TSTP Solution File: RNG088+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : RNG088+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n014.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 : Fri Sep 1 21:59:37 EDT 2023
% Result : Theorem 0.22s 0.44s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 93
% Syntax : Number of formulae : 270 ( 83 unt; 0 def)
% Number of atoms : 860 ( 97 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 891 ( 301 ~; 298 |; 170 &)
% ( 84 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 71 ( 69 usr; 62 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 15 con; 0-3 aty)
% Number of variables : 351 (; 315 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f620,plain,
$false,
inference(avatar_sat_refutation,[],[f194,f199,f204,f209,f214,f219,f224,f233,f238,f243,f248,f253,f258,f263,f268,f273,f278,f282,f289,f294,f299,f304,f309,f314,f318,f322,f326,f330,f334,f338,f342,f346,f350,f354,f389,f397,f401,f405,f409,f413,f417,f421,f474,f478,f497,f501,f505,f513,f517,f521,f537,f541,f559,f563,f567,f571,f581,f603,f607,f611,f618,f619]) ).
fof(f619,plain,
( ~ spl19_11
| ~ spl19_13
| spl19_9
| ~ spl19_53 ),
inference(avatar_split_clause,[],[f549,f539,f230,f250,f240]) ).
fof(f240,plain,
( spl19_11
<=> aElementOf0(xl,xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_11])]) ).
fof(f250,plain,
( spl19_13
<=> aElementOf0(xn,xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_13])]) ).
fof(f230,plain,
( spl19_9
<=> aElementOf0(sdtpldt0(xl,xn),xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_9])]) ).
fof(f539,plain,
( spl19_53
<=> ! [X2,X0] :
( aElementOf0(sdtpldt0(X0,X2),xJ)
| ~ aElementOf0(X2,xJ)
| ~ aElementOf0(X0,xJ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_53])]) ).
fof(f549,plain,
( ~ aElementOf0(xn,xJ)
| ~ aElementOf0(xl,xJ)
| spl19_9
| ~ spl19_53 ),
inference(resolution,[],[f540,f232]) ).
fof(f232,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| spl19_9 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f540,plain,
( ! [X2,X0] :
( aElementOf0(sdtpldt0(X0,X2),xJ)
| ~ aElementOf0(X2,xJ)
| ~ aElementOf0(X0,xJ) )
| ~ spl19_53 ),
inference(avatar_component_clause,[],[f539]) ).
fof(f618,plain,
spl19_61,
inference(avatar_split_clause,[],[f165,f616]) ).
fof(f616,plain,
( spl19_61
<=> ! [X4,X0,X2,X1] :
( aElementOf0(X4,X2)
| ~ aElementOf0(X4,X0)
| ~ aElementOf0(X4,X1)
| ~ sP1(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_61])]) ).
fof(f165,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X2)
| ~ aElementOf0(X4,X0)
| ~ aElementOf0(X4,X1)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ( ( ~ aElementOf0(sK13(X0,X1,X2),X0)
| ~ aElementOf0(sK13(X0,X1,X2),X1)
| ~ aElementOf0(sK13(X0,X1,X2),X2) )
& ( ( aElementOf0(sK13(X0,X1,X2),X0)
& aElementOf0(sK13(X0,X1,X2),X1) )
| aElementOf0(sK13(X0,X1,X2),X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aElementOf0(X4,X0)
| ~ aElementOf0(X4,X1) )
& ( ( aElementOf0(X4,X0)
& aElementOf0(X4,X1) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| ~ sP1(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f96,f97]) ).
