TSTP Solution File: NUM564+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM564+1 : 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 : n021.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 08:38:29 EDT 2024
% Result : Theorem 0.22s 0.44s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 75
% Syntax : Number of formulae : 358 ( 36 unt; 0 def)
% Number of atoms : 1194 ( 224 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 1375 ( 539 ~; 562 |; 160 &)
% ( 77 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 49 ( 47 usr; 31 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 7 con; 0-3 aty)
% Number of variables : 391 ( 366 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1670,plain,
$false,
inference(avatar_sat_refutation,[],[f511,f527,f589,f605,f612,f614,f632,f636,f680,f711,f760,f763,f795,f801,f866,f879,f882,f1065,f1069,f1084,f1093,f1122,f1388,f1392,f1629,f1641,f1650,f1669]) ).
fof(f1669,plain,
( ~ spl33_1
| spl33_2
| ~ spl33_9 ),
inference(avatar_contradiction_clause,[],[f1668]) ).
fof(f1668,plain,
( $false
| ~ spl33_1
| spl33_2
| ~ spl33_9 ),
inference(subsumption_resolution,[],[f1667,f505]) ).
fof(f505,plain,
( aSet0(xS)
| ~ spl33_1 ),
inference(avatar_component_clause,[],[f504]) ).
fof(f504,plain,
( spl33_1
<=> aSet0(xS) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_1])]) ).
fof(f1667,plain,
( ~ aSet0(xS)
| spl33_2
| ~ spl33_9 ),
inference(subsumption_resolution,[],[f1666,f510]) ).
fof(f510,plain,
( ~ isFinite0(xS)
| spl33_2 ),
inference(avatar_component_clause,[],[f508]) ).
fof(f508,plain,
( spl33_2
<=> isFinite0(xS) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_2])]) ).
fof(f1666,plain,
( isFinite0(xS)
| ~ aSet0(xS)
| ~ spl33_9 ),
inference(subsumption_resolution,[],[f1665,f494]) ).
fof(f494,plain,
aElementOf0(sz00,szNzAzT0),
inference(forward_demodulation,[],[f298,f297]) ).
fof(f297,plain,
sz00 = xK,
inference(cnf_transformation,[],[f78]) ).
fof(f78,axiom,
sz00 = xK,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3462) ).
fof(f298,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[],[f74]) ).
fof(f74,axiom,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
fof(f1665,plain,
( ~ aElementOf0(sz00,szNzAzT0)
| isFinite0(xS)
| ~ aSet0(xS)
| ~ spl33_9 ),
inference(subsumption_resolution,[],[f1664,f706]) ).
fof(f706,plain,
( slcrc0 = szDzozmdt0(xc)
| ~ spl33_9 ),
inference(avatar_component_clause,[],[f704]) ).
fof(f704,plain,
( spl33_9
<=> slcrc0 = szDzozmdt0(xc) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_9])]) ).
fof(f1664,plain,
( slcrc0 != szDzozmdt0(xc)
| ~ aElementOf0(sz00,szNzAzT0)
| isFinite0(xS)
| ~ aSet0(xS) ),
inference(superposition,[],[f383,f497]) ).
fof(f497,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,sz00),
inference(forward_demodulation,[],[f300,f297]) ).
fof(f300,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(cnf_transformation,[],[f76]) ).
fof(f76,axiom,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aFunction0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3453) ).
fof(f383,plain,
! [X0,X1] :
( slcrc0 != slbdtsldtrb0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
! [X0] :
( ! [X1] :
( slcrc0 != slbdtsldtrb0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0) )
| isFinite0(X0)
| ~ aSet0(X0) ),
inference(flattening,[],[f133]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( slcrc0 != slbdtsldtrb0(X0,X1)
| ~ aElementOf0(X1,szNzAzT0) )
| isFinite0(X0)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,axiom,
! [X0] :
( ( ~ isFinite0(X0)
& aSet0(X0) )
=> ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> slcrc0 != slbdtsldtrb0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSelNSet) ).
fof(f1650,plain,
( ~ spl33_29
| spl33_30
| spl33_15 ),
inference(avatar_split_clause,[],[f1471,f859,f1647,f1643]) ).
fof(f1643,plain,
( spl33_29
<=> aSubsetOf0(slbdtrb0(szmzizndt0(xS)),slcrc0) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_29])]) ).
fof(f1647,plain,
( spl33_30
<=> sdtlseqdt0(szmzizndt0(xS),sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_30])]) ).
fof(f859,plain,
( spl33_15
<=> slcrc0 = xS ),
introduced(avatar_definition,[new_symbols(naming,[spl33_15])]) ).
fof(f1471,plain,
( sdtlseqdt0(szmzizndt0(xS),sz00)
| ~ aSubsetOf0(slbdtrb0(szmzizndt0(xS)),slcrc0)
| spl33_15 ),
inference(superposition,[],[f1466,f896]) ).
fof(f896,plain,
( szmzizndt0(xS) = sbrdtbr0(slbdtrb0(szmzizndt0(xS)))
| spl33_15 ),
inference(resolution,[],[f892,f367]) ).
fof(f367,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sbrdtbr0(slbdtrb0(X0)) = X0 ),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
! [X0] :
( sbrdtbr0(slbdtrb0(X0)) = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sbrdtbr0(slbdtrb0(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardSeg) ).
fof(f892,plain,
( aElementOf0(szmzizndt0(xS),szNzAzT0)
| spl33_15 ),
inference(subsumption_resolution,[],[f857,f860]) ).
fof(f860,plain,
( slcrc0 != xS
| spl33_15 ),
inference(avatar_component_clause,[],[f859]) ).
fof(f857,plain,
( aElementOf0(szmzizndt0(xS),szNzAzT0)
| slcrc0 = xS ),
inference(subsumption_resolution,[],[f855,f304]) ).
fof(f304,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f75]) ).
fof(f75,axiom,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(f855,plain,
( aElementOf0(szmzizndt0(xS),szNzAzT0)
| slcrc0 = xS
| ~ aSubsetOf0(xS,szNzAzT0) ),
inference(resolution,[],[f853,f477]) ).
fof(f477,plain,
! [X0] :
( aElementOf0(szmzizndt0(X0),X0)
| slcrc0 = X0
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(equality_resolution,[],[f396]) ).
fof(f396,plain,
! [X0,X1] :
( aElementOf0(X1,X0)
| szmzizndt0(X0) != X1
| slcrc0 = X0
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f256]) ).
fof(f256,plain,
! [X0] :
( ! [X1] :
( ( szmzizndt0(X0) = X1
| ( ~ sdtlseqdt0(X1,sK25(X0,X1))
& aElementOf0(sK25(X0,X1),X0) )
| ~ aElementOf0(X1,X0) )
& ( ( ! [X3] :
( sdtlseqdt0(X1,X3)
| ~ aElementOf0(X3,X0) )
& aElementOf0(X1,X0) )
| szmzizndt0(X0) != X1 ) )
| slcrc0 = X0
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f254,f255]) ).
fof(f255,plain,
! [X0,X1] :
( ? [X2] :
( ~ sdtlseqdt0(X1,X2)
& aElementOf0(X2,X0) )
=> ( ~ sdtlseqdt0(X1,sK25(X0,X1))
& aElementOf0(sK25(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f254,plain,
! [X0] :
( ! [X1] :
( ( szmzizndt0(X0) = X1
| ? [X2] :
( ~ sdtlseqdt0(X1,X2)
& aElementOf0(X2,X0) )
| ~ aElementOf0(X1,X0) )
& ( ( ! [X3] :
( sdtlseqdt0(X1,X3)
| ~ aElementOf0(X3,X0) )
& aElementOf0(X1,X0) )
| szmzizndt0(X0) != X1 ) )
| slcrc0 = X0
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(rectify,[],[f253]) ).
