%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL011+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 12:33:04 PM UTC 2026
% Result : Theorem 2.53s 0.81s
% Output : CNFRefutation 3.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 16
% Syntax : Number of formulae : 264 ( 258 unt; 0 def)
% Number of atoms : 270 ( 269 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 : 7 ( 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 : 246 ( 26 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c1,conjecture,
! [X0,X1,X2] :
( meet(X0,composition(converse(X1),X2)) = zero
=> meet(composition(X1,X0),X2) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c2,negated_conjecture,
~ ! [X0_2,X1_2,X2_2] :
( meet(X0_2,composition(converse(X1_2),X2_2)) = zero
=> meet(composition(X1_2,X0_2),X2_2) = zero ),
inference(negate_conjecture,[status(cth)],[c1]) ).
fof(c3,plain,
( meet(x0,composition(converse(x1),x2)) = zero
& meet(composition(x1,x0),x2) != zero ),
inference(clausify,[status(esa)],[c2]) ).
cnf(c4,plain,
meet(composition(x1,x0),x2) != zero,
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(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/sandbox/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/sandbox/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/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,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_2)) = join(join(X0_2,X1_2),X2_2),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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(x1,x0),x2),zero) = meet(composition(x1,x0),x2),
inference(substitution,[status(thm)],[c101]) ).
cnf(c103,plain,
meet(composition(x1,x0),x2) = join(meet(composition(x1,x0),x2),zero),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c104,plain,
meet(X,X3) = complement(join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c105,plain,
join(complement(X3),complement(X)) = join(complement(X),complement(X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c106,plain,
join(complement(X),complement(X3)) = join(complement(X3),complement(X)),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c107,plain,
complement(join(complement(X),complement(X3))) = complement(join(complement(X3),complement(X))),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c109,plain,
complement(join(complement(X3),complement(X))) = meet(X3,X),
inference(symmetry,[status(thm)],[c108]) ).
cnf(c110,plain,
complement(join(complement(X),complement(X3))) = meet(X3,X),
inference(transitivity,[status(thm)],[c107,c109]) ).
cnf(c111,plain,
meet(X,X3) = meet(X3,X),
inference(transitivity,[status(thm)],[c104,c110]) ).
cnf(c112,plain,
meet(zero,X) = meet(X,zero),
inference(substitution,[status(thm)],[c111]) ).
cnf(c113,plain,
meet(X,zero) = meet(zero,X),
inference(substitution,[status(thm)],[c111]) ).
cnf(c114,plain,
meet(zero,X) = complement(join(complement(zero),complement(X))),
inference(substitution,[status(thm)],[c8]) ).
cnf(c115,plain,
join(X,zero) = join(zero,X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c116,plain,
join(zero,X) = join(X,zero),
inference(symmetry,[status(thm)],[c115]) ).
cnf(c117,plain,
join(zero,X) = X,
inference(transitivity,[status(thm)],[c116,c101]) ).
cnf(c118,plain,
join(zero,complement(zero)) = complement(zero),
inference(substitution,[status(thm)],[c117]) ).
cnf(c119,plain,
complement(zero) = join(zero,complement(zero)),
inference(symmetry,[status(thm)],[c118]) ).
cnf(c120,plain,
top = join(zero,complement(zero)),
inference(substitution,[status(thm)],[c33]) ).
cnf(c121,plain,
join(zero,complement(zero)) = top,
inference(symmetry,[status(thm)],[c120]) ).
cnf(c122,plain,
complement(zero) = top,
inference(transitivity,[status(thm)],[c119,c121]) ).
cnf(c123,plain,
join(complement(zero),complement(X)) = join(top,complement(X)),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
complement(join(complement(zero),complement(X))) = complement(join(top,complement(X))),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
join(complement(X),top) = join(top,complement(X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c126,plain,
join(top,complement(X)) = join(complement(X),top),
inference(symmetry,[status(thm)],[c125]) ).
cnf(c127,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c128,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(symmetry,[status(thm)],[c127]) ).
cnf(c129,plain,
join(X3,join(X,complement(X3))) = join(X3,join(complement(X3),X)),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
join(X3,join(complement(X3),X)) = join(join(X3,complement(X3)),X),
inference(substitution,[status(thm)],[c31]) ).
cnf(c131,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c33]) ).
cnf(c132,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c131]) ).
cnf(c133,plain,
join(join(X3,complement(X3)),X) = join(top,X),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
join(top,X) = join(X,top),
inference(substitution,[status(thm)],[c5]) ).
