%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : REL018-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 : Sun Sep 27 08:24:17 AM UTC 2026
% Result : Unsatisfiable 142.71s 29.88s
% Output : CNFRefutation 142.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 15
% Syntax : Number of clauses : 210 ( 210 unt; 0 nHn; 30 RR)
% Number of literals : 210 ( 209 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 298 ( 22 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(goals_14,negated_conjecture,
composition(sk1,top) = sk1 ).
cnf(goals_15,negated_conjecture,
composition(complement(sk1),top) != complement(sk1) ).
cnf(maddux1_join_commutativity_1,axiom,
join(X0,X1) = join(X1,X0) ).
cnf(maddux2_join_associativity_2,axiom,
join(X0,join(X1,X2)) = join(join(X0,X1),X2) ).
cnf(maddux3_a_kind_of_de_Morgan_3,axiom,
X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) ).
cnf(maddux4_definiton_of_meet_4,axiom,
meet(X0,X1) = complement(join(complement(X0),complement(X1))) ).
cnf(composition_associativity_5,axiom,
composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2) ).
cnf(composition_identity_6,axiom,
composition(X0,one) = X0 ).
cnf(composition_distributivity_7,axiom,
composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)) ).
cnf(converse_idempotence_8,axiom,
converse(converse(X0)) = X0 ).
cnf(converse_additivity_9,axiom,
converse(join(X0,X1)) = join(converse(X0),converse(X1)) ).
cnf(converse_multiplicativity_10,axiom,
converse(composition(X0,X1)) = composition(converse(X1),converse(X0)) ).
cnf(converse_cancellativity_11,axiom,
join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1) ).
cnf(def_top_12,axiom,
top = join(X0,complement(X0)) ).
cnf(def_zero_13,axiom,
zero = meet(X0,complement(X0)) ).
cnf(c0,plain,
composition(sk1,top) = sk1,
inference(clausification,[status(esa)],[goals_14]) ).
cnf(c1,plain,
composition(complement(sk1),top) != complement(sk1),
inference(clausification,[status(esa)],[goals_15]) ).
cnf(c2,plain,
join(X0,X1) = join(X1,X0),
inference(clausification,[status(esa)],[maddux1_join_commutativity_1]) ).
cnf(c3,plain,
join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(clausification,[status(esa)],[maddux2_join_associativity_2]) ).
cnf(c4,plain,
X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(clausification,[status(esa)],[maddux3_a_kind_of_de_Morgan_3]) ).
cnf(c5,plain,
meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(clausification,[status(esa)],[maddux4_definiton_of_meet_4]) ).
cnf(c6,plain,
composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(clausification,[status(esa)],[composition_associativity_5]) ).
cnf(c7,plain,
composition(X0,one) = X0,
inference(clausification,[status(esa)],[composition_identity_6]) ).
cnf(c8,plain,
composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(clausification,[status(esa)],[composition_distributivity_7]) ).
cnf(c9,plain,
converse(converse(X0)) = X0,
inference(clausification,[status(esa)],[converse_idempotence_8]) ).
cnf(c10,plain,
converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(clausification,[status(esa)],[converse_additivity_9]) ).
cnf(c11,plain,
converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(clausification,[status(esa)],[converse_multiplicativity_10]) ).
cnf(c12,plain,
join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(clausification,[status(esa)],[converse_cancellativity_11]) ).
cnf(c13,plain,
top = join(X0,complement(X0)),
inference(clausification,[status(esa)],[def_top_12]) ).
cnf(c14,plain,
zero = meet(X0,complement(X0)),
inference(clausification,[status(esa)],[def_zero_13]) ).
cnf(d0,plain,
X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(demodulation,[status(thm)],[c4,c2]) ).
cnf(d1,plain,
X0 = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(demodulation,[status(thm)],[d0,c5]) ).
