%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL047+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 : Tue Sep 29 12:34:08 PM UTC 2026
% Result : Theorem 15.76s 3.14s
% Output : Refutation 16.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 18
% Syntax : Number of formulae : 155 ( 150 unt; 7 def)
% Number of atoms : 165 ( 164 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 7 ~; 0 |; 8 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 13 con; 0-2 aty)
% Number of variables : 150 ( 144 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity) ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
fof(f4,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence) ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity) ).
fof(f11,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity) ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top) ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero) ).
fof(f14,conjecture,
! [X0,X1,X2] :
( ( join(X0,X1) = X1
& join(X0,X2) = X2 )
=> join(X0,meet(X1,X2)) = meet(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f15,negated_conjecture,
~ ! [X0,X1,X2] :
( ( join(X0,X1) = X1
& join(X0,X2) = X2 )
=> join(X0,meet(X1,X2)) = meet(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
? [X0,X1,X2] :
( meet(X1,X2) != join(X0,meet(X1,X2))
& join(X0,X1) = X1
& join(X0,X2) = X2 ),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
? [X0,X1,X2] :
( meet(X1,X2) != join(X0,meet(X1,X2))
& join(X0,X1) = X1
& join(X0,X2) = X2 ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
( meet(sK1,sK2) != join(sK0,meet(sK1,sK2))
& sK1 = join(sK0,sK1)
& sK2 = join(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f17]) ).
fof(f19,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f20,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f21,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f22,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f24,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f26,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f28,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f29,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f30,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f31,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f32,plain,
sK2 = join(sK0,sK2),
inference(cnf_transformation,[],[f18]) ).
fof(f33,plain,
sK1 = join(sK0,sK1),
inference(cnf_transformation,[],[f18]) ).
fof(f34,plain,
meet(sK1,sK2) != join(sK0,meet(sK1,sK2)),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f31,f22]) ).
fof(f36,plain,
complement(join(complement(sK1),complement(sK2))) != join(sK0,complement(join(complement(sK1),complement(sK2)))),
inference(definition_unfolding,[],[f34,f22,f22]) ).
fof(f37,definition,
sF3 = complement(sK1),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f38,plain,
complement(sK1) = sF3,
inference(reorient_equations,[],[f37]) ).
fof(f39,definition,
sF4 = complement(sK2),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f40,plain,
complement(sK2) = sF4,
inference(reorient_equations,[],[f39]) ).
fof(f41,definition,
sF5 = join(sF3,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f42,plain,
join(sF3,sF4) = sF5,
inference(reorient_equations,[],[f41]) ).
fof(f43,definition,
sF6 = complement(sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f44,plain,
complement(sF5) = sF6,
inference(reorient_equations,[],[f43]) ).
fof(f45,definition,
sF7 = join(sK0,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f46,plain,
join(sK0,sF6) = sF7,
inference(reorient_equations,[],[f45]) ).
fof(f47,plain,
sF6 != sF7,
inference(definition_folding,[],[f36,f46,f44,f42,f40,f38,f44,f42,f40,f38]) ).
fof(f48,definition,
sF8 = join(sK0,sK1),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f49,plain,
join(sK0,sK1) = sF8,
inference(reorient_equations,[],[f48]) ).
fof(f50,plain,
sK1 = sF8,
inference(definition_folding,[],[f33,f49]) ).
fof(f51,definition,
sF9 = join(sK0,sK2),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f52,plain,
join(sK0,sK2) = sF9,
inference(reorient_equations,[],[f51]) ).
fof(f53,plain,
sK2 = sF9,
inference(definition_folding,[],[f32,f52]) ).
fof(f54,plain,
sK1 = join(sK0,sK1),
inference(forward_demodulation,[],[f49,f50]) ).
fof(f55,plain,
sK2 = join(sK0,sK2),
inference(forward_demodulation,[],[f52,f53]) ).
fof(f74,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X1),X0))) = X1,
inference(superposition,[],[f21,f19]) ).
