%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL041+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 12:33:29 PM UTC 2026
% Result : Theorem 19.14s 2.99s
% Output : CNFRefutation 22.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 73
% Number of leaves : 16
% Syntax : Number of formulae : 402 ( 396 unt; 0 def)
% Number of atoms : 408 ( 407 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 5 ~; 0 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 543 ( 33 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c1,conjecture,
! [X0] :
( join(composition(converse(X0),X0),one) = one
=> ! [X1] : meet(composition(X0,X1),composition(X0,complement(X1))) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c2,negated_conjecture,
~ ! [X0_2] :
( join(composition(converse(X0_2),X0_2),one) = one
=> ! [X1_2] : meet(composition(X0_2,X1_2),composition(X0_2,complement(X1_2))) = zero ),
inference(negate_conjecture,[status(cth)],[c1]) ).
fof(c3,plain,
( join(composition(converse(x0),x0),one) = one
& meet(composition(x0,x1),composition(x0,complement(x1))) != zero ),
inference(clausify,[status(esa)],[c2]) ).
cnf(c4,plain,
meet(composition(x0,x1),composition(x0,complement(x1))) != zero,
inference(clausify,[status(thm)],[c3]) ).
cnf(c5,axiom,
join(X0_2,X1_2) = join(X1_2,X0_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
cnf(c6,plain,
join(zero,X) = join(X,zero),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
join(X,zero) = join(zero,X),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,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(c9,plain,
meet(X,X) = complement(join(complement(X),complement(X))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
join(zero,meet(X,X)) = join(zero,complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,axiom,
zero = meet(X0_2,complement(X0_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero) ).
cnf(c12,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
join(zero,complement(join(complement(X),complement(X)))) = join(meet(X,complement(X)),complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
meet(X,X3) = complement(join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c15,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)],[c14]) ).
cnf(c16,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(c17,plain,
X3 = join(complement(join(complement(X3),complement(X))),complement(join(complement(X3),X))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
join(complement(join(complement(X3),complement(X))),complement(join(complement(X3),X))) = X3,
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
join(meet(X3,X),complement(join(complement(X3),X))) = X3,
inference(transitivity,[status(thm)],[c15,c18]) ).
cnf(c20,plain,
join(meet(X,complement(X)),complement(join(complement(X),complement(X)))) = X,
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
join(zero,complement(join(complement(X),complement(X)))) = X,
inference(transitivity,[status(thm)],[c13,c20]) ).
cnf(c22,plain,
join(zero,meet(X,X)) = X,
inference(transitivity,[status(thm)],[c10,c21]) ).
cnf(c23,plain,
X = join(zero,meet(X,X)),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
join(zero,X) = join(zero,join(zero,meet(X,X))),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
join(X,zero) = join(zero,X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c26,plain,
join(zero,X) = join(X,zero),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
join(zero,join(zero,X)) = join(zero,join(X,zero)),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
join(zero,X) = join(X,zero),
inference(substitution,[status(thm)],[c5]) ).
cnf(c29,plain,
join(X,zero) = join(zero,X),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
join(zero,join(X,zero)) = join(zero,join(zero,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(zero,join(zero,X)) = join(join(zero,zero),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(complement(X),complement(complement(X))),
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
complement(top) = complement(join(complement(X),complement(complement(X)))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
meet(X,complement(X)) = complement(join(complement(X),complement(complement(X)))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c37,plain,
complement(join(complement(X),complement(complement(X)))) = meet(X,complement(X)),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c39,plain,
meet(X,complement(X)) = zero,
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
complement(join(complement(X),complement(complement(X)))) = zero,
inference(transitivity,[status(thm)],[c37,c39]) ).
cnf(c41,plain,
complement(top) = zero,
inference(transitivity,[status(thm)],[c35,c40]) ).
cnf(c42,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
join(zero,zero) = join(zero,complement(top)),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c45,plain,
join(zero,complement(top)) = join(complement(top),complement(top)),
inference(congruence,[status(thm)],[c44]) ).
cnf(c46,axiom,
converse(converse(X0_2)) = X0_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence) ).
cnf(c47,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
composition(converse(one),X) = composition(converse(one),converse(converse(X))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,axiom,
converse(composition(X0_2,X1_2)) = composition(converse(X1_2),converse(X0_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity) ).
cnf(c51,plain,
converse(composition(X,one)) = composition(converse(one),converse(X)),
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
composition(converse(one),converse(X)) = converse(composition(X,one)),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,axiom,
composition(X0_2,one) = X0_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity) ).
cnf(c54,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
converse(composition(X,one)) = converse(X),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
composition(converse(one),converse(X)) = converse(X),
inference(transitivity,[status(thm)],[c52,c55]) ).
cnf(c57,plain,
composition(converse(one),converse(converse(X))) = converse(converse(X)),
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c59,plain,
composition(converse(one),converse(converse(X))) = X,
inference(transitivity,[status(thm)],[c57,c58]) ).
cnf(c60,plain,
composition(converse(one),X) = X,
inference(transitivity,[status(thm)],[c49,c59]) ).
cnf(c61,plain,
composition(converse(one),complement(X)) = complement(X),
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
complement(X) = composition(converse(one),complement(X)),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,plain,
join(complement(X),complement(X)) = join(complement(X),composition(converse(one),complement(X))),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
composition(converse(one),composition(one,X)) = composition(one,X),
inference(substitution,[status(thm)],[c60]) ).
cnf(c65,plain,
composition(one,X) = composition(converse(one),composition(one,X)),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,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(c67,plain,
composition(X3,composition(one,X)) = composition(composition(X3,one),X),
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c53]) ).
cnf(c69,plain,
composition(composition(X3,one),X) = composition(X3,X),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
composition(X3,composition(one,X)) = composition(X3,X),
inference(transitivity,[status(thm)],[c67,c69]) ).
cnf(c71,plain,
composition(converse(one),composition(one,X)) = composition(converse(one),X),
inference(substitution,[status(thm)],[c70]) ).
cnf(c72,plain,
composition(converse(one),composition(one,X)) = X,
inference(transitivity,[status(thm)],[c71,c60]) ).
cnf(c73,plain,
composition(one,X) = X,
inference(transitivity,[status(thm)],[c65,c72]) ).
cnf(c74,plain,
X = composition(one,X),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
complement(X) = complement(composition(one,X)),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
composition(converse(one),complement(X)) = composition(converse(one),complement(composition(one,X))),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
join(complement(X),composition(converse(one),complement(X))) = join(complement(X),composition(converse(one),complement(composition(one,X)))),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,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)],[c5]) ).
cnf(c79,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)],[c78]) ).
