%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL036-1 : 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 : 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 12:34:01 PM UTC 2026
% Result : Unsatisfiable 6.16s 2.72s
% Output : Refutation 12.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 50
% Syntax : Number of formulae : 282 ( 125 unt; 36 def)
% Number of atoms : 619 ( 222 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 660 ( 323 ~; 314 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 25 ( 23 usr; 24 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 19 con; 0-2 aty)
% Number of variables : 158 ( 0 sgn 158 !; 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(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,
composition(sk1,top) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14) ).
fof(f18,plain,
sk1 = composition(sk1,top),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
join(composition(meet(sk2,converse(sk1)),sk3),composition(meet(sk2,converse(sk1)),meet(sk1,sk3))) != composition(meet(sk2,converse(sk1)),meet(sk1,sk3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_15) ).
fof(f20,plain,
composition(meet(sk2,converse(sk1)),meet(sk1,sk3)) != join(composition(meet(sk2,converse(sk1)),sk3),composition(meet(sk2,converse(sk1)),meet(sk1,sk3))),
inference(reorient_equations,[],[f19]) ).
fof(f21,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f22,plain,
composition(complement(join(complement(sk2),complement(converse(sk1)))),complement(join(complement(sk1),complement(sk3)))) != join(composition(complement(join(complement(sk2),complement(converse(sk1)))),sk3),composition(complement(join(complement(sk2),complement(converse(sk1)))),complement(join(complement(sk1),complement(sk3))))),
inference(definition_unfolding,[],[f20,f6,f6,f6,f6,f6]) ).
fof(f23,definition,
sF0 = composition(sk1,top),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f24,plain,
composition(sk1,top) = sF0,
inference(reorient_equations,[],[f23]) ).
fof(f25,plain,
sk1 = sF0,
inference(definition_folding,[],[f18,f24]) ).
fof(f26,definition,
sF1 = complement(sk2),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f27,plain,
complement(sk2) = sF1,
inference(reorient_equations,[],[f26]) ).
fof(f28,definition,
sF2 = converse(sk1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f29,plain,
converse(sk1) = sF2,
inference(reorient_equations,[],[f28]) ).
fof(f30,definition,
sF3 = complement(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f31,plain,
complement(sF2) = sF3,
inference(reorient_equations,[],[f30]) ).
fof(f32,definition,
sF4 = join(sF1,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f33,plain,
join(sF1,sF3) = sF4,
inference(reorient_equations,[],[f32]) ).
fof(f34,definition,
sF5 = complement(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f35,plain,
complement(sF4) = sF5,
inference(reorient_equations,[],[f34]) ).
fof(f36,definition,
sF6 = complement(sk1),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f37,plain,
complement(sk1) = sF6,
inference(reorient_equations,[],[f36]) ).
fof(f38,definition,
sF7 = complement(sk3),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f39,plain,
complement(sk3) = sF7,
inference(reorient_equations,[],[f38]) ).
fof(f40,definition,
sF8 = join(sF6,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f41,plain,
join(sF6,sF7) = sF8,
inference(reorient_equations,[],[f40]) ).
fof(f42,definition,
sF9 = complement(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f43,plain,
complement(sF8) = sF9,
inference(reorient_equations,[],[f42]) ).
fof(f44,definition,
sF10 = composition(sF5,sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f45,plain,
composition(sF5,sF9) = sF10,
inference(reorient_equations,[],[f44]) ).
fof(f46,definition,
sF11 = composition(sF5,sk3),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f47,plain,
composition(sF5,sk3) = sF11,
inference(reorient_equations,[],[f46]) ).
fof(f48,definition,
sF12 = join(sF11,sF10),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f49,plain,
join(sF11,sF10) = sF12,
inference(reorient_equations,[],[f48]) ).
fof(f50,plain,
sF10 != sF12,
inference(definition_folding,[],[f22,f49,f45,f43,f41,f39,f37,f35,f33,f31,f29,f27,f47,f35,f33,f31,f29,f27,f45,f43,f41,f39,f37,f35,f33,f31,f29,f27]) ).
fof(f51,plain,
zero = complement(top),
inference(backward_demodulation,[],[f21,f15]) ).
fof(f52,plain,
sF0 = composition(sF0,top),
inference(forward_demodulation,[],[f24,f25]) ).
fof(f53,plain,
sF2 = converse(sF0),
inference(forward_demodulation,[],[f29,f25]) ).
fof(f54,plain,
sF6 = complement(sF0),
inference(forward_demodulation,[],[f37,f25]) ).
fof(f56,definition,
( spl13_1
<=> sF0 = composition(sF0,top) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f58,plain,
( sF0 = composition(sF0,top)
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f59,plain,
spl13_1,
inference(avatar_split_clause,[],[f52,f56]) ).
fof(f78,definition,
( spl13_3
<=> sF10 = sF12 ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f80,plain,
( sF10 != sF12
| spl13_3 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f81,plain,
~ spl13_3,
inference(avatar_split_clause,[],[f50,f78]) ).
fof(f83,definition,
( spl13_4
<=> composition(sF5,sF9) = sF10 ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
fof(f85,plain,
( composition(sF5,sF9) = sF10
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f86,plain,
spl13_4,
inference(avatar_split_clause,[],[f45,f83]) ).
fof(f92,definition,
( spl13_5
<=> join(sF11,sF10) = sF12 ),
introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition]) ).
fof(f94,plain,
( join(sF11,sF10) = sF12
| ~ spl13_5 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f95,plain,
spl13_5,
inference(avatar_split_clause,[],[f49,f92]) ).
fof(f97,definition,
( spl13_6
<=> complement(sk3) = sF7 ),
introduced(definition,[new_symbols(definition,[spl13_6])],[avatar_definition]) ).
fof(f99,plain,
( complement(sk3) = sF7
| ~ spl13_6 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f100,plain,
spl13_6,
inference(avatar_split_clause,[],[f39,f97]) ).
