TSTP Solution File: NUM560+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM560+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n006.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 : Sun May 5 08:38:02 EDT 2024
% Result : Theorem 0.20s 0.38s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 62 ( 24 unt; 0 def)
% Number of atoms : 182 ( 26 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 178 ( 58 ~; 39 |; 54 &)
% ( 19 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 13 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 41 ( 30 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f475,plain,
$false,
inference(avatar_sat_refutation,[],[f419,f424,f429,f434,f439,f444,f449,f454,f459,f464,f468,f473,f474]) ).
fof(f474,plain,
( spl22_2
| ~ spl22_3
| ~ spl22_11 ),
inference(avatar_split_clause,[],[f469,f466,f426,f421]) ).
fof(f421,plain,
( spl22_2
<=> aElementOf0(sK8,szDzozmdt0(xF)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_2])]) ).
fof(f426,plain,
( spl22_3
<=> aElementOf0(sK8,sdtlbdtrb0(xF,xy)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_3])]) ).
fof(f466,plain,
( spl22_11
<=> ! [X1] :
( aElementOf0(X1,szDzozmdt0(xF))
| ~ aElementOf0(X1,sdtlbdtrb0(xF,xy)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_11])]) ).
fof(f469,plain,
( aElementOf0(sK8,szDzozmdt0(xF))
| ~ spl22_3
| ~ spl22_11 ),
inference(resolution,[],[f467,f428]) ).
fof(f428,plain,
( aElementOf0(sK8,sdtlbdtrb0(xF,xy))
| ~ spl22_3 ),
inference(avatar_component_clause,[],[f426]) ).
fof(f467,plain,
( ! [X1] :
( ~ aElementOf0(X1,sdtlbdtrb0(xF,xy))
| aElementOf0(X1,szDzozmdt0(xF)) )
| ~ spl22_11 ),
inference(avatar_component_clause,[],[f466]) ).
fof(f473,plain,
spl22_12,
inference(avatar_split_clause,[],[f256,f471]) ).
fof(f471,plain,
( spl22_12
<=> ! [X1] :
( xy = sdtlpdtrp0(xF,X1)
| ~ aElementOf0(X1,sdtlbdtrb0(xF,xy)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_12])]) ).
fof(f256,plain,
! [X1] :
( xy = sdtlpdtrp0(xF,X1)
| ~ aElementOf0(X1,sdtlbdtrb0(xF,xy)) ),
inference(cnf_transformation,[],[f187]) ).
fof(f187,plain,
( ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
& ~ aElementOf0(sK8,szDzozmdt0(xF))
& aElementOf0(sK8,sdtlbdtrb0(xF,xy))
& ! [X1] :
( ( aElementOf0(X1,sdtlbdtrb0(xF,xy))
| xy != sdtlpdtrp0(xF,X1)
| ~ aElementOf0(X1,szDzozmdt0(xF)) )
& ( ( xy = sdtlpdtrp0(xF,X1)
& aElementOf0(X1,szDzozmdt0(xF)) )
| ~ aElementOf0(X1,sdtlbdtrb0(xF,xy)) ) )
& aSet0(sdtlbdtrb0(xF,xy)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f185,f186]) ).
fof(f186,plain,
( ? [X0] :
( ~ aElementOf0(X0,szDzozmdt0(xF))
& aElementOf0(X0,sdtlbdtrb0(xF,xy)) )
=> ( ~ aElementOf0(sK8,szDzozmdt0(xF))
& aElementOf0(sK8,sdtlbdtrb0(xF,xy)) ) ),
introduced(choice_axiom,[]) ).
fof(f185,plain,
( ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
& ? [X0] :
( ~ aElementOf0(X0,szDzozmdt0(xF))
& aElementOf0(X0,sdtlbdtrb0(xF,xy)) )
& ! [X1] :
( ( aElementOf0(X1,sdtlbdtrb0(xF,xy))
| xy != sdtlpdtrp0(xF,X1)
| ~ aElementOf0(X1,szDzozmdt0(xF)) )
& ( ( xy = sdtlpdtrp0(xF,X1)
& aElementOf0(X1,szDzozmdt0(xF)) )
| ~ aElementOf0(X1,sdtlbdtrb0(xF,xy)) ) )
& aSet0(sdtlbdtrb0(xF,xy)) ),
inference(rectify,[],[f184]) ).