cnf(c80,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(c81,plain,
join(composition(converse(X),complement(composition(X,X3))),complement(X3)) = complement(X3),
inference(substitution,[status(thm)],[c80]) ).
cnf(c82,plain,
join(complement(X3),composition(converse(X),complement(composition(X,X3)))) = complement(X3),
inference(transitivity,[status(thm)],[c79,c81]) ).
cnf(c83,plain,
join(complement(X),composition(converse(one),complement(composition(one,X)))) = complement(X),
inference(substitution,[status(thm)],[c82]) ).
cnf(c84,plain,
join(complement(X),composition(converse(one),complement(X))) = complement(X),
inference(transitivity,[status(thm)],[c77,c83]) ).
cnf(c85,plain,
join(complement(X),complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c63,c84]) ).
cnf(c86,plain,
join(complement(top),complement(top)) = complement(top),
inference(substitution,[status(thm)],[c85]) ).
cnf(c87,plain,
join(complement(top),complement(top)) = zero,
inference(transitivity,[status(thm)],[c86,c41]) ).
cnf(c88,plain,
join(zero,complement(top)) = zero,
inference(transitivity,[status(thm)],[c45,c87]) ).
cnf(c89,plain,
join(zero,zero) = zero,
inference(transitivity,[status(thm)],[c43,c88]) ).
cnf(c90,plain,
join(join(zero,zero),X) = join(zero,X),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
join(zero,X) = join(X,zero),
inference(substitution,[status(thm)],[c5]) ).
cnf(c92,plain,
join(join(zero,zero),X) = join(X,zero),
inference(transitivity,[status(thm)],[c90,c91]) ).
cnf(c93,plain,
join(zero,join(zero,X)) = join(X,zero),
inference(transitivity,[status(thm)],[c32,c92]) ).
cnf(c94,plain,
join(zero,join(X,zero)) = join(X,zero),
inference(transitivity,[status(thm)],[c30,c93]) ).
cnf(c95,plain,
join(zero,join(zero,X)) = join(X,zero),
inference(transitivity,[status(thm)],[c27,c94]) ).
cnf(c96,plain,
join(zero,join(zero,meet(X,X))) = join(meet(X,X),zero),
inference(substitution,[status(thm)],[c95]) ).
cnf(c97,plain,
join(meet(X,X),zero) = join(zero,meet(X,X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c98,plain,
join(meet(X,X),zero) = X,
inference(transitivity,[status(thm)],[c97,c22]) ).
cnf(c99,plain,
join(zero,join(zero,meet(X,X))) = X,
inference(transitivity,[status(thm)],[c96,c98]) ).
cnf(c100,plain,
join(zero,X) = X,
inference(transitivity,[status(thm)],[c24,c99]) ).
cnf(c101,plain,
join(X,zero) = X,
inference(transitivity,[status(thm)],[c7,c100]) ).
cnf(c102,plain,
join(meet(composition(x0,X),composition(x0,complement(X))),zero) = meet(composition(x0,X),composition(x0,complement(X))),
inference(substitution,[status(thm)],[c101]) ).
cnf(c103,plain,
meet(composition(x0,X),composition(x0,complement(X))) = join(meet(composition(x0,X),composition(x0,complement(X))),zero),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c104,plain,
join(X,zero) = join(zero,X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c105,plain,
join(zero,X) = join(X,zero),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
join(zero,X) = X,
inference(transitivity,[status(thm)],[c105,c101]) ).
cnf(c107,plain,
join(zero,composition(X,zero)) = composition(X,zero),
inference(substitution,[status(thm)],[c106]) ).
cnf(c108,plain,
composition(X,zero) = join(zero,composition(X,zero)),
inference(symmetry,[status(thm)],[c107]) ).
cnf(c109,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c110,plain,
composition(top,zero) = composition(top,complement(top)),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
join(X,top) = join(top,X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c112,plain,
join(top,X) = join(X,top),
inference(symmetry,[status(thm)],[c111]) ).
cnf(c113,plain,
join(complement(X),top) = join(top,complement(X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c114,plain,
join(top,complement(X)) = join(complement(X),top),
inference(symmetry,[status(thm)],[c113]) ).
cnf(c115,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c116,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(symmetry,[status(thm)],[c115]) ).
cnf(c117,plain,
join(X3,join(X,complement(X3))) = join(X3,join(complement(X3),X)),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
join(X3,join(complement(X3),X)) = join(join(X3,complement(X3)),X),
inference(substitution,[status(thm)],[c31]) ).
cnf(c119,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c33]) ).
cnf(c120,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c119]) ).
cnf(c121,plain,
join(join(X3,complement(X3)),X) = join(top,X),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
join(top,X) = join(X,top),
inference(substitution,[status(thm)],[c5]) ).
cnf(c123,plain,
join(join(X3,complement(X3)),X) = join(X,top),
inference(transitivity,[status(thm)],[c121,c122]) ).
cnf(c124,plain,
join(X3,join(complement(X3),X)) = join(X,top),
inference(transitivity,[status(thm)],[c118,c123]) ).
cnf(c125,plain,
join(X3,join(X,complement(X3))) = join(X,top),
inference(transitivity,[status(thm)],[c117,c124]) ).
cnf(c126,plain,
join(X,join(complement(X),complement(X))) = join(complement(X),top),
inference(substitution,[status(thm)],[c125]) ).
cnf(c127,plain,
join(complement(X),top) = join(X,join(complement(X),complement(X))),
inference(symmetry,[status(thm)],[c126]) ).
cnf(c128,plain,
join(X,join(complement(X),complement(X))) = join(X,complement(X)),
inference(congruence,[status(thm)],[c85]) ).
cnf(c129,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c33]) ).
cnf(c130,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c129]) ).
cnf(c131,plain,
join(X,join(complement(X),complement(X))) = top,
inference(transitivity,[status(thm)],[c128,c130]) ).
cnf(c132,plain,
join(complement(X),top) = top,
inference(transitivity,[status(thm)],[c127,c131]) ).
cnf(c133,plain,
join(top,complement(X)) = top,
inference(transitivity,[status(thm)],[c114,c132]) ).
cnf(c134,plain,
top = join(top,complement(X)),
inference(symmetry,[status(thm)],[c133]) ).
cnf(c135,plain,
join(X,top) = join(X,join(top,complement(X))),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c125]) ).
cnf(c137,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c125]) ).
cnf(c138,plain,
join(top,top) = join(X,join(top,complement(X))),
inference(symmetry,[status(thm)],[c137]) ).
cnf(c139,plain,
join(X,join(top,complement(X))) = join(X,top),
inference(congruence,[status(thm)],[c133]) ).