fof(f97,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X2) )
& ( ( aElementOf0(X3,X0)
& aElementOf0(X3,X1) )
| aElementOf0(X3,X2) ) )
=> ( ( ~ aElementOf0(sK13(X0,X1,X2),X0)
| ~ aElementOf0(sK13(X0,X1,X2),X1)
| ~ aElementOf0(sK13(X0,X1,X2),X2) )
& ( ( aElementOf0(sK13(X0,X1,X2),X0)
& aElementOf0(sK13(X0,X1,X2),X1) )
| aElementOf0(sK13(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f96,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ? [X3] :
( ( ~ aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X2) )
& ( ( aElementOf0(X3,X0)
& aElementOf0(X3,X1) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aElementOf0(X4,X0)
| ~ aElementOf0(X4,X1) )
& ( ( aElementOf0(X4,X0)
& aElementOf0(X4,X1) )
| ~ aElementOf0(X4,X2) ) )
& aSet0(X2) )
| ~ sP1(X0,X1,X2) ) ),
inference(rectify,[],[f95]) ).
fof(f95,plain,
! [X1,X0,X2] :
( ( sP1(X1,X0,X2)
| ? [X3] :
( ( ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0)
| ~ aElementOf0(X3,X2) )
& ( ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0) )
& ( ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| ~ sP1(X1,X0,X2) ) ),
inference(flattening,[],[f94]) ).
fof(f94,plain,
! [X1,X0,X2] :
( ( sP1(X1,X0,X2)
| ? [X3] :
( ( ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0)
| ~ aElementOf0(X3,X2) )
& ( ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0) )
& ( ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| ~ sP1(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X1,X0,X2] :
( sP1(X1,X0,X2)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& aSet0(X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f611,plain,
spl19_60,
inference(avatar_split_clause,[],[f161,f609]) ).
fof(f609,plain,
( spl19_60
<=> ! [X2,X0,X1] :
( sdtasasdt0(X0,X1) = X2
| ~ sP1(X1,X0,X2)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_60])]) ).
fof(f161,plain,
! [X2,X0,X1] :
( sdtasasdt0(X0,X1) = X2
| ~ sP1(X1,X0,X2)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtasasdt0(X0,X1) = X2
| ~ sP1(X1,X0,X2) )
& ( sP1(X1,X0,X2)
| sdtasasdt0(X0,X1) != X2 ) )
| ~ sP2(X0,X1) ),
inference(nnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( ! [X2] :
( sdtasasdt0(X0,X1) = X2
<=> sP1(X1,X0,X2) )
| ~ sP2(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f607,plain,
spl19_59,
inference(avatar_split_clause,[],[f160,f605]) ).
fof(f605,plain,
( spl19_59
<=> ! [X2,X0,X1] :
( sP1(X1,X0,X2)
| sdtasasdt0(X0,X1) != X2
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_59])]) ).
fof(f160,plain,
! [X2,X0,X1] :
( sP1(X1,X0,X2)
| sdtasasdt0(X0,X1) != X2
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f603,plain,
spl19_58,
inference(avatar_split_clause,[],[f148,f601]) ).
fof(f601,plain,
( spl19_58
<=> ! [X0,X1] :
( sP0(X0,X1)
| aElement0(sK8(X0,X1))
| aElementOf0(sK9(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_58])]) ).
fof(f148,plain,
! [X0,X1] :
( sP0(X0,X1)
| aElement0(sK8(X0,X1))
| aElementOf0(sK9(X0,X1),X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ~ aElementOf0(sdtasdt0(sK8(X0,X1),X1),X0)
& aElement0(sK8(X0,X1)) )
| ( ~ aElementOf0(sdtpldt0(X1,sK9(X0,X1)),X0)
& aElementOf0(sK9(X0,X1),X0) ) )
& ( ( ! [X4] :
( aElementOf0(sdtasdt0(X4,X1),X0)
| ~ aElement0(X4) )
& ! [X5] :
( aElementOf0(sdtpldt0(X1,X5),X0)
| ~ aElementOf0(X5,X0) ) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f81,f83,f82]) ).
