%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : GRP114-1 : TPTP v9.0.0. Released v1.2.0.
% 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 06:43:25 AM UTC 2025
% Result : Unsatisfiable 61.08s 61.25s
% Output : CNFRefutation 61.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of clauses : 74 ( 74 unt; 0 nHn; 4 RR)
% Number of literals : 74 ( 73 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 : 125 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
multiply(positive_part(a),negative_part(a)) != a,
file('theBenchmark.p',prove_product) ).
cnf(c1,axiom,
inverse(identity) = identity,
file('theBenchmark.p',inverse_of_identity) ).
cnf(c4,axiom,
inverse(inverse(X)) = X,
file('theBenchmark.p',inverse_involution) ).
cnf(c5,axiom,
multiply(identity,X) = X,
file('GRP004-0.ax',left_identity) ).
cnf(c6,axiom,
positive_part(X) = union(X,identity),
file('theBenchmark.p',positive_part) ).
cnf(c7,plain,
union(X,identity) = positive_part(X),
inference(equational,[status(thm)],[c6]) ).
cnf(c9,axiom,
negative_part(X) = intersection(X,identity),
file('theBenchmark.p',negative_part) ).
cnf(c10,plain,
intersection(X,identity) = negative_part(X),
inference(equational,[status(thm)],[c9]) ).
cnf(c12,axiom,
intersection(X,Y) = intersection(Y,X),
file('theBenchmark.p',intersection_commutative) ).
cnf(c13,axiom,
union(X,Y) = union(Y,X),
file('theBenchmark.p',union_commutative) ).
cnf(c14,plain,
union(identity,X) = positive_part(X),
inference(equational,[status(thm)],[c7,c13]) ).
cnf(c15,plain,
intersection(identity,X) = negative_part(X),
inference(equational,[status(thm)],[c10,c12]) ).
cnf(c16,axiom,
multiply(inverse(X),X) = identity,
file('GRP004-0.ax',left_inverse) ).
cnf(c17,plain,
multiply(X,inverse(X)) = identity,
inference(equational,[status(thm)],[c4,c16]) ).
cnf(c18,axiom,
intersection(union(X,Y),Y) = Y,
file('theBenchmark.p',intersection_union_absorbtion) ).
cnf(c19,plain,
intersection(X,union(Y,X)) = X,
inference(equational,[status(thm)],[c12,c18]) ).
cnf(c20,plain,
negative_part(positive_part(X)) = identity,
inference(equational,[status(thm)],[c7,c15,c19]) ).
cnf(c21,axiom,
union(intersection(X,Y),Y) = Y,
file('theBenchmark.p',union_intersection_absorbtion) ).
cnf(c22,plain,
union(X,intersection(Y,X)) = X,
inference(equational,[status(thm)],[c13,c21]) ).
cnf(c23,plain,
positive_part(negative_part(X)) = identity,
inference(equational,[status(thm)],[c10,c14,c22]) ).
cnf(c26,plain,
intersection(X,positive_part(X)) = X,
inference(equational,[status(thm)],[c14,c19]) ).
cnf(c30,axiom,
inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)),
file('theBenchmark.p',inverse_product_lemma) ).
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,c5,c31]) ).
cnf(c33,plain,
multiply(X,identity) = X,
inference(equational,[status(thm)],[c4,c32]) ).
cnf(c34,axiom,
intersection(X,intersection(Y,Z)) = intersection(intersection(X,Y),Z),
file('theBenchmark.p',intersection_associative) ).
cnf(c35,plain,
intersection(intersection(X,Y),Z) = intersection(X,intersection(Y,Z)),
inference(equational,[status(thm)],[c34]) ).
cnf(c36,plain,
intersection(X,negative_part(Y)) = negative_part(intersection(X,Y)),
inference(equational,[status(thm)],[c10,c35]) ).
cnf(c37,plain,
intersection(negative_part(X),Y) = negative_part(intersection(X,Y)),
inference(equational,[status(thm)],[c10,c15,c35,c36]) ).