cnf(c140,plain,
join(top,top) = join(X,top),
inference(transitivity,[status(thm)],[c138,c139]) ).
cnf(c141,plain,
join(X,join(top,complement(X))) = join(X3,top),
inference(transitivity,[status(thm)],[c136,c140]) ).
cnf(c142,plain,
join(X,top) = join(X3,top),
inference(transitivity,[status(thm)],[c135,c141]) ).
cnf(c143,plain,
join(X3,top) = join(X,top),
inference(symmetry,[status(thm)],[c142]) ).
cnf(c144,plain,
join(X,top) = join(zero,top),
inference(substitution,[status(thm)],[c142]) ).
cnf(c145,plain,
join(zero,top) = top,
inference(substitution,[status(thm)],[c106]) ).
cnf(c146,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c144,c145]) ).
cnf(c147,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c143,c146]) ).
cnf(c148,plain,
join(top,X) = top,
inference(transitivity,[status(thm)],[c112,c147]) ).
cnf(c149,plain,
join(top,one) = top,
inference(substitution,[status(thm)],[c148]) ).
cnf(c150,plain,
top = join(top,one),
inference(symmetry,[status(thm)],[c149]) ).
cnf(c151,plain,
composition(top,complement(top)) = composition(join(top,one),complement(top)),
inference(congruence,[status(thm)],[c150]) ).
cnf(c152,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c153,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c152]) ).
cnf(c154,plain,
join(X,converse(complement(converse(X)))) = join(converse(converse(X)),converse(complement(converse(X)))),
inference(congruence,[status(thm)],[c153]) ).
cnf(c155,axiom,
converse(join(X0_2,X1_2)) = join(converse(X0_2),converse(X1_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity) ).
cnf(c156,plain,
converse(join(X,complement(X))) = join(converse(X),converse(complement(X))),
inference(substitution,[status(thm)],[c155]) ).
cnf(c157,plain,
join(converse(X),converse(complement(X))) = converse(join(X,complement(X))),
inference(symmetry,[status(thm)],[c156]) ).
cnf(c158,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c33]) ).
cnf(c159,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c158]) ).
cnf(c160,plain,
converse(join(X,complement(X))) = converse(top),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
join(converse(X),converse(complement(X))) = converse(top),
inference(transitivity,[status(thm)],[c157,c160]) ).
cnf(c162,plain,
join(converse(converse(X)),converse(complement(converse(X)))) = converse(top),
inference(substitution,[status(thm)],[c161]) ).
cnf(c163,plain,
join(X,converse(complement(converse(X)))) = converse(top),
inference(transitivity,[status(thm)],[c154,c162]) ).
cnf(c164,plain,
join(top,converse(complement(converse(top)))) = converse(top),
inference(substitution,[status(thm)],[c163]) ).
cnf(c165,plain,
converse(top) = join(top,converse(complement(converse(top)))),
inference(symmetry,[status(thm)],[c164]) ).
cnf(c166,plain,
join(top,converse(complement(converse(top)))) = top,
inference(substitution,[status(thm)],[c148]) ).
cnf(c167,plain,
converse(top) = top,
inference(transitivity,[status(thm)],[c165,c166]) ).
cnf(c168,plain,
top = converse(top),
inference(symmetry,[status(thm)],[c167]) ).
cnf(c169,plain,
join(top,one) = join(converse(top),one),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
composition(join(top,one),complement(top)) = composition(join(converse(top),one),complement(top)),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
X = composition(one,X),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c172,plain,
join(X3,composition(X,X3)) = join(composition(one,X3),composition(X,X3)),
inference(congruence,[status(thm)],[c171]) ).
cnf(c173,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(c174,plain,
composition(join(one,X),X3) = join(composition(one,X3),composition(X,X3)),
inference(substitution,[status(thm)],[c173]) ).
cnf(c175,plain,
join(composition(one,X3),composition(X,X3)) = composition(join(one,X),X3),
inference(symmetry,[status(thm)],[c174]) ).
cnf(c176,plain,
join(one,X) = join(X,one),
inference(substitution,[status(thm)],[c5]) ).
cnf(c177,plain,
composition(join(one,X),X3) = composition(join(X,one),X3),
inference(congruence,[status(thm)],[c176]) ).
cnf(c178,plain,
join(composition(one,X3),composition(X,X3)) = composition(join(X,one),X3),
inference(transitivity,[status(thm)],[c175,c177]) ).
cnf(c179,plain,
join(X3,composition(X,X3)) = composition(join(X,one),X3),
inference(transitivity,[status(thm)],[c172,c178]) ).
cnf(c180,plain,
join(complement(top),composition(converse(top),complement(top))) = composition(join(converse(top),one),complement(top)),
inference(substitution,[status(thm)],[c179]) ).
cnf(c181,plain,
composition(join(converse(top),one),complement(top)) = join(complement(top),composition(converse(top),complement(top))),
inference(symmetry,[status(thm)],[c180]) ).
cnf(c182,plain,
join(top,one) = top,
inference(substitution,[status(thm)],[c148]) ).
cnf(c183,plain,
top = join(top,one),
inference(symmetry,[status(thm)],[c182]) ).
cnf(c184,plain,
composition(top,top) = composition(join(top,one),top),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,plain,
join(top,composition(X,top)) = composition(join(X,one),top),
inference(substitution,[status(thm)],[c179]) ).
cnf(c186,plain,
composition(join(X,one),top) = join(top,composition(X,top)),
inference(symmetry,[status(thm)],[c185]) ).
cnf(c187,plain,
join(top,composition(X,top)) = top,
inference(substitution,[status(thm)],[c148]) ).
cnf(c188,plain,
composition(join(X,one),top) = top,
inference(transitivity,[status(thm)],[c186,c187]) ).
cnf(c189,plain,
composition(join(top,one),top) = top,
inference(substitution,[status(thm)],[c188]) ).
cnf(c190,plain,
composition(top,top) = top,
inference(transitivity,[status(thm)],[c184,c189]) ).
cnf(c191,plain,
top = composition(top,top),
inference(symmetry,[status(thm)],[c190]) ).
cnf(c192,plain,
complement(top) = complement(composition(top,top)),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
composition(converse(top),complement(top)) = composition(converse(top),complement(composition(top,top))),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
join(complement(top),composition(converse(top),complement(top))) = join(complement(top),composition(converse(top),complement(composition(top,top)))),
inference(congruence,[status(thm)],[c193]) ).
cnf(c195,plain,
join(complement(top),composition(converse(top),complement(composition(top,top)))) = complement(top),
inference(substitution,[status(thm)],[c82]) ).
