%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL043+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 12:33:31 PM UTC 2026
% Result : Theorem 12.62s 2.28s
% Output : CNFRefutation 15.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 70
% Number of leaves : 17
% Syntax : Number of formulae : 553 ( 547 unt; 0 def)
% Number of atoms : 559 ( 558 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 5 ~; 0 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 826 ( 64 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c1,conjecture,
! [X0,X1,X2] :
( join(composition(X0,converse(X1)),X2) = X2
=> join(composition(complement(X2),X1),complement(X0)) = complement(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c2,negated_conjecture,
~ ! [X0_2,X1_2,X2_2] :
( join(composition(X0_2,converse(X1_2)),X2_2) = X2_2
=> join(composition(complement(X2_2),X1_2),complement(X0_2)) = complement(X0_2) ),
inference(negate_conjecture,[status(cth)],[c1]) ).
fof(c3,plain,
( join(composition(x0,converse(x1)),x2) = x2
& join(composition(complement(x2),x1),complement(x0)) != complement(x0) ),
inference(clausify,[status(esa)],[c2]) ).
cnf(c4,plain,
join(composition(complement(x2),x1),complement(x0)) != complement(x0),
inference(clausify,[status(thm)],[c3]) ).
cnf(c5,axiom,
join(X0_2,X1_2) = join(X1_2,X0_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
cnf(c6,plain,
join(meet(join(X,complement(X3)),meet(X3,X)),complement(X3)) = join(complement(X3),meet(join(X,complement(X3)),meet(X3,X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
join(complement(X3),meet(join(X,complement(X3)),meet(X3,X))) = join(meet(join(X,complement(X3)),meet(X3,X)),complement(X3)),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
join(meet(X,X3),complement(join(X3,complement(X)))) = join(complement(join(X3,complement(X))),meet(X,X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c9,plain,
join(complement(join(X3,complement(X))),meet(X,X3)) = join(meet(X,X3),complement(join(X3,complement(X)))),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
join(X3,complement(X)) = join(complement(X),X3),
inference(substitution,[status(thm)],[c5]) ).
cnf(c11,plain,
complement(join(X3,complement(X))) = complement(join(complement(X),X3)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
join(meet(X,X3),complement(join(X3,complement(X)))) = join(meet(X,X3),complement(join(complement(X),X3))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,axiom,
meet(X0_2,X1_2) = complement(join(complement(X0_2),complement(X1_2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
cnf(c14,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c13]) ).
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/sandbox/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,X3),complement(join(complement(X),X3))) = X,
inference(substitution,[status(thm)],[c19]) ).
cnf(c21,plain,
join(meet(X,X3),complement(join(X3,complement(X)))) = X,
inference(transitivity,[status(thm)],[c12,c20]) ).
cnf(c22,plain,
join(complement(join(X3,complement(X))),meet(X,X3)) = X,
inference(transitivity,[status(thm)],[c9,c21]) ).
cnf(c23,plain,
join(complement(join(X,complement(X3))),meet(X3,X)) = X3,
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
X3 = join(complement(join(X,complement(X3))),meet(X3,X)),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
complement(X3) = complement(join(complement(join(X,complement(X3))),meet(X3,X))),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
join(meet(join(X,complement(X3)),meet(X3,X)),complement(X3)) = join(meet(join(X,complement(X3)),meet(X3,X)),complement(join(complement(join(X,complement(X3))),meet(X3,X)))),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
join(meet(join(X,complement(X3)),meet(X3,X)),complement(join(complement(join(X,complement(X3))),meet(X3,X)))) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c28,plain,
join(meet(join(X,complement(X3)),meet(X3,X)),complement(X3)) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c26,c27]) ).
cnf(c29,plain,
join(complement(X3),meet(join(X,complement(X3)),meet(X3,X))) = join(X,complement(X3)),
inference(transitivity,[status(thm)],[c7,c28]) ).
cnf(c30,plain,
join(complement(x0),meet(join(composition(complement(x2),x1),complement(x0)),meet(x0,composition(complement(x2),x1)))) = join(composition(complement(x2),x1),complement(x0)),
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
join(composition(complement(x2),x1),complement(x0)) = join(complement(x0),meet(join(composition(complement(x2),x1),complement(x0)),meet(x0,composition(complement(x2),x1)))),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
meet(X,X3) = complement(join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c33,plain,
join(complement(X3),complement(X)) = join(complement(X),complement(X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c34,plain,
join(complement(X),complement(X3)) = join(complement(X3),complement(X)),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
complement(join(complement(X),complement(X3))) = complement(join(complement(X3),complement(X))),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c37,plain,
complement(join(complement(X3),complement(X))) = meet(X3,X),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
complement(join(complement(X),complement(X3))) = meet(X3,X),
inference(transitivity,[status(thm)],[c35,c37]) ).
cnf(c39,plain,
meet(X,X3) = meet(X3,X),
inference(transitivity,[status(thm)],[c32,c38]) ).
cnf(c40,plain,
meet(x0,composition(complement(x2),x1)) = meet(composition(complement(x2),x1),x0),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
join(complement(join(complement(X3),X)),X4) = join(X4,complement(join(complement(X3),X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c42,plain,
join(X,complement(join(complement(X4),X3))) = join(complement(join(complement(X4),X3)),X),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
join(meet(X4,X3),join(X,complement(join(complement(X4),X3)))) = join(meet(X4,X3),join(complement(join(complement(X4),X3)),X)),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,axiom,
join(X0_2,join(X1_2,X2_2)) = join(join(X0_2,X1_2),X2_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity) ).
cnf(c45,plain,
join(meet(X4,X3),join(complement(join(complement(X4),X3)),X)) = join(join(meet(X4,X3),complement(join(complement(X4),X3))),X),
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
join(join(meet(X4,X3),complement(join(complement(X4),X3))),X) = join(X4,X),
inference(congruence,[status(thm)],[c19]) ).
cnf(c47,plain,
join(meet(X4,X3),join(complement(join(complement(X4),X3)),X)) = join(X4,X),
inference(transitivity,[status(thm)],[c45,c46]) ).
cnf(c48,plain,
join(meet(X4,X3),join(X,complement(join(complement(X4),X3)))) = join(X4,X),
inference(transitivity,[status(thm)],[c43,c47]) ).
cnf(c49,plain,
join(meet(X3,X),join(zero,complement(join(complement(X3),X)))) = join(X3,zero),
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
join(X3,zero) = join(meet(X3,X),join(zero,complement(join(complement(X3),X)))),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
join(complement(X),zero) = join(zero,complement(X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c52,plain,
join(zero,complement(X)) = join(complement(X),zero),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c39]) ).
cnf(c54,plain,
join(meet(X3,X),complement(join(complement(X),X3))) = join(meet(X,X3),complement(join(complement(X),X3))),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
join(meet(X,X3),complement(join(complement(X),X3))) = X,
inference(substitution,[status(thm)],[c19]) ).
cnf(c56,plain,
join(meet(X3,X),complement(join(complement(X),X3))) = X,
inference(transitivity,[status(thm)],[c54,c55]) ).
cnf(c57,plain,
join(meet(top,meet(X,zero)),complement(join(complement(meet(X,zero)),top))) = meet(X,zero),
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,plain,
meet(X,zero) = join(meet(top,meet(X,zero)),complement(join(complement(meet(X,zero)),top))),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,plain,
meet(X,zero) = meet(zero,X),
inference(substitution,[status(thm)],[c39]) ).
cnf(c60,plain,
meet(top,meet(X,zero)) = meet(top,meet(zero,X)),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
meet(top,meet(zero,X)) = meet(meet(zero,X),top),
inference(substitution,[status(thm)],[c39]) ).
cnf(c62,axiom,
top = join(X0_2,complement(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
cnf(c63,plain,
top = join(complement(X),complement(complement(X))),
inference(substitution,[status(thm)],[c62]) ).
cnf(c64,plain,
complement(top) = complement(join(complement(X),complement(complement(X)))),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
meet(X,complement(X)) = complement(join(complement(X),complement(complement(X)))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c66,plain,
complement(join(complement(X),complement(complement(X)))) = meet(X,complement(X)),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c67,axiom,
zero = meet(X0_2,complement(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
cnf(c68,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c69,plain,
meet(X,complement(X)) = zero,
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
complement(join(complement(X),complement(complement(X)))) = zero,
inference(transitivity,[status(thm)],[c66,c69]) ).
cnf(c71,plain,
complement(top) = zero,
inference(transitivity,[status(thm)],[c64,c70]) ).
cnf(c72,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
join(zero,complement(X)) = join(complement(top),complement(X)),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
complement(join(zero,complement(X))) = complement(join(complement(top),complement(X))),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
meet(top,X) = complement(join(complement(top),complement(X))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c76,plain,
complement(join(complement(top),complement(X))) = meet(top,X),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c77,plain,
meet(X,top) = meet(top,X),
inference(substitution,[status(thm)],[c39]) ).
cnf(c78,plain,
meet(top,X) = meet(X,top),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,plain,
complement(join(complement(top),complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c76,c78]) ).
cnf(c80,plain,
complement(join(zero,complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c74,c79]) ).
cnf(c81,plain,
complement(join(zero,complement(meet(zero,X)))) = meet(meet(zero,X),top),
inference(substitution,[status(thm)],[c80]) ).
cnf(c82,plain,
meet(meet(zero,X),top) = complement(join(zero,complement(meet(zero,X)))),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,plain,
join(meet(X3,X),join(complement(meet(X3,X)),complement(join(complement(X3),X)))) = join(X3,complement(meet(X3,X))),
inference(substitution,[status(thm)],[c48]) ).
cnf(c84,plain,
join(X3,complement(meet(X3,X))) = join(meet(X3,X),join(complement(meet(X3,X)),complement(join(complement(X3),X)))),
inference(symmetry,[status(thm)],[c83]) ).
cnf(c85,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c86,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c87,plain,
join(X3,join(complement(X3),X)) = join(X3,join(X,complement(X3))),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c89,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c90,plain,
join(X3,join(X,complement(X3))) = join(X3,join(complement(X3),X)),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
join(X3,join(complement(X3),X)) = join(join(X3,complement(X3)),X),
inference(substitution,[status(thm)],[c44]) ).
cnf(c92,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c62]) ).
