%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP167-2 : 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 60.40s 60.87s
% Output : CNFRefutation 60.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of clauses : 64 ( 64 unt; 0 nHn; 4 RR)
% Number of literals : 64 ( 63 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 : 104 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)),
file('theBenchmark.p',prove_lat4) ).
cnf(c1,axiom,
inverse(identity) = identity,
file('theBenchmark.p',lat4_1) ).
cnf(c4,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c5,axiom,
inverse(inverse(X)) = X,
file('theBenchmark.p',lat4_2) ).
cnf(c6,axiom,
positive_part(X) = least_upper_bound(X,identity),
file('theBenchmark.p',lat4_4) ).
cnf(c7,plain,
least_upper_bound(X,identity) = positive_part(X),
inference(equational,[status(thm)],[c6]) ).
cnf(c9,axiom,
negative_part(X) = greatest_lower_bound(X,identity),
file('theBenchmark.p',lat4_5) ).
cnf(c10,plain,
greatest_lower_bound(X,identity) = negative_part(X),
inference(equational,[status(thm)],[c9]) ).
cnf(c12,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('GRP004-2.ax',symmetry_of_lub) ).
cnf(c13,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('GRP004-2.ax',symmetry_of_glb) ).
cnf(c14,plain,
greatest_lower_bound(identity,X) = negative_part(X),
inference(equational,[status(thm)],[c10,c13]) ).
cnf(c15,plain,
least_upper_bound(identity,X) = positive_part(X),
inference(equational,[status(thm)],[c7,c12]) ).
cnf(c16,axiom,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c18,axiom,
greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('GRP004-2.ax',glb_absorbtion) ).
cnf(c19,plain,
negative_part(positive_part(X)) = identity,
inference(equational,[status(thm)],[c14,c15,c18]) ).
cnf(c21,axiom,
least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('GRP004-2.ax',lub_absorbtion) ).
cnf(c22,plain,
positive_part(negative_part(X)) = identity,
inference(equational,[status(thm)],[c14,c15,c21]) ).
cnf(c23,plain,
least_upper_bound(X,negative_part(X)) = X,
inference(equational,[status(thm)],[c10,c21]) ).
cnf(c24,plain,
positive_part(positive_part(X)) = positive_part(X),
inference(equational,[status(thm)],[c7,c19,c23]) ).
cnf(c30,axiom,
inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)),
file('theBenchmark.p',lat4_3) ).
cnf(c31,plain,
multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
inference(equational,[status(thm)],[c30]) ).
cnf(c32,plain,
inverse(multiply(X,identity)) = inverse(X),
inference(equational,[status(thm)],[c1,c4,c31]) ).
cnf(c33,plain,
multiply(X,identity) = X,
inference(equational,[status(thm)],[c5,c32]) ).
cnf(c42,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('GRP004-0.ax',associativity) ).
cnf(c49,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c4,c16,c42]) ).
cnf(c62,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference(equational,[status(thm)],[c5,c31,c49]) ).
cnf(c67,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(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c67]) ).
cnf(c69,plain,
least_upper_bound(X,multiply(X,Y)) = multiply(X,positive_part(Y)),
inference(equational,[status(thm)],[c15,c33,c68]) ).
cnf(c70,plain,
multiply(inverse(X),least_upper_bound(X,Y)) = positive_part(multiply(inverse(X),Y)),
inference(equational,[status(thm)],[c15,c16,c68]) ).
cnf(c71,plain,
multiply(inverse(X),positive_part(X)) = positive_part(inverse(X)),
inference(equational,[status(thm)],[c7,c33,c70]) ).
cnf(c72,plain,
positive_part(inverse(negative_part(X))) = inverse(negative_part(X)),
inference(equational,[status(thm)],[c22,c33,c71]) ).
cnf(c80,axiom,
multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('GRP004-2.ax',monotony_glb1) ).
cnf(c81,plain,
greatest_lower_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,greatest_lower_bound(Y,Z)),
inference(equational,[status(thm)],[c80]) ).
cnf(c82,plain,
greatest_lower_bound(X,multiply(X,Y)) = multiply(X,negative_part(Y)),
inference(equational,[status(thm)],[c14,c33,c81]) ).
cnf(c83,plain,
multiply(inverse(X),greatest_lower_bound(X,Y)) = negative_part(multiply(inverse(X),Y)),
inference(equational,[status(thm)],[c14,c16,c81]) ).
cnf(c84,plain,
multiply(inverse(X),negative_part(X)) = negative_part(inverse(X)),
inference(equational,[status(thm)],[c10,c33,c83]) ).
cnf(c88,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_6) ).
