%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL018+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 12:33:09 PM UTC 2026
% Result : Theorem 0.68s 0.57s
% Output : CNFRefutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 15
% Syntax : Number of formulae : 297 ( 291 unt; 0 def)
% Number of atoms : 303 ( 302 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 5 ~; 0 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 292 ( 20 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c1,conjecture,
! [X0] :
( composition(X0,top) = X0
=> composition(complement(X0),top) = complement(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c2,negated_conjecture,
~ ! [X0_2] :
( composition(X0_2,top) = X0_2
=> composition(complement(X0_2),top) = complement(X0_2) ),
inference(negate_conjecture,[status(cth)],[c1]) ).
fof(c3,plain,
( composition(x0,top) = x0
& composition(complement(x0),top) != complement(x0) ),
inference(clausify,[status(esa)],[c2]) ).
cnf(c4,plain,
composition(complement(x0),top) != complement(x0),
inference(clausify,[status(thm)],[c3]) ).
cnf(c5,axiom,
converse(converse(X0_2)) = X0_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence) ).
cnf(c6,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
composition(X,top) = composition(converse(converse(X)),top),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
join(X,composition(X,top)) = join(X,composition(converse(converse(X)),top)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,axiom,
converse(composition(X0_2,X1)) = composition(converse(X1),converse(X0_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity) ).
cnf(c11,plain,
converse(composition(top,X)) = composition(converse(X),converse(top)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,axiom,
join(X0_2,X1_2) = join(X1_2,X0_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
cnf(c13,plain,
join(converse(X3),X) = join(X,converse(X3)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
join(X3,converse(X)) = join(converse(X),X3),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
converse(join(X3,converse(X))) = converse(join(converse(X),X3)),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,axiom,
converse(join(X0_2,X1_2)) = join(converse(X0_2),converse(X1_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity) ).
cnf(c17,plain,
converse(join(converse(X),X3)) = join(converse(converse(X)),converse(X3)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c19,plain,
join(converse(converse(X)),converse(X3)) = join(X,converse(X3)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
converse(join(converse(X),X3)) = join(X,converse(X3)),
inference(transitivity,[status(thm)],[c17,c19]) ).
cnf(c21,plain,
converse(join(X3,converse(X))) = join(X,converse(X3)),
inference(transitivity,[status(thm)],[c15,c20]) ).
cnf(c22,plain,
converse(join(top,converse(X))) = join(X,converse(top)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
join(X,converse(top)) = converse(join(top,converse(X))),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
join(X,top) = join(top,X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c25,plain,
join(top,X) = join(X,top),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
join(complement(X),top) = join(top,complement(X)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c27,plain,
join(top,complement(X)) = join(complement(X),top),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c29,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
join(X3,join(X,complement(X3))) = join(X3,join(complement(X3),X)),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,axiom,
join(X0_2,join(X1_2,X2)) = join(join(X0_2,X1_2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity) ).
cnf(c32,plain,
join(X3,join(complement(X3),X)) = join(join(X3,complement(X3)),X),
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,axiom,
top = join(X0_2,complement(X0_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top) ).
cnf(c34,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
join(join(X3,complement(X3)),X) = join(top,X),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
join(top,X) = join(X,top),
inference(substitution,[status(thm)],[c12]) ).
cnf(c38,plain,
join(join(X3,complement(X3)),X) = join(X,top),
inference(transitivity,[status(thm)],[c36,c37]) ).
cnf(c39,plain,
join(X3,join(complement(X3),X)) = join(X,top),
inference(transitivity,[status(thm)],[c32,c38]) ).
cnf(c40,plain,
join(X3,join(X,complement(X3))) = join(X,top),
inference(transitivity,[status(thm)],[c30,c39]) ).
cnf(c41,plain,
join(X,join(complement(X),complement(X))) = join(complement(X),top),
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
join(complement(X),top) = join(X,join(complement(X),complement(X))),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
converse(composition(converse(X3),X)) = composition(converse(X),converse(converse(X3))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c44,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c45,plain,
composition(converse(X),converse(converse(X3))) = composition(converse(X),X3),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,plain,
converse(composition(converse(X3),X)) = composition(converse(X),X3),
inference(transitivity,[status(thm)],[c43,c45]) ).
cnf(c47,plain,
converse(composition(converse(X),one)) = composition(converse(one),X),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
composition(converse(one),X) = converse(composition(converse(X),one)),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,axiom,
composition(X0_2,one) = X0_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity) ).
cnf(c50,plain,
composition(converse(X),one) = converse(X),
inference(substitution,[status(thm)],[c49]) ).
