%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL016-4 : 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 : n008.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 12:33:45 PM UTC 2026
% Result : Unsatisfiable 9.04s 2.35s
% Output : Refutation 10.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 32
% Syntax : Number of formulae : 161 ( 146 unt; 20 def)
% Number of atoms : 178 ( 155 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 20 ~; 15 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 23 con; 0-2 aty)
% Number of variables : 136 ( 0 sgn 136 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
fof(f2,axiom,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
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_3) ).
fof(f4,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
fof(f6,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(reorient_equations,[],[f5]) ).
fof(f8,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity_6) ).
fof(f9,axiom,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity_7) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f11,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity_9) ).
fof(f12,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
fof(f13,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity_11) ).
fof(f14,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(reorient_equations,[],[f13]) ).
fof(f16,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero_13) ).
fof(f23,negated_conjecture,
( join(meet(composition(sk1,sk2),complement(composition(sk1,sk3))),meet(composition(sk1,meet(sk2,complement(sk3))),complement(composition(sk1,sk3)))) != meet(composition(sk1,meet(sk2,complement(sk3))),complement(composition(sk1,sk3)))
| join(meet(composition(sk1,meet(sk2,complement(sk3))),complement(composition(sk1,sk3))),meet(composition(sk1,sk2),complement(composition(sk1,sk3)))) != meet(composition(sk1,sk2),complement(composition(sk1,sk3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_17) ).
fof(f24,plain,
( meet(composition(sk1,meet(sk2,complement(sk3))),complement(composition(sk1,sk3))) != join(meet(composition(sk1,sk2),complement(composition(sk1,sk3))),meet(composition(sk1,meet(sk2,complement(sk3))),complement(composition(sk1,sk3))))
| meet(composition(sk1,sk2),complement(composition(sk1,sk3))) != join(meet(composition(sk1,meet(sk2,complement(sk3))),complement(composition(sk1,sk3))),meet(composition(sk1,sk2),complement(composition(sk1,sk3)))) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f29,plain,
( complement(join(complement(composition(sk1,complement(join(complement(sk2),complement(complement(sk3)))))),complement(complement(composition(sk1,sk3))))) != join(complement(join(complement(composition(sk1,sk2)),complement(complement(composition(sk1,sk3))))),complement(join(complement(composition(sk1,complement(join(complement(sk2),complement(complement(sk3)))))),complement(complement(composition(sk1,sk3))))))
| complement(join(complement(composition(sk1,sk2)),complement(complement(composition(sk1,sk3))))) != join(complement(join(complement(composition(sk1,complement(join(complement(sk2),complement(complement(sk3)))))),complement(complement(composition(sk1,sk3))))),complement(join(complement(composition(sk1,sk2)),complement(complement(composition(sk1,sk3)))))) ),
inference(definition_unfolding,[],[f24,f6,f6,f6,f6,f6,f6,f6,f6,f6]) ).
fof(f30,definition,
sF0 = complement(sk2),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f31,plain,
complement(sk2) = sF0,
inference(reorient_equations,[],[f30]) ).
fof(f32,definition,
sF1 = complement(sk3),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f33,plain,
complement(sk3) = sF1,
inference(reorient_equations,[],[f32]) ).
fof(f34,definition,
sF2 = complement(sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f35,plain,
complement(sF1) = sF2,
inference(reorient_equations,[],[f34]) ).
fof(f36,definition,
sF3 = join(sF0,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f37,plain,
join(sF0,sF2) = sF3,
inference(reorient_equations,[],[f36]) ).
fof(f38,definition,
sF4 = complement(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f39,plain,
complement(sF3) = sF4,
inference(reorient_equations,[],[f38]) ).
fof(f40,definition,
sF5 = composition(sk1,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f41,plain,
composition(sk1,sF4) = sF5,
inference(reorient_equations,[],[f40]) ).
fof(f42,definition,
sF6 = complement(sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f43,plain,
complement(sF5) = sF6,
inference(reorient_equations,[],[f42]) ).