cnf(c93,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
join(join(X3,complement(X3)),X) = join(top,X),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
join(top,X) = join(X,top),
inference(substitution,[status(thm)],[c5]) ).
cnf(c96,plain,
join(join(X3,complement(X3)),X) = join(X,top),
inference(transitivity,[status(thm)],[c94,c95]) ).
cnf(c97,plain,
join(X3,join(complement(X3),X)) = join(X,top),
inference(transitivity,[status(thm)],[c91,c96]) ).
cnf(c98,plain,
join(X3,join(X,complement(X3))) = join(X,top),
inference(transitivity,[status(thm)],[c90,c97]) ).
cnf(c99,plain,
join(X3,join(complement(X3),X)) = join(X,top),
inference(transitivity,[status(thm)],[c87,c98]) ).
cnf(c100,plain,
join(meet(X3,X),join(complement(meet(X3,X)),complement(join(complement(X3),X)))) = join(complement(join(complement(X3),X)),top),
inference(substitution,[status(thm)],[c99]) ).
cnf(c101,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c62]) ).
cnf(c102,plain,
join(X3,top) = join(X3,join(X,complement(X))),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,plain,
join(complement(X),X) = join(X,complement(X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c104,plain,
join(X,complement(X)) = join(complement(X),X),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,plain,
join(X3,join(X,complement(X))) = join(X3,join(complement(X),X)),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
join(join(X3,X),X4) = join(X4,join(X3,X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c107,plain,
join(X4,join(X3,X)) = join(join(X3,X),X4),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c108,plain,
join(X3,join(X,X4)) = join(join(X3,X),X4),
inference(substitution,[status(thm)],[c44]) ).
cnf(c109,plain,
join(join(X3,X),X4) = join(X3,join(X,X4)),
inference(symmetry,[status(thm)],[c108]) ).
cnf(c110,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c111,plain,
join(X3,join(X,X4)) = join(X3,join(X4,X)),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
join(join(X3,X),X4) = join(X3,join(X4,X)),
inference(transitivity,[status(thm)],[c109,c111]) ).
cnf(c113,plain,
join(X4,join(X3,X)) = join(X3,join(X4,X)),
inference(transitivity,[status(thm)],[c107,c112]) ).
cnf(c114,plain,
join(complement(X),join(X3,X)) = join(X3,join(complement(X),X)),
inference(substitution,[status(thm)],[c113]) ).
cnf(c115,plain,
join(X3,join(complement(X),X)) = join(complement(X),join(X3,X)),
inference(symmetry,[status(thm)],[c114]) ).
cnf(c116,plain,
join(complement(X),join(X3,X)) = join(join(complement(X),X3),X),
inference(substitution,[status(thm)],[c44]) ).
cnf(c117,plain,
join(meet(X,X3),complement(join(complement(X),X3))) = X,
inference(substitution,[status(thm)],[c19]) ).
cnf(c118,plain,
X = join(meet(X,X3),complement(join(complement(X),X3))),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,plain,
join(join(complement(X),X3),X) = join(join(complement(X),X3),join(meet(X,X3),complement(join(complement(X),X3)))),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
join(join(complement(X),X3),join(meet(X,X3),complement(join(complement(X),X3)))) = join(meet(X,X3),top),
inference(substitution,[status(thm)],[c98]) ).
cnf(c121,plain,
join(meet(X,X3),top) = join(top,meet(X,X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c122,axiom,
composition(X0_2,one) = X0_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).
cnf(c123,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c122]) ).
cnf(c124,plain,
X = composition(X,one),
inference(symmetry,[status(thm)],[c123]) ).
cnf(c125,plain,
meet(X3,X) = meet(X3,composition(X,one)),
inference(congruence,[status(thm)],[c124]) ).
cnf(c126,plain,
join(top,meet(X3,X)) = join(top,meet(X3,composition(X,one))),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
meet(X4,composition(X3,X)) = meet(composition(X3,X),X4),
inference(substitution,[status(thm)],[c39]) ).
cnf(c128,plain,
join(top,meet(X4,composition(X3,X))) = join(top,meet(composition(X3,X),X4)),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
join(meet(composition(X3,X),X4),top) = join(top,meet(composition(X3,X),X4)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c130,plain,
join(top,meet(composition(X3,X),X4)) = join(meet(composition(X3,X),X4),top),
inference(symmetry,[status(thm)],[c129]) ).
cnf(c131,plain,
top = join(meet(composition(X3,meet(X,composition(converse(X3),X4))),X4),complement(meet(composition(X3,meet(X,composition(converse(X3),X4))),X4))),
inference(substitution,[status(thm)],[c62]) ).
cnf(c132,plain,
join(meet(composition(X3,X),X4),top) = join(meet(composition(X3,X),X4),join(meet(composition(X3,meet(X,composition(converse(X3),X4))),X4),complement(meet(composition(X3,meet(X,composition(converse(X3),X4))),X4)))),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,axiom,
join(meet(composition(X0_2,X1_2),X2_2),meet(composition(X0_2,meet(X1_2,composition(converse(X0_2),X2_2))),X2_2)) = meet(composition(X0_2,meet(X1_2,composition(converse(X0_2),X2_2))),X2_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular_law_1) ).
cnf(c134,plain,
join(meet(composition(X3,X),X4),meet(composition(X3,meet(X,composition(converse(X3),X4))),X4)) = meet(composition(X3,meet(X,composition(converse(X3),X4))),X4),
inference(substitution,[status(thm)],[c133]) ).
cnf(c135,plain,
meet(composition(X3,meet(X,composition(converse(X3),X4))),X4) = join(meet(composition(X3,X),X4),meet(composition(X3,meet(X,composition(converse(X3),X4))),X4)),
inference(symmetry,[status(thm)],[c134]) ).
cnf(c136,plain,
complement(meet(composition(X3,meet(X,composition(converse(X3),X4))),X4)) = complement(join(meet(composition(X3,X),X4),meet(composition(X3,meet(X,composition(converse(X3),X4))),X4))),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
join(meet(composition(X3,meet(X,composition(converse(X3),X4))),X4),complement(meet(composition(X3,meet(X,composition(converse(X3),X4))),X4))) = join(meet(composition(X3,meet(X,composition(converse(X3),X4))),X4),complement(join(meet(composition(X3,X),X4),meet(composition(X3,meet(X,composition(converse(X3),X4))),X4)))),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
join(meet(composition(X3,X),X4),join(meet(composition(X3,meet(X,composition(converse(X3),X4))),X4),complement(meet(composition(X3,meet(X,composition(converse(X3),X4))),X4)))) = join(meet(composition(X3,X),X4),join(meet(composition(X3,meet(X,composition(converse(X3),X4))),X4),complement(join(meet(composition(X3,X),X4),meet(composition(X3,meet(X,composition(converse(X3),X4))),X4))))),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,plain,
join(X3,join(X,complement(join(X3,X)))) = join(join(X3,X),complement(join(X3,X))),
inference(substitution,[status(thm)],[c44]) ).
cnf(c140,plain,
top = join(join(X3,X),complement(join(X3,X))),
inference(substitution,[status(thm)],[c62]) ).
cnf(c141,plain,
join(join(X3,X),complement(join(X3,X))) = top,
inference(symmetry,[status(thm)],[c140]) ).
cnf(c142,plain,
join(X3,join(X,complement(join(X3,X)))) = top,
inference(transitivity,[status(thm)],[c139,c141]) ).
cnf(c143,plain,
join(meet(composition(X3,X),X4),join(meet(composition(X3,meet(X,composition(converse(X3),X4))),X4),complement(join(meet(composition(X3,X),X4),meet(composition(X3,meet(X,composition(converse(X3),X4))),X4))))) = top,
inference(substitution,[status(thm)],[c142]) ).
cnf(c144,plain,
join(meet(composition(X3,X),X4),join(meet(composition(X3,meet(X,composition(converse(X3),X4))),X4),complement(meet(composition(X3,meet(X,composition(converse(X3),X4))),X4)))) = top,
inference(transitivity,[status(thm)],[c138,c143]) ).
cnf(c145,plain,
join(meet(composition(X3,X),X4),top) = top,
inference(transitivity,[status(thm)],[c132,c144]) ).
cnf(c146,plain,
join(top,meet(composition(X3,X),X4)) = top,
inference(transitivity,[status(thm)],[c130,c145]) ).
cnf(c147,plain,
join(top,meet(X4,composition(X3,X))) = top,
inference(transitivity,[status(thm)],[c128,c146]) ).
cnf(c148,plain,
join(top,meet(X3,composition(X,one))) = top,
inference(substitution,[status(thm)],[c147]) ).
cnf(c149,plain,
join(top,meet(X3,X)) = top,
inference(transitivity,[status(thm)],[c126,c148]) ).
cnf(c150,plain,
join(top,meet(X,X3)) = top,
inference(substitution,[status(thm)],[c149]) ).
cnf(c151,plain,
join(meet(X,X3),top) = top,
inference(transitivity,[status(thm)],[c121,c150]) ).
cnf(c152,plain,
join(join(complement(X),X3),join(meet(X,X3),complement(join(complement(X),X3)))) = top,
inference(transitivity,[status(thm)],[c120,c151]) ).
cnf(c153,plain,
join(join(complement(X),X3),X) = top,
inference(transitivity,[status(thm)],[c119,c152]) ).
cnf(c154,plain,
join(complement(X),join(X3,X)) = top,
inference(transitivity,[status(thm)],[c116,c153]) ).
cnf(c155,plain,
join(X3,join(complement(X),X)) = top,
inference(transitivity,[status(thm)],[c115,c154]) ).
cnf(c156,plain,
join(X3,join(X,complement(X))) = top,
inference(transitivity,[status(thm)],[c105,c155]) ).
cnf(c157,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c102,c156]) ).
cnf(c158,plain,
join(complement(join(complement(X3),X)),top) = top,
inference(substitution,[status(thm)],[c157]) ).
cnf(c159,plain,
join(meet(X3,X),join(complement(meet(X3,X)),complement(join(complement(X3),X)))) = top,
inference(transitivity,[status(thm)],[c100,c158]) ).
cnf(c160,plain,
join(X3,complement(meet(X3,X))) = top,
inference(transitivity,[status(thm)],[c84,c159]) ).
cnf(c161,plain,
join(zero,complement(meet(zero,X))) = top,
inference(substitution,[status(thm)],[c160]) ).
