%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP167-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 10:09:30 AM UTC 2026
% Result : Unsatisfiable 1.45s 0.61s
% Output : CNFRefutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 17
% Syntax : Number of clauses : 203 ( 203 unt; 0 nHn; 6 RR)
% Number of literals : 203 ( 202 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 : 270 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lat4) ).
cnf(c2,axiom,
inverse(inverse(X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c4,plain,
positive_part(X2) = positive_part(inverse(inverse(X2))),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
multiply(positive_part(X2),negative_part(X2)) = multiply(positive_part(inverse(inverse(X2))),negative_part(X2)),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c7,plain,
identity = inverse(identity),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
multiply(inverse(X2),identity) = multiply(inverse(X2),inverse(identity)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,axiom,
inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_3) ).
cnf(c10,plain,
inverse(multiply(identity,X2)) = multiply(inverse(X2),inverse(identity)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
multiply(inverse(X2),inverse(identity)) = inverse(multiply(identity,X2)),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c13,plain,
inverse(multiply(identity,X2)) = inverse(X2),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
multiply(inverse(X2),inverse(identity)) = inverse(X2),
inference(transitivity,[status(thm)],[c11,c13]) ).
cnf(c15,plain,
multiply(inverse(X2),identity) = inverse(X2),
inference(transitivity,[status(thm)],[c8,c14]) ).
cnf(c16,plain,
multiply(inverse(negative_part(X2)),identity) = inverse(negative_part(X2)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
inverse(negative_part(X2)) = multiply(inverse(negative_part(X2)),identity),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,axiom,
greatest_lower_bound(X2,Y2) = greatest_lower_bound(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
cnf(c19,plain,
greatest_lower_bound(multiply(X3,X2),X2) = greatest_lower_bound(X2,multiply(X3,X2)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
greatest_lower_bound(X3,multiply(X2,X3)) = greatest_lower_bound(multiply(X2,X3),X3),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
X2 = multiply(identity,X2),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c22,plain,
greatest_lower_bound(multiply(X2,X3),X3) = greatest_lower_bound(multiply(X2,X3),multiply(identity,X3)),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,axiom,
multiply(greatest_lower_bound(Y2,Z),X2) = greatest_lower_bound(multiply(Y2,X2),multiply(Z,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb2) ).
cnf(c24,plain,
multiply(greatest_lower_bound(X2,identity),X3) = greatest_lower_bound(multiply(X2,X3),multiply(identity,X3)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
greatest_lower_bound(multiply(X2,X3),multiply(identity,X3)) = multiply(greatest_lower_bound(X2,identity),X3),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,axiom,
negative_part(X2) = greatest_lower_bound(X2,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c27,plain,
greatest_lower_bound(X2,identity) = negative_part(X2),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
multiply(greatest_lower_bound(X2,identity),X3) = multiply(negative_part(X2),X3),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
greatest_lower_bound(multiply(X2,X3),multiply(identity,X3)) = multiply(negative_part(X2),X3),
inference(transitivity,[status(thm)],[c25,c28]) ).
cnf(c30,plain,
greatest_lower_bound(multiply(X2,X3),X3) = multiply(negative_part(X2),X3),
inference(transitivity,[status(thm)],[c22,c29]) ).
cnf(c31,plain,
greatest_lower_bound(X3,multiply(X2,X3)) = multiply(negative_part(X2),X3),
inference(transitivity,[status(thm)],[c20,c30]) ).
cnf(c32,plain,
greatest_lower_bound(inverse(X2),multiply(X2,inverse(X2))) = multiply(negative_part(X2),inverse(X2)),
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
multiply(negative_part(X2),inverse(X2)) = greatest_lower_bound(inverse(X2),multiply(X2,inverse(X2))),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c35,plain,
multiply(X2,inverse(X2)) = multiply(inverse(inverse(X2)),inverse(X2)),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,axiom,
multiply(inverse(X2),X2) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
cnf(c37,plain,
multiply(inverse(inverse(X2)),inverse(X2)) = identity,
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
multiply(X2,inverse(X2)) = identity,
inference(transitivity,[status(thm)],[c35,c37]) ).
