TSTP Solution File: NUM533+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM533+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n005.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 : Tue May 21 02:07:51 EDT 2024
% Result : Theorem 0.13s 0.39s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 47
% Syntax : Number of formulae : 160 ( 28 unt; 0 def)
% Number of atoms : 546 ( 39 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 677 ( 291 ~; 297 |; 37 &)
% ( 41 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 43 ( 41 usr; 38 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 127 ( 118 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f300,plain,
$false,
inference(avatar_sat_refutation,[],[f66,f71,f76,f81,f86,f91,f96,f101,f105,f109,f113,f121,f125,f134,f142,f146,f153,f166,f171,f175,f181,f192,f201,f205,f222,f235,f237,f248,f254,f260,f268,f279,f286,f296,f299]) ).
fof(f299,plain,
( ~ spl2_4
| spl2_3
| ~ spl2_6
| ~ spl2_16
| ~ spl2_37 ),
inference(avatar_split_clause,[],[f298,f294,f144,f88,f73,f78]) ).
fof(f78,plain,
( spl2_4
<=> aSet0(xA) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
fof(f73,plain,
( spl2_3
<=> aSubsetOf0(xA,xC) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
fof(f88,plain,
( spl2_6
<=> aSet0(xC) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).
fof(f144,plain,
( spl2_16
<=> ! [X0,X1] :
( aSubsetOf0(X1,X0)
| ~ aElementOf0(sK0(X0,X1),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).
fof(f294,plain,
( spl2_37
<=> ! [X0] :
( aElementOf0(sK0(X0,xA),xC)
| ~ aSet0(X0)
| aSubsetOf0(xA,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_37])]) ).
fof(f298,plain,
( ~ aSet0(xC)
| aSubsetOf0(xA,xC)
| ~ aSet0(xA)
| ~ spl2_16
| ~ spl2_37 ),
inference(duplicate_literal_removal,[],[f297]) ).
fof(f297,plain,
( ~ aSet0(xC)
| aSubsetOf0(xA,xC)
| aSubsetOf0(xA,xC)
| ~ aSet0(xA)
| ~ aSet0(xC)
| ~ spl2_16
| ~ spl2_37 ),
inference(resolution,[],[f295,f145]) ).
fof(f145,plain,
( ! [X0,X1] :
( ~ aElementOf0(sK0(X0,X1),X0)
| aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ~ aSet0(X0) )
| ~ spl2_16 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f295,plain,
( ! [X0] :
( aElementOf0(sK0(X0,xA),xC)
| ~ aSet0(X0)
| aSubsetOf0(xA,X0) )
| ~ spl2_37 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f296,plain,
( spl2_37
| ~ spl2_22
| ~ spl2_32 ),
inference(avatar_split_clause,[],[f263,f246,f179,f294]) ).
fof(f179,plain,
( spl2_22
<=> ! [X0] :
( ~ aElementOf0(X0,xB)
| aElementOf0(X0,xC) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_22])]) ).
fof(f246,plain,
( spl2_32
<=> ! [X0] :
( aElementOf0(sK0(X0,xA),xB)
| ~ aSet0(X0)
| aSubsetOf0(xA,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_32])]) ).
fof(f263,plain,
( ! [X0] :
( aElementOf0(sK0(X0,xA),xC)
| ~ aSet0(X0)
| aSubsetOf0(xA,X0) )
| ~ spl2_22
| ~ spl2_32 ),
inference(resolution,[],[f180,f247]) ).
fof(f247,plain,
( ! [X0] :
( aElementOf0(sK0(X0,xA),xB)
| ~ aSet0(X0)
| aSubsetOf0(xA,X0) )
| ~ spl2_32 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f180,plain,
( ! [X0] :
( ~ aElementOf0(X0,xB)
| aElementOf0(X0,xC) )
| ~ spl2_22 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f286,plain,
( spl2_19
| ~ spl2_7
| ~ spl2_28 ),
inference(avatar_split_clause,[],[f226,f215,f93,f163]) ).
fof(f163,plain,
( spl2_19
<=> isFinite0(xA) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_19])]) ).
fof(f93,plain,
( spl2_7
<=> isFinite0(slcrc0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).