cnf(c162,plain,
complement(join(zero,complement(meet(zero,X)))) = complement(top),
inference(congruence,[status(thm)],[c161]) ).
cnf(c163,plain,
complement(join(zero,complement(meet(zero,X)))) = zero,
inference(transitivity,[status(thm)],[c162,c71]) ).
cnf(c164,plain,
meet(meet(zero,X),top) = zero,
inference(transitivity,[status(thm)],[c82,c163]) ).
cnf(c165,plain,
meet(top,meet(zero,X)) = zero,
inference(transitivity,[status(thm)],[c61,c164]) ).
cnf(c166,plain,
meet(top,meet(X,zero)) = zero,
inference(transitivity,[status(thm)],[c60,c165]) ).
cnf(c167,plain,
join(meet(top,meet(X,zero)),complement(join(complement(meet(X,zero)),top))) = join(zero,complement(join(complement(meet(X,zero)),top))),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,plain,
join(complement(meet(X,zero)),top) = top,
inference(substitution,[status(thm)],[c157]) ).
cnf(c169,plain,
complement(join(complement(meet(X,zero)),top)) = complement(top),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,plain,
join(zero,complement(join(complement(meet(X,zero)),top))) = join(zero,complement(top)),
inference(congruence,[status(thm)],[c169]) ).
cnf(c171,plain,
join(zero,complement(top)) = join(zero,zero),
inference(congruence,[status(thm)],[c71]) ).
cnf(c172,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c173,plain,
join(zero,zero) = join(zero,complement(top)),
inference(congruence,[status(thm)],[c172]) ).
cnf(c174,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c175,plain,
join(zero,complement(top)) = join(complement(top),complement(top)),
inference(congruence,[status(thm)],[c174]) ).
cnf(c176,axiom,
converse(composition(X0_2,X1_2)) = composition(converse(X1_2),converse(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
cnf(c177,plain,
converse(composition(converse(X3),X)) = composition(converse(X),converse(converse(X3))),
inference(substitution,[status(thm)],[c176]) ).
cnf(c178,axiom,
converse(converse(X0_2)) = X0_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
cnf(c179,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c178]) ).
cnf(c180,plain,
composition(converse(X),converse(converse(X3))) = composition(converse(X),X3),
inference(congruence,[status(thm)],[c179]) ).
cnf(c181,plain,
converse(composition(converse(X3),X)) = composition(converse(X),X3),
inference(transitivity,[status(thm)],[c177,c180]) ).
cnf(c182,plain,
converse(composition(converse(X),one)) = composition(converse(one),X),
inference(substitution,[status(thm)],[c181]) ).
cnf(c183,plain,
composition(converse(one),X) = converse(composition(converse(X),one)),
inference(symmetry,[status(thm)],[c182]) ).
cnf(c184,plain,
composition(converse(X),one) = converse(X),
inference(substitution,[status(thm)],[c122]) ).
cnf(c185,plain,
converse(composition(converse(X),one)) = converse(converse(X)),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c178]) ).
cnf(c187,plain,
converse(composition(converse(X),one)) = X,
inference(transitivity,[status(thm)],[c185,c186]) ).
cnf(c188,plain,
composition(converse(one),X) = X,
inference(transitivity,[status(thm)],[c183,c187]) ).
cnf(c189,plain,
composition(converse(one),composition(one,X)) = composition(one,X),
inference(substitution,[status(thm)],[c188]) ).
cnf(c190,plain,
composition(one,X) = composition(converse(one),composition(one,X)),
inference(symmetry,[status(thm)],[c189]) ).
cnf(c191,axiom,
composition(X0_2,composition(X1_2,X2_2)) = composition(composition(X0_2,X1_2),X2_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity) ).
cnf(c192,plain,
composition(X3,composition(one,X)) = composition(composition(X3,one),X),
inference(substitution,[status(thm)],[c191]) ).
cnf(c193,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c122]) ).
cnf(c194,plain,
composition(composition(X3,one),X) = composition(X3,X),
inference(congruence,[status(thm)],[c193]) ).
cnf(c195,plain,
composition(X3,composition(one,X)) = composition(X3,X),
inference(transitivity,[status(thm)],[c192,c194]) ).
cnf(c196,plain,
composition(converse(one),composition(one,X)) = composition(converse(one),X),
inference(substitution,[status(thm)],[c195]) ).
cnf(c197,plain,
composition(converse(one),composition(one,X)) = X,
inference(transitivity,[status(thm)],[c196,c188]) ).
cnf(c198,plain,
composition(one,X) = X,
inference(transitivity,[status(thm)],[c190,c197]) ).
cnf(c199,plain,
X = composition(one,X),
inference(symmetry,[status(thm)],[c198]) ).
cnf(c200,plain,
complement(X) = complement(composition(one,X)),
inference(congruence,[status(thm)],[c199]) ).
cnf(c201,plain,
join(complement(X),complement(X)) = join(complement(X),complement(composition(one,X))),
inference(congruence,[status(thm)],[c200]) ).
cnf(c202,plain,
converse(converse(one)) = one,
inference(substitution,[status(thm)],[c178]) ).
cnf(c203,plain,
one = converse(converse(one)),
inference(symmetry,[status(thm)],[c202]) ).
cnf(c204,plain,
composition(one,X) = composition(converse(converse(one)),X),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
complement(composition(one,X)) = complement(composition(converse(converse(one)),X)),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
join(complement(X),complement(composition(one,X))) = join(complement(X),complement(composition(converse(converse(one)),X))),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
composition(converse(one),complement(composition(converse(converse(one)),X))) = complement(composition(converse(converse(one)),X)),
inference(substitution,[status(thm)],[c188]) ).
cnf(c208,plain,
complement(composition(converse(converse(one)),X)) = composition(converse(one),complement(composition(converse(converse(one)),X))),
inference(symmetry,[status(thm)],[c207]) ).
cnf(c209,plain,
join(complement(X),complement(composition(converse(converse(one)),X))) = join(complement(X),composition(converse(one),complement(composition(converse(converse(one)),X)))),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c178]) ).
cnf(c211,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c210]) ).
cnf(c212,plain,
composition(X,complement(composition(converse(X),X3))) = composition(converse(converse(X)),complement(composition(converse(X),X3))),
inference(congruence,[status(thm)],[c211]) ).
cnf(c213,plain,
join(complement(X3),composition(X,complement(composition(converse(X),X3)))) = join(complement(X3),composition(converse(converse(X)),complement(composition(converse(X),X3)))),
inference(congruence,[status(thm)],[c212]) ).
cnf(c214,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(c215,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)],[c214]) ).
cnf(c216,axiom,
join(composition(converse(X0_2),complement(composition(X0_2,X1_2))),complement(X1_2)) = complement(X1_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity) ).
cnf(c217,plain,
join(composition(converse(X),complement(composition(X,X3))),complement(X3)) = complement(X3),
inference(substitution,[status(thm)],[c216]) ).
cnf(c218,plain,
join(complement(X3),composition(converse(X),complement(composition(X,X3)))) = complement(X3),
inference(transitivity,[status(thm)],[c215,c217]) ).
cnf(c219,plain,
join(complement(X3),composition(converse(converse(X)),complement(composition(converse(X),X3)))) = complement(X3),
inference(substitution,[status(thm)],[c218]) ).
cnf(c220,plain,
join(complement(X3),composition(X,complement(composition(converse(X),X3)))) = complement(X3),
inference(transitivity,[status(thm)],[c213,c219]) ).
cnf(c221,plain,
join(complement(X),composition(converse(one),complement(composition(converse(converse(one)),X)))) = complement(X),
inference(substitution,[status(thm)],[c220]) ).
cnf(c222,plain,
join(complement(X),complement(composition(converse(converse(one)),X))) = complement(X),
inference(transitivity,[status(thm)],[c209,c221]) ).
cnf(c223,plain,
join(complement(X),complement(composition(one,X))) = complement(X),
inference(transitivity,[status(thm)],[c206,c222]) ).
cnf(c224,plain,
join(complement(X),complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c201,c223]) ).
cnf(c225,plain,
join(complement(top),complement(top)) = complement(top),
inference(substitution,[status(thm)],[c224]) ).
cnf(c226,plain,
join(complement(top),complement(top)) = zero,
inference(transitivity,[status(thm)],[c225,c71]) ).
cnf(c227,plain,
join(zero,complement(top)) = zero,
inference(transitivity,[status(thm)],[c175,c226]) ).
cnf(c228,plain,
join(zero,zero) = zero,
inference(transitivity,[status(thm)],[c173,c227]) ).
cnf(c229,plain,
join(zero,complement(top)) = zero,
inference(transitivity,[status(thm)],[c171,c228]) ).
cnf(c230,plain,
join(zero,complement(join(complement(meet(X,zero)),top))) = zero,
inference(transitivity,[status(thm)],[c170,c229]) ).
cnf(c231,plain,
join(meet(top,meet(X,zero)),complement(join(complement(meet(X,zero)),top))) = zero,
inference(transitivity,[status(thm)],[c167,c230]) ).
cnf(c232,plain,
meet(X,zero) = zero,
inference(transitivity,[status(thm)],[c58,c231]) ).
cnf(c233,plain,
meet(complement(X),zero) = zero,
inference(substitution,[status(thm)],[c232]) ).
cnf(c234,plain,
zero = meet(complement(X),zero),
inference(symmetry,[status(thm)],[c233]) ).
cnf(c235,plain,
join(complement(X),zero) = join(complement(X),meet(complement(X),zero)),
inference(congruence,[status(thm)],[c234]) ).
cnf(c236,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c237,plain,
meet(complement(X),zero) = meet(complement(X),complement(top)),
inference(congruence,[status(thm)],[c236]) ).
cnf(c238,plain,
join(complement(X),meet(complement(X),zero)) = join(complement(X),meet(complement(X),complement(top))),
inference(congruence,[status(thm)],[c237]) ).
cnf(c239,plain,
complement(X) = join(complement(X),complement(X)),
inference(symmetry,[status(thm)],[c224]) ).
cnf(c240,plain,
meet(top,complement(X)) = meet(top,join(complement(X),complement(X))),
inference(congruence,[status(thm)],[c239]) ).
cnf(c241,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c62]) ).
