%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : REL011-2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/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 106.31s 20.60s
% Output : CNFRefutation 106.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 16
% Syntax : Number of clauses : 117 ( 117 unt; 0 nHn; 28 RR)
% Number of literals : 117 ( 116 equ; 3 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 : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 136 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(goals_17,negated_conjecture,
meet(sk1,composition(converse(sk2),sk3)) = zero ).
cnf(goals_18,negated_conjecture,
meet(composition(sk2,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(sk1,composition(converse(sk2),sk3)) = zero,
inference(clausification,[status(esa)],[goals_17]) ).
cnf(c1,plain,
meet(composition(sk2,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(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(c15,plain,
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))),
inference(clausification,[status(esa)],[dedekind_law_14]) ).
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(X0,join(X1,complement(join(X0,X1)))),
inference(superposition,[status(thm)],[c3,c13]) ).
cnf(d8,plain,
top = join(X0,join(complement(X0),complement(top))),
inference(superposition,[status(thm)],[c13,d7]) ).
cnf(d9,plain,
top = join(X0,join(complement(X0),zero)),
inference(demodulation,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
top = join(X0,join(zero,complement(X0))),
inference(demodulation,[status(thm)],[d9,c2]) ).
cnf(d11,plain,
meet(X0,top) = complement(join(complement(X0),zero)),
inference(superposition,[status(thm)],[d6,c5]) ).
cnf(d12,plain,
meet(X0,top) = complement(join(zero,complement(X0))),
inference(demodulation,[status(thm)],[d11,c2]) ).
cnf(d13,plain,
meet(top,X0) = complement(join(zero,complement(X0))),
inference(superposition,[status(thm)],[d6,c5]) ).
cnf(d14,plain,
meet(X0,top) = meet(top,X0),
inference(superposition,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
zero = meet(top,zero),
inference(superposition,[status(thm)],[d6,c14]) ).
cnf(d16,plain,
zero = meet(zero,top),
inference(demodulation,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
zero = join(zero,complement(join(complement(zero),top))),
inference(superposition,[status(thm)],[d16,d2]) ).
cnf(d18,plain,
zero = join(zero,complement(join(top,complement(zero)))),
inference(demodulation,[status(thm)],[d17,c2]) ).
cnf(d19,plain,
top = join(join(top,complement(zero)),zero),
inference(superposition,[status(thm)],[d18,d10]) ).
cnf(d20,plain,
top = join(top,join(complement(zero),zero)),
inference(demodulation,[status(thm)],[d19,c3]) ).
cnf(d21,plain,
top = join(top,join(zero,complement(zero))),
inference(demodulation,[status(thm)],[d20,c2]) ).
cnf(d22,plain,
top = join(top,top),
inference(demodulation,[status(thm)],[d21,c13]) ).
cnf(d23,plain,
top = join(top,zero),
inference(superposition,[status(thm)],[d6,c13]) ).
cnf(d24,plain,
top = join(zero,top),
inference(demodulation,[status(thm)],[d23,c2]) ).
cnf(d25,plain,
join(zero,join(top,X0)) = join(top,X0),
inference(superposition,[status(thm)],[d24,c3]) ).
cnf(d26,plain,
join(zero,join(X0,top)) = join(top,X0),
inference(superposition,[status(thm)],[c2,d25]) ).
cnf(d27,plain,
join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[status(thm)],[c13,c3]) ).
cnf(d28,plain,
join(top,top) = join(top,complement(zero)),
inference(superposition,[status(thm)],[d27,d26]) ).
cnf(d29,plain,
top = join(top,complement(zero)),
inference(demodulation,[status(thm)],[d28,d22]) ).
cnf(d30,plain,
zero = join(zero,complement(top)),
inference(demodulation,[status(thm)],[d18,d29]) ).
cnf(d31,plain,
zero = join(zero,zero),
inference(demodulation,[status(thm)],[d30,d6]) ).
cnf(d32,plain,
join(zero,join(zero,X0)) = join(zero,X0),
inference(superposition,[status(thm)],[d31,c3]) ).
cnf(d33,plain,
join(zero,X0) = join(zero,meet(X0,X0)),
inference(superposition,[status(thm)],[d4,d32]) ).
