%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP114-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:09:17 AM UTC 2026
% Result : Unsatisfiable 2.86s 0.87s
% Output : CNFRefutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 19
% Syntax : Number of clauses : 298 ( 298 unt; 0 nHn; 5 RR)
% Number of literals : 298 ( 297 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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 : 464 ( 29 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(positive_part(a),negative_part(a)) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_product) ).
cnf(c2,axiom,
inverse(inverse(X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(X2,identity) = multiply(inverse(inverse(X2)),identity),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c6,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(inverse(X2),identity) = multiply(inverse(X2),inverse(identity)),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,axiom,
inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_product_lemma) ).
cnf(c9,plain,
inverse(multiply(identity,X2)) = multiply(inverse(X2),inverse(identity)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(inverse(X2),inverse(identity)) = inverse(multiply(identity,X2)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c12,plain,
inverse(multiply(identity,X2)) = inverse(X2),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
multiply(inverse(X2),inverse(identity)) = inverse(X2),
inference(transitivity,[status(thm)],[c10,c12]) ).
cnf(c14,plain,
multiply(inverse(X2),identity) = inverse(X2),
inference(transitivity,[status(thm)],[c7,c13]) ).
cnf(c15,plain,
multiply(inverse(inverse(X2)),identity) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
multiply(inverse(inverse(X2)),identity) = X2,
inference(transitivity,[status(thm)],[c15,c2]) ).
cnf(c17,plain,
multiply(X2,identity) = X2,
inference(transitivity,[status(thm)],[c4,c16]) ).
cnf(c18,plain,
X2 = multiply(X2,identity),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
union(X2,multiply(X2,X3)) = union(multiply(X2,identity),multiply(X2,X3)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,axiom,
multiply(X2,union(Y2,Z)) = union(multiply(X2,Y2),multiply(X2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_union1) ).
cnf(c21,plain,
multiply(X3,union(identity,X2)) = union(multiply(X3,identity),multiply(X3,X2)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
union(multiply(X3,identity),multiply(X3,X2)) = multiply(X3,union(identity,X2)),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,axiom,
union(X2,Y2) = union(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_commutative) ).
cnf(c24,plain,
union(X2,identity) = union(identity,X2),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
union(identity,X2) = union(X2,identity),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,axiom,
positive_part(X2) = union(X2,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c27,plain,
union(X2,identity) = positive_part(X2),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
union(identity,X2) = positive_part(X2),
inference(transitivity,[status(thm)],[c25,c27]) ).
cnf(c29,plain,
multiply(X3,union(identity,X2)) = multiply(X3,positive_part(X2)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
union(multiply(X3,identity),multiply(X3,X2)) = multiply(X3,positive_part(X2)),
inference(transitivity,[status(thm)],[c22,c29]) ).
cnf(c31,plain,
union(X3,multiply(X3,X2)) = multiply(X3,positive_part(X2)),
inference(transitivity,[status(thm)],[c19,c30]) ).
cnf(c32,plain,
union(negative_part(X2),multiply(negative_part(X2),X2)) = multiply(negative_part(X2),positive_part(X2)),
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
multiply(negative_part(X2),positive_part(X2)) = union(negative_part(X2),multiply(negative_part(X2),X2)),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,axiom,
intersection(X2,Y2) = intersection(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_commutative) ).
cnf(c35,plain,
intersection(multiply(X2,X3),X3) = intersection(X3,multiply(X2,X3)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
intersection(X3,multiply(X2,X3)) = intersection(multiply(X2,X3),X3),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
X2 = multiply(identity,X2),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c38,plain,
intersection(multiply(X2,X3),X3) = intersection(multiply(X2,X3),multiply(identity,X3)),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,axiom,
multiply(intersection(Y2,Z2),X2) = intersection(multiply(Y2,X2),multiply(Z2,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_intersection2) ).
cnf(c40,plain,
multiply(intersection(X2,identity),X3) = intersection(multiply(X2,X3),multiply(identity,X3)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
intersection(multiply(X2,X3),multiply(identity,X3)) = multiply(intersection(X2,identity),X3),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,axiom,
negative_part(X2) = intersection(X2,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c43,plain,
intersection(X2,identity) = negative_part(X2),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
multiply(intersection(X2,identity),X3) = multiply(negative_part(X2),X3),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
intersection(multiply(X2,X3),multiply(identity,X3)) = multiply(negative_part(X2),X3),
inference(transitivity,[status(thm)],[c41,c44]) ).
cnf(c46,plain,
intersection(multiply(X2,X3),X3) = multiply(negative_part(X2),X3),
inference(transitivity,[status(thm)],[c38,c45]) ).
cnf(c47,plain,
intersection(X3,multiply(X2,X3)) = multiply(negative_part(X2),X3),
inference(transitivity,[status(thm)],[c36,c46]) ).
cnf(c48,plain,
intersection(X2,multiply(X2,X2)) = multiply(negative_part(X2),X2),
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
multiply(negative_part(X2),X2) = intersection(X2,multiply(X2,X2)),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
X2 = multiply(X2,identity),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c51,plain,
intersection(X3,multiply(X3,X2)) = intersection(multiply(X3,identity),multiply(X3,X2)),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,axiom,
multiply(X2,intersection(Y2,Z2)) = intersection(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_intersection1) ).
cnf(c53,plain,
multiply(X3,intersection(identity,X2)) = intersection(multiply(X3,identity),multiply(X3,X2)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
intersection(multiply(X3,identity),multiply(X3,X2)) = multiply(X3,intersection(identity,X2)),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
intersection(X2,identity) = intersection(identity,X2),
inference(substitution,[status(thm)],[c34]) ).
