TSTP Solution File: NUM561+1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : NUM561+1 : TPTP v8.1.2. Released v4.0.0.
% 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 : n017.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 12:11:24 EDT 2023
% Result : Theorem 0.22s 0.44s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 13 unt; 0 def)
% Number of atoms : 163 ( 39 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 203 ( 79 ~; 76 |; 36 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 77 (; 61 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f430,plain,
$false,
inference(avatar_sat_refutation,[],[f423,f429]) ).
fof(f429,plain,
~ spl16_1,
inference(avatar_contradiction_clause,[],[f428]) ).
fof(f428,plain,
( $false
| ~ spl16_1 ),
inference(subsumption_resolution,[],[f427,f414]) ).
fof(f414,plain,
( aSet0(szDzozmdt0(xF))
| ~ spl16_1 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f413,plain,
( spl16_1
<=> aSet0(szDzozmdt0(xF)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1])]) ).
fof(f427,plain,
~ aSet0(szDzozmdt0(xF)),
inference(resolution,[],[f426,f258]) ).
fof(f258,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( aSet0(X0)
=> aSubsetOf0(X0,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.H4AlJqna20/Vampire---4.8_13061',mSubRefl) ).
fof(f426,plain,
~ aSubsetOf0(szDzozmdt0(xF),szDzozmdt0(xF)),
inference(subsumption_resolution,[],[f425,f241]) ).
fof(f241,plain,
aFunction0(xF),
inference(cnf_transformation,[],[f69]) ).
fof(f69,axiom,
aFunction0(xF),
file('/export/starexec/sandbox2/tmp/tmp.H4AlJqna20/Vampire---4.8_13061',m__2911) ).
fof(f425,plain,
( ~ aSubsetOf0(szDzozmdt0(xF),szDzozmdt0(xF))
| ~ aFunction0(xF) ),
inference(subsumption_resolution,[],[f424,f242]) ).
fof(f242,plain,
aElementOf0(xx,szDzozmdt0(xF)),
inference(cnf_transformation,[],[f70]) ).
fof(f70,axiom,
aElementOf0(xx,szDzozmdt0(xF)),
file('/export/starexec/sandbox2/tmp/tmp.H4AlJqna20/Vampire---4.8_13061',m__2911_02) ).
fof(f424,plain,
( ~ aElementOf0(xx,szDzozmdt0(xF))
| ~ aSubsetOf0(szDzozmdt0(xF),szDzozmdt0(xF))
| ~ aFunction0(xF) ),
inference(resolution,[],[f240,f368]) ).
fof(f368,plain,
! [X0,X1,X7] :
( aElementOf0(sdtlpdtrp0(X0,X7),sdtlcdtrc0(X0,X1))
| ~ aElementOf0(X7,X1)
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(equality_resolution,[],[f367]) ).
fof(f367,plain,
! [X2,X0,X1,X7] :
( aElementOf0(sdtlpdtrp0(X0,X7),X2)
| ~ aElementOf0(X7,X1)
| sdtlcdtrc0(X0,X1) != X2
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(equality_resolution,[],[f253]) ).
fof(f253,plain,
! [X2,X0,X1,X6,X7] :
( aElementOf0(X6,X2)
| sdtlpdtrp0(X0,X7) != X6
| ~ aElementOf0(X7,X1)
| sdtlcdtrc0(X0,X1) != X2
| ~ aSubsetOf0(X1,szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f180]) ).
fof(f180,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( sdtlcdtrc0(X0,X1) = X2
| ( ( ! [X4] :
( sdtlpdtrp0(X0,X4) != sK0(X0,X1,X2)
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(sK0(X0,X1,X2),X2) )
& ( ( sK0(X0,X1,X2) = sdtlpdtrp0(X0,sK1(X0,X1,X2))
& aElementOf0(sK1(X0,X1,X2),X1) )
| aElementOf0(sK0(X0,X1,X2),X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X6] :
( ( aElementOf0(X6,X2)
| ! [X7] :
( sdtlpdtrp0(X0,X7) != X6
| ~ aElementOf0(X7,X1) ) )
& ( ( sdtlpdtrp0(X0,sK2(X0,X1,X6)) = X6
& aElementOf0(sK2(X0,X1,X6),X1) )
| ~ aElementOf0(X6,X2) ) )
& aSet0(X2) )
| sdtlcdtrc0(X0,X1) != X2 ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f176,f179,f178,f177]) ).
fof(f177,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(X3,X2) )
& ( ? [X5] :
( sdtlpdtrp0(X0,X5) = X3
& aElementOf0(X5,X1) )
| aElementOf0(X3,X2) ) )
=> ( ( ! [X4] :
( sdtlpdtrp0(X0,X4) != sK0(X0,X1,X2)
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(sK0(X0,X1,X2),X2) )
& ( ? [X5] :
( sdtlpdtrp0(X0,X5) = sK0(X0,X1,X2)
& aElementOf0(X5,X1) )
| aElementOf0(sK0(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f178,plain,
! [X0,X1,X2] :
( ? [X5] :
( sdtlpdtrp0(X0,X5) = sK0(X0,X1,X2)
& aElementOf0(X5,X1) )
=> ( sK0(X0,X1,X2) = sdtlpdtrp0(X0,sK1(X0,X1,X2))
& aElementOf0(sK1(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f179,plain,
! [X0,X1,X6] :
( ? [X8] :
( sdtlpdtrp0(X0,X8) = X6
& aElementOf0(X8,X1) )
=> ( sdtlpdtrp0(X0,sK2(X0,X1,X6)) = X6
& aElementOf0(sK2(X0,X1,X6),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f176,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( sdtlcdtrc0(X0,X1) = X2
| ? [X3] :
( ( ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(X3,X2) )
& ( ? [X5] :
( sdtlpdtrp0(X0,X5) = X3
& aElementOf0(X5,X1) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X6] :
( ( aElementOf0(X6,X2)
| ! [X7] :
( sdtlpdtrp0(X0,X7) != X6
| ~ aElementOf0(X7,X1) ) )
& ( ? [X8] :
( sdtlpdtrp0(X0,X8) = X6
& aElementOf0(X8,X1) )
| ~ aElementOf0(X6,X2) ) )
& aSet0(X2) )
| sdtlcdtrc0(X0,X1) != X2 ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(rectify,[],[f175]) ).