fof(f44,definition,
sF7 = composition(sk1,sk3),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f45,plain,
composition(sk1,sk3) = sF7,
inference(reorient_equations,[],[f44]) ).
fof(f46,definition,
sF8 = complement(sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f47,plain,
complement(sF7) = sF8,
inference(reorient_equations,[],[f46]) ).
fof(f48,definition,
sF9 = complement(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f49,plain,
complement(sF8) = sF9,
inference(reorient_equations,[],[f48]) ).
fof(f50,definition,
sF10 = join(sF6,sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f51,plain,
join(sF6,sF9) = sF10,
inference(reorient_equations,[],[f50]) ).
fof(f52,definition,
sF11 = complement(sF10),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f53,plain,
complement(sF10) = sF11,
inference(reorient_equations,[],[f52]) ).
fof(f54,definition,
sF12 = composition(sk1,sk2),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f55,plain,
composition(sk1,sk2) = sF12,
inference(reorient_equations,[],[f54]) ).
fof(f56,definition,
sF13 = complement(sF12),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f57,plain,
complement(sF12) = sF13,
inference(reorient_equations,[],[f56]) ).
fof(f58,definition,
sF14 = join(sF13,sF9),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f59,plain,
join(sF13,sF9) = sF14,
inference(reorient_equations,[],[f58]) ).
fof(f60,definition,
sF15 = complement(sF14),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f61,plain,
complement(sF14) = sF15,
inference(reorient_equations,[],[f60]) ).
fof(f62,definition,
sF16 = join(sF15,sF11),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f63,plain,
join(sF15,sF11) = sF16,
inference(reorient_equations,[],[f62]) ).
fof(f64,definition,
sF17 = join(sF11,sF15),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f65,plain,
join(sF11,sF15) = sF17,
inference(reorient_equations,[],[f64]) ).
fof(f66,plain,
( sF11 != sF16
| sF15 != sF17 ),
inference(definition_folding,[],[f29,f65,f61,f59,f49,f47,f45,f57,f55,f53,f51,f49,f47,f45,f43,f41,f39,f37,f35,f33,f31,f61,f59,f49,f47,f45,f57,f55,f63,f53,f51,f49,f47,f45,f43,f41,f39,f37,f35,f33,f31,f61,f59,f49,f47,f45,f57,f55,f53,f51,f49,f47,f45,f43,f41,f39,f37,f35,f33,f31]) ).
fof(f68,definition,
( spl18_1
<=> sF15 = sF17 ),
introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition]) ).
fof(f70,plain,
( sF15 != sF17
| spl18_1 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f72,definition,
( spl18_2
<=> sF11 = sF16 ),
introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition]) ).
fof(f73,plain,
( sF11 = sF16
| ~ spl18_2 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f75,plain,
( ~ spl18_1
| ~ spl18_2 ),
inference(avatar_split_clause,[],[f66,f72,f68]) ).
fof(f126,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[],[f12,f10]) ).
fof(f128,plain,
! [X2,X0,X1] : composition(join(converse(X1),X2),converse(X0)) = join(converse(composition(X0,X1)),composition(X2,converse(X0))),
inference(superposition,[],[f9,f12]) ).
fof(f154,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X1),X0))) = X1,
inference(superposition,[],[f4,f1]) ).
fof(f155,plain,
! [X0,X1] : join(complement(join(complement(X1),complement(X0))),complement(join(X0,complement(X1)))) = X1,
inference(superposition,[],[f4,f1]) ).
fof(f156,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(superposition,[],[f4,f1]) ).
fof(f160,plain,
sF10 = join(sF9,sF6),
inference(superposition,[],[f51,f1]) ).
fof(f161,plain,
sF14 = join(sF9,sF13),
inference(superposition,[],[f59,f1]) ).
fof(f162,plain,
sF16 = join(sF11,sF15),
inference(superposition,[],[f63,f1]) ).
fof(f163,plain,
sF16 = sF17,
inference(forward_demodulation,[],[f162,f65]) ).
