%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : REL013-1 : 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 : n011.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 08:24:15 AM UTC 2026
% Result : Unsatisfiable 101.02s 28.95s
% Output : CNFRefutation 101.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 14
% Syntax : Number of clauses : 124 ( 122 unt; 0 nHn; 12 RR)
% Number of literals : 126 ( 125 equ; 6 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 181 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(goals_14,negated_conjecture,
( composition(zero,sk1) != zero
| composition(sk1,zero) != 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(c0,plain,
( composition(zero,sk1) != zero
| composition(sk1,zero) != zero ),
inference(clausification,[status(esa)],[goals_14]) ).
cnf(c1,plain,
join(X0,X1) = join(X1,X0),
inference(clausification,[status(esa)],[maddux1_join_commutativity_1]) ).
cnf(c2,plain,
join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(clausification,[status(esa)],[maddux2_join_associativity_2]) ).
cnf(c3,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(c4,plain,
complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(clausification,[status(esa)],[maddux4_definiton_of_meet_4]) ).
cnf(c5,plain,
composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2)),
inference(clausification,[status(esa)],[composition_associativity_5]) ).
cnf(c6,plain,
composition(X0,one) = X0,
inference(clausification,[status(esa)],[composition_identity_6]) ).
cnf(c7,plain,
join(composition(X0,X1),composition(X2,X1)) = composition(join(X0,X2),X1),
inference(clausification,[status(esa)],[composition_distributivity_7]) ).
cnf(c8,plain,
converse(converse(X0)) = X0,
inference(clausification,[status(esa)],[converse_idempotence_8]) ).
cnf(c9,plain,
join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(clausification,[status(esa)],[converse_additivity_9]) ).
cnf(c10,plain,
composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(clausification,[status(esa)],[converse_multiplicativity_10]) ).
cnf(c11,plain,
complement(X0) = join(composition(converse(X1),complement(composition(X1,X0))),complement(X0)),
inference(clausification,[status(esa)],[converse_cancellativity_11]) ).
cnf(c12,plain,
join(X0,complement(X0)) = top,
inference(clausification,[status(esa)],[def_top_12]) ).
cnf(c13,plain,
meet(X0,complement(X0)) = zero,
inference(clausification,[status(esa)],[def_zero_13]) ).
cnf(d0,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(demodulation,[status(thm)],[c3,c1]) ).
cnf(d1,plain,
join(complement(join(complement(X0),X1)),meet(X0,X1)) = X0,
inference(demodulation,[status(thm)],[d0,c4]) ).
cnf(d2,plain,
join(meet(X0,X1),complement(join(complement(X0),X1))) = X0,
inference(demodulation,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
join(zero,complement(join(complement(X0),complement(X0)))) = X0,
inference(superposition,[status(thm)],[c13,d2]) ).
cnf(d4,plain,
join(zero,meet(X0,X0)) = X0,
inference(demodulation,[status(thm)],[d3,c4]) ).
cnf(d5,plain,
join(X2,join(X0,X1)) = join(X0,join(X1,X2)),
inference(superposition,[status(thm)],[c2,c1]) ).
cnf(d6,plain,
complement(top) = meet(X0,complement(X0)),
inference(superposition,[status(thm)],[c12,c4]) ).
cnf(d7,plain,
complement(top) = zero,
inference(demodulation,[status(thm)],[d6,c13]) ).
cnf(d8,plain,
composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[status(thm)],[c8,c10]) ).
cnf(d9,plain,
composition(X0,composition(X1,one)) = composition(X0,X1),
inference(superposition,[status(thm)],[c5,c6]) ).
cnf(d10,plain,
composition(X1,X0) = composition(X1,X0),
inference(demodulation,[status(thm)],[d9,c6]) ).
cnf(d11,plain,
X0 = composition(X0,one),
inference(superposition,[status(thm)],[c6,d10]) ).
cnf(d12,plain,
composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[d11,d8]) ).
cnf(d13,plain,
composition(converse(one),X0) = X0,
inference(demodulation,[status(thm)],[d12,c8]) ).
cnf(d14,plain,
one = converse(one),
inference(superposition,[status(thm)],[d13,c6]) ).