cnf(c196,plain,
join(complement(top),composition(converse(top),complement(composition(top,top)))) = zero,
inference(transitivity,[status(thm)],[c195,c41]) ).
cnf(c197,plain,
join(complement(top),composition(converse(top),complement(top))) = zero,
inference(transitivity,[status(thm)],[c194,c196]) ).
cnf(c198,plain,
composition(join(converse(top),one),complement(top)) = zero,
inference(transitivity,[status(thm)],[c181,c197]) ).
cnf(c199,plain,
composition(join(top,one),complement(top)) = zero,
inference(transitivity,[status(thm)],[c170,c198]) ).
cnf(c200,plain,
composition(top,complement(top)) = zero,
inference(transitivity,[status(thm)],[c151,c199]) ).
cnf(c201,plain,
composition(top,zero) = zero,
inference(transitivity,[status(thm)],[c110,c200]) ).
cnf(c202,plain,
zero = composition(top,zero),
inference(symmetry,[status(thm)],[c201]) ).
cnf(c203,plain,
join(zero,composition(X,zero)) = join(composition(top,zero),composition(X,zero)),
inference(congruence,[status(thm)],[c202]) ).
cnf(c204,plain,
composition(join(top,X),zero) = join(composition(top,zero),composition(X,zero)),
inference(substitution,[status(thm)],[c173]) ).
cnf(c205,plain,
join(composition(top,zero),composition(X,zero)) = composition(join(top,X),zero),
inference(symmetry,[status(thm)],[c204]) ).
cnf(c206,plain,
composition(join(top,X),zero) = composition(top,zero),
inference(congruence,[status(thm)],[c148]) ).
cnf(c207,plain,
composition(join(top,X),zero) = zero,
inference(transitivity,[status(thm)],[c206,c201]) ).
cnf(c208,plain,
join(composition(top,zero),composition(X,zero)) = zero,
inference(transitivity,[status(thm)],[c205,c207]) ).
cnf(c209,plain,
join(zero,composition(X,zero)) = zero,
inference(transitivity,[status(thm)],[c203,c208]) ).
cnf(c210,plain,
composition(X,zero) = zero,
inference(transitivity,[status(thm)],[c108,c209]) ).
cnf(c211,plain,
composition(meet(x0,composition(composition(x0,X),converse(complement(X)))),zero) = zero,
inference(substitution,[status(thm)],[c210]) ).
cnf(c212,plain,
zero = composition(meet(x0,composition(composition(x0,X),converse(complement(X)))),zero),
inference(symmetry,[status(thm)],[c211]) ).
cnf(c213,plain,
join(meet(composition(x0,X),composition(x0,complement(X))),zero) = join(meet(composition(x0,X),composition(x0,complement(X))),composition(meet(x0,composition(composition(x0,X),converse(complement(X)))),zero)),
inference(congruence,[status(thm)],[c212]) ).
cnf(c214,plain,
meet(X,X3) = complement(join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c215,plain,
join(complement(X3),complement(X)) = join(complement(X),complement(X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c216,plain,
join(complement(X),complement(X3)) = join(complement(X3),complement(X)),
inference(symmetry,[status(thm)],[c215]) ).
cnf(c217,plain,
complement(join(complement(X),complement(X3))) = complement(join(complement(X3),complement(X))),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c219,plain,
complement(join(complement(X3),complement(X))) = meet(X3,X),
inference(symmetry,[status(thm)],[c218]) ).
cnf(c220,plain,
complement(join(complement(X),complement(X3))) = meet(X3,X),
inference(transitivity,[status(thm)],[c217,c219]) ).
cnf(c221,plain,
meet(X,X3) = meet(X3,X),
inference(transitivity,[status(thm)],[c214,c220]) ).
cnf(c222,plain,
meet(composition(x0,complement(X)),composition(x0,X)) = meet(composition(x0,X),composition(x0,complement(X))),
inference(substitution,[status(thm)],[c221]) ).
cnf(c223,plain,
meet(composition(x0,X),composition(x0,complement(X))) = meet(composition(x0,complement(X)),composition(x0,X)),
inference(symmetry,[status(thm)],[c222]) ).
cnf(c224,plain,
join(meet(composition(x0,X),composition(x0,complement(X))),composition(meet(x0,composition(composition(x0,X),converse(complement(X)))),zero)) = join(meet(composition(x0,complement(X)),composition(x0,X)),composition(meet(x0,composition(composition(x0,X),converse(complement(X)))),zero)),
inference(congruence,[status(thm)],[c223]) ).
cnf(c225,plain,
meet(complement(X),composition(converse(x0),composition(x0,X))) = meet(composition(converse(x0),composition(x0,X)),complement(X)),
inference(substitution,[status(thm)],[c221]) ).
cnf(c226,plain,
composition(X,composition(X4,X3)) = composition(composition(X,X4),X3),
inference(substitution,[status(thm)],[c66]) ).
cnf(c227,plain,
join(X4,composition(X3,composition(X,X4))) = join(X4,composition(composition(X3,X),X4)),
inference(congruence,[status(thm)],[c226]) ).
cnf(c228,plain,
join(X4,composition(composition(X3,X),X4)) = composition(join(composition(X3,X),one),X4),
inference(substitution,[status(thm)],[c179]) ).
cnf(c229,plain,
join(composition(X3,X),one) = join(one,composition(X3,X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c230,plain,
composition(join(composition(X3,X),one),X4) = composition(join(one,composition(X3,X)),X4),
inference(congruence,[status(thm)],[c229]) ).
cnf(c231,plain,
join(X4,composition(composition(X3,X),X4)) = composition(join(one,composition(X3,X)),X4),
inference(transitivity,[status(thm)],[c228,c230]) ).
cnf(c232,plain,
join(X4,composition(X3,composition(X,X4))) = composition(join(one,composition(X3,X)),X4),
inference(transitivity,[status(thm)],[c227,c231]) ).
cnf(c233,plain,
join(X,composition(converse(x0),composition(x0,X))) = composition(join(one,composition(converse(x0),x0)),X),
inference(substitution,[status(thm)],[c232]) ).
cnf(c234,plain,
join(composition(converse(x0),x0),one) = join(one,composition(converse(x0),x0)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c235,plain,
join(one,composition(converse(x0),x0)) = join(composition(converse(x0),x0),one),
inference(symmetry,[status(thm)],[c234]) ).