cnf(c39,plain,
greatest_lower_bound(inverse(X2),multiply(X2,inverse(X2))) = greatest_lower_bound(inverse(X2),identity),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,plain,
negative_part(inverse(X2)) = greatest_lower_bound(inverse(X2),identity),
inference(substitution,[status(thm)],[c26]) ).
cnf(c41,plain,
greatest_lower_bound(inverse(X2),identity) = negative_part(inverse(X2)),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
greatest_lower_bound(inverse(X2),multiply(X2,inverse(X2))) = negative_part(inverse(X2)),
inference(transitivity,[status(thm)],[c39,c41]) ).
cnf(c43,plain,
multiply(negative_part(X2),inverse(X2)) = negative_part(inverse(X2)),
inference(transitivity,[status(thm)],[c33,c42]) ).
cnf(c44,plain,
negative_part(inverse(X2)) = multiply(negative_part(X2),inverse(X2)),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
multiply(inverse(negative_part(X2)),negative_part(inverse(X2))) = multiply(inverse(negative_part(X2)),multiply(negative_part(X2),inverse(X2))),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,axiom,
multiply(multiply(X2,Y2),Z2) = multiply(X2,multiply(Y2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
cnf(c47,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
multiply(inverse(X3),multiply(X3,X2)) = multiply(multiply(inverse(X3),X3),X2),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c36]) ).
cnf(c50,plain,
multiply(multiply(inverse(X3),X3),X2) = X2,
inference(transitivity,[status(thm)],[c49,c12]) ).
cnf(c51,plain,
multiply(inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c48,c50]) ).
cnf(c52,plain,
multiply(inverse(negative_part(X2)),multiply(negative_part(X2),inverse(X2))) = inverse(X2),
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
multiply(inverse(negative_part(X2)),negative_part(inverse(X2))) = inverse(X2),
inference(transitivity,[status(thm)],[c45,c52]) ).
cnf(c54,plain,
inverse(X2) = multiply(inverse(negative_part(X2)),negative_part(inverse(X2))),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
positive_part(inverse(X2)) = positive_part(multiply(inverse(negative_part(X2)),negative_part(inverse(X2)))),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
multiply(negative_part(X2),positive_part(inverse(X2))) = multiply(negative_part(X2),positive_part(multiply(inverse(negative_part(X2)),negative_part(inverse(X2))))),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
X2 = inverse(inverse(X2)),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c58,plain,
multiply(X3,positive_part(multiply(inverse(X3),X2))) = multiply(inverse(inverse(X3)),positive_part(multiply(inverse(X3),X2))),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,axiom,
least_upper_bound(X2,Y2) = least_upper_bound(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).
cnf(c60,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
multiply(inverse(X3),least_upper_bound(X3,X2)) = multiply(inverse(X3),least_upper_bound(X2,X3)),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,axiom,
multiply(X2,least_upper_bound(Y2,Z2)) = least_upper_bound(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub1) ).
cnf(c64,plain,
multiply(inverse(X3),least_upper_bound(X2,X3)) = least_upper_bound(multiply(inverse(X3),X2),multiply(inverse(X3),X3)),
inference(substitution,[status(thm)],[c63]) ).
cnf(c65,plain,
least_upper_bound(multiply(inverse(X3),X2),multiply(inverse(X3),X3)) = least_upper_bound(multiply(inverse(X3),X2),identity),
inference(congruence,[status(thm)],[c36]) ).
cnf(c66,axiom,
positive_part(X2) = least_upper_bound(X2,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_4) ).
cnf(c67,plain,
positive_part(multiply(inverse(X3),X2)) = least_upper_bound(multiply(inverse(X3),X2),identity),
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
least_upper_bound(multiply(inverse(X3),X2),identity) = positive_part(multiply(inverse(X3),X2)),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
least_upper_bound(multiply(inverse(X3),X2),multiply(inverse(X3),X3)) = positive_part(multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c65,c68]) ).