fof(f75,plain,
! [X0,X1] : join(complement(join(complement(X1),complement(X0))),complement(join(X0,complement(X1)))) = X1,
inference(superposition,[],[f21,f19]) ).
fof(f76,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(superposition,[],[f21,f19]) ).
fof(f85,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),complement(X1))),join(complement(join(complement(X0),X1)),X2)),
inference(superposition,[],[f20,f21]) ).
fof(f89,plain,
! [X0] : join(sK0,join(sF6,X0)) = join(sF7,X0),
inference(superposition,[],[f20,f46]) ).
fof(f94,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f19,f20]) ).
fof(f220,plain,
zero = complement(join(sF6,complement(sF6))),
inference(superposition,[],[f35,f44]) ).
fof(f251,plain,
zero = complement(top),
inference(forward_demodulation,[],[f220,f30]) ).
fof(f382,plain,
! [X0,X1] : complement(X1) = join(composition(X0,complement(composition(converse(X0),X1))),complement(X1)),
inference(superposition,[],[f29,f26]) ).
fof(f399,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[],[f28,f26]) ).
fof(f432,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f399,f24]) ).
fof(f444,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f432,f26]) ).
fof(f458,plain,
one = converse(one),
inference(superposition,[],[f24,f444]) ).
fof(f462,plain,
! [X0] : composition(one,X0) = X0,
inference(superposition,[],[f444,f458]) ).
fof(f475,plain,
! [X0] : complement(X0) = join(complement(composition(converse(one),X0)),complement(X0)),
inference(superposition,[],[f382,f462]) ).
fof(f476,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f475,f444]) ).
fof(f492,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = join(X0,complement(join(complement(X0),X1))),
inference(superposition,[],[f85,f476]) ).
fof(f499,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = X0,
inference(forward_demodulation,[],[f492,f21]) ).
fof(f516,plain,
! [X0,X1] : join(X1,complement(join(X0,complement(X1)))) = X1,
inference(superposition,[],[f499,f19]) ).
fof(f518,plain,
! [X0] : join(X0,complement(complement(X0))) = X0,
inference(superposition,[],[f499,f499]) ).
fof(f521,plain,
! [X0] : join(X0,zero) = X0,
inference(superposition,[],[f499,f35]) ).
fof(f525,plain,
! [X2,X0,X1] : join(X1,X0) = join(complement(join(complement(X0),X2)),join(X1,X0)),
inference(superposition,[],[f94,f499]) ).
fof(f564,plain,
! [X0] : join(zero,X0) = X0,
inference(superposition,[],[f19,f521]) ).
fof(f586,plain,
! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),join(complement(join(complement(X0),complement(complement(X0)))),X1)),
inference(superposition,[],[f85,f518]) ).
fof(f598,plain,
! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),join(zero,X1)),
inference(forward_demodulation,[],[f586,f35]) ).
fof(f601,plain,
! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),X1),
inference(forward_demodulation,[],[f598,f564]) ).
fof(f605,plain,
! [X0] : join(sK1,X0) = join(complement(sF3),X0),
inference(superposition,[],[f601,f38]) ).
fof(f606,plain,
! [X0] : join(sK2,X0) = join(complement(sF4),X0),
inference(superposition,[],[f601,f40]) ).
fof(f607,plain,
! [X0] : join(sF5,X0) = join(complement(sF6),X0),
inference(superposition,[],[f601,f44]) ).
fof(f625,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X0,X1))),
inference(superposition,[],[f499,f601]) ).
fof(f634,plain,
! [X0,X1] : join(X0,X1) = join(X1,complement(complement(X0))),
inference(superposition,[],[f19,f601]) ).
fof(f641,plain,
! [X0] : complement(complement(X0)) = join(X0,zero),
inference(superposition,[],[f521,f601]) ).
fof(f642,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[],[f641,f521]) ).
fof(f668,plain,
sK1 = complement(sF3),
inference(superposition,[],[f642,f38]) ).
fof(f669,plain,
sK2 = complement(sF4),
inference(superposition,[],[f642,f40]) ).
fof(f670,plain,
sF5 = complement(sF6),
inference(superposition,[],[f642,f44]) ).
