%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : REL010-2 : 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 : n006.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 08:24:14 AM UTC 2026
% Result : Unsatisfiable 149.60s 44.95s
% Output : CNFRefutation 149.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 16
% Syntax : Number of clauses : 175 ( 175 unt; 0 nHn; 30 RR)
% Number of literals : 175 ( 174 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 265 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(goals_17,negated_conjecture,
meet(composition(sk1,sk2),sk3) = zero ).
cnf(goals_18,negated_conjecture,
meet(sk2,composition(converse(sk1),sk3)) != zero ).
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(dedekind_law_14,axiom,
join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))) ).
cnf(c0,plain,
meet(composition(sk1,sk2),sk3) = zero,
inference(clausification,[status(esa)],[goals_17]) ).
cnf(c1,plain,
meet(sk2,composition(converse(sk1),sk3)) != zero,
inference(clausification,[status(esa)],[goals_18]) ).
cnf(c2,plain,
join(X0,X1) = join(X1,X0),
inference(clausification,[status(esa)],[maddux1_join_commutativity_1]) ).
cnf(c3,plain,
join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(clausification,[status(esa)],[maddux2_join_associativity_2]) ).
cnf(c4,plain,
join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(clausification,[status(esa)],[maddux3_a_kind_of_de_Morgan_3]) ).
cnf(c5,plain,
complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(clausification,[status(esa)],[maddux4_definiton_of_meet_4]) ).
cnf(c6,plain,
composition(composition(X0,X1),X2) = composition(X0,composition(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,
join(composition(X0,X1),composition(X2,X1)) = composition(join(X0,X2),X1),
inference(clausification,[status(esa)],[composition_distributivity_7]) ).
cnf(c9,plain,
converse(converse(X0)) = X0,
inference(clausification,[status(esa)],[converse_idempotence_8]) ).
cnf(c10,plain,
join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(clausification,[status(esa)],[converse_additivity_9]) ).
cnf(c11,plain,
composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(clausification,[status(esa)],[converse_multiplicativity_10]) ).
cnf(c12,plain,
complement(X0) = join(composition(converse(X1),complement(composition(X1,X0))),complement(X0)),
inference(clausification,[status(esa)],[converse_cancellativity_11]) ).
cnf(c13,plain,
join(X0,complement(X0)) = top,
inference(clausification,[status(esa)],[def_top_12]) ).
cnf(c14,plain,
meet(X0,complement(X0)) = zero,
inference(clausification,[status(esa)],[def_zero_13]) ).
cnf(c15,plain,
composition(meet(X0,composition(X1,converse(X2))),meet(X2,composition(converse(X0),X1))) = join(meet(composition(X0,X2),X1),composition(meet(X0,composition(X1,converse(X2))),meet(X2,composition(converse(X0),X1)))),
inference(clausification,[status(esa)],[dedekind_law_14]) ).
cnf(d0,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(demodulation,[status(thm)],[c4,c2]) ).
cnf(d1,plain,
join(complement(join(complement(X0),X1)),meet(X0,X1)) = X0,
inference(demodulation,[status(thm)],[d0,c5]) ).
cnf(d2,plain,
join(meet(X0,X1),complement(join(complement(X0),X1))) = X0,
inference(demodulation,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
join(zero,complement(join(complement(X0),complement(X0)))) = X0,
inference(superposition,[status(thm)],[c14,d2]) ).
cnf(d4,plain,
join(zero,meet(X0,X0)) = X0,
inference(demodulation,[status(thm)],[d3,c5]) ).
cnf(d5,plain,
complement(top) = meet(X0,complement(X0)),
inference(superposition,[status(thm)],[c13,c5]) ).
cnf(d6,plain,
complement(top) = zero,
inference(demodulation,[status(thm)],[d5,c14]) ).
cnf(d7,plain,
join(top,zero) = top,
inference(superposition,[status(thm)],[d6,c13]) ).
cnf(d8,plain,
join(zero,top) = top,
inference(demodulation,[status(thm)],[d7,c2]) ).
cnf(d9,plain,
join(top,X0) = join(zero,join(top,X0)),
inference(superposition,[status(thm)],[d8,c3]) ).
cnf(d10,plain,
join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[status(thm)],[c3,c2]) ).
cnf(d11,plain,
join(X0,join(X1,complement(join(X0,X1)))) = top,
inference(superposition,[status(thm)],[c3,c13]) ).