fof(f82,plain,
! [X0,X1] :
( ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,X1),X0)
& aElement0(X2) )
=> ( ~ aElementOf0(sdtasdt0(sK8(X0,X1),X1),X0)
& aElement0(sK8(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
! [X0,X1] :
( ? [X3] :
( ~ aElementOf0(sdtpldt0(X1,X3),X0)
& aElementOf0(X3,X0) )
=> ( ~ aElementOf0(sdtpldt0(X1,sK9(X0,X1)),X0)
& aElementOf0(sK9(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,X1),X0)
& aElement0(X2) )
| ? [X3] :
( ~ aElementOf0(sdtpldt0(X1,X3),X0)
& aElementOf0(X3,X0) ) )
& ( ( ! [X4] :
( aElementOf0(sdtasdt0(X4,X1),X0)
| ~ aElement0(X4) )
& ! [X5] :
( aElementOf0(sdtpldt0(X1,X5),X0)
| ~ aElementOf0(X5,X0) ) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,X1),X0)
& aElement0(X2) )
| ? [X3] :
( ~ aElementOf0(sdtpldt0(X1,X3),X0)
& aElementOf0(X3,X0) ) )
& ( ( ! [X2] :
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2) )
& ! [X3] :
( aElementOf0(sdtpldt0(X1,X3),X0)
| ~ aElementOf0(X3,X0) ) )
| ~ sP0(X0,X1) ) ),
inference(flattening,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ~ aElementOf0(sdtasdt0(X2,X1),X0)
& aElement0(X2) )
| ? [X3] :
( ~ aElementOf0(sdtpldt0(X1,X3),X0)
& aElementOf0(X3,X0) ) )
& ( ( ! [X2] :
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2) )
& ! [X3] :
( aElementOf0(sdtpldt0(X1,X3),X0)
| ~ aElementOf0(X3,X0) ) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ( ! [X2] :
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2) )
& ! [X3] :
( aElementOf0(sdtpldt0(X1,X3),X0)
| ~ aElementOf0(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f581,plain,
( ~ spl19_10
| ~ spl19_12
| spl19_8
| ~ spl19_52 ),
inference(avatar_split_clause,[],[f542,f535,f226,f245,f235]) ).
fof(f235,plain,
( spl19_10
<=> aElementOf0(xk,xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_10])]) ).
fof(f245,plain,
( spl19_12
<=> aElementOf0(xm,xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_12])]) ).
fof(f226,plain,
( spl19_8
<=> aElementOf0(sdtpldt0(xk,xm),xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_8])]) ).
fof(f535,plain,
( spl19_52
<=> ! [X5,X3] :
( aElementOf0(sdtpldt0(X3,X5),xI)
| ~ aElementOf0(X5,xI)
| ~ aElementOf0(X3,xI) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_52])]) ).
fof(f542,plain,
( ~ aElementOf0(xm,xI)
| ~ aElementOf0(xk,xI)
| spl19_8
| ~ spl19_52 ),
inference(resolution,[],[f536,f228]) ).
fof(f228,plain,
( ~ aElementOf0(sdtpldt0(xk,xm),xI)
| spl19_8 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f536,plain,
( ! [X3,X5] :
( aElementOf0(sdtpldt0(X3,X5),xI)
| ~ aElementOf0(X5,xI)
| ~ aElementOf0(X3,xI) )
| ~ spl19_52 ),
inference(avatar_component_clause,[],[f535]) ).
fof(f571,plain,
spl19_57,
inference(avatar_split_clause,[],[f184,f569]) ).
fof(f569,plain,
( spl19_57
<=> ! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_57])]) ).
fof(f184,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox/tmp/tmp.x8c0eKl87C/Vampire---4.8_26890',mAddComm) ).
fof(f567,plain,
spl19_56,
inference(avatar_split_clause,[],[f183,f565]) ).
fof(f565,plain,
( spl19_56
<=> ! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_56])]) ).
fof(f183,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/tmp/tmp.x8c0eKl87C/Vampire---4.8_26890',mMulComm) ).
fof(f563,plain,
spl19_55,
inference(avatar_split_clause,[],[f178,f561]) ).
