%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL041-2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:33:29 PM UTC 2026
% Result : Unsatisfiable 18.97s 3.02s
% Output : CNFRefutation 22.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 73
% Number of leaves : 16
% Syntax : Number of clauses : 396 ( 396 unt; 0 nHn; 49 RR)
% Number of literals : 396 ( 395 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 535 ( 33 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
meet(composition(sk1,sk2),composition(sk1,complement(sk2))) != zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_18) ).
cnf(c2,axiom,
join(A,B) = join(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
cnf(c3,plain,
join(zero,X) = join(X,zero),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
join(X,zero) = join(zero,X),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
meet(A2,B2) = complement(join(complement(A2),complement(B2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
cnf(c6,plain,
meet(X,X) = complement(join(complement(X),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
join(zero,meet(X,X)) = join(zero,complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,axiom,
zero = meet(A2,complement(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero_13) ).
cnf(c9,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
join(zero,complement(join(complement(X),complement(X)))) = join(meet(X,complement(X)),complement(join(complement(X),complement(X)))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
meet(X,X2) = complement(join(complement(X),complement(X2))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c12,plain,
join(meet(X2,X),complement(join(complement(X2),X))) = join(complement(join(complement(X2),complement(X))),complement(join(complement(X2),X))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,axiom,
A2 = join(complement(join(complement(A2),complement(B2))),complement(join(complement(A2),B2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
cnf(c14,plain,
X2 = join(complement(join(complement(X2),complement(X))),complement(join(complement(X2),X))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
join(complement(join(complement(X2),complement(X))),complement(join(complement(X2),X))) = X2,
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
join(meet(X2,X),complement(join(complement(X2),X))) = X2,
inference(transitivity,[status(thm)],[c12,c15]) ).
cnf(c17,plain,
join(meet(X,complement(X)),complement(join(complement(X),complement(X)))) = X,
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
join(zero,complement(join(complement(X),complement(X)))) = X,
inference(transitivity,[status(thm)],[c10,c17]) ).
cnf(c19,plain,
join(zero,meet(X,X)) = X,
inference(transitivity,[status(thm)],[c7,c18]) ).
cnf(c20,plain,
X = join(zero,meet(X,X)),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
join(zero,X) = join(zero,join(zero,meet(X,X))),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
join(X,zero) = join(zero,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c23,plain,
join(zero,X) = join(X,zero),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
join(zero,join(zero,X)) = join(zero,join(X,zero)),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
join(zero,X) = join(X,zero),
inference(substitution,[status(thm)],[c2]) ).
cnf(c26,plain,
join(X,zero) = join(zero,X),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
join(zero,join(X,zero)) = join(zero,join(zero,X)),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,axiom,
join(A2,join(B2,C)) = join(join(A2,B2),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
cnf(c29,plain,
join(zero,join(zero,X)) = join(join(zero,zero),X),
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,axiom,
top = join(A2,complement(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top_12) ).
cnf(c31,plain,
top = join(complement(X),complement(complement(X))),
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
complement(top) = complement(join(complement(X),complement(complement(X)))),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
meet(X,complement(X)) = complement(join(complement(X),complement(complement(X)))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c34,plain,
complement(join(complement(X),complement(complement(X)))) = meet(X,complement(X)),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c36,plain,
meet(X,complement(X)) = zero,
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
complement(join(complement(X),complement(complement(X)))) = zero,
inference(transitivity,[status(thm)],[c34,c36]) ).
cnf(c38,plain,
complement(top) = zero,
inference(transitivity,[status(thm)],[c32,c37]) ).
cnf(c39,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
join(zero,zero) = join(zero,complement(top)),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c42,plain,
join(zero,complement(top)) = join(complement(top),complement(top)),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,axiom,
converse(converse(A2)) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence_8) ).
cnf(c44,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c43]) ).
cnf(c45,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,plain,
composition(converse(one),X) = composition(converse(one),converse(converse(X))),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,axiom,
converse(composition(A2,B2)) = composition(converse(B2),converse(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
cnf(c48,plain,
converse(composition(X,one)) = composition(converse(one),converse(X)),
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
composition(converse(one),converse(X)) = converse(composition(X,one)),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,axiom,
composition(A2,one) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity_6) ).
cnf(c51,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c50]) ).
cnf(c52,plain,
converse(composition(X,one)) = converse(X),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
composition(converse(one),converse(X)) = converse(X),
inference(transitivity,[status(thm)],[c49,c52]) ).
cnf(c54,plain,
composition(converse(one),converse(converse(X))) = converse(converse(X)),
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c43]) ).
cnf(c56,plain,
composition(converse(one),converse(converse(X))) = X,
inference(transitivity,[status(thm)],[c54,c55]) ).
cnf(c57,plain,
composition(converse(one),X) = X,
inference(transitivity,[status(thm)],[c46,c56]) ).
cnf(c58,plain,
composition(converse(one),complement(X)) = complement(X),
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
complement(X) = composition(converse(one),complement(X)),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,plain,
join(complement(X),complement(X)) = join(complement(X),composition(converse(one),complement(X))),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
composition(converse(one),composition(one,X)) = composition(one,X),
inference(substitution,[status(thm)],[c57]) ).
cnf(c62,plain,
composition(one,X) = composition(converse(one),composition(one,X)),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c63,axiom,
composition(A2,composition(B2,C2)) = composition(composition(A2,B2),C2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity_5) ).
cnf(c64,plain,
composition(X2,composition(one,X)) = composition(composition(X2,one),X),
inference(substitution,[status(thm)],[c63]) ).
cnf(c65,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c50]) ).
cnf(c66,plain,
composition(composition(X2,one),X) = composition(X2,X),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
composition(X2,composition(one,X)) = composition(X2,X),
inference(transitivity,[status(thm)],[c64,c66]) ).
cnf(c68,plain,
composition(converse(one),composition(one,X)) = composition(converse(one),X),
inference(substitution,[status(thm)],[c67]) ).
cnf(c69,plain,
composition(converse(one),composition(one,X)) = X,
inference(transitivity,[status(thm)],[c68,c57]) ).
cnf(c70,plain,
composition(one,X) = X,
inference(transitivity,[status(thm)],[c62,c69]) ).
cnf(c71,plain,
X = composition(one,X),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c72,plain,
complement(X) = complement(composition(one,X)),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
composition(converse(one),complement(X)) = composition(converse(one),complement(composition(one,X))),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
join(complement(X),composition(converse(one),complement(X))) = join(complement(X),composition(converse(one),complement(composition(one,X)))),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
join(composition(converse(X),complement(composition(X,X2))),complement(X2)) = join(complement(X2),composition(converse(X),complement(composition(X,X2)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c76,plain,
join(complement(X2),composition(converse(X),complement(composition(X,X2)))) = join(composition(converse(X),complement(composition(X,X2))),complement(X2)),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c77,axiom,
join(composition(converse(A2),complement(composition(A2,B2))),complement(B2)) = complement(B2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity_11) ).
