%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL005-2 : 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 : n026.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 12:33:38 PM UTC 2026
% Result : Unsatisfiable 9.70s 2.42s
% Output : Refutation 12.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 27
% Syntax : Number of formulae : 146 ( 133 unt; 15 def)
% Number of atoms : 159 ( 141 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 30 ( 17 ~; 11 |; 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 : 23 ( 23 usr; 18 con; 0-2 aty)
% Number of variables : 128 ( 0 sgn 128 !; 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(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(f15,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top_12) ).
fof(f16,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero_13) ).
fof(f17,negated_conjecture,
( join(converse(meet(sk1,sk2)),meet(converse(sk1),converse(sk2))) != meet(converse(sk1),converse(sk2))
| join(meet(converse(sk1),converse(sk2)),converse(meet(sk1,sk2))) != converse(meet(sk1,sk2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14) ).
fof(f18,plain,
( meet(converse(sk1),converse(sk2)) != join(converse(meet(sk1,sk2)),meet(converse(sk1),converse(sk2)))
| converse(meet(sk1,sk2)) != join(meet(converse(sk1),converse(sk2)),converse(meet(sk1,sk2))) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f20,plain,
( complement(join(complement(converse(sk1)),complement(converse(sk2)))) != join(converse(complement(join(complement(sk1),complement(sk2)))),complement(join(complement(converse(sk1)),complement(converse(sk2)))))
| converse(complement(join(complement(sk1),complement(sk2)))) != join(complement(join(complement(converse(sk1)),complement(converse(sk2)))),converse(complement(join(complement(sk1),complement(sk2))))) ),
inference(definition_unfolding,[],[f18,f6,f6,f6,f6,f6,f6]) ).
fof(f21,definition,
sF0 = converse(sk1),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f22,plain,
converse(sk1) = sF0,
inference(reorient_equations,[],[f21]) ).
fof(f23,definition,
sF1 = complement(sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f24,plain,
complement(sF0) = sF1,
inference(reorient_equations,[],[f23]) ).
fof(f25,definition,
sF2 = converse(sk2),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f26,plain,
converse(sk2) = sF2,
inference(reorient_equations,[],[f25]) ).
fof(f27,definition,
sF3 = complement(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f28,plain,
complement(sF2) = sF3,
inference(reorient_equations,[],[f27]) ).
fof(f29,definition,
sF4 = join(sF1,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f30,plain,
join(sF1,sF3) = sF4,
inference(reorient_equations,[],[f29]) ).
fof(f31,definition,
sF5 = complement(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f32,plain,
complement(sF4) = sF5,
inference(reorient_equations,[],[f31]) ).
fof(f33,definition,
sF6 = complement(sk1),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f34,plain,
complement(sk1) = sF6,
inference(reorient_equations,[],[f33]) ).
fof(f35,definition,
sF7 = complement(sk2),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f36,plain,
complement(sk2) = sF7,
inference(reorient_equations,[],[f35]) ).
fof(f37,definition,
sF8 = join(sF6,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f38,plain,
join(sF6,sF7) = sF8,
inference(reorient_equations,[],[f37]) ).
fof(f39,definition,
sF9 = complement(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f40,plain,
complement(sF8) = sF9,
inference(reorient_equations,[],[f39]) ).
fof(f41,definition,
sF10 = converse(sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f42,plain,
converse(sF9) = sF10,
inference(reorient_equations,[],[f41]) ).
fof(f43,definition,
sF11 = join(sF10,sF5),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f44,plain,
join(sF10,sF5) = sF11,
inference(reorient_equations,[],[f43]) ).
fof(f45,definition,
sF12 = join(sF5,sF10),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f46,plain,
join(sF5,sF10) = sF12,
inference(reorient_equations,[],[f45]) ).
fof(f47,plain,
( sF5 != sF11
| sF10 != sF12 ),
inference(definition_folding,[],[f20,f46,f42,f40,f38,f36,f34,f32,f30,f28,f26,f24,f22,f42,f40,f38,f36,f34,f44,f32,f30,f28,f26,f24,f22,f42,f40,f38,f36,f34,f32,f30,f28,f26,f24,f22]) ).
