TSTP Solution File: SET135-6 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET135-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 15:38:13 EDT 2023
% Result : Unsatisfiable 92.05s 13.64s
% Output : Refutation 92.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 83
% Number of leaves : 29
% Syntax : Number of formulae : 264 ( 85 unt; 0 def)
% Number of atoms : 515 ( 117 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 462 ( 211 ~; 251 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 9 con; 0-3 aty)
% Number of variables : 363 (; 363 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f712432,plain,
$false,
inference(unit_resulting_resolution,[],[f93,f712414,f110]) ).
fof(f110,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(superposition,[],[f9,f12]) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',singleton_set) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',unordered_pair2) ).
fof(f712414,plain,
~ member(u,singleton(u)),
inference(resolution,[],[f712396,f24]) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,complement(X0))
| ~ member(X4,X0) ),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',complement1) ).
fof(f712396,plain,
member(u,complement(singleton(u))),
inference(resolution,[],[f711858,f21]) ).
fof(f21,axiom,
! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X0) ),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',intersection1) ).
fof(f711858,plain,
member(u,intersection(complement(singleton(u)),universal_class)),
inference(subsumption_resolution,[],[f711832,f556840]) ).
fof(f556840,plain,
! [X0] : ~ member(X0,null_class),
inference(subsumption_resolution,[],[f556508,f15778]) ).
fof(f15778,plain,
! [X4] : subclass(null_class,X4),
inference(subsumption_resolution,[],[f15775,f4]) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',class_elements_are_sets) ).
fof(f15775,plain,
! [X4] :
( ~ subclass(null_class,universal_class)
| subclass(null_class,X4) ),
inference(duplicate_literal_removal,[],[f15705]) ).
fof(f15705,plain,
! [X4] :
( ~ subclass(null_class,universal_class)
| subclass(null_class,X4)
| subclass(null_class,X4) ),
inference(resolution,[],[f138,f666]) ).
fof(f666,plain,
! [X4] :
( ~ member(not_subclass_element(null_class,X4),universal_class)
| subclass(null_class,X4) ),
inference(superposition,[],[f107,f653]) ).
fof(f653,plain,
null_class = complement(universal_class),
inference(resolution,[],[f652,f4]) ).
fof(f652,plain,
! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class ),
inference(duplicate_literal_removal,[],[f642]) ).
fof(f642,plain,
! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class
| complement(X0) = null_class ),
inference(resolution,[],[f137,f106]) ).
fof(f106,plain,
! [X0] :
( ~ member(regular(complement(X0)),X0)
| complement(X0) = null_class ),
inference(resolution,[],[f66,f24]) ).
fof(f66,axiom,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',regularity1) ).
fof(f137,plain,
! [X2,X3] :
( member(regular(X2),X3)
| ~ subclass(X2,X3)
| null_class = X2 ),
inference(resolution,[],[f1,f66]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) ),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',subclass_members) ).
fof(f107,plain,
! [X0,X1] :
( ~ member(not_subclass_element(complement(X0),X1),X0)
| subclass(complement(X0),X1) ),
inference(resolution,[],[f2,f24]) ).
fof(f2,axiom,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',not_subclass_members1) ).
fof(f138,plain,
! [X6,X4,X5] :
( member(not_subclass_element(X4,X6),X5)
| ~ subclass(X4,X5)
| subclass(X4,X6) ),
inference(resolution,[],[f1,f2]) ).
fof(f556508,plain,
! [X0] :
( ~ subclass(null_class,null_class)
| ~ member(X0,null_class) ),
inference(superposition,[],[f555824,f653]) ).
fof(f555824,plain,
! [X678,X676] :
( ~ subclass(complement(X676),null_class)
| ~ member(X678,null_class) ),
inference(subsumption_resolution,[],[f555101,f554600]) ).
fof(f554600,plain,
! [X3,X4,X5] :
( ~ member(X5,null_class)
| member(X5,X4)
| ~ subclass(X3,null_class) ),
inference(superposition,[],[f22,f554418]) ).
fof(f554418,plain,
! [X192,X193] :
( null_class = intersection(X192,X193)
| ~ subclass(X192,null_class) ),
inference(forward_demodulation,[],[f554417,f262889]) ).
fof(f262889,plain,
null_class = symmetric_difference(singleton(x),sF1),
inference(resolution,[],[f262794,f2245]) ).
fof(f2245,plain,
! [X1] :
( ~ subclass(X1,null_class)
| null_class = X1 ),
inference(subsumption_resolution,[],[f2240,f4]) ).
fof(f2240,plain,
! [X1] :
( ~ subclass(X1,null_class)
| null_class = X1
| ~ subclass(X1,universal_class) ),
inference(duplicate_literal_removal,[],[f2237]) ).
fof(f2237,plain,
! [X1] :
( ~ subclass(X1,null_class)
| null_class = X1
| ~ subclass(X1,universal_class)
| null_class = X1 ),
inference(resolution,[],[f678,f137]) ).
fof(f678,plain,
! [X2] :
( ~ member(regular(X2),universal_class)
| ~ subclass(X2,null_class)
| null_class = X2 ),
inference(resolution,[],[f659,f137]) ).
fof(f659,plain,
! [X0] :
( ~ member(X0,null_class)
| ~ member(X0,universal_class) ),
inference(superposition,[],[f24,f653]) ).
fof(f262794,plain,
subclass(symmetric_difference(singleton(x),sF1),null_class),
inference(superposition,[],[f20086,f71940]) ).
fof(f71940,plain,
symmetric_difference(singleton(x),sF1) = intersection(complement(intersection(singleton(x),sF1)),null_class),
inference(forward_demodulation,[],[f71918,f101]) ).
fof(f101,plain,
null_class = sF2,
inference(definition_folding,[],[f94,f100,f99,f98]) ).
fof(f98,plain,
set_builder(z,null_class) = sF0,
introduced(function_definition,[]) ).
fof(f99,plain,
set_builder(u,sF0) = sF1,
introduced(function_definition,[]) ).
fof(f100,plain,
set_builder(x,sF1) = sF2,
introduced(function_definition,[]) ).
fof(f94,axiom,
null_class = set_builder(x,set_builder(u,set_builder(z,null_class))),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',prove_corollary_3_to_member_of_triple_2) ).