fof(f102,definition,
( spl13_7
<=> sF2 = converse(sF0) ),
introduced(definition,[new_symbols(definition,[spl13_7])],[avatar_definition]) ).
fof(f104,plain,
( sF2 = converse(sF0)
| ~ spl13_7 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f105,plain,
spl13_7,
inference(avatar_split_clause,[],[f53,f102]) ).
fof(f110,definition,
( spl13_8
<=> sF6 = complement(sF0) ),
introduced(definition,[new_symbols(definition,[spl13_8])],[avatar_definition]) ).
fof(f112,plain,
( sF6 = complement(sF0)
| ~ spl13_8 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f113,plain,
spl13_8,
inference(avatar_split_clause,[],[f54,f110]) ).
fof(f117,definition,
( spl13_9
<=> complement(sk2) = sF1 ),
introduced(definition,[new_symbols(definition,[spl13_9])],[avatar_definition]) ).
fof(f119,plain,
( complement(sk2) = sF1
| ~ spl13_9 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f120,plain,
spl13_9,
inference(avatar_split_clause,[],[f27,f117]) ).
fof(f125,plain,
( complement(top) = join(composition(converse(sF0),complement(sF0)),complement(top))
| ~ spl13_1 ),
inference(superposition,[],[f14,f58]) ).
fof(f138,plain,
( complement(top) = join(complement(top),composition(converse(sF0),complement(sF0)))
| ~ spl13_1 ),
inference(forward_demodulation,[],[f125,f1]) ).
fof(f141,plain,
( complement(top) = join(complement(top),composition(converse(sF0),sF6))
| ~ spl13_1
| ~ spl13_8 ),
inference(forward_demodulation,[],[f138,f112]) ).
fof(f142,plain,
( complement(top) = join(complement(top),composition(sF2,sF6))
| ~ spl13_1
| ~ spl13_7
| ~ spl13_8 ),
inference(forward_demodulation,[],[f141,f104]) ).
fof(f143,plain,
( zero = join(zero,composition(sF2,sF6))
| ~ spl13_1
| ~ spl13_7
| ~ spl13_8 ),
inference(forward_demodulation,[],[f142,f51]) ).
fof(f145,definition,
( spl13_10
<=> complement(sF4) = sF5 ),
introduced(definition,[new_symbols(definition,[spl13_10])],[avatar_definition]) ).
fof(f147,plain,
( complement(sF4) = sF5
| ~ spl13_10 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f148,plain,
spl13_10,
inference(avatar_split_clause,[],[f35,f145]) ).
fof(f153,definition,
( spl13_11
<=> complement(sF2) = sF3 ),
introduced(definition,[new_symbols(definition,[spl13_11])],[avatar_definition]) ).
fof(f155,plain,
( complement(sF2) = sF3
| ~ spl13_11 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f156,plain,
spl13_11,
inference(avatar_split_clause,[],[f31,f153]) ).
fof(f161,definition,
( spl13_12
<=> complement(sF8) = sF9 ),
introduced(definition,[new_symbols(definition,[spl13_12])],[avatar_definition]) ).
fof(f163,plain,
( complement(sF8) = sF9
| ~ spl13_12 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f164,plain,
spl13_12,
inference(avatar_split_clause,[],[f43,f161]) ).
fof(f177,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X1),X0))) = X1,
inference(superposition,[],[f4,f1]) ).
fof(f187,plain,
! [X0] : join(complement(join(complement(X0),complement(complement(complement(X0))))),complement(top)) = X0,
inference(superposition,[],[f4,f15]) ).
fof(f192,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f187,f1]) ).
fof(f202,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(forward_demodulation,[],[f177,f1]) ).
fof(f212,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f192,f51]) ).
fof(f251,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(f260,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f263,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(X2,complement(join(complement(X0),complement(X1))))),
inference(forward_demodulation,[],[f251,f260]) ).
fof(f269,definition,
( spl13_13
<=> join(sF6,sF7) = sF8 ),
introduced(definition,[new_symbols(definition,[spl13_13])],[avatar_definition]) ).
fof(f271,plain,
( join(sF6,sF7) = sF8
| ~ spl13_13 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f272,plain,
spl13_13,
inference(avatar_split_clause,[],[f41,f269]) ).
fof(f275,definition,
( spl13_14
<=> zero = complement(top) ),
introduced(definition,[new_symbols(definition,[spl13_14])],[avatar_definition]) ).
fof(f277,plain,
( zero = complement(top)
| ~ spl13_14 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f278,plain,
spl13_14,
inference(avatar_split_clause,[],[f51,f275]) ).
fof(f280,definition,
( spl13_15
<=> join(sF1,sF3) = sF4 ),
introduced(definition,[new_symbols(definition,[spl13_15])],[avatar_definition]) ).
fof(f282,plain,
( join(sF1,sF3) = sF4
| ~ spl13_15 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f283,plain,
spl13_15,
inference(avatar_split_clause,[],[f33,f280]) ).
fof(f286,definition,
( spl13_16
<=> composition(sF5,sk3) = sF11 ),
introduced(definition,[new_symbols(definition,[spl13_16])],[avatar_definition]) ).
fof(f288,plain,
( composition(sF5,sk3) = sF11
| ~ spl13_16 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f289,plain,
spl13_16,
inference(avatar_split_clause,[],[f47,f286]) ).
fof(f313,plain,
! [X0,X1] : composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[],[f12,f10]) ).
fof(f317,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(f339,plain,
! [X0] : complement(X0) = join(complement(join(complement(complement(X0)),X0)),complement(top)),
inference(superposition,[],[f202,f15]) ).
fof(f347,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(complement(complement(X0)),X0))),
inference(forward_demodulation,[],[f339,f1]) ).
fof(f365,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f347,f1]) ).
fof(f372,plain,
( ! [X0] : complement(X0) = join(zero,complement(join(X0,complement(complement(X0)))))
| ~ spl13_14 ),
inference(forward_demodulation,[],[f365,f277]) ).
fof(f378,plain,
( ! [X0] : complement(complement(X0)) = X0
| ~ spl13_14 ),
inference(backward_demodulation,[],[f212,f372]) ).