cnf(d2,plain,
X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(demodulation,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
X0 = join(zero,complement(join(complement(X0),complement(X0)))),
inference(superposition,[status(thm)],[c14,d2]) ).
cnf(d4,plain,
X0 = join(zero,meet(X0,X0)),
inference(demodulation,[status(thm)],[d3,c5]) ).
cnf(d5,plain,
meet(X0,complement(X0)) = complement(top),
inference(superposition,[status(thm)],[c13,c5]) ).
cnf(d6,plain,
zero = complement(top),
inference(demodulation,[status(thm)],[d5,c14]) ).
cnf(d7,plain,
top = join(top,zero),
inference(superposition,[status(thm)],[d6,c13]) ).
cnf(d8,plain,
join(top,join(zero,X0)) = join(top,X0),
inference(superposition,[status(thm)],[d7,c3]) ).
cnf(d9,plain,
join(top,join(X0,zero)) = join(top,X0),
inference(superposition,[status(thm)],[c2,d8]) ).
cnf(d10,plain,
join(top,X0) = join(top,meet(X0,X0)),
inference(superposition,[status(thm)],[d4,d8]) ).
cnf(d11,plain,
join(X0,join(X1,complement(join(X0,X1)))) = top,
inference(superposition,[status(thm)],[c13,c3]) ).
cnf(d12,plain,
meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(superposition,[status(thm)],[c2,c5]) ).
cnf(d13,plain,
X0 = join(meet(X0,complement(X1)),meet(X0,X1)),
inference(superposition,[status(thm)],[c5,d2]) ).
cnf(d14,plain,
X0 = join(meet(X0,X1),meet(X0,complement(X1))),
inference(demodulation,[status(thm)],[d13,c2]) ).
cnf(d15,plain,
zero = meet(top,zero),
inference(superposition,[status(thm)],[d6,c14]) ).
cnf(d16,plain,
top = join(zero,meet(top,complement(zero))),
inference(superposition,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
X0 = join(meet(X0,complement(X1)),meet(X1,X0)),
inference(superposition,[status(thm)],[d12,d2]) ).
cnf(d18,plain,
X0 = join(meet(X1,X0),meet(X0,complement(X1))),
inference(demodulation,[status(thm)],[d17,c2]) ).
cnf(d19,plain,
X0 = join(meet(top,X0),meet(X0,zero)),
inference(superposition,[status(thm)],[d6,d18]) ).
cnf(d20,plain,
meet(X0,X1) = meet(X1,X0),
inference(superposition,[status(thm)],[d12,c5]) ).
cnf(d21,plain,
X0 = join(meet(top,X0),meet(zero,X0)),
inference(superposition,[status(thm)],[d20,d19]) ).
cnf(d22,plain,
complement(zero) = join(meet(top,complement(zero)),zero),
inference(superposition,[status(thm)],[c14,d21]) ).
cnf(d23,plain,
complement(zero) = join(zero,meet(top,complement(zero))),
inference(demodulation,[status(thm)],[d22,c2]) ).
cnf(d24,plain,
complement(zero) = top,
inference(demodulation,[status(thm)],[d23,d16]) ).
cnf(d25,plain,
meet(zero,X0) = complement(join(complement(X0),top)),
inference(superposition,[status(thm)],[d24,d12]) ).
cnf(d26,plain,
meet(zero,X0) = complement(join(top,complement(X0))),
inference(demodulation,[status(thm)],[d25,c2]) ).
cnf(d27,plain,
meet(zero,zero) = complement(join(top,top)),
inference(superposition,[status(thm)],[d24,d26]) ).
cnf(d28,plain,
join(top,join(top,meet(zero,zero))) = top,
inference(superposition,[status(thm)],[d27,d11]) ).
cnf(d29,plain,
join(top,join(top,zero)) = top,
inference(demodulation,[status(thm)],[d28,d10]) ).
cnf(d30,plain,
join(top,top) = top,
inference(demodulation,[status(thm)],[d29,d9]) ).