cnf(d15,plain,
composition(one,X0) = X0,
inference(demodulation,[status(thm)],[d13,d14]) ).
cnf(d16,plain,
complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(demodulation,[status(thm)],[c11,c1]) ).
cnf(d17,plain,
complement(top) = join(zero,composition(converse(X0),complement(composition(X0,top)))),
inference(superposition,[status(thm)],[d7,d16]) ).
cnf(d18,plain,
zero = join(zero,composition(converse(X0),complement(composition(X0,top)))),
inference(demodulation,[status(thm)],[d17,d7]) ).
cnf(d19,plain,
X0 = composition(one,X0),
inference(superposition,[status(thm)],[d15,d10]) ).
cnf(d20,plain,
zero = join(zero,composition(converse(one),complement(top))),
inference(superposition,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
zero = join(zero,composition(one,complement(top))),
inference(demodulation,[status(thm)],[d20,d14]) ).
cnf(d22,plain,
zero = join(zero,complement(top)),
inference(demodulation,[status(thm)],[d21,d15]) ).
cnf(d23,plain,
zero = join(zero,zero),
inference(demodulation,[status(thm)],[d22,d7]) ).
cnf(d24,plain,
join(X0,zero) = join(zero,join(zero,X0)),
inference(superposition,[status(thm)],[d23,d5]) ).
cnf(d25,plain,
join(X0,composition(X1,one)) = composition(join(X0,X1),one),
inference(superposition,[status(thm)],[c6,c7]) ).
cnf(d26,plain,
join(X1,X0) = composition(join(X1,X0),one),
inference(demodulation,[status(thm)],[d25,c6]) ).
cnf(d27,plain,
join(X0,X1) = join(X0,X1),
inference(demodulation,[status(thm)],[d26,c6]) ).
cnf(d28,plain,
X0 = join(zero,meet(X0,X0)),
inference(superposition,[status(thm)],[d4,d27]) ).
cnf(d29,plain,
join(meet(X0,X0),zero) = join(zero,X0),
inference(superposition,[status(thm)],[d28,d24]) ).
cnf(d30,plain,
join(zero,meet(X0,X0)) = join(zero,X0),
inference(demodulation,[status(thm)],[d29,c1]) ).
cnf(d31,plain,
X0 = join(zero,X0),
inference(demodulation,[status(thm)],[d30,d4]) ).
cnf(d32,plain,
join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[status(thm)],[c2,c1]) ).
cnf(d33,plain,
join(X2,join(X0,X1)) = join(join(X1,X2),X0),
inference(superposition,[status(thm)],[d32,c1]) ).
cnf(d34,plain,
join(zero,join(X0,zero)) = join(zero,X0),
inference(superposition,[status(thm)],[d23,d33]) ).
cnf(d35,plain,
join(X0,zero) = join(zero,X0),
inference(demodulation,[status(thm)],[d34,d31]) ).
cnf(d36,plain,
join(X0,zero) = X0,
inference(demodulation,[status(thm)],[d35,d31]) ).
cnf(d37,plain,
join(converse(X1),X0) = converse(join(X1,converse(X0))),
inference(superposition,[status(thm)],[c8,c9]) ).
cnf(d38,plain,
join(converse(zero),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[d31,d37]) ).
cnf(d39,plain,
join(converse(zero),X0) = X0,
inference(demodulation,[status(thm)],[d38,c8]) ).
cnf(d40,plain,
zero = converse(zero),
inference(superposition,[status(thm)],[d39,d36]) ).
cnf(d41,plain,
composition(join(X0,X2),X1) = join(composition(X2,X1),composition(X0,X1)),
inference(superposition,[status(thm)],[c7,c1]) ).
cnf(d42,plain,
composition(join(X2,X0),X1) = composition(join(X0,X2),X1),
inference(superposition,[status(thm)],[d41,c7]) ).
cnf(d43,plain,
converse(join(X0,X1)) = join(converse(X1),converse(X0)),
inference(superposition,[status(thm)],[c9,c1]) ).
cnf(d44,plain,
converse(join(X0,one)) = join(one,converse(X0)),
inference(superposition,[status(thm)],[d14,d43]) ).