fof(f679,plain,
! [X0,X1] : complement(X0) = join(complement(join(complement(X1),X0)),complement(join(X0,X1))),
inference(superposition,[],[f74,f642]) ).
fof(f688,plain,
! [X0] : join(X0,X0) = X0,
inference(superposition,[],[f476,f642]) ).
fof(f702,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X0,X1)),
inference(superposition,[],[f20,f688]) ).
fof(f802,plain,
! [X0,X1] : complement(X1) = join(complement(X1),complement(join(X0,X1))),
inference(superposition,[],[f625,f19]) ).
fof(f826,plain,
complement(sF3) = join(complement(sF3),complement(sF5)),
inference(superposition,[],[f625,f42]) ).
fof(f859,plain,
complement(sF3) = join(sK1,complement(sF5)),
inference(forward_demodulation,[],[f826,f605]) ).
fof(f877,plain,
complement(sF3) = join(sK1,sF6),
inference(forward_demodulation,[],[f859,f44]) ).
fof(f887,plain,
sK1 = join(sK1,sF6),
inference(forward_demodulation,[],[f877,f668]) ).
fof(f1044,plain,
complement(sF6) = join(complement(sF6),complement(sK1)),
inference(superposition,[],[f802,f887]) ).
fof(f1045,plain,
complement(sF6) = join(sF5,complement(sK1)),
inference(forward_demodulation,[],[f1044,f607]) ).
fof(f1047,plain,
complement(sF6) = join(sF5,sF3),
inference(forward_demodulation,[],[f1045,f38]) ).
fof(f1048,plain,
sF5 = join(sF5,sF3),
inference(forward_demodulation,[],[f1047,f670]) ).
fof(f1457,plain,
! [X0,X1] : complement(X1) = join(complement(join(complement(X0),X1)),complement(join(X0,X1))),
inference(superposition,[],[f679,f19]) ).
fof(f1505,plain,
! [X0,X1] : join(complement(X1),X0) = join(complement(complement(X0)),complement(join(complement(join(complement(X1),X0)),join(X0,X1)))),
inference(superposition,[],[f21,f679]) ).
fof(f1512,plain,
! [X0,X1] : join(X0,X1) = join(complement(join(complement(join(X0,X1)),complement(complement(join(complement(X1),X0))))),complement(complement(X0))),
inference(superposition,[],[f75,f679]) ).
fof(f1523,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(complement(join(X0,X1)),complement(complement(join(complement(X1),X0)))))),
inference(forward_demodulation,[],[f1512,f634]) ).
fof(f1530,plain,
! [X0,X1] : join(complement(X1),X0) = join(X0,complement(join(complement(join(complement(X1),X0)),join(X0,X1)))),
inference(forward_demodulation,[],[f1505,f601]) ).
fof(f1590,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(join(complement(X1),X0),complement(join(X0,X1))))),
inference(forward_demodulation,[],[f1523,f634]) ).
fof(f1595,plain,
! [X0,X1] : join(complement(X1),X0) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f1530,f525]) ).
fof(f1635,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(complement(X1),join(X0,complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f1590,f20]) ).
fof(f1658,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(complement(X1),join(complement(X1),X0)))),
inference(forward_demodulation,[],[f1635,f1595]) ).
fof(f1670,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(complement(X1),X0))),
inference(forward_demodulation,[],[f1658,f702]) ).
fof(f1676,plain,
! [X0,X1] : join(complement(X0),X1) = join(X1,complement(join(X0,X1))),
inference(superposition,[],[f1595,f19]) ).
fof(f1688,plain,
! [X0,X1] : join(complement(complement(join(complement(X0),complement(X1)))),complement(join(complement(X0),X1))) = join(complement(join(complement(X0),X1)),complement(X0)),
inference(superposition,[],[f1595,f76]) ).
fof(f1689,plain,
! [X0,X1] : join(complement(complement(join(complement(X0),X1))),complement(join(complement(X1),complement(X0)))) = join(complement(join(complement(X1),complement(X0))),complement(X0)),
inference(superposition,[],[f1595,f74]) ).