cnf(d31,plain,
meet(join(complement(X0),complement(X1)),X2) = complement(join(meet(X0,X1),complement(X2))),
inference(superposition,[status(thm)],[c5,c5]) ).
cnf(d32,plain,
meet(X0,top) = complement(join(complement(X0),zero)),
inference(superposition,[status(thm)],[d6,c5]) ).
cnf(d33,plain,
meet(X0,top) = complement(join(zero,complement(X0))),
inference(demodulation,[status(thm)],[d32,c2]) ).
cnf(d34,plain,
meet(join(complement(X0),complement(X1)),top) = complement(join(zero,meet(X0,X1))),
inference(superposition,[status(thm)],[c5,d33]) ).
cnf(d35,plain,
complement(join(meet(X0,X1),complement(top))) = complement(join(zero,meet(X0,X1))),
inference(demodulation,[status(thm)],[d34,d31]) ).
cnf(d36,plain,
complement(join(complement(top),meet(X0,X1))) = complement(join(zero,meet(X0,X1))),
inference(demodulation,[status(thm)],[d35,c2]) ).
cnf(d37,plain,
complement(join(zero,meet(X0,X1))) = complement(join(zero,meet(X0,X1))),
inference(demodulation,[status(thm)],[d36,d6]) ).
cnf(d38,plain,
complement(X0) = complement(join(zero,meet(X0,X0))),
inference(superposition,[status(thm)],[d4,d37]) ).
cnf(d39,plain,
complement(X0) = complement(X0),
inference(demodulation,[status(thm)],[d38,d4]) ).
cnf(d40,plain,
complement(join(top,top)) = meet(zero,zero),
inference(superposition,[status(thm)],[d27,d39]) ).
cnf(d41,plain,
complement(top) = meet(zero,zero),
inference(demodulation,[status(thm)],[d40,d30]) ).
cnf(d42,plain,
zero = meet(zero,zero),
inference(demodulation,[status(thm)],[d41,d6]) ).
cnf(d43,plain,
zero = join(zero,zero),
inference(superposition,[status(thm)],[d42,d4]) ).
cnf(d44,plain,
join(zero,join(zero,X0)) = join(zero,X0),
inference(superposition,[status(thm)],[d43,c3]) ).
cnf(d45,plain,
join(zero,X0) = join(zero,meet(X0,X0)),
inference(superposition,[status(thm)],[d4,d44]) ).
cnf(d46,plain,
join(zero,X0) = X0,
inference(demodulation,[status(thm)],[d45,d4]) ).
cnf(d47,plain,
join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[status(thm)],[c3,c2]) ).
cnf(d48,plain,
join(zero,join(zero,X0)) = join(X0,zero),
inference(superposition,[status(thm)],[d43,d47]) ).
cnf(d49,plain,
join(zero,X0) = join(X0,zero),
inference(demodulation,[status(thm)],[d48,d46]) ).
cnf(d50,plain,
X0 = join(X0,zero),
inference(demodulation,[status(thm)],[d49,d46]) ).
cnf(d51,plain,
join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[status(thm)],[c13,c3]) ).
cnf(d52,plain,
top = join(join(complement(X0),complement(X1)),meet(X1,X0)),
inference(superposition,[status(thm)],[d12,c13]) ).
cnf(d53,plain,
top = join(complement(X0),join(complement(X1),meet(X1,X0))),
inference(demodulation,[status(thm)],[d52,c3]) ).
cnf(d54,plain,
X0 = meet(X0,X0),
inference(demodulation,[status(thm)],[d4,d46]) ).
cnf(d55,plain,
top = join(complement(X0),join(complement(X0),X0)),
inference(superposition,[status(thm)],[d54,d53]) ).
cnf(d56,plain,
top = join(X0,join(complement(X0),complement(X0))),
inference(demodulation,[status(thm)],[d55,d47]) ).
cnf(d57,plain,
top = join(top,complement(X0)),
inference(demodulation,[status(thm)],[d56,d51]) ).