fof(f253,plain,
! [X0] :
( ! [X1] :
( ( szmzizndt0(X0) = X1
| ? [X2] :
( ~ sdtlseqdt0(X1,X2)
& aElementOf0(X2,X0) )
| ~ aElementOf0(X1,X0) )
& ( ( ! [X2] :
( sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,X0) )
& aElementOf0(X1,X0) )
| szmzizndt0(X0) != X1 ) )
| slcrc0 = X0
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(flattening,[],[f252]) ).
fof(f252,plain,
! [X0] :
( ! [X1] :
( ( szmzizndt0(X0) = X1
| ? [X2] :
( ~ sdtlseqdt0(X1,X2)
& aElementOf0(X2,X0) )
| ~ aElementOf0(X1,X0) )
& ( ( ! [X2] :
( sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,X0) )
& aElementOf0(X1,X0) )
| szmzizndt0(X0) != X1 ) )
| slcrc0 = X0
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(nnf_transformation,[],[f152]) ).
fof(f152,plain,
! [X0] :
( ! [X1] :
( szmzizndt0(X0) = X1
<=> ( ! [X2] :
( sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,X0) )
& aElementOf0(X1,X0) ) )
| slcrc0 = X0
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(flattening,[],[f151]) ).
fof(f151,plain,
! [X0] :
( ! [X1] :
( szmzizndt0(X0) = X1
<=> ( ! [X2] :
( sdtlseqdt0(X1,X2)
| ~ aElementOf0(X2,X0) )
& aElementOf0(X1,X0) ) )
| slcrc0 = X0
| ~ aSubsetOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0] :
( ( slcrc0 != X0
& aSubsetOf0(X0,szNzAzT0) )
=> ! [X1] :
( szmzizndt0(X0) = X1
<=> ( ! [X2] :
( aElementOf0(X2,X0)
=> sdtlseqdt0(X1,X2) )
& aElementOf0(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMin) ).
fof(f853,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,szNzAzT0) ),
inference(subsumption_resolution,[],[f845,f313]) ).
fof(f313,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(f845,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,szNzAzT0)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f353,f304]) ).
fof(f353,plain,
! [X3,X0,X1] :
( ~ aSubsetOf0(X1,X0)
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f236]) ).
fof(f236,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ( ~ aElementOf0(sK20(X0,X1),X0)
& aElementOf0(sK20(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,[sK20])],[f234,f235]) ).
fof(f235,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
=> ( ~ aElementOf0(sK20(X0,X1),X0)
& aElementOf0(sK20(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f234,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,[],[f233]) ).
fof(f233,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,[],[f232]) ).
fof(f232,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,[],[f110]) ).
fof(f110,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/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(f1466,plain,
! [X0] :
( sdtlseqdt0(sbrdtbr0(X0),sz00)
| ~ aSubsetOf0(X0,slcrc0) ),
inference(subsumption_resolution,[],[f1465,f479]) ).
fof(f479,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f400]) ).
fof(f400,plain,
! [X0] :
( aSet0(X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f261]) ).
fof(f261,plain,
! [X0] :
( ( slcrc0 = X0
| aElementOf0(sK26(X0),X0)
| ~ aSet0(X0) )
& ( ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f259,f260]) ).
fof(f260,plain,
! [X0] :
( ? [X1] : aElementOf0(X1,X0)
=> aElementOf0(sK26(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f259,plain,
! [X0] :
( ( slcrc0 = X0
| ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0) )
& ( ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(rectify,[],[f258]) ).
fof(f258,plain,
! [X0] :
( ( slcrc0 = X0
| ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0) )
& ( ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(flattening,[],[f257]) ).
fof(f257,plain,
! [X0] :
( ( slcrc0 = X0
| ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0) )
& ( ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(nnf_transformation,[],[f153]) ).
fof(f153,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(f1465,plain,
! [X0] :
( sdtlseqdt0(sbrdtbr0(X0),sz00)
| ~ aSubsetOf0(X0,slcrc0)
| ~ aSet0(slcrc0) ),
inference(subsumption_resolution,[],[f1460,f310]) ).
fof(f310,plain,
isFinite0(slcrc0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
isFinite0(slcrc0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEmpFin) ).
fof(f1460,plain,
! [X0] :
( sdtlseqdt0(sbrdtbr0(X0),sz00)
| ~ aSubsetOf0(X0,slcrc0)
| ~ isFinite0(slcrc0)
| ~ aSet0(slcrc0) ),
inference(superposition,[],[f350,f512]) ).
fof(f512,plain,
sz00 = sbrdtbr0(slcrc0),
inference(subsumption_resolution,[],[f471,f479]) ).
fof(f471,plain,
( sz00 = sbrdtbr0(slcrc0)
| ~ aSet0(slcrc0) ),
inference(equality_resolution,[],[f345]) ).
fof(f345,plain,
! [X0] :
( sz00 = sbrdtbr0(X0)
| slcrc0 != X0
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f230]) ).
fof(f230,plain,
! [X0] :
( ( ( sz00 = sbrdtbr0(X0)
| slcrc0 != X0 )
& ( slcrc0 = X0
| sz00 != sbrdtbr0(X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0] :
( ( sz00 = sbrdtbr0(X0)
<=> slcrc0 = X0 )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] :
( aSet0(X0)
=> ( sz00 = sbrdtbr0(X0)
<=> slcrc0 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
fof(f350,plain,
! [X0,X1] :
( sdtlseqdt0(sbrdtbr0(X1),sbrdtbr0(X0))
| ~ aSubsetOf0(X1,X0)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0] :
( ! [X1] :
( sdtlseqdt0(sbrdtbr0(X1),sbrdtbr0(X0))
| ~ aSubsetOf0(X1,X0)
| ~ isFinite0(X0) )
| ~ aSet0(X0) ),
inference(flattening,[],[f106]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( sdtlseqdt0(sbrdtbr0(X1),sbrdtbr0(X0))
| ~ aSubsetOf0(X1,X0)
| ~ isFinite0(X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( ( aSubsetOf0(X1,X0)
& isFinite0(X0) )
=> sdtlseqdt0(sbrdtbr0(X1),sbrdtbr0(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardSub) ).
fof(f1641,plain,
( ~ spl33_27
| spl33_28
| ~ spl33_16 ),
inference(avatar_split_clause,[],[f1470,f863,f1638,f1634]) ).
fof(f1634,plain,
( spl33_27
<=> aSubsetOf0(slbdtrb0(sK26(xS)),slcrc0) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_27])]) ).
fof(f1638,plain,
( spl33_28
<=> sdtlseqdt0(sK26(xS),sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_28])]) ).
fof(f863,plain,
( spl33_16
<=> aElementOf0(sK26(xS),szNzAzT0) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_16])]) ).
fof(f1470,plain,
( sdtlseqdt0(sK26(xS),sz00)
| ~ aSubsetOf0(slbdtrb0(sK26(xS)),slcrc0)
| ~ spl33_16 ),
inference(superposition,[],[f1466,f887]) ).
fof(f887,plain,
( sK26(xS) = sbrdtbr0(slbdtrb0(sK26(xS)))
| ~ spl33_16 ),
inference(resolution,[],[f865,f367]) ).
fof(f865,plain,
( aElementOf0(sK26(xS),szNzAzT0)
| ~ spl33_16 ),
inference(avatar_component_clause,[],[f863]) ).
fof(f1629,plain,
( ~ spl33_25
| spl33_26 ),
inference(avatar_split_clause,[],[f1468,f1626,f1622]) ).
fof(f1622,plain,
( spl33_25
<=> aSubsetOf0(slbdtrb0(szszuzczcdt0(sz00)),slcrc0) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_25])]) ).
fof(f1626,plain,
( spl33_26
<=> sdtlseqdt0(szszuzczcdt0(sz00),sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_26])]) ).
fof(f1468,plain,
( sdtlseqdt0(szszuzczcdt0(sz00),sz00)
| ~ aSubsetOf0(slbdtrb0(szszuzczcdt0(sz00)),slcrc0) ),
inference(superposition,[],[f1466,f812]) ).