cnf(d12,plain,
join(X0,join(complement(X0),complement(top))) = top,
inference(superposition,[status(thm)],[c13,d11]) ).
cnf(d13,plain,
join(X0,join(complement(X0),zero)) = top,
inference(demodulation,[status(thm)],[d12,d6]) ).
cnf(d14,plain,
join(X0,join(zero,complement(X0))) = top,
inference(demodulation,[status(thm)],[d13,c2]) ).
cnf(d15,plain,
complement(join(complement(X0),zero)) = meet(X0,top),
inference(superposition,[status(thm)],[d6,c5]) ).
cnf(d16,plain,
complement(join(zero,complement(X0))) = meet(X0,top),
inference(demodulation,[status(thm)],[d15,c2]) ).
cnf(d17,plain,
complement(top) = meet(zero,top),
inference(superposition,[status(thm)],[c13,d16]) ).
cnf(d18,plain,
zero = meet(zero,top),
inference(demodulation,[status(thm)],[d17,d6]) ).
cnf(d19,plain,
join(zero,complement(join(complement(zero),top))) = zero,
inference(superposition,[status(thm)],[d18,d2]) ).
cnf(d20,plain,
join(zero,complement(join(top,complement(zero)))) = zero,
inference(demodulation,[status(thm)],[d19,c2]) ).
cnf(d21,plain,
join(join(top,complement(zero)),zero) = top,
inference(superposition,[status(thm)],[d20,d14]) ).
cnf(d22,plain,
join(top,join(complement(zero),zero)) = top,
inference(demodulation,[status(thm)],[d21,c3]) ).
cnf(d23,plain,
join(zero,join(top,complement(zero))) = top,
inference(demodulation,[status(thm)],[d22,d10]) ).
cnf(d24,plain,
join(top,complement(zero)) = top,
inference(demodulation,[status(thm)],[d23,d9]) ).
cnf(d25,plain,
join(zero,complement(top)) = zero,
inference(demodulation,[status(thm)],[d20,d24]) ).
cnf(d26,plain,
join(zero,zero) = zero,
inference(demodulation,[status(thm)],[d25,d6]) ).
cnf(d27,plain,
join(zero,X0) = join(zero,join(zero,X0)),
inference(superposition,[status(thm)],[d26,c3]) ).
cnf(d28,plain,
join(zero,meet(X0,X0)) = join(zero,X0),
inference(superposition,[status(thm)],[d4,d27]) ).
cnf(d29,plain,
X0 = join(zero,X0),
inference(demodulation,[status(thm)],[d28,d4]) ).
cnf(d30,plain,
join(X2,join(X0,X1)) = join(X0,join(X1,X2)),
inference(superposition,[status(thm)],[c3,c2]) ).
cnf(d31,plain,
join(zero,X0) = join(zero,join(X0,zero)),
inference(superposition,[status(thm)],[d27,d30]) ).
cnf(d32,plain,
X0 = join(zero,join(X0,zero)),
inference(demodulation,[status(thm)],[d31,d29]) ).
cnf(d33,plain,
X0 = join(X0,zero),
inference(demodulation,[status(thm)],[d32,d29]) ).
cnf(d34,plain,
join(join(complement(X0),complement(X1)),meet(X0,X1)) = top,
inference(superposition,[status(thm)],[c5,c13]) ).
cnf(d35,plain,
join(complement(X0),join(complement(X1),meet(X0,X1))) = top,
inference(demodulation,[status(thm)],[d34,c3]) ).
cnf(d36,plain,
join(meet(X0,join(complement(X1),meet(X0,X1))),complement(top)) = X0,
inference(superposition,[status(thm)],[d35,d2]) ).
cnf(d37,plain,
join(complement(top),meet(X0,join(complement(X1),meet(X0,X1)))) = X0,
inference(demodulation,[status(thm)],[d36,c2]) ).
cnf(d38,plain,
join(zero,meet(X0,join(complement(X1),meet(X0,X1)))) = X0,
inference(demodulation,[status(thm)],[d37,d6]) ).
cnf(d39,plain,
meet(X0,join(complement(X1),meet(X0,X1))) = X0,
inference(demodulation,[status(thm)],[d38,d29]) ).
cnf(d40,plain,
meet(X0,X0) = X0,
inference(demodulation,[status(thm)],[d4,d29]) ).
cnf(d41,plain,
meet(X0,join(complement(X0),X0)) = X0,
inference(superposition,[status(thm)],[d40,d39]) ).