fof(f381,plain,
( ! [X0] : complement(X0) = join(zero,complement(join(X0,X0)))
| ~ spl13_14 ),
inference(backward_demodulation,[],[f372,f378]) ).
fof(f386,plain,
( sk2 = complement(sF1)
| ~ spl13_9
| ~ spl13_14 ),
inference(superposition,[],[f378,f119]) ).
fof(f387,plain,
( sk3 = complement(sF7)
| ~ spl13_6
| ~ spl13_14 ),
inference(superposition,[],[f378,f99]) ).
fof(f388,plain,
( sF0 = complement(sF6)
| ~ spl13_8
| ~ spl13_14 ),
inference(superposition,[],[f378,f112]) ).
fof(f389,plain,
( sF2 = complement(sF3)
| ~ spl13_11
| ~ spl13_14 ),
inference(superposition,[],[f378,f155]) ).
fof(f392,plain,
( ! [X0,X1] : complement(X0) = join(complement(join(X0,complement(X1))),complement(join(X0,X1)))
| ~ spl13_14 ),
inference(superposition,[],[f4,f378]) ).
fof(f397,plain,
( ! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0)))
| ~ spl13_14 ),
inference(superposition,[],[f202,f378]) ).
fof(f402,plain,
( ! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(X0,complement(X1))))
| ~ spl13_14 ),
inference(forward_demodulation,[],[f392,f1]) ).
fof(f412,plain,
( ! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(X1,complement(X0))))
| ~ spl13_14 ),
inference(superposition,[],[f402,f1]) ).
fof(f514,plain,
( ! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),complement(join(complement(join(X0,X1)),join(complement(X1),X0))))
| ~ spl13_14 ),
inference(superposition,[],[f4,f397]) ).
fof(f523,plain,
( ! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),complement(join(X0,join(complement(join(X0,X1)),complement(X1)))))
| ~ spl13_14 ),
inference(forward_demodulation,[],[f514,f260]) ).
fof(f541,plain,
( ! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),complement(join(X0,join(complement(X1),complement(join(X0,X1))))))
| ~ spl13_14 ),
inference(forward_demodulation,[],[f523,f1]) ).
fof(f555,plain,
( ! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1))))))
| ~ spl13_14 ),
inference(forward_demodulation,[],[f541,f378]) ).
fof(f590,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f313,f8]) ).
fof(f600,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f590,f10]) ).
fof(f609,plain,
! [X0] : complement(X0) = join(complement(composition(one,X0)),complement(X0)),
inference(superposition,[],[f14,f600]) ).
fof(f616,plain,
one = converse(one),
inference(superposition,[],[f8,f600]) ).
fof(f617,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f600,f616]) ).
fof(f622,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(one,X0))),
inference(forward_demodulation,[],[f609,f1]) ).
fof(f625,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f622,f617]) ).
fof(f644,plain,
( top = complement(zero)
| ~ spl13_14 ),
inference(superposition,[],[f378,f277]) ).
fof(f666,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f317,f12]) ).
fof(f678,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f666,f11]) ).
fof(f687,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f678,f11]) ).
fof(f693,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f687,f12]) ).
fof(f715,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f10,f693]) ).
fof(f729,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f715,f10]) ).
fof(f766,plain,
( ! [X0] : composition(sF5,join(sk3,X0)) = join(sF11,composition(sF5,X0))
| ~ spl13_16 ),
inference(superposition,[],[f729,f288]) ).
fof(f782,plain,
! [X2,X0,X1] : join(composition(X0,X2),composition(X0,X1)) = composition(X0,join(X1,X2)),
inference(superposition,[],[f1,f729]) ).
fof(f783,plain,
! [X2,X0,X1] : composition(X0,join(X2,X1)) = composition(X0,join(X1,X2)),
inference(forward_demodulation,[],[f782,f729]) ).
fof(f806,plain,
( join(sF11,sF10) = composition(sF5,join(sk3,sF9))
| ~ spl13_4
| ~ spl13_16 ),
inference(superposition,[],[f766,f85]) ).
fof(f814,plain,
( join(sF11,sF10) = composition(sF5,join(sF9,sk3))
| ~ spl13_4
| ~ spl13_16 ),
inference(forward_demodulation,[],[f806,f783]) ).
fof(f815,plain,
( sF12 = composition(sF5,join(sF9,sk3))
| ~ spl13_4
| ~ spl13_5
| ~ spl13_16 ),
inference(forward_demodulation,[],[f814,f94]) ).
fof(f817,definition,
( spl13_18
<=> sk3 = complement(sF7) ),
introduced(definition,[new_symbols(definition,[spl13_18])],[avatar_definition]) ).
fof(f819,plain,
( sk3 = complement(sF7)
| ~ spl13_18 ),
inference(avatar_component_clause,[],[f817]) ).
fof(f820,plain,
( spl13_18
| ~ spl13_6
| ~ spl13_14 ),
inference(avatar_split_clause,[],[f387,f275,f97,f817]) ).
fof(f822,definition,
( spl13_19
<=> sk2 = complement(sF1) ),
introduced(definition,[new_symbols(definition,[spl13_19])],[avatar_definition]) ).
fof(f824,plain,
( sk2 = complement(sF1)
| ~ spl13_19 ),
inference(avatar_component_clause,[],[f822]) ).
fof(f825,plain,
( spl13_19
| ~ spl13_9
| ~ spl13_14 ),
inference(avatar_split_clause,[],[f386,f275,f117,f822]) ).
fof(f910,plain,
! [X0,X1] : join(X0,X1) = join(complement(join(complement(X0),complement(X0))),join(X1,complement(top))),
inference(superposition,[],[f263,f15]) ).
fof(f938,plain,
! [X0,X1] : join(X0,X1) = join(complement(top),join(complement(join(complement(X0),complement(X0))),X1)),
inference(forward_demodulation,[],[f910,f260]) ).
