%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP172-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n001.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 1.08s 1.27s
% Output : CNFRefutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 9 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 31 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
least_upper_bound(identity,multiply(a,b)) != multiply(a,b),
file('theBenchmark.p',prove_p04d) ).
cnf(c3,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c4,axiom,
greatest_lower_bound(identity,a) = identity,
file('theBenchmark.p',p04d_1) ).
cnf(c5,axiom,
greatest_lower_bound(identity,b) = identity,
file('theBenchmark.p',p04d_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(c9,plain,
greatest_lower_bound(b,identity) = identity,
inference(equational,[status(thm)],[c5,c6]) ).
cnf(c10,axiom,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c11,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('GRP004-2.ax',lub_absorbtion) ).
cnf(c13,plain,
least_upper_bound(b,identity) = b,
inference(equational,[status(thm)],[c9,c11]) ).
cnf(c14,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('GRP004-2.ax',glb_absorbtion) ).
cnf(c17,axiom,
greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z),
file('GRP004-2.ax',associativity_of_glb) ).
cnf(c18,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(equational,[status(thm)],[c17]) ).
cnf(c21,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('GRP004-0.ax',associativity) ).
cnf(c24,plain,
greatest_lower_bound(identity,greatest_lower_bound(a,X)) = greatest_lower_bound(identity,X),
inference(equational,[status(thm)],[c4,c18]) ).
cnf(c29,plain,
greatest_lower_bound(identity,least_upper_bound(a,X)) = identity,
inference(equational,[status(thm)],[c4,c14,c24]) ).
cnf(c32,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c3,c10,c21]) ).
cnf(c34,plain,
multiply(inverse(inverse(X)),identity) = X,
inference(equational,[status(thm)],[c10,c32]) ).
cnf(c37,plain,
multiply(inverse(inverse(X)),Y) = multiply(X,Y),
inference(equational,[status(thm)],[c32]) ).
cnf(c38,plain,
multiply(X,identity) = X,
inference(equational,[status(thm)],[c34,c37]) ).
cnf(c63,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_lub1) ).
cnf(c68,plain,
least_upper_bound(X,multiply(X,b)) = multiply(X,b),
inference(equational,[status(thm)],[c7,c13,c38,c63]) ).
cnf(c77,plain,
greatest_lower_bound(multiply(a,b),identity) = identity,
inference(equational,[status(thm)],[c6,c29,c68]) ).
cnf(c113,plain,
least_upper_bound(multiply(a,b),identity) = multiply(a,b),
inference(equational,[status(thm)],[c11,c77]) ).
cnf(g1,plain,
least_upper_bound(identity,multiply(a,b)) = multiply(a,b),
inference(equational,[status(thm)],[c7,c113]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.10 % Problem : GRP172-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.04/0.10 % Command : run_Leo-III %s %d THM
% 0.09/0.28 % Computer : n001.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon Jul 14 08:13:34 EDT 2025
% 0.09/0.29 % CPUTime :
% 1.08/1.27 % SZS status Unsatisfiable
% 1.08/1.27 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------