fof(f561,plain,
( spl19_55
<=> ! [X2,X0,X1] :
( aSet0(X2)
| sdtpldt1(X0,X1) != X2
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_55])]) ).
fof(f178,plain,
! [X2,X0,X1] :
( aSet0(X2)
| sdtpldt1(X0,X1) != X2
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt1(X0,X1) = X2
| ~ sP3(X1,X0,X2)
| ~ aSet0(X2) )
& ( ( sP3(X1,X0,X2)
& aSet0(X2) )
| sdtpldt1(X0,X1) != X2 ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f105]) ).
fof(f105,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt1(X0,X1) = X2
| ~ sP3(X1,X0,X2)
| ~ aSet0(X2) )
& ( ( sP3(X1,X0,X2)
& aSet0(X2) )
| sdtpldt1(X0,X1) != X2 ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( ! [X2] :
( sdtpldt1(X0,X1) = X2
<=> ( sP3(X1,X0,X2)
& aSet0(X2) ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f52,f74]) ).
fof(f74,plain,
! [X1,X0,X2] :
( sP3(X1,X0,X2)
<=> ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f52,plain,
! [X0,X1] :
( ! [X2] :
( sdtpldt1(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) ) )
& aSet0(X2) ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
! [X0,X1] :
( ! [X2] :
( sdtpldt1(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) ) )
& aSet0(X2) ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1] :
( ( aSet0(X1)
& aSet0(X0) )
=> ! [X2] :
( sdtpldt1(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,X1)
& aElementOf0(X4,X0) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.x8c0eKl87C/Vampire---4.8_26890',mDefSSum) ).
fof(f559,plain,
spl19_54,
inference(avatar_split_clause,[],[f146,f557]) ).
fof(f557,plain,
( spl19_54
<=> ! [X5,X0,X1] :
( aElementOf0(sdtpldt0(X1,X5),X0)
| ~ aElementOf0(X5,X0)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_54])]) ).
fof(f146,plain,
! [X0,X1,X5] :
( aElementOf0(sdtpldt0(X1,X5),X0)
| ~ aElementOf0(X5,X0)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f541,plain,
spl19_53,
inference(avatar_split_clause,[],[f113,f539]) ).
fof(f113,plain,
! [X2,X0] :
( aElementOf0(sdtpldt0(X0,X2),xJ)
| ~ aElementOf0(X2,xJ)
| ~ aElementOf0(X0,xJ) ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
( aIdeal0(xJ)
& ! [X0] :
( ( ! [X1] :
( aElementOf0(sdtasdt0(X1,X0),xJ)
| ~ aElement0(X1) )
& ! [X2] :
( aElementOf0(sdtpldt0(X0,X2),xJ)
| ~ aElementOf0(X2,xJ) ) )
| ~ aElementOf0(X0,xJ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [X3] :
( ( ! [X4] :
( aElementOf0(sdtasdt0(X4,X3),xI)
| ~ aElement0(X4) )
& ! [X5] :
( aElementOf0(sdtpldt0(X3,X5),xI)
| ~ aElementOf0(X5,xI) ) )
| ~ aElementOf0(X3,xI) )
& aSet0(xI) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,plain,
( aIdeal0(xJ)
& ! [X0] :
( aElementOf0(X0,xJ)
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xJ) )
& ! [X2] :
( aElementOf0(X2,xJ)
=> aElementOf0(sdtpldt0(X0,X2),xJ) ) ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [X3] :
( aElementOf0(X3,xI)
=> ( ! [X4] :
( aElement0(X4)
=> aElementOf0(sdtasdt0(X4,X3),xI) )
& ! [X5] :
( aElementOf0(X5,xI)
=> aElementOf0(sdtpldt0(X3,X5),xI) ) ) )
& aSet0(xI) ),
inference(rectify,[],[f25]) ).