fof(f49,definition,
( spl13_1
<=> sF10 = sF12 ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f51,plain,
( sF10 != sF12
| spl13_1 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f53,definition,
( spl13_2
<=> sF5 = sF11 ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f56,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(avatar_split_clause,[],[f47,f53,f49]) ).
fof(f57,plain,
zero = complement(top),
inference(backward_demodulation,[],[f19,f15]) ).
fof(f58,plain,
sF8 = join(sF6,complement(sk2)),
inference(forward_demodulation,[],[f38,f36]) ).
fof(f59,plain,
sF11 = join(sF5,sF10),
inference(forward_demodulation,[],[f44,f1]) ).
fof(f60,plain,
sF8 = join(complement(sk2),sF6),
inference(forward_demodulation,[],[f58,f1]) ).
fof(f61,plain,
sF11 = sF12,
inference(backward_demodulation,[],[f46,f59]) ).
fof(f62,plain,
sF8 = join(complement(sk2),complement(sk1)),
inference(forward_demodulation,[],[f60,f34]) ).
fof(f63,plain,
join(complement(sk1),complement(sk2)) = sF8,
inference(forward_demodulation,[],[f62,f1]) ).
fof(f64,plain,
( sF10 != sF11
| spl13_1 ),
inference(forward_demodulation,[],[f51,f61]) ).
fof(f65,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(X0),complement(join(complement(join(complement(X0),complement(X1))),join(complement(X0),X1)))),
inference(superposition,[],[f4,f4]) ).
fof(f74,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(superposition,[],[f1,f4]) ).
fof(f80,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(X0),complement(join(join(complement(X0),X1),complement(join(complement(X0),complement(X1)))))),
inference(forward_demodulation,[],[f65,f1]) ).
fof(f82,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(X0),complement(join(complement(X0),join(X1,complement(join(complement(X0),complement(X1))))))),
inference(forward_demodulation,[],[f80,f2]) ).
fof(f139,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[],[f11,f10]) ).
fof(f145,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(f152,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f154,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(X2,complement(join(complement(X0),complement(X1))))),
inference(forward_demodulation,[],[f145,f152]) ).
fof(f164,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[],[f2,f15]) ).
fof(f187,plain,
! [X0,X1] : composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[],[f12,f10]) ).
fof(f208,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f187,f8]) ).
fof(f218,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f208,f10]) ).
fof(f227,plain,
! [X0] : complement(X0) = join(complement(composition(one,X0)),complement(X0)),
inference(superposition,[],[f14,f218]) ).
fof(f233,plain,
one = converse(one),
inference(superposition,[],[f8,f218]) ).
fof(f234,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f218,f233]) ).
fof(f238,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(one,X0))),
inference(forward_demodulation,[],[f227,f1]) ).
fof(f241,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f238,f234]) ).
fof(f326,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),complement(complement(X1))))) = join(complement(join(complement(X0),X1)),X0),
inference(superposition,[],[f154,f4]) ).
fof(f327,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(X0,complement(join(complement(X0),complement(X1)))),
inference(superposition,[],[f154,f241]) ).
fof(f334,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),complement(X1)))) = X0,
inference(forward_demodulation,[],[f327,f74]) ).
fof(f335,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),complement(complement(X1))))) = join(X0,complement(join(complement(X0),X1))),
inference(forward_demodulation,[],[f326,f1]) ).
fof(f348,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = X0,
inference(forward_demodulation,[],[f335,f334]) ).
fof(f373,plain,
! [X2,X0,X1] : join(complement(X0),X2) = join(join(complement(X0),X2),complement(join(X0,X1))),
inference(superposition,[],[f348,f154]) ).
fof(f375,plain,
! [X0,X1] : join(X1,complement(join(X0,complement(X1)))) = X1,
inference(superposition,[],[f348,f1]) ).
fof(f376,plain,
! [X0] : join(X0,complement(top)) = X0,
inference(superposition,[],[f348,f15]) ).