cnf(d42,plain,
meet(X0,join(X0,complement(X0))) = X0,
inference(demodulation,[status(thm)],[d41,c2]) ).
cnf(d43,plain,
meet(X0,top) = X0,
inference(demodulation,[status(thm)],[d42,c13]) ).
cnf(d44,plain,
complement(complement(X0)) = meet(X0,top),
inference(demodulation,[status(thm)],[d16,d29]) ).
cnf(d45,plain,
complement(complement(X0)) = X0,
inference(demodulation,[status(thm)],[d44,d43]) ).
cnf(d46,plain,
join(top,X1) = join(X0,join(complement(X0),X1)),
inference(superposition,[status(thm)],[c13,c3]) ).
cnf(d47,plain,
join(X0,composition(X1,one)) = composition(join(X0,X1),one),
inference(superposition,[status(thm)],[c7,c8]) ).
cnf(d48,plain,
join(X1,X0) = composition(join(X1,X0),one),
inference(demodulation,[status(thm)],[d47,c7]) ).
cnf(d49,plain,
join(X0,X1) = join(X0,X1),
inference(demodulation,[status(thm)],[d48,c7]) ).
cnf(d50,plain,
X0 = join(zero,meet(X0,X0)),
inference(superposition,[status(thm)],[d4,d49]) ).
cnf(d51,plain,
X0 = meet(X0,X0),
inference(demodulation,[status(thm)],[d50,d29]) ).
cnf(d52,plain,
join(complement(X0),join(complement(X0),X0)) = top,
inference(superposition,[status(thm)],[d51,d35]) ).
cnf(d53,plain,
join(X0,join(complement(X0),complement(X0))) = top,
inference(demodulation,[status(thm)],[d52,d10]) ).
cnf(d54,plain,
join(top,complement(X0)) = top,
inference(demodulation,[status(thm)],[d53,d46]) ).
cnf(d55,plain,
join(X0,top) = top,
inference(superposition,[status(thm)],[d54,d11]) ).
cnf(d56,plain,
join(composition(join(X0,X2),X1),X3) = join(composition(X0,X1),join(composition(X2,X1),X3)),
inference(superposition,[status(thm)],[c8,c3]) ).
cnf(d57,plain,
join(composition(join(X2,X0),X1),join(zero,complement(composition(X0,X1)))) = join(composition(X2,X1),top),
inference(superposition,[status(thm)],[d14,d56]) ).
cnf(d58,plain,
join(complement(composition(X1,X2)),join(composition(join(X0,X1),X2),zero)) = join(composition(X0,X2),top),
inference(demodulation,[status(thm)],[d57,d10]) ).
cnf(d59,plain,
join(zero,join(complement(composition(X0,X1)),composition(join(X2,X0),X1))) = join(composition(X2,X1),top),
inference(demodulation,[status(thm)],[d58,d10]) ).
cnf(d60,plain,
join(complement(composition(X0,X1)),composition(join(X2,X0),X1)) = join(composition(X2,X1),top),
inference(demodulation,[status(thm)],[d59,d29]) ).
cnf(d61,plain,
join(complement(composition(X2,X1)),composition(join(X0,X2),X1)) = top,
inference(demodulation,[status(thm)],[d60,d55]) ).
cnf(d62,plain,
composition(join(X0,X2),X1) = join(composition(X2,X1),composition(X0,X1)),
inference(superposition,[status(thm)],[c8,c2]) ).
cnf(d63,plain,
composition(join(X2,X0),X1) = composition(join(X0,X2),X1),
inference(superposition,[status(thm)],[d62,c8]) ).
cnf(d64,plain,
composition(X0,composition(X1,one)) = composition(X0,X1),
inference(superposition,[status(thm)],[c6,c7]) ).
cnf(d65,plain,
composition(X1,X0) = composition(X1,X0),
inference(demodulation,[status(thm)],[d64,c7]) ).
cnf(d66,plain,
complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(demodulation,[status(thm)],[c12,c2]) ).
cnf(d67,plain,
complement(top) = join(zero,composition(converse(X0),complement(composition(X0,top)))),
inference(superposition,[status(thm)],[d6,d66]) ).
cnf(d68,plain,
zero = join(zero,composition(converse(X0),complement(composition(X0,top)))),
inference(demodulation,[status(thm)],[d67,d6]) ).
cnf(d69,plain,
zero = composition(converse(X0),complement(composition(X0,top))),
inference(demodulation,[status(thm)],[d68,d29]) ).