fof(f25,axiom,
( aIdeal0(xJ)
& ! [X0] :
( aElementOf0(X0,xJ)
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xJ) )
& ! [X1] :
( aElementOf0(X1,xJ)
=> aElementOf0(sdtpldt0(X0,X1),xJ) ) ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xI) )
& ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) ) ) )
& aSet0(xI) ),
file('/export/starexec/sandbox/tmp/tmp.x8c0eKl87C/Vampire---4.8_26890',m__870) ).
fof(f537,plain,
spl19_52,
inference(avatar_split_clause,[],[f109,f535]) ).
fof(f109,plain,
! [X3,X5] :
( aElementOf0(sdtpldt0(X3,X5),xI)
| ~ aElementOf0(X5,xI)
| ~ aElementOf0(X3,xI) ),
inference(cnf_transformation,[],[f38]) ).
fof(f521,plain,
spl19_51,
inference(avatar_split_clause,[],[f164,f519]) ).
fof(f519,plain,
( spl19_51
<=> ! [X4,X0,X2,X1] :
( aElementOf0(X4,X0)
| ~ aElementOf0(X4,X2)
| ~ sP1(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_51])]) ).
fof(f164,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X0)
| ~ aElementOf0(X4,X2)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f98]) ).
fof(f517,plain,
spl19_50,
inference(avatar_split_clause,[],[f163,f515]) ).
fof(f515,plain,
( spl19_50
<=> ! [X4,X0,X1,X2] :
( aElementOf0(X4,X1)
| ~ aElementOf0(X4,X2)
| ~ sP1(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_50])]) ).
fof(f163,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X1)
| ~ aElementOf0(X4,X2)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f98]) ).
fof(f513,plain,
spl19_49,
inference(avatar_split_clause,[],[f147,f511]) ).
fof(f511,plain,
( spl19_49
<=> ! [X4,X0,X1] :
( aElementOf0(sdtasdt0(X4,X1),X0)
| ~ aElement0(X4)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_49])]) ).
fof(f147,plain,
! [X0,X1,X4] :
( aElementOf0(sdtasdt0(X4,X1),X0)
| ~ aElement0(X4)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f505,plain,
spl19_48,
inference(avatar_split_clause,[],[f114,f503]) ).
fof(f503,plain,
( spl19_48
<=> ! [X0,X1] :
( aElementOf0(sdtasdt0(X1,X0),xJ)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xJ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_48])]) ).
fof(f114,plain,
! [X0,X1] :
( aElementOf0(sdtasdt0(X1,X0),xJ)
| ~ aElement0(X1)
| ~ aElementOf0(X0,xJ) ),
inference(cnf_transformation,[],[f38]) ).
fof(f501,plain,
spl19_47,
inference(avatar_split_clause,[],[f110,f499]) ).
fof(f499,plain,
( spl19_47
<=> ! [X4,X3] :
( aElementOf0(sdtasdt0(X4,X3),xI)
| ~ aElement0(X4)
| ~ aElementOf0(X3,xI) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_47])]) ).
fof(f110,plain,
! [X3,X4] :
( aElementOf0(sdtasdt0(X4,X3),xI)
| ~ aElement0(X4)
| ~ aElementOf0(X3,xI) ),
inference(cnf_transformation,[],[f38]) ).
fof(f497,plain,
( ~ spl19_3
| spl19_46
| ~ spl19_11
| ~ spl19_28 ),
inference(avatar_split_clause,[],[f358,f324,f240,f494,f201]) ).
fof(f201,plain,
( spl19_3
<=> aSet0(xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_3])]) ).
fof(f494,plain,
( spl19_46
<=> aElement0(xl) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_46])]) ).
fof(f324,plain,
( spl19_28
<=> ! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_28])]) ).
fof(f358,plain,
( aElement0(xl)
| ~ aSet0(xJ)
| ~ spl19_11
| ~ spl19_28 ),
inference(resolution,[],[f325,f242]) ).