fof(f970,plain,
! [X0,X1] : join(X0,X1) = join(complement(top),join(complement(complement(X0)),X1)),
inference(forward_demodulation,[],[f938,f625]) ).
fof(f987,plain,
( ! [X0,X1] : join(X0,X1) = join(complement(top),join(X0,X1))
| ~ spl13_14 ),
inference(forward_demodulation,[],[f970,f378]) ).
fof(f998,plain,
( ! [X0,X1] : join(X0,X1) = join(zero,join(X0,X1))
| ~ spl13_14 ),
inference(forward_demodulation,[],[f987,f277]) ).
fof(f1015,definition,
( spl13_20
<=> sF0 = complement(sF6) ),
introduced(definition,[new_symbols(definition,[spl13_20])],[avatar_definition]) ).
fof(f1017,plain,
( sF0 = complement(sF6)
| ~ spl13_20 ),
inference(avatar_component_clause,[],[f1015]) ).
fof(f1018,plain,
( spl13_20
| ~ spl13_8
| ~ spl13_14 ),
inference(avatar_split_clause,[],[f388,f275,f110,f1015]) ).
fof(f1025,plain,
( ! [X0] : complement(zero) = join(complement(complement(X0)),complement(join(zero,complement(complement(join(X0,X0))))))
| ~ spl13_14 ),
inference(superposition,[],[f402,f381]) ).
fof(f1028,plain,
( ! [X0] : complement(zero) = join(complement(complement(X0)),complement(join(zero,join(X0,X0))))
| ~ spl13_14 ),
inference(forward_demodulation,[],[f1025,f378]) ).
fof(f1031,plain,
( ! [X0] : complement(zero) = join(complement(complement(X0)),complement(join(X0,X0)))
| ~ spl13_14 ),
inference(forward_demodulation,[],[f1028,f998]) ).
fof(f1034,plain,
( ! [X0] : complement(zero) = join(X0,complement(join(X0,X0)))
| ~ spl13_14 ),
inference(forward_demodulation,[],[f1031,f378]) ).
fof(f1037,plain,
( ! [X0] : top = join(X0,complement(join(X0,X0)))
| ~ spl13_14 ),
inference(forward_demodulation,[],[f1034,f644]) ).
fof(f1052,plain,
( ! [X0] : join(complement(top),complement(join(complement(X0),join(complement(X0),complement(X0))))) = X0
| ~ spl13_14 ),
inference(superposition,[],[f4,f1037]) ).
fof(f1058,plain,
( ! [X0] : join(complement(top),complement(join(complement(X0),complement(X0)))) = X0
| ~ spl13_14 ),
inference(forward_demodulation,[],[f1052,f625]) ).
fof(f1068,plain,
( ! [X0] : join(complement(top),complement(complement(X0))) = X0
| ~ spl13_14 ),
inference(forward_demodulation,[],[f1058,f625]) ).
fof(f1076,plain,
( ! [X0] : join(complement(top),X0) = X0
| ~ spl13_14 ),
inference(forward_demodulation,[],[f1068,f378]) ).
fof(f1080,plain,
( ! [X0] : join(zero,X0) = X0
| ~ spl13_14 ),
inference(forward_demodulation,[],[f1076,f277]) ).
fof(f1086,plain,
( ! [X0] : complement(X0) = complement(join(X0,X0))
| ~ spl13_14 ),
inference(backward_demodulation,[],[f381,f1080]) ).
fof(f1092,plain,
( zero = composition(sF2,sF6)
| ~ spl13_1
| ~ spl13_7
| ~ spl13_8
| ~ spl13_14 ),
inference(backward_demodulation,[],[f143,f1080]) ).
fof(f1120,plain,
( ! [X0] : complement(complement(X0)) = join(X0,X0)
| ~ spl13_14 ),
inference(superposition,[],[f378,f1086]) ).
fof(f1123,plain,
( ! [X0] : join(X0,X0) = X0
| ~ spl13_14 ),
inference(forward_demodulation,[],[f1120,f378]) ).
fof(f1214,plain,
( ! [X0,X1] : join(X0,X1) = join(X0,join(X0,X1))
| ~ spl13_14 ),
inference(superposition,[],[f2,f1123]) ).
fof(f1268,definition,
( spl13_21
<=> zero = composition(sF2,sF6) ),
introduced(definition,[new_symbols(definition,[spl13_21])],[avatar_definition]) ).
fof(f1270,plain,
( zero = composition(sF2,sF6)
| ~ spl13_21 ),
inference(avatar_component_clause,[],[f1268]) ).
fof(f1271,plain,
( spl13_21
| ~ spl13_1
| ~ spl13_7
| ~ spl13_8
| ~ spl13_14 ),
inference(avatar_split_clause,[],[f1092,f275,f110,f102,f56,f1268]) ).
fof(f1274,plain,
( ! [X0] : composition(join(sF2,X0),sF6) = join(zero,composition(X0,sF6))
| ~ spl13_21 ),
inference(superposition,[],[f9,f1270]) ).
fof(f1283,plain,
( ! [X0] : composition(X0,sF6) = composition(join(sF2,X0),sF6)
| ~ spl13_14
| ~ spl13_21 ),
inference(forward_demodulation,[],[f1274,f1080]) ).
fof(f1322,plain,
( complement(sF3) = join(complement(sF4),complement(join(sF3,complement(sF1))))
| ~ spl13_14
| ~ spl13_15 ),
inference(superposition,[],[f412,f282]) ).
fof(f1323,plain,
( complement(sF7) = join(complement(sF8),complement(join(sF7,complement(sF6))))
| ~ spl13_13
| ~ spl13_14 ),
inference(superposition,[],[f412,f271]) ).
fof(f1347,plain,
( ! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(join(complement(join(X0,complement(X1))),join(X1,X0))),complement(complement(X0)))
| ~ spl13_14 ),
inference(superposition,[],[f397,f412]) ).
fof(f1357,plain,
( ! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(complement(join(X0,complement(X1))),join(X1,X0))))
| ~ spl13_14 ),
inference(forward_demodulation,[],[f1347,f1]) ).