cnf(c56,plain,
intersection(identity,X2) = intersection(X2,identity),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
intersection(X2,identity) = negative_part(X2),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c58,plain,
intersection(identity,X2) = negative_part(X2),
inference(transitivity,[status(thm)],[c56,c57]) ).
cnf(c59,plain,
multiply(X3,intersection(identity,X2)) = multiply(X3,negative_part(X2)),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
intersection(multiply(X3,identity),multiply(X3,X2)) = multiply(X3,negative_part(X2)),
inference(transitivity,[status(thm)],[c54,c59]) ).
cnf(c61,plain,
intersection(X3,multiply(X3,X2)) = multiply(X3,negative_part(X2)),
inference(transitivity,[status(thm)],[c51,c60]) ).
cnf(c62,plain,
intersection(X2,multiply(X2,X2)) = multiply(X2,negative_part(X2)),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
multiply(negative_part(X2),X2) = multiply(X2,negative_part(X2)),
inference(transitivity,[status(thm)],[c49,c62]) ).
cnf(c64,plain,
union(negative_part(X2),multiply(negative_part(X2),X2)) = union(negative_part(X2),multiply(X2,negative_part(X2))),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
union(multiply(X2,X3),X3) = union(X3,multiply(X2,X3)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c66,plain,
union(X3,multiply(X2,X3)) = union(multiply(X2,X3),X3),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c67,plain,
X2 = multiply(identity,X2),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c68,plain,
union(multiply(X2,X3),X3) = union(multiply(X2,X3),multiply(identity,X3)),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,axiom,
multiply(union(Y2,Z2),X2) = union(multiply(Y2,X2),multiply(Z2,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_union2) ).
cnf(c70,plain,
multiply(union(X2,identity),X3) = union(multiply(X2,X3),multiply(identity,X3)),
inference(substitution,[status(thm)],[c69]) ).
cnf(c71,plain,
union(multiply(X2,X3),multiply(identity,X3)) = multiply(union(X2,identity),X3),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c72,plain,
union(X2,identity) = positive_part(X2),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c73,plain,
multiply(union(X2,identity),X3) = multiply(positive_part(X2),X3),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
union(multiply(X2,X3),multiply(identity,X3)) = multiply(positive_part(X2),X3),
inference(transitivity,[status(thm)],[c71,c73]) ).
cnf(c75,plain,
union(multiply(X2,X3),X3) = multiply(positive_part(X2),X3),
inference(transitivity,[status(thm)],[c68,c74]) ).
cnf(c76,plain,
union(X3,multiply(X2,X3)) = multiply(positive_part(X2),X3),
inference(transitivity,[status(thm)],[c66,c75]) ).
cnf(c77,plain,
union(negative_part(X2),multiply(X2,negative_part(X2))) = multiply(positive_part(X2),negative_part(X2)),
inference(substitution,[status(thm)],[c76]) ).
cnf(c78,plain,
union(negative_part(X2),multiply(negative_part(X2),X2)) = multiply(positive_part(X2),negative_part(X2)),
inference(transitivity,[status(thm)],[c64,c77]) ).
cnf(c79,plain,
multiply(negative_part(X2),positive_part(X2)) = multiply(positive_part(X2),negative_part(X2)),
inference(transitivity,[status(thm)],[c33,c78]) ).
cnf(c80,plain,
multiply(positive_part(X2),negative_part(X2)) = multiply(negative_part(X2),positive_part(X2)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c82,plain,
negative_part(X2) = negative_part(inverse(inverse(X2))),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
multiply(negative_part(X2),positive_part(X2)) = multiply(negative_part(inverse(inverse(X2))),positive_part(X2)),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
multiply(inverse(positive_part(X2)),identity) = inverse(positive_part(X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c85,plain,
inverse(positive_part(X2)) = multiply(inverse(positive_part(X2)),identity),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c86,plain,
union(negative_part(inverse(X2)),negative_part(X2)) = union(negative_part(X2),negative_part(inverse(X2))),
inference(substitution,[status(thm)],[c23]) ).
cnf(c87,plain,
union(negative_part(X2),negative_part(inverse(X2))) = union(negative_part(inverse(X2)),negative_part(X2)),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c88,plain,
intersection(X2,multiply(inverse(X2),X2)) = multiply(negative_part(inverse(X2)),X2),
inference(substitution,[status(thm)],[c47]) ).
cnf(c89,plain,
multiply(negative_part(inverse(X2)),X2) = intersection(X2,multiply(inverse(X2),X2)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c90,axiom,
multiply(inverse(X2),X2) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c91,plain,
intersection(X2,multiply(inverse(X2),X2)) = intersection(X2,identity),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
intersection(X2,identity) = negative_part(X2),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c93,plain,
intersection(X2,multiply(inverse(X2),X2)) = negative_part(X2),
inference(transitivity,[status(thm)],[c91,c92]) ).
cnf(c94,plain,
multiply(negative_part(inverse(X2)),X2) = negative_part(X2),
inference(transitivity,[status(thm)],[c89,c93]) ).
cnf(c95,plain,
negative_part(X2) = multiply(negative_part(inverse(X2)),X2),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,plain,
union(negative_part(inverse(X2)),negative_part(X2)) = union(negative_part(inverse(X2)),multiply(negative_part(inverse(X2)),X2)),
inference(congruence,[status(thm)],[c95]) ).
cnf(c97,plain,
union(negative_part(inverse(X2)),multiply(negative_part(inverse(X2)),X2)) = multiply(negative_part(inverse(X2)),positive_part(X2)),
inference(substitution,[status(thm)],[c31]) ).