fof(f175,plain,
( sF15 != sF16
| spl18_1 ),
inference(superposition,[],[f70,f163]) ).
fof(f181,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f128,f12]) ).
fof(f190,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f181,f11]) ).
fof(f193,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f190,f11]) ).
fof(f195,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f193,f12]) ).
fof(f208,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f10,f195]) ).
fof(f219,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f208,f10]) ).
fof(f233,plain,
! [X0] : composition(sk1,join(sk2,X0)) = join(sF12,composition(sk1,X0)),
inference(superposition,[],[f219,f55]) ).
fof(f239,plain,
! [X0] : composition(sk1,join(X0,sF4)) = join(composition(sk1,X0),sF5),
inference(superposition,[],[f219,f41]) ).
fof(f368,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),complement(X1))),join(complement(join(complement(X0),X1)),X2)),
inference(superposition,[],[f2,f4]) ).
fof(f384,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f555,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f126,f8]) ).
fof(f569,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f555,f10]) ).
fof(f591,plain,
one = converse(one),
inference(superposition,[],[f8,f569]) ).
fof(f606,plain,
! [X0] : composition(one,X0) = X0,
inference(superposition,[],[f569,f591]) ).
fof(f622,plain,
! [X0] : complement(X0) = join(composition(converse(one),complement(X0)),complement(X0)),
inference(superposition,[],[f14,f606]) ).
fof(f635,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f622,f569]) ).
fof(f647,plain,
sF11 = join(sF11,sF11),
inference(superposition,[],[f635,f53]) ).
fof(f659,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = join(X0,complement(join(complement(X0),X1))),
inference(superposition,[],[f368,f635]) ).
fof(f661,plain,
! [X0,X1] : join(complement(X0),X1) = join(complement(X0),join(complement(X0),X1)),
inference(superposition,[],[f2,f635]) ).
fof(f663,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = X0,
inference(forward_demodulation,[],[f659,f4]) ).
fof(f689,plain,
! [X0] : join(X0,complement(complement(X0))) = X0,
inference(superposition,[],[f663,f663]) ).
fof(f690,plain,
! [X0] : join(X0,zero) = X0,
inference(superposition,[],[f663,f25]) ).
fof(f724,plain,
! [X0] : join(zero,X0) = X0,
inference(superposition,[],[f1,f690]) ).
fof(f738,plain,
! [X2,X0,X1] : join(X1,X0) = join(complement(join(complement(X0),X2)),join(X1,X0)),
inference(superposition,[],[f384,f663]) ).
fof(f876,plain,
! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),join(complement(join(complement(X0),complement(complement(X0)))),X1)),
inference(superposition,[],[f368,f689]) ).
fof(f889,plain,
! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),join(zero,X1)),
inference(forward_demodulation,[],[f876,f25]) ).
fof(f894,plain,
! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),X1),
inference(forward_demodulation,[],[f889,f724]) ).
fof(f898,plain,
! [X0] : join(sk2,X0) = join(complement(sF0),X0),
inference(superposition,[],[f894,f31]) ).
fof(f906,plain,
! [X0] : join(sF12,X0) = join(complement(sF13),X0),
inference(superposition,[],[f894,f57]) ).
fof(f924,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X0,X1))),
inference(superposition,[],[f663,f894]) ).
fof(f933,plain,
! [X0,X1] : join(X0,X1) = join(X1,complement(complement(X0))),
inference(superposition,[],[f1,f894]) ).
fof(f940,plain,
! [X0] : complement(complement(X0)) = join(X0,zero),
inference(superposition,[],[f690,f894]) ).
fof(f941,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[],[f940,f690]) ).
fof(f969,plain,
sk3 = complement(sF1),
inference(superposition,[],[f941,f33]) ).
fof(f973,plain,
sF7 = complement(sF8),
inference(superposition,[],[f941,f47]) ).
fof(f986,plain,
! [X0,X1] : complement(X0) = join(complement(join(complement(X1),X0)),complement(join(X0,X1))),
inference(superposition,[],[f154,f941]) ).