fof(f1369,plain,
( complement(sF7) = join(complement(sF8),complement(join(sF7,sF0)))
| ~ spl13_13
| ~ spl13_14
| ~ spl13_20 ),
inference(forward_demodulation,[],[f1323,f1017]) ).
fof(f1370,plain,
( complement(sF3) = join(complement(sF4),complement(join(sF3,sk2)))
| ~ spl13_14
| ~ spl13_15
| ~ spl13_19 ),
inference(forward_demodulation,[],[f1322,f824]) ).
fof(f1385,plain,
( ! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(join(X1,X0),complement(join(X0,complement(X1))))))
| ~ spl13_14 ),
inference(forward_demodulation,[],[f1357,f1]) ).
fof(f1396,plain,
( complement(sF7) = join(sF9,complement(join(sF7,sF0)))
| ~ spl13_12
| ~ spl13_13
| ~ spl13_14
| ~ spl13_20 ),
inference(forward_demodulation,[],[f1369,f163]) ).
fof(f1397,plain,
( complement(sF3) = join(sF5,complement(join(sF3,sk2)))
| ~ spl13_10
| ~ spl13_14
| ~ spl13_15
| ~ spl13_19 ),
inference(forward_demodulation,[],[f1370,f147]) ).
fof(f1411,plain,
( ! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(X1,join(X0,complement(join(X0,complement(X1)))))))
| ~ spl13_14 ),
inference(forward_demodulation,[],[f1385,f2]) ).
fof(f1420,plain,
( sk3 = join(sF9,complement(join(sF7,sF0)))
| ~ spl13_12
| ~ spl13_13
| ~ spl13_14
| ~ spl13_18
| ~ spl13_20 ),
inference(forward_demodulation,[],[f1396,f819]) ).
fof(f1421,plain,
( sF2 = join(sF5,complement(join(sF3,sk2)))
| ~ spl13_10
| ~ spl13_11
| ~ spl13_14
| ~ spl13_15
| ~ spl13_19 ),
inference(forward_demodulation,[],[f1397,f389]) ).
fof(f1432,plain,
( ! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1)))))))
| ~ spl13_14 ),
inference(forward_demodulation,[],[f1411,f378]) ).
fof(f1445,plain,
( ! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1)))))))
| ~ spl13_14 ),
inference(forward_demodulation,[],[f1432,f378]) ).
fof(f1875,plain,
( ! [X0,X1] : join(X0,X1) = join(X1,join(X0,X1))
| ~ spl13_14 ),
inference(superposition,[],[f1214,f1]) ).
fof(f1884,plain,
( ! [X0,X1] : complement(X0) = join(complement(join(X1,X0)),complement(X0))
| ~ spl13_14 ),
inference(superposition,[],[f1214,f412]) ).
fof(f1925,plain,
( ! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X1,X0)))
| ~ spl13_14 ),
inference(forward_demodulation,[],[f1884,f1]) ).
fof(f1937,plain,
( ! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,complement(X1))))
| ~ spl13_14 ),
inference(backward_demodulation,[],[f555,f1925]) ).
fof(f1941,plain,
( ! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,X1))))
| ~ spl13_14 ),
inference(backward_demodulation,[],[f1445,f1937]) ).
fof(f1947,plain,
( ! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1)))
| ~ spl13_14 ),
inference(forward_demodulation,[],[f1941,f1875]) ).
fof(f2058,plain,
( ! [X0,X1] : join(X1,complement(X0)) = join(X1,complement(join(X0,X1)))
| ~ spl13_14 ),
inference(superposition,[],[f1947,f1]) ).
fof(f2076,plain,
( join(sF6,complement(sF7)) = join(sF6,complement(sF8))
| ~ spl13_13
| ~ spl13_14 ),
inference(superposition,[],[f1947,f271]) ).
fof(f2116,plain,
( join(sF6,complement(sF7)) = join(sF6,sF9)
| ~ spl13_12
| ~ spl13_13
| ~ spl13_14 ),
inference(forward_demodulation,[],[f2076,f163]) ).
fof(f2143,plain,
( join(sF6,sk3) = join(sF6,sF9)
| ~ spl13_12
| ~ spl13_13
| ~ spl13_14
| ~ spl13_18 ),
inference(forward_demodulation,[],[f2116,f819]) ).
fof(f2218,plain,
( join(sF3,complement(sF1)) = join(sF3,complement(sF4))
| ~ spl13_14
| ~ spl13_15 ),
inference(superposition,[],[f2058,f282]) ).
fof(f2219,plain,
( join(sF7,complement(sF6)) = join(sF7,complement(sF8))
| ~ spl13_13
| ~ spl13_14 ),
inference(superposition,[],[f2058,f271]) ).
fof(f2262,plain,
( join(sF7,complement(sF6)) = join(sF7,sF9)
| ~ spl13_12
| ~ spl13_13
| ~ spl13_14 ),
inference(forward_demodulation,[],[f2219,f163]) ).
fof(f2263,plain,
( join(sF3,complement(sF1)) = join(sF3,sF5)
| ~ spl13_10
| ~ spl13_14
| ~ spl13_15 ),
inference(forward_demodulation,[],[f2218,f147]) ).
fof(f2290,plain,
( join(sF7,sF0) = join(sF7,sF9)
| ~ spl13_12
| ~ spl13_13
| ~ spl13_14
| ~ spl13_20 ),
inference(forward_demodulation,[],[f2262,f1017]) ).
fof(f2291,plain,
( join(sF3,sk2) = join(sF3,sF5)
| ~ spl13_10
| ~ spl13_14
| ~ spl13_15
| ~ spl13_19 ),
inference(forward_demodulation,[],[f2263,f824]) ).
fof(f2309,plain,
( sk3 = join(sF9,complement(join(sF7,sF9)))
| ~ spl13_12
| ~ spl13_13
| ~ spl13_14
| ~ spl13_18
| ~ spl13_20 ),
inference(backward_demodulation,[],[f1420,f2290]) ).