fof(f242,plain,
( aElementOf0(xl,xJ)
| ~ spl19_11 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f325,plain,
( ! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) )
| ~ spl19_28 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f478,plain,
spl19_45,
inference(avatar_split_clause,[],[f145,f476]) ).
fof(f476,plain,
( spl19_45
<=> ! [X0] :
( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_45])]) ).
fof(f145,plain,
! [X0] :
( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] :
( ( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
& smndt0(X0) = sdtasdt0(smndt0(sz10),X0) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( aElement0(X0)
=> ( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
& smndt0(X0) = sdtasdt0(smndt0(sz10),X0) ) ),
file('/export/starexec/sandbox/tmp/tmp.x8c0eKl87C/Vampire---4.8_26890',mMulMnOne) ).
fof(f474,plain,
spl19_44,
inference(avatar_split_clause,[],[f144,f472]) ).
fof(f472,plain,
( spl19_44
<=> ! [X0] :
( smndt0(X0) = sdtasdt0(smndt0(sz10),X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_44])]) ).
fof(f144,plain,
! [X0] :
( smndt0(X0) = sdtasdt0(smndt0(sz10),X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f421,plain,
spl19_43,
inference(avatar_split_clause,[],[f182,f419]) ).
fof(f419,plain,
( spl19_43
<=> ! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_43])]) ).
fof(f182,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> aElement0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.x8c0eKl87C/Vampire---4.8_26890',mSortsB) ).
fof(f417,plain,
spl19_42,
inference(avatar_split_clause,[],[f181,f415]) ).
fof(f415,plain,
( spl19_42
<=> ! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_42])]) ).
fof(f181,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> aElement0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.x8c0eKl87C/Vampire---4.8_26890',mSortsB_02) ).
fof(f413,plain,
spl19_41,
inference(avatar_split_clause,[],[f155,f411]) ).
fof(f411,plain,
( spl19_41
<=> ! [X0] :
( aIdeal0(X0)
| ~ sP0(X0,sK10(X0))
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_41])]) ).
fof(f155,plain,
! [X0] :
( aIdeal0(X0)
| ~ sP0(X0,sK10(X0))
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0] :
( ( aIdeal0(X0)
| ( ~ sP0(X0,sK10(X0))
& aElementOf0(sK10(X0),X0) )
| ~ aSet0(X0) )
& ( ( ! [X2] :
( sP0(X0,X2)
| ~ aElementOf0(X2,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f87,f88]) ).
fof(f88,plain,
! [X0] :
( ? [X1] :
( ~ sP0(X0,X1)
& aElementOf0(X1,X0) )
=> ( ~ sP0(X0,sK10(X0))
& aElementOf0(sK10(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
! [X0] :
( ( aIdeal0(X0)
| ? [X1] :
( ~ sP0(X0,X1)
& aElementOf0(X1,X0) )
| ~ aSet0(X0) )
& ( ( ! [X2] :
( sP0(X0,X2)
| ~ aElementOf0(X2,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(rectify,[],[f86]) ).
fof(f86,plain,
! [X0] :
( ( aIdeal0(X0)
| ? [X1] :
( ~ sP0(X0,X1)
& aElementOf0(X1,X0) )
| ~ aSet0(X0) )
& ( ( ! [X1] :
( sP0(X0,X1)
| ~ aElementOf0(X1,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(flattening,[],[f85]) ).
fof(f85,plain,
! [X0] :
( ( aIdeal0(X0)
| ? [X1] :
( ~ sP0(X0,X1)
& aElementOf0(X1,X0) )
| ~ aSet0(X0) )
& ( ( ! [X1] :
( sP0(X0,X1)
| ~ aElementOf0(X1,X0) )
& aSet0(X0) )
| ~ aIdeal0(X0) ) ),
inference(nnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( sP0(X0,X1)
| ~ aElementOf0(X1,X0) )
& aSet0(X0) ) ),
inference(definition_folding,[],[f46,f69]) ).