cnf(c78,plain,
join(composition(converse(X),complement(composition(X,X2))),complement(X2)) = complement(X2),
inference(substitution,[status(thm)],[c77]) ).
cnf(c79,plain,
join(complement(X2),composition(converse(X),complement(composition(X,X2)))) = complement(X2),
inference(transitivity,[status(thm)],[c76,c78]) ).
cnf(c80,plain,
join(complement(X),composition(converse(one),complement(composition(one,X)))) = complement(X),
inference(substitution,[status(thm)],[c79]) ).
cnf(c81,plain,
join(complement(X),composition(converse(one),complement(X))) = complement(X),
inference(transitivity,[status(thm)],[c74,c80]) ).
cnf(c82,plain,
join(complement(X),complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c60,c81]) ).
cnf(c83,plain,
join(complement(top),complement(top)) = complement(top),
inference(substitution,[status(thm)],[c82]) ).
cnf(c84,plain,
join(complement(top),complement(top)) = zero,
inference(transitivity,[status(thm)],[c83,c38]) ).
cnf(c85,plain,
join(zero,complement(top)) = zero,
inference(transitivity,[status(thm)],[c42,c84]) ).
cnf(c86,plain,
join(zero,zero) = zero,
inference(transitivity,[status(thm)],[c40,c85]) ).
cnf(c87,plain,
join(join(zero,zero),X) = join(zero,X),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
join(zero,X) = join(X,zero),
inference(substitution,[status(thm)],[c2]) ).
cnf(c89,plain,
join(join(zero,zero),X) = join(X,zero),
inference(transitivity,[status(thm)],[c87,c88]) ).
cnf(c90,plain,
join(zero,join(zero,X)) = join(X,zero),
inference(transitivity,[status(thm)],[c29,c89]) ).
cnf(c91,plain,
join(zero,join(X,zero)) = join(X,zero),
inference(transitivity,[status(thm)],[c27,c90]) ).
cnf(c92,plain,
join(zero,join(zero,X)) = join(X,zero),
inference(transitivity,[status(thm)],[c24,c91]) ).
cnf(c93,plain,
join(zero,join(zero,meet(X,X))) = join(meet(X,X),zero),
inference(substitution,[status(thm)],[c92]) ).
cnf(c94,plain,
join(meet(X,X),zero) = join(zero,meet(X,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c95,plain,
join(meet(X,X),zero) = X,
inference(transitivity,[status(thm)],[c94,c19]) ).
cnf(c96,plain,
join(zero,join(zero,meet(X,X))) = X,
inference(transitivity,[status(thm)],[c93,c95]) ).
cnf(c97,plain,
join(zero,X) = X,
inference(transitivity,[status(thm)],[c21,c96]) ).
cnf(c98,plain,
join(X,zero) = X,
inference(transitivity,[status(thm)],[c4,c97]) ).
cnf(c99,plain,
join(meet(composition(sk1,X),composition(sk1,complement(X))),zero) = meet(composition(sk1,X),composition(sk1,complement(X))),
inference(substitution,[status(thm)],[c98]) ).
cnf(c100,plain,
meet(composition(sk1,X),composition(sk1,complement(X))) = join(meet(composition(sk1,X),composition(sk1,complement(X))),zero),
inference(symmetry,[status(thm)],[c99]) ).
cnf(c101,plain,
join(X,zero) = join(zero,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c102,plain,
join(zero,X) = join(X,zero),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
join(zero,X) = X,
inference(transitivity,[status(thm)],[c102,c98]) ).
cnf(c104,plain,
join(zero,composition(X,zero)) = composition(X,zero),
inference(substitution,[status(thm)],[c103]) ).
cnf(c105,plain,
composition(X,zero) = join(zero,composition(X,zero)),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c107,plain,
composition(top,zero) = composition(top,complement(top)),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
join(X,top) = join(top,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c109,plain,
join(top,X) = join(X,top),
inference(symmetry,[status(thm)],[c108]) ).
cnf(c110,plain,
join(complement(X),top) = join(top,complement(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c111,plain,
join(top,complement(X)) = join(complement(X),top),
inference(symmetry,[status(thm)],[c110]) ).
cnf(c112,plain,
join(complement(X2),X) = join(X,complement(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c113,plain,
join(X,complement(X2)) = join(complement(X2),X),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,plain,
join(X2,join(X,complement(X2))) = join(X2,join(complement(X2),X)),
inference(congruence,[status(thm)],[c113]) ).
cnf(c115,plain,
join(X2,join(complement(X2),X)) = join(join(X2,complement(X2)),X),
inference(substitution,[status(thm)],[c28]) ).
cnf(c116,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c30]) ).
cnf(c117,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c116]) ).
cnf(c118,plain,
join(join(X2,complement(X2)),X) = join(top,X),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
join(top,X) = join(X,top),
inference(substitution,[status(thm)],[c2]) ).
cnf(c120,plain,
join(join(X2,complement(X2)),X) = join(X,top),
inference(transitivity,[status(thm)],[c118,c119]) ).
cnf(c121,plain,
join(X2,join(complement(X2),X)) = join(X,top),
inference(transitivity,[status(thm)],[c115,c120]) ).
cnf(c122,plain,
join(X2,join(X,complement(X2))) = join(X,top),
inference(transitivity,[status(thm)],[c114,c121]) ).
cnf(c123,plain,
join(X,join(complement(X),complement(X))) = join(complement(X),top),
inference(substitution,[status(thm)],[c122]) ).
cnf(c124,plain,
join(complement(X),top) = join(X,join(complement(X),complement(X))),
inference(symmetry,[status(thm)],[c123]) ).
cnf(c125,plain,
join(X,join(complement(X),complement(X))) = join(X,complement(X)),
inference(congruence,[status(thm)],[c82]) ).
cnf(c126,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c30]) ).
cnf(c127,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c126]) ).
cnf(c128,plain,
join(X,join(complement(X),complement(X))) = top,
inference(transitivity,[status(thm)],[c125,c127]) ).
cnf(c129,plain,
join(complement(X),top) = top,
inference(transitivity,[status(thm)],[c124,c128]) ).
cnf(c130,plain,
join(top,complement(X)) = top,
inference(transitivity,[status(thm)],[c111,c129]) ).
cnf(c131,plain,
top = join(top,complement(X)),
inference(symmetry,[status(thm)],[c130]) ).
cnf(c132,plain,
join(X,top) = join(X,join(top,complement(X))),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c122]) ).
cnf(c134,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c122]) ).
cnf(c135,plain,
join(top,top) = join(X,join(top,complement(X))),
inference(symmetry,[status(thm)],[c134]) ).