fof(f2310,plain,
( sF2 = join(sF5,complement(join(sF3,sF5)))
| ~ spl13_10
| ~ spl13_11
| ~ spl13_14
| ~ spl13_15
| ~ spl13_19 ),
inference(backward_demodulation,[],[f1421,f2291]) ).
fof(f2321,plain,
( sk3 = join(sF9,complement(sF7))
| ~ spl13_12
| ~ spl13_13
| ~ spl13_14
| ~ spl13_18
| ~ spl13_20 ),
inference(forward_demodulation,[],[f2309,f2058]) ).
fof(f2322,plain,
( sF2 = join(sF5,complement(sF3))
| ~ spl13_10
| ~ spl13_11
| ~ spl13_14
| ~ spl13_15
| ~ spl13_19 ),
inference(forward_demodulation,[],[f2310,f2058]) ).
fof(f2330,plain,
( sk3 = join(sF9,sk3)
| ~ spl13_12
| ~ spl13_13
| ~ spl13_14
| ~ spl13_18
| ~ spl13_20 ),
inference(forward_demodulation,[],[f2321,f819]) ).
fof(f2331,plain,
( sF2 = join(sF5,sF2)
| ~ spl13_10
| ~ spl13_11
| ~ spl13_14
| ~ spl13_15
| ~ spl13_19 ),
inference(forward_demodulation,[],[f2322,f389]) ).
fof(f2337,plain,
( composition(sF5,sk3) = sF12
| ~ spl13_4
| ~ spl13_5
| ~ spl13_12
| ~ spl13_13
| ~ spl13_14
| ~ spl13_16
| ~ spl13_18
| ~ spl13_20 ),
inference(backward_demodulation,[],[f815,f2330]) ).
fof(f2338,plain,
( sF2 = join(sF2,sF5)
| ~ spl13_10
| ~ spl13_11
| ~ spl13_14
| ~ spl13_15
| ~ spl13_19 ),
inference(forward_demodulation,[],[f2331,f1]) ).
fof(f2344,plain,
( sF11 = sF12
| ~ spl13_4
| ~ spl13_5
| ~ spl13_12
| ~ spl13_13
| ~ spl13_14
| ~ spl13_16
| ~ spl13_18
| ~ spl13_20 ),
inference(forward_demodulation,[],[f2337,f288]) ).
fof(f2348,plain,
( sF10 != sF11
| spl13_3
| ~ spl13_4
| ~ spl13_5
| ~ spl13_12
| ~ spl13_13
| ~ spl13_14
| ~ spl13_16
| ~ spl13_18
| ~ spl13_20 ),
inference(backward_demodulation,[],[f80,f2344]) ).
fof(f2368,definition,
( spl13_23
<=> sF10 = sF11 ),
introduced(definition,[new_symbols(definition,[spl13_23])],[avatar_definition]) ).
fof(f2370,plain,
( sF10 != sF11
| spl13_23 ),
inference(avatar_component_clause,[],[f2368]) ).
fof(f2371,plain,
( ~ spl13_23
| spl13_3
| ~ spl13_4
| ~ spl13_5
| ~ spl13_12
| ~ spl13_13
| ~ spl13_14
| ~ spl13_16
| ~ spl13_18
| ~ spl13_20 ),
inference(avatar_split_clause,[],[f2348,f1015,f817,f286,f275,f269,f161,f92,f83,f78,f2368]) ).
fof(f5625,definition,
( spl13_38
<=> join(sF6,sk3) = join(sF6,sF9) ),
introduced(definition,[new_symbols(definition,[spl13_38])],[avatar_definition]) ).
fof(f5627,plain,
( join(sF6,sk3) = join(sF6,sF9)
| ~ spl13_38 ),
inference(avatar_component_clause,[],[f5625]) ).
fof(f5628,plain,
( spl13_38
| ~ spl13_12
| ~ spl13_13
| ~ spl13_14
| ~ spl13_18 ),
inference(avatar_split_clause,[],[f2143,f817,f275,f269,f161,f5625]) ).
fof(f7184,definition,
( spl13_45
<=> sF2 = join(sF2,sF5) ),
introduced(definition,[new_symbols(definition,[spl13_45])],[avatar_definition]) ).
fof(f7186,plain,
( sF2 = join(sF2,sF5)
| ~ spl13_45 ),
inference(avatar_component_clause,[],[f7184]) ).
fof(f7187,plain,
( spl13_45
| ~ spl13_10
| ~ spl13_11
| ~ spl13_14
| ~ spl13_15
| ~ spl13_19 ),
inference(avatar_split_clause,[],[f2338,f822,f280,f275,f153,f145,f7184]) ).
fof(f7188,plain,
( composition(sF2,sF6) = composition(sF5,sF6)
| ~ spl13_14
| ~ spl13_21
| ~ spl13_45 ),
inference(superposition,[],[f1283,f7186]) ).
fof(f7208,plain,
( zero = composition(sF5,sF6)
| ~ spl13_14
| ~ spl13_21
| ~ spl13_45 ),
inference(forward_demodulation,[],[f7188,f1270]) ).
fof(f9129,definition,
( spl13_54
<=> zero = composition(sF5,sF6) ),
introduced(definition,[new_symbols(definition,[spl13_54])],[avatar_definition]) ).
fof(f9131,plain,
( zero = composition(sF5,sF6)
| ~ spl13_54 ),
inference(avatar_component_clause,[],[f9129]) ).
fof(f9132,plain,
( spl13_54
| ~ spl13_14
| ~ spl13_21
| ~ spl13_45 ),
inference(avatar_split_clause,[],[f7208,f7184,f1268,f275,f9129]) ).
fof(f9142,plain,
( ! [X0] : composition(sF5,join(sF6,X0)) = join(zero,composition(sF5,X0))
| ~ spl13_54 ),
inference(superposition,[],[f729,f9131]) ).
fof(f9157,plain,
( ! [X0] : composition(sF5,X0) = composition(sF5,join(sF6,X0))
| ~ spl13_14
| ~ spl13_54 ),
inference(forward_demodulation,[],[f9142,f1080]) ).