fof(f379,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),X0) = join(X0,X0),
inference(superposition,[],[f154,f348]) ).
fof(f384,plain,
! [X2,X0,X1] : join(X0,X1) = join(complement(complement(X0)),join(X1,complement(join(complement(X0),complement(complement(join(complement(complement(X0)),X2))))))),
inference(superposition,[],[f154,f348]) ).
fof(f389,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = join(X0,X0),
inference(forward_demodulation,[],[f379,f1]) ).
fof(f392,plain,
! [X0] : join(X0,zero) = X0,
inference(forward_demodulation,[],[f376,f57]) ).
fof(f394,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(X0),complement(join(complement(X0),X1))),
inference(backward_demodulation,[],[f82,f375]) ).
fof(f395,plain,
! [X2,X0,X1] : join(complement(X0),X2) = join(complement(X0),join(X2,complement(join(X0,X1)))),
inference(forward_demodulation,[],[f373,f2]) ).
fof(f399,plain,
! [X0] : join(X0,X0) = X0,
inference(forward_demodulation,[],[f389,f348]) ).
fof(f400,plain,
! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),X1),
inference(backward_demodulation,[],[f384,f395]) ).
fof(f431,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X0,X1))),
inference(superposition,[],[f348,f400]) ).
fof(f439,plain,
! [X0,X1] : complement(complement(X0)) = join(X0,complement(join(complement(complement(complement(X0))),X1))),
inference(superposition,[],[f348,f400]) ).
fof(f440,plain,
! [X0,X1] : complement(complement(X0)) = join(X0,complement(join(complement(X0),X1))),
inference(forward_demodulation,[],[f439,f400]) ).
fof(f450,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[],[f440,f348]) ).
fof(f502,plain,
! [X0,X1] : join(complement(X0),complement(complement(X0))) = join(complement(X0),complement(complement(join(complement(complement(X0)),X1)))),
inference(superposition,[],[f394,f348]) ).
fof(f510,plain,
! [X0,X1] : join(complement(X0),complement(complement(X0))) = join(complement(X0),join(complement(complement(X0)),X1)),
inference(forward_demodulation,[],[f502,f450]) ).
fof(f517,plain,
! [X0,X1] : join(complement(X0),complement(complement(X0))) = join(top,X1),
inference(forward_demodulation,[],[f510,f164]) ).
fof(f525,plain,
! [X1] : top = join(top,X1),
inference(forward_demodulation,[],[f517,f15]) ).
fof(f587,plain,
! [X0,X1] : complement(X1) = join(complement(X1),complement(join(X0,X1))),
inference(superposition,[],[f431,f1]) ).
fof(f640,plain,
! [X0] : complement(complement(X0)) = join(complement(complement(X0)),complement(top)),
inference(superposition,[],[f587,f15]) ).
fof(f675,plain,
! [X0] : complement(complement(X0)) = join(complement(top),complement(complement(X0))),
inference(forward_demodulation,[],[f640,f1]) ).
fof(f686,plain,
! [X0] : join(complement(top),X0) = X0,
inference(forward_demodulation,[],[f675,f450]) ).
fof(f694,plain,
! [X0] : join(zero,X0) = X0,
inference(forward_demodulation,[],[f686,f57]) ).
fof(f767,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1))),
inference(superposition,[],[f394,f450]) ).
fof(f775,plain,
! [X0,X1] : join(X1,complement(join(X0,X1))) = join(X1,complement(X0)),
inference(superposition,[],[f767,f1]) ).
fof(f977,plain,
! [X0] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[],[f139,f15]) ).
fof(f1015,plain,
! [X0] : join(X0,complement(converse(complement(converse(X0))))) = join(X0,complement(converse(top))),
inference(superposition,[],[f767,f977]) ).
fof(f1016,plain,
! [X0] : join(converse(complement(converse(X0))),complement(X0)) = join(converse(complement(converse(X0))),complement(converse(top))),
inference(superposition,[],[f775,f977]) ).
