm)],[c8,c35]) ).
cnf(c37,plain,
inverse(inverse(X)) = X,
inference(equational,[status(thm)],[c31,c35]) ).
cnf(c38,plain,
multiply(X,inverse(X)) = identity,
inference(equational,[status(thm)],[c8,c34]) ).
cnf(c49,axiom,
multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_glb2) ).
cnf(c50,plain,
greatest_lower_bound(X,multiply(a,X)) = multiply(a,X),
inference(equational,[status(thm)],[c3,c5,c13,c49]) ).
cnf(c51,plain,
identity = inverse(a),
inference(equational,[status(thm)],[c14,c38,c50]) ).
cnf(c52,plain,
inverse(a) = a,
inference(equational,[status(thm)],[c36,c37,c51]) ).
cnf(g1,plain,
identity = a,
inference(equational,[status(thm)],[c51,c52]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : GRP173-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.05/0.09 % Command : run_Leo-III %s %d THM
% 0.08/0.29 % Computer : n007.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Mon Jul 14 08:13:49 EDT 2025
% 0.08/0.29 % CPUTime :
% 0.90/1.04 % SZS status Unsatisfiable
% 0.90/1.04 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------