cnf(d58,plain,
meet(X0,zero) = complement(join(top,complement(X0))),
inference(superposition,[status(thm)],[d24,d12]) ).
cnf(d59,plain,
meet(X0,zero) = complement(top),
inference(demodulation,[status(thm)],[d58,d57]) ).
cnf(d60,plain,
meet(X0,zero) = zero,
inference(demodulation,[status(thm)],[d59,d6]) ).
cnf(d61,plain,
X0 = join(meet(X0,X1),complement(join(X1,complement(X0)))),
inference(superposition,[status(thm)],[c2,d2]) ).
cnf(d62,plain,
X0 = join(meet(X0,zero),complement(complement(X0))),
inference(superposition,[status(thm)],[d46,d61]) ).
cnf(d63,plain,
X0 = join(complement(complement(X0)),meet(X0,zero)),
inference(demodulation,[status(thm)],[d62,c2]) ).
cnf(d64,plain,
X0 = join(complement(complement(X0)),zero),
inference(demodulation,[status(thm)],[d63,d60]) ).
cnf(d65,plain,
X0 = complement(complement(X0)),
inference(demodulation,[status(thm)],[d64,d50]) ).
cnf(d66,plain,
complement(complement(X0)) = X0,
inference(superposition,[status(thm)],[d65,d39]) ).
cnf(d67,plain,
meet(X0,top) = complement(complement(X0)),
inference(demodulation,[status(thm)],[d33,d46]) ).
cnf(d68,plain,
meet(X0,top) = X0,
inference(demodulation,[status(thm)],[d67,d65]) ).
cnf(d69,plain,
meet(join(zero,complement(X0)),X1) = complement(join(meet(X0,top),complement(X1))),
inference(superposition,[status(thm)],[d33,c5]) ).
cnf(d70,plain,
meet(X1,join(zero,complement(X0))) = complement(join(complement(X1),meet(X0,top))),
inference(superposition,[status(thm)],[d33,c5]) ).
cnf(d71,plain,
meet(join(zero,complement(X2)),join(complement(X0),meet(X1,top))) = complement(join(meet(X2,top),meet(X0,join(zero,complement(X1))))),
inference(superposition,[status(thm)],[d70,d69]) ).
cnf(d72,plain,
meet(complement(X0),join(complement(X1),meet(X2,top))) = complement(join(meet(X0,top),meet(X1,join(zero,complement(X2))))),
inference(demodulation,[status(thm)],[d71,d46]) ).
cnf(d73,plain,
meet(complement(X1),join(complement(X2),X0)) = complement(join(meet(X1,top),meet(X2,join(zero,complement(X0))))),
inference(demodulation,[status(thm)],[d72,d68]) ).
cnf(d74,plain,
meet(complement(X0),join(complement(X1),X2)) = complement(join(X0,meet(X1,join(zero,complement(X2))))),
inference(demodulation,[status(thm)],[d73,d68]) ).
cnf(d75,plain,
meet(complement(X1),join(complement(X2),X0)) = complement(join(X1,meet(X2,complement(X0)))),
inference(demodulation,[status(thm)],[d74,d46]) ).
cnf(d76,plain,
join(X0,top) = join(top,complement(complement(X0))),
inference(superposition,[status(thm)],[c13,d51]) ).
cnf(d77,plain,
join(X0,top) = top,
inference(demodulation,[status(thm)],[d76,d57]) ).
cnf(d78,plain,
join(top,join(top,X0)) = join(top,X0),
inference(superposition,[status(thm)],[d30,c3]) ).
cnf(d79,plain,
join(top,join(X0,top)) = join(top,X0),
inference(superposition,[status(thm)],[d78,d47]) ).
cnf(d80,plain,
join(top,top) = join(top,X0),
inference(demodulation,[status(thm)],[d79,d77]) ).