cnf(c70,plain,
multiply(inverse(X3),least_upper_bound(X2,X3)) = positive_part(multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c64,c69]) ).
cnf(c71,plain,
multiply(inverse(X3),least_upper_bound(X3,X2)) = positive_part(multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c62,c70]) ).
cnf(c72,plain,
positive_part(multiply(inverse(X3),X2)) = multiply(inverse(X3),least_upper_bound(X3,X2)),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
multiply(inverse(inverse(X3)),positive_part(multiply(inverse(X3),X2))) = multiply(inverse(inverse(X3)),multiply(inverse(X3),least_upper_bound(X3,X2))),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),least_upper_bound(X3,X2))) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c51]) ).
cnf(c75,plain,
multiply(inverse(inverse(X3)),positive_part(multiply(inverse(X3),X2))) = least_upper_bound(X3,X2),
inference(transitivity,[status(thm)],[c73,c74]) ).
cnf(c76,plain,
multiply(X3,positive_part(multiply(inverse(X3),X2))) = least_upper_bound(X3,X2),
inference(transitivity,[status(thm)],[c58,c75]) ).
cnf(c77,plain,
multiply(negative_part(X2),positive_part(multiply(inverse(negative_part(X2)),negative_part(inverse(X2))))) = least_upper_bound(negative_part(X2),negative_part(inverse(X2))),
inference(substitution,[status(thm)],[c76]) ).
cnf(c78,plain,
least_upper_bound(negative_part(X2),negative_part(X3)) = least_upper_bound(negative_part(X3),negative_part(X2)),
inference(substitution,[status(thm)],[c59]) ).
cnf(c79,plain,
least_upper_bound(negative_part(X3),negative_part(X2)) = least_upper_bound(negative_part(X2),negative_part(X3)),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
greatest_lower_bound(X2,identity) = greatest_lower_bound(identity,X2),
inference(substitution,[status(thm)],[c18]) ).
cnf(c81,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c82,plain,
greatest_lower_bound(X2,identity) = negative_part(X2),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c83,plain,
greatest_lower_bound(identity,X2) = negative_part(X2),
inference(transitivity,[status(thm)],[c81,c82]) ).
cnf(c84,plain,
negative_part(X2) = greatest_lower_bound(identity,X2),
inference(symmetry,[status(thm)],[c83]) ).
cnf(c85,plain,
least_upper_bound(negative_part(X2),negative_part(X3)) = least_upper_bound(negative_part(X2),greatest_lower_bound(identity,X3)),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
negative_part(X2) = greatest_lower_bound(identity,X2),
inference(symmetry,[status(thm)],[c83]) ).
cnf(c87,plain,
least_upper_bound(negative_part(X2),greatest_lower_bound(identity,X3)) = least_upper_bound(greatest_lower_bound(identity,X2),greatest_lower_bound(identity,X3)),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,axiom,
greatest_lower_bound(X2,least_upper_bound(Y2,Z2)) = least_upper_bound(greatest_lower_bound(X2,Y2),greatest_lower_bound(X2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_7) ).
cnf(c89,plain,
greatest_lower_bound(identity,least_upper_bound(X2,X3)) = least_upper_bound(greatest_lower_bound(identity,X2),greatest_lower_bound(identity,X3)),
inference(substitution,[status(thm)],[c88]) ).
cnf(c90,plain,
least_upper_bound(greatest_lower_bound(identity,X2),greatest_lower_bound(identity,X3)) = greatest_lower_bound(identity,least_upper_bound(X2,X3)),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
greatest_lower_bound(identity,least_upper_bound(X2,X3)) = negative_part(least_upper_bound(X2,X3)),
inference(substitution,[status(thm)],[c83]) ).
cnf(c92,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c59]) ).