cnf(c242,plain,
meet(top,join(complement(X),complement(X))) = meet(join(X,complement(X)),join(complement(X),complement(X))),
inference(congruence,[status(thm)],[c241]) ).
cnf(c243,plain,
join(complement(X),complement(X3)) = join(complement(X3),complement(X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c244,plain,
join(complement(X3),complement(X)) = join(complement(X),complement(X3)),
inference(symmetry,[status(thm)],[c243]) ).
cnf(c245,plain,
meet(join(X3,complement(X)),join(complement(X3),complement(X))) = meet(join(X3,complement(X)),join(complement(X),complement(X3))),
inference(congruence,[status(thm)],[c244]) ).
cnf(c246,plain,
join(complement(X),X3) = join(X3,complement(X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c247,plain,
join(X3,complement(X)) = join(complement(X),X3),
inference(symmetry,[status(thm)],[c246]) ).
cnf(c248,plain,
meet(join(X3,complement(X)),join(complement(X),complement(X3))) = meet(join(complement(X),X3),join(complement(X),complement(X3))),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c250,plain,
join(meet(X4,X3),complement(X)) = join(complement(join(complement(X4),complement(X3))),complement(X)),
inference(congruence,[status(thm)],[c249]) ).
cnf(c251,plain,
complement(join(meet(X4,X3),complement(X))) = complement(join(complement(join(complement(X4),complement(X3))),complement(X))),
inference(congruence,[status(thm)],[c250]) ).
cnf(c252,plain,
meet(join(complement(X4),complement(X3)),X) = complement(join(complement(join(complement(X4),complement(X3))),complement(X))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c253,plain,
complement(join(complement(join(complement(X4),complement(X3))),complement(X))) = meet(join(complement(X4),complement(X3)),X),
inference(symmetry,[status(thm)],[c252]) ).
cnf(c254,plain,
meet(X,join(complement(X4),complement(X3))) = meet(join(complement(X4),complement(X3)),X),
inference(substitution,[status(thm)],[c39]) ).
cnf(c255,plain,
meet(join(complement(X4),complement(X3)),X) = meet(X,join(complement(X4),complement(X3))),
inference(symmetry,[status(thm)],[c254]) ).
cnf(c256,plain,
complement(join(complement(join(complement(X4),complement(X3))),complement(X))) = meet(X,join(complement(X4),complement(X3))),
inference(transitivity,[status(thm)],[c253,c255]) ).
cnf(c257,plain,
complement(join(meet(X4,X3),complement(X))) = meet(X,join(complement(X4),complement(X3))),
inference(transitivity,[status(thm)],[c251,c256]) ).
cnf(c258,plain,
complement(join(meet(X,X3),complement(join(complement(X),X3)))) = meet(join(complement(X),X3),join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c257]) ).
cnf(c259,plain,
meet(join(complement(X),X3),join(complement(X),complement(X3))) = complement(join(meet(X,X3),complement(join(complement(X),X3)))),
inference(symmetry,[status(thm)],[c258]) ).
cnf(c260,plain,
join(meet(X,X3),complement(join(complement(X),X3))) = X,
inference(substitution,[status(thm)],[c19]) ).
cnf(c261,plain,
complement(join(meet(X,X3),complement(join(complement(X),X3)))) = complement(X),
inference(congruence,[status(thm)],[c260]) ).
cnf(c262,plain,
meet(join(complement(X),X3),join(complement(X),complement(X3))) = complement(X),
inference(transitivity,[status(thm)],[c259,c261]) ).
cnf(c263,plain,
meet(join(X3,complement(X)),join(complement(X),complement(X3))) = complement(X),
inference(transitivity,[status(thm)],[c248,c262]) ).
cnf(c264,plain,
meet(join(X3,complement(X)),join(complement(X3),complement(X))) = complement(X),
inference(transitivity,[status(thm)],[c245,c263]) ).
cnf(c265,plain,
meet(join(X,complement(X)),join(complement(X),complement(X))) = complement(X),
inference(substitution,[status(thm)],[c264]) ).
cnf(c266,plain,
meet(top,join(complement(X),complement(X))) = complement(X),
inference(transitivity,[status(thm)],[c242,c265]) ).
cnf(c267,plain,
meet(top,complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c240,c266]) ).
cnf(c268,plain,
complement(X) = meet(top,complement(X)),
inference(symmetry,[status(thm)],[c267]) ).
cnf(c269,plain,
join(complement(X),meet(complement(X),complement(top))) = join(meet(top,complement(X)),meet(complement(X),complement(top))),
inference(congruence,[status(thm)],[c268]) ).
cnf(c270,plain,
meet(X3,X) = meet(X,X3),
inference(substitution,[status(thm)],[c39]) ).
cnf(c271,plain,
join(meet(X3,X),meet(X,complement(X3))) = join(meet(X,X3),meet(X,complement(X3))),
inference(congruence,[status(thm)],[c270]) ).
cnf(c272,plain,
join(meet(X3,complement(X)),meet(X3,X)) = join(meet(X3,X),meet(X3,complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c273,plain,
join(meet(X3,X),meet(X3,complement(X))) = join(meet(X3,complement(X)),meet(X3,X)),
inference(symmetry,[status(thm)],[c272]) ).
cnf(c274,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c275,plain,
join(meet(X3,complement(X)),meet(X3,X)) = join(meet(X3,complement(X)),complement(join(complement(X3),complement(X)))),
inference(congruence,[status(thm)],[c274]) ).
cnf(c276,plain,
join(meet(X3,complement(X)),complement(join(complement(X3),complement(X)))) = X3,
inference(substitution,[status(thm)],[c19]) ).
cnf(c277,plain,
join(meet(X3,complement(X)),meet(X3,X)) = X3,
inference(transitivity,[status(thm)],[c275,c276]) ).
cnf(c278,plain,
join(meet(X3,X),meet(X3,complement(X))) = X3,
inference(transitivity,[status(thm)],[c273,c277]) ).
cnf(c279,plain,
join(meet(X,X3),meet(X,complement(X3))) = X,
inference(substitution,[status(thm)],[c278]) ).
cnf(c280,plain,
join(meet(X3,X),meet(X,complement(X3))) = X,
inference(transitivity,[status(thm)],[c271,c279]) ).
cnf(c281,plain,
join(meet(top,complement(X)),meet(complement(X),complement(top))) = complement(X),
inference(substitution,[status(thm)],[c280]) ).
cnf(c282,plain,
join(complement(X),meet(complement(X),complement(top))) = complement(X),
inference(transitivity,[status(thm)],[c269,c281]) ).
cnf(c283,plain,
join(complement(X),meet(complement(X),zero)) = complement(X),
inference(transitivity,[status(thm)],[c238,c282]) ).
cnf(c284,plain,
join(complement(X),zero) = complement(X),
inference(transitivity,[status(thm)],[c235,c283]) ).
cnf(c285,plain,
join(zero,complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c52,c284]) ).
cnf(c286,plain,
join(zero,complement(join(complement(X3),X))) = complement(join(complement(X3),X)),
inference(substitution,[status(thm)],[c285]) ).
cnf(c287,plain,
join(meet(X3,X),join(zero,complement(join(complement(X3),X)))) = join(meet(X3,X),complement(join(complement(X3),X))),
inference(congruence,[status(thm)],[c286]) ).
cnf(c288,plain,
join(meet(X3,X),join(zero,complement(join(complement(X3),X)))) = X3,
inference(transitivity,[status(thm)],[c287,c19]) ).
cnf(c289,plain,
join(X,zero) = X,
inference(transitivity,[status(thm)],[c50,c288]) ).
cnf(c290,plain,
join(meet(composition(complement(x2),x1),x0),zero) = meet(composition(complement(x2),x1),x0),
inference(substitution,[status(thm)],[c289]) ).
cnf(c291,plain,
meet(composition(complement(x2),x1),x0) = join(meet(composition(complement(x2),x1),x0),zero),
inference(symmetry,[status(thm)],[c290]) ).
cnf(c292,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c293,plain,
join(zero,complement(join(zero,complement(X)))) = complement(join(zero,complement(X))),
inference(substitution,[status(thm)],[c285]) ).
cnf(c294,plain,
complement(join(zero,complement(X))) = join(zero,complement(join(zero,complement(X)))),
inference(symmetry,[status(thm)],[c293]) ).
cnf(c295,plain,
join(zero,complement(join(zero,complement(X)))) = join(zero,meet(X,top)),
inference(congruence,[status(thm)],[c80]) ).
cnf(c296,plain,
join(meet(X,top),zero) = join(zero,meet(X,top)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c297,plain,
join(zero,meet(X,top)) = join(meet(X,top),zero),
inference(symmetry,[status(thm)],[c296]) ).
cnf(c298,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c299,plain,
join(meet(X,top),zero) = join(meet(X,top),complement(top)),
inference(congruence,[status(thm)],[c298]) ).
cnf(c300,plain,
join(complement(X),top) = top,
inference(substitution,[status(thm)],[c157]) ).
cnf(c301,plain,
top = join(complement(X),top),
inference(symmetry,[status(thm)],[c300]) ).
cnf(c302,plain,
complement(top) = complement(join(complement(X),top)),
inference(congruence,[status(thm)],[c301]) ).
cnf(c303,plain,
join(meet(X,top),complement(top)) = join(meet(X,top),complement(join(complement(X),top))),
inference(congruence,[status(thm)],[c302]) ).
cnf(c304,plain,
join(meet(X,top),complement(join(complement(X),top))) = X,
inference(substitution,[status(thm)],[c19]) ).
cnf(c305,plain,
join(meet(X,top),complement(top)) = X,
inference(transitivity,[status(thm)],[c303,c304]) ).
cnf(c306,plain,
join(meet(X,top),zero) = X,
inference(transitivity,[status(thm)],[c299,c305]) ).
cnf(c307,plain,
join(zero,meet(X,top)) = X,
inference(transitivity,[status(thm)],[c297,c306]) ).
cnf(c308,plain,
join(zero,complement(join(zero,complement(X)))) = X,
inference(transitivity,[status(thm)],[c295,c307]) ).
cnf(c309,plain,
complement(join(zero,complement(X))) = X,
inference(transitivity,[status(thm)],[c294,c308]) ).
cnf(c310,plain,
meet(X,top) = X,
inference(transitivity,[status(thm)],[c292,c309]) ).