cnf(d45,plain,
zero = composition(converse(X0),complement(composition(X0,top))),
inference(demodulation,[status(thm)],[d18,d31]) ).
cnf(d46,plain,
join(top,X1) = join(X0,join(complement(X0),X1)),
inference(superposition,[status(thm)],[c12,c2]) ).
cnf(d47,plain,
join(join(complement(X0),complement(X1)),meet(X0,X1)) = top,
inference(superposition,[status(thm)],[c4,c12]) ).
cnf(d48,plain,
join(complement(X0),join(complement(X1),meet(X0,X1))) = top,
inference(demodulation,[status(thm)],[d47,c2]) ).
cnf(d49,plain,
X0 = meet(X0,X0),
inference(demodulation,[status(thm)],[d28,d31]) ).
cnf(d50,plain,
join(complement(X0),join(complement(X0),X0)) = top,
inference(superposition,[status(thm)],[d49,d48]) ).
cnf(d51,plain,
join(X0,join(complement(X0),complement(X0))) = top,
inference(demodulation,[status(thm)],[d50,d32]) ).
cnf(d52,plain,
join(top,complement(X0)) = top,
inference(demodulation,[status(thm)],[d51,d46]) ).
cnf(d53,plain,
join(meet(X0,join(complement(X1),meet(X0,X1))),complement(top)) = X0,
inference(superposition,[status(thm)],[d48,d2]) ).
cnf(d54,plain,
join(complement(top),meet(X0,join(complement(X1),meet(X0,X1)))) = X0,
inference(demodulation,[status(thm)],[d53,c1]) ).
cnf(d55,plain,
join(zero,meet(X0,join(complement(X1),meet(X0,X1)))) = X0,
inference(demodulation,[status(thm)],[d54,d7]) ).
cnf(d56,plain,
meet(X0,join(complement(X1),meet(X0,X1))) = X0,
inference(demodulation,[status(thm)],[d55,d31]) ).
cnf(d57,plain,
meet(X0,join(complement(X0),X0)) = X0,
inference(superposition,[status(thm)],[d49,d56]) ).
cnf(d58,plain,
meet(X0,join(X0,complement(X0))) = X0,
inference(demodulation,[status(thm)],[d57,c1]) ).
cnf(d59,plain,
meet(X0,top) = X0,
inference(demodulation,[status(thm)],[d58,c12]) ).
cnf(d60,plain,
complement(join(complement(X0),zero)) = meet(X0,top),
inference(superposition,[status(thm)],[d7,c4]) ).
cnf(d61,plain,
complement(join(zero,complement(X0))) = meet(X0,top),
inference(demodulation,[status(thm)],[d60,c1]) ).
cnf(d62,plain,
complement(complement(X0)) = meet(X0,top),
inference(demodulation,[status(thm)],[d61,d31]) ).
cnf(d63,plain,
complement(complement(X0)) = X0,
inference(demodulation,[status(thm)],[d62,d59]) ).
cnf(d64,plain,
join(top,X0) = top,
inference(superposition,[status(thm)],[d63,d52]) ).
cnf(d65,plain,
join(composition(X1,X0),X0) = composition(join(X1,converse(one)),X0),
inference(superposition,[status(thm)],[d13,c7]) ).
cnf(d66,plain,
join(X1,composition(X0,X1)) = composition(join(X0,converse(one)),X1),
inference(demodulation,[status(thm)],[d65,c1]) ).
cnf(d67,plain,
join(X0,composition(X1,X0)) = composition(join(X1,one),X0),
inference(demodulation,[status(thm)],[d66,d14]) ).
cnf(d68,plain,
composition(join(X0,one),top) = top,
inference(superposition,[status(thm)],[d67,d64]) ).
cnf(d69,plain,
zero = composition(converse(join(X0,one)),complement(top)),
inference(superposition,[status(thm)],[d68,d45]) ).
cnf(d70,plain,
zero = composition(join(one,converse(X0)),complement(top)),
inference(demodulation,[status(thm)],[d69,d44]) ).
cnf(d71,plain,
zero = composition(join(one,converse(X0)),zero),
inference(demodulation,[status(thm)],[d70,d7]) ).