fof(f812,plain,
szszuzczcdt0(sz00) = sbrdtbr0(slbdtrb0(szszuzczcdt0(sz00))),
inference(resolution,[],[f544,f494]) ).
fof(f544,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| szszuzczcdt0(X0) = sbrdtbr0(slbdtrb0(szszuzczcdt0(X0))) ),
inference(resolution,[],[f367,f368]) ).
fof(f368,plain,
! [X0] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0] :
( ( sz00 != szszuzczcdt0(X0)
& aElementOf0(szszuzczcdt0(X0),szNzAzT0) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( sz00 != szszuzczcdt0(X0)
& aElementOf0(szszuzczcdt0(X0),szNzAzT0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).
fof(f1392,plain,
spl33_23,
inference(avatar_contradiction_clause,[],[f1391]) ).
fof(f1391,plain,
( $false
| spl33_23 ),
inference(subsumption_resolution,[],[f1390,f313]) ).
fof(f1390,plain,
( ~ aSet0(szNzAzT0)
| spl33_23 ),
inference(subsumption_resolution,[],[f1389,f514]) ).
fof(f514,plain,
aElement0(sz00),
inference(subsumption_resolution,[],[f513,f479]) ).
fof(f513,plain,
( aElement0(sz00)
| ~ aSet0(slcrc0) ),
inference(superposition,[],[f342,f512]) ).
fof(f342,plain,
! [X0] :
( aElement0(sbrdtbr0(X0))
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0] :
( aElement0(sbrdtbr0(X0))
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( aSet0(X0)
=> aElement0(sbrdtbr0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardS) ).
fof(f1389,plain,
( ~ aElement0(sz00)
| ~ aSet0(szNzAzT0)
| spl33_23 ),
inference(resolution,[],[f1383,f484]) ).
fof(f484,plain,
! [X0,X1] :
( aSet0(sdtmndt0(X0,X1))
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(equality_resolution,[],[f423]) ).
fof(f423,plain,
! [X2,X0,X1] :
( aSet0(X2)
| sdtmndt0(X0,X1) != X2
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f274]) ).
fof(f274,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X0,X1) = X2
| ~ sP8(X1,X0,X2)
| ~ aSet0(X2) )
& ( ( sP8(X1,X0,X2)
& aSet0(X2) )
| sdtmndt0(X0,X1) != X2 ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f273]) ).
fof(f273,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X0,X1) = X2
| ~ sP8(X1,X0,X2)
| ~ aSet0(X2) )
& ( ( sP8(X1,X0,X2)
& aSet0(X2) )
| sdtmndt0(X0,X1) != X2 ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f203]) ).
fof(f203,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X0,X1) = X2
<=> ( sP8(X1,X0,X2)
& aSet0(X2) ) )
| ~ aElement0(X1)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f161,f202]) ).
fof(f202,plain,
! [X1,X0,X2] :
( sP8(X1,X0,X2)
<=> ! [X3] :
( aElementOf0(X3,X2)
<=> ( X1 != X3
& aElementOf0(X3,X0)
& aElement0(X3) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f161,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,[],[f160]) ).
fof(f160,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/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(f1383,plain,
( ~ aSet0(sdtmndt0(szNzAzT0,sz00))
| spl33_23 ),
inference(avatar_component_clause,[],[f1381]) ).
fof(f1381,plain,
( spl33_23
<=> aSet0(sdtmndt0(szNzAzT0,sz00)) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_23])]) ).
fof(f1388,plain,
( ~ spl33_23
| ~ spl33_24 ),
inference(avatar_split_clause,[],[f1379,f1385,f1381]) ).
fof(f1385,plain,
( spl33_24
<=> isFinite0(sdtmndt0(szNzAzT0,sz00)) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_24])]) ).
fof(f1379,plain,
( ~ isFinite0(sdtmndt0(szNzAzT0,sz00))
| ~ aSet0(sdtmndt0(szNzAzT0,sz00)) ),
inference(subsumption_resolution,[],[f1378,f514]) ).
fof(f1378,plain,
( ~ isFinite0(sdtmndt0(szNzAzT0,sz00))
| ~ aSet0(sdtmndt0(szNzAzT0,sz00))
| ~ aElement0(sz00) ),
inference(subsumption_resolution,[],[f1374,f502]) ).
fof(f502,plain,
~ isFinite0(szNzAzT0),
inference(subsumption_resolution,[],[f501,f313]) ).
fof(f501,plain,
( ~ isFinite0(szNzAzT0)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f384,f314]) ).
fof(f314,plain,
isCountable0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f384,plain,
! [X0] :
( ~ isCountable0(X0)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(flattening,[],[f135]) ).
fof(f135,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ( isCountable0(X0)
& aSet0(X0) )
=> ~ isFinite0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin) ).
fof(f1374,plain,
( isFinite0(szNzAzT0)
| ~ isFinite0(sdtmndt0(szNzAzT0,sz00))
| ~ aSet0(sdtmndt0(szNzAzT0,sz00))
| ~ aElement0(sz00) ),
inference(superposition,[],[f358,f1365]) ).
fof(f1365,plain,
szNzAzT0 = sdtpldt0(sdtmndt0(szNzAzT0,sz00),sz00),
inference(subsumption_resolution,[],[f1355,f313]) ).
fof(f1355,plain,
( szNzAzT0 = sdtpldt0(sdtmndt0(szNzAzT0,sz00),sz00)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f349,f494]) ).
fof(f349,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| sdtpldt0(sdtmndt0(X0,X1),X1) = X0
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( sdtpldt0(sdtmndt0(X0,X1),X1) = X0
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> sdtpldt0(sdtmndt0(X0,X1),X1) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mConsDiff) ).
fof(f358,plain,
! [X0,X1] :
( isFinite0(sdtpldt0(X1,X0))
| ~ isFinite0(X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0] :
( ! [X1] :
( isFinite0(sdtpldt0(X1,X0))
| ~ isFinite0(X1)
| ~ aSet0(X1) )
| ~ aElement0(X0) ),
inference(flattening,[],[f115]) ).
fof(f115,plain,
! [X0] :
( ! [X1] :
( isFinite0(sdtpldt0(X1,X0))
| ~ isFinite0(X1)
| ~ aSet0(X1) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( ( isFinite0(X1)
& aSet0(X1) )
=> isFinite0(sdtpldt0(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFConsSet) ).
fof(f1122,plain,
( ~ spl33_1
| ~ spl33_5
| ~ spl33_6
| spl33_9
| ~ spl33_10 ),
inference(avatar_contradiction_clause,[],[f1121]) ).
fof(f1121,plain,
( $false
| ~ spl33_1
| ~ spl33_5
| ~ spl33_6
| spl33_9
| ~ spl33_10 ),
inference(subsumption_resolution,[],[f1120,f631]) ).
fof(f631,plain,
( aSet0(szDzozmdt0(xc))
| ~ spl33_6 ),
inference(avatar_component_clause,[],[f629]) ).
fof(f629,plain,
( spl33_6
<=> aSet0(szDzozmdt0(xc)) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_6])]) ).
fof(f1120,plain,
( ~ aSet0(szDzozmdt0(xc))
| ~ spl33_1
| ~ spl33_5
| ~ spl33_6
| spl33_9
| ~ spl33_10 ),
inference(subsumption_resolution,[],[f1119,f705]) ).
fof(f705,plain,
( slcrc0 != szDzozmdt0(xc)
| spl33_9 ),
inference(avatar_component_clause,[],[f704]) ).
fof(f1119,plain,
( slcrc0 = szDzozmdt0(xc)
| ~ aSet0(szDzozmdt0(xc))
| ~ spl33_1
| ~ spl33_5
| ~ spl33_6
| spl33_9
| ~ spl33_10 ),
inference(subsumption_resolution,[],[f1116,f498]) ).
fof(f498,plain,
~ aElementOf0(slcrc0,szDzozmdt0(xc)),
inference(superposition,[],[f296,f497]) ).