fof(f175,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( sdtlcdtrc0(X0,X1) = X2
| ? [X3] :
( ( ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(X3,X2) )
& ( ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) ) )
& ( ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| sdtlcdtrc0(X0,X1) != X2 ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(flattening,[],[f174]) ).
fof(f174,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( sdtlcdtrc0(X0,X1) = X2
| ? [X3] :
( ( ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) )
| ~ aElementOf0(X3,X2) )
& ( ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| ! [X4] :
( sdtlpdtrp0(X0,X4) != X3
| ~ aElementOf0(X4,X1) ) )
& ( ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| sdtlcdtrc0(X0,X1) != X2 ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(nnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( sdtlcdtrc0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) ) )
& aSet0(X2) ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,axiom,
! [X0] :
( aFunction0(X0)
=> ! [X1] :
( aSubsetOf0(X1,szDzozmdt0(X0))
=> ! [X2] :
( sdtlcdtrc0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( sdtlpdtrp0(X0,X4) = X3
& aElementOf0(X4,X1) ) )
& aSet0(X2) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.H4AlJqna20/Vampire---4.8_13061',mDefSImg) ).
fof(f240,plain,
~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(flattening,[],[f72]) ).
fof(f72,negated_conjecture,
~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(negated_conjecture,[],[f71]) ).
fof(f71,conjecture,
aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
file('/export/starexec/sandbox2/tmp/tmp.H4AlJqna20/Vampire---4.8_13061',m__) ).
fof(f423,plain,
spl16_1,
inference(avatar_contradiction_clause,[],[f422]) ).
fof(f422,plain,
( $false
| spl16_1 ),
inference(subsumption_resolution,[],[f421,f241]) ).
fof(f421,plain,
( ~ aFunction0(xF)
| spl16_1 ),
inference(resolution,[],[f415,f248]) ).
fof(f248,plain,
! [X0] :
( aSet0(szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0] :
( aSet0(szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f64]) ).
fof(f64,axiom,
! [X0] :
( aFunction0(X0)
=> aSet0(szDzozmdt0(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.H4AlJqna20/Vampire---4.8_13061',mDomSet) ).
fof(f415,plain,
( ~ aSet0(szDzozmdt0(xF))
| spl16_1 ),
inference(avatar_component_clause,[],[f413]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.15 % Problem : NUM561+1 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.16 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.37 % Computer : n017.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 : Fri Aug 25 09:33:55 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.15/0.37 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.37 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.H4AlJqna20/Vampire---4.8_13061
% 0.15/0.37 % (13196)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.41 % (13202)lrs+10_1024_av=off:bsr=on:br=off:ep=RSTC:fsd=off:irw=on:nm=4:nwc=1.1:sims=off:urr=on:stl=125_440 on Vampire---4 for (440ds/0Mi)
% 0.22/0.43 % (13198)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.22/0.43 % (13197)lrs+1011_1_bd=preordered:flr=on:fsd=off:fsr=off:irw=on:lcm=reverse:msp=off:nm=2:nwc=10.0:sos=on:sp=reverse_weighted_frequency:tgt=full:stl=62_562 on Vampire---4 for (562ds/0Mi)
% 0.22/0.43 % (13199)lrs+10_4:5_amm=off:bsr=on:bce=on:flr=on:fsd=off:fde=unused:gs=on:gsem=on:lcm=predicate:sos=all:tgt=ground:stl=62_514 on Vampire---4 for (514ds/0Mi)
% 0.22/0.43 % (13201)ott+11_8:1_aac=none:amm=sco:anc=none:er=known:flr=on:fde=unused:irw=on:nm=0:nwc=1.2:nicw=on:sims=off:sos=all:sac=on_470 on Vampire---4 for (470ds/0Mi)
% 0.22/0.43 % (13203)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.22/0.43 % (13200)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.22/0.44 % (13203)First to succeed.
% 0.22/0.44 % (13203)Refutation found. Thanks to Tanya!
% 0.22/0.44 % SZS status Theorem for Vampire---4
% 0.22/0.44 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.44 % (13203)------------------------------
% 0.22/0.44 % (13203)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.44 % (13203)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.44 % (13203)Termination reason: Refutation
% 0.22/0.44
% 0.22/0.44 % (13203)Memory used [KB]: 5756
% 0.22/0.44 % (13203)Time elapsed: 0.007 s
% 0.22/0.44 % (13203)------------------------------
% 0.22/0.44 % (13203)------------------------------
% 0.22/0.44 % (13196)Success in time 0.067 s
% 0.22/0.44 % Vampire---4.8 exiting
%------------------------------------------------------------------------------