fof(f1710,plain,
join(complement(sF4),sF3) = join(sF3,complement(sF5)),
inference(superposition,[],[f1595,f42]) ).
fof(f1774,plain,
join(complement(sF4),sF3) = join(sF3,sF6),
inference(forward_demodulation,[],[f1710,f44]) ).
fof(f1787,plain,
! [X0,X1] : join(join(complement(X0),X1),complement(join(complement(X1),complement(X0)))) = join(complement(join(complement(X1),complement(X0))),complement(X0)),
inference(forward_demodulation,[],[f1689,f601]) ).
fof(f1788,plain,
! [X0,X1] : join(join(complement(X0),complement(X1)),complement(join(complement(X0),X1))) = join(complement(join(complement(X0),X1)),complement(X0)),
inference(forward_demodulation,[],[f1688,f601]) ).
fof(f1812,plain,
join(sK2,sF3) = join(sF3,sF6),
inference(forward_demodulation,[],[f1774,f606]) ).
fof(f1822,plain,
! [X0,X1] : join(complement(X0),join(X1,complement(join(complement(X1),complement(X0))))) = join(complement(join(complement(X1),complement(X0))),complement(X0)),
inference(forward_demodulation,[],[f1787,f20]) ).
fof(f1823,plain,
! [X0,X1] : join(complement(X0),join(complement(X1),complement(join(complement(X0),X1)))) = join(complement(join(complement(X0),X1)),complement(X0)),
inference(forward_demodulation,[],[f1788,f20]) ).
fof(f1845,plain,
! [X0,X1] : join(complement(X0),X1) = join(complement(join(complement(X1),complement(X0))),complement(X0)),
inference(forward_demodulation,[],[f1822,f499]) ).
fof(f1846,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(join(complement(X0),X1)),complement(X0)),
inference(forward_demodulation,[],[f1823,f802]) ).
fof(f2093,plain,
join(sK2,complement(sK2)) = join(complement(sK0),sK2),
inference(superposition,[],[f1676,f55]) ).
fof(f2170,plain,
top = join(complement(sK0),sK2),
inference(forward_demodulation,[],[f2093,f30]) ).
fof(f2257,plain,
join(complement(sK2),sF3) = join(sF3,complement(join(sF3,sF6))),
inference(superposition,[],[f1676,f1812]) ).
fof(f2258,plain,
join(complement(sK2),sF3) = join(complement(sF6),sF3),
inference(forward_demodulation,[],[f2257,f1595]) ).
fof(f2263,plain,
join(sF5,sF3) = join(complement(sK2),sF3),
inference(forward_demodulation,[],[f2258,f607]) ).
fof(f2267,plain,
join(sF4,sF3) = join(sF5,sF3),
inference(forward_demodulation,[],[f2263,f40]) ).
fof(f2270,plain,
sF5 = join(sF4,sF3),
inference(forward_demodulation,[],[f2267,f1048]) ).
fof(f2304,plain,
join(sK2,sK0) = join(sK2,complement(top)),
inference(superposition,[],[f1670,f2170]) ).
fof(f2323,plain,
join(sK2,sK0) = join(sK2,zero),
inference(forward_demodulation,[],[f2304,f251]) ).
fof(f2334,plain,
sK2 = join(sK2,sK0),
inference(forward_demodulation,[],[f2323,f521]) ).
fof(f2360,plain,
! [X0] : join(X0,sK2) = join(sK0,join(X0,sK2)),
inference(superposition,[],[f94,f2334]) ).
fof(f2605,plain,
complement(sF3) = join(complement(join(complement(sF5),sF3)),complement(sF5)),
inference(superposition,[],[f1457,f1048]) ).
fof(f2660,plain,
complement(sF3) = join(complement(sF5),complement(sF3)),
inference(forward_demodulation,[],[f2605,f1846]) ).
fof(f2747,plain,
sK1 = join(complement(sF5),sK1),
inference(forward_demodulation,[],[f2660,f668]) ).