fof(c236,conjecture,
! [X0_2] :
( join(composition(converse(X0_2),X0_2),one) = one
=> ! [X1_2] : meet(composition(X0_2,X1_2),composition(X0_2,complement(X1_2))) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c237,negated_conjecture,
~ ! [X0_2] :
( join(composition(converse(X0_2),X0_2),one) = one
=> ! [X1_2] : meet(composition(X0_2,X1_2),composition(X0_2,complement(X1_2))) = zero ),
inference(negate_conjecture,[status(cth)],[c236]) ).
fof(c238,plain,
( join(composition(converse(x0),x0),one) = one
& meet(composition(x0,x1),composition(x0,complement(x1))) != zero ),
inference(clausify,[status(esa)],[c237]) ).
cnf(c239,plain,
join(composition(converse(x0),x0),one) = one,
inference(clausify,[status(thm)],[c238]) ).
cnf(c240,plain,
join(one,composition(converse(x0),x0)) = one,
inference(transitivity,[status(thm)],[c235,c239]) ).
cnf(c241,plain,
composition(join(one,composition(converse(x0),x0)),X) = composition(one,X),
inference(congruence,[status(thm)],[c240]) ).
cnf(c242,plain,
composition(join(one,composition(converse(x0),x0)),X) = X,
inference(transitivity,[status(thm)],[c241,c73]) ).
cnf(c243,plain,
join(X,composition(converse(x0),composition(x0,X))) = X,
inference(transitivity,[status(thm)],[c233,c242]) ).
cnf(c244,plain,
X = join(X,composition(converse(x0),composition(x0,X))),
inference(symmetry,[status(thm)],[c243]) ).
cnf(c245,plain,
complement(X) = complement(join(X,composition(converse(x0),composition(x0,X)))),
inference(congruence,[status(thm)],[c244]) ).
cnf(c246,plain,
meet(composition(converse(x0),composition(x0,X)),complement(X)) = meet(composition(converse(x0),composition(x0,X)),complement(join(X,composition(converse(x0),composition(x0,X))))),
inference(congruence,[status(thm)],[c245]) ).
cnf(c247,plain,
join(X3,X) = join(X,X3),
inference(substitution,[status(thm)],[c5]) ).
cnf(c248,plain,
join(X,X3) = join(X3,X),
inference(symmetry,[status(thm)],[c247]) ).
cnf(c249,plain,
complement(join(X,X3)) = complement(join(X3,X)),
inference(congruence,[status(thm)],[c248]) ).
cnf(c250,plain,
meet(X3,complement(join(X,X3))) = meet(X3,complement(join(X3,X))),
inference(congruence,[status(thm)],[c249]) ).
cnf(c251,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c252,plain,
join(X3,X) = join(X,X3),
inference(symmetry,[status(thm)],[c251]) ).
cnf(c253,plain,
complement(join(X3,X)) = complement(join(X,X3)),
inference(congruence,[status(thm)],[c252]) ).
cnf(c254,plain,
meet(X3,complement(join(X3,X))) = meet(X3,complement(join(X,X3))),
inference(congruence,[status(thm)],[c253]) ).
cnf(c255,plain,
meet(complement(X3),complement(X)) = meet(complement(X),complement(X3)),
inference(substitution,[status(thm)],[c221]) ).
cnf(c256,plain,
join(zero,complement(X)) = complement(X),
inference(substitution,[status(thm)],[c106]) ).
cnf(c257,plain,
complement(X) = join(zero,complement(X)),
inference(symmetry,[status(thm)],[c256]) ).
cnf(c258,plain,
meet(complement(X),complement(X3)) = meet(join(zero,complement(X)),complement(X3)),
inference(congruence,[status(thm)],[c257]) ).
cnf(c259,plain,
join(zero,join(X3,complement(X))) = join(X3,complement(X)),
inference(substitution,[status(thm)],[c106]) ).
cnf(c260,plain,
join(X3,complement(X)) = join(zero,join(X3,complement(X))),
inference(symmetry,[status(thm)],[c259]) ).
cnf(c261,plain,
complement(join(X3,complement(X))) = complement(join(zero,join(X3,complement(X)))),
inference(congruence,[status(thm)],[c260]) ).
cnf(c262,plain,
meet(X3,complement(X)) = meet(complement(X),X3),
inference(substitution,[status(thm)],[c221]) ).
cnf(c263,plain,
complement(meet(X3,complement(X))) = complement(meet(complement(X),X3)),
inference(congruence,[status(thm)],[c262]) ).
cnf(c264,plain,
join(zero,complement(X)) = complement(X),
inference(substitution,[status(thm)],[c106]) ).
cnf(c265,plain,
complement(X) = join(zero,complement(X)),
inference(symmetry,[status(thm)],[c264]) ).
cnf(c266,plain,
meet(complement(X),X3) = meet(join(zero,complement(X)),X3),
inference(congruence,[status(thm)],[c265]) ).
cnf(c267,plain,
complement(meet(complement(X),X3)) = complement(meet(join(zero,complement(X)),X3)),
inference(congruence,[status(thm)],[c266]) ).
cnf(c268,plain,
join(complement(X),complement(X3)) = join(complement(X3),complement(X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c269,plain,
join(complement(X3),complement(X)) = join(complement(X),complement(X3)),
inference(symmetry,[status(thm)],[c268]) ).
cnf(c270,plain,
meet(top,X) = meet(X,top),
inference(substitution,[status(thm)],[c221]) ).
cnf(c271,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c272,plain,
join(zero,complement(X)) = join(complement(top),complement(X)),
inference(congruence,[status(thm)],[c271]) ).
cnf(c273,plain,
complement(join(zero,complement(X))) = complement(join(complement(top),complement(X))),
inference(congruence,[status(thm)],[c272]) ).
cnf(c274,plain,
meet(top,X) = complement(join(complement(top),complement(X))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c275,plain,
complement(join(complement(top),complement(X))) = meet(top,X),
inference(symmetry,[status(thm)],[c274]) ).
cnf(c276,plain,
meet(X,top) = meet(top,X),
inference(substitution,[status(thm)],[c221]) ).
cnf(c277,plain,
meet(top,X) = meet(X,top),
inference(symmetry,[status(thm)],[c276]) ).
cnf(c278,plain,
complement(join(complement(top),complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c275,c277]) ).
cnf(c279,plain,
complement(join(zero,complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c273,c278]) ).
cnf(c280,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c279]) ).
cnf(c281,plain,
join(zero,complement(X)) = complement(X),
inference(substitution,[status(thm)],[c106]) ).
cnf(c282,plain,
complement(join(zero,complement(X))) = complement(complement(X)),
inference(congruence,[status(thm)],[c281]) ).
cnf(c283,plain,
join(zero,complement(complement(X))) = complement(complement(X)),
inference(substitution,[status(thm)],[c106]) ).