fof(f71918,plain,
symmetric_difference(singleton(x),sF1) = intersection(complement(intersection(singleton(x),sF1)),sF2),
inference(superposition,[],[f1858,f100]) ).
fof(f1858,plain,
! [X2,X1] : symmetric_difference(singleton(X1),X2) = intersection(complement(intersection(singleton(X1),X2)),set_builder(X1,X2)),
inference(superposition,[],[f102,f92]) ).
fof(f92,axiom,
! [X0,X1] : union(singleton(X0),X1) = set_builder(X0,X1),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',definition_of_set_builder) ).
fof(f102,plain,
! [X0,X1] : symmetric_difference(X0,X1) = intersection(complement(intersection(X0,X1)),union(X0,X1)),
inference(forward_demodulation,[],[f27,f26]) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',union) ).
fof(f27,axiom,
! [X0,X1] : intersection(complement(intersection(X0,X1)),complement(intersection(complement(X0),complement(X1)))) = symmetric_difference(X0,X1),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',symmetric_difference) ).
fof(f20086,plain,
! [X0,X1] : subclass(intersection(X0,X1),X1),
inference(duplicate_literal_removal,[],[f19999]) ).
fof(f19999,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X1)
| subclass(intersection(X0,X1),X1) ),
inference(resolution,[],[f120,f3]) ).
fof(f3,axiom,
! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',not_subclass_members2) ).
fof(f120,plain,
! [X6,X4,X5] :
( member(not_subclass_element(intersection(X4,X5),X6),X5)
| subclass(intersection(X4,X5),X6) ),
inference(resolution,[],[f22,f2]) ).
fof(f554417,plain,
! [X192,X193] :
( ~ subclass(X192,symmetric_difference(singleton(x),sF1))
| null_class = intersection(X192,X193) ),
inference(subsumption_resolution,[],[f554055,f475538]) ).
fof(f475538,plain,
! [X3,X4] :
( null_class = X3
| ~ member(X4,null_class) ),
inference(subsumption_resolution,[],[f475434,f659]) ).
fof(f475434,plain,
! [X3,X4] :
( null_class = X3
| ~ member(X4,null_class)
| member(X4,universal_class) ),
inference(resolution,[],[f845,f4]) ).
fof(f845,plain,
! [X2,X0,X1] :
( ~ subclass(regular(X1),X2)
| null_class = X1
| ~ member(X0,null_class)
| member(X0,X2) ),
inference(resolution,[],[f257,f1]) ).
fof(f257,plain,
! [X2,X1] :
( member(X2,regular(X1))
| ~ member(X2,null_class)
| null_class = X1 ),
inference(superposition,[],[f22,f67]) ).
fof(f67,axiom,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',regularity2) ).
fof(f554055,plain,
! [X192,X193] :
( ~ subclass(X192,symmetric_difference(singleton(x),sF1))
| null_class = intersection(X192,X193)
| member(regular(intersection(X192,X193)),null_class) ),
inference(resolution,[],[f13561,f126711]) ).
fof(f126711,plain,
! [X54] :
( ~ member(X54,symmetric_difference(singleton(x),sF1))
| member(X54,null_class) ),
inference(superposition,[],[f22,f71940]) ).
fof(f13561,plain,
! [X2,X0,X1] :
( member(regular(intersection(X0,X1)),X2)
| ~ subclass(X0,X2)
| intersection(X0,X1) = null_class ),
inference(resolution,[],[f113,f1]) ).
fof(f113,plain,
! [X2,X3] :
( member(regular(intersection(X2,X3)),X2)
| null_class = intersection(X2,X3) ),
inference(resolution,[],[f21,f66]) ).
fof(f22,axiom,
! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X1) ),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',intersection2) ).
fof(f555101,plain,
! [X678,X677,X676] :
( ~ member(X678,null_class)
| ~ member(X678,union(X676,X677))
| ~ subclass(complement(X676),null_class) ),
inference(superposition,[],[f567,f554418]) ).
fof(f567,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(complement(X0),complement(X1)))
| ~ member(X2,union(X0,X1)) ),
inference(superposition,[],[f24,f26]) ).
fof(f711832,plain,
( member(u,null_class)
| member(u,intersection(complement(singleton(u)),universal_class)) ),
inference(superposition,[],[f620339,f711412]) ).
fof(f711412,plain,
null_class = symmetric_difference(complement(singleton(u)),universal_class),
inference(forward_demodulation,[],[f711411,f250489]) ).
fof(f250489,plain,
! [X34] : null_class = intersection(null_class,X34),
inference(resolution,[],[f19515,f2245]) ).
fof(f19515,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literal_removal,[],[f19428]) ).
fof(f19428,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[],[f114,f3]) ).
fof(f114,plain,
! [X6,X4,X5] :
( member(not_subclass_element(intersection(X4,X5),X6),X4)
| subclass(intersection(X4,X5),X6) ),
inference(resolution,[],[f21,f2]) ).
fof(f711411,plain,
intersection(null_class,universal_class) = symmetric_difference(complement(singleton(u)),universal_class),
inference(forward_demodulation,[],[f711410,f681236]) ).
fof(f681236,plain,
null_class = sF1,
inference(subsumption_resolution,[],[f663131,f681177]) ).
fof(f681177,plain,
! [X0] : ~ member(X0,sF1),
inference(subsumption_resolution,[],[f681166,f24]) ).
fof(f681166,plain,
! [X0] :
( member(X0,complement(sF1))
| ~ member(X0,sF1) ),
inference(resolution,[],[f681164,f664985]) ).
fof(f664985,plain,
! [X2,X1] :
( ~ member(u,X1)
| member(X2,X1)
| ~ member(X2,sF1) ),
inference(superposition,[],[f21,f663976]) ).
fof(f663976,plain,
! [X8] :
( sF1 = intersection(X8,sF1)
| ~ member(u,X8) ),
inference(subsumption_resolution,[],[f663954,f20086]) ).
fof(f663954,plain,
! [X8] :
( ~ member(u,X8)
| ~ subclass(intersection(X8,sF1),sF1)
| sF1 = intersection(X8,sF1) ),
inference(resolution,[],[f663485,f7]) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',subclass_implies_equal) ).
fof(f663485,plain,
! [X29] :
( subclass(sF1,intersection(X29,sF1))
| ~ member(u,X29) ),
inference(duplicate_literal_removal,[],[f663472]) ).