fof(f296,plain,
~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(flattening,[],[f80]) ).
fof(f80,negated_conjecture,
~ aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(negated_conjecture,[],[f79]) ).
fof(f79,conjecture,
aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f1116,plain,
( aElementOf0(slcrc0,szDzozmdt0(xc))
| slcrc0 = szDzozmdt0(xc)
| ~ aSet0(szDzozmdt0(xc))
| ~ spl33_1
| ~ spl33_5
| ~ spl33_6
| spl33_9
| ~ spl33_10 ),
inference(superposition,[],[f402,f1108]) ).
fof(f1108,plain,
( slcrc0 = sK26(szDzozmdt0(xc))
| ~ spl33_1
| ~ spl33_5
| ~ spl33_6
| spl33_9
| ~ spl33_10 ),
inference(subsumption_resolution,[],[f1107,f1075]) ).
fof(f1075,plain,
( aSet0(sK26(szDzozmdt0(xc)))
| ~ spl33_1
| ~ spl33_10 ),
inference(subsumption_resolution,[],[f1073,f505]) ).
fof(f1073,plain,
( aSet0(sK26(szDzozmdt0(xc)))
| ~ aSet0(xS)
| ~ spl33_10 ),
inference(resolution,[],[f710,f352]) ).
fof(f352,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f236]) ).
fof(f710,plain,
( aSubsetOf0(sK26(szDzozmdt0(xc)),xS)
| ~ spl33_10 ),
inference(avatar_component_clause,[],[f708]) ).
fof(f708,plain,
( spl33_10
<=> aSubsetOf0(sK26(szDzozmdt0(xc)),xS) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_10])]) ).
fof(f1107,plain,
( slcrc0 = sK26(szDzozmdt0(xc))
| ~ aSet0(sK26(szDzozmdt0(xc)))
| ~ spl33_5
| ~ spl33_6
| spl33_9 ),
inference(trivial_inequality_removal,[],[f1101]) ).
fof(f1101,plain,
( sz00 != sz00
| slcrc0 = sK26(szDzozmdt0(xc))
| ~ aSet0(sK26(szDzozmdt0(xc)))
| ~ spl33_5
| ~ spl33_6
| spl33_9 ),
inference(superposition,[],[f344,f1099]) ).
fof(f1099,plain,
( sz00 = sbrdtbr0(sK26(szDzozmdt0(xc)))
| ~ spl33_5
| ~ spl33_6
| spl33_9 ),
inference(subsumption_resolution,[],[f1098,f631]) ).
fof(f1098,plain,
( sz00 = sbrdtbr0(sK26(szDzozmdt0(xc)))
| ~ aSet0(szDzozmdt0(xc))
| ~ spl33_5
| spl33_9 ),
inference(subsumption_resolution,[],[f1096,f705]) ).
fof(f1096,plain,
( sz00 = sbrdtbr0(sK26(szDzozmdt0(xc)))
| slcrc0 = szDzozmdt0(xc)
| ~ aSet0(szDzozmdt0(xc))
| ~ spl33_5 ),
inference(resolution,[],[f1095,f402]) ).
fof(f1095,plain,
( ! [X0] :
( ~ aElementOf0(X0,szDzozmdt0(xc))
| sz00 = sbrdtbr0(X0) )
| ~ spl33_5 ),
inference(resolution,[],[f446,f639]) ).
fof(f639,plain,
( sP10(sz00,xS,szDzozmdt0(xc))
| ~ spl33_5 ),
inference(subsumption_resolution,[],[f622,f626]) ).
fof(f626,plain,
( sP11(xS,sz00)
| ~ spl33_5 ),
inference(avatar_component_clause,[],[f625]) ).
fof(f625,plain,
( spl33_5
<=> sP11(xS,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_5])]) ).
fof(f622,plain,
( sP10(sz00,xS,szDzozmdt0(xc))
| ~ sP11(xS,sz00) ),
inference(superposition,[],[f488,f497]) ).
fof(f488,plain,
! [X0,X1] :
( sP10(X1,X0,slbdtsldtrb0(X0,X1))
| ~ sP11(X0,X1) ),
inference(equality_resolution,[],[f442]) ).
fof(f442,plain,
! [X2,X0,X1] :
( sP10(X1,X0,X2)
| slbdtsldtrb0(X0,X1) != X2
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f286]) ).
fof(f286,plain,
! [X0,X1] :
( ! [X2] :
( ( slbdtsldtrb0(X0,X1) = X2
| ~ sP10(X1,X0,X2) )
& ( sP10(X1,X0,X2)
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ sP11(X0,X1) ),
inference(nnf_transformation,[],[f207]) ).
fof(f207,plain,
! [X0,X1] :
( ! [X2] :
( slbdtsldtrb0(X0,X1) = X2
<=> sP10(X1,X0,X2) )
| ~ sP11(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f446,plain,
! [X2,X0,X1,X4] :
( ~ sP10(X0,X1,X2)
| ~ aElementOf0(X4,X2)
| sbrdtbr0(X4) = X0 ),
inference(cnf_transformation,[],[f291]) ).
fof(f291,plain,
! [X0,X1,X2] :
( ( sP10(X0,X1,X2)
| ( ( sbrdtbr0(sK32(X0,X1,X2)) != X0
| ~ aSubsetOf0(sK32(X0,X1,X2),X1)
| ~ aElementOf0(sK32(X0,X1,X2),X2) )
& ( ( sbrdtbr0(sK32(X0,X1,X2)) = X0
& aSubsetOf0(sK32(X0,X1,X2),X1) )
| aElementOf0(sK32(X0,X1,X2),X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| sbrdtbr0(X4) != X0
| ~ aSubsetOf0(X4,X1) )
& ( ( sbrdtbr0(X4) = X0
& aSubsetOf0(X4,X1) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| ~ sP10(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f289,f290]) ).
fof(f290,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( sbrdtbr0(X3) != X0
| ~ aSubsetOf0(X3,X1)
| ~ aElementOf0(X3,X2) )
& ( ( sbrdtbr0(X3) = X0
& aSubsetOf0(X3,X1) )
| aElementOf0(X3,X2) ) )
=> ( ( sbrdtbr0(sK32(X0,X1,X2)) != X0
| ~ aSubsetOf0(sK32(X0,X1,X2),X1)
| ~ aElementOf0(sK32(X0,X1,X2),X2) )
& ( ( sbrdtbr0(sK32(X0,X1,X2)) = X0
& aSubsetOf0(sK32(X0,X1,X2),X1) )
| aElementOf0(sK32(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f289,plain,
! [X0,X1,X2] :
( ( sP10(X0,X1,X2)
| ? [X3] :
( ( sbrdtbr0(X3) != X0
| ~ aSubsetOf0(X3,X1)
| ~ aElementOf0(X3,X2) )
& ( ( sbrdtbr0(X3) = X0
& aSubsetOf0(X3,X1) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| sbrdtbr0(X4) != X0
| ~ aSubsetOf0(X4,X1) )
& ( ( sbrdtbr0(X4) = X0
& aSubsetOf0(X4,X1) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| ~ sP10(X0,X1,X2) ) ),
inference(rectify,[],[f288]) ).
fof(f288,plain,
! [X1,X0,X2] :
( ( sP10(X1,X0,X2)
| ? [X3] :
( ( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| ~ aElementOf0(X3,X2) )
& ( ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0) )
& ( ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| ~ sP10(X1,X0,X2) ) ),
inference(flattening,[],[f287]) ).
fof(f287,plain,
! [X1,X0,X2] :
( ( sP10(X1,X0,X2)
| ? [X3] :
( ( sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0)
| ~ aElementOf0(X3,X2) )
& ( ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| sbrdtbr0(X3) != X1
| ~ aSubsetOf0(X3,X0) )
& ( ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| ~ sP10(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f206]) ).
fof(f206,plain,
! [X1,X0,X2] :
( sP10(X1,X0,X2)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f344,plain,
! [X0] :
( sz00 != sbrdtbr0(X0)
| slcrc0 = X0
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f230]) ).