cnf(c135,plain,
join(join(X3,complement(X3)),X) = join(X,top),
inference(transitivity,[status(thm)],[c133,c134]) ).
cnf(c136,plain,
join(X3,join(complement(X3),X)) = join(X,top),
inference(transitivity,[status(thm)],[c130,c135]) ).
cnf(c137,plain,
join(X3,join(X,complement(X3))) = join(X,top),
inference(transitivity,[status(thm)],[c129,c136]) ).
cnf(c138,plain,
join(X,join(complement(X),complement(X))) = join(complement(X),top),
inference(substitution,[status(thm)],[c137]) ).
cnf(c139,plain,
join(complement(X),top) = join(X,join(complement(X),complement(X))),
inference(symmetry,[status(thm)],[c138]) ).
cnf(c140,plain,
join(X,join(complement(X),complement(X))) = join(X,complement(X)),
inference(congruence,[status(thm)],[c85]) ).
cnf(c141,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c33]) ).
cnf(c142,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c141]) ).
cnf(c143,plain,
join(X,join(complement(X),complement(X))) = top,
inference(transitivity,[status(thm)],[c140,c142]) ).
cnf(c144,plain,
join(complement(X),top) = top,
inference(transitivity,[status(thm)],[c139,c143]) ).
cnf(c145,plain,
join(top,complement(X)) = top,
inference(transitivity,[status(thm)],[c126,c144]) ).
cnf(c146,plain,
complement(join(top,complement(X))) = complement(top),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
complement(join(top,complement(X))) = zero,
inference(transitivity,[status(thm)],[c146,c41]) ).
cnf(c148,plain,
complement(join(complement(zero),complement(X))) = zero,
inference(transitivity,[status(thm)],[c124,c147]) ).
cnf(c149,plain,
meet(zero,X) = zero,
inference(transitivity,[status(thm)],[c114,c148]) ).
cnf(c150,plain,
meet(X,zero) = zero,
inference(transitivity,[status(thm)],[c113,c149]) ).
cnf(c151,plain,
meet(zero,X) = zero,
inference(transitivity,[status(thm)],[c112,c150]) ).
cnf(c152,plain,
meet(zero,x2) = zero,
inference(substitution,[status(thm)],[c151]) ).
cnf(c153,plain,
zero = meet(zero,x2),
inference(symmetry,[status(thm)],[c152]) ).
cnf(c154,plain,
join(meet(composition(x1,x0),x2),zero) = join(meet(composition(x1,x0),x2),meet(zero,x2)),
inference(congruence,[status(thm)],[c153]) ).
cnf(c155,plain,
join(zero,composition(X,zero)) = composition(X,zero),
inference(substitution,[status(thm)],[c117]) ).
cnf(c156,plain,
composition(X,zero) = join(zero,composition(X,zero)),
inference(symmetry,[status(thm)],[c155]) ).
cnf(c157,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c158,plain,
composition(top,zero) = composition(top,complement(top)),
inference(congruence,[status(thm)],[c157]) ).
cnf(c159,plain,
join(X,top) = join(top,X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c160,plain,
join(top,X) = join(X,top),
inference(symmetry,[status(thm)],[c159]) ).
cnf(c161,plain,
top = join(top,complement(X)),
inference(symmetry,[status(thm)],[c145]) ).
cnf(c162,plain,
join(X,top) = join(X,join(top,complement(X))),
inference(congruence,[status(thm)],[c161]) ).
cnf(c163,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c137]) ).
cnf(c164,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c137]) ).
cnf(c165,plain,
join(top,top) = join(X,join(top,complement(X))),
inference(symmetry,[status(thm)],[c164]) ).
cnf(c166,plain,
join(X,join(top,complement(X))) = join(X,top),
inference(congruence,[status(thm)],[c145]) ).
cnf(c167,plain,
join(top,top) = join(X,top),
inference(transitivity,[status(thm)],[c165,c166]) ).
cnf(c168,plain,
join(X,join(top,complement(X))) = join(X3,top),
inference(transitivity,[status(thm)],[c163,c167]) ).
cnf(c169,plain,
join(X,top) = join(X3,top),
inference(transitivity,[status(thm)],[c162,c168]) ).
cnf(c170,plain,
join(X3,top) = join(X,top),
inference(symmetry,[status(thm)],[c169]) ).