fof(f215,plain,
( spl2_28
<=> slcrc0 = xA ),
introduced(avatar_definition,[new_symbols(naming,[spl2_28])]) ).
fof(f226,plain,
( isFinite0(xA)
| ~ spl2_7
| ~ spl2_28 ),
inference(superposition,[],[f95,f217]) ).
fof(f217,plain,
( slcrc0 = xA
| ~ spl2_28 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f95,plain,
( isFinite0(slcrc0)
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f279,plain,
( spl2_36
| ~ spl2_22
| ~ spl2_29 ),
inference(avatar_split_clause,[],[f261,f219,f179,f276]) ).
fof(f276,plain,
( spl2_36
<=> aElementOf0(sK1(xA),xC) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_36])]) ).
fof(f219,plain,
( spl2_29
<=> aElementOf0(sK1(xA),xB) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_29])]) ).
fof(f261,plain,
( aElementOf0(sK1(xA),xC)
| ~ spl2_22
| ~ spl2_29 ),
inference(resolution,[],[f180,f221]) ).
fof(f221,plain,
( aElementOf0(sK1(xA),xB)
| ~ spl2_29 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f268,plain,
( ~ spl2_5
| spl2_35
| ~ spl2_15
| ~ spl2_22 ),
inference(avatar_split_clause,[],[f183,f179,f140,f266,f83]) ).
fof(f83,plain,
( spl2_5
<=> aSet0(xB) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
fof(f266,plain,
( spl2_35
<=> ! [X0] :
( aElementOf0(sK0(X0,xB),xC)
| ~ aSet0(X0)
| aSubsetOf0(xB,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_35])]) ).
fof(f140,plain,
( spl2_15
<=> ! [X0,X1] :
( aSubsetOf0(X1,X0)
| aElementOf0(sK0(X0,X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_15])]) ).
fof(f183,plain,
( ! [X0] :
( aElementOf0(sK0(X0,xB),xC)
| aSubsetOf0(xB,X0)
| ~ aSet0(xB)
| ~ aSet0(X0) )
| ~ spl2_15
| ~ spl2_22 ),
inference(resolution,[],[f180,f141]) ).
fof(f141,plain,
( ! [X0,X1] :
( aElementOf0(sK0(X0,X1),X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ~ aSet0(X0) )
| ~ spl2_15 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f260,plain,
( spl2_34
| ~ spl2_30
| ~ spl2_33 ),
inference(avatar_split_clause,[],[f256,f252,f228,f258]) ).
fof(f258,plain,
( spl2_34
<=> ! [X0] :
( xB = X0
| ~ aSubsetOf0(X0,xB)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_34])]) ).
fof(f228,plain,
( spl2_30
<=> slcrc0 = xB ),
introduced(avatar_definition,[new_symbols(naming,[spl2_30])]) ).
fof(f252,plain,
( spl2_33
<=> ! [X0] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X0,slcrc0)
| slcrc0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_33])]) ).
fof(f256,plain,
( ! [X0] :
( xB = X0
| ~ aSubsetOf0(X0,xB)
| ~ aSet0(X0) )
| ~ spl2_30
| ~ spl2_33 ),
inference(forward_demodulation,[],[f255,f230]) ).
fof(f230,plain,
( slcrc0 = xB
| ~ spl2_30 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f255,plain,
( ! [X0] :
( ~ aSubsetOf0(X0,xB)
| ~ aSet0(X0)
| slcrc0 = X0 )
| ~ spl2_30
| ~ spl2_33 ),
inference(forward_demodulation,[],[f253,f230]) ).
fof(f253,plain,
( ! [X0] :
( ~ aSubsetOf0(X0,slcrc0)
| ~ aSet0(X0)
| slcrc0 = X0 )
| ~ spl2_33 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f254,plain,
( ~ spl2_8
| spl2_33
| ~ spl2_17
| ~ spl2_27 ),
inference(avatar_split_clause,[],[f213,f203,f151,f252,f98]) ).
fof(f98,plain,
( spl2_8
<=> aSet0(slcrc0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).
fof(f151,plain,
( spl2_17
<=> ! [X0,X1] :
( X0 = X1
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_17])]) ).
fof(f203,plain,
( spl2_27
<=> ! [X0] :
( aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_27])]) ).