fof(f998,plain,
sF7 = sF9,
inference(forward_demodulation,[],[f973,f49]) ).
fof(f999,plain,
sk3 = sF2,
inference(forward_demodulation,[],[f969,f35]) ).
fof(f1001,plain,
sF7 = composition(sk1,sF2),
inference(superposition,[],[f45,f999]) ).
fof(f1003,plain,
sF9 = composition(sk1,sF2),
inference(forward_demodulation,[],[f1001,f998]) ).
fof(f1102,plain,
! [X0,X1] : complement(X1) = join(complement(X1),complement(join(X0,X1))),
inference(superposition,[],[f924,f1]) ).
fof(f2164,plain,
! [X0,X1] : join(complement(X1),X0) = join(complement(complement(X0)),complement(join(complement(join(complement(X1),X0)),join(X0,X1)))),
inference(superposition,[],[f4,f986]) ).
fof(f2171,plain,
! [X0,X1] : join(X0,X1) = join(complement(join(complement(join(X0,X1)),complement(complement(join(complement(X1),X0))))),complement(complement(X0))),
inference(superposition,[],[f155,f986]) ).
fof(f2184,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(complement(join(X0,X1)),complement(complement(join(complement(X1),X0)))))),
inference(forward_demodulation,[],[f2171,f933]) ).
fof(f2190,plain,
! [X0,X1] : join(complement(X1),X0) = join(X0,complement(join(complement(join(complement(X1),X0)),join(X0,X1)))),
inference(forward_demodulation,[],[f2164,f894]) ).
fof(f2239,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(join(complement(X1),X0),complement(join(X0,X1))))),
inference(forward_demodulation,[],[f2184,f933]) ).
fof(f2245,plain,
! [X0,X1] : join(complement(X1),X0) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f2190,f738]) ).
fof(f2270,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(complement(X1),join(X0,complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f2239,f2]) ).
fof(f2290,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(complement(X1),join(complement(X1),X0)))),
inference(forward_demodulation,[],[f2270,f2245]) ).
fof(f2298,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(complement(X1),X0))),
inference(forward_demodulation,[],[f2290,f661]) ).
fof(f2303,plain,
! [X0,X1] : join(complement(X0),X1) = join(X1,complement(join(X0,X1))),
inference(superposition,[],[f2245,f1]) ).
fof(f2316,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,[],[f2245,f156]) ).
fof(f2428,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,[],[f2316,f894]) ).
fof(f2473,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,[],[f2428,f2]) ).
fof(f2494,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(join(complement(X0),X1)),complement(X0)),
inference(forward_demodulation,[],[f2473,f1102]) ).
fof(f2539,plain,
! [X0,X1] : join(complement(join(complement(complement(X0)),X1)),X0) = join(complement(join(complement(complement(X0)),X1)),complement(complement(X0))),
inference(superposition,[],[f2298,f663]) ).
fof(f2622,plain,
! [X0,X1] : join(complement(join(complement(complement(X0)),X1)),X0) = join(complement(complement(X0)),complement(X1)),
inference(forward_demodulation,[],[f2539,f2494]) ).
fof(f2677,plain,
! [X0,X1] : join(X0,complement(X1)) = join(complement(join(complement(complement(X0)),X1)),X0),
inference(forward_demodulation,[],[f2622,f894]) ).
fof(f2717,plain,
! [X0,X1] : join(X0,complement(X1)) = join(complement(join(X0,X1)),X0),
inference(forward_demodulation,[],[f2677,f894]) ).
fof(f2780,plain,
join(complement(sF0),sF2) = join(sF2,complement(sF3)),
inference(superposition,[],[f2303,f37]) ).
fof(f2787,plain,
join(complement(sF13),sF9) = join(sF9,complement(sF14)),
inference(superposition,[],[f2303,f59]) ).
fof(f2864,plain,
join(complement(sF13),sF9) = join(sF9,sF15),
inference(forward_demodulation,[],[f2787,f61]) ).