fof(f402,plain,
! [X0] :
( aElementOf0(sK26(X0),X0)
| slcrc0 = X0
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f261]) ).
fof(f1093,plain,
( spl33_21
| spl33_22
| spl33_15 ),
inference(avatar_split_clause,[],[f894,f859,f1090,f1086]) ).
fof(f1086,plain,
( spl33_21
<=> aElement0(sK21(szmzizndt0(xS))) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_21])]) ).
fof(f1090,plain,
( spl33_22
<=> sz00 = szmzizndt0(xS) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_22])]) ).
fof(f894,plain,
( sz00 = szmzizndt0(xS)
| aElement0(sK21(szmzizndt0(xS)))
| spl33_15 ),
inference(resolution,[],[f892,f662]) ).
fof(f662,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sz00 = X0
| aElement0(sK21(X0)) ),
inference(subsumption_resolution,[],[f661,f313]) ).
fof(f661,plain,
! [X0] :
( sz00 = X0
| ~ aElementOf0(X0,szNzAzT0)
| aElement0(sK21(X0))
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f370,f348]) ).
fof(f348,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,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/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f370,plain,
! [X0] :
( aElementOf0(sK21(X0),szNzAzT0)
| sz00 = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f238]) ).
fof(f238,plain,
! [X0] :
( ( szszuzczcdt0(sK21(X0)) = X0
& aElementOf0(sK21(X0),szNzAzT0) )
| sz00 = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f129,f237]) ).
fof(f237,plain,
! [X0] :
( ? [X1] :
( szszuzczcdt0(X1) = X0
& aElementOf0(X1,szNzAzT0) )
=> ( szszuzczcdt0(sK21(X0)) = X0
& aElementOf0(sK21(X0),szNzAzT0) ) ),
introduced(choice_axiom,[]) ).
fof(f129,plain,
! [X0] :
( ? [X1] :
( szszuzczcdt0(X1) = X0
& aElementOf0(X1,szNzAzT0) )
| sz00 = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f128]) ).
fof(f128,plain,
! [X0] :
( ? [X1] :
( szszuzczcdt0(X1) = X0
& aElementOf0(X1,szNzAzT0) )
| sz00 = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ? [X1] :
( szszuzczcdt0(X1) = X0
& aElementOf0(X1,szNzAzT0) )
| sz00 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtra) ).
fof(f1084,plain,
( spl33_19
| spl33_20
| ~ spl33_16 ),
inference(avatar_split_clause,[],[f885,f863,f1081,f1077]) ).
fof(f1077,plain,
( spl33_19
<=> aElement0(sK21(sK26(xS))) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_19])]) ).
fof(f1081,plain,
( spl33_20
<=> sz00 = sK26(xS) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_20])]) ).
fof(f885,plain,
( sz00 = sK26(xS)
| aElement0(sK21(sK26(xS)))
| ~ spl33_16 ),
inference(resolution,[],[f865,f662]) ).
fof(f1069,plain,
spl33_17,
inference(avatar_contradiction_clause,[],[f1068]) ).
fof(f1068,plain,
( $false
| spl33_17 ),
inference(subsumption_resolution,[],[f1067,f299]) ).
fof(f299,plain,
aFunction0(xc),
inference(cnf_transformation,[],[f76]) ).
fof(f1067,plain,
( ~ aFunction0(xc)
| spl33_17 ),
inference(subsumption_resolution,[],[f1066,f514]) ).
fof(f1066,plain,
( ~ aElement0(sz00)
| ~ aFunction0(xc)
| spl33_17 ),
inference(resolution,[],[f1060,f413]) ).
fof(f413,plain,
! [X0,X1] :
( sP7(X0,X1)
| ~ aElement0(X1)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f201]) ).
fof(f201,plain,
! [X0,X1] :
( sP7(X0,X1)
| ~ aElement0(X1)
| ~ aFunction0(X0) ),
inference(definition_folding,[],[f157,f200,f199]) ).
fof(f199,plain,
! [X1,X0,X2] :
( sP6(X1,X0,X2)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& aSet0(X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f200,plain,
! [X0,X1] :
( ! [X2] :
( sdtlbdtrb0(X0,X1) = X2
<=> sP6(X1,X0,X2) )
| ~ sP7(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f157,plain,
! [X0,X1] :
( ! [X2] :
( sdtlbdtrb0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& aSet0(X2) ) )
| ~ aElement0(X1)
| ~ aFunction0(X0) ),
inference(flattening,[],[f156]) ).
fof(f156,plain,
! [X0,X1] :
( ! [X2] :
( sdtlbdtrb0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& aSet0(X2) ) )
| ~ aElement0(X1)
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f66]) ).
fof(f66,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aFunction0(X0) )
=> ! [X2] :
( sdtlbdtrb0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sdtlpdtrp0(X0,X3) = X1
& aElementOf0(X3,szDzozmdt0(X0)) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPtt) ).
fof(f1060,plain,
( ~ sP7(xc,sz00)
| spl33_17 ),
inference(avatar_component_clause,[],[f1058]) ).
fof(f1058,plain,
( spl33_17
<=> sP7(xc,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_17])]) ).
fof(f1065,plain,
( ~ spl33_17
| spl33_18
| ~ spl33_9 ),
inference(avatar_split_clause,[],[f956,f704,f1062,f1058]) ).
fof(f1062,plain,
( spl33_18
<=> sP6(sz00,xc,slcrc0) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_18])]) ).
fof(f956,plain,
( sP6(sz00,xc,slcrc0)
| ~ sP7(xc,sz00)
| ~ spl33_9 ),
inference(superposition,[],[f480,f931]) ).
fof(f931,plain,
( slcrc0 = sdtlbdtrb0(xc,sz00)
| ~ spl33_9 ),
inference(resolution,[],[f929,f514]) ).
fof(f929,plain,
( ! [X0] :
( ~ aElement0(X0)
| slcrc0 = sdtlbdtrb0(xc,X0) )
| ~ spl33_9 ),
inference(subsumption_resolution,[],[f927,f784]) ).
fof(f784,plain,
( ! [X0] :
( aSet0(sdtlbdtrb0(xc,X0))
| ~ aElement0(X0) )
| ~ spl33_9 ),
inference(subsumption_resolution,[],[f781,f479]) ).
fof(f781,plain,
( ! [X0] :
( ~ aElement0(X0)
| aSet0(sdtlbdtrb0(xc,X0))
| ~ aSet0(slcrc0) )
| ~ spl33_9 ),
inference(resolution,[],[f728,f352]) ).
fof(f728,plain,
( ! [X0] :
( aSubsetOf0(sdtlbdtrb0(xc,X0),slcrc0)
| ~ aElement0(X0) )
| ~ spl33_9 ),
inference(subsumption_resolution,[],[f723,f299]) ).
fof(f723,plain,
( ! [X0] :
( aSubsetOf0(sdtlbdtrb0(xc,X0),slcrc0)
| ~ aElement0(X0)
| ~ aFunction0(xc) )
| ~ spl33_9 ),
inference(superposition,[],[f403,f706]) ).
fof(f403,plain,
! [X0,X1] :
( aSubsetOf0(sdtlbdtrb0(X0,X1),szDzozmdt0(X0))
| ~ aElement0(X1)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f155]) ).
fof(f155,plain,
! [X0,X1] :
( aSubsetOf0(sdtlbdtrb0(X0,X1),szDzozmdt0(X0))
| ~ aElement0(X1)
| ~ aFunction0(X0) ),
inference(flattening,[],[f154]) ).
fof(f154,plain,
! [X0,X1] :
( aSubsetOf0(sdtlbdtrb0(X0,X1),szDzozmdt0(X0))
| ~ aElement0(X1)
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aFunction0(X0) )
=> aSubsetOf0(sdtlbdtrb0(X0,X1),szDzozmdt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPttSet) ).