fof(f663472,plain,
! [X29] :
( ~ member(u,X29)
| subclass(sF1,intersection(X29,sF1))
| subclass(sF1,intersection(X29,sF1)) ),
inference(superposition,[],[f132700,f663038]) ).
fof(f663038,plain,
! [X1] :
( u = not_subclass_element(sF1,X1)
| subclass(sF1,X1) ),
inference(resolution,[],[f662995,f2]) ).
fof(f662995,plain,
! [X0] :
( ~ member(X0,sF1)
| u = X0 ),
inference(resolution,[],[f662981,f766]) ).
fof(f766,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1 ),
inference(duplicate_literal_removal,[],[f765]) ).
fof(f765,plain,
! [X0,X1] :
( ~ member(X1,singleton(X0))
| X0 = X1
| X0 = X1 ),
inference(superposition,[],[f8,f12]) ).
fof(f8,axiom,
! [X2,X0,X1] :
( ~ member(X2,unordered_pair(X0,X1))
| X0 = X2
| X1 = X2 ),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',unordered_pair_member) ).
fof(f662981,plain,
! [X0] :
( member(X0,singleton(u))
| ~ member(X0,sF1) ),
inference(subsumption_resolution,[],[f662908,f52491]) ).
fof(f52491,plain,
! [X82,X83,X84] :
( ~ member(X82,X84)
| ~ member(X82,X83)
| member(X82,universal_class) ),
inference(resolution,[],[f1180,f4]) ).
fof(f1180,plain,
! [X8,X6,X9,X7] :
( ~ subclass(intersection(X8,X7),X9)
| ~ member(X6,X8)
| ~ member(X6,X7)
| member(X6,X9) ),
inference(resolution,[],[f23,f1]) ).
fof(f23,axiom,
! [X0,X1,X4] :
( member(X4,intersection(X0,X1))
| ~ member(X4,X1)
| ~ member(X4,X0) ),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',intersection3) ).
fof(f662908,plain,
! [X0] :
( ~ member(X0,sF1)
| member(X0,singleton(u))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f661773,f25]) ).
fof(f25,axiom,
! [X0,X4] :
( member(X4,complement(X0))
| member(X4,X0)
| ~ member(X4,universal_class) ),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',complement2) ).
fof(f661773,plain,
! [X0] :
( ~ member(X0,complement(singleton(u)))
| ~ member(X0,sF1) ),
inference(superposition,[],[f568170,f661102]) ).
fof(f661102,plain,
sF1 = set_builder(u,null_class),
inference(superposition,[],[f99,f661082]) ).
fof(f661082,plain,
null_class = sF0,
inference(resolution,[],[f661054,f2245]) ).
fof(f661054,plain,
subclass(sF0,null_class),
inference(subsumption_resolution,[],[f661045,f661021]) ).
fof(f661021,plain,
! [X0] :
( member(z,sF1)
| subclass(sF0,X0) ),
inference(resolution,[],[f661020,f625027]) ).
fof(f625027,plain,
! [X2,X3] :
( ~ subclass(sF0,X3)
| member(z,X3)
| subclass(sF0,X2) ),
inference(duplicate_literal_removal,[],[f624992]) ).
fof(f624992,plain,
! [X2,X3] :
( member(z,X3)
| ~ subclass(sF0,X3)
| subclass(sF0,X2)
| subclass(sF0,X2) ),
inference(superposition,[],[f138,f619195]) ).
fof(f619195,plain,
! [X0] :
( z = not_subclass_element(sF0,X0)
| subclass(sF0,X0) ),
inference(resolution,[],[f619161,f2]) ).
fof(f619161,plain,
! [X0] :
( ~ member(X0,sF0)
| z = X0 ),
inference(resolution,[],[f619152,f766]) ).
fof(f619152,plain,
! [X0] :
( member(X0,singleton(z))
| ~ member(X0,sF0) ),
inference(subsumption_resolution,[],[f619084,f52491]) ).
fof(f619084,plain,
! [X0] :
( ~ member(X0,sF0)
| member(X0,singleton(z))
| ~ member(X0,universal_class) ),
inference(resolution,[],[f619077,f25]) ).
fof(f619077,plain,
! [X3] :
( ~ member(X3,complement(singleton(z)))
| ~ member(X3,sF0) ),
inference(superposition,[],[f568170,f98]) ).
fof(f661020,plain,
subclass(sF0,sF1),
inference(subsumption_resolution,[],[f661008,f393391]) ).
fof(f393391,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ subclass(X0,complement(X0)) ),
inference(duplicate_literal_removal,[],[f393314]) ).
fof(f393314,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ subclass(X0,complement(X0))
| subclass(X0,X1) ),
inference(resolution,[],[f15716,f2]) ).
fof(f15716,plain,
! [X41,X42,X43] :
( ~ member(not_subclass_element(X41,X43),X42)
| subclass(X41,X43)
| ~ subclass(X41,complement(X42)) ),
inference(resolution,[],[f138,f24]) ).
fof(f661008,plain,
( subclass(sF0,sF1)
| subclass(sF0,complement(sF0)) ),
inference(resolution,[],[f660958,f625028]) ).
fof(f625028,plain,
! [X1] :
( ~ member(z,X1)
| subclass(sF0,X1) ),
inference(duplicate_literal_removal,[],[f624991]) ).
fof(f624991,plain,
! [X1] :
( ~ member(z,X1)
| subclass(sF0,X1)
| subclass(sF0,X1) ),
inference(superposition,[],[f3,f619195]) ).
fof(f660958,plain,
( member(z,complement(sF0))
| subclass(sF0,sF1) ),
inference(superposition,[],[f655317,f99]) ).
fof(f655317,plain,
! [X36,X35] :
( subclass(sF0,set_builder(X35,X36))
| member(z,complement(X36)) ),
inference(superposition,[],[f625103,f92]) ).
fof(f625103,plain,
! [X29,X30] :
( subclass(sF0,union(X29,X30))
| member(z,complement(X30)) ),
inference(subsumption_resolution,[],[f625072,f619255]) ).
fof(f619255,plain,
! [X0] :
( member(z,universal_class)
| subclass(sF0,X0) ),
inference(resolution,[],[f619251,f2]) ).