fof(f2869,plain,
join(complement(sF0),sF2) = join(sF2,sF4),
inference(forward_demodulation,[],[f2780,f39]) ).
fof(f2905,plain,
join(sF9,sF15) = join(sF12,sF9),
inference(forward_demodulation,[],[f2864,f906]) ).
fof(f2910,plain,
join(sF2,sF4) = join(sk2,sF2),
inference(forward_demodulation,[],[f2869,f898]) ).
fof(f3392,plain,
join(sF9,sF15) = join(sF9,sF12),
inference(superposition,[],[f1,f2905]) ).
fof(f4414,plain,
join(sF12,composition(sk1,sF2)) = composition(sk1,join(sF2,sF4)),
inference(superposition,[],[f233,f2910]) ).
fof(f4458,plain,
join(sF12,composition(sk1,sF2)) = join(composition(sk1,sF2),sF5),
inference(forward_demodulation,[],[f4414,f239]) ).
fof(f4466,plain,
join(sF12,sF9) = join(sF9,sF5),
inference(forward_demodulation,[],[f4458,f1003]) ).
fof(f4471,plain,
join(sF9,sF15) = join(sF9,sF5),
inference(forward_demodulation,[],[f4466,f2905]) ).
fof(f4472,plain,
join(sF9,sF12) = join(sF9,sF5),
inference(forward_demodulation,[],[f4471,f3392]) ).
fof(f4568,plain,
join(sF9,complement(sF12)) = join(complement(join(sF9,sF5)),sF9),
inference(superposition,[],[f2717,f4472]) ).
fof(f4569,plain,
join(sF9,complement(sF12)) = join(sF9,complement(sF5)),
inference(forward_demodulation,[],[f4568,f2717]) ).
fof(f4578,plain,
join(sF9,sF6) = join(sF9,complement(sF12)),
inference(forward_demodulation,[],[f4569,f43]) ).
fof(f4583,plain,
join(sF9,sF6) = join(sF9,sF13),
inference(forward_demodulation,[],[f4578,f57]) ).
fof(f4587,plain,
sF14 = join(sF9,sF6),
inference(forward_demodulation,[],[f4583,f161]) ).
fof(f4591,plain,
sF10 = sF14,
inference(forward_demodulation,[],[f4587,f160]) ).
fof(f4593,plain,
complement(sF10) = sF15,
inference(superposition,[],[f61,f4591]) ).
fof(f4594,plain,
sF11 = sF15,
inference(forward_demodulation,[],[f4593,f53]) ).
fof(f4599,plain,
sF16 = join(sF11,sF11),
inference(superposition,[],[f63,f4594]) ).
fof(f4600,plain,
sF11 = sF16,
inference(forward_demodulation,[],[f4599,f647]) ).
fof(f4602,plain,
spl18_2,
inference(avatar_split_clause,[],[f4600,f72]) ).
fof(f4605,plain,
( sF11 != sF15
| spl18_1
| ~ spl18_2 ),
inference(superposition,[],[f175,f73]) ).
fof(f4606,plain,
( $false
| spl18_1
| ~ spl18_2 ),
inference(forward_subsumption_resolution,[],[f4605,f4594]) ).
fof(f4607,plain,
( spl18_1
| ~ spl18_2 ),
inference(avatar_contradiction_clause,[],[f4606]) ).
cnf(s1,plain,
( ~ spl18_1
| ~ spl18_2 ),
inference(sat_conversion,[],[f75]) ).
cnf(s2,plain,
spl18_2,
inference(sat_conversion,[],[f4602]) ).
cnf(s4,plain,
( spl18_1
| ~ spl18_2 ),
inference(sat_conversion,[],[f4607]) ).
cnf(s5,plain,
spl18_1,
inference(rat,[],[s4,s2]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s2,s5]) ).
fof(f4608,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL016-4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.47 % Computer : n008.cluster.edu
% 0.21/0.47 % Model : x86_64 x86_64
% 0.21/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.47 % Memory : 8046.5625MB
% 0.21/0.47 % OS : Linux 6.8.0-71-generic
% 0.21/0.47 % CPULimit : 300
% 0.21/0.47 % WCLimit : 300
% 0.21/0.47 % DateTime : Sun Sep 27 22:52:24 UTC 2026
% 0.21/0.47 % CPUTime :
% 0.21/0.47 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.53 Running first-order theorem proving
% 0.25/0.53 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
% 9.04/2.35 % (1696282)Input is clausal, will run a generic CNF schedule.