fof(f2823,plain,
sK1 = join(sF6,sK1),
inference(forward_demodulation,[],[f2747,f44]) ).
fof(f5887,plain,
! [X0,X1] : join(complement(join(X1,complement(complement(X0)))),X0) = join(complement(complement(X0)),complement(join(X1,complement(complement(X0))))),
inference(superposition,[],[f1845,f516]) ).
fof(f5993,plain,
! [X0,X1] : join(complement(X1),complement(complement(X0))) = join(complement(join(X1,complement(complement(X0)))),X0),
inference(forward_demodulation,[],[f5887,f1676]) ).
fof(f6051,plain,
! [X0,X1] : join(complement(X1),complement(complement(X0))) = join(complement(join(X0,X1)),X0),
inference(forward_demodulation,[],[f5993,f634]) ).
fof(f6081,plain,
! [X0,X1] : join(X0,complement(X1)) = join(complement(join(X0,X1)),X0),
inference(forward_demodulation,[],[f6051,f634]) ).
fof(f6458,plain,
join(complement(sF5),sF3) = join(sF3,complement(sF4)),
inference(superposition,[],[f6081,f42]) ).
fof(f6590,plain,
join(complement(sF5),sF3) = join(sF3,sK2),
inference(forward_demodulation,[],[f6458,f669]) ).
fof(f6676,plain,
join(sF3,sK2) = join(sF6,sF3),
inference(forward_demodulation,[],[f6590,f44]) ).
fof(f14827,plain,
join(sK0,sK1) = join(sF7,sK1),
inference(superposition,[],[f89,f2823]) ).
fof(f14829,plain,
join(sK0,join(sF3,sK2)) = join(sF7,sF3),
inference(superposition,[],[f89,f6676]) ).
fof(f14928,plain,
join(sF3,sK2) = join(sF7,sF3),
inference(forward_demodulation,[],[f14829,f2360]) ).
fof(f14930,plain,
sK1 = join(sF7,sK1),
inference(forward_demodulation,[],[f14827,f54]) ).
fof(f15024,plain,
complement(sF7) = join(complement(sF7),complement(sK1)),
inference(superposition,[],[f625,f14930]) ).
fof(f15059,plain,
complement(sF7) = join(complement(sF7),sF3),
inference(forward_demodulation,[],[f15024,f38]) ).
fof(f15160,plain,
join(sF3,complement(join(sF3,sK2))) = join(complement(sF7),sF3),
inference(superposition,[],[f1676,f14928]) ).
fof(f15174,plain,
complement(sF7) = join(sF3,complement(join(sF3,sK2))),
inference(forward_demodulation,[],[f15160,f15059]) ).
fof(f15182,plain,
complement(sF7) = join(complement(sK2),sF3),
inference(forward_demodulation,[],[f15174,f1595]) ).
fof(f15188,plain,
join(sF4,sF3) = complement(sF7),
inference(forward_demodulation,[],[f15182,f40]) ).
fof(f15193,plain,
sF5 = complement(sF7),
inference(forward_demodulation,[],[f15188,f2270]) ).
fof(f15241,plain,
complement(sF5) = sF7,
inference(superposition,[],[f642,f15193]) ).
fof(f15258,plain,
sF6 = sF7,
inference(forward_demodulation,[],[f15241,f44]) ).
fof(f15288,plain,
$false,
inference(forward_subsumption_resolution,[],[f15258,f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL047+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n017.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 22:52:35 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.76/3.14 % (3048820)Detected formulas, will run a generic FOF schedule.
% 15.76/3.14 % (3048871)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=300581794:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 15.76/3.14 % (3048871)Instruction limit reached!
