TSTP Solution File: NUM625+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : NUM625+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 : 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 12:13:21 EDT 2023
% Result : Theorem 0.24s 0.46s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 51 ( 18 unt; 0 def)
% Number of atoms : 243 ( 44 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 310 ( 118 ~; 110 |; 66 &)
% ( 9 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 2 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 76 (; 68 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1300,plain,
$false,
inference(avatar_sat_refutation,[],[f698,f1297]) ).
fof(f1297,plain,
~ spl25_3,
inference(avatar_contradiction_clause,[],[f1296]) ).
fof(f1296,plain,
( $false
| ~ spl25_3 ),
inference(subsumption_resolution,[],[f1295,f634]) ).
fof(f634,plain,
( aSet0(xQ)
| ~ spl25_3 ),
inference(avatar_component_clause,[],[f633]) ).
fof(f633,plain,
( spl25_3
<=> aSet0(xQ) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_3])]) ).
fof(f1295,plain,
( ~ aSet0(xQ)
| ~ spl25_3 ),
inference(subsumption_resolution,[],[f1294,f721]) ).
fof(f721,plain,
( aElement0(xp)
| ~ spl25_3 ),
inference(subsumption_resolution,[],[f720,f634]) ).
fof(f720,plain,
( aElement0(xp)
| ~ aSet0(xQ) ),
inference(resolution,[],[f344,f458]) ).
fof(f458,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f176]) ).
fof(f176,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.0gksYj2cm7/Vampire---4.8_22485',mEOfElem) ).
fof(f344,plain,
aElementOf0(xp,xQ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,axiom,
aElementOf0(xp,xQ),
file('/export/starexec/sandbox/tmp/tmp.0gksYj2cm7/Vampire---4.8_22485',m__5173) ).
fof(f1294,plain,
( ~ aElement0(xp)
| ~ aSet0(xQ) ),
inference(subsumption_resolution,[],[f1275,f606]) ).
fof(f606,plain,
aElementOf0(xp,xP),
inference(forward_demodulation,[],[f346,f339]) ).
fof(f339,plain,
xp = xx,
inference(cnf_transformation,[],[f120]) ).
fof(f120,axiom,
xp = xx,
file('/export/starexec/sandbox/tmp/tmp.0gksYj2cm7/Vampire---4.8_22485',m__5496) ).
fof(f346,plain,
aElementOf0(xx,xP),
inference(cnf_transformation,[],[f113]) ).
fof(f113,axiom,
aElementOf0(xx,xP),
file('/export/starexec/sandbox/tmp/tmp.0gksYj2cm7/Vampire---4.8_22485',m__5348) ).
fof(f1275,plain,
( ~ aElementOf0(xp,xP)
| ~ aElement0(xp)
| ~ aSet0(xQ) ),
inference(superposition,[],[f594,f608]) ).
fof(f608,plain,
xP = sdtmndt0(xQ,xp),
inference(forward_demodulation,[],[f378,f348]) ).
fof(f348,plain,
xp = szmzizndt0(xQ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,axiom,
xp = szmzizndt0(xQ),
file('/export/starexec/sandbox/tmp/tmp.0gksYj2cm7/Vampire---4.8_22485',m__5147) ).
fof(f378,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(cnf_transformation,[],[f104]) ).
fof(f104,axiom,
( xP = sdtmndt0(xQ,szmzizndt0(xQ))
& aSet0(xP) ),
file('/export/starexec/sandbox/tmp/tmp.0gksYj2cm7/Vampire---4.8_22485',m__5164) ).
fof(f594,plain,
! [X0,X4] :
( ~ aElementOf0(X4,sdtmndt0(X0,X4))
| ~ aElement0(X4)
| ~ aSet0(X0) ),
inference(equality_resolution,[],[f593]) ).
fof(f593,plain,
! [X2,X0,X4] :
( ~ aElementOf0(X4,X2)
| sdtmndt0(X0,X4) != X2
| ~ aElement0(X4)
| ~ aSet0(X0) ),
inference(equality_resolution,[],[f527]) ).
fof(f527,plain,
! [X2,X0,X1,X4] :
( X1 != X4
| ~ aElementOf0(X4,X2)
| sdtmndt0(X0,X1) != X2
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f323]) ).
fof(f323,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X0,X1) = X2
| ( ( sK21(X0,X1,X2) = X1
| ~ aElementOf0(sK21(X0,X1,X2),X0)
| ~ aElement0(sK21(X0,X1,X2))
| ~ aElementOf0(sK21(X0,X1,X2),X2) )
& ( ( sK21(X0,X1,X2) != X1
& aElementOf0(sK21(X0,X1,X2),X0)
& aElement0(sK21(X0,X1,X2)) )
| aElementOf0(sK21(X0,X1,X2),X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| X1 = X4
| ~ aElementOf0(X4,X0)
| ~ aElement0(X4) )
& ( ( X1 != X4
& aElementOf0(X4,X0)
& aElement0(X4) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| sdtmndt0(X0,X1) != X2 ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f321,f322]) ).