cnf(d70,plain,
composition(converse(X0),complement(composition(X0,top))) = zero,
inference(superposition,[status(thm)],[d69,d65]) ).
cnf(d71,plain,
composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[status(thm)],[c9,c11]) ).
cnf(d72,plain,
X0 = composition(X0,one),
inference(superposition,[status(thm)],[c7,d65]) ).
cnf(d73,plain,
composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[d72,d71]) ).
cnf(d74,plain,
composition(converse(one),X0) = X0,
inference(demodulation,[status(thm)],[d73,c9]) ).
cnf(d75,plain,
composition(converse(X0),one) = converse(X0),
inference(superposition,[status(thm)],[d74,d71]) ).
cnf(d76,plain,
converse(X0) = converse(X0),
inference(demodulation,[status(thm)],[d75,c7]) ).
cnf(d77,plain,
X0 = converse(converse(X0)),
inference(superposition,[status(thm)],[c9,d76]) ).
cnf(d78,plain,
composition(X0,complement(composition(converse(X0),top))) = zero,
inference(superposition,[status(thm)],[d77,d70]) ).
cnf(d79,plain,
join(top,X0) = join(zero,join(X0,top)),
inference(superposition,[status(thm)],[c2,d9]) ).
cnf(d80,plain,
join(top,complement(zero)) = join(top,top),
inference(superposition,[status(thm)],[d46,d79]) ).
cnf(d81,plain,
top = join(top,top),
inference(demodulation,[status(thm)],[d80,d24]) ).
cnf(d82,plain,
join(top,X0) = join(top,join(top,X0)),
inference(superposition,[status(thm)],[d81,c3]) ).
cnf(d83,plain,
join(top,join(X0,top)) = join(top,X0),
inference(superposition,[status(thm)],[d82,d10]) ).
cnf(d84,plain,
join(top,top) = join(top,X0),
inference(demodulation,[status(thm)],[d83,d55]) ).
cnf(d85,plain,
top = join(top,X0),
inference(demodulation,[status(thm)],[d84,d55]) ).
cnf(d86,plain,
converse(one) = one,
inference(superposition,[status(thm)],[d74,d72]) ).
cnf(d87,plain,
join(X0,composition(X1,X0)) = composition(join(converse(one),X1),X0),
inference(superposition,[status(thm)],[d74,c8]) ).
cnf(d88,plain,
join(X0,composition(X1,X0)) = composition(join(one,X1),X0),
inference(demodulation,[status(thm)],[d87,d86]) ).
cnf(d89,plain,
top = composition(join(one,X0),top),
inference(superposition,[status(thm)],[d88,d85]) ).
cnf(d90,plain,
converse(join(X0,X1)) = join(converse(X1),converse(X0)),
inference(superposition,[status(thm)],[c10,c2]) ).
cnf(d91,plain,
converse(join(X0,one)) = join(one,converse(X0)),
inference(superposition,[status(thm)],[d86,d90]) ).
cnf(d92,plain,
top = composition(converse(join(X0,one)),top),
inference(superposition,[status(thm)],[d91,d89]) ).
cnf(d93,plain,
composition(join(X0,one),complement(top)) = zero,
inference(superposition,[status(thm)],[d92,d78]) ).
cnf(d94,plain,
composition(join(X0,one),zero) = zero,
inference(demodulation,[status(thm)],[d93,d6]) ).
cnf(d95,plain,
zero = composition(join(one,X0),zero),
inference(superposition,[status(thm)],[d94,d63]) ).
cnf(d96,plain,
join(complement(composition(X0,zero)),zero) = top,
inference(superposition,[status(thm)],[d95,d61]) ).
cnf(d97,plain,
complement(composition(X0,zero)) = top,
inference(demodulation,[status(thm)],[d96,d33]) ).
cnf(d98,plain,
complement(top) = composition(X0,zero),
inference(superposition,[status(thm)],[d97,d45]) ).
cnf(d99,plain,
zero = composition(X0,zero),
inference(demodulation,[status(thm)],[d98,d6]) ).
cnf(d100,plain,
complement(join(complement(X1),complement(X0))) = meet(X0,X1),
inference(superposition,[status(thm)],[c2,c5]) ).
cnf(d101,plain,
meet(X1,X0) = meet(X0,X1),
inference(superposition,[status(thm)],[d100,c5]) ).
cnf(d102,plain,
X0 = meet(top,X0),
inference(superposition,[status(thm)],[d43,d101]) ).
