%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL001+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 12:32:57 PM UTC 2026
% Result : Theorem 0.47s 0.49s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 12
% Syntax : Number of formulae : 178 ( 178 unt; 0 def)
% Number of atoms : 178 ( 177 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 200 ( 8 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,conjecture,
join(zero,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c2,negated_conjecture,
~ ! [X0_2] : join(zero,X0_2) = X0_2,
inference(negate_conjecture,[status(cth)],[c1]) ).
cnf(c3,plain,
join(zero,x0) != x0,
inference(clausify,[status(esa)],[c2]) ).
cnf(c4,axiom,
meet(X0_2,X1) = complement(join(complement(X0_2),complement(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
cnf(c5,plain,
meet(X,X3) = complement(join(complement(X),complement(X3))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,axiom,
join(X0_2,X1_2) = join(X1_2,X0_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
cnf(c7,plain,
join(complement(X3),complement(X)) = join(complement(X),complement(X3)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
join(complement(X),complement(X3)) = join(complement(X3),complement(X)),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
complement(join(complement(X),complement(X3))) = complement(join(complement(X3),complement(X))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c11,plain,
complement(join(complement(X3),complement(X))) = meet(X3,X),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
complement(join(complement(X),complement(X3))) = meet(X3,X),
inference(transitivity,[status(thm)],[c9,c11]) ).
cnf(c13,plain,
meet(X,X3) = meet(X3,X),
inference(transitivity,[status(thm)],[c5,c12]) ).
cnf(c14,plain,
meet(top,complement(X)) = meet(complement(X),top),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,axiom,
top = join(X0_2,complement(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
cnf(c16,plain,
top = join(complement(X),complement(complement(X))),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
complement(top) = complement(join(complement(X),complement(complement(X)))),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
meet(X,complement(X)) = complement(join(complement(X),complement(complement(X)))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c19,plain,
complement(join(complement(X),complement(complement(X)))) = meet(X,complement(X)),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,axiom,
zero = meet(X0_2,complement(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
cnf(c21,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
meet(X,complement(X)) = zero,
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
complement(join(complement(X),complement(complement(X)))) = zero,
inference(transitivity,[status(thm)],[c19,c22]) ).
cnf(c24,plain,
complement(top) = zero,
inference(transitivity,[status(thm)],[c17,c23]) ).
cnf(c25,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
join(zero,complement(X)) = join(complement(top),complement(X)),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
complement(join(zero,complement(X))) = complement(join(complement(top),complement(X))),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
meet(top,X) = complement(join(complement(top),complement(X))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c29,plain,
complement(join(complement(top),complement(X))) = meet(top,X),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
meet(X,top) = meet(top,X),
inference(substitution,[status(thm)],[c13]) ).
cnf(c31,plain,
meet(top,X) = meet(X,top),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
complement(join(complement(top),complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c29,c31]) ).
cnf(c33,plain,
complement(join(zero,complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c27,c32]) ).
cnf(c34,plain,
complement(join(zero,complement(complement(X)))) = meet(complement(X),top),
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
meet(complement(X),top) = complement(join(zero,complement(complement(X)))),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c37,plain,
join(zero,complement(complement(X))) = join(meet(X,complement(X)),complement(complement(X))),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,axiom,
converse(composition(X0_2,X1_2)) = composition(converse(X1_2),converse(X0_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
cnf(c39,plain,
converse(composition(converse(X3),X)) = composition(converse(X),converse(converse(X3))),
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,axiom,
converse(converse(X0_2)) = X0_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
cnf(c41,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
composition(converse(X),converse(converse(X3))) = composition(converse(X),X3),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
converse(composition(converse(X3),X)) = composition(converse(X),X3),
inference(transitivity,[status(thm)],[c39,c42]) ).
cnf(c44,plain,
converse(composition(converse(X),one)) = composition(converse(one),X),
inference(substitution,[status(thm)],[c43]) ).
cnf(c45,plain,
composition(converse(one),X) = converse(composition(converse(X),one)),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,axiom,
composition(X0_2,one) = X0_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).
cnf(c47,plain,
composition(converse(X),one) = converse(X),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
converse(composition(converse(X),one)) = converse(converse(X)),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c40]) ).
cnf(c50,plain,
converse(composition(converse(X),one)) = X,
inference(transitivity,[status(thm)],[c48,c49]) ).
cnf(c51,plain,
composition(converse(one),X) = X,
inference(transitivity,[status(thm)],[c45,c50]) ).