fof(f927,plain,
( ! [X0] :
( ~ aElement0(X0)
| slcrc0 = sdtlbdtrb0(xc,X0)
| ~ aSet0(sdtlbdtrb0(xc,X0)) )
| ~ spl33_9 ),
inference(resolution,[],[f849,f402]) ).
fof(f849,plain,
( ! [X0,X1] :
( ~ aElementOf0(X0,sdtlbdtrb0(xc,X1))
| ~ aElement0(X1) )
| ~ spl33_9 ),
inference(subsumption_resolution,[],[f848,f479]) ).
fof(f848,plain,
( ! [X0,X1] :
( ~ aElementOf0(X0,sdtlbdtrb0(xc,X1))
| ~ aSet0(slcrc0)
| ~ aElement0(X1) )
| ~ spl33_9 ),
inference(subsumption_resolution,[],[f842,f478]) ).
fof(f478,plain,
! [X2] : ~ aElementOf0(X2,slcrc0),
inference(equality_resolution,[],[f401]) ).
fof(f401,plain,
! [X2,X0] :
( ~ aElementOf0(X2,X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f261]) ).
fof(f842,plain,
( ! [X0,X1] :
( ~ aElementOf0(X0,sdtlbdtrb0(xc,X1))
| aElementOf0(X0,slcrc0)
| ~ aSet0(slcrc0)
| ~ aElement0(X1) )
| ~ spl33_9 ),
inference(resolution,[],[f353,f728]) ).
fof(f480,plain,
! [X0,X1] :
( sP6(X1,X0,sdtlbdtrb0(X0,X1))
| ~ sP7(X0,X1) ),
inference(equality_resolution,[],[f404]) ).
fof(f404,plain,
! [X2,X0,X1] :
( sP6(X1,X0,X2)
| sdtlbdtrb0(X0,X1) != X2
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f262]) ).
fof(f262,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtlbdtrb0(X0,X1) = X2
| ~ sP6(X1,X0,X2) )
& ( sP6(X1,X0,X2)
| sdtlbdtrb0(X0,X1) != X2 ) )
| ~ sP7(X0,X1) ),
inference(nnf_transformation,[],[f200]) ).
fof(f882,plain,
( spl33_2
| ~ spl33_15 ),
inference(avatar_contradiction_clause,[],[f881]) ).
fof(f881,plain,
( $false
| spl33_2
| ~ spl33_15 ),
inference(subsumption_resolution,[],[f872,f310]) ).
fof(f872,plain,
( ~ isFinite0(slcrc0)
| spl33_2
| ~ spl33_15 ),
inference(superposition,[],[f510,f861]) ).
fof(f861,plain,
( slcrc0 = xS
| ~ spl33_15 ),
inference(avatar_component_clause,[],[f859]) ).
fof(f879,plain,
~ spl33_15,
inference(avatar_contradiction_clause,[],[f878]) ).
fof(f878,plain,
( $false
| ~ spl33_15 ),
inference(subsumption_resolution,[],[f869,f495]) ).
fof(f495,plain,
~ isCountable0(slcrc0),
inference(subsumption_resolution,[],[f473,f479]) ).
fof(f473,plain,
( ~ isCountable0(slcrc0)
| ~ aSet0(slcrc0) ),
inference(equality_resolution,[],[f385]) ).
fof(f385,plain,
! [X0] :
( slcrc0 != X0
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
! [X0] :
( slcrc0 != X0
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(flattening,[],[f137]) ).
fof(f137,plain,
! [X0] :
( slcrc0 != X0
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( ( isCountable0(X0)
& aSet0(X0) )
=> slcrc0 != X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin_01) ).
fof(f869,plain,
( isCountable0(slcrc0)
| ~ spl33_15 ),
inference(superposition,[],[f305,f861]) ).
fof(f305,plain,
isCountable0(xS),
inference(cnf_transformation,[],[f75]) ).
fof(f866,plain,
( spl33_15
| spl33_16
| ~ spl33_1 ),
inference(avatar_split_clause,[],[f856,f504,f863,f859]) ).
fof(f856,plain,
( aElementOf0(sK26(xS),szNzAzT0)
| slcrc0 = xS
| ~ spl33_1 ),
inference(subsumption_resolution,[],[f854,f505]) ).
fof(f854,plain,
( aElementOf0(sK26(xS),szNzAzT0)
| slcrc0 = xS
| ~ aSet0(xS) ),
inference(resolution,[],[f853,f402]) ).
fof(f801,plain,
( ~ spl33_9
| spl33_13 ),
inference(avatar_contradiction_clause,[],[f800]) ).
fof(f800,plain,
( $false
| ~ spl33_9
| spl33_13 ),
inference(subsumption_resolution,[],[f799,f729]) ).
fof(f729,plain,
( sP1(slcrc0,xc)
| ~ spl33_9 ),
inference(subsumption_resolution,[],[f724,f299]) ).
fof(f724,plain,
( sP1(slcrc0,xc)
| ~ aFunction0(xc)
| ~ spl33_9 ),
inference(superposition,[],[f550,f706]) ).
fof(f550,plain,
! [X0] :
( sP1(szDzozmdt0(X0),X0)
| ~ aFunction0(X0) ),
inference(subsumption_resolution,[],[f549,f315]) ).
fof(f315,plain,
! [X0] :
( aSet0(szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0] :
( aSet0(szDzozmdt0(X0))
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f64]) ).
fof(f64,axiom,
! [X0] :
( aFunction0(X0)
=> aSet0(szDzozmdt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDomSet) ).
fof(f549,plain,
! [X0] :
( sP1(szDzozmdt0(X0),X0)
| ~ aFunction0(X0)
| ~ aSet0(szDzozmdt0(X0)) ),
inference(resolution,[],[f325,f343]) ).
fof(f343,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( aSet0(X0)
=> aSubsetOf0(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
fof(f325,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,szDzozmdt0(X0))
| sP1(X1,X0)
| ~ aFunction0(X0) ),
inference(cnf_transformation,[],[f192]) ).
fof(f192,plain,
! [X0] :
( ! [X1] :
( sP1(X1,X0)
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(definition_folding,[],[f94,f191,f190]) ).
fof(f190,plain,
! [X2,X0,X1] :
( sP0(X2,X0,X1)
<=> ( ! [X3] :
( sdtlpdtrp0(X0,X3) = sdtlpdtrp0(X2,X3)
| ~ aElementOf0(X3,X1) )
& szDzozmdt0(X2) = X1
& aFunction0(X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f191,plain,
! [X1,X0] :
( ! [X2] :
( sdtexdt0(X0,X1) = X2
<=> sP0(X2,X0,X1) )
| ~ sP1(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f94,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( sdtexdt0(X0,X1) = X2
<=> ( ! [X3] :
( sdtlpdtrp0(X0,X3) = sdtlpdtrp0(X2,X3)
| ~ aElementOf0(X3,X1) )
& szDzozmdt0(X2) = X1
& aFunction0(X2) ) )
| ~ aSubsetOf0(X1,szDzozmdt0(X0)) )
| ~ aFunction0(X0) ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,axiom,
! [X0] :
( aFunction0(X0)
=> ! [X1] :
( aSubsetOf0(X1,szDzozmdt0(X0))
=> ! [X2] :
( sdtexdt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X1)
=> sdtlpdtrp0(X0,X3) = sdtlpdtrp0(X2,X3) )
& szDzozmdt0(X2) = X1
& aFunction0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefRst) ).
fof(f799,plain,
( ~ sP1(slcrc0,xc)
| spl33_13 ),
inference(resolution,[],[f790,f618]) ).
fof(f618,plain,
! [X0,X1] :
( aFunction0(sdtexdt0(X1,X0))
| ~ sP1(X0,X1) ),
inference(resolution,[],[f466,f320]) ).
fof(f320,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| aFunction0(X0) ),
inference(cnf_transformation,[],[f218]) ).