cnf(c93,plain,
negative_part(least_upper_bound(X2,X3)) = negative_part(least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
greatest_lower_bound(identity,least_upper_bound(X2,X3)) = negative_part(least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c91,c93]) ).
cnf(c95,plain,
least_upper_bound(greatest_lower_bound(identity,X2),greatest_lower_bound(identity,X3)) = negative_part(least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c90,c94]) ).
cnf(c96,plain,
least_upper_bound(negative_part(X2),greatest_lower_bound(identity,X3)) = negative_part(least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c87,c95]) ).
cnf(c97,plain,
least_upper_bound(negative_part(X2),negative_part(X3)) = negative_part(least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c85,c96]) ).
cnf(c98,plain,
least_upper_bound(negative_part(X3),negative_part(X2)) = negative_part(least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c79,c97]) ).
cnf(c99,plain,
least_upper_bound(negative_part(X2),negative_part(inverse(X2))) = negative_part(least_upper_bound(X2,inverse(X2))),
inference(substitution,[status(thm)],[c98]) ).
cnf(c100,plain,
least_upper_bound(inverse(X2),X2) = least_upper_bound(X2,inverse(X2)),
inference(substitution,[status(thm)],[c59]) ).
cnf(c101,plain,
least_upper_bound(X2,inverse(X2)) = least_upper_bound(inverse(X2),X2),
inference(symmetry,[status(thm)],[c100]) ).
cnf(c102,plain,
negative_part(least_upper_bound(X2,inverse(X2))) = negative_part(least_upper_bound(inverse(X2),X2)),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,plain,
least_upper_bound(negative_part(inverse(X2)),negative_part(X2)) = negative_part(least_upper_bound(inverse(X2),X2)),
inference(substitution,[status(thm)],[c98]) ).
cnf(c104,plain,
negative_part(least_upper_bound(inverse(X2),X2)) = least_upper_bound(negative_part(inverse(X2)),negative_part(X2)),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,plain,
multiply(negative_part(inverse(X2)),positive_part(multiply(inverse(negative_part(inverse(X2))),negative_part(X2)))) = least_upper_bound(negative_part(inverse(X2)),negative_part(X2)),
inference(substitution,[status(thm)],[c76]) ).
cnf(c106,plain,
least_upper_bound(negative_part(inverse(X2)),negative_part(X2)) = multiply(negative_part(inverse(X2)),positive_part(multiply(inverse(negative_part(inverse(X2))),negative_part(X2)))),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c107,plain,
greatest_lower_bound(X2,multiply(inverse(X2),X2)) = multiply(negative_part(inverse(X2)),X2),
inference(substitution,[status(thm)],[c31]) ).
cnf(c108,plain,
multiply(negative_part(inverse(X2)),X2) = greatest_lower_bound(X2,multiply(inverse(X2),X2)),
inference(symmetry,[status(thm)],[c107]) ).
cnf(c109,plain,
greatest_lower_bound(X2,multiply(inverse(X2),X2)) = greatest_lower_bound(X2,identity),
inference(congruence,[status(thm)],[c36]) ).
cnf(c110,plain,
greatest_lower_bound(X2,identity) = negative_part(X2),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c111,plain,
greatest_lower_bound(X2,multiply(inverse(X2),X2)) = negative_part(X2),
inference(transitivity,[status(thm)],[c109,c110]) ).
cnf(c112,plain,
multiply(negative_part(inverse(X2)),X2) = negative_part(X2),
inference(transitivity,[status(thm)],[c108,c111]) ).
cnf(c113,plain,
negative_part(X2) = multiply(negative_part(inverse(X2)),X2),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,plain,
multiply(inverse(negative_part(inverse(X2))),negative_part(X2)) = multiply(inverse(negative_part(inverse(X2))),multiply(negative_part(inverse(X2)),X2)),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
multiply(inverse(negative_part(inverse(X2))),multiply(negative_part(inverse(X2)),X2)) = X2,
inference(substitution,[status(thm)],[c51]) ).