cnf(c52,plain,
composition(converse(one),complement(X)) = complement(X),
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
complement(X) = composition(converse(one),complement(X)),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
join(complement(X),complement(X)) = join(complement(X),composition(converse(one),complement(X))),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
composition(converse(one),composition(one,X)) = composition(one,X),
inference(substitution,[status(thm)],[c51]) ).
cnf(c56,plain,
composition(one,X) = composition(converse(one),composition(one,X)),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,axiom,
composition(X0_2,composition(X1_2,X2)) = composition(composition(X0_2,X1_2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity) ).
cnf(c58,plain,
composition(X3,composition(one,X)) = composition(composition(X3,one),X),
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c46]) ).
cnf(c60,plain,
composition(composition(X3,one),X) = composition(X3,X),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
composition(X3,composition(one,X)) = composition(X3,X),
inference(transitivity,[status(thm)],[c58,c60]) ).
cnf(c62,plain,
composition(converse(one),composition(one,X)) = composition(converse(one),X),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
composition(converse(one),composition(one,X)) = X,
inference(transitivity,[status(thm)],[c62,c51]) ).
cnf(c64,plain,
composition(one,X) = X,
inference(transitivity,[status(thm)],[c56,c63]) ).
cnf(c65,plain,
X = composition(one,X),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
complement(X) = complement(composition(one,X)),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
composition(converse(one),complement(X)) = composition(converse(one),complement(composition(one,X))),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
join(complement(X),composition(converse(one),complement(X))) = join(complement(X),composition(converse(one),complement(composition(one,X)))),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,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)],[c6]) ).
cnf(c70,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)],[c69]) ).
cnf(c71,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(c72,plain,
join(composition(converse(X),complement(composition(X,X3))),complement(X3)) = complement(X3),
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
join(complement(X3),composition(converse(X),complement(composition(X,X3)))) = complement(X3),
inference(transitivity,[status(thm)],[c70,c72]) ).
cnf(c74,plain,
join(complement(X),composition(converse(one),complement(composition(one,X)))) = complement(X),
inference(substitution,[status(thm)],[c73]) ).
cnf(c75,plain,
join(complement(X),composition(converse(one),complement(X))) = complement(X),
inference(transitivity,[status(thm)],[c68,c74]) ).
cnf(c76,plain,
join(complement(X),complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c54,c75]) ).
cnf(c77,plain,
complement(X) = join(complement(X),complement(X)),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
complement(complement(X)) = complement(join(complement(X),complement(X))),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
join(meet(X,complement(X)),complement(complement(X))) = join(meet(X,complement(X)),complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c81,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)],[c80]) ).
cnf(c82,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(c83,plain,
X3 = join(complement(join(complement(X3),complement(X))),complement(join(complement(X3),X))),
inference(substitution,[status(thm)],[c82]) ).
cnf(c84,plain,
join(complement(join(complement(X3),complement(X))),complement(join(complement(X3),X))) = X3,
inference(symmetry,[status(thm)],[c83]) ).
cnf(c85,plain,
join(meet(X3,X),complement(join(complement(X3),X))) = X3,
inference(transitivity,[status(thm)],[c81,c84]) ).
cnf(c86,plain,
join(meet(X,complement(X)),complement(join(complement(X),complement(X)))) = X,
inference(substitution,[status(thm)],[c85]) ).
cnf(c87,plain,
join(meet(X,complement(X)),complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c79,c86]) ).
cnf(c88,plain,
join(zero,complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c37,c87]) ).
cnf(c89,plain,
complement(join(zero,complement(complement(X)))) = complement(X),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
meet(complement(X),top) = complement(X),
inference(transitivity,[status(thm)],[c35,c89]) ).
cnf(c91,plain,
meet(top,complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c14,c90]) ).
cnf(c92,plain,
complement(X) = meet(top,complement(X)),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c93,plain,
join(zero,complement(X)) = join(zero,meet(top,complement(X))),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
meet(top,X) = meet(X,top),
inference(substitution,[status(thm)],[c13]) ).
cnf(c95,plain,
join(zero,meet(top,X)) = join(zero,meet(X,top)),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
meet(zero,X) = meet(X,zero),
inference(substitution,[status(thm)],[c13]) ).
cnf(c97,plain,
join(meet(X,top),meet(zero,X)) = join(meet(X,top),meet(X,zero)),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c99,plain,
meet(X,zero) = meet(X,complement(top)),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
join(meet(X,top),meet(X,zero)) = join(meet(X,top),meet(X,complement(top))),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
join(meet(X3,complement(X)),meet(X3,X)) = join(meet(X3,X),meet(X3,complement(X))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c102,plain,
join(meet(X3,X),meet(X3,complement(X))) = join(meet(X3,complement(X)),meet(X3,X)),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
meet(X3,X) = complement(join(complement(X3),complement(X))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c104,plain,
join(meet(X3,complement(X)),meet(X3,X)) = join(meet(X3,complement(X)),complement(join(complement(X3),complement(X)))),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
join(meet(X3,complement(X)),complement(join(complement(X3),complement(X)))) = X3,
inference(substitution,[status(thm)],[c85]) ).