cnf(d103,plain,
top = join(X0,complement(X0)),
inference(superposition,[status(thm)],[c13,d49]) ).
cnf(d104,plain,
top = complement(zero),
inference(superposition,[status(thm)],[d29,d103]) ).
cnf(d105,plain,
complement(join(zero,complement(X0))) = meet(top,X0),
inference(superposition,[status(thm)],[d6,c5]) ).
cnf(d106,plain,
complement(join(meet(top,X0),complement(X1))) = meet(X1,join(zero,complement(X0))),
inference(superposition,[status(thm)],[d105,d100]) ).
cnf(d107,plain,
complement(join(X0,complement(X1))) = meet(X1,join(zero,complement(X0))),
inference(demodulation,[status(thm)],[d106,d102]) ).
cnf(d108,plain,
complement(join(X0,complement(X1))) = meet(X1,complement(X0)),
inference(demodulation,[status(thm)],[d107,d29]) ).
cnf(d109,plain,
join(complement(X0),X2) = join(complement(X0),join(composition(converse(X1),complement(composition(X1,X0))),X2)),
inference(superposition,[status(thm)],[d66,c3]) ).
cnf(d110,plain,
join(complement(join(zero,complement(X0))),X1) = join(meet(top,X0),join(composition(converse(X2),complement(composition(X2,join(zero,complement(X0))))),X1)),
inference(superposition,[status(thm)],[d105,d109]) ).
cnf(d111,plain,
join(meet(X0,complement(zero)),X1) = join(meet(top,X0),join(composition(converse(X2),complement(composition(X2,join(zero,complement(X0))))),X1)),
inference(demodulation,[status(thm)],[d110,d108]) ).
cnf(d112,plain,
join(meet(X0,top),X1) = join(meet(top,X0),join(composition(converse(X2),complement(composition(X2,join(zero,complement(X0))))),X1)),
inference(demodulation,[status(thm)],[d111,d104]) ).
cnf(d113,plain,
join(X0,X1) = join(meet(top,X0),join(composition(converse(X2),complement(composition(X2,join(zero,complement(X0))))),X1)),
inference(demodulation,[status(thm)],[d112,d43]) ).
cnf(d114,plain,
join(X0,X1) = join(X0,join(composition(converse(X2),complement(composition(X2,join(zero,complement(X0))))),X1)),
inference(demodulation,[status(thm)],[d113,d102]) ).
cnf(d115,plain,
join(X0,X1) = join(X0,join(composition(converse(X2),complement(composition(X2,complement(X0)))),X1)),
inference(demodulation,[status(thm)],[d114,d29]) ).
cnf(d116,plain,
complement(join(zero,meet(X1,X0))) = meet(top,join(complement(X0),complement(X1))),
inference(superposition,[status(thm)],[d100,d105]) ).
cnf(d117,plain,
complement(meet(X0,X1)) = meet(top,join(complement(X1),complement(X0))),
inference(demodulation,[status(thm)],[d116,d29]) ).
cnf(d118,plain,
complement(meet(X1,X0)) = join(complement(X0),complement(X1)),
inference(demodulation,[status(thm)],[d117,d102]) ).
cnf(d119,plain,
join(complement(X1),complement(X0)) = complement(meet(X1,X0)),
inference(superposition,[status(thm)],[d118,c2]) ).
cnf(d120,plain,
complement(join(complement(X1),X0)) = meet(complement(X0),X1),
inference(superposition,[status(thm)],[d45,d100]) ).
cnf(d121,plain,
join(complement(join(complement(X0),complement(X1))),X2) = join(meet(X0,X1),join(composition(converse(X3),complement(composition(X3,join(complement(X0),complement(X1))))),X2)),
inference(superposition,[status(thm)],[c5,d109]) ).
cnf(d122,plain,
join(meet(complement(complement(X1)),X0),X2) = join(meet(X0,X1),join(composition(converse(X3),complement(composition(X3,join(complement(X0),complement(X1))))),X2)),
inference(demodulation,[status(thm)],[d121,d120]) ).
cnf(d123,plain,
join(meet(X0,X1),X2) = join(meet(X1,X0),join(composition(converse(X3),complement(composition(X3,join(complement(X1),complement(X0))))),X2)),
inference(demodulation,[status(thm)],[d122,d45]) ).
cnf(d124,plain,
join(meet(X1,X0),X2) = join(meet(X0,X1),join(composition(converse(X3),complement(composition(X3,complement(meet(X0,X1))))),X2)),
inference(demodulation,[status(thm)],[d123,d119]) ).