cnf(c116,plain,
multiply(inverse(negative_part(inverse(X2))),negative_part(X2)) = X2,
inference(transitivity,[status(thm)],[c114,c115]) ).
cnf(c117,plain,
positive_part(multiply(inverse(negative_part(inverse(X2))),negative_part(X2))) = positive_part(X2),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
multiply(negative_part(inverse(X2)),positive_part(multiply(inverse(negative_part(inverse(X2))),negative_part(X2)))) = multiply(negative_part(inverse(X2)),positive_part(X2)),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
greatest_lower_bound(positive_part(X2),multiply(inverse(X2),positive_part(X2))) = multiply(negative_part(inverse(X2)),positive_part(X2)),
inference(substitution,[status(thm)],[c31]) ).
cnf(c120,plain,
multiply(negative_part(inverse(X2)),positive_part(X2)) = greatest_lower_bound(positive_part(X2),multiply(inverse(X2),positive_part(X2))),
inference(symmetry,[status(thm)],[c119]) ).
cnf(c121,plain,
multiply(inverse(X2),positive_part(X2)) = multiply(inverse(X2),least_upper_bound(X2,identity)),
inference(congruence,[status(thm)],[c66]) ).
cnf(c122,plain,
multiply(inverse(X2),least_upper_bound(X2,identity)) = positive_part(multiply(inverse(X2),identity)),
inference(substitution,[status(thm)],[c71]) ).
cnf(c123,plain,
positive_part(multiply(inverse(X2),identity)) = positive_part(inverse(X2)),
inference(congruence,[status(thm)],[c15]) ).
cnf(c124,plain,
multiply(inverse(X2),least_upper_bound(X2,identity)) = positive_part(inverse(X2)),
inference(transitivity,[status(thm)],[c122,c123]) ).
cnf(c125,plain,
multiply(inverse(X2),positive_part(X2)) = positive_part(inverse(X2)),
inference(transitivity,[status(thm)],[c121,c124]) ).
cnf(c126,plain,
greatest_lower_bound(positive_part(X2),multiply(inverse(X2),positive_part(X2))) = greatest_lower_bound(positive_part(X2),positive_part(inverse(X2))),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
greatest_lower_bound(positive_part(X2),positive_part(X3)) = greatest_lower_bound(positive_part(X3),positive_part(X2)),
inference(substitution,[status(thm)],[c18]) ).
cnf(c128,plain,
greatest_lower_bound(positive_part(X3),positive_part(X2)) = greatest_lower_bound(positive_part(X2),positive_part(X3)),
inference(symmetry,[status(thm)],[c127]) ).
cnf(c129,plain,
least_upper_bound(X2,identity) = least_upper_bound(identity,X2),
inference(substitution,[status(thm)],[c59]) ).
cnf(c130,plain,
least_upper_bound(identity,X2) = least_upper_bound(X2,identity),
inference(symmetry,[status(thm)],[c129]) ).
cnf(c131,plain,
least_upper_bound(X2,identity) = positive_part(X2),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c132,plain,
least_upper_bound(identity,X2) = positive_part(X2),
inference(transitivity,[status(thm)],[c130,c131]) ).
cnf(c133,plain,
positive_part(X2) = least_upper_bound(identity,X2),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c134,plain,
greatest_lower_bound(positive_part(X2),positive_part(X3)) = greatest_lower_bound(positive_part(X2),least_upper_bound(identity,X3)),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
positive_part(X2) = least_upper_bound(identity,X2),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c136,plain,
greatest_lower_bound(positive_part(X2),least_upper_bound(identity,X3)) = greatest_lower_bound(least_upper_bound(identity,X2),least_upper_bound(identity,X3)),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,axiom,
least_upper_bound(X2,greatest_lower_bound(Y2,Z2)) = greatest_lower_bound(least_upper_bound(X2,Y2),least_upper_bound(X2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_6) ).
cnf(c138,plain,
least_upper_bound(identity,greatest_lower_bound(X2,X3)) = greatest_lower_bound(least_upper_bound(identity,X2),least_upper_bound(identity,X3)),
inference(substitution,[status(thm)],[c137]) ).