cnf(c106,plain,
join(meet(X3,complement(X)),meet(X3,X)) = X3,
inference(transitivity,[status(thm)],[c104,c105]) ).
cnf(c107,plain,
join(meet(X3,X),meet(X3,complement(X))) = X3,
inference(transitivity,[status(thm)],[c102,c106]) ).
cnf(c108,plain,
join(meet(X,top),meet(X,complement(top))) = X,
inference(substitution,[status(thm)],[c107]) ).
cnf(c109,plain,
join(meet(X,top),meet(X,zero)) = X,
inference(transitivity,[status(thm)],[c100,c108]) ).
cnf(c110,plain,
join(meet(X,top),meet(zero,X)) = X,
inference(transitivity,[status(thm)],[c97,c109]) ).
cnf(c111,plain,
join(meet(complement(zero),top),meet(zero,complement(zero))) = complement(zero),
inference(substitution,[status(thm)],[c110]) ).
cnf(c112,plain,
complement(zero) = join(meet(complement(zero),top),meet(zero,complement(zero))),
inference(symmetry,[status(thm)],[c111]) ).
cnf(c113,plain,
zero = meet(zero,complement(zero)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c114,plain,
meet(zero,complement(zero)) = zero,
inference(symmetry,[status(thm)],[c113]) ).
cnf(c115,plain,
join(meet(complement(zero),top),meet(zero,complement(zero))) = join(meet(complement(zero),top),zero),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,plain,
join(meet(complement(zero),top),zero) = join(zero,meet(complement(zero),top)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c117,plain,
meet(top,complement(zero)) = meet(complement(zero),top),
inference(substitution,[status(thm)],[c13]) ).
cnf(c118,plain,
meet(complement(zero),top) = meet(top,complement(zero)),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,plain,
join(zero,meet(complement(zero),top)) = join(zero,meet(top,complement(zero))),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
meet(top,complement(zero)) = complement(zero),
inference(substitution,[status(thm)],[c91]) ).
cnf(c121,plain,
join(zero,meet(top,complement(zero))) = join(zero,complement(zero)),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
top = join(zero,complement(zero)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c123,plain,
join(zero,complement(zero)) = top,
inference(symmetry,[status(thm)],[c122]) ).
cnf(c124,plain,
join(zero,meet(top,complement(zero))) = top,
inference(transitivity,[status(thm)],[c121,c123]) ).
cnf(c125,plain,
join(zero,meet(complement(zero),top)) = top,
inference(transitivity,[status(thm)],[c119,c124]) ).
cnf(c126,plain,
join(meet(complement(zero),top),zero) = top,
inference(transitivity,[status(thm)],[c116,c125]) ).
cnf(c127,plain,
join(meet(complement(zero),top),meet(zero,complement(zero))) = top,
inference(transitivity,[status(thm)],[c115,c126]) ).
cnf(c128,plain,
complement(zero) = top,
inference(transitivity,[status(thm)],[c112,c127]) ).
cnf(c129,plain,
top = complement(zero),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
meet(X,top) = meet(X,complement(zero)),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
join(zero,meet(X,top)) = join(zero,meet(X,complement(zero))),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,plain,
meet(X,zero) = meet(zero,X),
inference(substitution,[status(thm)],[c13]) ).
cnf(c133,plain,
meet(zero,X) = complement(join(complement(zero),complement(X))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c134,plain,
join(complement(zero),complement(X)) = join(top,complement(X)),
inference(congruence,[status(thm)],[c128]) ).
cnf(c135,plain,
complement(join(complement(zero),complement(X))) = complement(join(top,complement(X))),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
join(complement(X),top) = join(top,complement(X)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c137,plain,
join(top,complement(X)) = join(complement(X),top),
inference(symmetry,[status(thm)],[c136]) ).
cnf(c138,plain,
join(complement(X3),X) = join(X,complement(X3)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c139,plain,
join(X,complement(X3)) = join(complement(X3),X),
inference(symmetry,[status(thm)],[c138]) ).
cnf(c140,plain,
join(X3,join(X,complement(X3))) = join(X3,join(complement(X3),X)),
inference(congruence,[status(thm)],[c139]) ).
cnf(c141,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(c142,plain,
join(X3,join(complement(X3),X)) = join(join(X3,complement(X3)),X),
inference(substitution,[status(thm)],[c141]) ).