cnf(c98,plain,
intersection(positive_part(X2),multiply(inverse(X2),positive_part(X2))) = multiply(negative_part(inverse(X2)),positive_part(X2)),
inference(substitution,[status(thm)],[c47]) ).
cnf(c99,plain,
multiply(negative_part(inverse(X2)),positive_part(X2)) = intersection(positive_part(X2),multiply(inverse(X2),positive_part(X2))),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c100,plain,
multiply(inverse(X2),positive_part(X2)) = multiply(inverse(X2),union(X2,identity)),
inference(congruence,[status(thm)],[c26]) ).
cnf(c101,plain,
union(X2,X3) = union(X3,X2),
inference(substitution,[status(thm)],[c23]) ).
cnf(c102,plain,
union(X3,X2) = union(X2,X3),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
multiply(inverse(X3),union(X3,X2)) = multiply(inverse(X3),union(X2,X3)),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
multiply(inverse(X3),union(X2,X3)) = union(multiply(inverse(X3),X2),multiply(inverse(X3),X3)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c105,plain,
union(multiply(inverse(X3),X2),multiply(inverse(X3),X3)) = union(multiply(inverse(X3),X2),identity),
inference(congruence,[status(thm)],[c90]) ).
cnf(c106,plain,
positive_part(multiply(inverse(X3),X2)) = union(multiply(inverse(X3),X2),identity),
inference(substitution,[status(thm)],[c26]) ).
cnf(c107,plain,
union(multiply(inverse(X3),X2),identity) = positive_part(multiply(inverse(X3),X2)),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c108,plain,
union(multiply(inverse(X3),X2),multiply(inverse(X3),X3)) = positive_part(multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c105,c107]) ).
cnf(c109,plain,
multiply(inverse(X3),union(X2,X3)) = positive_part(multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c104,c108]) ).
cnf(c110,plain,
multiply(inverse(X3),union(X3,X2)) = positive_part(multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c103,c109]) ).
cnf(c111,plain,
multiply(inverse(X2),union(X2,identity)) = positive_part(multiply(inverse(X2),identity)),
inference(substitution,[status(thm)],[c110]) ).
cnf(c112,plain,
positive_part(multiply(inverse(X2),identity)) = positive_part(inverse(X2)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c113,plain,
multiply(inverse(X2),union(X2,identity)) = positive_part(inverse(X2)),
inference(transitivity,[status(thm)],[c111,c112]) ).
cnf(c114,plain,
multiply(inverse(X2),positive_part(X2)) = positive_part(inverse(X2)),
inference(transitivity,[status(thm)],[c100,c113]) ).
cnf(c115,plain,
intersection(positive_part(X2),multiply(inverse(X2),positive_part(X2))) = intersection(positive_part(X2),positive_part(inverse(X2))),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
multiply(negative_part(inverse(X2)),positive_part(X2)) = intersection(positive_part(X2),positive_part(inverse(X2))),
inference(transitivity,[status(thm)],[c99,c115]) ).
cnf(c117,plain,
union(negative_part(inverse(X2)),multiply(negative_part(inverse(X2)),X2)) = intersection(positive_part(X2),positive_part(inverse(X2))),
inference(transitivity,[status(thm)],[c97,c116]) ).
cnf(c118,plain,
union(negative_part(inverse(X2)),negative_part(X2)) = intersection(positive_part(X2),positive_part(inverse(X2))),
inference(transitivity,[status(thm)],[c96,c117]) ).
cnf(c119,plain,
union(negative_part(X2),negative_part(inverse(X2))) = intersection(positive_part(X2),positive_part(inverse(X2))),
inference(transitivity,[status(thm)],[c87,c118]) ).
cnf(c120,plain,
intersection(positive_part(X2),positive_part(inverse(X2))) = union(negative_part(X2),negative_part(inverse(X2))),
inference(symmetry,[status(thm)],[c119]) ).
cnf(c121,plain,
union(X2,X3) = union(X3,X2),
inference(substitution,[status(thm)],[c23]) ).
cnf(c122,plain,
union(X3,X2) = union(X2,X3),
inference(symmetry,[status(thm)],[c121]) ).
cnf(c123,plain,
negative_part(union(X3,X2)) = negative_part(union(X2,X3)),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
union(X2,negative_part(union(X3,X2))) = union(X2,negative_part(union(X2,X3))),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
union(X3,union(X2,negative_part(union(X3,X2)))) = union(X3,union(X2,negative_part(union(X2,X3)))),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
union(union(X2,X4),X3) = union(X3,union(X2,X4)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c127,plain,
union(X4,union(X3,X2)) = union(union(X3,X2),X4),
inference(symmetry,[status(thm)],[c126]) ).
cnf(c128,axiom,
union(X2,union(Y2,Z2)) = union(union(X2,Y2),Z2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_associative) ).
cnf(c129,plain,
union(X3,union(X2,X4)) = union(union(X3,X2),X4),
inference(substitution,[status(thm)],[c128]) ).
cnf(c130,plain,
union(union(X3,X2),X4) = union(X3,union(X2,X4)),
inference(symmetry,[status(thm)],[c129]) ).
cnf(c131,plain,
union(X2,X3) = union(X3,X2),
inference(substitution,[status(thm)],[c23]) ).
cnf(c132,plain,
union(X3,union(X2,X4)) = union(X3,union(X4,X2)),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
union(union(X3,X2),X4) = union(X3,union(X4,X2)),
inference(transitivity,[status(thm)],[c130,c132]) ).
cnf(c134,plain,
union(X4,union(X3,X2)) = union(X3,union(X4,X2)),
inference(transitivity,[status(thm)],[c127,c133]) ).