cnf(c139,plain,
greatest_lower_bound(least_upper_bound(identity,X2),least_upper_bound(identity,X3)) = least_upper_bound(identity,greatest_lower_bound(X2,X3)),
inference(symmetry,[status(thm)],[c138]) ).
cnf(c140,plain,
least_upper_bound(identity,greatest_lower_bound(X2,X3)) = positive_part(greatest_lower_bound(X2,X3)),
inference(substitution,[status(thm)],[c132]) ).
cnf(c141,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c18]) ).
cnf(c142,plain,
positive_part(greatest_lower_bound(X2,X3)) = positive_part(greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c141]) ).
cnf(c143,plain,
least_upper_bound(identity,greatest_lower_bound(X2,X3)) = positive_part(greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c140,c142]) ).
cnf(c144,plain,
greatest_lower_bound(least_upper_bound(identity,X2),least_upper_bound(identity,X3)) = positive_part(greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c139,c143]) ).
cnf(c145,plain,
greatest_lower_bound(positive_part(X2),least_upper_bound(identity,X3)) = positive_part(greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c136,c144]) ).
cnf(c146,plain,
greatest_lower_bound(positive_part(X2),positive_part(X3)) = positive_part(greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c134,c145]) ).
cnf(c147,plain,
greatest_lower_bound(positive_part(X3),positive_part(X2)) = positive_part(greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c128,c146]) ).
cnf(c148,plain,
greatest_lower_bound(positive_part(X2),positive_part(inverse(X2))) = positive_part(greatest_lower_bound(X2,inverse(X2))),
inference(substitution,[status(thm)],[c147]) ).
cnf(c149,plain,
greatest_lower_bound(positive_part(X2),multiply(inverse(X2),positive_part(X2))) = positive_part(greatest_lower_bound(X2,inverse(X2))),
inference(transitivity,[status(thm)],[c126,c148]) ).
cnf(c150,plain,
multiply(negative_part(inverse(X2)),positive_part(X2)) = positive_part(greatest_lower_bound(X2,inverse(X2))),
inference(transitivity,[status(thm)],[c120,c149]) ).
cnf(c151,plain,
multiply(negative_part(inverse(X2)),positive_part(multiply(inverse(negative_part(inverse(X2))),negative_part(X2)))) = positive_part(greatest_lower_bound(X2,inverse(X2))),
inference(transitivity,[status(thm)],[c118,c150]) ).
cnf(c152,plain,
least_upper_bound(negative_part(inverse(X2)),negative_part(X2)) = positive_part(greatest_lower_bound(X2,inverse(X2))),
inference(transitivity,[status(thm)],[c106,c151]) ).
cnf(c153,plain,
negative_part(least_upper_bound(inverse(X2),X2)) = positive_part(greatest_lower_bound(X2,inverse(X2))),
inference(transitivity,[status(thm)],[c104,c152]) ).
cnf(c154,plain,
negative_part(least_upper_bound(X2,inverse(X2))) = positive_part(greatest_lower_bound(X2,inverse(X2))),
inference(transitivity,[status(thm)],[c102,c153]) ).
cnf(c155,plain,
positive_part(positive_part(X2)) = least_upper_bound(positive_part(X2),identity),
inference(substitution,[status(thm)],[c66]) ).
cnf(c156,plain,
greatest_lower_bound(identity,positive_part(X2)) = negative_part(positive_part(X2)),
inference(substitution,[status(thm)],[c83]) ).
cnf(c157,plain,
negative_part(positive_part(X2)) = greatest_lower_bound(identity,positive_part(X2)),
inference(symmetry,[status(thm)],[c156]) ).
cnf(c158,plain,
positive_part(X2) = least_upper_bound(identity,X2),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c159,plain,
greatest_lower_bound(identity,positive_part(X2)) = greatest_lower_bound(identity,least_upper_bound(identity,X2)),
inference(congruence,[status(thm)],[c158]) ).
