%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : REL023+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 : n009.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 08:24:19 AM UTC 2026
% Result : Theorem 72.98s 14.45s
% Output : CNFRefutation 72.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 9
% Syntax : Number of formulae : 128 ( 128 unt; 0 def)
% Number of atoms : 128 ( 127 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 6 ( 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 : 160 ( 15 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0) ).
fof(maddux2_join_associativity,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2) ).
fof(maddux3_a_kind_of_de_Morgan,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) ).
fof(maddux4_definiton_of_meet,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))) ).
fof(composition_distributivity,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)) ).
fof(converse_cancellativity,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1) ).
fof(def_top,axiom,
! [X0] : top = join(X0,complement(X0)) ).
fof(def_zero,axiom,
! [X0] : zero = meet(X0,complement(X0)) ).
fof(goals,conjecture,
! [X0,X1,X2] : join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) = composition(X0,meet(X1,X2)) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] : join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) = composition(X0,meet(X1,X2)),
inference(negate_conjecture,[status(cth)],[goals]) ).
cnf(c0,plain,
join(X0,X1) = join(X1,X0),
inference(clausification,[status(esa)],[maddux1_join_commutativity]) ).
cnf(c1,plain,
join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(clausification,[status(esa)],[maddux2_join_associativity]) ).
cnf(c2,plain,
X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(clausification,[status(esa)],[maddux3_a_kind_of_de_Morgan]) ).
cnf(c3,plain,
meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(clausification,[status(esa)],[maddux4_definiton_of_meet]) ).
cnf(c6,plain,
composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(clausification,[status(esa)],[composition_distributivity]) ).
cnf(c10,plain,
join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(clausification,[status(esa)],[converse_cancellativity]) ).
cnf(c11,plain,
top = join(X0,complement(X0)),
inference(clausification,[status(esa)],[def_top]) ).
cnf(c12,plain,
zero = meet(X0,complement(X0)),
inference(clausification,[status(esa)],[def_zero]) ).
cnf(c16,plain,
join(composition(meet(sK34,converse(sK35)),meet(sK35,sK36)),composition(sK34,meet(sK35,sK36))) != composition(sK34,meet(sK35,sK36)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(demodulation,[status(thm)],[c2,c0]) ).
cnf(d1,plain,
X0 = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(demodulation,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(demodulation,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
X0 = join(zero,complement(join(complement(X0),complement(X0)))),
inference(superposition,[status(thm)],[c12,d2]) ).
cnf(d4,plain,
X0 = join(zero,meet(X0,X0)),
inference(demodulation,[status(thm)],[d3,c3]) ).
cnf(d5,plain,
join(X2,join(X0,X1)) = join(X0,join(X1,X2)),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d6,plain,
meet(X0,complement(X0)) = complement(top),
inference(superposition,[status(thm)],[c11,c3]) ).
cnf(d7,plain,
zero = complement(top),
inference(demodulation,[status(thm)],[d6,c12]) ).
cnf(d8,plain,
X0 = join(meet(X0,complement(X1)),meet(X0,X1)),
inference(superposition,[status(thm)],[c3,d2]) ).
cnf(d9,plain,
X0 = join(meet(X0,X1),meet(X0,complement(X1))),
inference(demodulation,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
meet(top,X0) = complement(join(zero,complement(X0))),
inference(superposition,[status(thm)],[d7,c3]) ).
cnf(d11,plain,
meet(X0,top) = complement(join(complement(X0),zero)),
inference(superposition,[status(thm)],[d7,c3]) ).
cnf(d12,plain,
meet(X0,top) = complement(join(zero,complement(X0))),
inference(demodulation,[status(thm)],[d11,c0]) ).
cnf(d13,plain,
meet(top,X0) = meet(X0,top),
inference(superposition,[status(thm)],[d12,d10]) ).
cnf(d14,plain,
meet(zero,top) = complement(top),
inference(superposition,[status(thm)],[c11,d12]) ).
cnf(d15,plain,
meet(zero,top) = zero,
inference(demodulation,[status(thm)],[d14,d7]) ).
cnf(d16,plain,
meet(top,zero) = zero,
inference(demodulation,[status(thm)],[d15,d13]) ).
cnf(d17,plain,
top = join(zero,meet(top,complement(zero))),
inference(superposition,[status(thm)],[d16,d9]) ).
cnf(d18,plain,
meet(X0,X1) = complement(join(complement(X1),complement(X0))),
inference(superposition,[status(thm)],[c0,c3]) ).
cnf(d19,plain,
meet(X0,X1) = meet(X1,X0),
inference(superposition,[status(thm)],[d18,c3]) ).