fof(f184,plain,
( ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
& ? [X1] :
( ~ aElementOf0(X1,szDzozmdt0(xF))
& aElementOf0(X1,sdtlbdtrb0(xF,xy)) )
& ! [X0] :
( ( aElementOf0(X0,sdtlbdtrb0(xF,xy))
| xy != sdtlpdtrp0(xF,X0)
| ~ aElementOf0(X0,szDzozmdt0(xF)) )
& ( ( xy = sdtlpdtrp0(xF,X0)
& aElementOf0(X0,szDzozmdt0(xF)) )
| ~ aElementOf0(X0,sdtlbdtrb0(xF,xy)) ) )
& aSet0(sdtlbdtrb0(xF,xy)) ),
inference(flattening,[],[f183]) ).
fof(f183,plain,
( ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
& ? [X1] :
( ~ aElementOf0(X1,szDzozmdt0(xF))
& aElementOf0(X1,sdtlbdtrb0(xF,xy)) )
& ! [X0] :
( ( aElementOf0(X0,sdtlbdtrb0(xF,xy))
| xy != sdtlpdtrp0(xF,X0)
| ~ aElementOf0(X0,szDzozmdt0(xF)) )
& ( ( xy = sdtlpdtrp0(xF,X0)
& aElementOf0(X0,szDzozmdt0(xF)) )
| ~ aElementOf0(X0,sdtlbdtrb0(xF,xy)) ) )
& aSet0(sdtlbdtrb0(xF,xy)) ),
inference(nnf_transformation,[],[f80]) ).
fof(f80,plain,
( ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
& ? [X1] :
( ~ aElementOf0(X1,szDzozmdt0(xF))
& aElementOf0(X1,sdtlbdtrb0(xF,xy)) )
& ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xF,xy))
<=> ( xy = sdtlpdtrp0(xF,X0)
& aElementOf0(X0,szDzozmdt0(xF)) ) )
& aSet0(sdtlbdtrb0(xF,xy)) ),
inference(flattening,[],[f79]) ).
fof(f79,plain,
( ~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
& ? [X1] :
( ~ aElementOf0(X1,szDzozmdt0(xF))
& aElementOf0(X1,sdtlbdtrb0(xF,xy)) )
& ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xF,xy))
<=> ( xy = sdtlpdtrp0(xF,X0)
& aElementOf0(X0,szDzozmdt0(xF)) ) )
& aSet0(sdtlbdtrb0(xF,xy)) ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,plain,
~ ( ( ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xF,xy))
<=> ( xy = sdtlpdtrp0(xF,X0)
& aElementOf0(X0,szDzozmdt0(xF)) ) )
& aSet0(sdtlbdtrb0(xF,xy)) )
=> ( aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
| ! [X1] :
( aElementOf0(X1,sdtlbdtrb0(xF,xy))
=> aElementOf0(X1,szDzozmdt0(xF)) ) ) ),
inference(rectify,[],[f69]) ).
fof(f69,negated_conjecture,
~ ( ( ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xF,xy))
<=> ( xy = sdtlpdtrp0(xF,X0)
& aElementOf0(X0,szDzozmdt0(xF)) ) )
& aSet0(sdtlbdtrb0(xF,xy)) )
=> ( aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
| ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xF,xy))
=> aElementOf0(X0,szDzozmdt0(xF)) ) ) ),
inference(negated_conjecture,[],[f68]) ).
fof(f68,conjecture,
( ( ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xF,xy))
<=> ( xy = sdtlpdtrp0(xF,X0)
& aElementOf0(X0,szDzozmdt0(xF)) ) )
& aSet0(sdtlbdtrb0(xF,xy)) )
=> ( aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF))
| ! [X0] :
( aElementOf0(X0,sdtlbdtrb0(xF,xy))
=> aElementOf0(X0,szDzozmdt0(xF)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f468,plain,
spl22_11,
inference(avatar_split_clause,[],[f255,f466]) ).
fof(f255,plain,
! [X1] :
( aElementOf0(X1,szDzozmdt0(xF))
| ~ aElementOf0(X1,sdtlbdtrb0(xF,xy)) ),
inference(cnf_transformation,[],[f187]) ).
fof(f464,plain,
spl22_10,
inference(avatar_split_clause,[],[f400,f461]) ).
fof(f461,plain,
( spl22_10
<=> aSet0(slcrc0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_10])]) ).
fof(f400,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f327]) ).
fof(f327,plain,
! [X0] :
( aSet0(X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f219]) ).
fof(f219,plain,
! [X0] :
( ( slcrc0 = X0
| aElementOf0(sK15(X0),X0)
| ~ aSet0(X0) )
& ( ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f217,f218]) ).
fof(f218,plain,
! [X0] :
( ? [X1] : aElementOf0(X1,X0)
=> aElementOf0(sK15(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f217,plain,
! [X0] :
( ( slcrc0 = X0
| ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0) )
& ( ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(rectify,[],[f216]) ).