cnf(d72,plain,
zero = composition(join(one,X0),zero),
inference(superposition,[status(thm)],[c8,d71]) ).
cnf(d73,plain,
composition(join(X0,one),zero) = zero,
inference(superposition,[status(thm)],[d72,d42]) ).
cnf(d74,plain,
composition(X0,zero) = composition(join(X0,one),zero),
inference(superposition,[status(thm)],[d67,d31]) ).
cnf(d75,plain,
composition(X0,zero) = zero,
inference(demodulation,[status(thm)],[d74,d73]) ).
cnf(d76,plain,
composition(converse(X0),zero) = converse(composition(zero,X0)),
inference(superposition,[status(thm)],[d40,d8]) ).
cnf(d77,plain,
zero = converse(composition(zero,X0)),
inference(demodulation,[status(thm)],[d76,d75]) ).
cnf(d78,plain,
converse(zero) = composition(zero,X0),
inference(superposition,[status(thm)],[d77,c8]) ).
cnf(d79,plain,
zero = composition(zero,X0),
inference(demodulation,[status(thm)],[d78,d40]) ).
cnf(d80,plain,
composition(zero,sk1) != zero,
inference(resolution,[status(thm)],[d75,c0]) ).
cnf(d81,plain,
zero != zero,
inference(demodulation,[status(thm)],[d80,d79]) ).
cnf(d82,plain,
join(meet(X0,complement(X1)),meet(X0,X1)) = X0,
inference(superposition,[status(thm)],[c4,d2]) ).
cnf(d83,plain,
join(meet(X0,X1),meet(X0,complement(X1))) = X0,
inference(demodulation,[status(thm)],[d82,c1]) ).
cnf(d84,plain,
complement(join(complement(X1),complement(X0))) = meet(X0,X1),
inference(superposition,[status(thm)],[c1,c4]) ).
cnf(d85,plain,
meet(X1,X0) = meet(X0,X1),
inference(superposition,[status(thm)],[d84,c4]) ).
cnf(d86,plain,
X0 = meet(top,X0),
inference(superposition,[status(thm)],[d59,d85]) ).
cnf(d87,plain,
complement(join(zero,complement(X0))) = meet(top,X0),
inference(superposition,[status(thm)],[d7,c4]) ).
cnf(d88,plain,
complement(join(zero,meet(X1,X0))) = meet(top,join(complement(X0),complement(X1))),
inference(superposition,[status(thm)],[d84,d87]) ).
cnf(d89,plain,
complement(meet(X0,X1)) = meet(top,join(complement(X1),complement(X0))),
inference(demodulation,[status(thm)],[d88,d31]) ).
cnf(d90,plain,
complement(meet(X1,X0)) = join(complement(X0),complement(X1)),
inference(demodulation,[status(thm)],[d89,d86]) ).
cnf(d91,plain,
join(meet(X2,join(complement(X0),complement(X1))),meet(X2,meet(X1,X0))) = X2,
inference(superposition,[status(thm)],[d84,d83]) ).
cnf(d92,plain,
join(meet(X0,meet(X2,X1)),meet(X0,join(complement(X1),complement(X2)))) = X0,
inference(demodulation,[status(thm)],[d91,c1]) ).
cnf(d93,plain,
join(meet(X2,meet(X1,X0)),meet(X2,complement(meet(X1,X0)))) = X2,
inference(demodulation,[status(thm)],[d92,d90]) ).
cnf(d94,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d93,d83]) ).
cnf(d95,plain,
$false,
inference(resolution,[status(thm)],[d94,d81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL013-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/5.45 % Computer : n011.cluster.edu
% 0.19/5.45 % Model : x86_64 x86_64
% 0.19/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.45 % Memory : 8046.5625MB
% 0.19/5.45 % OS : Linux 6.8.0-71-generic
% 0.19/5.45 % CPULimit : 300
% 0.19/5.45 % WCLimit : 300
% 0.19/5.45 % DateTime : Sat Sep 26 05:28:04 UTC 2026
% 0.19/5.45 % CPUTime :
% 0.19/5.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 101.02/28.95 % SZS status Unsatisfiable for theBenchmark.p
% 101.02/28.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------