cnf(c89,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)],[c88]) ).
cnf(c90,plain,
greatest_lower_bound(positive_part(X),positive_part(Y)) = positive_part(greatest_lower_bound(X,Y)),
inference(equational,[status(thm)],[c15,c89]) ).
cnf(c92,axiom,
multiply(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_glb2) ).
cnf(c93,plain,
greatest_lower_bound(multiply(X,Y),multiply(Z,Y)) = multiply(greatest_lower_bound(X,Z),Y),
inference(equational,[status(thm)],[c92]) ).
cnf(c94,plain,
greatest_lower_bound(X,multiply(Y,X)) = multiply(negative_part(Y),X),
inference(equational,[status(thm)],[c4,c14,c93]) ).
cnf(c103,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_7) ).
cnf(c104,plain,
least_upper_bound(greatest_lower_bound(X,Y),greatest_lower_bound(X,Z)) = greatest_lower_bound(X,least_upper_bound(Y,Z)),
inference(equational,[status(thm)],[c103]) ).
cnf(c105,plain,
least_upper_bound(negative_part(X),negative_part(Y)) = negative_part(least_upper_bound(X,Y)),
inference(equational,[status(thm)],[c14,c104]) ).
cnf(c108,axiom,
multiply(least_upper_bound(X,Y),Z) = least_upper_bound(multiply(X,Z),multiply(Y,Z)),
file('GRP004-2.ax',monotony_lub2) ).
cnf(c109,plain,
least_upper_bound(multiply(X,Y),multiply(Z,Y)) = multiply(least_upper_bound(X,Z),Y),
inference(equational,[status(thm)],[c108]) ).
cnf(c110,plain,
least_upper_bound(X,multiply(Y,X)) = multiply(positive_part(Y),X),
inference(equational,[status(thm)],[c4,c15,c109]) ).
cnf(c111,plain,
multiply(positive_part(inverse(X)),X) = positive_part(X),
inference(equational,[status(thm)],[c7,c16,c110]) ).
cnf(c113,plain,
multiply(positive_part(X),X) = multiply(X,positive_part(X)),
inference(equational,[status(thm)],[c69,c110]) ).
cnf(c170,plain,
multiply(X,negative_part(multiply(inverse(X),Y))) = greatest_lower_bound(X,Y),
inference(equational,[status(thm)],[c5,c49,c83]) ).
cnf(c183,plain,
multiply(negative_part(inverse(X)),positive_part(X)) = positive_part(greatest_lower_bound(X,inverse(X))),
inference(equational,[status(thm)],[c71,c90,c94]) ).
cnf(c186,plain,
multiply(positive_part(inverse(X)),negative_part(X)) = negative_part(least_upper_bound(X,inverse(X))),
inference(equational,[status(thm)],[c84,c105,c110]) ).
cnf(c190,plain,
multiply(inverse(positive_part(inverse(X))),positive_part(X)) = X,
inference(equational,[status(thm)],[c49,c111]) ).
cnf(c191,plain,
positive_part(greatest_lower_bound(X,inverse(X))) = negative_part(least_upper_bound(X,inverse(X))),
inference(equational,[status(thm)],[c13,c90,c170,c186,c190]) ).
cnf(c192,plain,
negative_part(least_upper_bound(X,inverse(X))) = identity,
inference(equational,[status(thm)],[c22,c24,c191]) ).
cnf(c202,plain,
multiply(negative_part(X),inverse(negative_part(inverse(X)))) = X,
inference(equational,[status(thm)],[c5,c62,c84]) ).
cnf(c213,plain,
multiply(positive_part(X),negative_part(X)) = multiply(negative_part(X),positive_part(X)),
inference(equational,[status(thm)],[c82,c94,c113]) ).
cnf(c222,plain,
multiply(positive_part(inverse(X)),multiply(X,Y)) = multiply(positive_part(X),Y),
inference(equational,[status(thm)],[c12,c49,c110]) ).
cnf(c223,plain,
inverse(negative_part(inverse(X))) = positive_part(X),
inference(equational,[status(thm)],[c4,c22,c33,c72,c183,c191,c192,c222]) ).
cnf(c227,plain,
multiply(negative_part(X),positive_part(X)) = X,
inference(equational,[status(thm)],[c202,c223]) ).
cnf(g1,plain,
a = multiply(positive_part(a),negative_part(a)),
inference(equational,[status(thm)],[c213,c227]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP167-2 : TPTP v9.0.0. Bugfixed v1.2.1.
% 0.06/0.11 % 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 :
% 60.40/60.87 % SZS status Unsatisfiable
% 60.40/60.87 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------