fof(f619251,plain,
! [X0] :
( ~ member(X0,sF0)
| member(z,universal_class) ),
inference(resolution,[],[f619157,f608098]) ).
fof(f608098,plain,
! [X21,X20] :
( subclass(singleton(X20),X21)
| member(X20,universal_class) ),
inference(resolution,[],[f607994,f556968]) ).
fof(f556968,plain,
! [X18,X17] :
( ~ subclass(X17,null_class)
| subclass(X17,X18) ),
inference(forward_demodulation,[],[f556846,f262889]) ).
fof(f556846,plain,
! [X18,X17] :
( ~ subclass(X17,symmetric_difference(singleton(x),sF1))
| subclass(X17,X18) ),
inference(subsumption_resolution,[],[f126762,f556840]) ).
fof(f126762,plain,
! [X18,X17] :
( member(not_subclass_element(X17,X18),null_class)
| ~ subclass(X17,symmetric_difference(singleton(x),sF1))
| subclass(X17,X18) ),
inference(resolution,[],[f126711,f138]) ).
fof(f607994,plain,
! [X0] :
( subclass(singleton(X0),null_class)
| member(X0,universal_class) ),
inference(resolution,[],[f607980,f22]) ).
fof(f607980,plain,
! [X4] :
( member(X4,intersection(universal_class,universal_class))
| subclass(singleton(X4),null_class) ),
inference(duplicate_literal_removal,[],[f607973]) ).
fof(f607973,plain,
! [X4] :
( member(X4,intersection(universal_class,universal_class))
| subclass(singleton(X4),null_class)
| subclass(singleton(X4),null_class) ),
inference(superposition,[],[f575894,f770]) ).
fof(f770,plain,
! [X3,X4] :
( not_subclass_element(singleton(X3),X4) = X3
| subclass(singleton(X3),X4) ),
inference(resolution,[],[f766,f2]) ).
fof(f575894,plain,
! [X60] :
( member(not_subclass_element(X60,null_class),intersection(universal_class,universal_class))
| subclass(X60,null_class) ),
inference(superposition,[],[f98842,f575758]) ).
fof(f575758,plain,
null_class = complement(intersection(universal_class,universal_class)),
inference(subsumption_resolution,[],[f575666,f567526]) ).
fof(f567526,plain,
! [X6] : subclass(union(null_class,null_class),X6),
inference(resolution,[],[f567478,f2]) ).
fof(f567478,plain,
! [X9] : ~ member(X9,union(null_class,null_class)),
inference(subsumption_resolution,[],[f567477,f562171]) ).
fof(f562171,plain,
! [X1] :
( ~ member(X1,union(null_class,null_class))
| member(X1,universal_class) ),
inference(forward_literal_rewriting,[],[f562130,f559274]) ).
fof(f559274,plain,
! [X0] :
( ~ member(X0,union(null_class,null_class))
| member(X0,symmetric_difference(universal_class,universal_class)) ),
inference(subsumption_resolution,[],[f559273,f52491]) ).
fof(f559273,plain,
! [X0] :
( ~ member(X0,universal_class)
| ~ member(X0,union(null_class,null_class))
| member(X0,symmetric_difference(universal_class,universal_class)) ),
inference(forward_demodulation,[],[f559203,f557150]) ).
fof(f557150,plain,
! [X4] : universal_class = union(X4,universal_class),
inference(resolution,[],[f556848,f184]) ).
fof(f184,plain,
! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 ),
inference(resolution,[],[f7,f4]) ).
fof(f556848,plain,
! [X32,X33] : subclass(X33,union(X32,universal_class)),
inference(subsumption_resolution,[],[f310500,f556840]) ).
fof(f310500,plain,
! [X32,X33] :
( member(not_subclass_element(X33,union(X32,universal_class)),null_class)
| subclass(X33,union(X32,universal_class)) ),
inference(forward_demodulation,[],[f310197,f262659]) ).
fof(f262659,plain,
! [X34] : null_class = intersection(X34,null_class),
inference(resolution,[],[f20086,f2245]) ).
fof(f310197,plain,
! [X32,X33] :
( member(not_subclass_element(X33,union(X32,universal_class)),intersection(complement(X32),null_class))
| subclass(X33,union(X32,universal_class)) ),
inference(superposition,[],[f98842,f662]) ).
fof(f662,plain,
! [X3] : union(X3,universal_class) = complement(intersection(complement(X3),null_class)),
inference(superposition,[],[f26,f653]) ).
fof(f559203,plain,
! [X0] :
( ~ member(X0,union(null_class,null_class))
| ~ member(X0,union(universal_class,universal_class))
| member(X0,symmetric_difference(universal_class,universal_class)) ),
inference(superposition,[],[f1861,f559175]) ).
fof(f559175,plain,
union(null_class,null_class) = complement(intersection(universal_class,universal_class)),
inference(forward_demodulation,[],[f559174,f250489]) ).
fof(f559174,plain,
complement(intersection(universal_class,universal_class)) = union(null_class,intersection(null_class,null_class)),
inference(forward_demodulation,[],[f559086,f557150]) ).
fof(f559086,plain,
union(null_class,intersection(null_class,null_class)) = complement(intersection(universal_class,union(universal_class,universal_class))),
inference(superposition,[],[f557074,f696]) ).
fof(f696,plain,
union(universal_class,universal_class) = complement(intersection(null_class,null_class)),
inference(superposition,[],[f661,f653]) ).
fof(f661,plain,
! [X2] : union(universal_class,X2) = complement(intersection(null_class,complement(X2))),
inference(superposition,[],[f26,f653]) ).
fof(f557074,plain,
! [X7] : union(null_class,X7) = complement(intersection(universal_class,complement(X7))),
inference(superposition,[],[f26,f557019]) ).
fof(f557019,plain,
universal_class = complement(null_class),
inference(resolution,[],[f556967,f184]) ).
fof(f556967,plain,
! [X30] : subclass(X30,complement(null_class)),
inference(forward_demodulation,[],[f556847,f555827]) ).
fof(f555827,plain,
! [X1123] : complement(null_class) = union(universal_class,X1123),
inference(subsumption_resolution,[],[f555509,f15778]) ).
fof(f555509,plain,
! [X1123] :
( complement(null_class) = union(universal_class,X1123)
| ~ subclass(null_class,null_class) ),
inference(superposition,[],[f661,f554418]) ).