cnf(d125,plain,
join(meet(X1,X0),X3) = join(meet(X0,X1),X3),
inference(demodulation,[status(thm)],[d124,d115]) ).
cnf(d126,plain,
meet(sk3,composition(sk1,sk2)) = zero,
inference(demodulation,[status(thm)],[c0,d101]) ).
cnf(d127,plain,
composition(meet(converse(X0),composition(X1,converse(X2))),meet(X2,composition(converse(converse(X0)),X1))) = join(meet(composition(converse(X0),X2),X1),composition(meet(converse(X0),composition(X1,converse(X2))),meet(X2,composition(X0,X1)))),
inference(superposition,[status(thm)],[c9,c15]) ).
cnf(d128,plain,
composition(meet(converse(X0),composition(X1,converse(X2))),meet(X2,composition(X0,X1))) = join(meet(composition(converse(X0),X2),X1),composition(meet(converse(X0),composition(X1,converse(X2))),meet(X2,composition(X0,X1)))),
inference(demodulation,[status(thm)],[d127,c9]) ).
cnf(d129,plain,
composition(meet(converse(sk1),composition(sk2,converse(sk3))),meet(sk3,composition(sk1,sk2))) = join(meet(composition(converse(sk1),sk3),sk2),composition(meet(converse(sk1),composition(sk2,converse(sk3))),zero)),
inference(superposition,[status(thm)],[d126,d128]) ).
cnf(d130,plain,
composition(meet(converse(sk1),composition(sk2,converse(sk3))),zero) = join(meet(composition(converse(sk1),sk3),sk2),composition(meet(converse(sk1),composition(sk2,converse(sk3))),zero)),
inference(demodulation,[status(thm)],[d129,d126]) ).
cnf(d131,plain,
zero = join(meet(composition(converse(sk1),sk3),sk2),composition(meet(converse(sk1),composition(sk2,converse(sk3))),zero)),
inference(demodulation,[status(thm)],[d130,d99]) ).
cnf(d132,plain,
zero = join(meet(sk2,composition(converse(sk1),sk3)),composition(meet(converse(sk1),composition(sk2,converse(sk3))),zero)),
inference(demodulation,[status(thm)],[d131,d125]) ).
cnf(d133,plain,
zero = join(meet(sk2,composition(converse(sk1),sk3)),zero),
inference(demodulation,[status(thm)],[d132,d99]) ).
cnf(d134,plain,
zero = meet(sk2,composition(converse(sk1),sk3)),
inference(demodulation,[status(thm)],[d133,d33]) ).
cnf(d135,plain,
zero != zero,
inference(demodulation,[status(thm)],[c1,d134]) ).
cnf(d136,plain,
join(meet(X0,complement(X1)),meet(X0,X1)) = X0,
inference(superposition,[status(thm)],[c5,d2]) ).
cnf(d137,plain,
join(meet(X0,X1),meet(X0,complement(X1))) = X0,
inference(demodulation,[status(thm)],[d136,c2]) ).
cnf(d138,plain,
join(meet(X2,join(complement(X0),complement(X1))),meet(X2,meet(X1,X0))) = X2,
inference(superposition,[status(thm)],[d100,d137]) ).
cnf(d139,plain,
join(meet(X0,meet(X2,X1)),meet(X0,join(complement(X1),complement(X2)))) = X0,
inference(demodulation,[status(thm)],[d138,c2]) ).
cnf(d140,plain,
join(meet(X2,meet(X1,X0)),meet(X2,complement(meet(X1,X0)))) = X2,
inference(demodulation,[status(thm)],[d139,d118]) ).
cnf(d141,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d140,d137]) ).
cnf(d142,plain,
$false,
inference(resolution,[status(thm)],[d141,d135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL010-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/10.38 % Computer : n006.cluster.edu
% 0.11/10.38 % Model : x86_64 x86_64
% 0.11/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.38 % Memory : 8046.5625MB
% 0.11/10.38 % OS : Linux 6.8.0-71-generic
% 0.11/10.38 % CPULimit : 300
% 0.11/10.38 % WCLimit : 300
% 0.11/10.38 % DateTime : Sat Sep 26 05:26:24 UTC 2026
% 0.11/10.38 % CPUTime :
% 0.11/10.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 149.60/44.95 % SZS status Unsatisfiable for theBenchmark.p
% 149.60/44.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------