cnf(c51,plain,
converse(composition(converse(X),one)) = converse(converse(X)),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c53,plain,
converse(composition(converse(X),one)) = X,
inference(transitivity,[status(thm)],[c51,c52]) ).
cnf(c54,plain,
composition(converse(one),X) = X,
inference(transitivity,[status(thm)],[c48,c53]) ).
cnf(c55,plain,
composition(converse(one),complement(X)) = complement(X),
inference(substitution,[status(thm)],[c54]) ).
cnf(c56,plain,
complement(X) = composition(converse(one),complement(X)),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
join(complement(X),complement(X)) = join(complement(X),composition(converse(one),complement(X))),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
composition(converse(one),composition(one,X)) = composition(one,X),
inference(substitution,[status(thm)],[c54]) ).
cnf(c59,plain,
composition(one,X) = composition(converse(one),composition(one,X)),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,axiom,
composition(X0_2,composition(X1_2,X2_2)) = composition(composition(X0_2,X1_2),X2_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_associativity) ).
cnf(c61,plain,
composition(X3,composition(one,X)) = composition(composition(X3,one),X),
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c49]) ).
cnf(c63,plain,
composition(composition(X3,one),X) = composition(X3,X),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
composition(X3,composition(one,X)) = composition(X3,X),
inference(transitivity,[status(thm)],[c61,c63]) ).
cnf(c65,plain,
composition(converse(one),composition(one,X)) = composition(converse(one),X),
inference(substitution,[status(thm)],[c64]) ).
cnf(c66,plain,
composition(converse(one),composition(one,X)) = X,
inference(transitivity,[status(thm)],[c65,c54]) ).
cnf(c67,plain,
composition(one,X) = X,
inference(transitivity,[status(thm)],[c59,c66]) ).
cnf(c68,plain,
X = composition(one,X),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
complement(X) = complement(composition(one,X)),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
composition(converse(one),complement(X)) = composition(converse(one),complement(composition(one,X))),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
join(complement(X),composition(converse(one),complement(X))) = join(complement(X),composition(converse(one),complement(composition(one,X)))),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
join(composition(converse(X),complement(composition(X,X3))),complement(X3)) = join(complement(X3),composition(converse(X),complement(composition(X,X3)))),
inference(substitution,[status(thm)],[c12]) ).
cnf(c73,plain,
join(complement(X3),composition(converse(X),complement(composition(X,X3)))) = join(composition(converse(X),complement(composition(X,X3))),complement(X3)),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c74,axiom,
join(composition(converse(X0_2),complement(composition(X0_2,X1_2))),complement(X1_2)) = complement(X1_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity) ).
cnf(c75,plain,
join(composition(converse(X),complement(composition(X,X3))),complement(X3)) = complement(X3),
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,plain,
join(complement(X3),composition(converse(X),complement(composition(X,X3)))) = complement(X3),
inference(transitivity,[status(thm)],[c73,c75]) ).
cnf(c77,plain,
join(complement(X),composition(converse(one),complement(composition(one,X)))) = complement(X),
inference(substitution,[status(thm)],[c76]) ).
cnf(c78,plain,
join(complement(X),composition(converse(one),complement(X))) = complement(X),
inference(transitivity,[status(thm)],[c71,c77]) ).
cnf(c79,plain,
join(complement(X),complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c57,c78]) ).
cnf(c80,plain,
join(X,join(complement(X),complement(X))) = join(X,complement(X)),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c33]) ).
cnf(c82,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
join(X,join(complement(X),complement(X))) = top,
inference(transitivity,[status(thm)],[c80,c82]) ).
cnf(c84,plain,
join(complement(X),top) = top,
inference(transitivity,[status(thm)],[c42,c83]) ).
cnf(c85,plain,
join(top,complement(X)) = top,
inference(transitivity,[status(thm)],[c27,c84]) ).
cnf(c86,plain,
top = join(top,complement(X)),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c87,plain,
join(X,top) = join(X,join(top,complement(X))),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c40]) ).
cnf(c89,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c40]) ).
cnf(c90,plain,
join(top,top) = join(X,join(top,complement(X))),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
join(X,join(top,complement(X))) = join(X,top),
inference(congruence,[status(thm)],[c85]) ).
cnf(c92,plain,
join(top,top) = join(X,top),
inference(transitivity,[status(thm)],[c90,c91]) ).
cnf(c93,plain,
join(X,join(top,complement(X))) = join(X3,top),
inference(transitivity,[status(thm)],[c88,c92]) ).