cnf(c135,plain,
union(X2,union(X3,negative_part(union(X2,X3)))) = union(X3,union(X2,negative_part(union(X2,X3)))),
inference(substitution,[status(thm)],[c134]) ).
cnf(c136,plain,
union(X3,union(X2,negative_part(union(X2,X3)))) = union(X2,union(X3,negative_part(union(X2,X3)))),
inference(symmetry,[status(thm)],[c135]) ).
cnf(c137,plain,
intersection(identity,union(X2,X3)) = negative_part(union(X2,X3)),
inference(substitution,[status(thm)],[c58]) ).
cnf(c138,plain,
negative_part(union(X2,X3)) = intersection(identity,union(X2,X3)),
inference(symmetry,[status(thm)],[c137]) ).
cnf(c139,plain,
union(X3,negative_part(union(X2,X3))) = union(X3,intersection(identity,union(X2,X3))),
inference(congruence,[status(thm)],[c138]) ).
cnf(c140,plain,
union(X2,union(X3,negative_part(union(X2,X3)))) = union(X2,union(X3,intersection(identity,union(X2,X3)))),
inference(congruence,[status(thm)],[c139]) ).
cnf(c141,plain,
union(X2,X3) = union(X3,X2),
inference(substitution,[status(thm)],[c23]) ).
cnf(c142,plain,
union(X3,X2) = union(X2,X3),
inference(symmetry,[status(thm)],[c141]) ).
cnf(c143,plain,
intersection(X2,union(X4,X3)) = intersection(X2,union(X3,X4)),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
union(X3,intersection(X2,union(X4,X3))) = union(X3,intersection(X2,union(X3,X4))),
inference(congruence,[status(thm)],[c143]) ).
cnf(c145,plain,
union(X4,union(X3,intersection(X2,union(X4,X3)))) = union(X4,union(X3,intersection(X2,union(X3,X4)))),
inference(congruence,[status(thm)],[c144]) ).
cnf(c146,plain,
union(X3,union(X4,intersection(X2,union(X3,X4)))) = union(X4,union(X3,intersection(X2,union(X3,X4)))),
inference(substitution,[status(thm)],[c134]) ).
cnf(c147,plain,
union(X4,union(X3,intersection(X2,union(X3,X4)))) = union(X3,union(X4,intersection(X2,union(X3,X4)))),
inference(symmetry,[status(thm)],[c146]) ).
cnf(c148,plain,
union(X3,union(X4,intersection(X2,union(X3,X4)))) = union(union(X3,X4),intersection(X2,union(X3,X4))),
inference(substitution,[status(thm)],[c128]) ).
cnf(c149,plain,
union(intersection(X2,X3),X3) = union(X3,intersection(X2,X3)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c150,plain,
union(X3,intersection(X2,X3)) = union(intersection(X2,X3),X3),
inference(symmetry,[status(thm)],[c149]) ).
cnf(c151,axiom,
union(intersection(X2,Y2),Y2) = Y2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_intersection_absorbtion) ).
cnf(c152,plain,
union(intersection(X2,X3),X3) = X3,
inference(substitution,[status(thm)],[c151]) ).
cnf(c153,plain,
union(X3,intersection(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c150,c152]) ).
cnf(c154,plain,
union(union(X3,X4),intersection(X2,union(X3,X4))) = union(X3,X4),
inference(substitution,[status(thm)],[c153]) ).
cnf(c155,plain,
union(X2,X3) = union(X3,X2),
inference(substitution,[status(thm)],[c23]) ).
cnf(c156,plain,
union(union(X3,X4),intersection(X2,union(X3,X4))) = union(X4,X3),
inference(transitivity,[status(thm)],[c154,c155]) ).
cnf(c157,plain,
union(X3,union(X4,intersection(X2,union(X3,X4)))) = union(X4,X3),
inference(transitivity,[status(thm)],[c148,c156]) ).
cnf(c158,plain,
union(X4,union(X3,intersection(X2,union(X3,X4)))) = union(X4,X3),
inference(transitivity,[status(thm)],[c147,c157]) ).
cnf(c159,plain,
union(X4,union(X3,intersection(X2,union(X4,X3)))) = union(X4,X3),
inference(transitivity,[status(thm)],[c145,c158]) ).
cnf(c160,plain,
union(X2,union(X3,intersection(identity,union(X2,X3)))) = union(X2,X3),
inference(substitution,[status(thm)],[c159]) ).
cnf(c161,plain,
union(X2,X3) = union(X3,X2),
inference(substitution,[status(thm)],[c23]) ).
cnf(c162,plain,
union(X2,union(X3,intersection(identity,union(X2,X3)))) = union(X3,X2),
inference(transitivity,[status(thm)],[c160,c161]) ).
cnf(c163,plain,
union(X2,union(X3,negative_part(union(X2,X3)))) = union(X3,X2),
inference(transitivity,[status(thm)],[c140,c162]) ).
cnf(c164,plain,
union(X3,union(X2,negative_part(union(X2,X3)))) = union(X3,X2),
inference(transitivity,[status(thm)],[c136,c163]) ).
cnf(c165,plain,
union(X3,union(X2,negative_part(union(X3,X2)))) = union(X3,X2),
inference(transitivity,[status(thm)],[c125,c164]) ).
cnf(c166,plain,
union(negative_part(X2),union(negative_part(inverse(X2)),negative_part(union(negative_part(X2),negative_part(inverse(X2)))))) = union(negative_part(X2),negative_part(inverse(X2))),
inference(substitution,[status(thm)],[c165]) ).
cnf(c167,plain,
union(negative_part(X2),negative_part(inverse(X2))) = union(negative_part(X2),union(negative_part(inverse(X2)),negative_part(union(negative_part(X2),negative_part(inverse(X2)))))),
inference(symmetry,[status(thm)],[c166]) ).