fof(f213,plain,
( ! [X0] :
( ~ aSet0(X0)
| slcrc0 = X0
| ~ aSubsetOf0(X0,slcrc0)
| ~ aSet0(slcrc0) )
| ~ spl2_17
| ~ spl2_27 ),
inference(duplicate_literal_removal,[],[f206]) ).
fof(f206,plain,
( ! [X0] :
( ~ aSet0(X0)
| slcrc0 = X0
| ~ aSubsetOf0(X0,slcrc0)
| ~ aSet0(slcrc0)
| ~ aSet0(X0) )
| ~ spl2_17
| ~ spl2_27 ),
inference(resolution,[],[f204,f152]) ).
fof(f152,plain,
( ! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| X0 = X1
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) )
| ~ spl2_17 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f204,plain,
( ! [X0] :
( aSubsetOf0(slcrc0,X0)
| ~ aSet0(X0) )
| ~ spl2_27 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f248,plain,
( ~ spl2_4
| spl2_32
| ~ spl2_15
| ~ spl2_21 ),
inference(avatar_split_clause,[],[f177,f173,f140,f246,f78]) ).
fof(f173,plain,
( spl2_21
<=> ! [X0] :
( ~ aElementOf0(X0,xA)
| aElementOf0(X0,xB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_21])]) ).
fof(f177,plain,
( ! [X0] :
( aElementOf0(sK0(X0,xA),xB)
| aSubsetOf0(xA,X0)
| ~ aSet0(xA)
| ~ aSet0(X0) )
| ~ spl2_15
| ~ spl2_21 ),
inference(resolution,[],[f174,f141]) ).
fof(f174,plain,
( ! [X0] :
( ~ aElementOf0(X0,xA)
| aElementOf0(X0,xB) )
| ~ spl2_21 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f237,plain,
( spl2_24
| ~ spl2_28
| ~ spl2_30 ),
inference(avatar_split_clause,[],[f236,f228,f215,f189]) ).
fof(f189,plain,
( spl2_24
<=> xA = xB ),
introduced(avatar_definition,[new_symbols(naming,[spl2_24])]) ).
fof(f236,plain,
( xA = xB
| ~ spl2_28
| ~ spl2_30 ),
inference(forward_demodulation,[],[f230,f217]) ).
fof(f235,plain,
( ~ spl2_5
| spl2_30
| spl2_31
| ~ spl2_13
| ~ spl2_22 ),
inference(avatar_split_clause,[],[f182,f179,f123,f232,f228,f83]) ).
fof(f232,plain,
( spl2_31
<=> aElementOf0(sK1(xB),xC) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_31])]) ).
fof(f123,plain,
( spl2_13
<=> ! [X0] :
( slcrc0 = X0
| aElementOf0(sK1(X0),X0)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_13])]) ).
fof(f182,plain,
( aElementOf0(sK1(xB),xC)
| slcrc0 = xB
| ~ aSet0(xB)
| ~ spl2_13
| ~ spl2_22 ),
inference(resolution,[],[f180,f124]) ).
fof(f124,plain,
( ! [X0] :
( aElementOf0(sK1(X0),X0)
| slcrc0 = X0
| ~ aSet0(X0) )
| ~ spl2_13 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f222,plain,
( ~ spl2_4
| spl2_28
| spl2_29
| ~ spl2_13
| ~ spl2_21 ),
inference(avatar_split_clause,[],[f176,f173,f123,f219,f215,f78]) ).
fof(f176,plain,
( aElementOf0(sK1(xA),xB)
| slcrc0 = xA
| ~ aSet0(xA)
| ~ spl2_13
| ~ spl2_21 ),
inference(resolution,[],[f174,f124]) ).
fof(f205,plain,
( ~ spl2_8
| spl2_27
| ~ spl2_9
| ~ spl2_15 ),
inference(avatar_split_clause,[],[f147,f140,f103,f203,f98]) ).
fof(f103,plain,
( spl2_9
<=> ! [X2] : ~ aElementOf0(X2,slcrc0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).
fof(f147,plain,
( ! [X0] :
( aSubsetOf0(slcrc0,X0)
| ~ aSet0(slcrc0)
| ~ aSet0(X0) )
| ~ spl2_9
| ~ spl2_15 ),
inference(resolution,[],[f141,f104]) ).