cnf(c94,plain,
join(X,top) = join(X3,top),
inference(transitivity,[status(thm)],[c87,c93]) ).
cnf(c95,plain,
join(X3,top) = join(X,top),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,plain,
join(complement(complement(X)),top) = join(top,complement(complement(X))),
inference(substitution,[status(thm)],[c12]) ).
cnf(c97,plain,
join(top,complement(complement(X))) = join(complement(complement(X)),top),
inference(symmetry,[status(thm)],[c96]) ).
cnf(c98,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c99,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(symmetry,[status(thm)],[c98]) ).
cnf(c100,plain,
join(X3,join(complement(X3),X)) = join(X3,join(X,complement(X3))),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
join(X3,join(complement(X3),X)) = join(X,top),
inference(transitivity,[status(thm)],[c100,c40]) ).
cnf(c102,plain,
join(X,join(complement(X),complement(complement(X)))) = join(complement(complement(X)),top),
inference(substitution,[status(thm)],[c101]) ).
cnf(c103,plain,
join(complement(complement(X)),top) = join(X,join(complement(X),complement(complement(X)))),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c104,plain,
top = join(complement(X),complement(complement(X))),
inference(substitution,[status(thm)],[c33]) ).
cnf(c105,plain,
join(complement(X),complement(complement(X))) = top,
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
join(X,join(complement(X),complement(complement(X)))) = join(X,top),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
join(complement(complement(X)),top) = join(X,top),
inference(transitivity,[status(thm)],[c103,c106]) ).
cnf(c108,plain,
join(top,complement(complement(X))) = join(X,top),
inference(transitivity,[status(thm)],[c97,c107]) ).
cnf(c109,plain,
join(X,top) = join(top,complement(complement(X))),
inference(symmetry,[status(thm)],[c108]) ).
cnf(c110,plain,
join(top,complement(complement(X))) = top,
inference(substitution,[status(thm)],[c85]) ).
cnf(c111,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c109,c110]) ).
cnf(c112,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c95,c111]) ).
cnf(c113,plain,
join(top,X) = top,
inference(transitivity,[status(thm)],[c25,c112]) ).
cnf(c114,plain,
join(top,converse(X)) = top,
inference(substitution,[status(thm)],[c113]) ).
cnf(c115,plain,
converse(join(top,converse(X))) = converse(top),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
join(X,converse(top)) = converse(top),
inference(transitivity,[status(thm)],[c23,c115]) ).
cnf(c117,plain,
converse(top) = join(X,converse(top)),
inference(symmetry,[status(thm)],[c116]) ).
cnf(c118,plain,
join(complement(X),converse(top)) = converse(top),
inference(substitution,[status(thm)],[c116]) ).
cnf(c119,plain,
converse(top) = join(complement(X),converse(top)),
inference(symmetry,[status(thm)],[c118]) ).
cnf(c120,plain,
join(X,converse(top)) = join(X,join(complement(X),converse(top))),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
join(X,join(complement(X),converse(top))) = join(converse(top),top),
inference(substitution,[status(thm)],[c101]) ).
cnf(c122,plain,
join(converse(top),top) = top,
inference(substitution,[status(thm)],[c111]) ).
cnf(c123,plain,
join(X,join(complement(X),converse(top))) = top,
inference(transitivity,[status(thm)],[c121,c122]) ).
cnf(c124,plain,
join(X,converse(top)) = top,
inference(transitivity,[status(thm)],[c120,c123]) ).
cnf(c125,plain,
converse(top) = top,
inference(transitivity,[status(thm)],[c117,c124]) ).
cnf(c126,plain,
composition(converse(X),converse(top)) = composition(converse(X),top),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
converse(composition(top,X)) = composition(converse(X),top),
inference(transitivity,[status(thm)],[c11,c126]) ).
cnf(c128,plain,
converse(composition(top,converse(X))) = composition(converse(converse(X)),top),
inference(substitution,[status(thm)],[c127]) ).
cnf(c129,plain,
composition(converse(converse(X)),top) = converse(composition(top,converse(X))),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
join(X,composition(converse(converse(X)),top)) = join(X,converse(composition(top,converse(X)))),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
join(X,converse(X3)) = join(converse(X3),X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c132,plain,
join(converse(X3),X) = join(X,converse(X3)),
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
converse(join(converse(X3),X)) = converse(join(X,converse(X3))),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
converse(join(X,converse(X3))) = join(X3,converse(X)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c135,plain,
converse(join(converse(X3),X)) = join(X3,converse(X)),
inference(transitivity,[status(thm)],[c133,c134]) ).