cnf(c168,plain,
negative_part(union(negative_part(X2),negative_part(inverse(X2)))) = negative_part(intersection(positive_part(X2),positive_part(inverse(X2)))),
inference(congruence,[status(thm)],[c119]) ).
cnf(c169,plain,
union(negative_part(inverse(X2)),negative_part(union(negative_part(X2),negative_part(inverse(X2))))) = union(negative_part(inverse(X2)),negative_part(intersection(positive_part(X2),positive_part(inverse(X2))))),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
union(negative_part(X2),union(negative_part(inverse(X2)),negative_part(union(negative_part(X2),negative_part(inverse(X2)))))) = union(negative_part(X2),union(negative_part(inverse(X2)),negative_part(intersection(positive_part(X2),positive_part(inverse(X2)))))),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
intersection(X2,positive_part(X3)) = intersection(positive_part(X3),X2),
inference(substitution,[status(thm)],[c34]) ).
cnf(c172,plain,
intersection(positive_part(X3),X2) = intersection(X2,positive_part(X3)),
inference(symmetry,[status(thm)],[c171]) ).
cnf(c173,plain,
negative_part(intersection(positive_part(X3),X2)) = negative_part(intersection(X2,positive_part(X3))),
inference(congruence,[status(thm)],[c172]) ).
cnf(c174,plain,
intersection(X3,negative_part(X2)) = intersection(X3,intersection(X2,identity)),
inference(congruence,[status(thm)],[c42]) ).
cnf(c175,axiom,
intersection(X2,intersection(Y2,Z2)) = intersection(intersection(X2,Y2),Z2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_associative) ).
cnf(c176,plain,
intersection(X3,intersection(X2,identity)) = intersection(intersection(X3,X2),identity),
inference(substitution,[status(thm)],[c175]) ).
cnf(c177,plain,
negative_part(intersection(X3,X2)) = intersection(intersection(X3,X2),identity),
inference(substitution,[status(thm)],[c42]) ).
cnf(c178,plain,
intersection(intersection(X3,X2),identity) = negative_part(intersection(X3,X2)),
inference(symmetry,[status(thm)],[c177]) ).
cnf(c179,plain,
intersection(X3,intersection(X2,identity)) = negative_part(intersection(X3,X2)),
inference(transitivity,[status(thm)],[c176,c178]) ).
cnf(c180,plain,
intersection(X3,negative_part(X2)) = negative_part(intersection(X3,X2)),
inference(transitivity,[status(thm)],[c174,c179]) ).
cnf(c181,plain,
intersection(X3,negative_part(positive_part(X2))) = negative_part(intersection(X3,positive_part(X2))),
inference(substitution,[status(thm)],[c180]) ).
cnf(c182,plain,
negative_part(intersection(X3,positive_part(X2))) = intersection(X3,negative_part(positive_part(X2))),
inference(symmetry,[status(thm)],[c181]) ).
cnf(c183,plain,
negative_part(positive_part(X2)) = negative_part(union(X2,identity)),
inference(congruence,[status(thm)],[c26]) ).
cnf(c184,plain,
intersection(identity,union(X2,identity)) = negative_part(union(X2,identity)),
inference(substitution,[status(thm)],[c58]) ).
cnf(c185,plain,
negative_part(union(X2,identity)) = intersection(identity,union(X2,identity)),
inference(symmetry,[status(thm)],[c184]) ).
cnf(c186,plain,
intersection(union(X2,X3),X3) = intersection(X3,union(X2,X3)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c187,plain,
intersection(X3,union(X2,X3)) = intersection(union(X2,X3),X3),
inference(symmetry,[status(thm)],[c186]) ).
cnf(c188,axiom,
intersection(union(X2,Y2),Y2) = Y2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_union_absorbtion) ).
cnf(c189,plain,
intersection(union(X2,X3),X3) = X3,
inference(substitution,[status(thm)],[c188]) ).
cnf(c190,plain,
intersection(X3,union(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c187,c189]) ).
cnf(c191,plain,
intersection(identity,union(X2,identity)) = identity,
inference(substitution,[status(thm)],[c190]) ).
cnf(c192,plain,
negative_part(union(X2,identity)) = identity,
inference(transitivity,[status(thm)],[c185,c191]) ).
cnf(c193,plain,
negative_part(positive_part(X2)) = identity,
inference(transitivity,[status(thm)],[c183,c192]) ).
cnf(c194,plain,
intersection(X3,negative_part(positive_part(X2))) = intersection(X3,identity),
inference(congruence,[status(thm)],[c193]) ).
cnf(c195,plain,
intersection(X2,identity) = negative_part(X2),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c196,plain,
intersection(X3,negative_part(positive_part(X2))) = negative_part(X3),
inference(transitivity,[status(thm)],[c194,c195]) ).
cnf(c197,plain,
negative_part(intersection(X3,positive_part(X2))) = negative_part(X3),
inference(transitivity,[status(thm)],[c182,c196]) ).
cnf(c198,plain,
negative_part(intersection(X2,positive_part(X3))) = negative_part(X2),
inference(substitution,[status(thm)],[c197]) ).
cnf(c199,plain,
negative_part(intersection(positive_part(X3),X2)) = negative_part(X2),
inference(transitivity,[status(thm)],[c173,c198]) ).
cnf(c200,plain,
negative_part(intersection(positive_part(X2),positive_part(inverse(X2)))) = negative_part(positive_part(inverse(X2))),
inference(substitution,[status(thm)],[c199]) ).
