TSTP Solution File: SET653+3 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET653+3 : 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 : n013.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 15:45:03 EDT 2023
% Result : Theorem 0.23s 0.44s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 54 ( 12 unt; 0 def)
% Number of atoms : 201 ( 2 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 238 ( 91 ~; 73 |; 46 &)
% ( 2 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 106 (; 82 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f324,plain,
$false,
inference(avatar_sat_refutation,[],[f291,f317,f323]) ).
fof(f323,plain,
~ spl15_3,
inference(avatar_contradiction_clause,[],[f322]) ).
fof(f322,plain,
( $false
| ~ spl15_3 ),
inference(subsumption_resolution,[],[f321,f137]) ).
fof(f137,plain,
ilf_type(sK3,sF14),
inference(definition_folding,[],[f91,f136]) ).
fof(f136,plain,
relation_type(sK0,sK2) = sF14,
introduced(function_definition,[]) ).
fof(f91,plain,
ilf_type(sK3,relation_type(sK0,sK2)),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
( ~ ilf_type(sK3,relation_type(sK1,sK2))
& subset(sK0,sK1)
& ilf_type(sK3,relation_type(sK0,sK2))
& ilf_type(sK2,set_type)
& ilf_type(sK1,set_type)
& ilf_type(sK0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f27,f60,f59,f58,f57]) ).
fof(f57,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X1,X2))
& subset(X0,X1)
& ilf_type(X3,relation_type(X0,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X1,X2))
& subset(sK0,X1)
& ilf_type(X3,relation_type(sK0,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(sK0,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f58,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X1,X2))
& subset(sK0,X1)
& ilf_type(X3,relation_type(sK0,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(sK1,X2))
& subset(sK0,sK1)
& ilf_type(X3,relation_type(sK0,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(sK1,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(sK1,X2))
& subset(sK0,sK1)
& ilf_type(X3,relation_type(sK0,X2)) )
& ilf_type(X2,set_type) )
=> ( ? [X3] :
( ~ ilf_type(X3,relation_type(sK1,sK2))
& subset(sK0,sK1)
& ilf_type(X3,relation_type(sK0,sK2)) )
& ilf_type(sK2,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
( ? [X3] :
( ~ ilf_type(X3,relation_type(sK1,sK2))
& subset(sK0,sK1)
& ilf_type(X3,relation_type(sK0,sK2)) )
=> ( ~ ilf_type(sK3,relation_type(sK1,sK2))
& subset(sK0,sK1)
& ilf_type(sK3,relation_type(sK0,sK2)) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X1,X2))
& subset(X0,X1)
& ilf_type(X3,relation_type(X0,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f26]) ).
fof(f26,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X1,X2))
& subset(X0,X1)
& ilf_type(X3,relation_type(X0,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X2))
=> ( subset(X0,X1)
=> ilf_type(X3,relation_type(X1,X2)) ) ) ) ) ),
inference(negated_conjecture,[],[f23]) ).
fof(f23,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X2))
=> ( subset(X0,X1)
=> ilf_type(X3,relation_type(X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zH4xP4BsPh/Vampire---4.8_4688',prove_relset_1_15) ).
fof(f321,plain,
( ~ ilf_type(sK3,sF14)
| ~ spl15_3 ),
inference(superposition,[],[f286,f136]) ).
fof(f286,plain,
( ! [X0] : ~ ilf_type(sK3,relation_type(X0,sK2))
| ~ spl15_3 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f285,plain,
( spl15_3
<=> ! [X0] : ~ ilf_type(sK3,relation_type(X0,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_3])]) ).
fof(f317,plain,
spl15_4,
inference(avatar_contradiction_clause,[],[f316]) ).
fof(f316,plain,
( $false
| spl15_4 ),
inference(subsumption_resolution,[],[f315,f92]) ).
fof(f92,plain,
subset(sK0,sK1),
inference(cnf_transformation,[],[f61]) ).
fof(f315,plain,
( ~ subset(sK0,sK1)
| spl15_4 ),
inference(subsumption_resolution,[],[f314,f137]) ).
fof(f314,plain,
( ~ ilf_type(sK3,sF14)
| ~ subset(sK0,sK1)
| spl15_4 ),
inference(superposition,[],[f302,f136]) ).
fof(f302,plain,
( ! [X0,X1] :
( ~ ilf_type(sK3,relation_type(X0,X1))
| ~ subset(X0,sK1) )
| spl15_4 ),
inference(resolution,[],[f293,f166]) ).
fof(f166,plain,
! [X2,X0,X1] :
( subset(domain_of(X2),X0)
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(subsumption_resolution,[],[f165,f94]) ).
fof(f94,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/tmp/tmp.zH4xP4BsPh/Vampire---4.8_4688',p22) ).