cnf(c136,plain,
converse(join(converse(X),composition(top,converse(X)))) = join(X,converse(composition(top,converse(X)))),
inference(substitution,[status(thm)],[c135]) ).
cnf(c137,plain,
join(X,converse(composition(top,converse(X)))) = converse(join(converse(X),composition(top,converse(X)))),
inference(symmetry,[status(thm)],[c136]) ).
cnf(c138,plain,
join(X,one) = join(one,X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c139,plain,
join(one,X) = join(X,one),
inference(symmetry,[status(thm)],[c138]) ).
cnf(c140,plain,
composition(join(one,X),X3) = composition(join(X,one),X3),
inference(congruence,[status(thm)],[c139]) ).
cnf(c141,plain,
join(one,X) = join(X,one),
inference(substitution,[status(thm)],[c12]) ).
cnf(c142,plain,
join(X,one) = join(one,X),
inference(symmetry,[status(thm)],[c141]) ).
cnf(c143,plain,
composition(join(X3,one),X) = composition(join(one,X3),X),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,axiom,
composition(join(X0_2,X1_2),X2_2) = join(composition(X0_2,X2_2),composition(X1_2,X2_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity) ).
cnf(c145,plain,
composition(join(one,X3),X) = join(composition(one,X),composition(X3,X)),
inference(substitution,[status(thm)],[c144]) ).
cnf(c146,plain,
join(composition(one,X),composition(X3,X)) = join(X,composition(X3,X)),
inference(congruence,[status(thm)],[c67]) ).
cnf(c147,plain,
composition(join(one,X3),X) = join(X,composition(X3,X)),
inference(transitivity,[status(thm)],[c145,c146]) ).
cnf(c148,plain,
composition(join(X3,one),X) = join(X,composition(X3,X)),
inference(transitivity,[status(thm)],[c143,c147]) ).
cnf(c149,plain,
composition(join(X,one),X3) = join(X3,composition(X,X3)),
inference(substitution,[status(thm)],[c148]) ).
cnf(c150,plain,
composition(join(one,X),X3) = join(X3,composition(X,X3)),
inference(transitivity,[status(thm)],[c140,c149]) ).
cnf(c151,plain,
composition(join(one,top),X) = join(X,composition(top,X)),
inference(substitution,[status(thm)],[c150]) ).
cnf(c152,plain,
join(X,composition(top,X)) = composition(join(one,top),X),
inference(symmetry,[status(thm)],[c151]) ).
cnf(c153,plain,
join(one,top) = top,
inference(substitution,[status(thm)],[c111]) ).
cnf(c154,plain,
composition(join(one,top),X) = composition(top,X),
inference(congruence,[status(thm)],[c153]) ).
cnf(c155,plain,
join(X,composition(top,X)) = composition(top,X),
inference(transitivity,[status(thm)],[c152,c154]) ).
cnf(c156,plain,
join(converse(X),composition(top,converse(X))) = composition(top,converse(X)),
inference(substitution,[status(thm)],[c155]) ).
cnf(c157,plain,
converse(join(converse(X),composition(top,converse(X)))) = converse(composition(top,converse(X))),
inference(congruence,[status(thm)],[c156]) ).
cnf(c158,plain,
converse(composition(top,converse(X))) = composition(converse(converse(X)),top),
inference(substitution,[status(thm)],[c127]) ).
cnf(c159,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c160,plain,
composition(converse(converse(X)),top) = composition(X,top),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
converse(composition(top,converse(X))) = composition(X,top),
inference(transitivity,[status(thm)],[c158,c160]) ).
cnf(c162,plain,
converse(join(converse(X),composition(top,converse(X)))) = composition(X,top),
inference(transitivity,[status(thm)],[c157,c161]) ).
cnf(c163,plain,
join(X,converse(composition(top,converse(X)))) = composition(X,top),
inference(transitivity,[status(thm)],[c137,c162]) ).
cnf(c164,plain,
join(X,composition(converse(converse(X)),top)) = composition(X,top),
inference(transitivity,[status(thm)],[c130,c163]) ).
cnf(c165,plain,
join(X,composition(X,top)) = composition(X,top),
inference(transitivity,[status(thm)],[c9,c164]) ).
cnf(c166,plain,
join(complement(x0),composition(complement(x0),top)) = composition(complement(x0),top),
inference(substitution,[status(thm)],[c165]) ).
cnf(c167,plain,
composition(complement(x0),top) = join(complement(x0),composition(complement(x0),top)),
inference(symmetry,[status(thm)],[c166]) ).