cnf(c171,plain,
join(X,top) = join(zero,top),
inference(substitution,[status(thm)],[c169]) ).
cnf(c172,plain,
join(zero,top) = top,
inference(substitution,[status(thm)],[c117]) ).
cnf(c173,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c171,c172]) ).
cnf(c174,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c170,c173]) ).
cnf(c175,plain,
join(top,X) = top,
inference(transitivity,[status(thm)],[c160,c174]) ).
cnf(c176,plain,
join(top,one) = top,
inference(substitution,[status(thm)],[c175]) ).
cnf(c177,plain,
top = join(top,one),
inference(symmetry,[status(thm)],[c176]) ).
cnf(c178,plain,
composition(top,complement(top)) = composition(join(top,one),complement(top)),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c180,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c179]) ).
cnf(c181,plain,
join(X,converse(complement(converse(X)))) = join(converse(converse(X)),converse(complement(converse(X)))),
inference(congruence,[status(thm)],[c180]) ).
cnf(c182,axiom,
converse(join(X0_2,X1_2)) = join(converse(X0_2),converse(X1_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity) ).
cnf(c183,plain,
converse(join(X,complement(X))) = join(converse(X),converse(complement(X))),
inference(substitution,[status(thm)],[c182]) ).
cnf(c184,plain,
join(converse(X),converse(complement(X))) = converse(join(X,complement(X))),
inference(symmetry,[status(thm)],[c183]) ).
cnf(c185,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c33]) ).
cnf(c186,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c185]) ).
cnf(c187,plain,
converse(join(X,complement(X))) = converse(top),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
join(converse(X),converse(complement(X))) = converse(top),
inference(transitivity,[status(thm)],[c184,c187]) ).
cnf(c189,plain,
join(converse(converse(X)),converse(complement(converse(X)))) = converse(top),
inference(substitution,[status(thm)],[c188]) ).
cnf(c190,plain,
join(X,converse(complement(converse(X)))) = converse(top),
inference(transitivity,[status(thm)],[c181,c189]) ).
cnf(c191,plain,
join(top,converse(complement(converse(top)))) = converse(top),
inference(substitution,[status(thm)],[c190]) ).
cnf(c192,plain,
converse(top) = join(top,converse(complement(converse(top)))),
inference(symmetry,[status(thm)],[c191]) ).
cnf(c193,plain,
join(top,converse(complement(converse(top)))) = top,
inference(substitution,[status(thm)],[c175]) ).
cnf(c194,plain,
converse(top) = top,
inference(transitivity,[status(thm)],[c192,c193]) ).
cnf(c195,plain,
top = converse(top),
inference(symmetry,[status(thm)],[c194]) ).
cnf(c196,plain,
join(top,one) = join(converse(top),one),
inference(congruence,[status(thm)],[c195]) ).
cnf(c197,plain,
composition(join(top,one),complement(top)) = composition(join(converse(top),one),complement(top)),
inference(congruence,[status(thm)],[c196]) ).
cnf(c198,plain,
X = composition(one,X),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c199,plain,
join(X3,composition(X,X3)) = join(composition(one,X3),composition(X,X3)),
inference(congruence,[status(thm)],[c198]) ).
cnf(c200,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(c201,plain,
composition(join(one,X),X3) = join(composition(one,X3),composition(X,X3)),
inference(substitution,[status(thm)],[c200]) ).
cnf(c202,plain,
join(composition(one,X3),composition(X,X3)) = composition(join(one,X),X3),
inference(symmetry,[status(thm)],[c201]) ).
cnf(c203,plain,
join(one,X) = join(X,one),
inference(substitution,[status(thm)],[c5]) ).
cnf(c204,plain,
composition(join(one,X),X3) = composition(join(X,one),X3),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
join(composition(one,X3),composition(X,X3)) = composition(join(X,one),X3),
inference(transitivity,[status(thm)],[c202,c204]) ).
cnf(c206,plain,
join(X3,composition(X,X3)) = composition(join(X,one),X3),
inference(transitivity,[status(thm)],[c199,c205]) ).
cnf(c207,plain,
join(complement(top),composition(converse(top),complement(top))) = composition(join(converse(top),one),complement(top)),
inference(substitution,[status(thm)],[c206]) ).
cnf(c208,plain,
composition(join(converse(top),one),complement(top)) = join(complement(top),composition(converse(top),complement(top))),
inference(symmetry,[status(thm)],[c207]) ).
cnf(c209,plain,
join(top,one) = top,
inference(substitution,[status(thm)],[c175]) ).