fof(f1022,plain,
top = converse(top),
inference(superposition,[],[f525,f977]) ).
fof(f1031,plain,
! [X0] : join(converse(complement(converse(X0))),complement(X0)) = join(complement(converse(top)),converse(complement(converse(X0)))),
inference(forward_demodulation,[],[f1016,f1]) ).
fof(f1032,plain,
! [X0] : join(X0,complement(top)) = join(X0,complement(converse(complement(converse(X0))))),
inference(forward_demodulation,[],[f1015,f1022]) ).
fof(f1049,plain,
! [X0] : join(converse(complement(converse(X0))),complement(X0)) = join(complement(top),converse(complement(converse(X0)))),
inference(forward_demodulation,[],[f1031,f1022]) ).
fof(f1050,plain,
! [X0] : join(X0,zero) = join(X0,complement(converse(complement(converse(X0))))),
inference(forward_demodulation,[],[f1032,f57]) ).
fof(f1059,plain,
! [X0] : join(converse(complement(converse(X0))),complement(X0)) = join(zero,converse(complement(converse(X0)))),
inference(forward_demodulation,[],[f1049,f57]) ).
fof(f1060,plain,
! [X0] : join(X0,complement(converse(complement(converse(X0))))) = X0,
inference(forward_demodulation,[],[f1050,f392]) ).
fof(f1064,plain,
! [X0] : converse(complement(converse(X0))) = join(converse(complement(converse(X0))),complement(X0)),
inference(forward_demodulation,[],[f1059,f694]) ).
fof(f1066,plain,
! [X0] : converse(complement(converse(X0))) = join(complement(X0),converse(complement(converse(X0)))),
inference(forward_demodulation,[],[f1064,f1]) ).
fof(f1139,plain,
! [X0] : converse(converse(X0)) = join(X0,converse(complement(converse(complement(converse(converse(X0))))))),
inference(superposition,[],[f139,f1060]) ).
fof(f1142,plain,
! [X0] : join(X0,converse(complement(converse(complement(X0))))) = X0,
inference(forward_demodulation,[],[f1139,f10]) ).
fof(f1155,plain,
! [X0] : complement(X0) = join(complement(X0),converse(complement(converse(X0)))),
inference(superposition,[],[f1142,f450]) ).
fof(f1192,plain,
! [X0] : complement(X0) = converse(complement(converse(X0))),
inference(backward_demodulation,[],[f1066,f1155]) ).
fof(f1239,plain,
complement(sk1) = converse(complement(sF0)),
inference(superposition,[],[f1192,f22]) ).
fof(f1240,plain,
complement(sk2) = converse(complement(sF2)),
inference(superposition,[],[f1192,f26]) ).
fof(f1242,plain,
! [X0] : complement(converse(X0)) = converse(complement(X0)),
inference(superposition,[],[f10,f1192]) ).
fof(f1272,plain,
complement(sk2) = converse(sF3),
inference(forward_demodulation,[],[f1240,f28]) ).
fof(f1273,plain,
complement(sk1) = converse(sF1),
inference(forward_demodulation,[],[f1239,f24]) ).
fof(f1350,plain,
! [X0] : converse(join(sF1,X0)) = join(complement(sk1),converse(X0)),
inference(superposition,[],[f11,f1273]) ).
fof(f2170,plain,
join(complement(sk1),complement(sk2)) = converse(join(sF1,sF3)),
inference(superposition,[],[f1350,f1272]) ).
fof(f2194,plain,
join(complement(sk1),complement(sk2)) = converse(sF4),
inference(forward_demodulation,[],[f2170,f30]) ).
fof(f2207,plain,
sF8 = converse(sF4),
inference(forward_demodulation,[],[f2194,f63]) ).
fof(f2236,plain,
complement(sF8) = converse(complement(sF4)),
inference(superposition,[],[f1242,f2207]) ).
fof(f2239,plain,
complement(sF8) = converse(sF5),
inference(forward_demodulation,[],[f2236,f32]) ).