cnf(c284,plain,
complement(complement(X)) = join(zero,complement(complement(X))),
inference(symmetry,[status(thm)],[c283]) ).
cnf(c285,plain,
complement(X) = join(complement(X),complement(X)),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c286,plain,
complement(complement(X)) = complement(join(complement(X),complement(X))),
inference(congruence,[status(thm)],[c285]) ).
cnf(c287,plain,
meet(X,X) = complement(join(complement(X),complement(X))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c288,plain,
complement(join(complement(X),complement(X))) = meet(X,X),
inference(symmetry,[status(thm)],[c287]) ).
cnf(c289,plain,
complement(complement(X)) = meet(X,X),
inference(transitivity,[status(thm)],[c286,c288]) ).
cnf(c290,plain,
join(zero,complement(complement(X))) = join(zero,meet(X,X)),
inference(congruence,[status(thm)],[c289]) ).
cnf(c291,plain,
join(zero,complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c290,c22]) ).
cnf(c292,plain,
complement(complement(X)) = X,
inference(transitivity,[status(thm)],[c284,c291]) ).
cnf(c293,plain,
complement(join(zero,complement(X))) = X,
inference(transitivity,[status(thm)],[c282,c292]) ).
cnf(c294,plain,
meet(X,top) = X,
inference(transitivity,[status(thm)],[c280,c293]) ).
cnf(c295,plain,
meet(top,X) = X,
inference(transitivity,[status(thm)],[c270,c294]) ).
cnf(c296,plain,
meet(top,join(complement(X),complement(X3))) = join(complement(X),complement(X3)),
inference(substitution,[status(thm)],[c295]) ).
cnf(c297,plain,
join(complement(X),complement(X3)) = meet(top,join(complement(X),complement(X3))),
inference(symmetry,[status(thm)],[c296]) ).
cnf(c298,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c221]) ).
cnf(c299,plain,
join(complement(X4),meet(X3,X)) = join(complement(X4),meet(X,X3)),
inference(congruence,[status(thm)],[c298]) ).
cnf(c300,plain,
complement(join(complement(X4),meet(X3,X))) = complement(join(complement(X4),meet(X,X3))),
inference(congruence,[status(thm)],[c299]) ).
cnf(c301,plain,
join(meet(X,X3),complement(X4)) = join(complement(X4),meet(X,X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c302,plain,
join(complement(X4),meet(X,X3)) = join(meet(X,X3),complement(X4)),
inference(symmetry,[status(thm)],[c301]) ).
cnf(c303,plain,
complement(join(complement(X4),meet(X,X3))) = complement(join(meet(X,X3),complement(X4))),
inference(congruence,[status(thm)],[c302]) ).
cnf(c304,plain,
meet(X,X3) = complement(join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c305,plain,
join(meet(X,X3),complement(X4)) = join(complement(join(complement(X),complement(X3))),complement(X4)),
inference(congruence,[status(thm)],[c304]) ).
cnf(c306,plain,
complement(join(meet(X,X3),complement(X4))) = complement(join(complement(join(complement(X),complement(X3))),complement(X4))),
inference(congruence,[status(thm)],[c305]) ).
cnf(c307,plain,
meet(join(complement(X),complement(X3)),X4) = complement(join(complement(join(complement(X),complement(X3))),complement(X4))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c308,plain,
complement(join(complement(join(complement(X),complement(X3))),complement(X4))) = meet(join(complement(X),complement(X3)),X4),
inference(symmetry,[status(thm)],[c307]) ).
cnf(c309,plain,
meet(X4,join(complement(X),complement(X3))) = meet(join(complement(X),complement(X3)),X4),
inference(substitution,[status(thm)],[c221]) ).
cnf(c310,plain,
meet(join(complement(X),complement(X3)),X4) = meet(X4,join(complement(X),complement(X3))),
inference(symmetry,[status(thm)],[c309]) ).
cnf(c311,plain,
join(complement(X),complement(X3)) = join(complement(X3),complement(X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c312,plain,
meet(X4,join(complement(X),complement(X3))) = meet(X4,join(complement(X3),complement(X))),
inference(congruence,[status(thm)],[c311]) ).
cnf(c313,plain,
meet(join(complement(X),complement(X3)),X4) = meet(X4,join(complement(X3),complement(X))),
inference(transitivity,[status(thm)],[c310,c312]) ).
cnf(c314,plain,
complement(join(complement(join(complement(X),complement(X3))),complement(X4))) = meet(X4,join(complement(X3),complement(X))),
inference(transitivity,[status(thm)],[c308,c313]) ).
cnf(c315,plain,
complement(join(meet(X,X3),complement(X4))) = meet(X4,join(complement(X3),complement(X))),
inference(transitivity,[status(thm)],[c306,c314]) ).
cnf(c316,plain,
complement(join(complement(X4),meet(X,X3))) = meet(X4,join(complement(X3),complement(X))),
inference(transitivity,[status(thm)],[c303,c315]) ).
cnf(c317,plain,
complement(join(complement(X4),meet(X3,X))) = meet(X4,join(complement(X3),complement(X))),
inference(transitivity,[status(thm)],[c300,c316]) ).
cnf(c318,plain,
complement(join(complement(top),meet(X,X3))) = meet(top,join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c317]) ).
cnf(c319,plain,
meet(top,join(complement(X),complement(X3))) = complement(join(complement(top),meet(X,X3))),
inference(symmetry,[status(thm)],[c318]) ).
cnf(c320,plain,
join(complement(top),meet(X,X3)) = join(zero,meet(X,X3)),
inference(congruence,[status(thm)],[c41]) ).
cnf(c321,plain,
complement(join(complement(top),meet(X,X3))) = complement(join(zero,meet(X,X3))),
inference(congruence,[status(thm)],[c320]) ).
cnf(c322,plain,
join(zero,meet(X,X3)) = meet(X,X3),
inference(substitution,[status(thm)],[c106]) ).
cnf(c323,plain,
complement(join(zero,meet(X,X3))) = complement(meet(X,X3)),
inference(congruence,[status(thm)],[c322]) ).
cnf(c324,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c221]) ).
cnf(c325,plain,
meet(X,X3) = meet(X3,X),
inference(symmetry,[status(thm)],[c324]) ).
cnf(c326,plain,
complement(meet(X,X3)) = complement(meet(X3,X)),
inference(congruence,[status(thm)],[c325]) ).
cnf(c327,plain,
complement(join(zero,meet(X,X3))) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c323,c326]) ).
cnf(c328,plain,
complement(join(complement(top),meet(X,X3))) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c321,c327]) ).