fof(f556847,plain,
! [X29,X30] : subclass(X30,union(universal_class,X29)),
inference(subsumption_resolution,[],[f310498,f556840]) ).
fof(f310498,plain,
! [X29,X30] :
( member(not_subclass_element(X30,union(universal_class,X29)),null_class)
| subclass(X30,union(universal_class,X29)) ),
inference(forward_demodulation,[],[f310195,f250489]) ).
fof(f310195,plain,
! [X29,X30] :
( member(not_subclass_element(X30,union(universal_class,X29)),intersection(null_class,complement(X29)))
| subclass(X30,union(universal_class,X29)) ),
inference(superposition,[],[f98842,f661]) ).
fof(f1861,plain,
! [X8,X6,X7] :
( ~ member(X8,complement(intersection(X6,X7)))
| ~ member(X8,union(X6,X7))
| member(X8,symmetric_difference(X6,X7)) ),
inference(superposition,[],[f23,f102]) ).
fof(f562130,plain,
! [X1] :
( ~ member(X1,symmetric_difference(universal_class,universal_class))
| member(X1,universal_class) ),
inference(superposition,[],[f22,f559275]) ).
fof(f559275,plain,
symmetric_difference(universal_class,universal_class) = intersection(union(null_class,null_class),universal_class),
inference(forward_demodulation,[],[f559206,f557150]) ).
fof(f559206,plain,
symmetric_difference(universal_class,universal_class) = intersection(union(null_class,null_class),union(universal_class,universal_class)),
inference(superposition,[],[f102,f559175]) ).
fof(f567477,plain,
! [X9] :
( ~ member(X9,universal_class)
| ~ member(X9,union(null_class,null_class)) ),
inference(forward_demodulation,[],[f567466,f563220]) ).
fof(f563220,plain,
universal_class = complement(domain_of(null_class)),
inference(resolution,[],[f563209,f184]) ).
fof(f563209,plain,
subclass(universal_class,complement(domain_of(null_class))),
inference(duplicate_literal_removal,[],[f563200]) ).
fof(f563200,plain,
( subclass(universal_class,complement(domain_of(null_class)))
| subclass(universal_class,complement(domain_of(null_class))) ),
inference(resolution,[],[f560200,f98842]) ).
fof(f560200,plain,
! [X0] :
( ~ member(not_subclass_element(universal_class,X0),domain_of(null_class))
| subclass(universal_class,X0) ),
inference(forward_demodulation,[],[f560186,f250489]) ).
fof(f560186,plain,
! [X0] :
( ~ member(not_subclass_element(universal_class,X0),domain_of(intersection(null_class,identity_relation)))
| subclass(universal_class,X0) ),
inference(superposition,[],[f616,f560174]) ).
fof(f560174,plain,
universal_class = diagonalise(null_class),
inference(resolution,[],[f557766,f19515]) ).
fof(f557766,plain,
! [X64] :
( ~ subclass(intersection(X64,identity_relation),null_class)
| universal_class = diagonalise(X64) ),
inference(forward_demodulation,[],[f557731,f557019]) ).
fof(f557731,plain,
! [X64] :
( complement(null_class) = diagonalise(X64)
| ~ subclass(intersection(X64,identity_relation),null_class) ),
inference(superposition,[],[f76,f557603]) ).
fof(f557603,plain,
! [X34] :
( null_class = domain_of(X34)
| ~ subclass(X34,null_class) ),
inference(resolution,[],[f557581,f66]) ).
fof(f557581,plain,
! [X62,X61] :
( ~ member(X62,domain_of(X61))
| ~ subclass(X61,null_class) ),
inference(trivial_inequality_removal,[],[f557562]) ).
fof(f557562,plain,
! [X62,X61] :
( null_class != null_class
| ~ member(X62,domain_of(X61))
| ~ subclass(X61,null_class) ),
inference(superposition,[],[f30,f554419]) ).
fof(f554419,plain,
! [X2,X3,X4] :
( null_class = restrict(X2,X3,X4)
| ~ subclass(X2,null_class) ),
inference(superposition,[],[f554418,f28]) ).
fof(f28,axiom,
! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',restriction1) ).
fof(f30,axiom,
! [X0,X4] :
( restrict(X0,singleton(X4),universal_class) != null_class
| ~ member(X4,domain_of(X0)) ),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',domain1) ).
fof(f76,axiom,
! [X5] : complement(domain_of(intersection(X5,identity_relation))) = diagonalise(X5),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',diagonalisation) ).
fof(f616,plain,
! [X2,X3] :
( ~ member(not_subclass_element(diagonalise(X2),X3),domain_of(intersection(X2,identity_relation)))
| subclass(diagonalise(X2),X3) ),
inference(superposition,[],[f107,f76]) ).
fof(f567466,plain,
! [X9] :
( ~ member(X9,union(null_class,null_class))
| ~ member(X9,complement(domain_of(null_class))) ),
inference(superposition,[],[f564069,f563408]) ).
fof(f563408,plain,
! [X19] : union(X19,null_class) = union(X19,domain_of(null_class)),
inference(forward_demodulation,[],[f563336,f557075]) ).
fof(f557075,plain,
! [X8] : union(X8,null_class) = complement(intersection(complement(X8),universal_class)),
inference(superposition,[],[f26,f557019]) ).
fof(f563336,plain,
! [X19] : union(X19,domain_of(null_class)) = complement(intersection(complement(X19),universal_class)),
inference(superposition,[],[f26,f563220]) ).
fof(f564069,plain,
! [X14,X13] :
( ~ member(X14,union(null_class,X13))
| ~ member(X14,complement(X13)) ),
inference(subsumption_resolution,[],[f564068,f52491]) ).
fof(f564068,plain,
! [X14,X13] :
( ~ member(X14,universal_class)
| ~ member(X14,union(null_class,X13))
| ~ member(X14,complement(X13)) ),
inference(forward_demodulation,[],[f564029,f563220]) ).
fof(f564029,plain,
! [X14,X13] :
( ~ member(X14,union(null_class,X13))
| ~ member(X14,complement(X13))
| ~ member(X14,complement(domain_of(null_class))) ),
inference(superposition,[],[f22471,f563407]) ).
fof(f563407,plain,
! [X18] : union(null_class,X18) = union(domain_of(null_class),X18),
inference(forward_demodulation,[],[f563335,f557074]) ).