% 9.04/2.35 % (1696287)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=212537551:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 9.04/2.35 % (1696290)lrs+10_1_sil=8000:sp=occurrence:random_seed=36106892:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 9.04/2.35 % (1696288)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2013688459:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 9.04/2.35 % (1696292)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1564879505:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 9.04/2.35 % (1696293)dis-21_1_sil=8000:lcm=predicate:random_seed=3491800000:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 9.04/2.35 % (1696291)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1201000994:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 9.04/2.35 % (1696289)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1226942484:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 9.04/2.35 % (1696293)Refutation not found, incomplete strategy
% 9.04/2.35 % (1696293)------------------------------
% 9.04/2.35 % (1696293)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.04/2.35 % (1696293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.04/2.35 % (1696293)CaDiCaL version: 2.1.3
% 9.04/2.35 % (1696293)Termination reason: Refutation not found, incomplete strategy
% 9.04/2.35 % (1696293)Time elapsed: 0.003 s
% 9.04/2.35 % (1696293)Peak memory usage: 88 MB
% 9.04/2.35 % (1696293)Instructions burned: 1 (million)
% 9.04/2.35 % (1696290)Instruction limit reached!
% 9.04/2.35 % (1696290)------------------------------
% 9.04/2.35 % (1696290)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.04/2.35 % (1696290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.04/2.35 % (1696290)CaDiCaL version: 2.1.3
% 9.04/2.35 % (1696290)Termination reason: Instruction limit
% 9.04/2.35 % (1696290)Termination phase: Saturation
% 9.04/2.35 % (1696290)Time elapsed: 0.108 s
% 9.04/2.35 % (1696290)Peak memory usage: 89 MB
% 9.04/2.35 % (1696290)Instructions burned: 107 (million)
% 9.04/2.35 % (1696291)Instruction limit reached!
% 9.04/2.35 % (1696291)------------------------------
% 9.04/2.35 % (1696291)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.04/2.35 % (1696291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.04/2.35 % (1696291)CaDiCaL version: 2.1.3
% 9.04/2.35 % (1696291)Termination reason: Instruction limit
% 9.04/2.35 % (1696291)Termination phase: Saturation
% 9.04/2.35 % (1696291)Time elapsed: 0.112 s
% 9.04/2.35 % (1696291)Peak memory usage: 89 MB
% 9.04/2.35 % (1696291)Instructions burned: 115 (million)
% 9.04/2.35 % (1696292)Instruction limit reached!