cnf(c160,axiom,
greatest_lower_bound(X2,least_upper_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',glb_absorbtion) ).
cnf(c161,plain,
greatest_lower_bound(identity,least_upper_bound(identity,X2)) = identity,
inference(substitution,[status(thm)],[c160]) ).
cnf(c162,plain,
greatest_lower_bound(identity,positive_part(X2)) = identity,
inference(transitivity,[status(thm)],[c159,c161]) ).
cnf(c163,plain,
negative_part(positive_part(X2)) = identity,
inference(transitivity,[status(thm)],[c157,c162]) ).
cnf(c164,plain,
identity = negative_part(positive_part(X2)),
inference(symmetry,[status(thm)],[c163]) ).
cnf(c165,plain,
least_upper_bound(positive_part(X2),identity) = least_upper_bound(positive_part(X2),negative_part(positive_part(X2))),
inference(congruence,[status(thm)],[c164]) ).
cnf(c166,plain,
least_upper_bound(X2,negative_part(X2)) = least_upper_bound(X2,greatest_lower_bound(X2,identity)),
inference(congruence,[status(thm)],[c26]) ).
cnf(c167,axiom,
least_upper_bound(X2,greatest_lower_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lub_absorbtion) ).
cnf(c168,plain,
least_upper_bound(X2,greatest_lower_bound(X2,identity)) = X2,
inference(substitution,[status(thm)],[c167]) ).
cnf(c169,plain,
least_upper_bound(X2,negative_part(X2)) = X2,
inference(transitivity,[status(thm)],[c166,c168]) ).
cnf(c170,plain,
least_upper_bound(positive_part(X2),negative_part(positive_part(X2))) = positive_part(X2),
inference(substitution,[status(thm)],[c169]) ).
cnf(c171,plain,
least_upper_bound(positive_part(X2),identity) = positive_part(X2),
inference(transitivity,[status(thm)],[c165,c170]) ).
cnf(c172,plain,
positive_part(positive_part(X2)) = positive_part(X2),
inference(transitivity,[status(thm)],[c155,c171]) ).
cnf(c173,plain,
positive_part(positive_part(greatest_lower_bound(X2,inverse(X2)))) = positive_part(greatest_lower_bound(X2,inverse(X2))),
inference(substitution,[status(thm)],[c172]) ).
cnf(c174,plain,
positive_part(greatest_lower_bound(X2,inverse(X2))) = positive_part(positive_part(greatest_lower_bound(X2,inverse(X2)))),
inference(symmetry,[status(thm)],[c173]) ).
cnf(c175,plain,
positive_part(greatest_lower_bound(X2,inverse(X2))) = negative_part(least_upper_bound(X2,inverse(X2))),
inference(symmetry,[status(thm)],[c154]) ).
cnf(c176,plain,
positive_part(positive_part(greatest_lower_bound(X2,inverse(X2)))) = positive_part(negative_part(least_upper_bound(X2,inverse(X2)))),
inference(congruence,[status(thm)],[c175]) ).
cnf(c177,plain,
negative_part(X2) = greatest_lower_bound(identity,X2),
inference(symmetry,[status(thm)],[c83]) ).
cnf(c178,plain,
positive_part(negative_part(X2)) = positive_part(greatest_lower_bound(identity,X2)),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
least_upper_bound(identity,greatest_lower_bound(identity,X2)) = positive_part(greatest_lower_bound(identity,X2)),
inference(substitution,[status(thm)],[c132]) ).
cnf(c180,plain,
positive_part(greatest_lower_bound(identity,X2)) = least_upper_bound(identity,greatest_lower_bound(identity,X2)),
inference(symmetry,[status(thm)],[c179]) ).
cnf(c181,plain,
least_upper_bound(identity,greatest_lower_bound(identity,X2)) = identity,
inference(substitution,[status(thm)],[c167]) ).