fof(f9428,plain,
( composition(sF5,sk3) = composition(sF5,join(sF6,sF9))
| ~ spl13_14
| ~ spl13_38
| ~ spl13_54 ),
inference(superposition,[],[f9157,f5627]) ).
fof(f9491,plain,
( composition(sF5,sF9) = composition(sF5,sk3)
| ~ spl13_14
| ~ spl13_38
| ~ spl13_54 ),
inference(forward_demodulation,[],[f9428,f9157]) ).
fof(f9509,plain,
( composition(sF5,sF9) = sF11
| ~ spl13_14
| ~ spl13_16
| ~ spl13_38
| ~ spl13_54 ),
inference(forward_demodulation,[],[f9491,f288]) ).
fof(f9512,plain,
( sF10 = sF11
| ~ spl13_4
| ~ spl13_14
| ~ spl13_16
| ~ spl13_38
| ~ spl13_54 ),
inference(forward_demodulation,[],[f9509,f85]) ).
fof(f9513,plain,
( $false
| ~ spl13_4
| ~ spl13_14
| ~ spl13_16
| spl13_23
| ~ spl13_38
| ~ spl13_54 ),
inference(forward_subsumption_resolution,[],[f9512,f2370]) ).
fof(f9514,plain,
( ~ spl13_4
| ~ spl13_14
| ~ spl13_16
| spl13_23
| ~ spl13_38
| ~ spl13_54 ),
inference(avatar_contradiction_clause,[],[f9513]) ).
cnf(s1,plain,
spl13_1,
inference(sat_conversion,[],[f59]) ).
cnf(s3,plain,
~ spl13_3,
inference(sat_conversion,[],[f81]) ).
cnf(s4,plain,
spl13_4,
inference(sat_conversion,[],[f86]) ).
cnf(s5,plain,
spl13_5,
inference(sat_conversion,[],[f95]) ).
cnf(s6,plain,
spl13_6,
inference(sat_conversion,[],[f100]) ).
cnf(s7,plain,
spl13_7,
inference(sat_conversion,[],[f105]) ).
cnf(s8,plain,
spl13_8,
inference(sat_conversion,[],[f113]) ).
cnf(s9,plain,
spl13_9,
inference(sat_conversion,[],[f120]) ).
cnf(s10,plain,
spl13_10,
inference(sat_conversion,[],[f148]) ).
cnf(s11,plain,
spl13_11,
inference(sat_conversion,[],[f156]) ).
cnf(s12,plain,
spl13_12,
inference(sat_conversion,[],[f164]) ).
cnf(s13,plain,
spl13_13,
inference(sat_conversion,[],[f272]) ).
cnf(s14,plain,
spl13_14,
inference(sat_conversion,[],[f278]) ).
cnf(s15,plain,
spl13_15,
inference(sat_conversion,[],[f283]) ).
cnf(s16,plain,
spl13_16,
inference(sat_conversion,[],[f289]) ).
cnf(s18,plain,
( ~ spl13_6
| ~ spl13_14
| spl13_18 ),
inference(sat_conversion,[],[f820]) ).
cnf(s19,plain,
( ~ spl13_9
| ~ spl13_14
| spl13_19 ),
inference(sat_conversion,[],[f825]) ).
cnf(s20,plain,
( ~ spl13_8
| ~ spl13_14
| spl13_20 ),
inference(sat_conversion,[],[f1018]) ).
cnf(s21,plain,
( ~ spl13_1
| ~ spl13_7
| ~ spl13_8
| ~ spl13_14
| spl13_21 ),
inference(sat_conversion,[],[f1271]) ).
cnf(s23,plain,
( spl13_3
| ~ spl13_4
| ~ spl13_5
| ~ spl13_12
| ~ spl13_13
| ~ spl13_14
| ~ spl13_16
| ~ spl13_18
| ~ spl13_20
| ~ spl13_23 ),
inference(sat_conversion,[],[f2371]) ).
cnf(s38,plain,
( ~ spl13_12
| ~ spl13_13
| ~ spl13_14
| ~ spl13_18
| spl13_38 ),
inference(sat_conversion,[],[f5628]) ).
cnf(s45,plain,
( ~ spl13_10
| ~ spl13_11
| ~ spl13_14
| ~ spl13_15
| ~ spl13_19
| spl13_45 ),
inference(sat_conversion,[],[f7187]) ).
cnf(s54,plain,
( ~ spl13_14
| ~ spl13_21
| ~ spl13_45
| spl13_54 ),
inference(sat_conversion,[],[f9132]) ).
cnf(s56,plain,
( ~ spl13_4
| ~ spl13_14
| ~ spl13_16
| spl13_23
| ~ spl13_38
| ~ spl13_54 ),
inference(sat_conversion,[],[f9514]) ).
cnf(s68,plain,
spl13_19,
inference(rat,[],[s19,s14,s9]) ).
cnf(s71,plain,
spl13_45,
inference(rat,[],[s45,s10,s11,s15,s14,s68]) ).
cnf(s73,plain,
spl13_20,
inference(rat,[],[s20,s14,s8]) ).
cnf(s80,plain,
spl13_18,
inference(rat,[],[s18,s14,s6]) ).
cnf(s82,plain,
spl13_38,
inference(rat,[],[s38,s12,s13,s14,s80]) ).
cnf(s86,plain,
~ spl13_23,
inference(rat,[],[s23,s4,s73,s80,s16,s14,s13,s12,s5,s3]) ).
cnf(s87,plain,
~ spl13_54,
inference(rat,[],[s56,s4,s82,s14,s16,s86]) ).
cnf(s88,plain,
~ spl13_21,
inference(rat,[],[s54,s71,s14,s87]) ).
cnf(s89,plain,
~ spl13_1,
inference(rat,[],[s21,s7,s14,s8,s88]) ).
cnf(s90,plain,
$false,
inference(rat,[],[s1,s89]) ).
fof(f9515,plain,
$false,
inference(avatar_sat_refutation,[],[s90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL036-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n026.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sun Sep 27 22:58:26 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.49 Running first-order theorem proving
% 0.20/0.49 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
% 6.16/2.72 % (3302627)Detected a unit-equality problem, will run specialized UEQ schedule.