cnf(c136,plain,
join(X,join(top,complement(X))) = join(X,top),
inference(congruence,[status(thm)],[c130]) ).
cnf(c137,plain,
join(top,top) = join(X,top),
inference(transitivity,[status(thm)],[c135,c136]) ).
cnf(c138,plain,
join(X,join(top,complement(X))) = join(X2,top),
inference(transitivity,[status(thm)],[c133,c137]) ).
cnf(c139,plain,
join(X,top) = join(X2,top),
inference(transitivity,[status(thm)],[c132,c138]) ).
cnf(c140,plain,
join(X2,top) = join(X,top),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c141,plain,
join(X,top) = join(zero,top),
inference(substitution,[status(thm)],[c139]) ).
cnf(c142,plain,
join(zero,top) = top,
inference(substitution,[status(thm)],[c103]) ).
cnf(c143,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c141,c142]) ).
cnf(c144,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c140,c143]) ).
cnf(c145,plain,
join(top,X) = top,
inference(transitivity,[status(thm)],[c109,c144]) ).
cnf(c146,plain,
join(top,one) = top,
inference(substitution,[status(thm)],[c145]) ).
cnf(c147,plain,
top = join(top,one),
inference(symmetry,[status(thm)],[c146]) ).
cnf(c148,plain,
composition(top,complement(top)) = composition(join(top,one),complement(top)),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c43]) ).
cnf(c150,plain,
X = converse(converse(X)),
inference(symmetry,[status(thm)],[c149]) ).
cnf(c151,plain,
join(X,converse(complement(converse(X)))) = join(converse(converse(X)),converse(complement(converse(X)))),
inference(congruence,[status(thm)],[c150]) ).
cnf(c152,axiom,
converse(join(A2,B2)) = join(converse(A2),converse(B2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity_9) ).
cnf(c153,plain,
converse(join(X,complement(X))) = join(converse(X),converse(complement(X))),
inference(substitution,[status(thm)],[c152]) ).
cnf(c154,plain,
join(converse(X),converse(complement(X))) = converse(join(X,complement(X))),
inference(symmetry,[status(thm)],[c153]) ).
cnf(c155,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c30]) ).
cnf(c156,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c155]) ).
cnf(c157,plain,
converse(join(X,complement(X))) = converse(top),
inference(congruence,[status(thm)],[c156]) ).
cnf(c158,plain,
join(converse(X),converse(complement(X))) = converse(top),
inference(transitivity,[status(thm)],[c154,c157]) ).
cnf(c159,plain,
join(converse(converse(X)),converse(complement(converse(X)))) = converse(top),
inference(substitution,[status(thm)],[c158]) ).
cnf(c160,plain,
join(X,converse(complement(converse(X)))) = converse(top),
inference(transitivity,[status(thm)],[c151,c159]) ).
cnf(c161,plain,
join(top,converse(complement(converse(top)))) = converse(top),
inference(substitution,[status(thm)],[c160]) ).
cnf(c162,plain,
converse(top) = join(top,converse(complement(converse(top)))),
inference(symmetry,[status(thm)],[c161]) ).
cnf(c163,plain,
join(top,converse(complement(converse(top)))) = top,
inference(substitution,[status(thm)],[c145]) ).
cnf(c164,plain,
converse(top) = top,
inference(transitivity,[status(thm)],[c162,c163]) ).
cnf(c165,plain,
top = converse(top),
inference(symmetry,[status(thm)],[c164]) ).
cnf(c166,plain,
join(top,one) = join(converse(top),one),
inference(congruence,[status(thm)],[c165]) ).
cnf(c167,plain,
composition(join(top,one),complement(top)) = composition(join(converse(top),one),complement(top)),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,plain,
X = composition(one,X),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c169,plain,
join(X2,composition(X,X2)) = join(composition(one,X2),composition(X,X2)),
inference(congruence,[status(thm)],[c168]) ).
cnf(c170,axiom,
composition(join(A2,B2),C2) = join(composition(A2,C2),composition(B2,C2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity_7) ).
cnf(c171,plain,
composition(join(one,X),X2) = join(composition(one,X2),composition(X,X2)),
inference(substitution,[status(thm)],[c170]) ).
cnf(c172,plain,
join(composition(one,X2),composition(X,X2)) = composition(join(one,X),X2),
inference(symmetry,[status(thm)],[c171]) ).
cnf(c173,plain,
join(one,X) = join(X,one),
inference(substitution,[status(thm)],[c2]) ).
cnf(c174,plain,
composition(join(one,X),X2) = composition(join(X,one),X2),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,plain,
join(composition(one,X2),composition(X,X2)) = composition(join(X,one),X2),
inference(transitivity,[status(thm)],[c172,c174]) ).
cnf(c176,plain,
join(X2,composition(X,X2)) = composition(join(X,one),X2),
inference(transitivity,[status(thm)],[c169,c175]) ).
cnf(c177,plain,
join(complement(top),composition(converse(top),complement(top))) = composition(join(converse(top),one),complement(top)),
inference(substitution,[status(thm)],[c176]) ).
cnf(c178,plain,
composition(join(converse(top),one),complement(top)) = join(complement(top),composition(converse(top),complement(top))),
inference(symmetry,[status(thm)],[c177]) ).
cnf(c179,plain,
join(top,one) = top,
inference(substitution,[status(thm)],[c145]) ).
cnf(c180,plain,
top = join(top,one),
inference(symmetry,[status(thm)],[c179]) ).
cnf(c181,plain,
composition(top,top) = composition(join(top,one),top),
inference(congruence,[status(thm)],[c180]) ).
cnf(c182,plain,
join(top,composition(X,top)) = composition(join(X,one),top),
inference(substitution,[status(thm)],[c176]) ).
cnf(c183,plain,
composition(join(X,one),top) = join(top,composition(X,top)),
inference(symmetry,[status(thm)],[c182]) ).
cnf(c184,plain,
join(top,composition(X,top)) = top,
inference(substitution,[status(thm)],[c145]) ).
cnf(c185,plain,
composition(join(X,one),top) = top,
inference(transitivity,[status(thm)],[c183,c184]) ).
cnf(c186,plain,
composition(join(top,one),top) = top,
inference(substitution,[status(thm)],[c185]) ).
cnf(c187,plain,
composition(top,top) = top,
inference(transitivity,[status(thm)],[c181,c186]) ).
cnf(c188,plain,
top = composition(top,top),
inference(symmetry,[status(thm)],[c187]) ).
cnf(c189,plain,
complement(top) = complement(composition(top,top)),
inference(congruence,[status(thm)],[c188]) ).
cnf(c190,plain,
composition(converse(top),complement(top)) = composition(converse(top),complement(composition(top,top))),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
join(complement(top),composition(converse(top),complement(top))) = join(complement(top),composition(converse(top),complement(composition(top,top)))),
inference(congruence,[status(thm)],[c190]) ).