cnf(c168,plain,
join(X,zero) = join(zero,X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c169,plain,
join(zero,X) = join(X,zero),
inference(symmetry,[status(thm)],[c168]) ).
cnf(c170,plain,
join(zero,X) = join(X,zero),
inference(substitution,[status(thm)],[c12]) ).
cnf(c171,plain,
join(X,zero) = join(zero,X),
inference(symmetry,[status(thm)],[c170]) ).
cnf(c172,axiom,
meet(X0_2,X1_2) = complement(join(complement(X0_2),complement(X1_2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
cnf(c173,plain,
meet(X,X) = complement(join(complement(X),complement(X))),
inference(substitution,[status(thm)],[c172]) ).
cnf(c174,plain,
join(zero,meet(X,X)) = join(zero,complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,axiom,
zero = meet(X0_2,complement(X0_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero) ).
cnf(c176,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c175]) ).
cnf(c177,plain,
join(zero,complement(join(complement(X),complement(X)))) = join(meet(X,complement(X)),complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c176]) ).
cnf(c178,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c172]) ).
cnf(c179,plain,
join(meet(X3,X),complement(join(complement(X3),X))) = join(complement(join(complement(X3),complement(X))),complement(join(complement(X3),X))),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,axiom,
X0_2 = join(complement(join(complement(X0_2),complement(X1_2))),complement(join(complement(X0_2),X1_2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
cnf(c181,plain,
X3 = join(complement(join(complement(X3),complement(X))),complement(join(complement(X3),X))),
inference(substitution,[status(thm)],[c180]) ).
cnf(c182,plain,
join(complement(join(complement(X3),complement(X))),complement(join(complement(X3),X))) = X3,
inference(symmetry,[status(thm)],[c181]) ).
cnf(c183,plain,
join(meet(X3,X),complement(join(complement(X3),X))) = X3,
inference(transitivity,[status(thm)],[c179,c182]) ).
cnf(c184,plain,
join(meet(X,complement(X)),complement(join(complement(X),complement(X)))) = X,
inference(substitution,[status(thm)],[c183]) ).
cnf(c185,plain,
join(zero,complement(join(complement(X),complement(X)))) = X,
inference(transitivity,[status(thm)],[c177,c184]) ).
cnf(c186,plain,
join(zero,meet(X,X)) = X,
inference(transitivity,[status(thm)],[c174,c185]) ).
cnf(c187,plain,
X = join(zero,meet(X,X)),
inference(symmetry,[status(thm)],[c186]) ).
cnf(c188,plain,
join(zero,X) = join(zero,join(zero,meet(X,X))),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
join(X,zero) = join(zero,X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c190,plain,
join(zero,X) = join(X,zero),
inference(symmetry,[status(thm)],[c189]) ).
cnf(c191,plain,
join(zero,join(zero,X)) = join(zero,join(X,zero)),
inference(congruence,[status(thm)],[c190]) ).
cnf(c192,plain,
join(zero,X) = join(X,zero),
inference(substitution,[status(thm)],[c12]) ).
cnf(c193,plain,
join(X,zero) = join(zero,X),
inference(symmetry,[status(thm)],[c192]) ).
cnf(c194,plain,
join(zero,join(X,zero)) = join(zero,join(zero,X)),
inference(congruence,[status(thm)],[c193]) ).
cnf(c195,plain,
join(zero,join(zero,X)) = join(join(zero,zero),X),
inference(substitution,[status(thm)],[c31]) ).
cnf(c196,plain,
top = join(complement(X),complement(complement(X))),
inference(substitution,[status(thm)],[c33]) ).
cnf(c197,plain,
complement(top) = complement(join(complement(X),complement(complement(X)))),
inference(congruence,[status(thm)],[c196]) ).
cnf(c198,plain,
meet(X,complement(X)) = complement(join(complement(X),complement(complement(X)))),
inference(substitution,[status(thm)],[c172]) ).
cnf(c199,plain,
complement(join(complement(X),complement(complement(X)))) = meet(X,complement(X)),
inference(symmetry,[status(thm)],[c198]) ).
cnf(c200,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c175]) ).
cnf(c201,plain,
meet(X,complement(X)) = zero,
inference(symmetry,[status(thm)],[c200]) ).
cnf(c202,plain,
complement(join(complement(X),complement(complement(X)))) = zero,
inference(transitivity,[status(thm)],[c199,c201]) ).
cnf(c203,plain,
complement(top) = zero,
inference(transitivity,[status(thm)],[c197,c202]) ).