cnf(d81,plain,
top = join(top,X0),
inference(demodulation,[status(thm)],[d80,d77]) ).
cnf(d82,plain,
X0 = join(meet(X0,join(complement(complement(X0)),X1)),complement(join(top,X1))),
inference(superposition,[status(thm)],[d51,d2]) ).
cnf(d83,plain,
X0 = join(complement(join(top,X1)),meet(X0,join(complement(complement(X0)),X1))),
inference(demodulation,[status(thm)],[d82,c2]) ).
cnf(d84,plain,
X1 = join(complement(top),meet(X1,join(complement(complement(X1)),X0))),
inference(demodulation,[status(thm)],[d83,d81]) ).
cnf(d85,plain,
X0 = join(zero,meet(X0,join(complement(complement(X0)),X1))),
inference(demodulation,[status(thm)],[d84,d6]) ).
cnf(d86,plain,
X0 = meet(X0,join(complement(complement(X0)),X1)),
inference(demodulation,[status(thm)],[d85,d46]) ).
cnf(d87,plain,
X0 = meet(X0,join(X0,X1)),
inference(demodulation,[status(thm)],[d86,d65]) ).
cnf(d88,plain,
join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))) = complement(X1),
inference(demodulation,[status(thm)],[c12,c2]) ).
cnf(d89,plain,
join(complement(X0),join(composition(converse(X1),complement(composition(X1,X0))),X2)) = join(complement(X0),X2),
inference(superposition,[status(thm)],[d88,c3]) ).
cnf(d90,plain,
complement(X0) = meet(complement(X0),join(complement(X0),X2)),
inference(superposition,[status(thm)],[d89,d87]) ).
cnf(d91,plain,
complement(X0) = complement(join(X0,meet(X0,complement(X1)))),
inference(demodulation,[status(thm)],[d90,d75]) ).
cnf(d92,plain,
complement(X1) = complement(join(X1,meet(X1,X0))),
inference(superposition,[status(thm)],[d65,d91]) ).
cnf(d93,plain,
complement(complement(X0)) = join(X0,meet(X0,X1)),
inference(superposition,[status(thm)],[d92,d66]) ).
cnf(d94,plain,
X0 = join(X0,meet(X0,X1)),
inference(demodulation,[status(thm)],[d93,d65]) ).
cnf(d95,plain,
X0 = join(X0,meet(X1,X0)),
inference(superposition,[status(thm)],[d20,d94]) ).
cnf(d96,plain,
meet(top,X0) = complement(join(zero,complement(X0))),
inference(superposition,[status(thm)],[d6,c5]) ).
cnf(d97,plain,
meet(top,X0) = complement(complement(X0)),
inference(demodulation,[status(thm)],[d96,d46]) ).
cnf(d98,plain,
meet(top,X0) = X0,
inference(demodulation,[status(thm)],[d97,d65]) ).
cnf(d99,plain,
meet(X2,join(complement(X0),complement(X1))) = complement(join(complement(X2),meet(X0,X1))),
inference(superposition,[status(thm)],[c5,c5]) ).
cnf(d100,plain,
meet(X0,join(zero,complement(X1))) = complement(join(complement(X0),meet(top,X1))),
inference(superposition,[status(thm)],[d6,d99]) ).
cnf(d101,plain,
meet(X1,complement(X0)) = complement(join(complement(X1),meet(top,X0))),
inference(demodulation,[status(thm)],[d100,d46]) ).
cnf(d102,plain,
meet(X1,complement(X0)) = complement(join(complement(X1),X0)),
inference(demodulation,[status(thm)],[d101,d98]) ).
cnf(d103,plain,
meet(X0,X1) = meet(X0,complement(complement(X1))),
inference(demodulation,[status(thm)],[c5,d102]) ).
cnf(d104,plain,
meet(X1,X0) = meet(X1,X0),
inference(demodulation,[status(thm)],[d103,d65]) ).