cnf(c311,plain,
meet(composition(zero,X),top) = composition(zero,X),
inference(substitution,[status(thm)],[c310]) ).
cnf(c312,plain,
composition(zero,X) = meet(composition(zero,X),top),
inference(symmetry,[status(thm)],[c311]) ).
cnf(c313,plain,
join(zero,complement(composition(zero,X))) = complement(composition(zero,X)),
inference(substitution,[status(thm)],[c285]) ).
cnf(c314,plain,
complement(composition(zero,X)) = join(zero,complement(composition(zero,X))),
inference(symmetry,[status(thm)],[c313]) ).
cnf(c315,plain,
converse(composition(converse(X),complement(composition(X,top)))) = composition(converse(complement(composition(X,top))),X),
inference(substitution,[status(thm)],[c181]) ).
cnf(c316,plain,
composition(converse(complement(composition(X,top))),X) = converse(composition(converse(X),complement(composition(X,top)))),
inference(symmetry,[status(thm)],[c315]) ).
cnf(c317,plain,
join(composition(converse(X),complement(composition(X,top))),zero) = composition(converse(X),complement(composition(X,top))),
inference(substitution,[status(thm)],[c289]) ).
cnf(c318,plain,
composition(converse(X),complement(composition(X,top))) = join(composition(converse(X),complement(composition(X,top))),zero),
inference(symmetry,[status(thm)],[c317]) ).
cnf(c319,plain,
join(zero,composition(converse(X),complement(composition(X,top)))) = join(composition(converse(X),complement(composition(X,top))),zero),
inference(substitution,[status(thm)],[c5]) ).
cnf(c320,plain,
join(composition(converse(X),complement(composition(X,top))),zero) = join(zero,composition(converse(X),complement(composition(X,top)))),
inference(symmetry,[status(thm)],[c319]) ).
cnf(c321,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c322,plain,
join(zero,composition(converse(X),complement(composition(X,top)))) = join(complement(top),composition(converse(X),complement(composition(X,top)))),
inference(congruence,[status(thm)],[c321]) ).
cnf(c323,plain,
join(complement(top),composition(converse(X),complement(composition(X,top)))) = complement(top),
inference(substitution,[status(thm)],[c218]) ).
cnf(c324,plain,
join(complement(top),composition(converse(X),complement(composition(X,top)))) = zero,
inference(transitivity,[status(thm)],[c323,c71]) ).
cnf(c325,plain,
join(zero,composition(converse(X),complement(composition(X,top)))) = zero,
inference(transitivity,[status(thm)],[c322,c324]) ).
cnf(c326,plain,
join(composition(converse(X),complement(composition(X,top))),zero) = zero,
inference(transitivity,[status(thm)],[c320,c325]) ).
cnf(c327,plain,
composition(converse(X),complement(composition(X,top))) = zero,
inference(transitivity,[status(thm)],[c318,c326]) ).
cnf(c328,plain,
converse(composition(converse(X),complement(composition(X,top)))) = converse(zero),
inference(congruence,[status(thm)],[c327]) ).
cnf(c329,plain,
meet(converse(zero),top) = converse(zero),
inference(substitution,[status(thm)],[c310]) ).
cnf(c330,plain,
converse(zero) = meet(converse(zero),top),
inference(symmetry,[status(thm)],[c329]) ).
cnf(c331,plain,
complement(join(zero,complement(converse(zero)))) = meet(converse(zero),top),
inference(substitution,[status(thm)],[c80]) ).
cnf(c332,plain,
meet(converse(zero),top) = complement(join(zero,complement(converse(zero)))),
inference(symmetry,[status(thm)],[c331]) ).
cnf(c333,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c178]) ).
cnf(c334,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c333]) ).
cnf(c335,plain,
join(X,complement(converse(zero))) = join(converse(converse(X)),complement(converse(zero))),
inference(congruence,[status(thm)],[c334]) ).
cnf(c336,plain,
join(complement(converse(zero)),converse(X)) = join(converse(X),complement(converse(zero))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c337,plain,
join(converse(X),complement(converse(zero))) = join(complement(converse(zero)),converse(X)),
inference(symmetry,[status(thm)],[c336]) ).
cnf(c338,plain,
meet(X,X) = complement(join(complement(X),complement(X))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c339,plain,
join(zero,meet(X,X)) = join(zero,complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c338]) ).
cnf(c340,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c67]) ).
cnf(c341,plain,
join(zero,complement(join(complement(X),complement(X)))) = join(meet(X,complement(X)),complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c340]) ).
cnf(c342,plain,
join(meet(X,complement(X)),complement(join(complement(X),complement(X)))) = X,
inference(substitution,[status(thm)],[c19]) ).
cnf(c343,plain,
join(zero,complement(join(complement(X),complement(X)))) = X,
inference(transitivity,[status(thm)],[c341,c342]) ).
cnf(c344,plain,
join(zero,meet(X,X)) = X,
inference(transitivity,[status(thm)],[c339,c343]) ).
cnf(c345,plain,
X = join(zero,meet(X,X)),
inference(symmetry,[status(thm)],[c344]) ).
cnf(c346,plain,
converse(X) = converse(join(zero,meet(X,X))),
inference(congruence,[status(thm)],[c345]) ).
cnf(c347,plain,
join(complement(converse(zero)),converse(X)) = join(complement(converse(zero)),converse(join(zero,meet(X,X)))),
inference(congruence,[status(thm)],[c346]) ).
cnf(c348,plain,
join(converse(X),X3) = join(X3,converse(X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c349,plain,
join(X3,converse(X)) = join(converse(X),X3),
inference(symmetry,[status(thm)],[c348]) ).
cnf(c350,plain,
join(converse(X4),join(X3,converse(X))) = join(converse(X4),join(converse(X),X3)),
inference(congruence,[status(thm)],[c349]) ).
cnf(c351,plain,
join(converse(X),join(converse(X4),X3)) = join(converse(X4),join(converse(X),X3)),
inference(substitution,[status(thm)],[c113]) ).
cnf(c352,plain,
join(converse(X4),join(converse(X),X3)) = join(converse(X),join(converse(X4),X3)),
inference(symmetry,[status(thm)],[c351]) ).
cnf(c353,plain,
join(converse(X),join(converse(X4),X3)) = join(join(converse(X),converse(X4)),X3),
inference(substitution,[status(thm)],[c44]) ).
cnf(c354,axiom,
converse(join(X0_2,X1_2)) = join(converse(X0_2),converse(X1_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity) ).
cnf(c355,plain,
converse(join(X,X3)) = join(converse(X),converse(X3)),
inference(substitution,[status(thm)],[c354]) ).
cnf(c356,plain,
join(converse(X),converse(X3)) = converse(join(X,X3)),
inference(symmetry,[status(thm)],[c355]) ).
cnf(c357,plain,
join(join(converse(X),converse(X4)),X3) = join(converse(join(X,X4)),X3),
inference(congruence,[status(thm)],[c356]) ).
cnf(c358,plain,
join(converse(join(X,X4)),X3) = join(X3,converse(join(X,X4))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c359,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c360,plain,
converse(join(X,X3)) = converse(join(X3,X)),
inference(congruence,[status(thm)],[c359]) ).
cnf(c361,plain,
join(X3,converse(join(X,X4))) = join(X3,converse(join(X4,X))),
inference(congruence,[status(thm)],[c360]) ).
cnf(c362,plain,
join(converse(join(X,X4)),X3) = join(X3,converse(join(X4,X))),
inference(transitivity,[status(thm)],[c358,c361]) ).
cnf(c363,plain,
join(join(converse(X),converse(X4)),X3) = join(X3,converse(join(X4,X))),
inference(transitivity,[status(thm)],[c357,c362]) ).
cnf(c364,plain,
join(converse(X),join(converse(X4),X3)) = join(X3,converse(join(X4,X))),
inference(transitivity,[status(thm)],[c353,c363]) ).
cnf(c365,plain,
join(converse(X4),join(converse(X),X3)) = join(X3,converse(join(X4,X))),
inference(transitivity,[status(thm)],[c352,c364]) ).
cnf(c366,plain,
join(converse(X4),join(X3,converse(X))) = join(X3,converse(join(X4,X))),
inference(transitivity,[status(thm)],[c350,c365]) ).
cnf(c367,plain,
join(converse(X3),join(complement(converse(X3)),converse(X))) = join(complement(converse(X3)),converse(join(X3,X))),
inference(substitution,[status(thm)],[c366]) ).
cnf(c368,plain,
join(complement(converse(X3)),converse(join(X3,X))) = join(converse(X3),join(complement(converse(X3)),converse(X))),
inference(symmetry,[status(thm)],[c367]) ).
cnf(c369,plain,
join(converse(X3),join(complement(converse(X3)),converse(X))) = join(converse(X),top),
inference(substitution,[status(thm)],[c99]) ).
cnf(c370,plain,
join(converse(X),top) = top,
inference(substitution,[status(thm)],[c157]) ).
cnf(c371,plain,
join(converse(X3),join(complement(converse(X3)),converse(X))) = top,
inference(transitivity,[status(thm)],[c369,c370]) ).
cnf(c372,plain,
join(complement(converse(X3)),converse(join(X3,X))) = top,
inference(transitivity,[status(thm)],[c368,c371]) ).
cnf(c373,plain,
join(complement(converse(zero)),converse(join(zero,meet(X,X)))) = top,
inference(substitution,[status(thm)],[c372]) ).
cnf(c374,plain,
join(complement(converse(zero)),converse(X)) = top,
inference(transitivity,[status(thm)],[c347,c373]) ).
cnf(c375,plain,
join(converse(X),complement(converse(zero))) = top,
inference(transitivity,[status(thm)],[c337,c374]) ).
cnf(c376,plain,
join(converse(converse(X)),complement(converse(zero))) = top,
inference(substitution,[status(thm)],[c375]) ).
cnf(c377,plain,
join(X,complement(converse(zero))) = top,
inference(transitivity,[status(thm)],[c335,c376]) ).
cnf(c378,plain,
join(zero,complement(converse(zero))) = top,
inference(substitution,[status(thm)],[c377]) ).
cnf(c379,plain,
complement(join(zero,complement(converse(zero)))) = complement(top),
inference(congruence,[status(thm)],[c378]) ).