cnf(c204,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c205,plain,
join(zero,zero) = join(zero,complement(top)),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c207,plain,
join(zero,complement(top)) = join(complement(top),complement(top)),
inference(congruence,[status(thm)],[c206]) ).
cnf(c208,plain,
join(complement(top),complement(top)) = complement(top),
inference(substitution,[status(thm)],[c79]) ).
cnf(c209,plain,
join(complement(top),complement(top)) = zero,
inference(transitivity,[status(thm)],[c208,c203]) ).
cnf(c210,plain,
join(zero,complement(top)) = zero,
inference(transitivity,[status(thm)],[c207,c209]) ).
cnf(c211,plain,
join(zero,zero) = zero,
inference(transitivity,[status(thm)],[c205,c210]) ).
cnf(c212,plain,
join(join(zero,zero),X) = join(zero,X),
inference(congruence,[status(thm)],[c211]) ).
cnf(c213,plain,
join(zero,X) = join(X,zero),
inference(substitution,[status(thm)],[c12]) ).
cnf(c214,plain,
join(join(zero,zero),X) = join(X,zero),
inference(transitivity,[status(thm)],[c212,c213]) ).
cnf(c215,plain,
join(zero,join(zero,X)) = join(X,zero),
inference(transitivity,[status(thm)],[c195,c214]) ).
cnf(c216,plain,
join(zero,join(X,zero)) = join(X,zero),
inference(transitivity,[status(thm)],[c194,c215]) ).
cnf(c217,plain,
join(zero,join(zero,X)) = join(X,zero),
inference(transitivity,[status(thm)],[c191,c216]) ).
cnf(c218,plain,
join(zero,join(zero,meet(X,X))) = join(meet(X,X),zero),
inference(substitution,[status(thm)],[c217]) ).
cnf(c219,plain,
meet(X,X) = complement(join(complement(X),complement(X))),
inference(substitution,[status(thm)],[c172]) ).
cnf(c220,plain,
complement(join(complement(X),complement(X))) = complement(complement(X)),
inference(congruence,[status(thm)],[c79]) ).
cnf(c221,plain,
meet(X,X) = complement(complement(X)),
inference(transitivity,[status(thm)],[c219,c220]) ).
cnf(c222,plain,
join(meet(X,X),zero) = join(complement(complement(X)),zero),
inference(congruence,[status(thm)],[c221]) ).
cnf(c223,plain,
join(complement(complement(X)),zero) = join(zero,complement(complement(X))),
inference(substitution,[status(thm)],[c12]) ).
cnf(c224,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c175]) ).
cnf(c225,plain,
join(zero,complement(complement(X))) = join(meet(X,complement(X)),complement(complement(X))),
inference(congruence,[status(thm)],[c224]) ).
cnf(c226,plain,
complement(X) = join(complement(X),complement(X)),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c227,plain,
complement(complement(X)) = complement(join(complement(X),complement(X))),
inference(congruence,[status(thm)],[c226]) ).
cnf(c228,plain,
join(meet(X,complement(X)),complement(complement(X))) = join(meet(X,complement(X)),complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c227]) ).
cnf(c229,plain,
join(meet(X,complement(X)),complement(join(complement(X),complement(X)))) = X,
inference(substitution,[status(thm)],[c183]) ).
cnf(c230,plain,
join(meet(X,complement(X)),complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c228,c229]) ).
cnf(c231,plain,
join(zero,complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c225,c230]) ).
cnf(c232,plain,
join(complement(complement(X)),zero) = X,
inference(transitivity,[status(thm)],[c223,c231]) ).
cnf(c233,plain,
join(meet(X,X),zero) = X,
inference(transitivity,[status(thm)],[c222,c232]) ).
cnf(c234,plain,
join(zero,join(zero,meet(X,X))) = X,
inference(transitivity,[status(thm)],[c218,c233]) ).
cnf(c235,plain,
join(zero,X) = X,
inference(transitivity,[status(thm)],[c188,c234]) ).
cnf(c236,plain,
join(X,zero) = X,
inference(transitivity,[status(thm)],[c171,c235]) ).
cnf(c237,plain,
join(zero,X) = X,
inference(transitivity,[status(thm)],[c169,c236]) ).
cnf(c238,plain,
join(zero,complement(zero)) = complement(zero),
inference(substitution,[status(thm)],[c237]) ).
cnf(c239,plain,
complement(zero) = join(zero,complement(zero)),
inference(symmetry,[status(thm)],[c238]) ).