cnf(c192,plain,
join(complement(top),composition(converse(top),complement(composition(top,top)))) = complement(top),
inference(substitution,[status(thm)],[c79]) ).
cnf(c193,plain,
join(complement(top),composition(converse(top),complement(composition(top,top)))) = zero,
inference(transitivity,[status(thm)],[c192,c38]) ).
cnf(c194,plain,
join(complement(top),composition(converse(top),complement(top))) = zero,
inference(transitivity,[status(thm)],[c191,c193]) ).
cnf(c195,plain,
composition(join(converse(top),one),complement(top)) = zero,
inference(transitivity,[status(thm)],[c178,c194]) ).
cnf(c196,plain,
composition(join(top,one),complement(top)) = zero,
inference(transitivity,[status(thm)],[c167,c195]) ).
cnf(c197,plain,
composition(top,complement(top)) = zero,
inference(transitivity,[status(thm)],[c148,c196]) ).
cnf(c198,plain,
composition(top,zero) = zero,
inference(transitivity,[status(thm)],[c107,c197]) ).
cnf(c199,plain,
zero = composition(top,zero),
inference(symmetry,[status(thm)],[c198]) ).
cnf(c200,plain,
join(zero,composition(X,zero)) = join(composition(top,zero),composition(X,zero)),
inference(congruence,[status(thm)],[c199]) ).
cnf(c201,plain,
composition(join(top,X),zero) = join(composition(top,zero),composition(X,zero)),
inference(substitution,[status(thm)],[c170]) ).
cnf(c202,plain,
join(composition(top,zero),composition(X,zero)) = composition(join(top,X),zero),
inference(symmetry,[status(thm)],[c201]) ).
cnf(c203,plain,
composition(join(top,X),zero) = composition(top,zero),
inference(congruence,[status(thm)],[c145]) ).
cnf(c204,plain,
composition(join(top,X),zero) = zero,
inference(transitivity,[status(thm)],[c203,c198]) ).
cnf(c205,plain,
join(composition(top,zero),composition(X,zero)) = zero,
inference(transitivity,[status(thm)],[c202,c204]) ).
cnf(c206,plain,
join(zero,composition(X,zero)) = zero,
inference(transitivity,[status(thm)],[c200,c205]) ).
cnf(c207,plain,
composition(X,zero) = zero,
inference(transitivity,[status(thm)],[c105,c206]) ).
cnf(c208,plain,
composition(meet(sk1,composition(composition(sk1,X),converse(complement(X)))),zero) = zero,
inference(substitution,[status(thm)],[c207]) ).
cnf(c209,plain,
zero = composition(meet(sk1,composition(composition(sk1,X),converse(complement(X)))),zero),
inference(symmetry,[status(thm)],[c208]) ).
cnf(c210,plain,
join(meet(composition(sk1,X),composition(sk1,complement(X))),zero) = join(meet(composition(sk1,X),composition(sk1,complement(X))),composition(meet(sk1,composition(composition(sk1,X),converse(complement(X)))),zero)),
inference(congruence,[status(thm)],[c209]) ).
cnf(c211,plain,
meet(X,X2) = complement(join(complement(X),complement(X2))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c212,plain,
join(complement(X2),complement(X)) = join(complement(X),complement(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c213,plain,
join(complement(X),complement(X2)) = join(complement(X2),complement(X)),
inference(symmetry,[status(thm)],[c212]) ).
cnf(c214,plain,
complement(join(complement(X),complement(X2))) = complement(join(complement(X2),complement(X))),
inference(congruence,[status(thm)],[c213]) ).
cnf(c215,plain,
meet(X2,X) = complement(join(complement(X2),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c216,plain,
complement(join(complement(X2),complement(X))) = meet(X2,X),
inference(symmetry,[status(thm)],[c215]) ).
cnf(c217,plain,
complement(join(complement(X),complement(X2))) = meet(X2,X),
inference(transitivity,[status(thm)],[c214,c216]) ).
cnf(c218,plain,
meet(X,X2) = meet(X2,X),
inference(transitivity,[status(thm)],[c211,c217]) ).
cnf(c219,plain,
meet(composition(sk1,complement(X)),composition(sk1,X)) = meet(composition(sk1,X),composition(sk1,complement(X))),
inference(substitution,[status(thm)],[c218]) ).
cnf(c220,plain,
meet(composition(sk1,X),composition(sk1,complement(X))) = meet(composition(sk1,complement(X)),composition(sk1,X)),
inference(symmetry,[status(thm)],[c219]) ).
cnf(c221,plain,
join(meet(composition(sk1,X),composition(sk1,complement(X))),composition(meet(sk1,composition(composition(sk1,X),converse(complement(X)))),zero)) = join(meet(composition(sk1,complement(X)),composition(sk1,X)),composition(meet(sk1,composition(composition(sk1,X),converse(complement(X)))),zero)),
inference(congruence,[status(thm)],[c220]) ).
cnf(c222,plain,
meet(complement(X),composition(converse(sk1),composition(sk1,X))) = meet(composition(converse(sk1),composition(sk1,X)),complement(X)),
inference(substitution,[status(thm)],[c218]) ).
cnf(c223,plain,
composition(X,composition(X3,X2)) = composition(composition(X,X3),X2),
inference(substitution,[status(thm)],[c63]) ).
cnf(c224,plain,
join(X3,composition(X2,composition(X,X3))) = join(X3,composition(composition(X2,X),X3)),
inference(congruence,[status(thm)],[c223]) ).
cnf(c225,plain,
join(X3,composition(composition(X2,X),X3)) = composition(join(composition(X2,X),one),X3),
inference(substitution,[status(thm)],[c176]) ).
cnf(c226,plain,
join(composition(X2,X),one) = join(one,composition(X2,X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c227,plain,
composition(join(composition(X2,X),one),X3) = composition(join(one,composition(X2,X)),X3),
inference(congruence,[status(thm)],[c226]) ).
cnf(c228,plain,
join(X3,composition(composition(X2,X),X3)) = composition(join(one,composition(X2,X)),X3),
inference(transitivity,[status(thm)],[c225,c227]) ).
cnf(c229,plain,
join(X3,composition(X2,composition(X,X3))) = composition(join(one,composition(X2,X)),X3),
inference(transitivity,[status(thm)],[c224,c228]) ).
cnf(c230,plain,
join(X,composition(converse(sk1),composition(sk1,X))) = composition(join(one,composition(converse(sk1),sk1)),X),
inference(substitution,[status(thm)],[c229]) ).
cnf(c231,plain,
join(composition(converse(sk1),sk1),one) = join(one,composition(converse(sk1),sk1)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c232,plain,
join(one,composition(converse(sk1),sk1)) = join(composition(converse(sk1),sk1),one),
inference(symmetry,[status(thm)],[c231]) ).