fof(f563335,plain,
! [X18] : union(domain_of(null_class),X18) = complement(intersection(universal_class,complement(X18))),
inference(superposition,[],[f26,f563220]) ).
fof(f22471,plain,
! [X2,X0,X1] :
( ~ member(X0,union(X1,X2))
| ~ member(X0,complement(X2))
| ~ member(X0,complement(X1)) ),
inference(resolution,[],[f567,f23]) ).
fof(f575666,plain,
( null_class = complement(intersection(universal_class,universal_class))
| ~ subclass(union(null_class,null_class),null_class) ),
inference(superposition,[],[f575639,f567517]) ).
fof(f567517,plain,
intersection(universal_class,universal_class) = symmetric_difference(union(null_class,null_class),universal_class),
inference(forward_demodulation,[],[f567516,f557019]) ).
fof(f567516,plain,
intersection(complement(null_class),universal_class) = symmetric_difference(union(null_class,null_class),universal_class),
inference(forward_demodulation,[],[f567515,f559175]) ).
fof(f567515,plain,
intersection(complement(null_class),universal_class) = symmetric_difference(complement(intersection(universal_class,universal_class)),universal_class),
inference(forward_demodulation,[],[f567514,f557150]) ).
fof(f567514,plain,
symmetric_difference(complement(intersection(universal_class,universal_class)),universal_class) = intersection(complement(null_class),union(complement(intersection(universal_class,universal_class)),universal_class)),
inference(forward_demodulation,[],[f567505,f557150]) ).
fof(f567505,plain,
symmetric_difference(complement(intersection(universal_class,universal_class)),union(universal_class,universal_class)) = intersection(complement(null_class),union(complement(intersection(universal_class,universal_class)),union(universal_class,universal_class))),
inference(superposition,[],[f1850,f567488]) ).
fof(f567488,plain,
null_class = symmetric_difference(universal_class,universal_class),
inference(subsumption_resolution,[],[f559201,f567478]) ).
fof(f559201,plain,
( member(regular(symmetric_difference(universal_class,universal_class)),union(null_class,null_class))
| null_class = symmetric_difference(universal_class,universal_class) ),
inference(superposition,[],[f13627,f559175]) ).
fof(f13627,plain,
! [X8,X9] :
( member(regular(symmetric_difference(X8,X9)),complement(intersection(X8,X9)))
| null_class = symmetric_difference(X8,X9) ),
inference(superposition,[],[f113,f102]) ).
fof(f1850,plain,
! [X10,X11] : symmetric_difference(complement(intersection(X10,X11)),union(X10,X11)) = intersection(complement(symmetric_difference(X10,X11)),union(complement(intersection(X10,X11)),union(X10,X11))),
inference(superposition,[],[f102,f102]) ).
fof(f575639,plain,
! [X1] :
( null_class = complement(symmetric_difference(X1,universal_class))
| ~ subclass(X1,null_class) ),
inference(forward_demodulation,[],[f575607,f567573]) ).
fof(f567573,plain,
null_class = union(null_class,null_class),
inference(forward_demodulation,[],[f567571,f567488]) ).
fof(f567571,plain,
union(null_class,null_class) = symmetric_difference(universal_class,universal_class),
inference(subsumption_resolution,[],[f562180,f567526]) ).
fof(f562180,plain,
( ~ subclass(union(null_class,null_class),symmetric_difference(universal_class,universal_class))
| union(null_class,null_class) = symmetric_difference(universal_class,universal_class) ),
inference(resolution,[],[f562165,f7]) ).
fof(f562165,plain,
subclass(symmetric_difference(universal_class,universal_class),union(null_class,null_class)),
inference(superposition,[],[f19515,f559275]) ).
fof(f575607,plain,
! [X1] :
( union(null_class,null_class) = complement(symmetric_difference(X1,universal_class))
| ~ subclass(X1,null_class) ),
inference(superposition,[],[f571874,f554418]) ).
fof(f571874,plain,
! [X3] : complement(symmetric_difference(X3,universal_class)) = union(intersection(X3,universal_class),null_class),
inference(superposition,[],[f557075,f557255]) ).
fof(f557255,plain,
! [X4] : symmetric_difference(X4,universal_class) = intersection(complement(intersection(X4,universal_class)),universal_class),
inference(superposition,[],[f102,f557150]) ).
fof(f98842,plain,
! [X6,X7] :
( member(not_subclass_element(X6,complement(X7)),X7)
| subclass(X6,complement(X7)) ),
inference(subsumption_resolution,[],[f98837,f4]) ).
fof(f98837,plain,
! [X6,X7] :
( member(not_subclass_element(X6,complement(X7)),X7)
| subclass(X6,complement(X7))
| ~ subclass(X6,universal_class) ),
inference(duplicate_literal_removal,[],[f98717]) ).
fof(f98717,plain,
! [X6,X7] :
( member(not_subclass_element(X6,complement(X7)),X7)
| subclass(X6,complement(X7))
| ~ subclass(X6,universal_class)
| subclass(X6,complement(X7)) ),
inference(resolution,[],[f551,f138]) ).
fof(f551,plain,
! [X6,X5] :
( ~ member(not_subclass_element(X5,complement(X6)),universal_class)
| member(not_subclass_element(X5,complement(X6)),X6)
| subclass(X5,complement(X6)) ),
inference(resolution,[],[f25,f3]) ).
fof(f619157,plain,
! [X0] :
( ~ subclass(singleton(z),null_class)
| ~ member(X0,sF0) ),
inference(subsumption_resolution,[],[f619151,f52491]) ).
fof(f619151,plain,
! [X0] :
( ~ member(X0,universal_class)
| ~ member(X0,sF0)
| ~ subclass(singleton(z),null_class) ),
inference(superposition,[],[f619077,f595017]) ).
fof(f595017,plain,
! [X68] :
( universal_class = complement(X68)
| ~ subclass(X68,null_class) ),
inference(resolution,[],[f594509,f184]) ).
fof(f594509,plain,
! [X31,X30] :
( subclass(X31,complement(X30))
| ~ subclass(X30,null_class) ),
inference(resolution,[],[f594493,f98842]) ).