cnf(c210,plain,
top = join(top,one),
inference(symmetry,[status(thm)],[c209]) ).
cnf(c211,plain,
composition(top,top) = composition(join(top,one),top),
inference(congruence,[status(thm)],[c210]) ).
cnf(c212,plain,
join(top,composition(X,top)) = composition(join(X,one),top),
inference(substitution,[status(thm)],[c206]) ).
cnf(c213,plain,
composition(join(X,one),top) = join(top,composition(X,top)),
inference(symmetry,[status(thm)],[c212]) ).
cnf(c214,plain,
join(top,composition(X,top)) = top,
inference(substitution,[status(thm)],[c175]) ).
cnf(c215,plain,
composition(join(X,one),top) = top,
inference(transitivity,[status(thm)],[c213,c214]) ).
cnf(c216,plain,
composition(join(top,one),top) = top,
inference(substitution,[status(thm)],[c215]) ).
cnf(c217,plain,
composition(top,top) = top,
inference(transitivity,[status(thm)],[c211,c216]) ).
cnf(c218,plain,
top = composition(top,top),
inference(symmetry,[status(thm)],[c217]) ).
cnf(c219,plain,
complement(top) = complement(composition(top,top)),
inference(congruence,[status(thm)],[c218]) ).
cnf(c220,plain,
composition(converse(top),complement(top)) = composition(converse(top),complement(composition(top,top))),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
join(complement(top),composition(converse(top),complement(top))) = join(complement(top),composition(converse(top),complement(composition(top,top)))),
inference(congruence,[status(thm)],[c220]) ).
cnf(c222,plain,
join(complement(top),composition(converse(top),complement(composition(top,top)))) = complement(top),
inference(substitution,[status(thm)],[c82]) ).
cnf(c223,plain,
join(complement(top),composition(converse(top),complement(composition(top,top)))) = zero,
inference(transitivity,[status(thm)],[c222,c41]) ).
cnf(c224,plain,
join(complement(top),composition(converse(top),complement(top))) = zero,
inference(transitivity,[status(thm)],[c221,c223]) ).
cnf(c225,plain,
composition(join(converse(top),one),complement(top)) = zero,
inference(transitivity,[status(thm)],[c208,c224]) ).
cnf(c226,plain,
composition(join(top,one),complement(top)) = zero,
inference(transitivity,[status(thm)],[c197,c225]) ).
cnf(c227,plain,
composition(top,complement(top)) = zero,
inference(transitivity,[status(thm)],[c178,c226]) ).
cnf(c228,plain,
composition(top,zero) = zero,
inference(transitivity,[status(thm)],[c158,c227]) ).
cnf(c229,plain,
zero = composition(top,zero),
inference(symmetry,[status(thm)],[c228]) ).
cnf(c230,plain,
join(zero,composition(X,zero)) = join(composition(top,zero),composition(X,zero)),
inference(congruence,[status(thm)],[c229]) ).
cnf(c231,plain,
composition(join(top,X),zero) = join(composition(top,zero),composition(X,zero)),
inference(substitution,[status(thm)],[c200]) ).
cnf(c232,plain,
join(composition(top,zero),composition(X,zero)) = composition(join(top,X),zero),
inference(symmetry,[status(thm)],[c231]) ).
cnf(c233,plain,
composition(join(top,X),zero) = composition(top,zero),
inference(congruence,[status(thm)],[c175]) ).
cnf(c234,plain,
composition(join(top,X),zero) = zero,
inference(transitivity,[status(thm)],[c233,c228]) ).
cnf(c235,plain,
join(composition(top,zero),composition(X,zero)) = zero,
inference(transitivity,[status(thm)],[c232,c234]) ).
cnf(c236,plain,
join(zero,composition(X,zero)) = zero,
inference(transitivity,[status(thm)],[c230,c235]) ).
cnf(c237,plain,
composition(X,zero) = zero,
inference(transitivity,[status(thm)],[c156,c236]) ).
cnf(c238,plain,
composition(x1,zero) = zero,
inference(substitution,[status(thm)],[c237]) ).
cnf(c239,plain,
zero = composition(x1,zero),
inference(symmetry,[status(thm)],[c238]) ).
cnf(c240,plain,
meet(zero,x2) = meet(composition(x1,zero),x2),
inference(congruence,[status(thm)],[c239]) ).