cnf(c329,plain,
meet(top,join(complement(X),complement(X3))) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c319,c328]) ).
cnf(c330,plain,
join(complement(X),complement(X3)) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c297,c329]) ).
cnf(c331,plain,
join(complement(X3),complement(X)) = complement(meet(X3,X)),
inference(transitivity,[status(thm)],[c269,c330]) ).
cnf(c332,plain,
join(complement(join(zero,complement(X))),complement(X3)) = complement(meet(join(zero,complement(X)),X3)),
inference(substitution,[status(thm)],[c331]) ).
cnf(c333,plain,
complement(meet(join(zero,complement(X)),X3)) = join(complement(join(zero,complement(X))),complement(X3)),
inference(symmetry,[status(thm)],[c332]) ).
cnf(c334,plain,
join(complement(join(zero,complement(X))),complement(X3)) = join(meet(X,top),complement(X3)),
inference(congruence,[status(thm)],[c279]) ).
cnf(c335,plain,
join(meet(X,top),complement(X3)) = join(X,complement(X3)),
inference(congruence,[status(thm)],[c294]) ).
cnf(c336,plain,
join(complement(join(zero,complement(X))),complement(X3)) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c334,c335]) ).
cnf(c337,plain,
complement(meet(join(zero,complement(X)),X3)) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c333,c336]) ).
cnf(c338,plain,
complement(meet(complement(X),X3)) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c267,c337]) ).
cnf(c339,plain,
complement(meet(X3,complement(X))) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c263,c338]) ).
cnf(c340,plain,
complement(meet(X,complement(X3))) = join(X3,complement(X)),
inference(substitution,[status(thm)],[c339]) ).
cnf(c341,plain,
join(X3,complement(X)) = complement(meet(X,complement(X3))),
inference(symmetry,[status(thm)],[c340]) ).
cnf(c342,plain,
join(zero,join(X3,complement(X))) = join(zero,complement(meet(X,complement(X3)))),
inference(congruence,[status(thm)],[c341]) ).
cnf(c343,plain,
complement(join(zero,join(X3,complement(X)))) = complement(join(zero,complement(meet(X,complement(X3))))),
inference(congruence,[status(thm)],[c342]) ).
cnf(c344,plain,
complement(join(zero,complement(meet(X,complement(X3))))) = meet(meet(X,complement(X3)),top),
inference(substitution,[status(thm)],[c279]) ).
cnf(c345,plain,
meet(meet(X,complement(X3)),top) = meet(X,complement(X3)),
inference(substitution,[status(thm)],[c294]) ).
cnf(c346,plain,
complement(join(zero,complement(meet(X,complement(X3))))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c344,c345]) ).
cnf(c347,plain,
complement(join(zero,join(X3,complement(X)))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c343,c346]) ).
cnf(c348,plain,
complement(join(X3,complement(X))) = meet(X,complement(X3)),
inference(transitivity,[status(thm)],[c261,c347]) ).
cnf(c349,plain,
complement(join(X3,complement(join(zero,complement(X))))) = meet(join(zero,complement(X)),complement(X3)),
inference(substitution,[status(thm)],[c348]) ).
cnf(c350,plain,
meet(join(zero,complement(X)),complement(X3)) = complement(join(X3,complement(join(zero,complement(X))))),
inference(symmetry,[status(thm)],[c349]) ).
cnf(c351,plain,
join(X3,complement(join(zero,complement(X)))) = join(X3,meet(X,top)),
inference(congruence,[status(thm)],[c279]) ).
cnf(c352,plain,
complement(join(X3,complement(join(zero,complement(X))))) = complement(join(X3,meet(X,top))),
inference(congruence,[status(thm)],[c351]) ).
cnf(c353,plain,
join(X3,meet(X,top)) = join(X3,X),
inference(congruence,[status(thm)],[c294]) ).
cnf(c354,plain,
complement(join(X3,meet(X,top))) = complement(join(X3,X)),
inference(congruence,[status(thm)],[c353]) ).
cnf(c355,plain,
complement(join(X3,complement(join(zero,complement(X))))) = complement(join(X3,X)),
inference(transitivity,[status(thm)],[c352,c354]) ).
cnf(c356,plain,
meet(join(zero,complement(X)),complement(X3)) = complement(join(X3,X)),
inference(transitivity,[status(thm)],[c350,c355]) ).
cnf(c357,plain,
meet(complement(X),complement(X3)) = complement(join(X3,X)),
inference(transitivity,[status(thm)],[c258,c356]) ).
cnf(c358,plain,
meet(complement(X3),complement(X)) = complement(join(X3,X)),
inference(transitivity,[status(thm)],[c255,c357]) ).
cnf(c359,plain,
meet(complement(X),complement(X3)) = complement(join(X,X3)),
inference(substitution,[status(thm)],[c358]) ).
cnf(c360,plain,
complement(join(X,X3)) = meet(complement(X),complement(X3)),
inference(symmetry,[status(thm)],[c359]) ).
cnf(c361,plain,
meet(X3,complement(join(X,X3))) = meet(X3,meet(complement(X),complement(X3))),
inference(congruence,[status(thm)],[c360]) ).
cnf(c362,plain,
meet(X,complement(X3)) = meet(complement(X3),X),
inference(substitution,[status(thm)],[c221]) ).
cnf(c363,plain,
meet(X3,meet(X,complement(X3))) = meet(X3,meet(complement(X3),X)),
inference(congruence,[status(thm)],[c362]) ).
cnf(c364,plain,
meet(X3,meet(complement(X3),X)) = complement(join(complement(X3),complement(meet(complement(X3),X)))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c365,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c221]) ).
cnf(c366,plain,
complement(meet(X3,X)) = complement(meet(X,X3)),
inference(congruence,[status(thm)],[c365]) ).
cnf(c367,plain,
join(X3,complement(meet(X3,X))) = join(X3,complement(meet(X,X3))),
inference(congruence,[status(thm)],[c366]) ).
cnf(c368,plain,
join(complement(X),complement(X3)) = complement(meet(X,X3)),
inference(substitution,[status(thm)],[c331]) ).
cnf(c369,plain,
complement(meet(X,X3)) = join(complement(X),complement(X3)),
inference(symmetry,[status(thm)],[c368]) ).
cnf(c370,plain,
join(X3,complement(meet(X,X3))) = join(X3,join(complement(X),complement(X3))),
inference(congruence,[status(thm)],[c369]) ).
cnf(c371,plain,
join(X3,join(complement(X),complement(X3))) = join(complement(X),top),
inference(substitution,[status(thm)],[c125]) ).