cnf(c143,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c144,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c143]) ).
cnf(c145,plain,
join(join(X3,complement(X3)),X) = join(top,X),
inference(congruence,[status(thm)],[c144]) ).
cnf(c146,plain,
join(top,X) = join(X,top),
inference(substitution,[status(thm)],[c6]) ).
cnf(c147,plain,
join(join(X3,complement(X3)),X) = join(X,top),
inference(transitivity,[status(thm)],[c145,c146]) ).
cnf(c148,plain,
join(X3,join(complement(X3),X)) = join(X,top),
inference(transitivity,[status(thm)],[c142,c147]) ).
cnf(c149,plain,
join(X3,join(X,complement(X3))) = join(X,top),
inference(transitivity,[status(thm)],[c140,c148]) ).
cnf(c150,plain,
join(X,join(complement(X),complement(X))) = join(complement(X),top),
inference(substitution,[status(thm)],[c149]) ).
cnf(c151,plain,
join(complement(X),top) = join(X,join(complement(X),complement(X))),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
join(X,join(complement(X),complement(X))) = join(X,complement(X)),
inference(congruence,[status(thm)],[c76]) ).
cnf(c153,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c154,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c153]) ).
cnf(c155,plain,
join(X,join(complement(X),complement(X))) = top,
inference(transitivity,[status(thm)],[c152,c154]) ).
cnf(c156,plain,
join(complement(X),top) = top,
inference(transitivity,[status(thm)],[c151,c155]) ).
cnf(c157,plain,
join(top,complement(X)) = top,
inference(transitivity,[status(thm)],[c137,c156]) ).
cnf(c158,plain,
complement(join(top,complement(X))) = complement(top),
inference(congruence,[status(thm)],[c157]) ).
cnf(c159,plain,
complement(join(top,complement(X))) = zero,
inference(transitivity,[status(thm)],[c158,c24]) ).
cnf(c160,plain,
complement(join(complement(zero),complement(X))) = zero,
inference(transitivity,[status(thm)],[c135,c159]) ).
cnf(c161,plain,
meet(zero,X) = zero,
inference(transitivity,[status(thm)],[c133,c160]) ).
cnf(c162,plain,
meet(X,zero) = zero,
inference(transitivity,[status(thm)],[c132,c161]) ).
cnf(c163,plain,
zero = meet(X,zero),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c164,plain,
join(zero,meet(X,complement(zero))) = join(meet(X,zero),meet(X,complement(zero))),
inference(congruence,[status(thm)],[c163]) ).
cnf(c165,plain,
join(meet(X,zero),meet(X,complement(zero))) = X,
inference(substitution,[status(thm)],[c107]) ).
cnf(c166,plain,
join(zero,meet(X,complement(zero))) = X,
inference(transitivity,[status(thm)],[c164,c165]) ).
cnf(c167,plain,
join(zero,meet(X,top)) = X,
inference(transitivity,[status(thm)],[c131,c166]) ).
cnf(c168,plain,
join(zero,meet(top,X)) = X,
inference(transitivity,[status(thm)],[c95,c167]) ).
cnf(c169,plain,
join(zero,meet(top,complement(X))) = complement(X),
inference(substitution,[status(thm)],[c168]) ).
cnf(c170,plain,
join(zero,complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c93,c169]) ).
cnf(c171,plain,
join(zero,complement(complement(X))) = complement(complement(X)),
inference(substitution,[status(thm)],[c170]) ).
cnf(c172,plain,
complement(complement(X)) = join(zero,complement(complement(X))),
inference(symmetry,[status(thm)],[c171]) ).
cnf(c173,plain,
complement(complement(X)) = X,
inference(transitivity,[status(thm)],[c172,c88]) ).
cnf(c174,plain,
X = complement(complement(X)),
inference(symmetry,[status(thm)],[c173]) ).
cnf(c175,plain,
join(zero,X) = join(zero,complement(complement(X))),
inference(congruence,[status(thm)],[c174]) ).
cnf(c176,plain,
join(zero,X) = X,
inference(transitivity,[status(thm)],[c175,c88]) ).
cnf(c177,plain,
join(zero,x0) = x0,
inference(substitution,[status(thm)],[c176]) ).
cnf(c178,plain,
$false,
inference(resolution,[status(thm)],[c3,c177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL001+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 22:50:54 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.49 Command-line arguments: --no-flatten-goal
% 0.47/0.49
% 0.47/0.49 % SZS status Theorem
% 0.47/0.49
% 0.47/0.50 % SZS output start CNFRefutation
% See solution above
% 0.47/0.57
% 0.47/0.57 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------