cnf(c240,plain,
top = join(zero,complement(zero)),
inference(substitution,[status(thm)],[c33]) ).
cnf(c241,plain,
join(zero,complement(zero)) = top,
inference(symmetry,[status(thm)],[c240]) ).
cnf(c242,plain,
complement(zero) = top,
inference(transitivity,[status(thm)],[c239,c241]) ).
cnf(c243,plain,
top = complement(zero),
inference(symmetry,[status(thm)],[c242]) ).
cnf(c244,plain,
composition(complement(x0),top) = composition(complement(x0),complement(zero)),
inference(congruence,[status(thm)],[c243]) ).
cnf(c245,plain,
join(complement(x0),composition(complement(x0),top)) = join(complement(x0),composition(complement(x0),complement(zero))),
inference(congruence,[status(thm)],[c244]) ).
cnf(c246,plain,
converse(converse(complement(x0))) = complement(x0),
inference(substitution,[status(thm)],[c5]) ).
cnf(c247,plain,
complement(x0) = converse(converse(complement(x0))),
inference(symmetry,[status(thm)],[c246]) ).
cnf(c248,plain,
composition(complement(x0),complement(zero)) = composition(converse(converse(complement(x0))),complement(zero)),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
join(complement(x0),composition(complement(x0),complement(zero))) = join(complement(x0),composition(converse(converse(complement(x0))),complement(zero))),
inference(congruence,[status(thm)],[c248]) ).
cnf(c250,plain,
converse(composition(converse(x0),complement(x0))) = composition(converse(complement(x0)),x0),
inference(substitution,[status(thm)],[c46]) ).
cnf(c251,plain,
composition(converse(complement(x0)),x0) = converse(composition(converse(x0),complement(x0))),
inference(symmetry,[status(thm)],[c250]) ).
cnf(c252,plain,
join(zero,composition(converse(x0),complement(x0))) = composition(converse(x0),complement(x0)),
inference(substitution,[status(thm)],[c237]) ).
cnf(c253,plain,
composition(converse(x0),complement(x0)) = join(zero,composition(converse(x0),complement(x0))),
inference(symmetry,[status(thm)],[c252]) ).
cnf(c254,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c255,plain,
join(zero,composition(converse(x0),complement(x0))) = join(complement(top),composition(converse(x0),complement(x0))),
inference(congruence,[status(thm)],[c254]) ).
fof(c256,conjecture,
! [X0_2] :
( composition(X0_2,top) = X0_2
=> composition(complement(X0_2),top) = complement(X0_2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c257,negated_conjecture,
~ ! [X0_2] :
( composition(X0_2,top) = X0_2
=> composition(complement(X0_2),top) = complement(X0_2) ),
inference(negate_conjecture,[status(cth)],[c256]) ).
fof(c258,plain,
( composition(x0,top) = x0
& composition(complement(x0),top) != complement(x0) ),
inference(clausify,[status(esa)],[c257]) ).
cnf(c259,plain,
composition(x0,top) = x0,
inference(clausify,[status(thm)],[c258]) ).
cnf(c260,plain,
x0 = composition(x0,top),
inference(symmetry,[status(thm)],[c259]) ).
cnf(c261,plain,
complement(x0) = complement(composition(x0,top)),
inference(congruence,[status(thm)],[c260]) ).
cnf(c262,plain,
composition(converse(x0),complement(x0)) = composition(converse(x0),complement(composition(x0,top))),
inference(congruence,[status(thm)],[c261]) ).
cnf(c263,plain,
join(complement(top),composition(converse(x0),complement(x0))) = join(complement(top),composition(converse(x0),complement(composition(x0,top)))),
inference(congruence,[status(thm)],[c262]) ).
cnf(c264,plain,
join(complement(top),composition(converse(x0),complement(composition(x0,top)))) = complement(top),
inference(substitution,[status(thm)],[c76]) ).
cnf(c265,plain,
join(complement(top),composition(converse(x0),complement(composition(x0,top)))) = zero,
inference(transitivity,[status(thm)],[c264,c203]) ).
cnf(c266,plain,
join(complement(top),composition(converse(x0),complement(x0))) = zero,
inference(transitivity,[status(thm)],[c263,c265]) ).
cnf(c267,plain,
join(zero,composition(converse(x0),complement(x0))) = zero,
inference(transitivity,[status(thm)],[c255,c266]) ).
cnf(c268,plain,
composition(converse(x0),complement(x0)) = zero,
inference(transitivity,[status(thm)],[c253,c267]) ).
cnf(c269,plain,
converse(composition(converse(x0),complement(x0))) = converse(zero),
inference(congruence,[status(thm)],[c268]) ).