cnf(c233,axiom,
join(composition(converse(sk1),sk1),one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c234,plain,
join(one,composition(converse(sk1),sk1)) = one,
inference(transitivity,[status(thm)],[c232,c233]) ).
cnf(c235,plain,
composition(join(one,composition(converse(sk1),sk1)),X) = composition(one,X),
inference(congruence,[status(thm)],[c234]) ).
cnf(c236,plain,
composition(join(one,composition(converse(sk1),sk1)),X) = X,
inference(transitivity,[status(thm)],[c235,c70]) ).
cnf(c237,plain,
join(X,composition(converse(sk1),composition(sk1,X))) = X,
inference(transitivity,[status(thm)],[c230,c236]) ).
cnf(c238,plain,
X = join(X,composition(converse(sk1),composition(sk1,X))),
inference(symmetry,[status(thm)],[c237]) ).
cnf(c239,plain,
complement(X) = complement(join(X,composition(converse(sk1),composition(sk1,X)))),
inference(congruence,[status(thm)],[c238]) ).
cnf(c240,plain,
meet(composition(converse(sk1),composition(sk1,X)),complement(X)) = meet(composition(converse(sk1),composition(sk1,X)),complement(join(X,composition(converse(sk1),composition(sk1,X))))),
inference(congruence,[status(thm)],[c239]) ).
cnf(c241,plain,
join(X2,X) = join(X,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c242,plain,
join(X,X2) = join(X2,X),
inference(symmetry,[status(thm)],[c241]) ).
cnf(c243,plain,
complement(join(X,X2)) = complement(join(X2,X)),
inference(congruence,[status(thm)],[c242]) ).
cnf(c244,plain,
meet(X2,complement(join(X,X2))) = meet(X2,complement(join(X2,X))),
inference(congruence,[status(thm)],[c243]) ).
cnf(c245,plain,
join(X,X2) = join(X2,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c246,plain,
join(X2,X) = join(X,X2),
inference(symmetry,[status(thm)],[c245]) ).
cnf(c247,plain,
complement(join(X2,X)) = complement(join(X,X2)),
inference(congruence,[status(thm)],[c246]) ).
cnf(c248,plain,
meet(X2,complement(join(X2,X))) = meet(X2,complement(join(X,X2))),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
meet(complement(X2),complement(X)) = meet(complement(X),complement(X2)),
inference(substitution,[status(thm)],[c218]) ).
cnf(c250,plain,
join(zero,complement(X)) = complement(X),
inference(substitution,[status(thm)],[c103]) ).
cnf(c251,plain,
complement(X) = join(zero,complement(X)),
inference(symmetry,[status(thm)],[c250]) ).
cnf(c252,plain,
meet(complement(X),complement(X2)) = meet(join(zero,complement(X)),complement(X2)),
inference(congruence,[status(thm)],[c251]) ).
cnf(c253,plain,
join(zero,join(X2,complement(X))) = join(X2,complement(X)),
inference(substitution,[status(thm)],[c103]) ).
cnf(c254,plain,
join(X2,complement(X)) = join(zero,join(X2,complement(X))),
inference(symmetry,[status(thm)],[c253]) ).
cnf(c255,plain,
complement(join(X2,complement(X))) = complement(join(zero,join(X2,complement(X)))),
inference(congruence,[status(thm)],[c254]) ).
cnf(c256,plain,
meet(X2,complement(X)) = meet(complement(X),X2),
inference(substitution,[status(thm)],[c218]) ).
cnf(c257,plain,
complement(meet(X2,complement(X))) = complement(meet(complement(X),X2)),
inference(congruence,[status(thm)],[c256]) ).
cnf(c258,plain,
join(zero,complement(X)) = complement(X),
inference(substitution,[status(thm)],[c103]) ).
cnf(c259,plain,
complement(X) = join(zero,complement(X)),
inference(symmetry,[status(thm)],[c258]) ).
cnf(c260,plain,
meet(complement(X),X2) = meet(join(zero,complement(X)),X2),
inference(congruence,[status(thm)],[c259]) ).
cnf(c261,plain,
complement(meet(complement(X),X2)) = complement(meet(join(zero,complement(X)),X2)),
inference(congruence,[status(thm)],[c260]) ).
cnf(c262,plain,
join(complement(X),complement(X2)) = join(complement(X2),complement(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c263,plain,
join(complement(X2),complement(X)) = join(complement(X),complement(X2)),
inference(symmetry,[status(thm)],[c262]) ).
cnf(c264,plain,
meet(top,X) = meet(X,top),
inference(substitution,[status(thm)],[c218]) ).
cnf(c265,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c266,plain,
join(zero,complement(X)) = join(complement(top),complement(X)),
inference(congruence,[status(thm)],[c265]) ).
cnf(c267,plain,
complement(join(zero,complement(X))) = complement(join(complement(top),complement(X))),
inference(congruence,[status(thm)],[c266]) ).
cnf(c268,plain,
meet(top,X) = complement(join(complement(top),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c269,plain,
complement(join(complement(top),complement(X))) = meet(top,X),
inference(symmetry,[status(thm)],[c268]) ).
cnf(c270,plain,
meet(X,top) = meet(top,X),
inference(substitution,[status(thm)],[c218]) ).
cnf(c271,plain,
meet(top,X) = meet(X,top),
inference(symmetry,[status(thm)],[c270]) ).
cnf(c272,plain,
complement(join(complement(top),complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c269,c271]) ).
cnf(c273,plain,
complement(join(zero,complement(X))) = meet(X,top),
inference(transitivity,[status(thm)],[c267,c272]) ).
cnf(c274,plain,
meet(X,top) = complement(join(zero,complement(X))),
inference(symmetry,[status(thm)],[c273]) ).
cnf(c275,plain,
join(zero,complement(X)) = complement(X),
inference(substitution,[status(thm)],[c103]) ).
cnf(c276,plain,
complement(join(zero,complement(X))) = complement(complement(X)),
inference(congruence,[status(thm)],[c275]) ).
cnf(c277,plain,
join(zero,complement(complement(X))) = complement(complement(X)),
inference(substitution,[status(thm)],[c103]) ).
cnf(c278,plain,
complement(complement(X)) = join(zero,complement(complement(X))),
inference(symmetry,[status(thm)],[c277]) ).
cnf(c279,plain,
complement(X) = join(complement(X),complement(X)),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c280,plain,
complement(complement(X)) = complement(join(complement(X),complement(X))),
inference(congruence,[status(thm)],[c279]) ).
cnf(c281,plain,
meet(X,X) = complement(join(complement(X),complement(X))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c282,plain,
complement(join(complement(X),complement(X))) = meet(X,X),
inference(symmetry,[status(thm)],[c281]) ).
cnf(c283,plain,
complement(complement(X)) = meet(X,X),
inference(transitivity,[status(thm)],[c280,c282]) ).