fof(f46,plain,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtasdt0(X2,X1),X0)
| ~ aElement0(X2) )
& ! [X3] :
( aElementOf0(sdtpldt0(X1,X3),X0)
| ~ aElementOf0(X3,X0) ) )
| ~ aElementOf0(X1,X0) )
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) )
& ! [X3] :
( aElementOf0(X3,X0)
=> aElementOf0(sdtpldt0(X1,X3),X0) ) ) )
& aSet0(X0) ) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( aIdeal0(X0)
<=> ( ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) )
& ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
& aSet0(X0) ) ),
file('/export/starexec/sandbox/tmp/tmp.x8c0eKl87C/Vampire---4.8_26890',mDefIdeal) ).
fof(f409,plain,
spl19_40,
inference(avatar_split_clause,[],[f154,f407]) ).
fof(f407,plain,
( spl19_40
<=> ! [X0] :
( aIdeal0(X0)
| aElementOf0(sK10(X0),X0)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_40])]) ).
fof(f154,plain,
! [X0] :
( aIdeal0(X0)
| aElementOf0(sK10(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f405,plain,
spl19_39,
inference(avatar_split_clause,[],[f153,f403]) ).
fof(f403,plain,
( spl19_39
<=> ! [X2,X0] :
( sP0(X0,X2)
| ~ aElementOf0(X2,X0)
| ~ aIdeal0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_39])]) ).
fof(f153,plain,
! [X2,X0] :
( sP0(X0,X2)
| ~ aElementOf0(X2,X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f401,plain,
spl19_38,
inference(avatar_split_clause,[],[f143,f399]) ).
fof(f399,plain,
( spl19_38
<=> ! [X0] :
( sz00 = sdtpldt0(smndt0(X0),X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_38])]) ).
fof(f143,plain,
! [X0] :
( sz00 = sdtpldt0(smndt0(X0),X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ( sz00 = sdtpldt0(smndt0(X0),X0)
& sz00 = sdtpldt0(X0,smndt0(X0)) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( aElement0(X0)
=> ( sz00 = sdtpldt0(smndt0(X0),X0)
& sz00 = sdtpldt0(X0,smndt0(X0)) ) ),
file('/export/starexec/sandbox/tmp/tmp.x8c0eKl87C/Vampire---4.8_26890',mAddInvr) ).
fof(f397,plain,
spl19_37,
inference(avatar_split_clause,[],[f142,f395]) ).
fof(f395,plain,
( spl19_37
<=> ! [X0] :
( sz00 = sdtpldt0(X0,smndt0(X0))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_37])]) ).
fof(f142,plain,
! [X0] :
( sz00 = sdtpldt0(X0,smndt0(X0))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f389,plain,
( ~ spl19_1
| spl19_36
| ~ spl19_10
| ~ spl19_28 ),
inference(avatar_split_clause,[],[f357,f324,f235,f386,f191]) ).
fof(f191,plain,
( spl19_1
<=> aSet0(xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_1])]) ).
fof(f386,plain,
( spl19_36
<=> aElement0(xk) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_36])]) ).
fof(f357,plain,
( aElement0(xk)
| ~ aSet0(xI)
| ~ spl19_10
| ~ spl19_28 ),
inference(resolution,[],[f325,f237]) ).
fof(f237,plain,
( aElementOf0(xk,xI)
| ~ spl19_10 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f354,plain,
spl19_35,
inference(avatar_split_clause,[],[f169,f352]) ).
fof(f352,plain,
( spl19_35
<=> ! [X0,X1] :
( sP2(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_35])]) ).
fof(f169,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(definition_folding,[],[f50,f72,f71]) ).
fof(f50,plain,
! [X0,X1] :
( ! [X2] :
( sdtasasdt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& aSet0(X2) ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(flattening,[],[f49]) ).