cnf(d105,plain,
top = join(join(complement(X0),complement(X1)),meet(X0,X1)),
inference(superposition,[status(thm)],[c5,c13]) ).
cnf(d106,plain,
top = join(complement(X0),join(complement(X1),meet(X0,X1))),
inference(demodulation,[status(thm)],[d105,c3]) ).
cnf(d107,plain,
X0 = join(meet(X0,join(complement(X1),meet(X0,X1))),complement(top)),
inference(superposition,[status(thm)],[d106,d2]) ).
cnf(d108,plain,
X0 = join(complement(top),meet(X0,join(complement(X1),meet(X0,X1)))),
inference(demodulation,[status(thm)],[d107,c2]) ).
cnf(d109,plain,
X0 = join(zero,meet(X0,join(complement(X1),meet(X0,X1)))),
inference(demodulation,[status(thm)],[d108,d6]) ).
cnf(d110,plain,
X0 = meet(X0,join(complement(X1),meet(X0,X1))),
inference(demodulation,[status(thm)],[d109,d46]) ).
cnf(d111,plain,
meet(X0,join(complement(X1),meet(X0,X1))) = X0,
inference(superposition,[status(thm)],[d110,d104]) ).
cnf(d112,plain,
meet(X1,join(X0,meet(X1,complement(X0)))) = X1,
inference(superposition,[status(thm)],[d65,d111]) ).
cnf(d113,plain,
meet(join(complement(X0),complement(X1)),top) = complement(join(zero,meet(X1,X0))),
inference(superposition,[status(thm)],[d12,d33]) ).
cnf(d114,plain,
complement(join(meet(X0,X1),complement(top))) = complement(join(zero,meet(X1,X0))),
inference(demodulation,[status(thm)],[d113,d31]) ).
cnf(d115,plain,
complement(join(complement(top),meet(X0,X1))) = complement(join(zero,meet(X1,X0))),
inference(demodulation,[status(thm)],[d114,c2]) ).
cnf(d116,plain,
complement(join(zero,meet(X0,X1))) = complement(join(zero,meet(X1,X0))),
inference(demodulation,[status(thm)],[d115,d6]) ).
cnf(d117,plain,
complement(meet(X0,X1)) = complement(join(zero,meet(X1,X0))),
inference(demodulation,[status(thm)],[d116,d46]) ).
cnf(d118,plain,
complement(meet(X1,X0)) = complement(meet(X0,X1)),
inference(demodulation,[status(thm)],[d117,d46]) ).
cnf(d119,plain,
meet(join(complement(X0),meet(X1,top)),top) = complement(join(zero,meet(X0,join(zero,complement(X1))))),
inference(superposition,[status(thm)],[d70,d33]) ).
cnf(d120,plain,
join(complement(X0),meet(X1,top)) = complement(join(zero,meet(X0,join(zero,complement(X1))))),
inference(demodulation,[status(thm)],[d119,d68]) ).
cnf(d121,plain,
join(complement(X1),X0) = complement(join(zero,meet(X1,join(zero,complement(X0))))),
inference(demodulation,[status(thm)],[d120,d68]) ).
cnf(d122,plain,
join(complement(X0),X1) = complement(meet(X0,join(zero,complement(X1)))),
inference(demodulation,[status(thm)],[d121,d46]) ).
cnf(d123,plain,
join(complement(X1),X0) = complement(meet(X1,complement(X0))),
inference(demodulation,[status(thm)],[d122,d46]) ).
cnf(d124,plain,
complement(meet(complement(X1),X0)) = join(complement(X0),X1),
inference(superposition,[status(thm)],[d123,d118]) ).
cnf(d125,plain,
complement(join(complement(X1),X0)) = meet(complement(X0),X1),
inference(superposition,[status(thm)],[d124,d66]) ).
cnf(d126,plain,
converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[status(thm)],[c9,c10]) ).
cnf(d127,plain,
converse(top) = join(X0,converse(complement(converse(X0)))),
inference(superposition,[status(thm)],[c13,d126]) ).