cnf(c201,plain,
union(negative_part(inverse(X2)),negative_part(intersection(positive_part(X2),positive_part(inverse(X2))))) = union(negative_part(inverse(X2)),negative_part(positive_part(inverse(X2)))),
inference(congruence,[status(thm)],[c200]) ).
cnf(c202,plain,
union(negative_part(X2),union(negative_part(inverse(X2)),negative_part(intersection(positive_part(X2),positive_part(inverse(X2)))))) = union(negative_part(X2),union(negative_part(inverse(X2)),negative_part(positive_part(inverse(X2))))),
inference(congruence,[status(thm)],[c201]) ).
cnf(c203,plain,
negative_part(positive_part(inverse(X2))) = identity,
inference(substitution,[status(thm)],[c193]) ).
cnf(c204,plain,
union(negative_part(inverse(X2)),negative_part(positive_part(inverse(X2)))) = union(negative_part(inverse(X2)),identity),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
union(negative_part(X2),union(negative_part(inverse(X2)),negative_part(positive_part(inverse(X2))))) = union(negative_part(X2),union(negative_part(inverse(X2)),identity)),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
positive_part(negative_part(inverse(X2))) = union(negative_part(inverse(X2)),identity),
inference(substitution,[status(thm)],[c26]) ).
cnf(c207,plain,
union(negative_part(inverse(X2)),identity) = positive_part(negative_part(inverse(X2))),
inference(symmetry,[status(thm)],[c206]) ).
cnf(c208,plain,
union(negative_part(X2),union(negative_part(inverse(X2)),identity)) = union(negative_part(X2),positive_part(negative_part(inverse(X2)))),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
union(X3,positive_part(X2)) = union(X3,union(X2,identity)),
inference(congruence,[status(thm)],[c26]) ).
cnf(c210,plain,
union(X3,union(X2,identity)) = union(union(X3,X2),identity),
inference(substitution,[status(thm)],[c128]) ).
cnf(c211,plain,
positive_part(union(X3,X2)) = union(union(X3,X2),identity),
inference(substitution,[status(thm)],[c26]) ).
cnf(c212,plain,
union(union(X3,X2),identity) = positive_part(union(X3,X2)),
inference(symmetry,[status(thm)],[c211]) ).
cnf(c213,plain,
union(X3,union(X2,identity)) = positive_part(union(X3,X2)),
inference(transitivity,[status(thm)],[c210,c212]) ).
cnf(c214,plain,
union(X3,positive_part(X2)) = positive_part(union(X3,X2)),
inference(transitivity,[status(thm)],[c209,c213]) ).
cnf(c215,plain,
union(negative_part(X2),positive_part(negative_part(inverse(X2)))) = positive_part(union(negative_part(X2),negative_part(inverse(X2)))),
inference(substitution,[status(thm)],[c214]) ).
cnf(c216,plain,
union(X2,negative_part(X3)) = union(negative_part(X3),X2),
inference(substitution,[status(thm)],[c23]) ).
cnf(c217,plain,
union(negative_part(X3),X2) = union(X2,negative_part(X3)),
inference(symmetry,[status(thm)],[c216]) ).
cnf(c218,plain,
positive_part(union(negative_part(X3),X2)) = positive_part(union(X2,negative_part(X3))),
inference(congruence,[status(thm)],[c217]) ).
cnf(c219,plain,
union(X3,positive_part(negative_part(X2))) = positive_part(union(X3,negative_part(X2))),
inference(substitution,[status(thm)],[c214]) ).
cnf(c220,plain,
positive_part(union(X3,negative_part(X2))) = union(X3,positive_part(negative_part(X2))),
inference(symmetry,[status(thm)],[c219]) ).
cnf(c221,plain,
positive_part(negative_part(X2)) = positive_part(intersection(X2,identity)),
inference(congruence,[status(thm)],[c42]) ).
cnf(c222,plain,
union(identity,intersection(X2,identity)) = positive_part(intersection(X2,identity)),
inference(substitution,[status(thm)],[c28]) ).
cnf(c223,plain,
positive_part(intersection(X2,identity)) = union(identity,intersection(X2,identity)),
inference(symmetry,[status(thm)],[c222]) ).
cnf(c224,plain,
union(identity,intersection(X2,identity)) = identity,
inference(substitution,[status(thm)],[c153]) ).
cnf(c225,plain,
positive_part(intersection(X2,identity)) = identity,
inference(transitivity,[status(thm)],[c223,c224]) ).
cnf(c226,plain,
positive_part(negative_part(X2)) = identity,
inference(transitivity,[status(thm)],[c221,c225]) ).
cnf(c227,plain,
union(X3,positive_part(negative_part(X2))) = union(X3,identity),
inference(congruence,[status(thm)],[c226]) ).
cnf(c228,plain,
union(X2,identity) = positive_part(X2),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c229,plain,
union(X3,positive_part(negative_part(X2))) = positive_part(X3),
inference(transitivity,[status(thm)],[c227,c228]) ).
cnf(c230,plain,
positive_part(union(X3,negative_part(X2))) = positive_part(X3),
inference(transitivity,[status(thm)],[c220,c229]) ).
cnf(c231,plain,
positive_part(union(X2,negative_part(X3))) = positive_part(X2),
inference(substitution,[status(thm)],[c230]) ).
cnf(c232,plain,
positive_part(union(negative_part(X3),X2)) = positive_part(X2),
inference(transitivity,[status(thm)],[c218,c231]) ).
cnf(c233,plain,
positive_part(union(negative_part(X2),negative_part(inverse(X2)))) = positive_part(negative_part(inverse(X2))),
inference(substitution,[status(thm)],[c232]) ).
cnf(c234,plain,
positive_part(negative_part(inverse(X2))) = identity,
inference(substitution,[status(thm)],[c226]) ).