cnf(d34,plain,
join(zero,X0) = X0,
inference(demodulation,[status(thm)],[d33,d4]) ).
cnf(d35,plain,
join(zero,join(X0,zero)) = join(zero,X0),
inference(superposition,[status(thm)],[c2,d32]) ).
cnf(d36,plain,
join(X0,zero) = join(zero,X0),
inference(demodulation,[status(thm)],[d35,d34]) ).
cnf(d37,plain,
join(X0,zero) = X0,
inference(demodulation,[status(thm)],[d36,d34]) ).
cnf(d38,plain,
converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c9,c11]) ).
cnf(d39,plain,
composition(X0,composition(X1,one)) = composition(X0,X1),
inference(superposition,[status(thm)],[c6,c7]) ).
cnf(d40,plain,
composition(X1,X0) = composition(X1,X0),
inference(demodulation,[status(thm)],[d39,c7]) ).
cnf(d41,plain,
X0 = composition(X0,one),
inference(superposition,[status(thm)],[c7,d40]) ).
cnf(d42,plain,
converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[status(thm)],[d41,d38]) ).
cnf(d43,plain,
X0 = composition(converse(one),X0),
inference(demodulation,[status(thm)],[d42,c9]) ).
cnf(d44,plain,
one = converse(one),
inference(superposition,[status(thm)],[d43,c7]) ).
cnf(d45,plain,
converse(join(X0,one)) = join(converse(X0),one),
inference(superposition,[status(thm)],[d44,c10]) ).
cnf(d46,plain,
converse(join(X0,one)) = join(one,converse(X0)),
inference(demodulation,[status(thm)],[d45,c2]) ).
cnf(d47,plain,
join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))) = complement(X1),
inference(demodulation,[status(thm)],[c12,c2]) ).
cnf(d48,plain,
join(zero,composition(converse(X0),complement(composition(X0,top)))) = complement(top),
inference(superposition,[status(thm)],[d6,d47]) ).
cnf(d49,plain,
composition(converse(X0),complement(composition(X0,top))) = complement(top),
inference(demodulation,[status(thm)],[d48,d34]) ).
cnf(d50,plain,
composition(converse(X0),complement(composition(X0,top))) = zero,
inference(demodulation,[status(thm)],[d49,d6]) ).
cnf(d51,plain,
join(X0,join(X1,complement(join(X0,X1)))) = top,
inference(superposition,[status(thm)],[c13,c3]) ).
cnf(d52,plain,
join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[status(thm)],[c3,c2]) ).
cnf(d53,plain,
top = join(join(complement(X0),complement(X1)),meet(X0,X1)),
inference(superposition,[status(thm)],[c5,c13]) ).
cnf(d54,plain,
top = join(complement(X0),join(complement(X1),meet(X0,X1))),
inference(demodulation,[status(thm)],[d53,c3]) ).
cnf(d55,plain,
X0 = meet(X0,X0),
inference(demodulation,[status(thm)],[d4,d34]) ).
cnf(d56,plain,
top = join(complement(X0),join(complement(X0),X0)),
inference(superposition,[status(thm)],[d55,d54]) ).
cnf(d57,plain,
top = join(X0,join(complement(X0),complement(X0))),
inference(demodulation,[status(thm)],[d56,d52]) ).
cnf(d58,plain,
top = join(top,complement(X0)),
inference(demodulation,[status(thm)],[d57,d27]) ).
cnf(d59,plain,
join(X0,top) = top,
inference(superposition,[status(thm)],[d58,d51]) ).
cnf(d60,plain,
join(top,X0) = top,
inference(superposition,[status(thm)],[d59,c2]) ).
cnf(d61,plain,
composition(join(X1,converse(one)),X0) = join(composition(X1,X0),X0),
inference(superposition,[status(thm)],[d43,c8]) ).
cnf(d62,plain,
composition(join(X0,one),X1) = join(composition(X0,X1),X1),
inference(demodulation,[status(thm)],[d61,d44]) ).
cnf(d63,plain,
composition(join(X0,one),X1) = join(X1,composition(X0,X1)),
inference(demodulation,[status(thm)],[d62,c2]) ).