fof(f165,plain,
! [X2,X0,X1] :
( subset(domain_of(X2),X0)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f125,f94]) ).
fof(f125,plain,
! [X2,X0,X1] :
( subset(domain_of(X2),X0)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( subset(range_of(X2),X1)
& subset(domain_of(X2),X0) )
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( subset(range_of(X2),X1)
& subset(domain_of(X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zH4xP4BsPh/Vampire---4.8_4688',p2) ).
fof(f293,plain,
( ! [X1] :
( ~ subset(domain_of(sK3),X1)
| ~ subset(X1,sK1) )
| spl15_4 ),
inference(resolution,[],[f290,f224]) ).
fof(f224,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(subsumption_resolution,[],[f223,f94]) ).
fof(f223,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f222,f94]) ).
fof(f222,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f123,f94]) ).
fof(f123,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f43]) ).
fof(f43,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zH4xP4BsPh/Vampire---4.8_4688',p1) ).
fof(f290,plain,
( ~ subset(domain_of(sK3),sK1)
| spl15_4 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f288,plain,
( spl15_4
<=> subset(domain_of(sK3),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_4])]) ).
fof(f291,plain,
( spl15_3
| ~ spl15_4 ),
inference(avatar_split_clause,[],[f283,f288,f285]) ).
fof(f283,plain,
! [X0] :
( ~ subset(domain_of(sK3),sK1)
| ~ ilf_type(sK3,relation_type(X0,sK2)) ),
inference(resolution,[],[f275,f135]) ).
fof(f135,plain,
~ ilf_type(sK3,sF13),
inference(definition_folding,[],[f93,f134]) ).
fof(f134,plain,
relation_type(sK1,sK2) = sF13,
introduced(function_definition,[]) ).
fof(f93,plain,
~ ilf_type(sK3,relation_type(sK1,sK2)),
inference(cnf_transformation,[],[f61]) ).
fof(f275,plain,
! [X0,X1] :
( ilf_type(X0,sF13)
| ~ subset(domain_of(X0),sK1)
| ~ ilf_type(X0,relation_type(X1,sK2)) ),
inference(superposition,[],[f257,f134]) ).
fof(f257,plain,
! [X2,X3,X0,X1] :
( ilf_type(X3,relation_type(X1,X2))
| ~ subset(domain_of(X3),X1)
| ~ ilf_type(X3,relation_type(X0,X2)) ),
inference(subsumption_resolution,[],[f256,f94]) ).
fof(f256,plain,
! [X2,X3,X0,X1] :
( ilf_type(X3,relation_type(X1,X2))
| ~ subset(domain_of(X3),X1)
| ~ ilf_type(X3,relation_type(X0,X2))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f255,f94]) ).
fof(f255,plain,
! [X2,X3,X0,X1] :
( ilf_type(X3,relation_type(X1,X2))
| ~ subset(domain_of(X3),X1)
| ~ ilf_type(X3,relation_type(X0,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f124,f94]) ).
fof(f124,plain,
! [X2,X3,X0,X1] :
( ilf_type(X3,relation_type(X1,X2))
| ~ subset(domain_of(X3),X1)
| ~ ilf_type(X3,relation_type(X0,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
| ~ subset(domain_of(X3),X1)
| ~ ilf_type(X3,relation_type(X0,X2)) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f45]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
| ~ subset(domain_of(X3),X1)
| ~ ilf_type(X3,relation_type(X0,X2)) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X2))
=> ( subset(domain_of(X3),X1)
=> ilf_type(X3,relation_type(X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.zH4xP4BsPh/Vampire---4.8_4688',p3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET653+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n013.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 14:15:32 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.zH4xP4BsPh/Vampire---4.8_4688
% 0.15/0.37 % (4795)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.43 % (4799)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)
% 0.23/0.43 % (4802)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)
% 0.23/0.43 % (4798)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)
% 0.23/0.43 % (4800)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)
% 0.23/0.43 % (4797)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)
% 0.23/0.43 % (4801)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.23/0.44 % (4801)First to succeed.
% 0.23/0.44 % (4801)Refutation found. Thanks to Tanya!
% 0.23/0.44 % SZS status Theorem for Vampire---4
% 0.23/0.44 % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.44 % (4801)------------------------------
% 0.23/0.44 % (4801)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.44 % (4801)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.44 % (4801)Termination reason: Refutation
% 0.23/0.44
% 0.23/0.44 % (4801)Memory used [KB]: 5628
% 0.23/0.44 % (4801)Time elapsed: 0.011 s
% 0.23/0.44 % (4801)------------------------------
% 0.23/0.44 % (4801)------------------------------
% 0.23/0.44 % (4795)Success in time 0.074 s
% 0.23/0.44 % Vampire---4.8 exiting
%------------------------------------------------------------------------------