TSTP Solution File: SET755+4 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET755+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 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 : n011.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 15:45:29 EDT 2023
% Result : Theorem 10.48s 1.90s
% Output : Refutation 10.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 8 unt; 0 def)
% Number of atoms : 124 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 130 ( 42 ~; 30 |; 47 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 97 (; 74 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25777,plain,
$false,
inference(subsumption_resolution,[],[f25732,f410]) ).
fof(f410,plain,
apply(sK0,sK5(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),sK10(sK0,sK3,sK5(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))),
inference(resolution,[],[f185,f156]) ).
fof(f156,plain,
! [X2,X0,X1] :
( apply(X0,X2,sK10(X0,X1,X2))
| ~ member(X2,inverse_image2(X0,X1)) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1) ) )
& ( ( apply(X0,X2,sK10(X0,X1,X2))
& member(sK10(X0,X1,X2),X1) )
| ~ member(X2,inverse_image2(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f100,f101]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ? [X4] :
( apply(X0,X2,X4)
& member(X4,X1) )
=> ( apply(X0,X2,sK10(X0,X1,X2))
& member(sK10(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1) ) )
& ( ? [X4] :
( apply(X0,X2,X4)
& member(X4,X1) )
| ~ member(X2,inverse_image2(X0,X1)) ) ),
inference(rectify,[],[f99]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1) ) )
& ( ? [X3] :
( apply(X0,X2,X3)
& member(X3,X1) )
| ~ member(X2,inverse_image2(X0,X1)) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1,X2] :
( member(X2,inverse_image2(X0,X1))
<=> ? [X3] :
( apply(X0,X2,X3)
& member(X3,X1) ) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X5,X1,X2] :
( member(X2,inverse_image2(X5,X1))
<=> ? [X4] :
( apply(X5,X2,X4)
& member(X4,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Yr6XDeYlzO/Vampire---4.8_3754',inverse_image2) ).
fof(f185,plain,
member(sK5(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,sK3)),
inference(resolution,[],[f122,f125]) ).
fof(f125,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK5(X0,X1),X1)
& member(sK5(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f72,f73]) ).
fof(f73,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK5(X0,X1),X1)
& member(sK5(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f72,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,[],[f71]) ).
fof(f71,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,[],[f61]) ).
fof(f61,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/sandbox2/tmp/tmp.Yr6XDeYlzO/Vampire---4.8_3754',subset) ).
fof(f122,plain,
~ subset(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
( ~ subset(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))
& subset(sK3,sK4)
& subset(sK4,sK2)
& subset(sK3,sK2)
& maps(sK0,sK1,sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f60,f69]) ).
fof(f69,plain,
( ? [X0,X1,X2,X3,X4] :
( ~ subset(inverse_image2(X0,X3),inverse_image2(X0,X4))
& subset(X3,X4)
& subset(X4,X2)
& subset(X3,X2)
& maps(X0,X1,X2) )
=> ( ~ subset(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))
& subset(sK3,sK4)
& subset(sK4,sK2)
& subset(sK3,sK2)
& maps(sK0,sK1,sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
? [X0,X1,X2,X3,X4] :
( ~ subset(inverse_image2(X0,X3),inverse_image2(X0,X4))
& subset(X3,X4)
& subset(X4,X2)
& subset(X3,X2)
& maps(X0,X1,X2) ),
inference(flattening,[],[f59]) ).
fof(f59,plain,
? [X0,X1,X2,X3,X4] :
( ~ subset(inverse_image2(X0,X3),inverse_image2(X0,X4))
& subset(X3,X4)
& subset(X4,X2)
& subset(X3,X2)
& maps(X0,X1,X2) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,plain,
~ ! [X0,X1,X2,X3,X4] :
( ( subset(X3,X4)
& subset(X4,X2)
& subset(X3,X2)
& maps(X0,X1,X2) )
=> subset(inverse_image2(X0,X3),inverse_image2(X0,X4)) ),
inference(rectify,[],[f30]) ).
fof(f30,negated_conjecture,
~ ! [X5,X0,X1,X2,X4] :
( ( subset(X2,X4)
& subset(X4,X1)
& subset(X2,X1)
& maps(X5,X0,X1) )
=> subset(inverse_image2(X5,X2),inverse_image2(X5,X4)) ),
inference(negated_conjecture,[],[f29]) ).
fof(f29,conjecture,
! [X5,X0,X1,X2,X4] :
( ( subset(X2,X4)
& subset(X4,X1)
& subset(X2,X1)
& maps(X5,X0,X1) )
=> subset(inverse_image2(X5,X2),inverse_image2(X5,X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.Yr6XDeYlzO/Vampire---4.8_3754',thIIa05) ).
fof(f25732,plain,
~ apply(sK0,sK5(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),sK10(sK0,sK3,sK5(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)))),
inference(resolution,[],[f2644,f445]) ).
fof(f445,plain,
! [X0] :
( ~ member(X0,sK4)
| ~ apply(sK0,sK5(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),X0) ),
inference(resolution,[],[f186,f157]) ).
fof(f157,plain,
! [X2,X3,X0,X1] :
( member(X2,inverse_image2(X0,X1))
| ~ apply(X0,X2,X3)
| ~ member(X3,X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f186,plain,
~ member(sK5(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4)),inverse_image2(sK0,sK4)),
inference(resolution,[],[f122,f126]) ).
fof(f126,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f2644,plain,
member(sK10(sK0,sK3,sK5(inverse_image2(sK0,sK3),inverse_image2(sK0,sK4))),sK4),
inference(resolution,[],[f345,f185]) ).
fof(f345,plain,
! [X31,X30] :
( ~ member(X31,inverse_image2(X30,sK3))
| member(sK10(X30,sK3,X31),sK4) ),
inference(resolution,[],[f180,f155]) ).
fof(f155,plain,
! [X2,X0,X1] :
( member(sK10(X0,X1,X2),X1)
| ~ member(X2,inverse_image2(X0,X1)) ),
inference(cnf_transformation,[],[f102]) ).
fof(f180,plain,
! [X0] :
( ~ member(X0,sK3)
| member(X0,sK4) ),
inference(resolution,[],[f121,f124]) ).
fof(f124,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f121,plain,
subset(sK3,sK4),
inference(cnf_transformation,[],[f70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SET755+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.10/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.35 % Computer : n011.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 09:57:54 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.15/0.35 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.Yr6XDeYlzO/Vampire---4.8_3754
% 0.15/0.36 % (3915)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42 % (3919)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)
% 0.22/0.42 % (3918)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)
% 0.22/0.42 % (3920)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)
% 0.22/0.42 % (3917)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)
% 0.22/0.42 % (3922)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)
% 0.22/0.42 % (3921)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 % (3916)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)
% 10.48/1.89 % (3918)First to succeed.
% 10.48/1.90 % (3918)Refutation found. Thanks to Tanya!
% 10.48/1.90 % SZS status Theorem for Vampire---4
% 10.48/1.90 % SZS output start Proof for Vampire---4
% See solution above
% 10.48/1.90 % (3918)------------------------------
% 10.48/1.90 % (3918)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 10.48/1.90 % (3918)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 10.48/1.90 % (3918)Termination reason: Refutation
% 10.48/1.90
% 10.48/1.90 % (3918)Memory used [KB]: 60126
% 10.48/1.90 % (3918)Time elapsed: 1.480 s
% 10.48/1.90 % (3918)------------------------------
% 10.48/1.90 % (3918)------------------------------
% 10.48/1.90 % (3915)Success in time 1.532 s
% 10.48/1.90 % Vampire---4.8 exiting
%------------------------------------------------------------------------------