cnf(d20,plain,
X0 = join(meet(X0,top),meet(X0,zero)),
inference(superposition,[status(thm)],[d7,d9]) ).
cnf(d21,plain,
X0 = join(meet(X0,top),meet(zero,X0)),
inference(superposition,[status(thm)],[d19,d20]) ).
cnf(d22,plain,
complement(zero) = join(meet(complement(zero),top),zero),
inference(superposition,[status(thm)],[c12,d21]) ).
cnf(d23,plain,
complement(zero) = join(zero,meet(complement(zero),top)),
inference(demodulation,[status(thm)],[d22,c0]) ).
cnf(d24,plain,
complement(zero) = join(zero,meet(top,complement(zero))),
inference(demodulation,[status(thm)],[d23,d19]) ).
cnf(d25,plain,
complement(zero) = top,
inference(demodulation,[status(thm)],[d24,d17]) ).
cnf(d26,plain,
meet(zero,X0) = complement(join(top,complement(X0))),
inference(superposition,[status(thm)],[d25,c3]) ).
cnf(d27,plain,
join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[status(thm)],[c11,c1]) ).
cnf(d28,plain,
join(X0,top) = join(top,complement(complement(X0))),
inference(superposition,[status(thm)],[c11,d27]) ).
cnf(d29,plain,
meet(zero,complement(X0)) = complement(join(X0,top)),
inference(superposition,[status(thm)],[d28,d26]) ).
cnf(d30,plain,
top = join(top,zero),
inference(superposition,[status(thm)],[d7,c11]) ).
cnf(d31,plain,
join(top,join(zero,X0)) = join(top,X0),
inference(superposition,[status(thm)],[d30,c1]) ).
cnf(d32,plain,
join(top,join(X0,zero)) = join(top,X0),
inference(superposition,[status(thm)],[c0,d31]) ).
cnf(d33,plain,
join(top,X0) = join(top,meet(X0,X0)),
inference(superposition,[status(thm)],[d4,d31]) ).
cnf(d34,plain,
top = join(X0,join(X1,complement(join(X0,X1)))),
inference(superposition,[status(thm)],[c1,c11]) ).
cnf(d35,plain,
join(meet(zero,X0),meet(X0,top)) = X0,
inference(superposition,[status(thm)],[d21,c0]) ).
cnf(d36,plain,
join(zero,meet(complement(zero),top)) = complement(zero),
inference(superposition,[status(thm)],[c12,d35]) ).
cnf(d37,plain,
join(zero,meet(top,complement(zero))) = complement(zero),
inference(demodulation,[status(thm)],[d36,d19]) ).
cnf(d38,plain,
join(zero,meet(top,top)) = complement(zero),
inference(demodulation,[status(thm)],[d37,d25]) ).
cnf(d39,plain,
top = complement(zero),
inference(demodulation,[status(thm)],[d38,d4]) ).
cnf(d40,plain,
meet(zero,zero) = complement(join(top,top)),
inference(superposition,[status(thm)],[d39,d26]) ).
cnf(d41,plain,
top = join(top,join(top,meet(zero,zero))),
inference(superposition,[status(thm)],[d40,d34]) ).
cnf(d42,plain,
top = join(top,join(top,zero)),
inference(demodulation,[status(thm)],[d41,d33]) ).
cnf(d43,plain,
top = join(top,top),
inference(demodulation,[status(thm)],[d42,d32]) ).
cnf(d44,plain,
meet(zero,complement(top)) = complement(top),
inference(superposition,[status(thm)],[d43,d29]) ).
cnf(d45,plain,
meet(zero,zero) = complement(top),
inference(demodulation,[status(thm)],[d44,d7]) ).
cnf(d46,plain,
meet(zero,zero) = zero,
inference(demodulation,[status(thm)],[d45,d7]) ).
cnf(d47,plain,
zero = join(zero,zero),
inference(superposition,[status(thm)],[d46,d4]) ).
cnf(d48,plain,
join(X0,zero) = join(zero,join(zero,X0)),
inference(superposition,[status(thm)],[d47,d5]) ).
cnf(d49,plain,
join(meet(X0,X0),zero) = join(zero,X0),
inference(superposition,[status(thm)],[d4,d48]) ).
cnf(d50,plain,
join(zero,meet(X0,X0)) = join(zero,X0),
inference(demodulation,[status(thm)],[d49,c0]) ).
cnf(d51,plain,
X0 = join(zero,X0),
inference(demodulation,[status(thm)],[d50,d4]) ).
