TSTP Solution File: SET653+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---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 : 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 : Fri Sep 1 23:40:20 EDT 2023
% Result : Theorem 0.22s 0.43s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 38 ( 7 unt; 0 def)
% Number of atoms : 205 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 287 ( 120 ~; 95 |; 46 &)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 84 (; 60 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f235,plain,
$false,
inference(resolution,[],[f234,f98]) ).
fof(f98,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/tmp/tmp.W1RWJUD6ig/Vampire---4.8_4307',p22) ).
fof(f234,plain,
~ ilf_type(sK2,set_type),
inference(resolution,[],[f233,f98]) ).
fof(f233,plain,
( ~ ilf_type(sK3,set_type)
| ~ ilf_type(sK2,set_type) ),
inference(resolution,[],[f232,f98]) ).
fof(f232,plain,
( ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK2,set_type)
| ~ ilf_type(sK3,set_type) ),
inference(resolution,[],[f229,f98]) ).
fof(f229,plain,
( ~ ilf_type(domain_of(sK5),set_type)
| ~ ilf_type(sK2,set_type)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK3,set_type) ),
inference(resolution,[],[f224,f95]) ).
fof(f95,plain,
ilf_type(sK5,relation_type(sK2,sK4)),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
( ~ ilf_type(sK5,relation_type(sK3,sK4))
& subset(sK2,sK3)
& ilf_type(sK5,relation_type(sK2,sK4))
& ilf_type(sK4,set_type)
& ilf_type(sK3,set_type)
& ilf_type(sK2,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f27,f63,f62,f61,f60]) ).
fof(f60,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(sK2,X1)
& ilf_type(X3,relation_type(sK2,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(sK2,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X1,X2))
& subset(sK2,X1)
& ilf_type(X3,relation_type(sK2,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(sK3,X2))
& subset(sK2,sK3)
& ilf_type(X3,relation_type(sK2,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(sK3,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(sK3,X2))
& subset(sK2,sK3)
& ilf_type(X3,relation_type(sK2,X2)) )
& ilf_type(X2,set_type) )
=> ( ? [X3] :
( ~ ilf_type(X3,relation_type(sK3,sK4))
& subset(sK2,sK3)
& ilf_type(X3,relation_type(sK2,sK4)) )
& ilf_type(sK4,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
( ? [X3] :
( ~ ilf_type(X3,relation_type(sK3,sK4))
& subset(sK2,sK3)
& ilf_type(X3,relation_type(sK2,sK4)) )
=> ( ~ ilf_type(sK5,relation_type(sK3,sK4))
& subset(sK2,sK3)
& ilf_type(sK5,relation_type(sK2,sK4)) ) ),
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/sandbox/tmp/tmp.W1RWJUD6ig/Vampire---4.8_4307',prove_relset_1_15) ).
fof(f224,plain,
( ~ ilf_type(sK5,relation_type(sK2,sK4))
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK2,set_type)
| ~ ilf_type(domain_of(sK5),set_type)
| ~ ilf_type(sK3,set_type) ),
inference(duplicate_literal_removal,[],[f223]) ).
fof(f223,plain,
( ~ ilf_type(sK5,relation_type(sK2,sK4))
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK2,set_type)
| ~ ilf_type(sK2,set_type)
| ~ ilf_type(domain_of(sK5),set_type)
| ~ ilf_type(sK3,set_type)
| ~ ilf_type(sK4,set_type) ),
inference(factoring,[],[f213]) ).
fof(f213,plain,
! [X18,X17] :
( ~ ilf_type(sK5,relation_type(sK2,X18))
| ~ ilf_type(sK5,relation_type(X17,sK4))
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(X17,set_type)
| ~ ilf_type(sK2,set_type)
| ~ ilf_type(domain_of(sK5),set_type)
| ~ ilf_type(sK3,set_type)
| ~ ilf_type(X18,set_type) ),
inference(resolution,[],[f190,f96]) ).
fof(f96,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f64]) ).
fof(f190,plain,
! [X2,X0,X1] :
( ~ subset(X1,sK3)
| ~ ilf_type(sK3,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK5,relation_type(X0,sK4))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(domain_of(sK5),set_type)
| ~ ilf_type(sK5,relation_type(X1,X2))
| ~ ilf_type(X2,set_type) ),
inference(duplicate_literal_removal,[],[f183]) ).
fof(f183,plain,
! [X2,X0,X1] :
( ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK3,set_type)
| ~ ilf_type(X0,set_type)
| ~ subset(X1,sK3)
| ~ ilf_type(sK5,relation_type(X0,sK4))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(domain_of(sK5),set_type)
| ~ ilf_type(sK5,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(resolution,[],[f168,f132]) ).
fof(f132,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/sandbox/tmp/tmp.W1RWJUD6ig/Vampire---4.8_4307',p2) ).
fof(f168,plain,
! [X2,X3] :
( ~ subset(domain_of(sK5),X3)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK3,set_type)
| ~ ilf_type(X2,set_type)
| ~ subset(X3,sK3)
| ~ ilf_type(sK5,relation_type(X2,sK4))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(domain_of(sK5),set_type) ),
inference(duplicate_literal_removal,[],[f165]) ).
fof(f165,plain,
! [X2,X3] :
( ~ ilf_type(sK5,relation_type(X2,sK4))
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK3,set_type)
| ~ ilf_type(X2,set_type)
| ~ subset(X3,sK3)
| ~ subset(domain_of(sK5),X3)
| ~ ilf_type(sK3,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(domain_of(sK5),set_type) ),
inference(resolution,[],[f163,f130]) ).
fof(f130,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/sandbox/tmp/tmp.W1RWJUD6ig/Vampire---4.8_4307',p1) ).
fof(f163,plain,
! [X0] :
( ~ subset(domain_of(sK5),sK3)
| ~ ilf_type(sK5,relation_type(X0,sK4))
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK3,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[],[f131,f97]) ).
fof(f97,plain,
~ ilf_type(sK5,relation_type(sK3,sK4)),
inference(cnf_transformation,[],[f64]) ).
fof(f131,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/sandbox/tmp/tmp.W1RWJUD6ig/Vampire---4.8_4307',p3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET653+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n012.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 : Wed Aug 30 15:42:23 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.42 % (4573)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42 % (4620)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.22/0.42 % (4619)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.22/0.42 % (4621)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.22/0.42 % (4622)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.22/0.42 % (4623)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.22/0.42 % (4624)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.22/0.42 % (4626)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.22/0.43 TRYING [1]
% 0.22/0.43 TRYING [2]
% 0.22/0.43 % (4624)First to succeed.
% 0.22/0.43 TRYING [3]
% 0.22/0.43 % (4623)Also succeeded, but the first one will report.
% 0.22/0.43 % (4624)Refutation found. Thanks to Tanya!
% 0.22/0.43 % SZS status Theorem for Vampire---4
% 0.22/0.43 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.43 % (4624)------------------------------
% 0.22/0.43 % (4624)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.43 % (4624)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.43 % (4624)Termination reason: Refutation
% 0.22/0.43
% 0.22/0.43 % (4624)Memory used [KB]: 1151
% 0.22/0.43 % (4624)Time elapsed: 0.011 s
% 0.22/0.43 % (4624)------------------------------
% 0.22/0.43 % (4624)------------------------------
% 0.22/0.43 % (4573)Success in time 0.071 s
% 0.22/0.43 % Vampire---4.8 exiting
%------------------------------------------------------------------------------