cnf(c284,plain,
join(zero,complement(complement(X))) = join(zero,meet(X,X)),
inference(congruence,[status(thm)],[c283]) ).
cnf(c285,plain,
join(zero,complement(complement(X))) = X,
inference(transitivity,[status(thm)],[c284,c19]) ).
cnf(c286,plain,
complement(complement(X)) = X,
inference(transitivity,[status(thm)],[c278,c285]) ).
cnf(c287,plain,
complement(join(zero,complement(X))) = X,
inference(transitivity,[status(thm)],[c276,c286]) ).
cnf(c288,plain,
meet(X,top) = X,
inference(transitivity,[status(thm)],[c274,c287]) ).
cnf(c289,plain,
meet(top,X) = X,
inference(transitivity,[status(thm)],[c264,c288]) ).
cnf(c290,plain,
meet(top,join(complement(X),complement(X2))) = join(complement(X),complement(X2)),
inference(substitution,[status(thm)],[c289]) ).
cnf(c291,plain,
join(complement(X),complement(X2)) = meet(top,join(complement(X),complement(X2))),
inference(symmetry,[status(thm)],[c290]) ).
cnf(c292,plain,
meet(X2,X) = meet(X,X2),
inference(substitution,[status(thm)],[c218]) ).
cnf(c293,plain,
join(complement(X3),meet(X2,X)) = join(complement(X3),meet(X,X2)),
inference(congruence,[status(thm)],[c292]) ).
cnf(c294,plain,
complement(join(complement(X3),meet(X2,X))) = complement(join(complement(X3),meet(X,X2))),
inference(congruence,[status(thm)],[c293]) ).
cnf(c295,plain,
join(meet(X,X2),complement(X3)) = join(complement(X3),meet(X,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c296,plain,
join(complement(X3),meet(X,X2)) = join(meet(X,X2),complement(X3)),
inference(symmetry,[status(thm)],[c295]) ).
cnf(c297,plain,
complement(join(complement(X3),meet(X,X2))) = complement(join(meet(X,X2),complement(X3))),
inference(congruence,[status(thm)],[c296]) ).
cnf(c298,plain,
meet(X,X2) = complement(join(complement(X),complement(X2))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c299,plain,
join(meet(X,X2),complement(X3)) = join(complement(join(complement(X),complement(X2))),complement(X3)),
inference(congruence,[status(thm)],[c298]) ).
cnf(c300,plain,
complement(join(meet(X,X2),complement(X3))) = complement(join(complement(join(complement(X),complement(X2))),complement(X3))),
inference(congruence,[status(thm)],[c299]) ).
cnf(c301,plain,
meet(join(complement(X),complement(X2)),X3) = complement(join(complement(join(complement(X),complement(X2))),complement(X3))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c302,plain,
complement(join(complement(join(complement(X),complement(X2))),complement(X3))) = meet(join(complement(X),complement(X2)),X3),
inference(symmetry,[status(thm)],[c301]) ).
cnf(c303,plain,
meet(X3,join(complement(X),complement(X2))) = meet(join(complement(X),complement(X2)),X3),
inference(substitution,[status(thm)],[c218]) ).
cnf(c304,plain,
meet(join(complement(X),complement(X2)),X3) = meet(X3,join(complement(X),complement(X2))),
inference(symmetry,[status(thm)],[c303]) ).
cnf(c305,plain,
join(complement(X),complement(X2)) = join(complement(X2),complement(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c306,plain,
meet(X3,join(complement(X),complement(X2))) = meet(X3,join(complement(X2),complement(X))),
inference(congruence,[status(thm)],[c305]) ).
cnf(c307,plain,
meet(join(complement(X),complement(X2)),X3) = meet(X3,join(complement(X2),complement(X))),
inference(transitivity,[status(thm)],[c304,c306]) ).
cnf(c308,plain,
complement(join(complement(join(complement(X),complement(X2))),complement(X3))) = meet(X3,join(complement(X2),complement(X))),
inference(transitivity,[status(thm)],[c302,c307]) ).
cnf(c309,plain,
complement(join(meet(X,X2),complement(X3))) = meet(X3,join(complement(X2),complement(X))),
inference(transitivity,[status(thm)],[c300,c308]) ).
cnf(c310,plain,
complement(join(complement(X3),meet(X,X2))) = meet(X3,join(complement(X2),complement(X))),
inference(transitivity,[status(thm)],[c297,c309]) ).
cnf(c311,plain,
complement(join(complement(X3),meet(X2,X))) = meet(X3,join(complement(X2),complement(X))),
inference(transitivity,[status(thm)],[c294,c310]) ).
cnf(c312,plain,
complement(join(complement(top),meet(X,X2))) = meet(top,join(complement(X),complement(X2))),
inference(substitution,[status(thm)],[c311]) ).
cnf(c313,plain,
meet(top,join(complement(X),complement(X2))) = complement(join(complement(top),meet(X,X2))),
inference(symmetry,[status(thm)],[c312]) ).
cnf(c314,plain,
join(complement(top),meet(X,X2)) = join(zero,meet(X,X2)),
inference(congruence,[status(thm)],[c38]) ).
cnf(c315,plain,
complement(join(complement(top),meet(X,X2))) = complement(join(zero,meet(X,X2))),
inference(congruence,[status(thm)],[c314]) ).
cnf(c316,plain,
join(zero,meet(X,X2)) = meet(X,X2),
inference(substitution,[status(thm)],[c103]) ).
cnf(c317,plain,
complement(join(zero,meet(X,X2))) = complement(meet(X,X2)),
inference(congruence,[status(thm)],[c316]) ).
cnf(c318,plain,
meet(X2,X) = meet(X,X2),
inference(substitution,[status(thm)],[c218]) ).
cnf(c319,plain,
meet(X,X2) = meet(X2,X),
inference(symmetry,[status(thm)],[c318]) ).
cnf(c320,plain,
complement(meet(X,X2)) = complement(meet(X2,X)),
inference(congruence,[status(thm)],[c319]) ).
cnf(c321,plain,
complement(join(zero,meet(X,X2))) = complement(meet(X2,X)),
inference(transitivity,[status(thm)],[c317,c320]) ).
cnf(c322,plain,
complement(join(complement(top),meet(X,X2))) = complement(meet(X2,X)),
inference(transitivity,[status(thm)],[c315,c321]) ).
cnf(c323,plain,
meet(top,join(complement(X),complement(X2))) = complement(meet(X2,X)),
inference(transitivity,[status(thm)],[c313,c322]) ).
cnf(c324,plain,
join(complement(X),complement(X2)) = complement(meet(X2,X)),
inference(transitivity,[status(thm)],[c291,c323]) ).
cnf(c325,plain,
join(complement(X2),complement(X)) = complement(meet(X2,X)),
inference(transitivity,[status(thm)],[c263,c324]) ).