cnf(c380,plain,
complement(join(zero,complement(converse(zero)))) = zero,
inference(transitivity,[status(thm)],[c379,c71]) ).
cnf(c381,plain,
meet(converse(zero),top) = zero,
inference(transitivity,[status(thm)],[c332,c380]) ).
cnf(c382,plain,
converse(zero) = zero,
inference(transitivity,[status(thm)],[c330,c381]) ).
cnf(c383,plain,
converse(composition(converse(X),complement(composition(X,top)))) = zero,
inference(transitivity,[status(thm)],[c328,c382]) ).
cnf(c384,plain,
composition(converse(complement(composition(X,top))),X) = zero,
inference(transitivity,[status(thm)],[c316,c383]) ).
cnf(c385,plain,
zero = composition(converse(complement(composition(X,top))),X),
inference(symmetry,[status(thm)],[c384]) ).
cnf(c386,plain,
join(zero,complement(composition(zero,X))) = join(composition(converse(complement(composition(X,top))),X),complement(composition(zero,X))),
inference(congruence,[status(thm)],[c385]) ).
cnf(c387,plain,
join(complement(composition(zero,X)),composition(X3,X)) = join(composition(X3,X),complement(composition(zero,X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c388,plain,
join(composition(X3,X),complement(composition(zero,X))) = join(complement(composition(zero,X)),composition(X3,X)),
inference(symmetry,[status(thm)],[c387]) ).
cnf(c389,plain,
X = join(zero,meet(X,X)),
inference(symmetry,[status(thm)],[c344]) ).
cnf(c390,plain,
composition(X3,X) = composition(join(zero,meet(X3,X3)),X),
inference(congruence,[status(thm)],[c389]) ).
cnf(c391,plain,
join(complement(composition(zero,X)),composition(X3,X)) = join(complement(composition(zero,X)),composition(join(zero,meet(X3,X3)),X)),
inference(congruence,[status(thm)],[c390]) ).
cnf(c392,plain,
join(composition(X4,X3),X) = join(X,composition(X4,X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c393,plain,
join(X3,composition(X,X4)) = join(composition(X,X4),X3),
inference(symmetry,[status(thm)],[c392]) ).
cnf(c394,plain,
join(composition(X5,X4),join(X3,composition(X,X4))) = join(composition(X5,X4),join(composition(X,X4),X3)),
inference(congruence,[status(thm)],[c393]) ).
cnf(c395,plain,
join(composition(X,X4),join(composition(X5,X4),X3)) = join(composition(X5,X4),join(composition(X,X4),X3)),
inference(substitution,[status(thm)],[c113]) ).
cnf(c396,plain,
join(composition(X5,X4),join(composition(X,X4),X3)) = join(composition(X,X4),join(composition(X5,X4),X3)),
inference(symmetry,[status(thm)],[c395]) ).
cnf(c397,plain,
join(composition(X,X4),join(composition(X5,X4),X3)) = join(join(composition(X,X4),composition(X5,X4)),X3),
inference(substitution,[status(thm)],[c44]) ).
cnf(c398,axiom,
composition(join(X0_2,X1_2),X2_2) = join(composition(X0_2,X2_2),composition(X1_2,X2_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity) ).
cnf(c399,plain,
composition(join(X,X4),X3) = join(composition(X,X3),composition(X4,X3)),
inference(substitution,[status(thm)],[c398]) ).
cnf(c400,plain,
join(composition(X,X3),composition(X4,X3)) = composition(join(X,X4),X3),
inference(symmetry,[status(thm)],[c399]) ).
cnf(c401,plain,
join(join(composition(X,X4),composition(X5,X4)),X3) = join(composition(join(X,X5),X4),X3),
inference(congruence,[status(thm)],[c400]) ).
cnf(c402,plain,
join(composition(join(X,X5),X4),X3) = join(X3,composition(join(X,X5),X4)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c403,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c404,plain,
composition(join(X,X4),X3) = composition(join(X4,X),X3),
inference(congruence,[status(thm)],[c403]) ).
cnf(c405,plain,
join(X3,composition(join(X,X5),X4)) = join(X3,composition(join(X5,X),X4)),
inference(congruence,[status(thm)],[c404]) ).
cnf(c406,plain,
join(composition(join(X,X5),X4),X3) = join(X3,composition(join(X5,X),X4)),
inference(transitivity,[status(thm)],[c402,c405]) ).
cnf(c407,plain,
join(join(composition(X,X4),composition(X5,X4)),X3) = join(X3,composition(join(X5,X),X4)),
inference(transitivity,[status(thm)],[c401,c406]) ).
cnf(c408,plain,
join(composition(X,X4),join(composition(X5,X4),X3)) = join(X3,composition(join(X5,X),X4)),
inference(transitivity,[status(thm)],[c397,c407]) ).
cnf(c409,plain,
join(composition(X5,X4),join(composition(X,X4),X3)) = join(X3,composition(join(X5,X),X4)),
inference(transitivity,[status(thm)],[c396,c408]) ).
cnf(c410,plain,
join(composition(X5,X4),join(X3,composition(X,X4))) = join(X3,composition(join(X5,X),X4)),
inference(transitivity,[status(thm)],[c394,c409]) ).
cnf(c411,plain,
join(composition(X4,X3),join(complement(composition(X4,X3)),composition(X,X3))) = join(complement(composition(X4,X3)),composition(join(X4,X),X3)),
inference(substitution,[status(thm)],[c410]) ).
cnf(c412,plain,
join(complement(composition(X4,X3)),composition(join(X4,X),X3)) = join(composition(X4,X3),join(complement(composition(X4,X3)),composition(X,X3))),
inference(symmetry,[status(thm)],[c411]) ).
cnf(c413,plain,
join(composition(X4,X3),join(complement(composition(X4,X3)),composition(X,X3))) = join(composition(X,X3),top),
inference(substitution,[status(thm)],[c99]) ).
cnf(c414,plain,
join(composition(X,X3),top) = top,
inference(substitution,[status(thm)],[c157]) ).
cnf(c415,plain,
join(composition(X4,X3),join(complement(composition(X4,X3)),composition(X,X3))) = top,
inference(transitivity,[status(thm)],[c413,c414]) ).
cnf(c416,plain,
join(complement(composition(X4,X3)),composition(join(X4,X),X3)) = top,
inference(transitivity,[status(thm)],[c412,c415]) ).
cnf(c417,plain,
join(complement(composition(zero,X)),composition(join(zero,meet(X3,X3)),X)) = top,
inference(substitution,[status(thm)],[c416]) ).
cnf(c418,plain,
join(complement(composition(zero,X)),composition(X3,X)) = top,
inference(transitivity,[status(thm)],[c391,c417]) ).
cnf(c419,plain,
join(composition(X3,X),complement(composition(zero,X))) = top,
inference(transitivity,[status(thm)],[c388,c418]) ).
cnf(c420,plain,
join(composition(converse(complement(composition(X,top))),X),complement(composition(zero,X))) = top,
inference(substitution,[status(thm)],[c419]) ).
cnf(c421,plain,
join(zero,complement(composition(zero,X))) = top,
inference(transitivity,[status(thm)],[c386,c420]) ).
cnf(c422,plain,
complement(composition(zero,X)) = top,
inference(transitivity,[status(thm)],[c314,c421]) ).
cnf(c423,plain,
top = complement(composition(zero,X)),
inference(symmetry,[status(thm)],[c422]) ).
cnf(c424,plain,
meet(composition(zero,X),top) = meet(composition(zero,X),complement(composition(zero,X))),
inference(congruence,[status(thm)],[c423]) ).
cnf(c425,plain,
zero = meet(composition(zero,X),complement(composition(zero,X))),
inference(substitution,[status(thm)],[c67]) ).
cnf(c426,plain,
meet(composition(zero,X),complement(composition(zero,X))) = zero,
inference(symmetry,[status(thm)],[c425]) ).
cnf(c427,plain,
meet(composition(zero,X),top) = zero,
inference(transitivity,[status(thm)],[c424,c426]) ).
cnf(c428,plain,
composition(zero,X) = zero,
inference(transitivity,[status(thm)],[c312,c427]) ).
cnf(c429,plain,
composition(zero,meet(x1,composition(converse(complement(x2)),x0))) = zero,
inference(substitution,[status(thm)],[c428]) ).
cnf(c430,plain,
zero = composition(zero,meet(x1,composition(converse(complement(x2)),x0))),
inference(symmetry,[status(thm)],[c429]) ).
cnf(c431,plain,
join(meet(composition(complement(x2),x1),x0),zero) = join(meet(composition(complement(x2),x1),x0),composition(zero,meet(x1,composition(converse(complement(x2)),x0)))),
inference(congruence,[status(thm)],[c430]) ).
cnf(c432,plain,
meet(complement(x2),composition(x0,converse(x1))) = meet(composition(x0,converse(x1)),complement(x2)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c433,plain,
join(complement(composition(x0,converse(x1))),zero) = complement(composition(x0,converse(x1))),
inference(substitution,[status(thm)],[c289]) ).
cnf(c434,plain,
complement(composition(x0,converse(x1))) = join(complement(composition(x0,converse(x1))),zero),
inference(symmetry,[status(thm)],[c433]) ).
cnf(c435,plain,
meet(complement(x2),complement(composition(x0,converse(x1)))) = meet(complement(x2),join(complement(composition(x0,converse(x1))),zero)),
inference(congruence,[status(thm)],[c434]) ).
cnf(c436,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c437,plain,
join(complement(composition(x0,converse(x1))),zero) = join(complement(composition(x0,converse(x1))),complement(top)),
inference(congruence,[status(thm)],[c436]) ).
cnf(c438,plain,
meet(complement(x2),join(complement(composition(x0,converse(x1))),zero)) = meet(complement(x2),join(complement(composition(x0,converse(x1))),complement(top))),
inference(congruence,[status(thm)],[c437]) ).
cnf(c439,plain,
join(complement(composition(x0,converse(x1))),x2) = join(x2,complement(composition(x0,converse(x1)))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c440,plain,
join(x2,complement(composition(x0,converse(x1)))) = join(complement(composition(x0,converse(x1))),x2),
inference(symmetry,[status(thm)],[c439]) ).
cnf(c441,plain,
join(X,composition(x0,converse(x1))) = join(composition(x0,converse(x1)),X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c442,plain,
join(composition(x0,converse(x1)),X) = join(X,composition(x0,converse(x1))),
inference(symmetry,[status(thm)],[c441]) ).