fof(f2255,plain,
sF9 = converse(sF5),
inference(forward_demodulation,[],[f2239,f40]) ).
fof(f2263,plain,
sF5 = converse(sF9),
inference(superposition,[],[f10,f2255]) ).
fof(f2280,plain,
sF5 = sF10,
inference(backward_demodulation,[],[f42,f2263]) ).
fof(f2284,plain,
sF11 = join(sF5,sF5),
inference(backward_demodulation,[],[f59,f2280]) ).
fof(f2285,plain,
( sF5 != sF11
| spl13_1 ),
inference(backward_demodulation,[],[f64,f2280]) ).
fof(f2314,plain,
( ~ spl13_2
| spl13_1 ),
inference(avatar_split_clause,[],[f2285,f49,f53]) ).
fof(f2315,plain,
sF5 = sF11,
inference(forward_demodulation,[],[f2284,f399]) ).
fof(f2330,plain,
spl13_2,
inference(avatar_split_clause,[],[f2315,f53]) ).
cnf(s1,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(sat_conversion,[],[f56]) ).
cnf(s2,plain,
( spl13_1
| ~ spl13_2 ),
inference(sat_conversion,[],[f2314]) ).
cnf(s3,plain,
spl13_2,
inference(sat_conversion,[],[f2330]) ).
cnf(s4,plain,
spl13_1,
inference(rat,[],[s2,s3]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s3,s4]) ).
fof(f2331,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL005-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 22:52:42 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 10.81/2.37 % (3295646)Input is clausal, will run a generic CNF schedule.
% 10.81/2.37 % (3295667)dis-21_1_sil=8000:lcm=predicate:random_seed=2898622817:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/117Mi)
% 10.81/2.37 % (3295667)Refutation not found, incomplete strategy
% 10.81/2.37 % (3295667)------------------------------
% 10.81/2.37 % (3295667)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.81/2.37 % (3295667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.81/2.37 % (3295667)CaDiCaL version: 2.1.3
% 10.81/2.37 % (3295667)Termination reason: Refutation not found, incomplete strategy
% 10.81/2.37 % (3295667)Time elapsed: 0.001 s
% 10.81/2.37 % (3295667)Peak memory usage: 88 MB
% 10.81/2.37 % (3295667)Instructions burned: 1 (million)
% 10.81/2.37 % (3295666)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=114517922:s2a=on:i=180:gtg=position_3000 on theBenchmark for (3000ds/180Mi)
% 10.81/2.37 % (3295665)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3588469374:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_3000 on theBenchmark for (3000ds/114Mi)
% 10.81/2.37 % (3295663)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2948929473:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_3000 on theBenchmark for (3000ds/137899Mi)
% 10.81/2.37 % (3295661)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=1373487285:i=140167_3000 on theBenchmark for (3000ds/140167Mi)
% 10.81/2.37 % (3295662)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3265732655:i=132376:av=off_3000 on theBenchmark for (3000ds/132376Mi)
% 10.81/2.37 % (3295664)lrs+10_1_sil=8000:sp=occurrence:random_seed=4077162020:i=107:sd=3:ss=axioms:sgt=8_3000 on theBenchmark for (3000ds/107Mi)
% 10.81/2.37 % (3295665)Instruction limit reached!
% 10.81/2.37 % (3295665)------------------------------
% 10.81/2.37 % (3295665)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.81/2.37 % (3295665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.81/2.37 % (3295665)CaDiCaL version: 2.1.3
% 10.81/2.37 % (3295665)Termination reason: Instruction limit
% 10.81/2.37 % (3295665)Termination phase: Saturation
% 10.81/2.37 % (3295665)Time elapsed: 0.113 s
% 10.81/2.37 % (3295665)Peak memory usage: 89 MB
% 10.81/2.37 % (3295665)Instructions burned: 114 (million)
% 10.81/2.37 % (3295667)------------------------------
% 10.81/2.37 % (3295667)------------------------------
% 10.81/2.37 % (3295664)Instruction limit reached!
