%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP167-4 : TPTP v9.0.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n016.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 158.43s 158.55s
% Output : CNFRefutation 158.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 17
% Syntax : Number of clauses : 67 ( 67 unt; 0 nHn; 4 RR)
% Number of literals : 67 ( 66 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 138 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
file('theBenchmark.p',prove_p19) ).
cnf(c1,axiom,
inverse(identity) = identity,
file('theBenchmark.p',p19_1) ).
cnf(c4,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c5,axiom,
inverse(inverse(X)) = X,
file('theBenchmark.p',p19_2) ).
cnf(c6,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('GRP004-2.ax',symmetry_of_lub) ).
cnf(c7,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('GRP004-2.ax',symmetry_of_glb) ).
cnf(c8,axiom,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c9,plain,
multiply(X,inverse(X)) = identity,
inference(equational,[status(thm)],[c5,c8]) ).
cnf(c10,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('GRP004-2.ax',lub_absorbtion) ).
cnf(c11,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('GRP004-2.ax',glb_absorbtion) ).
cnf(c12,plain,
greatest_lower_bound(X,least_upper_bound(Y,X)) = X,
inference(equational,[status(thm)],[c6,c11]) ).
cnf(c13,plain,
least_upper_bound(X,greatest_lower_bound(Y,X)) = X,
inference(equational,[status(thm)],[c7,c10]) ).
cnf(c14,axiom,
inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)),
file('theBenchmark.p',p19_3) ).
cnf(c15,plain,
multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
inference(equational,[status(thm)],[c14]) ).
cnf(c16,plain,
inverse(multiply(X,identity)) = inverse(X),
inference(equational,[status(thm)],[c1,c4,c15]) ).
cnf(c17,plain,
multiply(X,identity) = X,
inference(equational,[status(thm)],[c5,c16]) ).
cnf(c18,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(c19,plain,
least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c18]) ).
cnf(c20,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('GRP004-0.ax',associativity) ).
cnf(c21,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(c22,plain,
greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
inference(equational,[status(thm)],[c21]) ).
cnf(c26,plain,
inverse(multiply(inverse(X),Y)) = multiply(inverse(Y),X),
inference(equational,[status(thm)],[c5,c15]) ).
cnf(c28,plain,
least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(Y,least_upper_bound(X,Z)),
inference(equational,[status(thm)],[c6,c19]) ).
cnf(c29,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c4,c8,c20]) ).
cnf(c33,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference(equational,[status(thm)],[c5,c15,c29]) ).
cnf(c34,plain,
multiply(inverse(multiply(X,Y)),X) = inverse(Y),
inference(equational,[status(thm)],[c26,c29]) ).
cnf(c35,axiom,
multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_glb2) ).
cnf(c36,plain,
greatest_lower_bound(multiply(X,Y),multiply(Z,Y)) = multiply(greatest_lower_bound(X,Z),Y),
inference(equational,[status(thm)],[c35]) ).
cnf(c37,plain,
greatest_lower_bound(X,multiply(Y,X)) = multiply(greatest_lower_bound(identity,Y),X),
inference(equational,[status(thm)],[c4,c36]) ).
cnf(c38,plain,
greatest_lower_bound(X,multiply(Y,X)) = multiply(greatest_lower_bound(Y,identity),X),
inference(equational,[status(thm)],[c4,c7,c36]) ).
cnf(c41,axiom,
multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_lub2) ).
cnf(c42,plain,
least_upper_bound(multiply(X,Y),multiply(Z,Y)) = multiply(least_upper_bound(X,Z),Y),
inference(equational,[status(thm)],[c41]) ).
cnf(c44,plain,
least_upper_bound(X,multiply(Y,X)) = multiply(least_upper_bound(Y,identity),X),
inference(equational,[status(thm)],[c4,c6,c42]) ).
cnf(c47,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_lub1) ).
cnf(c48,plain,
least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c47]) ).
cnf(c49,plain,
least_upper_bound(X,multiply(X,Y)) = multiply(X,least_upper_bound(identity,Y)),
inference(equational,[status(thm)],[c17,c48]) ).
cnf(c50,plain,
least_upper_bound(X,multiply(X,Y)) = multiply(X,least_upper_bound(Y,identity)),
inference(equational,[status(thm)],[c6,c17,c48]) ).
cnf(c51,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_glb1) ).
cnf(c52,plain,
greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(equational,[status(thm)],[c51]) ).
cnf(c55,plain,
multiply(inverse(X),greatest_lower_bound(X,Y)) = greatest_lower_bound(identity,multiply(inverse(X),Y)),
inference(equational,[status(thm)],[c8,c52]) ).
cnf(c57,plain,
multiply(inverse(X),least_upper_bound(X,Y)) = least_upper_bound(identity,multiply(inverse(X),Y)),
inference(equational,[status(thm)],[c8,c48]) ).
cnf(c59,plain,
greatest_lower_bound(X,greatest_lower_bound(least_upper_bound(X,Y),Z)) = greatest_lower_bound(X,Z),
inference(equational,[status(thm)],[c11,c22]) ).
cnf(c60,plain,
least_upper_bound(X,least_upper_bound(greatest_lower_bound(X,Y),Z)) = least_upper_bound(X,Z),
inference(equational,[status(thm)],[c10,c19]) ).