% 15.76/3.14 % (3048871)------------------------------
% 15.76/3.14 % (3048871)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.76/3.14 % (3048871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.76/3.14 % (3048871)CaDiCaL version: 2.1.3
% 15.76/3.14 % (3048871)Termination reason: Instruction limit
% 15.76/3.14 % (3048871)Termination phase: Saturation
% 15.76/3.14 % (3048871)Time elapsed: 0.034 s
% 15.76/3.14 % (3048871)Peak memory usage: 88 MB
% 15.76/3.14 % (3048871)Instructions burned: 120 (million)
% 15.76/3.14 % (3048867)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2156781173:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 15.76/3.14 % (3048868)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2650902280:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 15.76/3.14 % (3048870)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2283290395:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 15.76/3.14 % (3048873)dis-21_1_sil=8000:lcm=predicate:random_seed=2943929027:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 15.76/3.14 % (3048872)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1250470492:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 15.76/3.14 % (3048873)Refutation not found, incomplete strategy
% 15.76/3.14 % (3048873)------------------------------
% 15.76/3.14 % (3048873)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.76/3.14 % (3048873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.76/3.14 % (3048873)CaDiCaL version: 2.1.3
% 15.76/3.14 % (3048873)Termination reason: Refutation not found, incomplete strategy
% 15.76/3.14 % (3048873)Time elapsed: 0.002 s
% 15.76/3.14 % (3048873)Peak memory usage: 88 MB
% 15.76/3.14 % (3048873)Instructions burned: 1 (million)
% 15.76/3.14 % (3048869)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1200364568:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 15.76/3.14 % (3048870)Instruction limit reached!
% 15.76/3.14 % (3048870)------------------------------
% 15.76/3.14 % (3048870)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.76/3.14 % (3048870)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.76/3.14 % (3048870)CaDiCaL version: 2.1.3
% 15.76/3.14 % (3048870)Termination reason: Instruction limit
% 15.76/3.14 % (3048870)Termination phase: Saturation
% 15.76/3.14 % (3048870)Time elapsed: 0.063 s
% 15.76/3.14 % (3048870)Peak memory usage: 88 MB
% 15.76/3.14 % (3048870)Instructions burned: 111 (million)
% 15.76/3.14 % (3048872)Instruction limit reached!
% 15.76/3.14 % (3048872)------------------------------
% 15.76/3.14 % (3048872)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.76/3.14 % (3048872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.76/3.14 % (3048872)CaDiCaL version: 2.1.3
% 15.76/3.14 % (3048872)Termination reason: Instruction limit
% 15.76/3.14 % (3048872)Termination phase: Saturation
% 15.76/3.14 % (3048872)Time elapsed: 0.083 s
% 15.76/3.14 % (3048872)Peak memory usage: 89 MB
% 15.76/3.14 % (3048872)Instructions burned: 139 (million)
% 15.76/3.14 % (3048875)lrs+10_1_sil=8000:sp=occurrence:random_seed=2757849925:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 15.76/3.14 % (3048875)Instruction limit reached!
% 15.76/3.14 % (3048875)------------------------------
% 15.76/3.14 % (3048875)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.76/3.14 % (3048875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.76/3.14 % (3048875)CaDiCaL version: 2.1.3
% 15.76/3.14 % (3048875)Termination reason: Instruction limit
% 15.76/3.14 % (3048875)Termination phase: Saturation
% 15.76/3.14 % (3048875)Time elapsed: 0.095 s
% 15.76/3.14 % (3048875)Peak memory usage: 91 MB
% 15.76/3.14 % (3048875)Instructions burned: 288 (million)
% 15.76/3.14 % (3048882)lrs+10_1_sil=32000:urr=on:br=off:random_seed=998314364:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 15.76/3.14 % (3048873)------------------------------
% 15.76/3.14 % (3048873)------------------------------
% 15.76/3.14 % (3048883)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1484667277:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 15.76/3.14 % (3048882)Instruction limit reached!
% 15.76/3.14 % (3048882)------------------------------
% 15.76/3.14 % (3048882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.76/3.14 % (3048882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.76/3.14 % (3048882)CaDiCaL version: 2.1.3
% 15.76/3.14 % (3048882)Termination reason: Instruction limit
% 15.76/3.14 % (3048882)Termination phase: Saturation
% 15.76/3.14 % (3048882)Time elapsed: 0.082 s
% 15.76/3.14 % (3048882)Peak memory usage: 89 MB
% 15.76/3.14 % (3048882)Instructions burned: 159 (million)
% 15.76/3.14 % (3048885)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1378917408:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 15.76/3.14 % (3048885)Instruction limit reached!