cnf(c443,plain,
join(x2,join(composition(x0,converse(x1)),X)) = join(x2,join(X,composition(x0,converse(x1)))),
inference(congruence,[status(thm)],[c442]) ).
cnf(c444,plain,
join(composition(x0,converse(x1)),X) = join(X,composition(x0,converse(x1))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c445,plain,
join(X,composition(x0,converse(x1))) = join(composition(x0,converse(x1)),X),
inference(symmetry,[status(thm)],[c444]) ).
cnf(c446,plain,
join(x2,join(X,composition(x0,converse(x1)))) = join(x2,join(composition(x0,converse(x1)),X)),
inference(congruence,[status(thm)],[c445]) ).
cnf(c447,plain,
join(x2,join(composition(x0,converse(x1)),X)) = join(join(x2,composition(x0,converse(x1))),X),
inference(substitution,[status(thm)],[c44]) ).
cnf(c448,plain,
join(composition(x0,converse(x1)),x2) = join(x2,composition(x0,converse(x1))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c449,plain,
join(x2,composition(x0,converse(x1))) = join(composition(x0,converse(x1)),x2),
inference(symmetry,[status(thm)],[c448]) ).
fof(c450,conjecture,
! [X0_2,X1_2,X2_2] :
( join(composition(X0_2,converse(X1_2)),X2_2) = X2_2
=> join(composition(complement(X2_2),X1_2),complement(X0_2)) = complement(X0_2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c451,negated_conjecture,
~ ! [X0_2,X1_2,X2_2] :
( join(composition(X0_2,converse(X1_2)),X2_2) = X2_2
=> join(composition(complement(X2_2),X1_2),complement(X0_2)) = complement(X0_2) ),
inference(negate_conjecture,[status(cth)],[c450]) ).
fof(c452,plain,
( join(composition(x0,converse(x1)),x2) = x2
& join(composition(complement(x2),x1),complement(x0)) != complement(x0) ),
inference(clausify,[status(esa)],[c451]) ).
cnf(c453,plain,
join(composition(x0,converse(x1)),x2) = x2,
inference(clausify,[status(thm)],[c452]) ).
cnf(c454,plain,
join(x2,composition(x0,converse(x1))) = x2,
inference(transitivity,[status(thm)],[c449,c453]) ).
cnf(c455,plain,
join(join(x2,composition(x0,converse(x1))),X) = join(x2,X),
inference(congruence,[status(thm)],[c454]) ).
cnf(c456,plain,
join(x2,X) = join(X,x2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c457,plain,
join(join(x2,composition(x0,converse(x1))),X) = join(X,x2),
inference(transitivity,[status(thm)],[c455,c456]) ).
cnf(c458,plain,
join(x2,join(composition(x0,converse(x1)),X)) = join(X,x2),
inference(transitivity,[status(thm)],[c447,c457]) ).
cnf(c459,plain,
join(x2,join(X,composition(x0,converse(x1)))) = join(X,x2),
inference(transitivity,[status(thm)],[c446,c458]) ).
cnf(c460,plain,
join(x2,join(composition(x0,converse(x1)),X)) = join(X,x2),
inference(transitivity,[status(thm)],[c443,c459]) ).
cnf(c461,plain,
join(x2,join(composition(x0,converse(x1)),complement(composition(x0,converse(x1))))) = join(complement(composition(x0,converse(x1))),x2),
inference(substitution,[status(thm)],[c460]) ).
cnf(c462,plain,
join(complement(composition(x0,converse(x1))),x2) = join(x2,join(composition(x0,converse(x1)),complement(composition(x0,converse(x1))))),
inference(symmetry,[status(thm)],[c461]) ).
cnf(c463,plain,
top = join(composition(x0,converse(x1)),complement(composition(x0,converse(x1)))),
inference(substitution,[status(thm)],[c62]) ).
cnf(c464,plain,
join(composition(x0,converse(x1)),complement(composition(x0,converse(x1)))) = top,
inference(symmetry,[status(thm)],[c463]) ).
cnf(c465,plain,
join(x2,join(composition(x0,converse(x1)),complement(composition(x0,converse(x1))))) = join(x2,top),
inference(congruence,[status(thm)],[c464]) ).
cnf(c466,plain,
join(x2,top) = top,
inference(substitution,[status(thm)],[c157]) ).
cnf(c467,plain,
join(x2,join(composition(x0,converse(x1)),complement(composition(x0,converse(x1))))) = top,
inference(transitivity,[status(thm)],[c465,c466]) ).
cnf(c468,plain,
join(complement(composition(x0,converse(x1))),x2) = top,
inference(transitivity,[status(thm)],[c462,c467]) ).
cnf(c469,plain,
join(x2,complement(composition(x0,converse(x1)))) = top,
inference(transitivity,[status(thm)],[c440,c468]) ).
cnf(c470,plain,
top = join(x2,complement(composition(x0,converse(x1)))),
inference(symmetry,[status(thm)],[c469]) ).
cnf(c471,plain,
complement(top) = complement(join(x2,complement(composition(x0,converse(x1))))),
inference(congruence,[status(thm)],[c470]) ).
cnf(c472,plain,
join(complement(composition(x0,converse(x1))),complement(top)) = join(complement(composition(x0,converse(x1))),complement(join(x2,complement(composition(x0,converse(x1)))))),
inference(congruence,[status(thm)],[c471]) ).
cnf(c473,plain,
meet(complement(x2),join(complement(composition(x0,converse(x1))),complement(top))) = meet(complement(x2),join(complement(composition(x0,converse(x1))),complement(join(x2,complement(composition(x0,converse(x1))))))),
inference(congruence,[status(thm)],[c472]) ).
cnf(c474,plain,
join(X,X3) = join(X3,X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c475,plain,
join(X3,X) = join(X,X3),
inference(symmetry,[status(thm)],[c474]) ).
cnf(c476,plain,
complement(join(X3,X)) = complement(join(X,X3)),
inference(congruence,[status(thm)],[c475]) ).
cnf(c477,plain,
join(X,complement(join(X3,X))) = join(X,complement(join(X,X3))),
inference(congruence,[status(thm)],[c476]) ).
cnf(c478,plain,
meet(complement(X3),join(X,complement(join(X3,X)))) = meet(complement(X3),join(X,complement(join(X,X3)))),
inference(congruence,[status(thm)],[c477]) ).
cnf(c479,plain,
X = meet(X,top),
inference(symmetry,[status(thm)],[c310]) ).
cnf(c480,plain,
join(X,X3) = join(X,meet(X3,top)),
inference(congruence,[status(thm)],[c479]) ).
cnf(c481,plain,
complement(join(X,X3)) = complement(join(X,meet(X3,top))),
inference(congruence,[status(thm)],[c480]) ).
cnf(c482,plain,
join(X,complement(join(X,X3))) = join(X,complement(join(X,meet(X3,top)))),
inference(congruence,[status(thm)],[c481]) ).
cnf(c483,plain,
meet(complement(X3),join(X,complement(join(X,X3)))) = meet(complement(X3),join(X,complement(join(X,meet(X3,top))))),
inference(congruence,[status(thm)],[c482]) ).
cnf(c484,plain,
complement(X) = join(zero,complement(X)),
inference(symmetry,[status(thm)],[c285]) ).
cnf(c485,plain,
meet(complement(X3),join(X,complement(join(X,meet(X3,top))))) = meet(join(zero,complement(X3)),join(X,complement(join(X,meet(X3,top))))),
inference(congruence,[status(thm)],[c484]) ).
cnf(c486,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c487,plain,
join(X,meet(X3,top)) = join(X,complement(join(zero,complement(X3)))),
inference(congruence,[status(thm)],[c486]) ).
cnf(c488,plain,
complement(join(X,meet(X3,top))) = complement(join(X,complement(join(zero,complement(X3))))),
inference(congruence,[status(thm)],[c487]) ).
cnf(c489,plain,
join(X,complement(join(X,meet(X3,top)))) = join(X,complement(join(X,complement(join(zero,complement(X3)))))),
inference(congruence,[status(thm)],[c488]) ).
cnf(c490,plain,
meet(join(zero,complement(X3)),join(X,complement(join(X,meet(X3,top))))) = meet(join(zero,complement(X3)),join(X,complement(join(X,complement(join(zero,complement(X3))))))),
inference(congruence,[status(thm)],[c489]) ).
cnf(c491,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c492,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(symmetry,[status(thm)],[c491]) ).
cnf(c493,plain,
complement(join(X,complement(X3))) = complement(join(complement(X3),X)),
inference(congruence,[status(thm)],[c492]) ).
cnf(c494,plain,
join(X,complement(join(X,complement(X3)))) = join(X,complement(join(complement(X3),X))),
inference(congruence,[status(thm)],[c493]) ).
cnf(c495,plain,
meet(X3,join(X,complement(join(X,complement(X3))))) = meet(X3,join(X,complement(join(complement(X3),X)))),
inference(congruence,[status(thm)],[c494]) ).
cnf(c496,plain,
join(meet(X3,join(X,complement(join(complement(X3),X)))),zero) = meet(X3,join(X,complement(join(complement(X3),X)))),
inference(substitution,[status(thm)],[c289]) ).
cnf(c497,plain,
meet(X3,join(X,complement(join(complement(X3),X)))) = join(meet(X3,join(X,complement(join(complement(X3),X)))),zero),
inference(symmetry,[status(thm)],[c496]) ).
cnf(c498,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c499,plain,
join(meet(X3,join(X,complement(join(complement(X3),X)))),zero) = join(meet(X3,join(X,complement(join(complement(X3),X)))),complement(top)),
inference(congruence,[status(thm)],[c498]) ).
cnf(c500,plain,
join(complement(X3),join(X,complement(join(complement(X3),X)))) = top,
inference(substitution,[status(thm)],[c142]) ).
cnf(c501,plain,
top = join(complement(X3),join(X,complement(join(complement(X3),X)))),
inference(symmetry,[status(thm)],[c500]) ).
cnf(c502,plain,
complement(top) = complement(join(complement(X3),join(X,complement(join(complement(X3),X))))),
inference(congruence,[status(thm)],[c501]) ).
