TSTP Solution File: SET067-6 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET067-6 : 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 : n004.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 15:36:14 EDT 2023
% Result : Unsatisfiable 0.22s 0.48s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 20
% Syntax : Number of formulae : 68 ( 17 unt; 0 def)
% Number of atoms : 137 ( 30 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 124 ( 55 ~; 69 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 10 con; 0-2 aty)
% Number of variables : 71 (; 71 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1643,plain,
$false,
inference(subsumption_resolution,[],[f1618,f678]) ).
fof(f678,plain,
inductive(universal_class),
inference(resolution,[],[f676,f50]) ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox2/tmp/tmp.mUL9m3Co1S/Vampire---4.8_7463',omega_is_inductive1) ).
fof(f676,plain,
! [X0] :
( ~ inductive(X0)
| inductive(universal_class) ),
inference(resolution,[],[f673,f203]) ).
fof(f203,plain,
! [X0] :
( member(null_class,universal_class)
| ~ inductive(X0) ),
inference(resolution,[],[f137,f4]) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/tmp/tmp.mUL9m3Co1S/Vampire---4.8_7463',class_elements_are_sets) ).
fof(f137,plain,
! [X0,X1] :
( ~ subclass(X0,X1)
| member(null_class,X1)
| ~ inductive(X0) ),
inference(resolution,[],[f1,f47]) ).
fof(f47,axiom,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.mUL9m3Co1S/Vampire---4.8_7463',inductive1) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.mUL9m3Co1S/Vampire---4.8_7463',subclass_members) ).
fof(f673,plain,
( ~ member(null_class,universal_class)
| inductive(universal_class) ),
inference(resolution,[],[f49,f4]) ).
fof(f49,axiom,
! [X0] :
( ~ subclass(image(successor_relation,X0),X0)
| ~ member(null_class,X0)
| inductive(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.mUL9m3Co1S/Vampire---4.8_7463',inductive3) ).
fof(f1618,plain,
~ inductive(universal_class),
inference(superposition,[],[f609,f1603]) ).
fof(f1603,plain,
universal_class = null_class,
inference(resolution,[],[f1588,f1398]) ).
fof(f1398,plain,
~ subclass(null_class,sF1),
inference(superposition,[],[f98,f1397]) ).
fof(f1397,plain,
null_class = sF0,
inference(subsumption_resolution,[],[f1394,f1186]) ).
fof(f1186,plain,
~ member(x,universal_class),
inference(subsumption_resolution,[],[f1182,f98]) ).
fof(f1182,plain,
( subclass(sF0,sF1)
| ~ member(x,universal_class) ),
inference(superposition,[],[f797,f97]) ).
fof(f97,plain,
unordered_pair(x,y) = sF1,
introduced(function_definition,[]) ).
fof(f797,plain,
! [X0] :
( subclass(sF0,unordered_pair(x,X0))
| ~ member(x,universal_class) ),
inference(resolution,[],[f793,f9]) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/tmp/tmp.mUL9m3Co1S/Vampire---4.8_7463',unordered_pair2) ).
fof(f793,plain,
! [X0] :
( ~ member(x,X0)
| subclass(sF0,X0) ),
inference(duplicate_literal_removal,[],[f790]) ).
fof(f790,plain,
! [X0] :
( ~ member(x,X0)
| subclass(sF0,X0)
| subclass(sF0,X0) ),
inference(superposition,[],[f3,f730]) ).
fof(f730,plain,
! [X0] :
( x = not_subclass_element(sF0,X0)
| subclass(sF0,X0) ),
inference(resolution,[],[f719,f2]) ).
fof(f2,axiom,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.mUL9m3Co1S/Vampire---4.8_7463',not_subclass_members1) ).
fof(f719,plain,
! [X0] :
( ~ member(X0,sF0)
| x = X0 ),
inference(superposition,[],[f712,f96]) ).
fof(f96,plain,
singleton(x) = sF0,
introduced(function_definition,[]) ).
fof(f712,plain,
! [X2,X1] :
( ~ member(X2,singleton(X1))
| X1 = X2 ),
inference(duplicate_literal_removal,[],[f711]) ).