cnf(d64,plain,
composition(join(X0,one),top) = top,
inference(superposition,[status(thm)],[d63,d60]) ).
cnf(d65,plain,
composition(converse(join(X0,one)),complement(top)) = zero,
inference(superposition,[status(thm)],[d64,d50]) ).
cnf(d66,plain,
composition(join(one,converse(X0)),complement(top)) = zero,
inference(demodulation,[status(thm)],[d65,d46]) ).
cnf(d67,plain,
composition(join(one,converse(X0)),zero) = zero,
inference(demodulation,[status(thm)],[d66,d6]) ).
cnf(d68,plain,
converse(X0) = composition(converse(X0),one),
inference(superposition,[status(thm)],[d43,d38]) ).
cnf(d69,plain,
converse(X0) = converse(X0),
inference(demodulation,[status(thm)],[d68,c7]) ).
cnf(d70,plain,
X0 = converse(converse(X0)),
inference(superposition,[status(thm)],[c9,d69]) ).
cnf(d71,plain,
composition(join(one,X0),zero) = zero,
inference(superposition,[status(thm)],[d70,d67]) ).
cnf(d72,plain,
composition(join(X0,one),zero) = zero,
inference(superposition,[status(thm)],[c2,d71]) ).
cnf(d73,plain,
composition(join(X0,one),zero) = composition(X0,zero),
inference(superposition,[status(thm)],[d63,d34]) ).
cnf(d74,plain,
zero = composition(X0,zero),
inference(demodulation,[status(thm)],[d73,d72]) ).
cnf(d75,plain,
meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(superposition,[status(thm)],[c2,c5]) ).
cnf(d76,plain,
meet(X0,X1) = meet(X1,X0),
inference(superposition,[status(thm)],[d75,c5]) ).
cnf(d77,plain,
join(meet(composition(sk2,sk1),sk3),composition(meet(sk2,composition(sk3,converse(sk1))),zero)) = composition(meet(sk2,composition(sk3,converse(sk1))),meet(sk1,composition(converse(sk2),sk3))),
inference(superposition,[status(thm)],[c0,c15]) ).
cnf(d78,plain,
join(meet(sk3,composition(sk2,sk1)),composition(meet(sk2,composition(sk3,converse(sk1))),zero)) = composition(meet(sk2,composition(sk3,converse(sk1))),meet(sk1,composition(converse(sk2),sk3))),
inference(demodulation,[status(thm)],[d77,d76]) ).
cnf(d79,plain,
join(meet(sk3,composition(sk2,sk1)),composition(meet(sk2,composition(sk3,converse(sk1))),zero)) = composition(meet(sk2,composition(sk3,converse(sk1))),zero),
inference(demodulation,[status(thm)],[d78,c0]) ).
cnf(d80,plain,
join(meet(sk3,composition(sk2,sk1)),zero) = composition(meet(sk2,composition(sk3,converse(sk1))),zero),
inference(demodulation,[status(thm)],[d79,d74]) ).
cnf(d81,plain,
join(meet(sk3,composition(sk2,sk1)),zero) = zero,
inference(demodulation,[status(thm)],[d80,d74]) ).
cnf(d82,plain,
meet(sk3,composition(sk2,sk1)) = zero,
inference(demodulation,[status(thm)],[d81,d37]) ).
cnf(d83,plain,
meet(sk3,composition(sk2,sk1)) != zero,
inference(demodulation,[status(thm)],[c1,d76]) ).
cnf(d84,plain,
$false,
inference(resolution,[status(thm)],[d83,d82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : REL011-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.39 % Computer : n011.cluster.edu
% 0.07/0.39 % Model : x86_64 x86_64
% 0.07/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.39 % Memory : 8046.5625MB
% 0.07/0.39 % OS : Linux 6.8.0-71-generic
% 0.07/0.39 % CPULimit : 300
% 0.07/0.39 % WCLimit : 300
% 0.07/0.39 % DateTime : Sat Sep 26 05:28:13 UTC 2026
% 0.07/0.40 % CPUTime :
% 0.07/0.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 106.31/20.60 % SZS status Unsatisfiable for theBenchmark.p
% 106.31/20.60 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------