fof(f218,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( sdtlpdtrp0(X0,sK14(X0,X1,X2)) != sdtlpdtrp0(X1,sK14(X0,X1,X2))
& aElementOf0(sK14(X0,X1,X2),X2) )
| szDzozmdt0(X0) != X2
| ~ aFunction0(X0) )
& ( ( ! [X4] :
( sdtlpdtrp0(X0,X4) = sdtlpdtrp0(X1,X4)
| ~ aElementOf0(X4,X2) )
& szDzozmdt0(X0) = X2
& aFunction0(X0) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f216,f217]) ).
fof(f217,plain,
! [X0,X1,X2] :
( ? [X3] :
( sdtlpdtrp0(X0,X3) != sdtlpdtrp0(X1,X3)
& aElementOf0(X3,X2) )
=> ( sdtlpdtrp0(X0,sK14(X0,X1,X2)) != sdtlpdtrp0(X1,sK14(X0,X1,X2))
& aElementOf0(sK14(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f216,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( sdtlpdtrp0(X0,X3) != sdtlpdtrp0(X1,X3)
& aElementOf0(X3,X2) )
| szDzozmdt0(X0) != X2
| ~ aFunction0(X0) )
& ( ( ! [X4] :
( sdtlpdtrp0(X0,X4) = sdtlpdtrp0(X1,X4)
| ~ aElementOf0(X4,X2) )
& szDzozmdt0(X0) = X2
& aFunction0(X0) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f215]) ).
fof(f215,plain,
! [X2,X0,X1] :
( ( sP0(X2,X0,X1)
| ? [X3] :
( sdtlpdtrp0(X0,X3) != sdtlpdtrp0(X2,X3)
& aElementOf0(X3,X1) )
| szDzozmdt0(X2) != X1
| ~ aFunction0(X2) )
& ( ( ! [X3] :
( sdtlpdtrp0(X0,X3) = sdtlpdtrp0(X2,X3)
| ~ aElementOf0(X3,X1) )
& szDzozmdt0(X2) = X1
& aFunction0(X2) )
| ~ sP0(X2,X0,X1) ) ),
inference(flattening,[],[f214]) ).
fof(f214,plain,
! [X2,X0,X1] :
( ( sP0(X2,X0,X1)
| ? [X3] :
( sdtlpdtrp0(X0,X3) != sdtlpdtrp0(X2,X3)
& aElementOf0(X3,X1) )
| szDzozmdt0(X2) != X1
| ~ aFunction0(X2) )
& ( ( ! [X3] :
( sdtlpdtrp0(X0,X3) = sdtlpdtrp0(X2,X3)
| ~ aElementOf0(X3,X1) )
& szDzozmdt0(X2) = X1
& aFunction0(X2) )
| ~ sP0(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f190]) ).
fof(f466,plain,
! [X0,X1] :
( sP0(sdtexdt0(X1,X0),X1,X0)
| ~ sP1(X0,X1) ),
inference(equality_resolution,[],[f318]) ).
fof(f318,plain,
! [X2,X0,X1] :
( sP0(X2,X1,X0)
| sdtexdt0(X1,X0) != X2
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f213]) ).
fof(f213,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtexdt0(X1,X0) = X2
| ~ sP0(X2,X1,X0) )
& ( sP0(X2,X1,X0)
| sdtexdt0(X1,X0) != X2 ) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f212]) ).
fof(f212,plain,
! [X1,X0] :
( ! [X2] :
( ( sdtexdt0(X0,X1) = X2
| ~ sP0(X2,X0,X1) )
& ( sP0(X2,X0,X1)
| sdtexdt0(X0,X1) != X2 ) )
| ~ sP1(X1,X0) ),
inference(nnf_transformation,[],[f191]) ).
fof(f790,plain,
( ~ aFunction0(sdtexdt0(xc,slcrc0))
| spl33_13 ),
inference(avatar_component_clause,[],[f788]) ).
fof(f788,plain,
( spl33_13
<=> aFunction0(sdtexdt0(xc,slcrc0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_13])]) ).
fof(f795,plain,
( ~ spl33_13
| spl33_14
| ~ spl33_9 ),
inference(avatar_split_clause,[],[f777,f704,f792,f788]) ).
fof(f792,plain,
( spl33_14
<=> sP1(slcrc0,sdtexdt0(xc,slcrc0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_14])]) ).
fof(f777,plain,
( sP1(slcrc0,sdtexdt0(xc,slcrc0))
| ~ aFunction0(sdtexdt0(xc,slcrc0))
| ~ spl33_9 ),
inference(superposition,[],[f550,f731]) ).
fof(f731,plain,
( slcrc0 = szDzozmdt0(sdtexdt0(xc,slcrc0))
| ~ spl33_9 ),
inference(resolution,[],[f729,f617]) ).
fof(f617,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| szDzozmdt0(sdtexdt0(X1,X0)) = X0 ),
inference(resolution,[],[f466,f321]) ).
fof(f321,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| szDzozmdt0(X0) = X2 ),
inference(cnf_transformation,[],[f218]) ).
fof(f763,plain,
spl33_12,
inference(avatar_contradiction_clause,[],[f762]) ).
fof(f762,plain,
( $false
| spl33_12 ),
inference(subsumption_resolution,[],[f761,f313]) ).
fof(f761,plain,
( ~ aSet0(szNzAzT0)
| spl33_12 ),
inference(resolution,[],[f759,f343]) ).
fof(f759,plain,
( ~ aSubsetOf0(szNzAzT0,szNzAzT0)
| spl33_12 ),
inference(avatar_component_clause,[],[f757]) ).
fof(f757,plain,
( spl33_12
<=> aSubsetOf0(szNzAzT0,szNzAzT0) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_12])]) ).
fof(f760,plain,
( spl33_11
| ~ spl33_12
| spl33_4 ),
inference(avatar_split_clause,[],[f746,f586,f757,f753]) ).
fof(f753,plain,
( spl33_11
<=> sP5(szmzizndt0(szNzAzT0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_11])]) ).
fof(f586,plain,
( spl33_4
<=> slcrc0 = szNzAzT0 ),
introduced(avatar_definition,[new_symbols(naming,[spl33_4])]) ).
fof(f746,plain,
( ~ aSubsetOf0(szNzAzT0,szNzAzT0)
| sP5(szmzizndt0(szNzAzT0))
| spl33_4 ),
inference(subsumption_resolution,[],[f738,f587]) ).
fof(f587,plain,
( slcrc0 != szNzAzT0
| spl33_4 ),
inference(avatar_component_clause,[],[f586]) ).
fof(f738,plain,
( slcrc0 = szNzAzT0
| ~ aSubsetOf0(szNzAzT0,szNzAzT0)
| sP5(szmzizndt0(szNzAzT0)) ),
inference(resolution,[],[f477,f381]) ).
fof(f381,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sP5(X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f198,plain,
! [X0] :
( sP5(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(definition_folding,[],[f130,f197,f196]) ).
fof(f196,plain,
! [X0,X1] :
( sP4(X0,X1)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& aSet0(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f197,plain,
! [X0] :
( ! [X1] :
( slbdtrb0(X0) = X1
<=> sP4(X0,X1) )
| ~ sP5(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( slbdtrb0(X0) = X1
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& aSet0(X1) ) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( slbdtrb0(X0) = X1
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSeg) ).
fof(f711,plain,
( spl33_9
| spl33_10
| ~ spl33_5
| ~ spl33_6 ),
inference(avatar_split_clause,[],[f702,f629,f625,f708,f704]) ).
fof(f702,plain,
( aSubsetOf0(sK26(szDzozmdt0(xc)),xS)
| slcrc0 = szDzozmdt0(xc)
| ~ spl33_5
| ~ spl33_6 ),
inference(subsumption_resolution,[],[f701,f631]) ).
fof(f701,plain,
( aSubsetOf0(sK26(szDzozmdt0(xc)),xS)
| slcrc0 = szDzozmdt0(xc)
| ~ aSet0(szDzozmdt0(xc))
| ~ spl33_5 ),
inference(resolution,[],[f700,f402]) ).