cnf(c182,plain,
positive_part(greatest_lower_bound(identity,X2)) = identity,
inference(transitivity,[status(thm)],[c180,c181]) ).
cnf(c183,plain,
positive_part(negative_part(X2)) = identity,
inference(transitivity,[status(thm)],[c178,c182]) ).
cnf(c184,plain,
positive_part(negative_part(least_upper_bound(X2,inverse(X2)))) = identity,
inference(substitution,[status(thm)],[c183]) ).
cnf(c185,plain,
positive_part(positive_part(greatest_lower_bound(X2,inverse(X2)))) = identity,
inference(transitivity,[status(thm)],[c176,c184]) ).
cnf(c186,plain,
positive_part(greatest_lower_bound(X2,inverse(X2))) = identity,
inference(transitivity,[status(thm)],[c174,c185]) ).
cnf(c187,plain,
negative_part(least_upper_bound(X2,inverse(X2))) = identity,
inference(transitivity,[status(thm)],[c154,c186]) ).
cnf(c188,plain,
least_upper_bound(negative_part(X2),negative_part(inverse(X2))) = identity,
inference(transitivity,[status(thm)],[c99,c187]) ).
cnf(c189,plain,
multiply(negative_part(X2),positive_part(multiply(inverse(negative_part(X2)),negative_part(inverse(X2))))) = identity,
inference(transitivity,[status(thm)],[c77,c188]) ).
cnf(c190,plain,
multiply(negative_part(X2),positive_part(inverse(X2))) = identity,
inference(transitivity,[status(thm)],[c56,c189]) ).
cnf(c191,plain,
identity = multiply(negative_part(X2),positive_part(inverse(X2))),
inference(symmetry,[status(thm)],[c190]) ).
cnf(c192,plain,
multiply(inverse(negative_part(X2)),identity) = multiply(inverse(negative_part(X2)),multiply(negative_part(X2),positive_part(inverse(X2)))),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
multiply(inverse(negative_part(X2)),multiply(negative_part(X2),positive_part(inverse(X2)))) = positive_part(inverse(X2)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c194,plain,
multiply(inverse(negative_part(X2)),identity) = positive_part(inverse(X2)),
inference(transitivity,[status(thm)],[c192,c193]) ).
cnf(c195,plain,
inverse(negative_part(X2)) = positive_part(inverse(X2)),
inference(transitivity,[status(thm)],[c17,c194]) ).
cnf(c196,plain,
inverse(negative_part(inverse(X2))) = positive_part(inverse(inverse(X2))),
inference(substitution,[status(thm)],[c195]) ).
cnf(c197,plain,
positive_part(inverse(inverse(X2))) = inverse(negative_part(inverse(X2))),
inference(symmetry,[status(thm)],[c196]) ).
cnf(c198,plain,
multiply(positive_part(inverse(inverse(X2))),negative_part(X2)) = multiply(inverse(negative_part(inverse(X2))),negative_part(X2)),
inference(congruence,[status(thm)],[c197]) ).
cnf(c199,plain,
multiply(positive_part(inverse(inverse(X2))),negative_part(X2)) = X2,
inference(transitivity,[status(thm)],[c198,c116]) ).
cnf(c200,plain,
multiply(positive_part(X2),negative_part(X2)) = X2,
inference(transitivity,[status(thm)],[c5,c199]) ).
cnf(c201,plain,
multiply(positive_part(a),negative_part(a)) = a,
inference(substitution,[status(thm)],[c200]) ).
cnf(c202,plain,
a = multiply(positive_part(a),negative_part(a)),
inference(symmetry,[status(thm)],[c201]) ).
cnf(c203,plain,
$false,
inference(resolution,[status(thm)],[c1,c202]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP167-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 09:38:14 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.45/0.61 Command-line arguments: --no-flatten-goal
% 1.45/0.61
% 1.45/0.61 % SZS status Unsatisfiable
% 1.45/0.61
% 1.45/0.62 % SZS output start CNFRefutation
% See solution above
% 1.76/0.69
% 1.76/0.69 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------