fof(f594493,plain,
! [X6,X7] :
( ~ member(X6,X7)
| ~ subclass(X7,null_class) ),
inference(subsumption_resolution,[],[f594480,f555819]) ).
fof(f555819,plain,
! [X65,X68,X66,X67] :
( ~ member(X68,X65)
| ~ member(X68,X66)
| member(X68,X67)
| ~ subclass(X65,null_class) ),
inference(subsumption_resolution,[],[f554621,f15778]) ).
fof(f554621,plain,
! [X65,X68,X66,X67] :
( ~ subclass(null_class,X67)
| ~ member(X68,X65)
| ~ member(X68,X66)
| member(X68,X67)
| ~ subclass(X65,null_class) ),
inference(superposition,[],[f1180,f554418]) ).
fof(f594480,plain,
! [X8,X6,X9,X7] :
( ~ member(X6,X7)
| ~ subclass(X7,null_class)
| ~ member(X6,cross_product(X8,X9)) ),
inference(superposition,[],[f593869,f17]) ).
fof(f17,axiom,
! [X0,X1,X4] :
( ordered_pair(first(X4),second(X4)) = X4
| ~ member(X4,cross_product(X0,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',cartesian_product4) ).
fof(f593869,plain,
! [X10,X11,X12] :
( ~ member(ordered_pair(X10,X11),X12)
| ~ subclass(X12,null_class) ),
inference(superposition,[],[f593804,f13]) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',ordered_pair) ).
fof(f593804,plain,
! [X2,X0,X1] :
( ~ member(unordered_pair(X1,X2),X0)
| ~ subclass(X0,null_class) ),
inference(subsumption_resolution,[],[f593773,f11]) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',unordered_pairs_in_universal) ).
fof(f593773,plain,
! [X2,X0,X1] :
( ~ subclass(X0,null_class)
| ~ member(unordered_pair(X1,X2),universal_class)
| ~ member(unordered_pair(X1,X2),X0) ),
inference(resolution,[],[f583900,f23]) ).
fof(f583900,plain,
! [X2,X3,X1] :
( ~ member(unordered_pair(X2,X3),intersection(X1,universal_class))
| ~ subclass(X1,null_class) ),
inference(resolution,[],[f575769,f18937]) ).
fof(f18937,plain,
! [X2,X3,X1] :
( ~ member(X1,symmetric_difference(X2,X3))
| ~ member(X1,intersection(X2,X3)) ),
inference(resolution,[],[f1859,f24]) ).
fof(f1859,plain,
! [X2,X0,X1] :
( member(X2,complement(intersection(X0,X1)))
| ~ member(X2,symmetric_difference(X0,X1)) ),
inference(superposition,[],[f21,f102]) ).
fof(f575769,plain,
! [X28,X29,X27] :
( member(unordered_pair(X28,X29),symmetric_difference(X27,universal_class))
| ~ subclass(X27,null_class) ),
inference(subsumption_resolution,[],[f575686,f556967]) ).
fof(f575686,plain,
! [X28,X29,X27] :
( ~ subclass(universal_class,complement(null_class))
| member(unordered_pair(X28,X29),symmetric_difference(X27,universal_class))
| ~ subclass(X27,null_class) ),
inference(superposition,[],[f557,f575639]) ).
fof(f557,plain,
! [X8,X9,X7] :
( ~ subclass(universal_class,complement(complement(X9)))
| member(unordered_pair(X7,X8),X9) ),
inference(subsumption_resolution,[],[f552,f11]) ).
fof(f552,plain,
! [X8,X9,X7] :
( member(unordered_pair(X7,X8),X9)
| ~ member(unordered_pair(X7,X8),universal_class)
| ~ subclass(universal_class,complement(complement(X9))) ),
inference(resolution,[],[f25,f218]) ).
fof(f218,plain,
! [X14,X12,X13] :
( ~ member(unordered_pair(X13,X14),X12)
| ~ subclass(universal_class,complement(X12)) ),
inference(resolution,[],[f139,f24]) ).
fof(f139,plain,
! [X8,X9,X7] :
( member(unordered_pair(X8,X9),X7)
| ~ subclass(universal_class,X7) ),
inference(resolution,[],[f1,f11]) ).
fof(f625072,plain,
! [X29,X30] :
( subclass(sF0,union(X29,X30))
| ~ member(z,universal_class)
| member(z,complement(X30)) ),
inference(resolution,[],[f625028,f85769]) ).
fof(f85769,plain,
! [X3,X4,X5] :
( member(X3,union(X4,X5))
| ~ member(X3,universal_class)
| member(X3,complement(X5)) ),
inference(resolution,[],[f568,f22]) ).
fof(f568,plain,
! [X3,X4,X5] :
( member(X5,intersection(complement(X3),complement(X4)))
| member(X5,union(X3,X4))
| ~ member(X5,universal_class) ),
inference(superposition,[],[f25,f26]) ).
fof(f661045,plain,
( subclass(sF0,null_class)
| ~ member(z,sF1) ),
inference(resolution,[],[f660963,f24]) ).
fof(f660963,plain,
( member(z,complement(sF1))
| subclass(sF0,null_class) ),
inference(forward_demodulation,[],[f660960,f101]) ).
fof(f660960,plain,
( subclass(sF0,sF2)
| member(z,complement(sF1)) ),
inference(superposition,[],[f655317,f100]) ).
fof(f568170,plain,
! [X4,X5] :
( ~ member(X5,set_builder(X4,null_class))
| ~ member(X5,complement(singleton(X4))) ),
inference(superposition,[],[f564126,f92]) ).
fof(f564126,plain,
! [X14,X13] :
( ~ member(X14,union(X13,null_class))
| ~ member(X14,complement(X13)) ),
inference(subsumption_resolution,[],[f564125,f52491]) ).
fof(f564125,plain,
! [X14,X13] :
( ~ member(X14,universal_class)
| ~ member(X14,union(X13,null_class))
| ~ member(X14,complement(X13)) ),
inference(forward_demodulation,[],[f564094,f563220]) ).
fof(f564094,plain,
! [X14,X13] :
( ~ member(X14,union(X13,null_class))
| ~ member(X14,complement(domain_of(null_class)))
| ~ member(X14,complement(X13)) ),
inference(superposition,[],[f22471,f563408]) ).
fof(f132700,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
| subclass(X0,intersection(X1,X0)) ),
inference(duplicate_literal_removal,[],[f132501]) ).