cnf(c326,plain,
join(complement(join(zero,complement(X))),complement(X2)) = complement(meet(join(zero,complement(X)),X2)),
inference(substitution,[status(thm)],[c325]) ).
cnf(c327,plain,
complement(meet(join(zero,complement(X)),X2)) = join(complement(join(zero,complement(X))),complement(X2)),
inference(symmetry,[status(thm)],[c326]) ).
cnf(c328,plain,
join(complement(join(zero,complement(X))),complement(X2)) = join(meet(X,top),complement(X2)),
inference(congruence,[status(thm)],[c273]) ).
cnf(c329,plain,
join(meet(X,top),complement(X2)) = join(X,complement(X2)),
inference(congruence,[status(thm)],[c288]) ).
cnf(c330,plain,
join(complement(join(zero,complement(X))),complement(X2)) = join(X,complement(X2)),
inference(transitivity,[status(thm)],[c328,c329]) ).
cnf(c331,plain,
complement(meet(join(zero,complement(X)),X2)) = join(X,complement(X2)),
inference(transitivity,[status(thm)],[c327,c330]) ).
cnf(c332,plain,
complement(meet(complement(X),X2)) = join(X,complement(X2)),
inference(transitivity,[status(thm)],[c261,c331]) ).
cnf(c333,plain,
complement(meet(X2,complement(X))) = join(X,complement(X2)),
inference(transitivity,[status(thm)],[c257,c332]) ).
cnf(c334,plain,
complement(meet(X,complement(X2))) = join(X2,complement(X)),
inference(substitution,[status(thm)],[c333]) ).
cnf(c335,plain,
join(X2,complement(X)) = complement(meet(X,complement(X2))),
inference(symmetry,[status(thm)],[c334]) ).
cnf(c336,plain,
join(zero,join(X2,complement(X))) = join(zero,complement(meet(X,complement(X2)))),
inference(congruence,[status(thm)],[c335]) ).
cnf(c337,plain,
complement(join(zero,join(X2,complement(X)))) = complement(join(zero,complement(meet(X,complement(X2))))),
inference(congruence,[status(thm)],[c336]) ).
cnf(c338,plain,
complement(join(zero,complement(meet(X,complement(X2))))) = meet(meet(X,complement(X2)),top),
inference(substitution,[status(thm)],[c273]) ).
cnf(c339,plain,
meet(meet(X,complement(X2)),top) = meet(X,complement(X2)),
inference(substitution,[status(thm)],[c288]) ).
cnf(c340,plain,
complement(join(zero,complement(meet(X,complement(X2))))) = meet(X,complement(X2)),
inference(transitivity,[status(thm)],[c338,c339]) ).
cnf(c341,plain,
complement(join(zero,join(X2,complement(X)))) = meet(X,complement(X2)),
inference(transitivity,[status(thm)],[c337,c340]) ).
cnf(c342,plain,
complement(join(X2,complement(X))) = meet(X,complement(X2)),
inference(transitivity,[status(thm)],[c255,c341]) ).
cnf(c343,plain,
complement(join(X2,complement(join(zero,complement(X))))) = meet(join(zero,complement(X)),complement(X2)),
inference(substitution,[status(thm)],[c342]) ).
cnf(c344,plain,
meet(join(zero,complement(X)),complement(X2)) = complement(join(X2,complement(join(zero,complement(X))))),
inference(symmetry,[status(thm)],[c343]) ).
cnf(c345,plain,
join(X2,complement(join(zero,complement(X)))) = join(X2,meet(X,top)),
inference(congruence,[status(thm)],[c273]) ).
cnf(c346,plain,
complement(join(X2,complement(join(zero,complement(X))))) = complement(join(X2,meet(X,top))),
inference(congruence,[status(thm)],[c345]) ).
cnf(c347,plain,
join(X2,meet(X,top)) = join(X2,X),
inference(congruence,[status(thm)],[c288]) ).
cnf(c348,plain,
complement(join(X2,meet(X,top))) = complement(join(X2,X)),
inference(congruence,[status(thm)],[c347]) ).
cnf(c349,plain,
complement(join(X2,complement(join(zero,complement(X))))) = complement(join(X2,X)),
inference(transitivity,[status(thm)],[c346,c348]) ).
cnf(c350,plain,
meet(join(zero,complement(X)),complement(X2)) = complement(join(X2,X)),
inference(transitivity,[status(thm)],[c344,c349]) ).
cnf(c351,plain,
meet(complement(X),complement(X2)) = complement(join(X2,X)),
inference(transitivity,[status(thm)],[c252,c350]) ).
cnf(c352,plain,
meet(complement(X2),complement(X)) = complement(join(X2,X)),
inference(transitivity,[status(thm)],[c249,c351]) ).
cnf(c353,plain,
meet(complement(X),complement(X2)) = complement(join(X,X2)),
inference(substitution,[status(thm)],[c352]) ).
cnf(c354,plain,
complement(join(X,X2)) = meet(complement(X),complement(X2)),
inference(symmetry,[status(thm)],[c353]) ).
cnf(c355,plain,
meet(X2,complement(join(X,X2))) = meet(X2,meet(complement(X),complement(X2))),
inference(congruence,[status(thm)],[c354]) ).
cnf(c356,plain,
meet(X,complement(X2)) = meet(complement(X2),X),
inference(substitution,[status(thm)],[c218]) ).
cnf(c357,plain,
meet(X2,meet(X,complement(X2))) = meet(X2,meet(complement(X2),X)),
inference(congruence,[status(thm)],[c356]) ).
cnf(c358,plain,
meet(X2,meet(complement(X2),X)) = complement(join(complement(X2),complement(meet(complement(X2),X)))),
inference(substitution,[status(thm)],[c5]) ).
cnf(c359,plain,
meet(X2,X) = meet(X,X2),
inference(substitution,[status(thm)],[c218]) ).
cnf(c360,plain,
complement(meet(X2,X)) = complement(meet(X,X2)),
inference(congruence,[status(thm)],[c359]) ).
cnf(c361,plain,
join(X2,complement(meet(X2,X))) = join(X2,complement(meet(X,X2))),
inference(congruence,[status(thm)],[c360]) ).
cnf(c362,plain,
join(complement(X),complement(X2)) = complement(meet(X,X2)),
inference(substitution,[status(thm)],[c325]) ).
cnf(c363,plain,
complement(meet(X,X2)) = join(complement(X),complement(X2)),
inference(symmetry,[status(thm)],[c362]) ).
cnf(c364,plain,
join(X2,complement(meet(X,X2))) = join(X2,join(complement(X),complement(X2))),
inference(congruence,[status(thm)],[c363]) ).
cnf(c365,plain,
join(X2,join(complement(X),complement(X2))) = join(complement(X),top),
inference(substitution,[status(thm)],[c122]) ).