cnf(d128,plain,
converse(top) = top,
inference(superposition,[status(thm)],[d81,d127]) ).
cnf(d129,plain,
converse(composition(top,X0)) = composition(converse(X0),top),
inference(superposition,[status(thm)],[d128,c11]) ).
cnf(d130,plain,
join(converse(X0),join(converse(X1),X2)) = join(converse(join(X0,X1)),X2),
inference(superposition,[status(thm)],[c10,c3]) ).
cnf(d131,plain,
join(X1,join(complement(X1),X0)) = top,
inference(demodulation,[status(thm)],[d51,d81]) ).
cnf(d132,plain,
join(X0,join(X1,complement(X0))) = top,
inference(superposition,[status(thm)],[c2,d131]) ).
cnf(d133,plain,
top = join(converse(join(X0,X1)),complement(converse(X0))),
inference(superposition,[status(thm)],[d132,d130]) ).
cnf(d134,plain,
top = join(complement(converse(X0)),converse(join(X0,X1))),
inference(demodulation,[status(thm)],[d133,c2]) ).
cnf(d135,plain,
composition(X0,composition(X1,one)) = composition(X0,X1),
inference(superposition,[status(thm)],[c6,c7]) ).
cnf(d136,plain,
composition(X1,X0) = composition(X1,X0),
inference(demodulation,[status(thm)],[d135,c7]) ).
cnf(d137,plain,
X0 = composition(X0,one),
inference(superposition,[status(thm)],[c7,d136]) ).
cnf(d138,plain,
converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c9,c11]) ).
cnf(d139,plain,
converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[status(thm)],[d137,d138]) ).
cnf(d140,plain,
X0 = composition(converse(one),X0),
inference(demodulation,[status(thm)],[d139,c9]) ).
cnf(d141,plain,
converse(one) = one,
inference(superposition,[status(thm)],[d140,d137]) ).
cnf(d142,plain,
composition(join(X1,converse(one)),X0) = join(composition(X1,X0),X0),
inference(superposition,[status(thm)],[d140,c8]) ).
cnf(d143,plain,
composition(join(X0,one),X1) = join(composition(X0,X1),X1),
inference(demodulation,[status(thm)],[d142,d141]) ).
cnf(d144,plain,
composition(join(X0,one),X1) = join(X1,composition(X0,X1)),
inference(demodulation,[status(thm)],[d143,c2]) ).
cnf(d145,plain,
join(X2,join(X0,X1)) = join(X0,join(X1,X2)),
inference(superposition,[status(thm)],[c3,c2]) ).
cnf(d146,plain,
join(top,X0) = join(top,join(X0,top)),
inference(superposition,[status(thm)],[d78,d145]) ).
cnf(d147,plain,
join(top,X0) = join(top,top),
inference(demodulation,[status(thm)],[d146,d77]) ).
cnf(d148,plain,
join(top,X0) = top,
inference(demodulation,[status(thm)],[d147,d77]) ).
cnf(d149,plain,
composition(top,X0) = join(X0,composition(top,X0)),
inference(superposition,[status(thm)],[d148,d144]) ).
cnf(d150,plain,
top = join(complement(converse(X0)),converse(composition(top,X0))),
inference(superposition,[status(thm)],[d149,d134]) ).
cnf(d151,plain,
top = join(complement(converse(X0)),composition(converse(X0),top)),
inference(demodulation,[status(thm)],[d150,d129]) ).
cnf(d152,plain,
top = join(complement(X0),composition(converse(converse(X0)),top)),
inference(superposition,[status(thm)],[c9,d151]) ).
cnf(d153,plain,
top = join(complement(X0),composition(X0,top)),
inference(demodulation,[status(thm)],[d152,c9]) ).
cnf(d154,plain,
complement(top) = meet(complement(composition(X0,top)),X0),
inference(superposition,[status(thm)],[d153,d125]) ).