fof(f700,plain,
( ! [X0] :
( ~ aElementOf0(X0,szDzozmdt0(xc))
| aSubsetOf0(X0,xS) )
| ~ spl33_5 ),
inference(resolution,[],[f445,f639]) ).
fof(f445,plain,
! [X2,X0,X1,X4] :
( ~ sP10(X0,X1,X2)
| ~ aElementOf0(X4,X2)
| aSubsetOf0(X4,X1) ),
inference(cnf_transformation,[],[f291]) ).
fof(f680,plain,
( spl33_7
| spl33_8
| spl33_4 ),
inference(avatar_split_clause,[],[f671,f586,f677,f673]) ).
fof(f673,plain,
( spl33_7
<=> aElement0(sK21(sK26(szNzAzT0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_7])]) ).
fof(f677,plain,
( spl33_8
<=> sz00 = sK26(szNzAzT0) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_8])]) ).
fof(f671,plain,
( sz00 = sK26(szNzAzT0)
| aElement0(sK21(sK26(szNzAzT0)))
| spl33_4 ),
inference(subsumption_resolution,[],[f670,f313]) ).
fof(f670,plain,
( sz00 = sK26(szNzAzT0)
| aElement0(sK21(sK26(szNzAzT0)))
| ~ aSet0(szNzAzT0)
| spl33_4 ),
inference(subsumption_resolution,[],[f668,f587]) ).
fof(f668,plain,
( sz00 = sK26(szNzAzT0)
| aElement0(sK21(sK26(szNzAzT0)))
| slcrc0 = szNzAzT0
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f662,f402]) ).
fof(f636,plain,
( ~ spl33_1
| spl33_5 ),
inference(avatar_contradiction_clause,[],[f635]) ).
fof(f635,plain,
( $false
| ~ spl33_1
| spl33_5 ),
inference(subsumption_resolution,[],[f634,f505]) ).
fof(f634,plain,
( ~ aSet0(xS)
| spl33_5 ),
inference(subsumption_resolution,[],[f633,f494]) ).
fof(f633,plain,
( ~ aElementOf0(sz00,szNzAzT0)
| ~ aSet0(xS)
| spl33_5 ),
inference(resolution,[],[f627,f451]) ).
fof(f451,plain,
! [X0,X1] :
( sP11(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f208]) ).
fof(f208,plain,
! [X0,X1] :
( sP11(X0,X1)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f169,f207,f206]) ).
fof(f169,plain,
! [X0,X1] :
( ! [X2] :
( slbdtsldtrb0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(flattening,[],[f168]) ).
fof(f168,plain,
! [X0,X1] :
( ! [X2] :
( slbdtsldtrb0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aSet0(X0) )
=> ! [X2] :
( slbdtsldtrb0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( sbrdtbr0(X3) = X1
& aSubsetOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
fof(f627,plain,
( ~ sP11(xS,sz00)
| spl33_5 ),
inference(avatar_component_clause,[],[f625]) ).
fof(f632,plain,
( ~ spl33_5
| spl33_6 ),
inference(avatar_split_clause,[],[f623,f629,f625]) ).
fof(f623,plain,
( aSet0(szDzozmdt0(xc))
| ~ sP11(xS,sz00) ),
inference(superposition,[],[f621,f497]) ).
fof(f621,plain,
! [X0,X1] :
( aSet0(slbdtsldtrb0(X0,X1))
| ~ sP11(X0,X1) ),
inference(resolution,[],[f488,f444]) ).
fof(f444,plain,
! [X2,X0,X1] :
( ~ sP10(X0,X1,X2)
| aSet0(X2) ),
inference(cnf_transformation,[],[f291]) ).
fof(f614,plain,
~ spl33_4,
inference(avatar_contradiction_clause,[],[f613]) ).
fof(f613,plain,
( $false
| ~ spl33_4 ),
inference(subsumption_resolution,[],[f600,f310]) ).
fof(f600,plain,
( ~ isFinite0(slcrc0)
| ~ spl33_4 ),
inference(superposition,[],[f502,f588]) ).
fof(f588,plain,
( slcrc0 = szNzAzT0
| ~ spl33_4 ),
inference(avatar_component_clause,[],[f586]) ).
fof(f612,plain,
~ spl33_4,
inference(avatar_contradiction_clause,[],[f611]) ).
fof(f611,plain,
( $false
| ~ spl33_4 ),
inference(subsumption_resolution,[],[f599,f478]) ).
fof(f599,plain,
( aElementOf0(sz00,slcrc0)
| ~ spl33_4 ),
inference(superposition,[],[f494,f588]) ).
fof(f605,plain,
~ spl33_4,
inference(avatar_contradiction_clause,[],[f604]) ).
fof(f604,plain,
( $false
| ~ spl33_4 ),
inference(subsumption_resolution,[],[f592,f495]) ).
fof(f592,plain,
( isCountable0(slcrc0)
| ~ spl33_4 ),
inference(superposition,[],[f314,f588]) ).
fof(f589,plain,
( spl33_3
| spl33_4 ),
inference(avatar_split_clause,[],[f580,f586,f582]) ).
fof(f582,plain,
( spl33_3
<=> sP5(sK26(szNzAzT0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl33_3])]) ).
fof(f580,plain,
( slcrc0 = szNzAzT0
| sP5(sK26(szNzAzT0)) ),
inference(subsumption_resolution,[],[f575,f313]) ).
fof(f575,plain,
( slcrc0 = szNzAzT0
| ~ aSet0(szNzAzT0)
| sP5(sK26(szNzAzT0)) ),
inference(resolution,[],[f402,f381]) ).
fof(f527,plain,
spl33_1,
inference(avatar_contradiction_clause,[],[f526]) ).
fof(f526,plain,
( $false
| spl33_1 ),
inference(subsumption_resolution,[],[f525,f313]) ).
fof(f525,plain,
( ~ aSet0(szNzAzT0)
| spl33_1 ),
inference(subsumption_resolution,[],[f521,f506]) ).
fof(f506,plain,
( ~ aSet0(xS)
| spl33_1 ),
inference(avatar_component_clause,[],[f504]) ).
fof(f521,plain,
( aSet0(xS)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f352,f304]) ).
fof(f511,plain,
( ~ spl33_1
| ~ spl33_2 ),
inference(avatar_split_clause,[],[f500,f508,f504]) ).
fof(f500,plain,
( ~ isFinite0(xS)
| ~ aSet0(xS) ),
inference(resolution,[],[f384,f305]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : NUM564+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36 % Computer : n021.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 3 14:12:38 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.16/0.36 % (28160)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.38 % (28172)WARNING: value z3 for option sas not known
% 0.16/0.38 % (28171)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.38 % (28169)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.38 % (28172)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)
% 0.16/0.38 % (28176)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)
% 0.16/0.38 % (28173)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.38 % (28177)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)
% 0.16/0.39 % (28175)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)
% 0.16/0.40 TRYING [1]
% 0.16/0.40 TRYING [1]
% 0.16/0.40 TRYING [2]
% 0.16/0.40 TRYING [2]
% 0.16/0.41 TRYING [3]
% 0.22/0.42 TRYING [3]
% 0.22/0.43 % (28172)First to succeed.
% 0.22/0.43 TRYING [1]
% 0.22/0.43 TRYING [2]
% 0.22/0.43 % (28172)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-28160"
% 0.22/0.44 % (28172)Refutation found. Thanks to Tanya!
% 0.22/0.44 % SZS status Theorem for theBenchmark
% 0.22/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.44 % (28172)------------------------------
% 0.22/0.44 % (28172)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.44 % (28172)Termination reason: Refutation
% 0.22/0.44
% 0.22/0.44 % (28172)Memory used [KB]: 1596
% 0.22/0.44 % (28172)Time elapsed: 0.053 s
% 0.22/0.44 % (28172)Instructions burned: 76 (million)
% 0.22/0.44 % (28160)Success in time 0.068 s
%------------------------------------------------------------------------------