% 15.76/3.14 % (3048885)------------------------------
% 15.76/3.14 % (3048885)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.76/3.14 % (3048885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.76/3.14 % (3048885)CaDiCaL version: 2.1.3
% 15.76/3.14 % (3048885)Termination reason: Instruction limit
% 15.76/3.14 % (3048885)Termination phase: Saturation
% 15.76/3.14 % (3048885)Time elapsed: 0.082 s
% 15.76/3.14 % (3048885)Peak memory usage: 91 MB
% 15.76/3.14 % (3048885)Instructions burned: 248 (million)
% 15.76/3.14 % (3048888)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=719605176:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 15.76/3.14 % (3048883)Instruction limit reached!
% 15.76/3.14 % (3048883)------------------------------
% 15.76/3.14 % (3048883)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.76/3.14 % (3048883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.76/3.14 % (3048883)CaDiCaL version: 2.1.3
% 15.76/3.14 % (3048883)Termination reason: Instruction limit
% 15.76/3.14 % (3048883)Termination phase: Saturation
% 15.76/3.14 % (3048883)Time elapsed: 0.233 s
% 15.76/3.14 % (3048883)Peak memory usage: 92 MB
% 15.76/3.14 % (3048883)Instructions burned: 325 (million)
% 15.76/3.14 % (3048889)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=347158473:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 15.76/3.14 % (3048899)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1241393181:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 15.76/3.14 % (3048899)Instruction limit reached!
% 15.76/3.14 % (3048899)------------------------------
% 15.76/3.14 % (3048899)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.76/3.14 % (3048899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.76/3.14 % (3048899)CaDiCaL version: 2.1.3
% 15.76/3.14 % (3048899)Termination reason: Instruction limit
% 15.76/3.14 % (3048899)Termination phase: Saturation
% 15.76/3.14 % (3048899)Time elapsed: 0.038 s
% 15.76/3.14 % (3048899)Peak memory usage: 89 MB
% 15.76/3.14 % (3048899)Instructions burned: 116 (million)
% 15.76/3.14 % (3048888)Instruction limit reached!
% 15.76/3.14 % (3048888)------------------------------
% 15.76/3.14 % (3048888)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.76/3.14 % (3048888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.76/3.14 % (3048888)CaDiCaL version: 2.1.3
% 15.76/3.14 % (3048888)Termination reason: Instruction limit
% 15.76/3.14 % (3048888)Termination phase: Saturation
% 15.76/3.14 % (3048888)Time elapsed: 0.266 s
% 15.76/3.14 % (3048888)Peak memory usage: 89 MB
% 15.76/3.14 % (3048888)Instructions burned: 294 (million)
% 15.76/3.14 % (3048902)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=782491360:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 15.76/3.14 % (3048902)Refutation not found, incomplete strategy
% 15.76/3.14 % (3048902)------------------------------
% 15.76/3.14 % (3048902)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.76/3.14 % (3048902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.76/3.14 % (3048902)CaDiCaL version: 2.1.3
% 15.76/3.14 % (3048902)Termination reason: Refutation not found, incomplete strategy
% 15.76/3.14 % (3048902)Time elapsed: 0.002 s
% 15.76/3.14 % (3048902)Peak memory usage: 88 MB
% 15.76/3.14 % (3048913)lrs+10_1_sil=8000:sp=occurrence:random_seed=2500486459:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 15.76/3.14 % (3048912)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2479386321:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 15.76/3.14 % (3048912)Instruction limit reached!