fof(f711,plain,
! [X2,X1] :
( ~ member(X2,singleton(X1))
| X1 = X2
| X1 = X2 ),
inference(superposition,[],[f8,f12]) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/tmp/tmp.mUL9m3Co1S/Vampire---4.8_7463',singleton_set) ).
fof(f8,axiom,
! [X2,X0,X1] :
( ~ member(X2,unordered_pair(X0,X1))
| X0 = X2
| X1 = X2 ),
file('/export/starexec/sandbox2/tmp/tmp.mUL9m3Co1S/Vampire---4.8_7463',unordered_pair_member) ).
fof(f3,axiom,
! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.mUL9m3Co1S/Vampire---4.8_7463',not_subclass_members2) ).
fof(f1394,plain,
( null_class = sF0
| member(x,universal_class) ),
inference(resolution,[],[f752,f4]) ).
fof(f752,plain,
! [X0] :
( ~ subclass(sF0,X0)
| null_class = sF0
| member(x,X0) ),
inference(resolution,[],[f749,f1]) ).
fof(f749,plain,
( member(x,sF0)
| null_class = sF0 ),
inference(duplicate_literal_removal,[],[f748]) ).
fof(f748,plain,
( member(x,sF0)
| null_class = sF0
| null_class = sF0 ),
inference(superposition,[],[f66,f729]) ).
fof(f729,plain,
( x = regular(sF0)
| null_class = sF0 ),
inference(resolution,[],[f719,f66]) ).
fof(f66,axiom,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.mUL9m3Co1S/Vampire---4.8_7463',regularity1) ).
fof(f98,plain,
~ subclass(sF0,sF1),
inference(definition_folding,[],[f92,f97,f96]) ).
fof(f92,axiom,
~ subclass(singleton(x),unordered_pair(x,y)),
file('/export/starexec/sandbox2/tmp/tmp.mUL9m3Co1S/Vampire---4.8_7463',prove_singleton_in_unordered_pair1_1) ).
fof(f1588,plain,
! [X4] :
( subclass(null_class,X4)
| universal_class = null_class ),
inference(resolution,[],[f1440,f1186]) ).
fof(f1440,plain,
! [X2,X3] :
( member(x,X3)
| subclass(null_class,X2)
| null_class = X3 ),
inference(resolution,[],[f1408,f274]) ).
fof(f274,plain,
! [X4,X5] :
( ~ member(X5,null_class)
| member(X5,X4)
| null_class = X4 ),
inference(superposition,[],[f21,f67]) ).
fof(f67,axiom,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
file('/export/starexec/sandbox2/tmp/tmp.mUL9m3Co1S/Vampire---4.8_7463',regularity2) ).
fof(f21,axiom,
! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.mUL9m3Co1S/Vampire---4.8_7463',intersection1) ).
fof(f1408,plain,
! [X5] :
( member(x,null_class)
| subclass(null_class,X5) ),
inference(superposition,[],[f792,f1397]) ).
fof(f792,plain,
! [X1] :
( member(x,sF0)
| subclass(sF0,X1) ),
inference(duplicate_literal_removal,[],[f791]) ).
fof(f791,plain,
! [X1] :
( member(x,sF0)
| subclass(sF0,X1)
| subclass(sF0,X1) ),
inference(superposition,[],[f2,f730]) ).
fof(f609,plain,
~ inductive(null_class),
inference(subsumption_resolution,[],[f608,f375]) ).
fof(f375,plain,
! [X3] :
( ~ inductive(null_class)
| ~ member(null_class,X3) ),
inference(duplicate_literal_removal,[],[f351]) ).
fof(f351,plain,
! [X3] :
( ~ inductive(null_class)
| ~ member(null_class,X3)
| ~ inductive(null_class)
| ~ member(null_class,X3) ),
inference(superposition,[],[f104,f278]) ).
fof(f278,plain,
! [X6] :
( null_class = complement(X6)
| ~ inductive(null_class)
| ~ member(null_class,X6) ),
inference(resolution,[],[f273,f24]) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,complement(X0))
| ~ member(X4,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.mUL9m3Co1S/Vampire---4.8_7463',complement1) ).