% 10.81/2.37 % (3295664)------------------------------
% 10.81/2.37 % (3295664)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.81/2.37 % (3295664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.81/2.37 % (3295664)CaDiCaL version: 2.1.3
% 10.81/2.37 % (3295664)Termination reason: Instruction limit
% 10.81/2.37 % (3295664)Termination phase: Saturation
% 10.81/2.37 % (3295664)Time elapsed: 0.102 s
% 10.81/2.37 % (3295664)Peak memory usage: 89 MB
% 10.81/2.37 % (3295664)Instructions burned: 107 (million)
% 10.81/2.37 % (3295666)Instruction limit reached!
% 10.81/2.37 % (3295666)------------------------------
% 10.81/2.37 % (3295666)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.81/2.37 % (3295666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.81/2.37 % (3295666)CaDiCaL version: 2.1.3
% 10.81/2.37 % (3295666)Termination reason: Instruction limit
% 10.81/2.37 % (3295666)Termination phase: Saturation
% 10.81/2.37 % (3295666)Time elapsed: 0.174 s
% 10.81/2.37 % (3295666)Peak memory usage: 90 MB
% 10.81/2.37 % (3295666)Instructions burned: 181 (million)
% 10.81/2.37 % (3295680)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=1631844936:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 10.81/2.37 % (3295680)Refutation not found, incomplete strategy
% 10.81/2.37 % (3295680)------------------------------
% 10.81/2.37 % (3295680)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.81/2.37 % (3295680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.81/2.37 % (3295680)CaDiCaL version: 2.1.3
% 10.81/2.37 % (3295680)Termination reason: Refutation not found, incomplete strategy
% 10.81/2.37 % (3295680)Time elapsed: 0.001 s
% 10.81/2.37 % (3295680)Peak memory usage: 88 MB
% 9.70/2.42 % (3295680)Instructions burned: 1 (million)
% 9.70/2.42 % (3295682)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2725007080:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 9.70/2.42 % (3295682)Refutation not found, incomplete strategy
% 9.70/2.42 % (3295682)------------------------------
% 9.70/2.42 % (3295682)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.70/2.42 % (3295682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.70/2.42 % (3295682)CaDiCaL version: 2.1.3
% 9.70/2.42 % (3295682)Termination reason: Refutation not found, incomplete strategy
% 9.70/2.42 % (3295682)Time elapsed: 0.002 s
% 9.70/2.42 % (3295682)Peak memory usage: 88 MB
% 9.70/2.42 % (3295682)Instructions burned: 1 (million)
% 9.70/2.42 % (3295681)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3833629817: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)
% 9.70/2.42 % (3295681)Refutation not found, incomplete strategy
% 9.70/2.42 % (3295681)------------------------------
% 9.70/2.42 % (3295681)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.70/2.42 % (3295681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.70/2.42 % (3295681)CaDiCaL version: 2.1.3
% 9.70/2.42 % (3295681)Termination reason: Refutation not found, incomplete strategy
% 9.70/2.42 % (3295681)Time elapsed: 0.003 s
% 9.70/2.42 % (3295681)Peak memory usage: 88 MB
% 9.70/2.42 % (3295681)Instructions burned: 1 (million)
% 9.70/2.42 % (3295683)lrs+10_64_to=lpo:sil=8000:random_seed=289099292:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 9.70/2.42 % (3295680)------------------------------
% 9.70/2.42 % (3295680)------------------------------
% 9.70/2.42 % (3295683)Instruction limit reached!
% 9.70/2.42 % (3295683)------------------------------
% 9.70/2.42 % (3295683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.70/2.42 % (3295683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.70/2.42 % (3295683)CaDiCaL version: 2.1.3
% 9.70/2.42 % (3295683)Termination reason: Instruction limit
% 9.70/2.42 % (3295683)Termination phase: Saturation
% 9.70/2.42 % (3295683)Time elapsed: 0.123 s
% 9.70/2.42 % (3295683)Peak memory usage: 89 MB
% 9.70/2.42 % (3295683)Instructions burned: 127 (million)
% 9.70/2.42 % (3295682)------------------------------
% 9.70/2.42 % (3295682)------------------------------
% 9.70/2.42 % (3295693)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2878958197:avsq=on:i=194:fgj=on:bd=preordered_2993 on theBenchmark for (2993ds/194Mi)
% 9.70/2.42 % (3295695)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2532607595:i=157:gtg=all_2992 on theBenchmark for (2992ds/157Mi)
% 9.70/2.42 % (3295681)------------------------------
% 9.70/2.42 % (3295681)------------------------------
% 9.70/2.42 % (3295693)Instruction limit reached!