cnf(c235,plain,
positive_part(union(negative_part(X2),negative_part(inverse(X2)))) = identity,
inference(transitivity,[status(thm)],[c233,c234]) ).
cnf(c236,plain,
union(negative_part(X2),positive_part(negative_part(inverse(X2)))) = identity,
inference(transitivity,[status(thm)],[c215,c235]) ).
cnf(c237,plain,
union(negative_part(X2),union(negative_part(inverse(X2)),identity)) = identity,
inference(transitivity,[status(thm)],[c208,c236]) ).
cnf(c238,plain,
union(negative_part(X2),union(negative_part(inverse(X2)),negative_part(positive_part(inverse(X2))))) = identity,
inference(transitivity,[status(thm)],[c205,c237]) ).
cnf(c239,plain,
union(negative_part(X2),union(negative_part(inverse(X2)),negative_part(intersection(positive_part(X2),positive_part(inverse(X2)))))) = identity,
inference(transitivity,[status(thm)],[c202,c238]) ).
cnf(c240,plain,
union(negative_part(X2),union(negative_part(inverse(X2)),negative_part(union(negative_part(X2),negative_part(inverse(X2)))))) = identity,
inference(transitivity,[status(thm)],[c170,c239]) ).
cnf(c241,plain,
union(negative_part(X2),negative_part(inverse(X2))) = identity,
inference(transitivity,[status(thm)],[c167,c240]) ).
cnf(c242,plain,
intersection(positive_part(X2),positive_part(inverse(X2))) = identity,
inference(transitivity,[status(thm)],[c120,c241]) ).
cnf(c243,plain,
identity = intersection(positive_part(X2),positive_part(inverse(X2))),
inference(symmetry,[status(thm)],[c242]) ).
cnf(c244,plain,
multiply(inverse(positive_part(X2)),identity) = multiply(inverse(positive_part(X2)),intersection(positive_part(X2),positive_part(inverse(X2)))),
inference(congruence,[status(thm)],[c243]) ).
cnf(c245,plain,
intersection(X2,X3) = intersection(X3,X2),
inference(substitution,[status(thm)],[c34]) ).
cnf(c246,plain,
intersection(X3,X2) = intersection(X2,X3),
inference(symmetry,[status(thm)],[c245]) ).
cnf(c247,plain,
multiply(inverse(X3),intersection(X3,X2)) = multiply(inverse(X3),intersection(X2,X3)),
inference(congruence,[status(thm)],[c246]) ).
cnf(c248,plain,
multiply(inverse(X3),intersection(X2,X3)) = intersection(multiply(inverse(X3),X2),multiply(inverse(X3),X3)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c249,plain,
intersection(multiply(inverse(X3),X2),multiply(inverse(X3),X3)) = intersection(multiply(inverse(X3),X2),identity),
inference(congruence,[status(thm)],[c90]) ).
cnf(c250,plain,
negative_part(multiply(inverse(X3),X2)) = intersection(multiply(inverse(X3),X2),identity),
inference(substitution,[status(thm)],[c42]) ).
cnf(c251,plain,
intersection(multiply(inverse(X3),X2),identity) = negative_part(multiply(inverse(X3),X2)),
inference(symmetry,[status(thm)],[c250]) ).
cnf(c252,plain,
intersection(multiply(inverse(X3),X2),multiply(inverse(X3),X3)) = negative_part(multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c249,c251]) ).
cnf(c253,plain,
multiply(inverse(X3),intersection(X2,X3)) = negative_part(multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c248,c252]) ).
cnf(c254,plain,
multiply(inverse(X3),intersection(X3,X2)) = negative_part(multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c247,c253]) ).
cnf(c255,plain,
multiply(inverse(positive_part(X2)),intersection(positive_part(X2),positive_part(inverse(X2)))) = negative_part(multiply(inverse(positive_part(X2)),positive_part(inverse(X2)))),
inference(substitution,[status(thm)],[c254]) ).
cnf(c256,plain,
union(inverse(X2),multiply(X2,inverse(X2))) = multiply(positive_part(X2),inverse(X2)),
inference(substitution,[status(thm)],[c76]) ).
cnf(c257,plain,
multiply(positive_part(X2),inverse(X2)) = union(inverse(X2),multiply(X2,inverse(X2))),
inference(symmetry,[status(thm)],[c256]) ).
cnf(c258,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c259,plain,
multiply(X2,inverse(X2)) = multiply(inverse(inverse(X2)),inverse(X2)),
inference(congruence,[status(thm)],[c258]) ).
cnf(c260,plain,
multiply(inverse(inverse(X2)),inverse(X2)) = identity,
inference(substitution,[status(thm)],[c90]) ).
cnf(c261,plain,
multiply(X2,inverse(X2)) = identity,
inference(transitivity,[status(thm)],[c259,c260]) ).
cnf(c262,plain,
union(inverse(X2),multiply(X2,inverse(X2))) = union(inverse(X2),identity),
inference(congruence,[status(thm)],[c261]) ).
cnf(c263,plain,
positive_part(inverse(X2)) = union(inverse(X2),identity),
inference(substitution,[status(thm)],[c26]) ).
cnf(c264,plain,
union(inverse(X2),identity) = positive_part(inverse(X2)),
inference(symmetry,[status(thm)],[c263]) ).
cnf(c265,plain,
union(inverse(X2),multiply(X2,inverse(X2))) = positive_part(inverse(X2)),
inference(transitivity,[status(thm)],[c262,c264]) ).
cnf(c266,plain,
multiply(positive_part(X2),inverse(X2)) = positive_part(inverse(X2)),
inference(transitivity,[status(thm)],[c257,c265]) ).