fof(f104,plain,
( ! [X2] : ~ aElementOf0(X2,slcrc0)
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f201,plain,
( ~ spl2_6
| ~ spl2_5
| ~ spl2_25
| spl2_26
| ~ spl2_2
| ~ spl2_17 ),
inference(avatar_split_clause,[],[f155,f151,f68,f198,f194,f83,f88]) ).
fof(f194,plain,
( spl2_25
<=> aSubsetOf0(xC,xB) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_25])]) ).
fof(f198,plain,
( spl2_26
<=> xB = xC ),
introduced(avatar_definition,[new_symbols(naming,[spl2_26])]) ).
fof(f68,plain,
( spl2_2
<=> aSubsetOf0(xB,xC) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
fof(f155,plain,
( xB = xC
| ~ aSubsetOf0(xC,xB)
| ~ aSet0(xB)
| ~ aSet0(xC)
| ~ spl2_2
| ~ spl2_17 ),
inference(resolution,[],[f152,f70]) ).
fof(f70,plain,
( aSubsetOf0(xB,xC)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f192,plain,
( ~ spl2_5
| ~ spl2_4
| ~ spl2_23
| spl2_24
| ~ spl2_1
| ~ spl2_17 ),
inference(avatar_split_clause,[],[f154,f151,f63,f189,f185,f78,f83]) ).
fof(f185,plain,
( spl2_23
<=> aSubsetOf0(xB,xA) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_23])]) ).
fof(f63,plain,
( spl2_1
<=> aSubsetOf0(xA,xB) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
fof(f154,plain,
( xA = xB
| ~ aSubsetOf0(xB,xA)
| ~ aSet0(xA)
| ~ aSet0(xB)
| ~ spl2_1
| ~ spl2_17 ),
inference(resolution,[],[f152,f65]) ).
fof(f65,plain,
( aSubsetOf0(xA,xB)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f181,plain,
( ~ spl2_6
| spl2_22
| ~ spl2_2
| ~ spl2_14 ),
inference(avatar_split_clause,[],[f136,f132,f68,f179,f88]) ).
fof(f132,plain,
( spl2_14
<=> ! [X0,X1,X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).
fof(f136,plain,
( ! [X0] :
( ~ aElementOf0(X0,xB)
| aElementOf0(X0,xC)
| ~ aSet0(xC) )
| ~ spl2_2
| ~ spl2_14 ),
inference(resolution,[],[f133,f70]) ).
fof(f133,plain,
( ! [X3,X0,X1] :
( ~ aSubsetOf0(X1,X0)
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0)
| ~ aSet0(X0) )
| ~ spl2_14 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f175,plain,
( ~ spl2_5
| spl2_21
| ~ spl2_1
| ~ spl2_14 ),
inference(avatar_split_clause,[],[f135,f132,f63,f173,f83]) ).
fof(f135,plain,
( ! [X0] :
( ~ aElementOf0(X0,xA)
| aElementOf0(X0,xB)
| ~ aSet0(xB) )
| ~ spl2_1
| ~ spl2_14 ),
inference(resolution,[],[f133,f65]) ).
fof(f171,plain,
( ~ spl2_6
| ~ spl2_20
| spl2_18
| ~ spl2_2
| ~ spl2_12 ),
inference(avatar_split_clause,[],[f127,f119,f68,f159,f168,f88]) ).
fof(f168,plain,
( spl2_20
<=> isFinite0(xC) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_20])]) ).
fof(f159,plain,
( spl2_18
<=> isFinite0(xB) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_18])]) ).
fof(f119,plain,
( spl2_12
<=> ! [X0,X1] :
( isFinite0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ isFinite0(X0)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_12])]) ).
fof(f127,plain,
( isFinite0(xB)
| ~ isFinite0(xC)
| ~ aSet0(xC)
| ~ spl2_2
| ~ spl2_12 ),
inference(resolution,[],[f120,f70]) ).