cnf(d155,plain,
zero = meet(complement(composition(X0,top)),X0),
inference(demodulation,[status(thm)],[d154,d6]) ).
cnf(d156,plain,
zero = meet(X0,complement(composition(X0,top))),
inference(demodulation,[status(thm)],[d155,d20]) ).
cnf(d157,plain,
meet(X0,join(composition(X0,top),zero)) = X0,
inference(superposition,[status(thm)],[d156,d112]) ).
cnf(d158,plain,
meet(X0,composition(X0,top)) = X0,
inference(demodulation,[status(thm)],[d157,d50]) ).
cnf(d159,plain,
composition(X0,top) = join(composition(X0,top),X0),
inference(superposition,[status(thm)],[d158,d95]) ).
cnf(d160,plain,
composition(X0,top) = join(X0,composition(X0,top)),
inference(demodulation,[status(thm)],[d159,c2]) ).
cnf(d161,plain,
join(complement(X1),composition(X0,complement(composition(converse(X0),X1)))) = complement(X1),
inference(superposition,[status(thm)],[c9,d88]) ).
cnf(d162,plain,
join(zero,join(X0,zero)) = join(zero,X0),
inference(superposition,[status(thm)],[d44,d47]) ).
cnf(d163,plain,
join(X0,zero) = join(zero,X0),
inference(demodulation,[status(thm)],[d162,d46]) ).
cnf(d164,plain,
join(X0,zero) = X0,
inference(demodulation,[status(thm)],[d163,d46]) ).
cnf(d165,plain,
converse(join(X1,converse(X0))) = join(converse(X1),X0),
inference(superposition,[status(thm)],[c9,c10]) ).
cnf(d166,plain,
converse(converse(X0)) = join(converse(zero),X0),
inference(superposition,[status(thm)],[d46,d165]) ).
cnf(d167,plain,
X0 = join(converse(zero),X0),
inference(demodulation,[status(thm)],[d166,c9]) ).
cnf(d168,plain,
zero = converse(zero),
inference(superposition,[status(thm)],[d167,d164]) ).
cnf(d169,plain,
join(zero,composition(converse(X0),complement(composition(X0,top)))) = complement(top),
inference(superposition,[status(thm)],[d6,d88]) ).
cnf(d170,plain,
composition(converse(X0),complement(composition(X0,top))) = complement(top),
inference(demodulation,[status(thm)],[d169,d46]) ).
cnf(d171,plain,
composition(converse(X0),complement(composition(X0,top))) = zero,
inference(demodulation,[status(thm)],[d170,d6]) ).
cnf(d172,plain,
sk1 = composition(sk1,top),
inference(superposition,[status(thm)],[c0,d136]) ).
cnf(d173,plain,
composition(converse(sk1),complement(sk1)) = zero,
inference(superposition,[status(thm)],[d172,d171]) ).
cnf(d174,plain,
converse(zero) = composition(converse(complement(sk1)),sk1),
inference(superposition,[status(thm)],[d173,d138]) ).
cnf(d175,plain,
zero = composition(converse(complement(sk1)),sk1),
inference(demodulation,[status(thm)],[d174,d168]) ).
cnf(d176,plain,
join(complement(sk1),composition(complement(sk1),complement(zero))) = complement(sk1),
inference(superposition,[status(thm)],[d175,d161]) ).
cnf(d177,plain,
join(complement(sk1),composition(complement(sk1),top)) = complement(sk1),
inference(demodulation,[status(thm)],[d176,d24]) ).
cnf(d178,plain,
composition(complement(sk1),top) = complement(sk1),
inference(demodulation,[status(thm)],[d177,d160]) ).
cnf(d179,plain,
$false,
inference(resolution,[status(thm)],[c1,d178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL018-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.41 % Computer : n001.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 05:35:41 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 142.71/29.88 % SZS status Unsatisfiable for theBenchmark.p
% 142.71/29.88 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------