cnf(c267,plain,
positive_part(inverse(X2)) = multiply(positive_part(X2),inverse(X2)),
inference(symmetry,[status(thm)],[c266]) ).
cnf(c268,plain,
multiply(inverse(positive_part(X2)),positive_part(inverse(X2))) = multiply(inverse(positive_part(X2)),multiply(positive_part(X2),inverse(X2))),
inference(congruence,[status(thm)],[c267]) ).
cnf(c269,axiom,
multiply(multiply(X2,Y2),Z2) = multiply(X2,multiply(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
cnf(c270,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c269]) ).
cnf(c271,plain,
multiply(inverse(X3),multiply(X3,X2)) = multiply(multiply(inverse(X3),X3),X2),
inference(symmetry,[status(thm)],[c270]) ).
cnf(c272,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c90]) ).
cnf(c273,plain,
multiply(multiply(inverse(X3),X3),X2) = X2,
inference(transitivity,[status(thm)],[c272,c11]) ).
cnf(c274,plain,
multiply(inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c271,c273]) ).
cnf(c275,plain,
multiply(inverse(positive_part(X2)),multiply(positive_part(X2),inverse(X2))) = inverse(X2),
inference(substitution,[status(thm)],[c274]) ).
cnf(c276,plain,
multiply(inverse(positive_part(X2)),positive_part(inverse(X2))) = inverse(X2),
inference(transitivity,[status(thm)],[c268,c275]) ).
cnf(c277,plain,
negative_part(multiply(inverse(positive_part(X2)),positive_part(inverse(X2)))) = negative_part(inverse(X2)),
inference(congruence,[status(thm)],[c276]) ).
cnf(c278,plain,
multiply(inverse(positive_part(X2)),intersection(positive_part(X2),positive_part(inverse(X2)))) = negative_part(inverse(X2)),
inference(transitivity,[status(thm)],[c255,c277]) ).
cnf(c279,plain,
multiply(inverse(positive_part(X2)),identity) = negative_part(inverse(X2)),
inference(transitivity,[status(thm)],[c244,c278]) ).
cnf(c280,plain,
inverse(positive_part(X2)) = negative_part(inverse(X2)),
inference(transitivity,[status(thm)],[c85,c279]) ).
cnf(c281,plain,
inverse(positive_part(inverse(X2))) = negative_part(inverse(inverse(X2))),
inference(substitution,[status(thm)],[c280]) ).
cnf(c282,plain,
negative_part(inverse(inverse(X2))) = inverse(positive_part(inverse(X2))),
inference(symmetry,[status(thm)],[c281]) ).
cnf(c283,plain,
multiply(negative_part(inverse(inverse(X2))),positive_part(X2)) = multiply(inverse(positive_part(inverse(X2))),positive_part(X2)),
inference(congruence,[status(thm)],[c282]) ).
cnf(c284,plain,
union(X2,multiply(inverse(X2),X2)) = multiply(positive_part(inverse(X2)),X2),
inference(substitution,[status(thm)],[c76]) ).
cnf(c285,plain,
multiply(positive_part(inverse(X2)),X2) = union(X2,multiply(inverse(X2),X2)),
inference(symmetry,[status(thm)],[c284]) ).
cnf(c286,plain,
union(X2,multiply(inverse(X2),X2)) = union(X2,identity),
inference(congruence,[status(thm)],[c90]) ).
cnf(c287,plain,
union(X2,identity) = positive_part(X2),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c288,plain,
union(X2,multiply(inverse(X2),X2)) = positive_part(X2),
inference(transitivity,[status(thm)],[c286,c287]) ).
cnf(c289,plain,
multiply(positive_part(inverse(X2)),X2) = positive_part(X2),
inference(transitivity,[status(thm)],[c285,c288]) ).
cnf(c290,plain,
positive_part(X2) = multiply(positive_part(inverse(X2)),X2),
inference(symmetry,[status(thm)],[c289]) ).
cnf(c291,plain,
multiply(inverse(positive_part(inverse(X2))),positive_part(X2)) = multiply(inverse(positive_part(inverse(X2))),multiply(positive_part(inverse(X2)),X2)),
inference(congruence,[status(thm)],[c290]) ).
cnf(c292,plain,
multiply(inverse(positive_part(inverse(X2))),multiply(positive_part(inverse(X2)),X2)) = X2,
inference(substitution,[status(thm)],[c274]) ).
cnf(c293,plain,
multiply(inverse(positive_part(inverse(X2))),positive_part(X2)) = X2,
inference(transitivity,[status(thm)],[c291,c292]) ).
cnf(c294,plain,
multiply(negative_part(inverse(inverse(X2))),positive_part(X2)) = X2,
inference(transitivity,[status(thm)],[c283,c293]) ).
cnf(c295,plain,
multiply(negative_part(X2),positive_part(X2)) = X2,
inference(transitivity,[status(thm)],[c83,c294]) ).
cnf(c296,plain,
multiply(positive_part(X2),negative_part(X2)) = X2,
inference(transitivity,[status(thm)],[c80,c295]) ).
cnf(c297,plain,
multiply(positive_part(a),negative_part(a)) = a,
inference(substitution,[status(thm)],[c296]) ).
cnf(c298,plain,
$false,
inference(resolution,[status(thm)],[c1,c297]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP114-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 09:19:21 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.86/0.87 Command-line arguments: --no-flatten-goal
% 2.86/0.87
% 2.86/0.87 % SZS status Unsatisfiable
% 2.86/0.87
% 2.86/0.89 % SZS output start CNFRefutation
% See solution above
% 3.61/1.01
% 3.61/1.01 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------