fof(f120,plain,
( ! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| isFinite0(X1)
| ~ isFinite0(X0)
| ~ aSet0(X0) )
| ~ spl2_12 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f166,plain,
( ~ spl2_5
| ~ spl2_18
| spl2_19
| ~ spl2_1
| ~ spl2_12 ),
inference(avatar_split_clause,[],[f126,f119,f63,f163,f159,f83]) ).
fof(f126,plain,
( isFinite0(xA)
| ~ isFinite0(xB)
| ~ aSet0(xB)
| ~ spl2_1
| ~ spl2_12 ),
inference(resolution,[],[f120,f65]) ).
fof(f153,plain,
spl2_17,
inference(avatar_split_clause,[],[f59,f151]) ).
fof(f59,plain,
! [X0,X1] :
( X0 = X1
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( X0 = X1
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f31]) ).
fof(f31,plain,
! [X0,X1] :
( X0 = X1
| ~ aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] :
( ( aSet0(X1)
& aSet0(X0) )
=> ( ( aSubsetOf0(X1,X0)
& aSubsetOf0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubASymm) ).
fof(f146,plain,
spl2_16,
inference(avatar_split_clause,[],[f54,f144]) ).
fof(f54,plain,
! [X0,X1] :
( aSubsetOf0(X1,X0)
| ~ aElementOf0(sK0(X0,X1),X0)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ( ~ aElementOf0(sK0(X0,X1),X0)
& aElementOf0(sK0(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,[sK0])],[f35,f36]) ).
fof(f36,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) )
=> ( ~ aElementOf0(sK0(X0,X1),X0)
& aElementOf0(sK0(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f35,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,[],[f34]) ).
fof(f34,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,[],[f33]) ).
fof(f33,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,[],[f27]) ).
fof(f27,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(f142,plain,
spl2_15,
inference(avatar_split_clause,[],[f53,f140]) ).
fof(f53,plain,
! [X0,X1] :
( aSubsetOf0(X1,X0)
| aElementOf0(sK0(X0,X1),X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f134,plain,
spl2_14,
inference(avatar_split_clause,[],[f52,f132]) ).
fof(f52,plain,
! [X3,X0,X1] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f125,plain,
spl2_13,
inference(avatar_split_clause,[],[f58,f123]) ).
fof(f58,plain,
! [X0] :
( slcrc0 = X0
| aElementOf0(sK1(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] :
( ( slcrc0 = X0
| aElementOf0(sK1(X0),X0)
| ~ aSet0(X0) )
& ( ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f40,f41]) ).
fof(f41,plain,
! [X0] :
( ? [X1] : aElementOf0(X1,X0)
=> aElementOf0(sK1(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
! [X0] :
( ( slcrc0 = X0
| ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0) )
& ( ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(rectify,[],[f39]) ).
fof(f39,plain,
! [X0] :
( ( slcrc0 = X0
| ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0) )
& ( ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
! [X0] :
( ( slcrc0 = X0
| ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0) )
& ( ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f30,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(f121,plain,
spl2_12,
inference(avatar_split_clause,[],[f55,f119]) ).
fof(f55,plain,
! [X0,X1] :
( isFinite0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0] :
( ! [X1] :
( isFinite0(X1)
| ~ aSubsetOf0(X1,X0) )
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(flattening,[],[f28]) ).
fof(f28,plain,
! [X0] :
( ! [X1] :
( isFinite0(X1)
| ~ aSubsetOf0(X1,X0) )
| ~ isFinite0(X0)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( ( isFinite0(X0)
& aSet0(X0) )
=> ! [X1] :
( aSubsetOf0(X1,X0)
=> isFinite0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubFSet) ).
fof(f113,plain,
spl2_11,
inference(avatar_split_clause,[],[f51,f111]) ).
fof(f111,plain,
( spl2_11
<=> ! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).
fof(f51,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f109,plain,
spl2_10,
inference(avatar_split_clause,[],[f50,f107]) ).
fof(f107,plain,
( spl2_10
<=> ! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).
fof(f50,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,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(f105,plain,
spl2_9,
inference(avatar_split_clause,[],[f60,f103]) ).
fof(f60,plain,
! [X2] : ~ aElementOf0(X2,slcrc0),
inference(equality_resolution,[],[f57]) ).
fof(f57,plain,
! [X2,X0] :
( ~ aElementOf0(X2,X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f42]) ).