% 9.04/2.35 % (1696292)------------------------------
% 9.04/2.35 % (1696292)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.04/2.35 % (1696292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.04/2.35 % (1696292)CaDiCaL version: 2.1.3
% 9.04/2.35 % (1696292)Termination reason: Instruction limit
% 9.04/2.35 % (1696292)Termination phase: Saturation
% 9.04/2.35 % (1696292)Time elapsed: 0.180 s
% 9.04/2.35 % (1696292)Peak memory usage: 90 MB
% 9.04/2.35 % (1696292)Instructions burned: 180 (million)
% 9.04/2.35 % (1696293)------------------------------
% 9.04/2.35 % (1696293)------------------------------
% 9.04/2.35 % (1696302)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=37759228:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 9.04/2.35 % (1696301)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=112853117:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 9.04/2.35 % (1696301)Refutation not found, incomplete strategy
% 9.04/2.35 % (1696301)------------------------------
% 9.04/2.35 % (1696301)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.04/2.35 % (1696301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.04/2.35 % (1696301)CaDiCaL version: 2.1.3
% 9.04/2.35 % (1696301)Termination reason: Refutation not found, incomplete strategy
% 9.04/2.35 % (1696301)Time elapsed: 0.004 s
% 9.04/2.35 % (1696301)Peak memory usage: 88 MB
% 9.04/2.35 % (1696301)Instructions burned: 1 (million)
% 9.04/2.35 % (1696302)Refutation not found, incomplete strategy
% 9.04/2.35 % (1696302)------------------------------
% 9.04/2.35 % (1696302)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.04/2.35 % (1696302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.04/2.35 % (1696302)CaDiCaL version: 2.1.3
% 9.04/2.35 % (1696302)Termination reason: Refutation not found, incomplete strategy
% 9.04/2.35 % (1696302)Time elapsed: 0.005 s
% 9.04/2.35 % (1696302)Peak memory usage: 88 MB
% 9.04/2.35 % (1696302)Instructions burned: 3 (million)
% 9.04/2.35 % (1696303)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1805679487:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 9.04/2.35 % (1696303)Refutation not found, incomplete strategy
% 9.04/2.35 % (1696303)------------------------------
% 9.04/2.35 % (1696303)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.04/2.35 % (1696303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.04/2.35 % (1696303)CaDiCaL version: 2.1.3
% 9.04/2.35 % (1696303)Termination reason: Refutation not found, incomplete strategy
% 9.04/2.35 % (1696303)Time elapsed: 0.003 s
% 9.04/2.35 % (1696303)Peak memory usage: 88 MB
% 9.04/2.35 % (1696303)Instructions burned: 1 (million)
% 9.04/2.35 % (1696306)lrs+10_64_to=lpo:sil=8000:random_seed=1829328409:i=126:bd=preordered_2993 on theBenchmark for (2993ds/126Mi)
% 9.04/2.35 % (1696302)------------------------------
% 9.04/2.35 % (1696302)------------------------------
% 9.04/2.35 % (1696301)------------------------------
% 9.04/2.35 % (1696301)------------------------------
% 9.04/2.35 % (1696306)Instruction limit reached!
% 9.04/2.35 % (1696306)------------------------------
% 9.04/2.35 % (1696306)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.04/2.35 % (1696306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.04/2.35 % (1696306)CaDiCaL version: 2.1.3
% 9.04/2.35 % (1696306)Termination reason: Instruction limit
% 9.04/2.35 % (1696306)Termination phase: Saturation
% 9.04/2.35 % (1696306)Time elapsed: 0.131 s
% 9.04/2.35 % (1696306)Peak memory usage: 89 MB
% 9.04/2.35 % (1696306)Instructions burned: 126 (million)
% 9.04/2.35 % (1696287)First to succeed.
% 9.04/2.35 % (1696287)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1696282"
% 9.04/2.35 % (1696303)------------------------------
% 9.04/2.35 % (1696303)------------------------------
% 9.04/2.35 % (1696309)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=287938194:avsq=on:i=194:fgj=on:bd=preordered_2989 on theBenchmark for (2989ds/194Mi)
% 9.04/2.35 % (1696287)Refutation found. Thanks to Tanya!
% 9.04/2.35 % SZS status Unsatisfiable for theBenchmark
% 9.04/2.35 % SZS output start Proof for theBenchmark
% See solution above
% 10.54/2.62 % (1696287)------------------------------
% 10.54/2.62 % (1696287)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.54/2.62 % (1696287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.54/2.62 % (1696287)CaDiCaL version: 2.1.3
% 10.54/2.62 % (1696287)Termination reason: Refutation
% 10.54/2.62 % (1696287)Time elapsed: 0.878 s
% 10.54/2.62 % (1696287)Peak memory usage: 134 MB
% 10.54/2.62 % (1696287)Instructions burned: 1457 (million)
% 10.54/2.62 % (1696287)------------------------------
% 10.54/2.62 % (1696287)------------------------------
% 10.54/2.62 % (1696282)Success in time 1.394 s
% 10.54/2.62 % Vampire exiting
%------------------------------------------------------------------------------