cnf(c366,plain,
join(complement(X),top) = top,
inference(substitution,[status(thm)],[c143]) ).
cnf(c367,plain,
join(X2,join(complement(X),complement(X2))) = top,
inference(transitivity,[status(thm)],[c365,c366]) ).
cnf(c368,plain,
join(X2,complement(meet(X,X2))) = top,
inference(transitivity,[status(thm)],[c364,c367]) ).
cnf(c369,plain,
join(X2,complement(meet(X2,X))) = top,
inference(transitivity,[status(thm)],[c361,c368]) ).
cnf(c370,plain,
join(complement(X2),complement(meet(complement(X2),X))) = top,
inference(substitution,[status(thm)],[c369]) ).
cnf(c371,plain,
complement(join(complement(X2),complement(meet(complement(X2),X)))) = complement(top),
inference(congruence,[status(thm)],[c370]) ).
cnf(c372,plain,
complement(join(complement(X2),complement(meet(complement(X2),X)))) = zero,
inference(transitivity,[status(thm)],[c371,c38]) ).
cnf(c373,plain,
meet(X2,meet(complement(X2),X)) = zero,
inference(transitivity,[status(thm)],[c358,c372]) ).
cnf(c374,plain,
meet(X2,meet(X,complement(X2))) = zero,
inference(transitivity,[status(thm)],[c357,c373]) ).
cnf(c375,plain,
meet(X2,meet(complement(X),complement(X2))) = zero,
inference(substitution,[status(thm)],[c374]) ).
cnf(c376,plain,
meet(X2,complement(join(X,X2))) = zero,
inference(transitivity,[status(thm)],[c355,c375]) ).
cnf(c377,plain,
meet(X2,complement(join(X2,X))) = zero,
inference(transitivity,[status(thm)],[c248,c376]) ).
cnf(c378,plain,
meet(X2,complement(join(X,X2))) = zero,
inference(transitivity,[status(thm)],[c244,c377]) ).
cnf(c379,plain,
meet(composition(converse(sk1),composition(sk1,X)),complement(join(X,composition(converse(sk1),composition(sk1,X))))) = zero,
inference(substitution,[status(thm)],[c378]) ).
cnf(c380,plain,
meet(composition(converse(sk1),composition(sk1,X)),complement(X)) = zero,
inference(transitivity,[status(thm)],[c240,c379]) ).
cnf(c381,plain,
meet(complement(X),composition(converse(sk1),composition(sk1,X))) = zero,
inference(transitivity,[status(thm)],[c222,c380]) ).
cnf(c382,plain,
zero = meet(complement(X),composition(converse(sk1),composition(sk1,X))),
inference(symmetry,[status(thm)],[c381]) ).
cnf(c383,plain,
composition(meet(sk1,composition(composition(sk1,X),converse(complement(X)))),zero) = composition(meet(sk1,composition(composition(sk1,X),converse(complement(X)))),meet(complement(X),composition(converse(sk1),composition(sk1,X)))),
inference(congruence,[status(thm)],[c382]) ).
cnf(c384,plain,
join(meet(composition(sk1,complement(X)),composition(sk1,X)),composition(meet(sk1,composition(composition(sk1,X),converse(complement(X)))),zero)) = join(meet(composition(sk1,complement(X)),composition(sk1,X)),composition(meet(sk1,composition(composition(sk1,X),converse(complement(X)))),meet(complement(X),composition(converse(sk1),composition(sk1,X))))),
inference(congruence,[status(thm)],[c383]) ).
cnf(c385,axiom,
join(meet(composition(A2,B2),C2),composition(meet(A2,composition(C2,converse(B2))),meet(B2,composition(converse(A2),C2)))) = composition(meet(A2,composition(C2,converse(B2))),meet(B2,composition(converse(A2),C2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dedekind_law_14) ).
cnf(c386,plain,
join(meet(composition(sk1,complement(X)),composition(sk1,X)),composition(meet(sk1,composition(composition(sk1,X),converse(complement(X)))),meet(complement(X),composition(converse(sk1),composition(sk1,X))))) = composition(meet(sk1,composition(composition(sk1,X),converse(complement(X)))),meet(complement(X),composition(converse(sk1),composition(sk1,X)))),
inference(substitution,[status(thm)],[c385]) ).
cnf(c387,plain,
composition(meet(sk1,composition(composition(sk1,X),converse(complement(X)))),meet(complement(X),composition(converse(sk1),composition(sk1,X)))) = composition(meet(sk1,composition(composition(sk1,X),converse(complement(X)))),zero),
inference(congruence,[status(thm)],[c381]) ).
cnf(c388,plain,
composition(meet(sk1,composition(composition(sk1,X),converse(complement(X)))),zero) = zero,
inference(substitution,[status(thm)],[c207]) ).
cnf(c389,plain,
composition(meet(sk1,composition(composition(sk1,X),converse(complement(X)))),meet(complement(X),composition(converse(sk1),composition(sk1,X)))) = zero,
inference(transitivity,[status(thm)],[c387,c388]) ).
cnf(c390,plain,
join(meet(composition(sk1,complement(X)),composition(sk1,X)),composition(meet(sk1,composition(composition(sk1,X),converse(complement(X)))),meet(complement(X),composition(converse(sk1),composition(sk1,X))))) = zero,
inference(transitivity,[status(thm)],[c386,c389]) ).
cnf(c391,plain,
join(meet(composition(sk1,complement(X)),composition(sk1,X)),composition(meet(sk1,composition(composition(sk1,X),converse(complement(X)))),zero)) = zero,
inference(transitivity,[status(thm)],[c384,c390]) ).
cnf(c392,plain,
join(meet(composition(sk1,X),composition(sk1,complement(X))),composition(meet(sk1,composition(composition(sk1,X),converse(complement(X)))),zero)) = zero,
inference(transitivity,[status(thm)],[c221,c391]) ).
cnf(c393,plain,
join(meet(composition(sk1,X),composition(sk1,complement(X))),zero) = zero,
inference(transitivity,[status(thm)],[c210,c392]) ).
cnf(c394,plain,
meet(composition(sk1,X),composition(sk1,complement(X))) = zero,
inference(transitivity,[status(thm)],[c100,c393]) ).
cnf(c395,plain,
meet(composition(sk1,sk2),composition(sk1,complement(sk2))) = zero,
inference(substitution,[status(thm)],[c394]) ).
cnf(c396,plain,
$false,
inference(resolution,[status(thm)],[c1,c395]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL041-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n017.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sun Sep 27 22:51:35 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.97/3.02 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 18.97/3.02
% 18.97/3.02 % SZS status Unsatisfiable
% 18.97/3.02
% 18.97/3.06 % SZS output start CNFRefutation
% See solution above
% 22.14/3.36
% 22.14/3.36 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------