% 9.70/2.42 % (3295693)------------------------------
% 9.70/2.42 % (3295693)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.70/2.42 % (3295693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.70/2.42 % (3295693)CaDiCaL version: 2.1.3
% 9.70/2.42 % (3295693)Termination reason: Instruction limit
% 9.70/2.42 % (3295693)Termination phase: Saturation
% 9.70/2.42 % (3295693)Time elapsed: 0.111 s
% 9.70/2.42 % (3295693)Peak memory usage: 90 MB
% 9.70/2.42 % (3295693)Instructions burned: 195 (million)
% 9.70/2.42 % (3295697)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=4269200053:i=3394:sd=4:ss=included:sgt=64_2991 on theBenchmark for (2991ds/3394Mi)
% 9.70/2.42 % (3295695)Instruction limit reached!
% 9.70/2.42 % (3295695)------------------------------
% 9.70/2.42 % (3295695)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.70/2.42 % (3295695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.70/2.42 % (3295695)CaDiCaL version: 2.1.3
% 9.70/2.42 % (3295695)Termination reason: Instruction limit
% 9.70/2.42 % (3295695)Termination phase: Saturation
% 9.70/2.42 % (3295695)Time elapsed: 0.141 s
% 9.70/2.42 % (3295695)Peak memory usage: 91 MB
% 9.70/2.42 % (3295695)Instructions burned: 157 (million)
% 9.70/2.42 % (3295703)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=2088297852:i=107_2990 on theBenchmark for (2990ds/107Mi)
% 9.70/2.42 % (3295703)Refutation not found, incomplete strategy
% 9.70/2.42 % (3295703)------------------------------
% 9.70/2.42 % (3295703)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.70/2.42 % (3295703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.70/2.42 % (3295703)CaDiCaL version: 2.1.3
% 9.70/2.42 % (3295703)Termination reason: Refutation not found, incomplete strategy
% 9.70/2.42 % (3295703)Time elapsed: 0.001 s
% 9.70/2.42 % (3295703)Peak memory usage: 88 MB
% 9.70/2.42 % (3295703)Instructions burned: 1 (million)
% 9.70/2.42 % (3295701)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=3713245637:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2990 on theBenchmark for (2990ds/106Mi)
% 9.70/2.42 % (3295701)Instruction limit reached!
% 9.70/2.42 % (3295701)------------------------------
% 9.70/2.42 % (3295701)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.70/2.42 % (3295701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.70/2.42 % (3295701)CaDiCaL version: 2.1.3
% 9.70/2.42 % (3295701)Termination reason: Instruction limit
% 9.70/2.42 % (3295701)Termination phase: Saturation
% 9.70/2.42 % (3295701)Time elapsed: 0.064 s
% 9.70/2.42 % (3295701)Peak memory usage: 89 MB
% 9.70/2.42 % (3295701)Instructions burned: 106 (million)
% 9.70/2.42 % (3295706)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=4187345155:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2989 on theBenchmark for (2989ds/242Mi)
% 9.70/2.42 % (3295703)------------------------------
% 9.70/2.42 % (3295703)------------------------------
% 9.70/2.42 % (3295709)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=67440997:cond=fast:i=5208:av=off_2988 on theBenchmark for (2988ds/5208Mi)
% 9.70/2.42 % (3295706)Instruction limit reached!