cnf(c270,plain,
join(converse(zero),zero) = converse(zero),
inference(substitution,[status(thm)],[c236]) ).
cnf(c271,plain,
converse(zero) = join(converse(zero),zero),
inference(symmetry,[status(thm)],[c270]) ).
cnf(c272,plain,
join(zero,join(zero,converse(zero))) = join(converse(zero),zero),
inference(substitution,[status(thm)],[c217]) ).
cnf(c273,plain,
join(converse(zero),zero) = join(zero,join(zero,converse(zero))),
inference(symmetry,[status(thm)],[c272]) ).
cnf(c274,plain,
converse(join(converse(X),zero)) = join(X,converse(zero)),
inference(substitution,[status(thm)],[c135]) ).
cnf(c275,plain,
join(X,converse(zero)) = converse(join(converse(X),zero)),
inference(symmetry,[status(thm)],[c274]) ).
cnf(c276,plain,
join(converse(X),zero) = converse(X),
inference(substitution,[status(thm)],[c236]) ).
cnf(c277,plain,
converse(join(converse(X),zero)) = converse(converse(X)),
inference(congruence,[status(thm)],[c276]) ).
cnf(c278,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c279,plain,
converse(join(converse(X),zero)) = X,
inference(transitivity,[status(thm)],[c277,c278]) ).
cnf(c280,plain,
join(X,converse(zero)) = X,
inference(transitivity,[status(thm)],[c275,c279]) ).
cnf(c281,plain,
join(zero,converse(zero)) = zero,
inference(substitution,[status(thm)],[c280]) ).
cnf(c282,plain,
join(zero,join(zero,converse(zero))) = join(zero,zero),
inference(congruence,[status(thm)],[c281]) ).
cnf(c283,plain,
join(zero,join(zero,converse(zero))) = zero,
inference(transitivity,[status(thm)],[c282,c211]) ).
cnf(c284,plain,
join(converse(zero),zero) = zero,
inference(transitivity,[status(thm)],[c273,c283]) ).
cnf(c285,plain,
converse(zero) = zero,
inference(transitivity,[status(thm)],[c271,c284]) ).
cnf(c286,plain,
converse(composition(converse(x0),complement(x0))) = zero,
inference(transitivity,[status(thm)],[c269,c285]) ).
cnf(c287,plain,
composition(converse(complement(x0)),x0) = zero,
inference(transitivity,[status(thm)],[c251,c286]) ).
cnf(c288,plain,
zero = composition(converse(complement(x0)),x0),
inference(symmetry,[status(thm)],[c287]) ).
cnf(c289,plain,
complement(zero) = complement(composition(converse(complement(x0)),x0)),
inference(congruence,[status(thm)],[c288]) ).
cnf(c290,plain,
composition(converse(converse(complement(x0))),complement(zero)) = composition(converse(converse(complement(x0))),complement(composition(converse(complement(x0)),x0))),
inference(congruence,[status(thm)],[c289]) ).
cnf(c291,plain,
join(complement(x0),composition(converse(converse(complement(x0))),complement(zero))) = join(complement(x0),composition(converse(converse(complement(x0))),complement(composition(converse(complement(x0)),x0)))),
inference(congruence,[status(thm)],[c290]) ).
cnf(c292,plain,
join(complement(x0),composition(converse(converse(complement(x0))),complement(composition(converse(complement(x0)),x0)))) = complement(x0),
inference(substitution,[status(thm)],[c76]) ).
cnf(c293,plain,
join(complement(x0),composition(converse(converse(complement(x0))),complement(zero))) = complement(x0),
inference(transitivity,[status(thm)],[c291,c292]) ).
cnf(c294,plain,
join(complement(x0),composition(complement(x0),complement(zero))) = complement(x0),
inference(transitivity,[status(thm)],[c249,c293]) ).
cnf(c295,plain,
join(complement(x0),composition(complement(x0),top)) = complement(x0),
inference(transitivity,[status(thm)],[c245,c294]) ).
cnf(c296,plain,
composition(complement(x0),top) = complement(x0),
inference(transitivity,[status(thm)],[c167,c295]) ).
cnf(c297,plain,
$false,
inference(resolution,[status(thm)],[c4,c296]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL018+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 22:47:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.68/0.57 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.68/0.57
% 0.68/0.57 % SZS status Theorem
% 0.68/0.57
% 0.68/0.58 % SZS output start CNFRefutation
% See solution above
% 1.79/0.69
% 1.79/0.69 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------