fof(f132501,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
| subclass(X0,intersection(X1,X0))
| subclass(X0,intersection(X1,X0)) ),
inference(resolution,[],[f1181,f2]) ).
fof(f1181,plain,
! [X10,X11,X12] :
( ~ member(not_subclass_element(X10,intersection(X11,X12)),X12)
| ~ member(not_subclass_element(X10,intersection(X11,X12)),X11)
| subclass(X10,intersection(X11,X12)) ),
inference(resolution,[],[f23,f3]) ).
fof(f681164,plain,
member(u,complement(sF1)),
inference(subsumption_resolution,[],[f681163,f595015]) ).
fof(f595015,plain,
! [X65] :
( member(u,complement(X65))
| ~ subclass(X65,null_class) ),
inference(resolution,[],[f594509,f144]) ).
fof(f144,plain,
! [X17] :
( ~ subclass(universal_class,X17)
| member(u,X17) ),
inference(resolution,[],[f1,f93]) ).
fof(f681163,plain,
( subclass(sF1,null_class)
| member(u,complement(sF1)) ),
inference(forward_demodulation,[],[f681159,f101]) ).
fof(f681159,plain,
( subclass(sF1,sF2)
| member(u,complement(sF1)) ),
inference(superposition,[],[f678348,f100]) ).
fof(f678348,plain,
! [X38,X37] :
( subclass(sF1,set_builder(X37,X38))
| member(u,complement(X38)) ),
inference(superposition,[],[f663600,f92]) ).
fof(f663600,plain,
! [X34,X33] :
( subclass(sF1,union(X33,X34))
| member(u,complement(X34)) ),
inference(subsumption_resolution,[],[f663549,f93]) ).
fof(f663549,plain,
! [X34,X33] :
( subclass(sF1,union(X33,X34))
| ~ member(u,universal_class)
| member(u,complement(X34)) ),
inference(resolution,[],[f663499,f85769]) ).
fof(f663499,plain,
! [X1] :
( ~ member(u,X1)
| subclass(sF1,X1) ),
inference(duplicate_literal_removal,[],[f663458]) ).
fof(f663458,plain,
! [X1] :
( ~ member(u,X1)
| subclass(sF1,X1)
| subclass(sF1,X1) ),
inference(superposition,[],[f3,f663038]) ).
fof(f663131,plain,
( member(u,sF1)
| null_class = sF1 ),
inference(duplicate_literal_removal,[],[f663106]) ).
fof(f663106,plain,
( member(u,sF1)
| null_class = sF1
| null_class = sF1 ),
inference(superposition,[],[f66,f663045]) ).
fof(f663045,plain,
( u = regular(sF1)
| null_class = sF1 ),
inference(resolution,[],[f662995,f66]) ).
fof(f711410,plain,
intersection(sF1,universal_class) = symmetric_difference(complement(singleton(u)),universal_class),
inference(forward_demodulation,[],[f711409,f557150]) ).
fof(f711409,plain,
symmetric_difference(complement(singleton(u)),universal_class) = intersection(sF1,union(complement(singleton(u)),universal_class)),
inference(forward_demodulation,[],[f711175,f557019]) ).
fof(f711175,plain,
symmetric_difference(complement(singleton(u)),complement(null_class)) = intersection(sF1,union(complement(singleton(u)),complement(null_class))),
inference(superposition,[],[f92437,f661102]) ).
fof(f92437,plain,
! [X62,X63] : symmetric_difference(complement(singleton(X62)),complement(X63)) = intersection(set_builder(X62,X63),union(complement(singleton(X62)),complement(X63))),
inference(superposition,[],[f1853,f92]) ).
fof(f1853,plain,
! [X0,X1] : symmetric_difference(complement(X0),complement(X1)) = intersection(union(X0,X1),union(complement(X0),complement(X1))),
inference(superposition,[],[f102,f26]) ).
fof(f620339,plain,
! [X31] :
( member(u,symmetric_difference(X31,universal_class))
| member(u,intersection(X31,universal_class)) ),
inference(resolution,[],[f99630,f557148]) ).
fof(f557148,plain,
! [X1] : member(u,union(X1,universal_class)),
inference(resolution,[],[f556848,f144]) ).
fof(f99630,plain,
! [X3,X4,X5] :
( ~ member(X3,union(X4,X5))
| member(X3,symmetric_difference(X4,X5))
| member(X3,intersection(X4,X5)) ),
inference(subsumption_resolution,[],[f99463,f52491]) ).
fof(f99463,plain,
! [X3,X4,X5] :
( ~ member(X3,union(X4,X5))
| member(X3,symmetric_difference(X4,X5))
| member(X3,intersection(X4,X5))
| ~ member(X3,universal_class) ),
inference(resolution,[],[f1861,f25]) ).
fof(f93,axiom,
member(u,universal_class),
file('/export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412',prove_corollary_3_to_member_of_triple_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET135-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 15:56:40 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.14/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.YqiL2Vqt5L/Vampire---4.8_31412
% 0.14/0.37 % (31557)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (31561)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.22/0.43 % (31563)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.22/0.43 % (31560)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 0.22/0.43 % (31558)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_1192 on Vampire---4 for (1192ds/0Mi)
% 0.22/0.43 % (31559)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.22/0.43 % (31564)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_520 on Vampire---4 for (520ds/0Mi)
% 0.22/0.44 % (31565)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 92.05/13.62 % (31558)First to succeed.
% 92.05/13.64 % (31558)Refutation found. Thanks to Tanya!
% 92.05/13.64 % SZS status Unsatisfiable for Vampire---4
% 92.05/13.64 % SZS output start Proof for Vampire---4
% See solution above
% 92.05/13.64 % (31558)------------------------------
% 92.05/13.64 % (31558)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 92.05/13.64 % (31558)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 92.05/13.64 % (31558)Termination reason: Refutation
% 92.05/13.64
% 92.05/13.64 % (31558)Memory used [KB]: 148910
% 92.05/13.64 % (31558)Time elapsed: 13.210 s
% 92.05/13.64 % (31558)------------------------------
% 92.05/13.64 % (31558)------------------------------
% 92.05/13.64 % (31557)Success in time 13.159 s
% 92.05/13.64 % Vampire---4.8 exiting
%------------------------------------------------------------------------------