cnf(d52,plain,
meet(top,X0) = complement(complement(X0)),
inference(demodulation,[status(thm)],[d10,d51]) ).
cnf(d53,plain,
X0 = join(zero,meet(X0,complement(complement(X0)))),
inference(superposition,[status(thm)],[c12,d9]) ).
cnf(d54,plain,
X0 = meet(X0,complement(complement(X0))),
inference(demodulation,[status(thm)],[d53,d51]) ).
cnf(d55,plain,
X0 = meet(X0,meet(top,X0)),
inference(demodulation,[status(thm)],[d54,d52]) ).
cnf(d56,plain,
zero = meet(join(zero,complement(X0)),meet(top,X0)),
inference(superposition,[status(thm)],[d10,c12]) ).
cnf(d57,plain,
zero = meet(meet(top,X0),join(zero,complement(X0))),
inference(demodulation,[status(thm)],[d56,d19]) ).
cnf(d58,plain,
meet(top,X0) = join(zero,complement(join(complement(meet(top,X0)),join(zero,complement(X0))))),
inference(superposition,[status(thm)],[d57,d2]) ).
cnf(d59,plain,
meet(top,X0) = complement(join(complement(meet(top,X0)),join(zero,complement(X0)))),
inference(demodulation,[status(thm)],[d58,d51]) ).
cnf(d60,plain,
meet(top,X0) = complement(join(complement(X0),join(complement(meet(top,X0)),zero))),
inference(demodulation,[status(thm)],[d59,d5]) ).
cnf(d61,plain,
meet(top,X0) = complement(join(zero,join(complement(X0),complement(meet(top,X0))))),
inference(demodulation,[status(thm)],[d60,d5]) ).
cnf(d62,plain,
meet(top,X0) = complement(join(complement(X0),complement(meet(top,X0)))),
inference(demodulation,[status(thm)],[d61,d51]) ).
cnf(d63,plain,
meet(top,X0) = meet(X0,meet(top,X0)),
inference(demodulation,[status(thm)],[d62,c3]) ).
cnf(d64,plain,
meet(top,X0) = X0,
inference(demodulation,[status(thm)],[d63,d55]) ).
cnf(d65,plain,
X0 = complement(complement(X0)),
inference(demodulation,[status(thm)],[d52,d64]) ).
cnf(d66,plain,
meet(X0,top) = X0,
inference(superposition,[status(thm)],[d64,d19]) ).
cnf(d67,plain,
meet(join(zero,complement(X0)),top) = complement(join(zero,meet(X0,top))),
inference(superposition,[status(thm)],[d12,d12]) ).
cnf(d68,plain,
meet(top,join(zero,complement(X0))) = complement(join(zero,meet(X0,top))),
inference(demodulation,[status(thm)],[d67,d19]) ).
cnf(d69,plain,
meet(top,complement(X0)) = complement(join(zero,meet(X0,top))),
inference(demodulation,[status(thm)],[d68,d51]) ).
cnf(d70,plain,
meet(top,complement(X0)) = complement(meet(X0,top)),
inference(demodulation,[status(thm)],[d69,d51]) ).
cnf(d71,plain,
complement(X0) = complement(meet(X0,top)),
inference(demodulation,[status(thm)],[d70,d64]) ).
cnf(d72,plain,
complement(X0) = complement(X0),
inference(demodulation,[status(thm)],[d71,d66]) ).
cnf(d73,plain,
complement(complement(X0)) = X0,
inference(superposition,[status(thm)],[d65,d72]) ).
cnf(d74,plain,
meet(complement(X0),X1) = complement(join(complement(X1),X0)),
inference(superposition,[status(thm)],[d65,d18]) ).
cnf(d75,plain,
meet(complement(X1),complement(X0)) = complement(join(X0,X1)),
inference(superposition,[status(thm)],[d65,d74]) ).
cnf(d76,plain,
meet(complement(X0),X1) = complement(join(X0,complement(X1))),
inference(superposition,[status(thm)],[d65,c3]) ).
cnf(d77,plain,
meet(complement(X1),complement(X0)) = complement(join(X1,X0)),
inference(superposition,[status(thm)],[d65,d76]) ).
cnf(d78,plain,
complement(join(X0,X1)) = complement(join(X1,X0)),
inference(superposition,[status(thm)],[d77,d75]) ).
cnf(d79,plain,
top = join(join(complement(X0),complement(X1)),meet(X0,X1)),
inference(superposition,[status(thm)],[c3,c11]) ).
cnf(d80,plain,
top = join(complement(X0),join(complement(X1),meet(X0,X1))),
inference(demodulation,[status(thm)],[d79,c1]) ).