% 6.16/2.72 % (3302632)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=2852299951:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 6.16/2.72 % (3302638)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2769152539:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 6.16/2.72 % (3302634)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2028852716:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 6.16/2.72 % (3302636)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1190642889:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 6.16/2.72 % (3302635)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2110700243:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 6.16/2.72 % (3302633)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2290864456:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 6.16/2.72 % (3302637)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=308429717:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 6.16/2.72 % (3302635)Instruction limit reached!
% 6.16/2.72 % (3302635)------------------------------
% 6.16/2.72 % (3302635)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.16/2.72 % (3302635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.16/2.72 % (3302635)CaDiCaL version: 2.1.3
% 6.16/2.72 % (3302635)Termination reason: Instruction limit
% 6.16/2.72 % (3302635)Termination phase: Saturation
% 6.16/2.72 % (3302635)Time elapsed: 0.144 s
% 6.16/2.72 % (3302635)Peak memory usage: 89 MB
% 6.16/2.72 % (3302635)Instructions burned: 137 (million)
% 6.16/2.72 % (3302636)Instruction limit reached!
% 6.16/2.72 % (3302636)------------------------------
% 6.16/2.72 % (3302636)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.16/2.72 % (3302636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.16/2.72 % (3302636)CaDiCaL version: 2.1.3
% 6.16/2.72 % (3302636)Termination reason: Instruction limit
% 6.16/2.72 % (3302636)Termination phase: Saturation
% 6.16/2.72 % (3302636)Time elapsed: 0.179 s
% 6.16/2.72 % (3302636)Peak memory usage: 90 MB
% 6.16/2.72 % (3302636)Instructions burned: 181 (million)
% 6.16/2.72 % (3302637)Instruction limit reached!
% 6.16/2.72 % (3302637)------------------------------
% 6.16/2.72 % (3302637)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.16/2.72 % (3302637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.16/2.72 % (3302637)CaDiCaL version: 2.1.3
% 6.16/2.72 % (3302637)Termination reason: Instruction limit
% 6.16/2.72 % (3302637)Termination phase: Saturation
% 6.16/2.72 % (3302637)Time elapsed: 0.277 s
% 6.16/2.72 % (3302637)Peak memory usage: 90 MB
% 6.16/2.72 % (3302637)Instructions burned: 257 (million)
% 6.16/2.72 % (3302646)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=699214421:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 6.16/2.72 % (3302647)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1454890589:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 6.16/2.72 % (3302648)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3940163805:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 6.16/2.72 % (3302648)Instruction limit reached!
% 6.16/2.72 % (3302648)------------------------------
% 6.16/2.72 % (3302648)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.16/2.72 % (3302648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.16/2.72 % (3302648)CaDiCaL version: 2.1.3
% 6.16/2.72 % (3302648)Termination reason: Instruction limit
% 6.16/2.72 % (3302648)Termination phase: Saturation
% 6.16/2.72 % (3302648)Time elapsed: 0.202 s
% 6.16/2.72 % (3302648)Peak memory usage: 92 MB
% 6.16/2.72 % (3302648)Instructions burned: 215 (million)
% 6.16/2.72 % (3302652)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=1258431071:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2990 on theBenchmark for (2990ds/317Mi)
% 6.16/2.72 % (3302638)Instruction limit reached!
% 6.16/2.72 % (3302638)------------------------------
% 6.16/2.72 % (3302638)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.16/2.72 % (3302638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.16/2.72 % (3302638)CaDiCaL version: 2.1.3
% 6.16/2.72 % (3302638)Termination reason: Instruction limit
% 6.16/2.72 % (3302638)Termination phase: Saturation
% 6.16/2.72 % (3302638)Time elapsed: 1.117 s
% 6.16/2.72 % (3302638)Peak memory usage: 99 MB
% 6.16/2.72 % (3302638)Instructions burned: 1187 (million)
% 6.16/2.72 % (3302632)First to succeed.
% 6.16/2.72 % (3302632)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3302627"
% 6.16/2.72 % (3302652)Instruction limit reached!
% 6.16/2.72 % (3302652)------------------------------
% 6.16/2.72 % (3302652)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.16/2.72 % (3302652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.16/2.72 % (3302652)CaDiCaL version: 2.1.3
% 6.16/2.72 % (3302652)Termination reason: Instruction limit
% 6.16/2.72 % (3302652)Termination phase: Saturation
% 6.16/2.72 % (3302652)Time elapsed: 0.301 s
% 6.16/2.72 % (3302652)Peak memory usage: 91 MB
% 6.16/2.72 % (3302652)Instructions burned: 317 (million)
% 6.16/2.72 % (3302654)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=1667005861:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2986 on theBenchmark for (2986ds/12125Mi)
% 6.16/2.72 % (3302632)Refutation found. Thanks to Tanya!
% 6.16/2.72 % SZS status Unsatisfiable for theBenchmark
% 6.16/2.72 % SZS output start Proof for theBenchmark
% See solution above
% 12.40/2.93 % (3302632)------------------------------
% 12.40/2.93 % (3302632)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.40/2.93 % (3302632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.40/2.93 % (3302632)CaDiCaL version: 2.1.3
% 12.40/2.93 % (3302632)Termination reason: Refutation
% 12.40/2.93 % (3302632)Time elapsed: 1.243 s
% 12.40/2.93 % (3302632)Peak memory usage: 143 MB
% 12.40/2.93 % (3302632)Instructions burned: 2168 (million)
% 12.40/2.93 % (3302632)------------------------------
% 12.40/2.93 % (3302632)------------------------------
% 12.40/2.93 % (3302627)Success in time 1.643 s
% 12.40/2.93 % Vampire exiting
%------------------------------------------------------------------------------