fof(f101,plain,
spl2_8,
inference(avatar_split_clause,[],[f61,f98]) ).
fof(f61,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f56]) ).
fof(f56,plain,
! [X0] :
( aSet0(X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f42]) ).
fof(f96,plain,
spl2_7,
inference(avatar_split_clause,[],[f49,f93]) ).
fof(f49,plain,
isFinite0(slcrc0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
isFinite0(slcrc0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEmpFin) ).
fof(f91,plain,
spl2_6,
inference(avatar_split_clause,[],[f48,f88]) ).
fof(f48,plain,
aSet0(xC),
inference(cnf_transformation,[],[f14]) ).
fof(f14,axiom,
( aSet0(xC)
& aSet0(xB)
& aSet0(xA) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__522) ).
fof(f86,plain,
spl2_5,
inference(avatar_split_clause,[],[f47,f83]) ).
fof(f47,plain,
aSet0(xB),
inference(cnf_transformation,[],[f14]) ).
fof(f81,plain,
spl2_4,
inference(avatar_split_clause,[],[f46,f78]) ).
fof(f46,plain,
aSet0(xA),
inference(cnf_transformation,[],[f14]) ).
fof(f76,plain,
~ spl2_3,
inference(avatar_split_clause,[],[f45,f73]) ).
fof(f45,plain,
~ aSubsetOf0(xA,xC),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
( ~ aSubsetOf0(xA,xC)
& aSubsetOf0(xB,xC)
& aSubsetOf0(xA,xB) ),
inference(flattening,[],[f24]) ).
fof(f24,plain,
( ~ aSubsetOf0(xA,xC)
& aSubsetOf0(xB,xC)
& aSubsetOf0(xA,xB) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,negated_conjecture,
~ ( ( aSubsetOf0(xB,xC)
& aSubsetOf0(xA,xB) )
=> aSubsetOf0(xA,xC) ),
inference(negated_conjecture,[],[f15]) ).
fof(f15,conjecture,
( ( aSubsetOf0(xB,xC)
& aSubsetOf0(xA,xB) )
=> aSubsetOf0(xA,xC) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f71,plain,
spl2_2,
inference(avatar_split_clause,[],[f44,f68]) ).
fof(f44,plain,
aSubsetOf0(xB,xC),
inference(cnf_transformation,[],[f25]) ).
fof(f66,plain,
spl2_1,
inference(avatar_split_clause,[],[f43,f63]) ).
fof(f43,plain,
aSubsetOf0(xA,xB),
inference(cnf_transformation,[],[f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM533+1 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n005.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 : Mon May 20 05:39:53 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (28042)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.38 % (28043)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.38 % (28049)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)
% 0.13/0.38 % (28044)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.38 % (28045)WARNING: value z3 for option sas not known
% 0.13/0.38 % (28045)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)
% 0.13/0.38 % (28046)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.38 % (28047)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)
% 0.13/0.39 TRYING [1]
% 0.13/0.39 TRYING [2]
% 0.13/0.39 TRYING [3]
% 0.13/0.39 TRYING [4]
% 0.13/0.39 TRYING [1]
% 0.13/0.39 TRYING [2]
% 0.13/0.39 TRYING [3]
% 0.13/0.39 TRYING [5]
% 0.13/0.39 % (28048)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)
% 0.13/0.39 % (28047)First to succeed.
% 0.13/0.39 TRYING [4]
% 0.13/0.39 % (28049)Also succeeded, but the first one will report.
% 0.13/0.39 TRYING [5]
% 0.13/0.39 % (28047)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-28042"
% 0.13/0.39 TRYING [6]
% 0.13/0.39 % (28047)Refutation found. Thanks to Tanya!
% 0.13/0.39 % SZS status Theorem for theBenchmark
% 0.13/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.39 % (28047)------------------------------
% 0.13/0.39 % (28047)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.39 % (28047)Termination reason: Refutation
% 0.13/0.39
% 0.13/0.39 % (28047)Memory used [KB]: 900
% 0.13/0.39 % (28047)Time elapsed: 0.029 s
% 0.13/0.39 % (28047)Instructions burned: 10 (million)
% 0.13/0.39 % (28042)Success in time 0.04 s
%------------------------------------------------------------------------------