TSTP Solution File: SET696+4 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET696+4 : TPTP v8.1.2. Released v2.2.0.
% 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 15:45:15 EDT 2023
% Result : Theorem 0.21s 0.42s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 55 ( 10 unt; 0 def)
% Number of atoms : 143 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 147 ( 59 ~; 46 |; 26 &)
% ( 9 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 81 (; 74 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f120,plain,
$false,
inference(avatar_sat_refutation,[],[f104,f113,f119]) ).
fof(f119,plain,
spl7_1,
inference(avatar_contradiction_clause,[],[f118]) ).
fof(f118,plain,
( $false
| spl7_1 ),
inference(subsumption_resolution,[],[f117,f106]) ).
fof(f106,plain,
( member(sK2(sF6,empty_set),sF6)
| spl7_1 ),
inference(resolution,[],[f99,f59]) ).
fof(f59,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f33,f34]) ).
fof(f34,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.PfCgTSSpdK/Vampire---4.8_29891',subset) ).
fof(f99,plain,
( ~ subset(sF6,empty_set)
| spl7_1 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f97,plain,
( spl7_1
<=> subset(sF6,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).
fof(f117,plain,
( ~ member(sK2(sF6,empty_set),sF6)
| spl7_1 ),
inference(resolution,[],[f116,f94]) ).
fof(f94,plain,
! [X0] :
( member(X0,sK0)
| ~ member(X0,sF6) ),
inference(superposition,[],[f81,f87]) ).
fof(f87,plain,
intersection(sF5,sK0) = sF6,
introduced(function_definition,[]) ).
fof(f81,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) )
& ( ( member(X0,X2)
& member(X0,X1) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f52]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) )
& ( ( member(X0,X2)
& member(X0,X1) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X2)
& member(X0,X1) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/tmp/tmp.PfCgTSSpdK/Vampire---4.8_29891',intersection) ).
fof(f116,plain,
( ~ member(sK2(sF6,empty_set),sK0)
| spl7_1 ),
inference(resolution,[],[f115,f92]) ).
fof(f92,plain,
! [X0] :
( ~ member(X0,sF5)
| ~ member(X0,sK0) ),
inference(superposition,[],[f78,f86]) ).
fof(f86,plain,
difference(sK1,sK0) = sF5,
introduced(function_definition,[]) ).
fof(f78,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) )
& ( ( ~ member(X0,X1)
& member(X0,X2) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) )
& ( ( ~ member(X0,X1)
& member(X0,X2) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
<=> ( ~ member(X0,X1)
& member(X0,X2) ) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1,X0,X3] :
( member(X1,difference(X3,X0))
<=> ( ~ member(X1,X0)
& member(X1,X3) ) ),
file('/export/starexec/sandbox/tmp/tmp.PfCgTSSpdK/Vampire---4.8_29891',difference) ).
fof(f115,plain,
( member(sK2(sF6,empty_set),sF5)
| spl7_1 ),
inference(resolution,[],[f106,f93]) ).
fof(f93,plain,
! [X0] :
( ~ member(X0,sF6)
| member(X0,sF5) ),
inference(superposition,[],[f80,f87]) ).
fof(f80,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f113,plain,
spl7_2,
inference(avatar_contradiction_clause,[],[f112]) ).
fof(f112,plain,
( $false
| spl7_2 ),
inference(subsumption_resolution,[],[f111,f56]) ).
fof(f56,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0] : ~ member(X0,empty_set),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X2] : ~ member(X2,empty_set),
file('/export/starexec/sandbox/tmp/tmp.PfCgTSSpdK/Vampire---4.8_29891',empty_set) ).
fof(f111,plain,
( member(sK2(empty_set,sF6),empty_set)
| spl7_2 ),
inference(resolution,[],[f103,f59]) ).
fof(f103,plain,
( ~ subset(empty_set,sF6)
| spl7_2 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f101,plain,
( spl7_2
<=> subset(empty_set,sF6) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).
fof(f104,plain,
( ~ spl7_1
| ~ spl7_2 ),
inference(avatar_split_clause,[],[f95,f101,f97]) ).
fof(f95,plain,
( ~ subset(empty_set,sF6)
| ~ subset(sF6,empty_set) ),
inference(resolution,[],[f57,f88]) ).
fof(f88,plain,
~ equal_set(sF6,empty_set),
inference(definition_folding,[],[f55,f87,f86]) ).
fof(f55,plain,
~ equal_set(intersection(difference(sK1,sK0),sK0),empty_set),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
( ~ equal_set(intersection(difference(sK1,sK0),sK0),empty_set)
& subset(sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f25,f30]) ).
fof(f30,plain,
( ? [X0,X1] :
( ~ equal_set(intersection(difference(X1,X0),X0),empty_set)
& subset(X0,X1) )
=> ( ~ equal_set(intersection(difference(sK1,sK0),sK0),empty_set)
& subset(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
? [X0,X1] :
( ~ equal_set(intersection(difference(X1,X0),X0),empty_set)
& subset(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,plain,
~ ! [X0,X1] :
( subset(X0,X1)
=> equal_set(intersection(difference(X1,X0),X0),empty_set) ),
inference(rectify,[],[f13]) ).
fof(f13,negated_conjecture,
~ ! [X0,X3] :
( subset(X0,X3)
=> equal_set(intersection(difference(X3,X0),X0),empty_set) ),
inference(negated_conjecture,[],[f12]) ).
fof(f12,conjecture,
! [X0,X3] :
( subset(X0,X3)
=> equal_set(intersection(difference(X3,X0),X0),empty_set) ),
file('/export/starexec/sandbox/tmp/tmp.PfCgTSSpdK/Vampire---4.8_29891',thI28) ).
fof(f57,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(flattening,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ( subset(X1,X0)
& subset(X0,X1) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.PfCgTSSpdK/Vampire---4.8_29891',equal_set) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET696+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.35 % Computer : n012.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat Aug 26 09:09:40 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.15/0.35 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.35 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.PfCgTSSpdK/Vampire---4.8_29891
% 0.15/0.36 % (29999)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (30004)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_424 on Vampire---4 for (424ds/0Mi)
% 0.21/0.42 % (30006)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.21/0.42 % (30002)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.21/0.42 % (30005)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.21/0.42 % (30003)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.21/0.42 % (30001)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.21/0.42 % (30005)First to succeed.
% 0.21/0.42 % (30003)Refutation not found, incomplete strategy% (30003)------------------------------
% 0.21/0.42 % (30003)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.42 % (30003)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.42 % (30003)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.42
% 0.21/0.42 % (30003)Memory used [KB]: 9978
% 0.21/0.42 % (30003)Time elapsed: 0.005 s
% 0.21/0.42 % (30003)------------------------------
% 0.21/0.42 % (30003)------------------------------
% 0.21/0.42 % (30004)Also succeeded, but the first one will report.
% 0.21/0.42 % (30006)Also succeeded, but the first one will report.
% 0.21/0.42 % (30005)Refutation found. Thanks to Tanya!
% 0.21/0.42 % SZS status Theorem for Vampire---4
% 0.21/0.42 % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.42 % (30005)------------------------------
% 0.21/0.42 % (30005)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.42 % (30005)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.42 % (30005)Termination reason: Refutation
% 0.21/0.42
% 0.21/0.42 % (30005)Memory used [KB]: 5500
% 0.21/0.42 % (30005)Time elapsed: 0.006 s
% 0.21/0.42 % (30005)------------------------------
% 0.21/0.42 % (30005)------------------------------
% 0.21/0.42 % (29999)Success in time 0.065 s
% 0.21/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------