% 15.76/3.14 % (3048912)------------------------------
% 15.76/3.14 % (3048912)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.76/3.14 % (3048912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.76/3.14 % (3048912)CaDiCaL version: 2.1.3
% 15.76/3.14 % (3048912)Termination reason: Instruction limit
% 15.76/3.14 % (3048912)Termination phase: Saturation
% 15.76/3.14 % (3048912)Time elapsed: 0.112 s
% 15.76/3.14 % (3048912)Peak memory usage: 88 MB
% 15.76/3.14 % (3048912)Instructions burned: 114 (million)
% 15.76/3.14 % (3048902)------------------------------
% 15.76/3.14 % (3048902)------------------------------
% 15.76/3.14 % (3048922)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2547559473:i=437:sd=1:aac=none:ss=included_2988 on theBenchmark for (2988ds/437Mi)
% 15.76/3.14 % (3048913)Instruction limit reached!
% 15.76/3.14 % (3048913)------------------------------
% 15.76/3.14 % (3048913)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.76/3.14 % (3048913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.76/3.14 % (3048913)CaDiCaL version: 2.1.3
% 15.76/3.14 % (3048913)Termination reason: Instruction limit
% 15.76/3.14 % (3048913)Termination phase: Saturation
% 15.76/3.14 % (3048913)Time elapsed: 0.469 s
% 15.76/3.14 % (3048913)Peak memory usage: 96 MB
% 15.76/3.14 % (3048913)Instructions burned: 909 (million)
% 15.76/3.14 % (3048924)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3017835964:i=5202:ss=axioms:sgt=16_2986 on theBenchmark for (2986ds/5202Mi)
% 15.76/3.14 % (3048926)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=3434104760:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2984 on theBenchmark for (2984ds/134Mi)
% 15.76/3.14 % (3048926)Refutation not found, incomplete strategy
% 15.76/3.14 % (3048926)------------------------------
% 15.76/3.14 % (3048926)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.76/3.14 % (3048926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.76/3.14 % (3048926)CaDiCaL version: 2.1.3
% 15.76/3.14 % (3048926)Termination reason: Refutation not found, incomplete strategy
% 15.76/3.14 % (3048926)Time elapsed: 0.001 s
% 15.76/3.14 % (3048926)Peak memory usage: 89 MB
% 15.76/3.14 % (3048867)First to succeed.
% 15.76/3.14 % (3048867)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3048820"
% 15.76/3.14 % (3048922)Instruction limit reached!
% 15.76/3.14 % (3048922)------------------------------
% 15.76/3.14 % (3048922)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.76/3.14 % (3048922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.76/3.14 % (3048922)CaDiCaL version: 2.1.3
% 15.76/3.14 % (3048922)Termination reason: Instruction limit
% 15.76/3.14 % (3048922)Termination phase: Saturation
% 15.76/3.14 % (3048922)Time elapsed: 0.366 s
% 15.76/3.14 % (3048922)Peak memory usage: 93 MB
% 15.76/3.14 % (3048922)Instructions burned: 437 (million)
% 15.76/3.14 % (3048926)------------------------------
% 15.76/3.14 % (3048926)------------------------------
% 15.76/3.14 % (3048931)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=86153746:st=8:i=592:sd=3:ep=RST:ss=axioms_2981 on theBenchmark for (2981ds/592Mi)
% 15.76/3.14 % (3048934)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=3651043549:st=3:i=13193:sd=3:ss=axioms_2980 on theBenchmark for (2980ds/13193Mi)
% 15.76/3.14 % (3048867)Refutation found. Thanks to Tanya!
% 15.76/3.14 % SZS status Theorem for theBenchmark
% 15.76/3.14 % SZS output start Proof for theBenchmark
% See solution above
% 16.59/3.40 % (3048867)------------------------------
% 16.59/3.40 % (3048867)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.59/3.40 % (3048867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.59/3.40 % (3048867)CaDiCaL version: 2.1.3
% 16.59/3.40 % (3048867)Termination reason: Refutation
% 16.59/3.40 % (3048867)Time elapsed: 1.638 s
% 16.59/3.40 % (3048867)Peak memory usage: 134 MB
% 16.59/3.40 % (3048867)Instructions burned: 1790 (million)
% 16.59/3.40 % (3048867)------------------------------
% 16.59/3.40 % (3048867)------------------------------
% 16.59/3.40 % (3048820)Success in time 2.285 s
% 16.59/3.40 % Vampire exiting
%------------------------------------------------------------------------------