% 9.70/2.42 % (3295706)------------------------------
% 9.70/2.42 % (3295706)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.70/2.42 % (3295706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.70/2.42 % (3295706)CaDiCaL version: 2.1.3
% 9.70/2.42 % (3295706)Termination reason: Instruction limit
% 9.70/2.42 % (3295706)Termination phase: Saturation
% 9.70/2.42 % (3295706)Time elapsed: 0.125 s
% 9.70/2.42 % (3295706)Peak memory usage: 89 MB
% 9.70/2.42 % (3295706)Instructions burned: 244 (million)
% 9.70/2.42 % (3295711)lrs+1011_16_sil=32000:erd=off:bce=on:random_seed=3662172002:i=134:sd=2:doe=on:ss=axioms:sgt=14_2987 on theBenchmark for (2987ds/134Mi)
% 9.70/2.42 % (3295711)Instruction limit reached!
% 9.70/2.42 % (3295711)------------------------------
% 9.70/2.42 % (3295711)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.70/2.42 % (3295711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.70/2.42 % (3295711)CaDiCaL version: 2.1.3
% 9.70/2.42 % (3295711)Termination reason: Instruction limit
% 9.70/2.42 % (3295711)Termination phase: Saturation
% 9.70/2.42 % (3295711)Time elapsed: 0.041 s
% 9.70/2.42 % (3295711)Peak memory usage: 89 MB
% 9.70/2.42 % (3295711)Instructions burned: 136 (million)
% 9.70/2.42 % (3295663)First to succeed.
% 9.70/2.42 % (3295663)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3295646"
% 9.70/2.42 % (3295662)Also succeeded, but the first one will report.
% 9.70/2.42 % (3295714)ott+10_5:4_to=lpo:sil=8000:prc=on:fde=unused:sp=unary_frequency:spb=goal:urr=on:random_seed=825208665:i=499:bd=all_2987 on theBenchmark for (2987ds/499Mi)
% 9.70/2.42 % (3295661)Also succeeded, but the first one will report.
% 9.70/2.42 % (3295716)lrs+10_64_to=lpo:sil=8000:prc=on:sp=reverse_frequency:nwc=5:alpa=false:flr=on:random_seed=953422778:i=191:fgj=on:bd=all_2986 on theBenchmark for (2986ds/191Mi)
% 9.70/2.42 % (3295716)Instruction limit reached!
% 9.70/2.42 % (3295716)------------------------------
% 9.70/2.42 % (3295716)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.70/2.42 % (3295716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.70/2.42 % (3295716)CaDiCaL version: 2.1.3
% 9.70/2.42 % (3295716)Termination reason: Instruction limit
% 9.70/2.42 % (3295716)Termination phase: Saturation
% 9.70/2.42 % (3295716)Time elapsed: 0.069 s
% 9.70/2.42 % (3295716)Peak memory usage: 90 MB
% 9.70/2.42 % (3295716)Instructions burned: 192 (million)
% 9.70/2.42 % (3295764)lrs-11_32_anc=all:sil=8000:spb=goal_then_units:sac=on:random_seed=2340200110:i=264:kws=precedence:fsr=off_2985 on theBenchmark for (2985ds/264Mi)
% 9.70/2.42 % (3295663)Refutation found. Thanks to Tanya!
% 9.70/2.42 % SZS status Unsatisfiable for theBenchmark
% 9.70/2.42 % SZS output start Proof for theBenchmark
% See solution above
% 12.08/2.62 % (3295663)------------------------------
% 12.08/2.62 % (3295663)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.08/2.62 % (3295663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.08/2.62 % (3295663)CaDiCaL version: 2.1.3
% 12.08/2.62 % (3295663)Termination reason: Refutation
% 12.08/2.62 % (3295663)Time elapsed: 1.168 s
% 12.08/2.62 % (3295663)Peak memory usage: 132 MB
% 12.08/2.62 % (3295663)Instructions burned: 1288 (million)
% 12.08/2.62 % (3295663)------------------------------
% 12.08/2.62 % (3295663)------------------------------
% 12.08/2.62 % (3295646)Success in time 1.635 s
% 12.08/2.62 % Vampire exiting
%------------------------------------------------------------------------------