fof(f273,plain,
! [X3] :
( member(null_class,X3)
| ~ inductive(null_class)
| null_class = X3 ),
inference(superposition,[],[f115,f67]) ).
fof(f115,plain,
! [X0,X1] :
( ~ inductive(intersection(X0,X1))
| member(null_class,X0) ),
inference(resolution,[],[f21,f47]) ).
fof(f104,plain,
! [X0] :
( ~ inductive(complement(X0))
| ~ member(null_class,X0) ),
inference(resolution,[],[f24,f47]) ).
fof(f608,plain,
( member(null_class,subset_relation)
| ~ inductive(null_class) ),
inference(subsumption_resolution,[],[f406,f606]) ).
fof(f606,plain,
! [X2,X3] :
( subclass(X2,X3)
| ~ inductive(null_class) ),
inference(subsumption_resolution,[],[f398,f375]) ).
fof(f398,plain,
! [X2,X3] :
( member(null_class,X2)
| subclass(X2,X3)
| ~ inductive(null_class) ),
inference(superposition,[],[f2,f382]) ).
fof(f382,plain,
! [X0] :
( null_class = X0
| ~ inductive(null_class) ),
inference(subsumption_resolution,[],[f271,f375]) ).
fof(f271,plain,
! [X0] :
( member(null_class,regular(X0))
| ~ inductive(null_class)
| null_class = X0 ),
inference(superposition,[],[f121,f67]) ).
fof(f121,plain,
! [X0,X1] :
( ~ inductive(intersection(X1,X0))
| member(null_class,X0) ),
inference(resolution,[],[f22,f47]) ).
fof(f22,axiom,
! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X1) ),
file('/export/starexec/sandbox2/tmp/tmp.mUL9m3Co1S/Vampire---4.8_7463',intersection2) ).
fof(f406,plain,
( member(null_class,subset_relation)
| ~ subclass(universal_class,identity_relation)
| ~ inductive(null_class) ),
inference(superposition,[],[f224,f382]) ).
fof(f224,plain,
! [X16,X15] :
( member(unordered_pair(X15,X16),subset_relation)
| ~ subclass(universal_class,identity_relation) ),
inference(resolution,[],[f140,f124]) ).
fof(f124,plain,
! [X0] :
( ~ member(X0,identity_relation)
| member(X0,subset_relation) ),
inference(superposition,[],[f22,f75]) ).
fof(f75,axiom,
identity_relation = intersection(inverse(subset_relation),subset_relation),
file('/export/starexec/sandbox2/tmp/tmp.mUL9m3Co1S/Vampire---4.8_7463',identity_relation) ).
fof(f140,plain,
! [X8,X9,X7] :
( member(unordered_pair(X8,X9),X7)
| ~ subclass(universal_class,X7) ),
inference(resolution,[],[f1,f11]) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/tmp/tmp.mUL9m3Co1S/Vampire---4.8_7463',unordered_pairs_in_universal) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SET067-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.13/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.37 % Computer : n004.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sat Aug 26 11:53:23 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.15/0.37 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.15/0.37 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.mUL9m3Co1S/Vampire---4.8_7463
% 0.15/0.38 % (7644)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.44 % (7648)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)
% 0.22/0.44 % (7647)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)
% 0.22/0.44 % (7645)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)
% 0.22/0.44 % (7649)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)
% 0.22/0.44 % (7650)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 % (7646)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)
% 0.22/0.44 % (7651)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)
% 0.22/0.48 % (7645)First to succeed.
% 0.22/0.48 % (7645)Refutation found. Thanks to Tanya!
% 0.22/0.48 % SZS status Unsatisfiable for Vampire---4
% 0.22/0.48 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.49 % (7645)------------------------------
% 0.22/0.49 % (7645)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.49 % (7645)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.49 % (7645)Termination reason: Refutation
% 0.22/0.49
% 0.22/0.49 % (7645)Memory used [KB]: 2430
% 0.22/0.49 % (7645)Time elapsed: 0.047 s
% 0.22/0.49 % (7645)------------------------------
% 0.22/0.49 % (7645)------------------------------
% 0.22/0.49 % (7644)Success in time 0.108 s
% 0.22/0.49 % Vampire---4.8 exiting
%------------------------------------------------------------------------------