fof(f216,plain,
! [X0] :
( ( slcrc0 = X0
| ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0) )
& ( ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(flattening,[],[f215]) ).
fof(f215,plain,
! [X0] :
( ( slcrc0 = X0
| ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0) )
& ( ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(nnf_transformation,[],[f135]) ).
fof(f135,plain,
! [X0] :
( slcrc0 = X0
<=> ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( slcrc0 = X0
<=> ( ~ ? [X1] : aElementOf0(X1,X0)
& aSet0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(f459,plain,
spl22_9,
inference(avatar_split_clause,[],[f267,f456]) ).
fof(f456,plain,
( spl22_9
<=> isCountable0(szNzAzT0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_9])]) ).
fof(f267,plain,
isCountable0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(f454,plain,
spl22_8,
inference(avatar_split_clause,[],[f266,f451]) ).
fof(f451,plain,
( spl22_8
<=> aSet0(szNzAzT0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_8])]) ).
fof(f266,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f449,plain,
spl22_7,
inference(avatar_split_clause,[],[f263,f446]) ).
fof(f446,plain,
( spl22_7
<=> isFinite0(slcrc0) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_7])]) ).
fof(f263,plain,
isFinite0(slcrc0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
isFinite0(slcrc0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEmpFin) ).
fof(f444,plain,
spl22_6,
inference(avatar_split_clause,[],[f262,f441]) ).
fof(f441,plain,
( spl22_6
<=> aElement0(xy) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_6])]) ).
fof(f262,plain,
aElement0(xy),
inference(cnf_transformation,[],[f67]) ).
fof(f67,axiom,
( aElement0(xy)
& aFunction0(xF) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2693) ).
fof(f439,plain,
spl22_5,
inference(avatar_split_clause,[],[f261,f436]) ).
fof(f436,plain,
( spl22_5
<=> aFunction0(xF) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_5])]) ).
fof(f261,plain,
aFunction0(xF),
inference(cnf_transformation,[],[f67]) ).
fof(f434,plain,
~ spl22_4,
inference(avatar_split_clause,[],[f260,f431]) ).
fof(f431,plain,
( spl22_4
<=> aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_4])]) ).
fof(f260,plain,
~ aSubsetOf0(sdtlbdtrb0(xF,xy),szDzozmdt0(xF)),
inference(cnf_transformation,[],[f187]) ).
fof(f429,plain,
spl22_3,
inference(avatar_split_clause,[],[f258,f426]) ).
fof(f258,plain,
aElementOf0(sK8,sdtlbdtrb0(xF,xy)),
inference(cnf_transformation,[],[f187]) ).
fof(f424,plain,
~ spl22_2,
inference(avatar_split_clause,[],[f259,f421]) ).
fof(f259,plain,
~ aElementOf0(sK8,szDzozmdt0(xF)),
inference(cnf_transformation,[],[f187]) ).
fof(f419,plain,
spl22_1,
inference(avatar_split_clause,[],[f254,f416]) ).
fof(f416,plain,
( spl22_1
<=> aSet0(sdtlbdtrb0(xF,xy)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1])]) ).
fof(f254,plain,
aSet0(sdtlbdtrb0(xF,xy)),
inference(cnf_transformation,[],[f187]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM560+2 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri May 3 14:11:23 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (7698)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.37 % (7704)WARNING: value z3 for option sas not known
% 0.20/0.37 % (7706)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 theBenchmark for (531ds/0Mi)
% 0.20/0.37 % (7707)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 theBenchmark for (522ds/0Mi)
% 0.20/0.37 % (7702)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.37 % (7703)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.37 % (7705)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.37 % (7704)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 theBenchmark for (569ds/0Mi)
% 0.20/0.38 % (7708)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 theBenchmark for (497ds/0Mi)
% 0.20/0.38 % (7706)First to succeed.
% 0.20/0.38 % (7707)Also succeeded, but the first one will report.
% 0.20/0.38 % (7706)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-7698"
% 0.20/0.38 % (7706)Refutation found. Thanks to Tanya!
% 0.20/0.38 % SZS status Theorem for theBenchmark
% 0.20/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.38 % (7706)------------------------------
% 0.20/0.38 % (7706)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.38 % (7706)Termination reason: Refutation
% 0.20/0.38
% 0.20/0.38 % (7706)Memory used [KB]: 1029
% 0.20/0.38 % (7706)Time elapsed: 0.010 s
% 0.20/0.38 % (7706)Instructions burned: 13 (million)
% 0.20/0.38 % (7698)Success in time 0.027 s
%------------------------------------------------------------------------------