cnf(c38,axiom,
union(X,union(Y,Z)) = union(union(X,Y),Z),
file('theBenchmark.p',union_associative) ).
cnf(c39,plain,
union(union(X,Y),Z) = union(X,union(Y,Z)),
inference(equational,[status(thm)],[c38]) ).
cnf(c40,plain,
union(X,positive_part(Y)) = positive_part(union(X,Y)),
inference(equational,[status(thm)],[c7,c39]) ).
cnf(c42,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('GRP004-0.ax',associativity) ).
cnf(c45,plain,
inverse(multiply(X,inverse(Y))) = multiply(Y,inverse(X)),
inference(equational,[status(thm)],[c4,c31]) ).
cnf(c46,plain,
inverse(multiply(inverse(X),Y)) = multiply(inverse(Y),X),
inference(equational,[status(thm)],[c4,c31]) ).
cnf(c51,plain,
negative_part(intersection(positive_part(X),Y)) = negative_part(Y),
inference(equational,[status(thm)],[c15,c20,c37]) ).
cnf(c52,plain,
positive_part(union(X,negative_part(Y))) = positive_part(X),
inference(equational,[status(thm)],[c7,c23,c40]) ).
cnf(c53,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference(equational,[status(thm)],[c5,c16,c42]) ).
cnf(c61,plain,
multiply(inverse(multiply(X,Y)),X) = inverse(Y),
inference(equational,[status(thm)],[c46,c53]) ).
cnf(c62,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference(equational,[status(thm)],[c4,c31,c53]) ).
cnf(c65,axiom,
multiply(X,union(Y,Z)) = union(multiply(X,Y),multiply(X,Z)),
file('theBenchmark.p',multiply_union1) ).
cnf(c66,plain,
union(multiply(X,Y),multiply(X,Z)) = multiply(X,union(Y,Z)),
inference(equational,[status(thm)],[c65]) ).
cnf(c67,plain,
union(X,multiply(X,Y)) = multiply(X,positive_part(Y)),
inference(equational,[status(thm)],[c14,c33,c66]) ).
cnf(c68,plain,
multiply(inverse(X),union(X,Y)) = positive_part(multiply(inverse(X),Y)),
inference(equational,[status(thm)],[c14,c16,c66]) ).
cnf(c69,plain,
multiply(inverse(X),positive_part(X)) = positive_part(inverse(X)),
inference(equational,[status(thm)],[c7,c33,c68]) ).
cnf(c77,axiom,
multiply(X,intersection(Y,Z)) = intersection(multiply(X,Y),multiply(X,Z)),
file('theBenchmark.p',multiply_intersection1) ).
cnf(c78,plain,
intersection(multiply(X,Y),multiply(X,Z)) = multiply(X,intersection(Y,Z)),
inference(equational,[status(thm)],[c77]) ).
cnf(c79,plain,
intersection(X,multiply(X,Y)) = multiply(X,negative_part(Y)),
inference(equational,[status(thm)],[c15,c33,c78]) ).
cnf(c85,axiom,
multiply(union(X,Y),Z) = union(multiply(X,Z),multiply(Y,Z)),
file('theBenchmark.p',multiply_union2) ).
cnf(c86,plain,
union(multiply(X,Y),multiply(Z,Y)) = multiply(union(X,Z),Y),
inference(equational,[status(thm)],[c85]) ).
cnf(c87,plain,
union(X,multiply(Y,X)) = multiply(positive_part(Y),X),
inference(equational,[status(thm)],[c5,c14,c86]) ).
cnf(c95,axiom,
multiply(intersection(X,Y),Z) = intersection(multiply(X,Z),multiply(Y,Z)),
file('theBenchmark.p',multiply_intersection2) ).
cnf(c96,plain,
intersection(multiply(X,Y),multiply(Z,Y)) = multiply(intersection(X,Z),Y),
inference(equational,[status(thm)],[c95]) ).