cnf(c241,plain,
join(meet(composition(x1,x0),x2),meet(zero,x2)) = join(meet(composition(x1,x0),x2),meet(composition(x1,zero),x2)),
inference(congruence,[status(thm)],[c240]) ).
fof(c242,conjecture,
! [X0_2,X1_2,X2_2] :
( meet(X0_2,composition(converse(X1_2),X2_2)) = zero
=> meet(composition(X1_2,X0_2),X2_2) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c243,negated_conjecture,
~ ! [X0_2,X1_2,X2_2] :
( meet(X0_2,composition(converse(X1_2),X2_2)) = zero
=> meet(composition(X1_2,X0_2),X2_2) = zero ),
inference(negate_conjecture,[status(cth)],[c242]) ).
fof(c244,plain,
( meet(x0,composition(converse(x1),x2)) = zero
& meet(composition(x1,x0),x2) != zero ),
inference(clausify,[status(esa)],[c243]) ).
cnf(c245,plain,
meet(x0,composition(converse(x1),x2)) = zero,
inference(clausify,[status(thm)],[c244]) ).
cnf(c246,plain,
zero = meet(x0,composition(converse(x1),x2)),
inference(symmetry,[status(thm)],[c245]) ).
cnf(c247,plain,
composition(x1,zero) = composition(x1,meet(x0,composition(converse(x1),x2))),
inference(congruence,[status(thm)],[c246]) ).
cnf(c248,plain,
meet(composition(x1,zero),x2) = meet(composition(x1,meet(x0,composition(converse(x1),x2))),x2),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
join(meet(composition(x1,x0),x2),meet(composition(x1,zero),x2)) = join(meet(composition(x1,x0),x2),meet(composition(x1,meet(x0,composition(converse(x1),x2))),x2)),
inference(congruence,[status(thm)],[c248]) ).
cnf(c250,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(c251,plain,
join(meet(composition(x1,x0),x2),meet(composition(x1,meet(x0,composition(converse(x1),x2))),x2)) = meet(composition(x1,meet(x0,composition(converse(x1),x2))),x2),
inference(substitution,[status(thm)],[c250]) ).
cnf(c252,plain,
composition(x1,meet(x0,composition(converse(x1),x2))) = composition(x1,zero),
inference(congruence,[status(thm)],[c245]) ).
cnf(c253,plain,
meet(composition(x1,meet(x0,composition(converse(x1),x2))),x2) = meet(composition(x1,zero),x2),
inference(congruence,[status(thm)],[c252]) ).
cnf(c254,plain,
composition(x1,zero) = zero,
inference(substitution,[status(thm)],[c237]) ).
cnf(c255,plain,
meet(composition(x1,zero),x2) = meet(zero,x2),
inference(congruence,[status(thm)],[c254]) ).
cnf(c256,plain,
meet(zero,x2) = zero,
inference(substitution,[status(thm)],[c151]) ).
cnf(c257,plain,
meet(composition(x1,zero),x2) = zero,
inference(transitivity,[status(thm)],[c255,c256]) ).
cnf(c258,plain,
meet(composition(x1,meet(x0,composition(converse(x1),x2))),x2) = zero,
inference(transitivity,[status(thm)],[c253,c257]) ).
cnf(c259,plain,
join(meet(composition(x1,x0),x2),meet(composition(x1,meet(x0,composition(converse(x1),x2))),x2)) = zero,
inference(transitivity,[status(thm)],[c251,c258]) ).
cnf(c260,plain,
join(meet(composition(x1,x0),x2),meet(composition(x1,zero),x2)) = zero,
inference(transitivity,[status(thm)],[c249,c259]) ).
cnf(c261,plain,
join(meet(composition(x1,x0),x2),meet(zero,x2)) = zero,
inference(transitivity,[status(thm)],[c241,c260]) ).
cnf(c262,plain,
join(meet(composition(x1,x0),x2),zero) = zero,
inference(transitivity,[status(thm)],[c154,c261]) ).
cnf(c263,plain,
meet(composition(x1,x0),x2) = zero,
inference(transitivity,[status(thm)],[c103,c262]) ).
cnf(c264,plain,
$false,
inference(resolution,[status(thm)],[c4,c263]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL011+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n003.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 22:52:57 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.53/0.81 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 2.53/0.81
% 2.53/0.81 % SZS status Theorem
% 2.53/0.81
% 2.53/0.83 % SZS output start CNFRefutation
% See solution above
% 3.26/1.00
% 3.26/1.00 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------