cnf(c372,plain,
join(complement(X),top) = top,
inference(substitution,[status(thm)],[c146]) ).
cnf(c373,plain,
join(X3,join(complement(X),complement(X3))) = top,
inference(transitivity,[status(thm)],[c371,c372]) ).
cnf(c374,plain,
join(X3,complement(meet(X,X3))) = top,
inference(transitivity,[status(thm)],[c370,c373]) ).
cnf(c375,plain,
join(X3,complement(meet(X3,X))) = top,
inference(transitivity,[status(thm)],[c367,c374]) ).
cnf(c376,plain,
join(complement(X3),complement(meet(complement(X3),X))) = top,
inference(substitution,[status(thm)],[c375]) ).
cnf(c377,plain,
complement(join(complement(X3),complement(meet(complement(X3),X)))) = complement(top),
inference(congruence,[status(thm)],[c376]) ).
cnf(c378,plain,
complement(join(complement(X3),complement(meet(complement(X3),X)))) = zero,
inference(transitivity,[status(thm)],[c377,c41]) ).
cnf(c379,plain,
meet(X3,meet(complement(X3),X)) = zero,
inference(transitivity,[status(thm)],[c364,c378]) ).
cnf(c380,plain,
meet(X3,meet(X,complement(X3))) = zero,
inference(transitivity,[status(thm)],[c363,c379]) ).
cnf(c381,plain,
meet(X3,meet(complement(X),complement(X3))) = zero,
inference(substitution,[status(thm)],[c380]) ).
cnf(c382,plain,
meet(X3,complement(join(X,X3))) = zero,
inference(transitivity,[status(thm)],[c361,c381]) ).
cnf(c383,plain,
meet(X3,complement(join(X3,X))) = zero,
inference(transitivity,[status(thm)],[c254,c382]) ).
cnf(c384,plain,
meet(X3,complement(join(X,X3))) = zero,
inference(transitivity,[status(thm)],[c250,c383]) ).
cnf(c385,plain,
meet(composition(converse(x0),composition(x0,X)),complement(join(X,composition(converse(x0),composition(x0,X))))) = zero,
inference(substitution,[status(thm)],[c384]) ).
cnf(c386,plain,
meet(composition(converse(x0),composition(x0,X)),complement(X)) = zero,
inference(transitivity,[status(thm)],[c246,c385]) ).
cnf(c387,plain,
meet(complement(X),composition(converse(x0),composition(x0,X))) = zero,
inference(transitivity,[status(thm)],[c225,c386]) ).
cnf(c388,plain,
zero = meet(complement(X),composition(converse(x0),composition(x0,X))),
inference(symmetry,[status(thm)],[c387]) ).
cnf(c389,plain,
composition(meet(x0,composition(composition(x0,X),converse(complement(X)))),zero) = composition(meet(x0,composition(composition(x0,X),converse(complement(X)))),meet(complement(X),composition(converse(x0),composition(x0,X)))),
inference(congruence,[status(thm)],[c388]) ).
cnf(c390,plain,
join(meet(composition(x0,complement(X)),composition(x0,X)),composition(meet(x0,composition(composition(x0,X),converse(complement(X)))),zero)) = join(meet(composition(x0,complement(X)),composition(x0,X)),composition(meet(x0,composition(composition(x0,X),converse(complement(X)))),meet(complement(X),composition(converse(x0),composition(x0,X))))),
inference(congruence,[status(thm)],[c389]) ).
cnf(c391,axiom,
join(meet(composition(X0_2,X1_2),X2_2),composition(meet(X0_2,composition(X2_2,converse(X1_2))),meet(X1_2,composition(converse(X0_2),X2_2)))) = composition(meet(X0_2,composition(X2_2,converse(X1_2))),meet(X1_2,composition(converse(X0_2),X2_2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dedekind_law) ).
cnf(c392,plain,
join(meet(composition(x0,complement(X)),composition(x0,X)),composition(meet(x0,composition(composition(x0,X),converse(complement(X)))),meet(complement(X),composition(converse(x0),composition(x0,X))))) = composition(meet(x0,composition(composition(x0,X),converse(complement(X)))),meet(complement(X),composition(converse(x0),composition(x0,X)))),
inference(substitution,[status(thm)],[c391]) ).
cnf(c393,plain,
composition(meet(x0,composition(composition(x0,X),converse(complement(X)))),meet(complement(X),composition(converse(x0),composition(x0,X)))) = composition(meet(x0,composition(composition(x0,X),converse(complement(X)))),zero),
inference(congruence,[status(thm)],[c387]) ).
cnf(c394,plain,
composition(meet(x0,composition(composition(x0,X),converse(complement(X)))),zero) = zero,
inference(substitution,[status(thm)],[c210]) ).
cnf(c395,plain,
composition(meet(x0,composition(composition(x0,X),converse(complement(X)))),meet(complement(X),composition(converse(x0),composition(x0,X)))) = zero,
inference(transitivity,[status(thm)],[c393,c394]) ).
cnf(c396,plain,
join(meet(composition(x0,complement(X)),composition(x0,X)),composition(meet(x0,composition(composition(x0,X),converse(complement(X)))),meet(complement(X),composition(converse(x0),composition(x0,X))))) = zero,
inference(transitivity,[status(thm)],[c392,c395]) ).
cnf(c397,plain,
join(meet(composition(x0,complement(X)),composition(x0,X)),composition(meet(x0,composition(composition(x0,X),converse(complement(X)))),zero)) = zero,
inference(transitivity,[status(thm)],[c390,c396]) ).
cnf(c398,plain,
join(meet(composition(x0,X),composition(x0,complement(X))),composition(meet(x0,composition(composition(x0,X),converse(complement(X)))),zero)) = zero,
inference(transitivity,[status(thm)],[c224,c397]) ).
cnf(c399,plain,
join(meet(composition(x0,X),composition(x0,complement(X))),zero) = zero,
inference(transitivity,[status(thm)],[c213,c398]) ).
cnf(c400,plain,
meet(composition(x0,X),composition(x0,complement(X))) = zero,
inference(transitivity,[status(thm)],[c103,c399]) ).
cnf(c401,plain,
meet(composition(x0,x1),composition(x0,complement(x1))) = zero,
inference(substitution,[status(thm)],[c400]) ).
cnf(c402,plain,
$false,
inference(resolution,[status(thm)],[c4,c401]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL041+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.39 % Computer : n009.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 22:56:15 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.14/2.99 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 19.14/2.99
% 19.14/2.99 % SZS status Theorem
% 19.14/2.99
% 19.14/3.02 % SZS output start CNFRefutation
% See solution above
% 22.42/3.32
% 22.42/3.32 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------