cnf(c97,plain,
intersection(X,multiply(Y,X)) = multiply(negative_part(Y),X),
inference(equational,[status(thm)],[c5,c15,c96]) ).
cnf(c98,plain,
multiply(negative_part(inverse(X)),X) = negative_part(X),
inference(equational,[status(thm)],[c10,c16,c97]) ).
cnf(c99,plain,
multiply(negative_part(X),inverse(X)) = negative_part(inverse(X)),
inference(equational,[status(thm)],[c10,c17,c97]) ).
cnf(c100,plain,
multiply(negative_part(X),X) = multiply(X,negative_part(X)),
inference(equational,[status(thm)],[c79,c97]) ).
cnf(c102,plain,
multiply(intersection(inverse(X),Y),X) = negative_part(multiply(Y,X)),
inference(equational,[status(thm)],[c15,c16,c96]) ).
cnf(c140,plain,
multiply(X,inverse(intersection(X,Y))) = inverse(negative_part(multiply(Y,inverse(X)))),
inference(equational,[status(thm)],[c4,c45,c102]) ).
cnf(c165,plain,
multiply(positive_part(X),inverse(positive_part(inverse(X)))) = X,
inference(equational,[status(thm)],[c4,c62,c69]) ).
cnf(c167,plain,
multiply(inverse(negative_part(inverse(X))),negative_part(X)) = X,
inference(equational,[status(thm)],[c4,c61,c99]) ).
cnf(c173,plain,
multiply(positive_part(X),negative_part(X)) = multiply(negative_part(X),positive_part(X)),
inference(equational,[status(thm)],[c67,c87,c100]) ).
cnf(c178,plain,
multiply(X,inverse(intersection(Y,X))) = inverse(negative_part(multiply(Y,inverse(X)))),
inference(equational,[status(thm)],[c12,c140]) ).
cnf(c188,plain,
multiply(negative_part(inverse(X)),multiply(X,Y)) = multiply(negative_part(X),Y),
inference(equational,[status(thm)],[c12,c53,c97]) ).
cnf(c190,plain,
multiply(negative_part(inverse(X)),positive_part(X)) = multiply(negative_part(X),positive_part(inverse(X))),
inference(equational,[status(thm)],[c4,c69,c188]) ).
cnf(c191,plain,
multiply(negative_part(X),positive_part(inverse(X))) = intersection(positive_part(X),positive_part(inverse(X))),
inference(equational,[status(thm)],[c69,c97,c190]) ).
cnf(c251,plain,
intersection(positive_part(X),union(X,negative_part(Y))) = union(X,negative_part(Y)),
inference(equational,[status(thm)],[c12,c26,c52]) ).
cnf(c253,plain,
negative_part(union(negative_part(X),negative_part(Y))) = union(negative_part(X),negative_part(Y)),
inference(equational,[status(thm)],[c15,c23,c251]) ).
cnf(c304,plain,
union(negative_part(X),negative_part(inverse(X))) = intersection(positive_part(X),positive_part(inverse(X))),
inference(equational,[status(thm)],[c13,c67,c98,c190,c191]) ).
cnf(c305,plain,
intersection(positive_part(X),positive_part(inverse(X))) = identity,
inference(equational,[status(thm)],[c20,c51,c253,c304]) ).
cnf(c306,plain,
inverse(negative_part(X)) = positive_part(inverse(X)),
inference(equational,[status(thm)],[c1,c33,c165,c178,c305]) ).
cnf(c310,plain,
multiply(negative_part(X),positive_part(X)) = X,
inference(equational,[status(thm)],[c4,c167,c173,c306]) ).
cnf(g1,plain,
multiply(positive_part(a),negative_part(a)) = a,
inference(equational,[status(thm)],[c173,c310]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP114-1 : TPTP v9.0.0. Released v1.2.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n007.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Jul 14 08:08:49 EDT 2025
% 0.12/0.32 % CPUTime :
% 61.08/61.25 % SZS status Unsatisfiable
% 61.08/61.25 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------