cnf(c503,plain,
join(meet(X3,join(X,complement(join(complement(X3),X)))),complement(top)) = join(meet(X3,join(X,complement(join(complement(X3),X)))),complement(join(complement(X3),join(X,complement(join(complement(X3),X)))))),
inference(congruence,[status(thm)],[c502]) ).
cnf(c504,plain,
join(meet(X3,join(X,complement(join(complement(X3),X)))),complement(join(complement(X3),join(X,complement(join(complement(X3),X)))))) = X3,
inference(substitution,[status(thm)],[c19]) ).
cnf(c505,plain,
join(meet(X3,join(X,complement(join(complement(X3),X)))),complement(top)) = X3,
inference(transitivity,[status(thm)],[c503,c504]) ).
cnf(c506,plain,
join(meet(X3,join(X,complement(join(complement(X3),X)))),zero) = X3,
inference(transitivity,[status(thm)],[c499,c505]) ).
cnf(c507,plain,
meet(X3,join(X,complement(join(complement(X3),X)))) = X3,
inference(transitivity,[status(thm)],[c497,c506]) ).
cnf(c508,plain,
meet(X3,join(X,complement(join(X,complement(X3))))) = X3,
inference(transitivity,[status(thm)],[c495,c507]) ).
cnf(c509,plain,
meet(join(zero,complement(X3)),join(X,complement(join(X,complement(join(zero,complement(X3))))))) = join(zero,complement(X3)),
inference(substitution,[status(thm)],[c508]) ).
cnf(c510,plain,
meet(join(zero,complement(X3)),join(X,complement(join(X,complement(join(zero,complement(X3))))))) = complement(X3),
inference(transitivity,[status(thm)],[c509,c285]) ).
cnf(c511,plain,
meet(join(zero,complement(X3)),join(X,complement(join(X,meet(X3,top))))) = complement(X3),
inference(transitivity,[status(thm)],[c490,c510]) ).
cnf(c512,plain,
meet(complement(X3),join(X,complement(join(X,meet(X3,top))))) = complement(X3),
inference(transitivity,[status(thm)],[c485,c511]) ).
cnf(c513,plain,
meet(complement(X3),join(X,complement(join(X,X3)))) = complement(X3),
inference(transitivity,[status(thm)],[c483,c512]) ).
cnf(c514,plain,
meet(complement(X3),join(X,complement(join(X3,X)))) = complement(X3),
inference(transitivity,[status(thm)],[c478,c513]) ).
cnf(c515,plain,
meet(complement(x2),join(complement(composition(x0,converse(x1))),complement(join(x2,complement(composition(x0,converse(x1))))))) = complement(x2),
inference(substitution,[status(thm)],[c514]) ).
cnf(c516,plain,
meet(complement(x2),join(complement(composition(x0,converse(x1))),complement(top))) = complement(x2),
inference(transitivity,[status(thm)],[c473,c515]) ).
cnf(c517,plain,
meet(complement(x2),join(complement(composition(x0,converse(x1))),zero)) = complement(x2),
inference(transitivity,[status(thm)],[c438,c516]) ).
cnf(c518,plain,
meet(complement(x2),complement(composition(x0,converse(x1)))) = complement(x2),
inference(transitivity,[status(thm)],[c435,c517]) ).
cnf(c519,plain,
complement(x2) = meet(complement(x2),complement(composition(x0,converse(x1)))),
inference(symmetry,[status(thm)],[c518]) ).
cnf(c520,plain,
meet(composition(x0,converse(x1)),complement(x2)) = meet(composition(x0,converse(x1)),meet(complement(x2),complement(composition(x0,converse(x1))))),
inference(congruence,[status(thm)],[c519]) ).
cnf(c521,plain,
meet(X,complement(X3)) = meet(complement(X3),X),
inference(substitution,[status(thm)],[c39]) ).
cnf(c522,plain,
meet(X3,meet(X,complement(X3))) = meet(X3,meet(complement(X3),X)),
inference(congruence,[status(thm)],[c521]) ).
cnf(c523,plain,
meet(X3,meet(complement(X3),X)) = complement(join(complement(X3),complement(meet(complement(X3),X)))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c524,plain,
join(complement(X3),complement(meet(complement(X3),X))) = top,
inference(substitution,[status(thm)],[c160]) ).
cnf(c525,plain,
complement(join(complement(X3),complement(meet(complement(X3),X)))) = complement(top),
inference(congruence,[status(thm)],[c524]) ).
cnf(c526,plain,
complement(join(complement(X3),complement(meet(complement(X3),X)))) = zero,
inference(transitivity,[status(thm)],[c525,c71]) ).
cnf(c527,plain,
meet(X3,meet(complement(X3),X)) = zero,
inference(transitivity,[status(thm)],[c523,c526]) ).
cnf(c528,plain,
meet(X3,meet(X,complement(X3))) = zero,
inference(transitivity,[status(thm)],[c522,c527]) ).
cnf(c529,plain,
meet(composition(x0,converse(x1)),meet(complement(x2),complement(composition(x0,converse(x1))))) = zero,
inference(substitution,[status(thm)],[c528]) ).
cnf(c530,plain,
meet(composition(x0,converse(x1)),complement(x2)) = zero,
inference(transitivity,[status(thm)],[c520,c529]) ).
cnf(c531,plain,
meet(complement(x2),composition(x0,converse(x1))) = zero,
inference(transitivity,[status(thm)],[c432,c530]) ).
cnf(c532,plain,
zero = meet(complement(x2),composition(x0,converse(x1))),
inference(symmetry,[status(thm)],[c531]) ).
cnf(c533,plain,
composition(zero,meet(x1,composition(converse(complement(x2)),x0))) = composition(meet(complement(x2),composition(x0,converse(x1))),meet(x1,composition(converse(complement(x2)),x0))),
inference(congruence,[status(thm)],[c532]) ).
cnf(c534,plain,
join(meet(composition(complement(x2),x1),x0),composition(zero,meet(x1,composition(converse(complement(x2)),x0)))) = join(meet(composition(complement(x2),x1),x0),composition(meet(complement(x2),composition(x0,converse(x1))),meet(x1,composition(converse(complement(x2)),x0)))),
inference(congruence,[status(thm)],[c533]) ).
cnf(c535,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/sandbox/benchmark/theBenchmark.p',dedekind_law) ).
cnf(c536,plain,
join(meet(composition(complement(x2),x1),x0),composition(meet(complement(x2),composition(x0,converse(x1))),meet(x1,composition(converse(complement(x2)),x0)))) = composition(meet(complement(x2),composition(x0,converse(x1))),meet(x1,composition(converse(complement(x2)),x0))),
inference(substitution,[status(thm)],[c535]) ).
cnf(c537,plain,
composition(meet(complement(x2),composition(x0,converse(x1))),meet(x1,composition(converse(complement(x2)),x0))) = composition(zero,meet(x1,composition(converse(complement(x2)),x0))),
inference(congruence,[status(thm)],[c531]) ).
cnf(c538,plain,
composition(zero,meet(x1,composition(converse(complement(x2)),x0))) = zero,
inference(substitution,[status(thm)],[c428]) ).
cnf(c539,plain,
composition(meet(complement(x2),composition(x0,converse(x1))),meet(x1,composition(converse(complement(x2)),x0))) = zero,
inference(transitivity,[status(thm)],[c537,c538]) ).
cnf(c540,plain,
join(meet(composition(complement(x2),x1),x0),composition(meet(complement(x2),composition(x0,converse(x1))),meet(x1,composition(converse(complement(x2)),x0)))) = zero,
inference(transitivity,[status(thm)],[c536,c539]) ).
cnf(c541,plain,
join(meet(composition(complement(x2),x1),x0),composition(zero,meet(x1,composition(converse(complement(x2)),x0)))) = zero,
inference(transitivity,[status(thm)],[c534,c540]) ).
cnf(c542,plain,
join(meet(composition(complement(x2),x1),x0),zero) = zero,
inference(transitivity,[status(thm)],[c431,c541]) ).
cnf(c543,plain,
meet(composition(complement(x2),x1),x0) = zero,
inference(transitivity,[status(thm)],[c291,c542]) ).
cnf(c544,plain,
meet(x0,composition(complement(x2),x1)) = zero,
inference(transitivity,[status(thm)],[c40,c543]) ).
cnf(c545,plain,
meet(join(composition(complement(x2),x1),complement(x0)),meet(x0,composition(complement(x2),x1))) = meet(join(composition(complement(x2),x1),complement(x0)),zero),
inference(congruence,[status(thm)],[c544]) ).
cnf(c546,plain,
join(complement(x0),meet(join(composition(complement(x2),x1),complement(x0)),meet(x0,composition(complement(x2),x1)))) = join(complement(x0),meet(join(composition(complement(x2),x1),complement(x0)),zero)),
inference(congruence,[status(thm)],[c545]) ).
cnf(c547,plain,
meet(join(composition(complement(x2),x1),complement(x0)),zero) = zero,
inference(substitution,[status(thm)],[c232]) ).
cnf(c548,plain,
join(complement(x0),meet(join(composition(complement(x2),x1),complement(x0)),zero)) = join(complement(x0),zero),
inference(congruence,[status(thm)],[c547]) ).
cnf(c549,plain,
join(complement(x0),zero) = complement(x0),
inference(substitution,[status(thm)],[c289]) ).
cnf(c550,plain,
join(complement(x0),meet(join(composition(complement(x2),x1),complement(x0)),zero)) = complement(x0),
inference(transitivity,[status(thm)],[c548,c549]) ).
cnf(c551,plain,
join(complement(x0),meet(join(composition(complement(x2),x1),complement(x0)),meet(x0,composition(complement(x2),x1)))) = complement(x0),
inference(transitivity,[status(thm)],[c546,c550]) ).
cnf(c552,plain,
join(composition(complement(x2),x1),complement(x0)) = complement(x0),
inference(transitivity,[status(thm)],[c31,c551]) ).
cnf(c553,plain,
$false,
inference(resolution,[status(thm)],[c4,c552]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL043+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n005.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.44 % DateTime : Sun Sep 27 22:56:46 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.62/2.28 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 12.62/2.28
% 12.62/2.28 % SZS status Theorem
% 12.62/2.28
% 14.18/2.32 % SZS output start CNFRefutation
% See solution above
% 15.76/2.60
% 15.76/2.60 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------