fof(f322,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) )
| aElementOf0(X3,X2) ) )
=> ( ( sK21(X0,X1,X2) = X1
| ~ aElementOf0(sK21(X0,X1,X2),X0)
| ~ aElement0(sK21(X0,X1,X2))
| ~ aElementOf0(sK21(X0,X1,X2),X2) )
& ( ( sK21(X0,X1,X2) != X1
& aElementOf0(sK21(X0,X1,X2),X0)
& aElement0(sK21(X0,X1,X2)) )
| aElementOf0(sK21(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f321,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X0,X1) = X2
| ? [X3] :
( ( X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| X1 = X4
| ~ aElementOf0(X4,X0)
| ~ aElement0(X4) )
& ( ( X1 != X4
& aElementOf0(X4,X0)
& aElement0(X4) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| sdtmndt0(X0,X1) != X2 ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(rectify,[],[f320]) ).
fof(f320,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X0,X1) = X2
| ? [X3] :
( ( X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3) )
& ( ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| sdtmndt0(X0,X1) != X2 ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f319]) ).
fof(f319,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X0,X1) = X2
| ? [X3] :
( ( X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3) )
& ( ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| sdtmndt0(X0,X1) != X2 ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f227]) ).
fof(f227,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f226]) ).
fof(f226,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aSet0(X0) )
=> ! [X2] :
( sdtmndt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0gksYj2cm7/Vampire---4.8_22485',mDefDiff) ).
fof(f698,plain,
spl25_3,
inference(avatar_split_clause,[],[f697,f633]) ).
fof(f697,plain,
aSet0(xQ),
inference(subsumption_resolution,[],[f685,f425]) ).
fof(f425,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox/tmp/tmp.0gksYj2cm7/Vampire---4.8_22485',mNATSet) ).
fof(f685,plain,
( aSet0(xQ)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f342,f462]) ).
fof(f462,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f284]) ).
fof(f284,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ( ~ aElementOf0(sK12(X0,X1),X0)
& aElementOf0(sK12(X0,X1),X1) )
| ~ aSet0(X1) )
& ( ( ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f282,f283]) ).
fof(f283,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
=> ( ~ aElementOf0(sK12(X0,X1),X0)
& aElementOf0(sK12(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f282,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f281]) ).
fof(f281,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(flattening,[],[f280]) ).
fof(f280,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
| ~ aSet0(X1) )
& ( ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f182]) ).
fof(f182,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) )
& aSet0(X1) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0gksYj2cm7/Vampire---4.8_22485',mDefSub) ).
fof(f342,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[],[f101]) ).
fof(f101,axiom,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox/tmp/tmp.0gksYj2cm7/Vampire---4.8_22485',m__5106) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : NUM625+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.16 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.37 % Computer : n013.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri Aug 25 10:50:32 EDT 2023
% 0.16/0.38 % CPUTime :
% 0.16/0.38 This is a FOF_CAX_RFO_SEQ problem
% 0.16/0.38 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.0gksYj2cm7/Vampire---4.8_22485
% 0.16/0.38 % (22610)Running in auto input_syntax mode. Trying TPTP
% 0.24/0.44 % (22619)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.24/0.44 % (22613)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.24/0.44 % (22615)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.24/0.44 % (22614)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)
% 0.24/0.44 % (22617)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)
% 0.24/0.44 % (22618)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)
% 0.24/0.45 % (22611)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)
% 0.24/0.46 % (22619)First to succeed.
% 0.24/0.46 % (22619)Refutation found. Thanks to Tanya!
% 0.24/0.46 % SZS status Theorem for Vampire---4
% 0.24/0.46 % SZS output start Proof for Vampire---4
% See solution above
% 0.24/0.46 % (22619)------------------------------
% 0.24/0.46 % (22619)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.24/0.46 % (22619)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.24/0.46 % (22619)Termination reason: Refutation
% 0.24/0.46
% 0.24/0.46 % (22619)Memory used [KB]: 6268
% 0.24/0.46 % (22619)Time elapsed: 0.018 s
% 0.24/0.46 % (22619)------------------------------
% 0.24/0.46 % (22619)------------------------------
% 0.24/0.46 % (22610)Success in time 0.077 s
% 0.24/0.46 % Vampire---4.8 exiting
%------------------------------------------------------------------------------