cnf(c65,plain,
multiply(greatest_lower_bound(X,identity),inverse(X)) = greatest_lower_bound(identity,inverse(X)),
inference(equational,[status(thm)],[c7,c9,c38]) ).
cnf(c90,plain,
least_upper_bound(X,least_upper_bound(Y,greatest_lower_bound(Z,X))) = least_upper_bound(Y,X),
inference(equational,[status(thm)],[c13,c28]) ).
cnf(c113,plain,
greatest_lower_bound(X,multiply(X,least_upper_bound(identity,Y))) = X,
inference(equational,[status(thm)],[c11,c49]) ).
cnf(c140,plain,
multiply(greatest_lower_bound(X,multiply(Y,X)),Z) = multiply(greatest_lower_bound(identity,Y),multiply(X,Z)),
inference(equational,[status(thm)],[c20,c37]) ).
cnf(c147,plain,
least_upper_bound(X,multiply(Y,multiply(Z,X))) = multiply(least_upper_bound(identity,multiply(Y,Z)),X),
inference(equational,[status(thm)],[c6,c20,c44]) ).
cnf(c157,plain,
multiply(X,least_upper_bound(identity,multiply(inverse(X),Y))) = least_upper_bound(X,Y),
inference(equational,[status(thm)],[c5,c29,c57]) ).
cnf(c346,plain,
multiply(least_upper_bound(X,multiply(X,Y)),Z) = multiply(X,multiply(least_upper_bound(Y,identity),Z)),
inference(equational,[status(thm)],[c20,c50]) ).
cnf(c414,plain,
multiply(least_upper_bound(identity,multiply(X,Y)),X) = multiply(X,least_upper_bound(identity,multiply(Y,X))),
inference(equational,[status(thm)],[c6,c50,c147]) ).
cnf(c434,plain,
multiply(greatest_lower_bound(identity,multiply(inverse(X),Y)),Z) = multiply(inverse(X),multiply(greatest_lower_bound(X,Y),Z)),
inference(equational,[status(thm)],[c20,c55]) ).
cnf(c437,plain,
greatest_lower_bound(least_upper_bound(X,Y),least_upper_bound(greatest_lower_bound(X,Z),Y)) = least_upper_bound(greatest_lower_bound(X,Z),Y),
inference(equational,[status(thm)],[c7,c12,c60]) ).
cnf(c455,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X))),greatest_lower_bound(X,identity)) = X,
inference(equational,[status(thm)],[c5,c34,c65]) ).
cnf(c483,plain,
multiply(inverse(X),multiply(greatest_lower_bound(X,identity),Y)) = multiply(greatest_lower_bound(identity,inverse(X)),Y),
inference(equational,[status(thm)],[c4,c140,c434]) ).
cnf(c513,plain,
multiply(inverse(greatest_lower_bound(X,identity)),greatest_lower_bound(Y,multiply(X,Y))) = Y,
inference(equational,[status(thm)],[c29,c38]) ).
cnf(c735,plain,
greatest_lower_bound(X,multiply(greatest_lower_bound(Y,identity),least_upper_bound(X,Z))) = greatest_lower_bound(X,multiply(Y,least_upper_bound(X,Z))),
inference(equational,[status(thm)],[c38,c59]) ).
cnf(c753,plain,
multiply(greatest_lower_bound(X,identity),inverse(greatest_lower_bound(identity,inverse(X)))) = X,
inference(equational,[status(thm)],[c5,c20,c33,c483]) ).
cnf(c771,plain,
multiply(least_upper_bound(identity,X),greatest_lower_bound(X,identity)) = multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,X)),
inference(equational,[status(thm)],[c414,c455,c753]) ).
cnf(c995,plain,
greatest_lower_bound(X,least_upper_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,Z))) = least_upper_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,Z)),
inference(equational,[status(thm)],[c10,c437]) ).
cnf(c1120,plain,
greatest_lower_bound(X,multiply(greatest_lower_bound(Y,identity),least_upper_bound(Z,X))) = greatest_lower_bound(X,multiply(Y,least_upper_bound(Z,X))),
inference(equational,[status(thm)],[c90,c735]) ).
cnf(c1179,plain,
multiply(least_upper_bound(X,identity),greatest_lower_bound(X,identity)) = multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,X)),
inference(equational,[status(thm)],[c4,c346,c771]) ).
cnf(c1203,plain,
least_upper_bound(greatest_lower_bound(X,identity),greatest_lower_bound(Y,multiply(X,Y))) = multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,Y)),
inference(equational,[status(thm)],[c157,c513]) ).
cnf(c1204,plain,
multiply(greatest_lower_bound(X,identity),least_upper_bound(identity,X)) = X,
inference(equational,[status(thm)],[c113,c995,c1120,c1203]) ).
cnf(c1215,plain,
multiply(greatest_lower_bound(X,identity),least_upper_bound(X,identity)) = X,
inference(equational,[status(thm)],[c6,c1204]) ).
cnf(g1,plain,
a = multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
inference(equational,[status(thm)],[c6,c1179,c1215]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP167-4 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.32 % Computer : n016.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 08:13:04 EDT 2025
% 0.11/0.32 % CPUTime :
% 158.43/158.55 % SZS status Unsatisfiable
% 158.43/158.55 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------