cnf(d81,plain,
X0 = meet(X0,X0),
inference(demodulation,[status(thm)],[d4,d51]) ).
cnf(d82,plain,
top = join(complement(X0),join(complement(X0),X0)),
inference(superposition,[status(thm)],[d81,d80]) ).
cnf(d83,plain,
top = join(X0,join(complement(X0),complement(X0))),
inference(demodulation,[status(thm)],[d82,d5]) ).
cnf(d84,plain,
top = join(top,complement(X0)),
inference(demodulation,[status(thm)],[d83,d27]) ).
cnf(d85,plain,
top = join(top,X0),
inference(superposition,[status(thm)],[d65,d84]) ).
cnf(d86,plain,
X0 = join(meet(X0,join(complement(complement(X0)),X1)),complement(join(top,X1))),
inference(superposition,[status(thm)],[d27,d2]) ).
cnf(d87,plain,
X0 = join(complement(join(top,X1)),meet(X0,join(complement(complement(X0)),X1))),
inference(demodulation,[status(thm)],[d86,c0]) ).
cnf(d88,plain,
X1 = join(complement(top),meet(X1,join(complement(complement(X1)),X0))),
inference(demodulation,[status(thm)],[d87,d85]) ).
cnf(d89,plain,
X0 = join(zero,meet(X0,join(complement(complement(X0)),X1))),
inference(demodulation,[status(thm)],[d88,d7]) ).
cnf(d90,plain,
X0 = meet(X0,join(complement(complement(X0)),X1)),
inference(demodulation,[status(thm)],[d89,d51]) ).
cnf(d91,plain,
X0 = meet(X0,join(X0,X1)),
inference(demodulation,[status(thm)],[d90,d65]) ).
cnf(d92,plain,
join(complement(X0),complement(X1)) = complement(meet(X0,X1)),
inference(superposition,[status(thm)],[c3,d65]) ).
cnf(d93,plain,
complement(X0) = meet(complement(X0),complement(meet(X0,X1))),
inference(superposition,[status(thm)],[d92,d91]) ).
cnf(d94,plain,
complement(X0) = complement(join(meet(X0,X1),X0)),
inference(demodulation,[status(thm)],[d93,d75]) ).
cnf(d95,plain,
complement(X0) = complement(join(X0,meet(X0,X1))),
inference(demodulation,[status(thm)],[d94,d78]) ).
cnf(d96,plain,
complement(complement(X0)) = join(X0,meet(X0,X1)),
inference(superposition,[status(thm)],[d95,d73]) ).
cnf(d97,plain,
X0 = join(X0,meet(X0,X1)),
inference(demodulation,[status(thm)],[d96,d65]) ).
cnf(d98,plain,
join(composition(sK34,meet(sK35,sK36)),composition(meet(sK34,converse(sK35)),meet(sK35,sK36))) != composition(sK34,meet(sK35,sK36)),
inference(demodulation,[status(thm)],[c16,c0]) ).
cnf(d99,plain,
composition(join(sK34,meet(sK34,converse(sK35))),meet(sK35,sK36)) != composition(sK34,meet(sK35,sK36)),
inference(demodulation,[status(thm)],[d98,c6]) ).
cnf(d100,plain,
composition(sK34,meet(sK35,sK36)) != composition(sK34,meet(sK35,sK36)),
inference(demodulation,[status(thm)],[d99,d97]) ).
cnf(d101,plain,
X0 = meet(X0,join(X1,X0)),
inference(superposition,[status(thm)],[c0,d91]) ).
cnf(d102,plain,
join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d103,plain,
X0 = meet(X0,join(X1,join(X2,X0))),
inference(superposition,[status(thm)],[d102,d91]) ).
cnf(d104,plain,
join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))) = complement(X1),
inference(demodulation,[status(thm)],[c10,c0]) ).
cnf(d105,plain,
join(complement(X0),join(composition(converse(X1),complement(composition(X1,X0))),X2)) = join(complement(X0),X2),
inference(superposition,[status(thm)],[d104,c1]) ).
cnf(d106,plain,
X2 = meet(X2,join(complement(X0),X2)),
inference(superposition,[status(thm)],[d105,d103]) ).
cnf(d107,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d106,d101]) ).
cnf(d108,plain,
$false,
inference(resolution,[status(thm)],[d107,d100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL023+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
% 0.12/0.37 % Computer : n009.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 05:31:59 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 72.98/14.45 % SZS status Theorem for theBenchmark.p
% 72.98/14.45 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------