fof(f49,plain,
! [X0,X1] :
( ! [X2] :
( sdtasasdt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& aSet0(X2) ) )
| ~ aSet0(X1)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0,X1] :
( ( aSet0(X1)
& aSet0(X0) )
=> ! [X2] :
( sdtasasdt0(X0,X1) = X2
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( aElementOf0(X3,X1)
& aElementOf0(X3,X0) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.x8c0eKl87C/Vampire---4.8_26890',mDefSInt) ).
fof(f350,plain,
spl19_34,
inference(avatar_split_clause,[],[f141,f348]) ).
fof(f348,plain,
( spl19_34
<=> ! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_34])]) ).
fof(f141,plain,
! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0] :
( ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( aElement0(X0)
=> ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.x8c0eKl87C/Vampire---4.8_26890',mAddZero) ).
fof(f346,plain,
spl19_33,
inference(avatar_split_clause,[],[f140,f344]) ).
fof(f344,plain,
( spl19_33
<=> ! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_33])]) ).
fof(f140,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f342,plain,
spl19_32,
inference(avatar_split_clause,[],[f139,f340]) ).
fof(f340,plain,
( spl19_32
<=> ! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_32])]) ).
fof(f139,plain,
! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] :
( ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( aElement0(X0)
=> ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.x8c0eKl87C/Vampire---4.8_26890',mMulUnit) ).
fof(f338,plain,
spl19_31,
inference(avatar_split_clause,[],[f138,f336]) ).
fof(f336,plain,
( spl19_31
<=> ! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_31])]) ).
fof(f138,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f334,plain,
spl19_30,
inference(avatar_split_clause,[],[f137,f332]) ).
fof(f332,plain,
( spl19_30
<=> ! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_30])]) ).
fof(f137,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0] :
( ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( aElement0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) ) ),
file('/export/starexec/sandbox/tmp/tmp.x8c0eKl87C/Vampire---4.8_26890',mMulZero) ).
fof(f330,plain,
spl19_29,
inference(avatar_split_clause,[],[f136,f328]) ).
fof(f328,plain,
( spl19_29
<=> ! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_29])]) ).
fof(f136,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f326,plain,
spl19_28,
inference(avatar_split_clause,[],[f134,f324]) ).
fof(f134,plain,
! [X0,X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.x8c0eKl87C/Vampire---4.8_26890',mEOfElem) ).
fof(f322,plain,
spl19_27,
inference(avatar_split_clause,[],[f162,f320]) ).
fof(f320,plain,
( spl19_27
<=> ! [X2,X0,X1] :
( aSet0(X2)
| ~ sP1(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_27])]) ).
fof(f162,plain,
! [X2,X0,X1] :
( aSet0(X2)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f98]) ).
fof(f318,plain,
spl19_26,
inference(avatar_split_clause,[],[f135,f316]) ).
fof(f316,plain,
( spl19_26
<=> ! [X0] :
( aElement0(smndt0(X0))
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_26])]) ).
fof(f135,plain,
! [X0] :
( aElement0(smndt0(X0))
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0] :
( aElement0(smndt0(X0))
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( aElement0(X0)
=> aElement0(smndt0(X0)) ),
file('/export/starexec/sandbox/tmp/tmp.x8c0eKl87C/Vampire---4.8_26890',mSortsU) ).
fof(f314,plain,
spl19_25,
inference(avatar_split_clause,[],[f129,f311]) ).
fof(f311,plain,
( spl19_25
<=> aElementOf0(xy,sdtpldt1(xI,xJ)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_25])]) ).
fof(f129,plain,
aElementOf0(xy,sdtpldt1(xI,xJ)),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& xy = sdtpldt0(sK4,sK5)
& aElementOf0(sK5,xJ)
& aElementOf0(sK4,xI)
& aElementOf0(xx,sdtpldt1(xI,xJ))
& xx = sdtpldt0(sK6,sK7)
& aElementOf0(sK7,xJ)
& aElementOf0(sK6,xI) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f32,f77,f76]) ).
fof(f76,plain,
( ? [X0,X1] :
( sdtpldt0(X0,X1) = xy
& aElementOf0(X1,xJ)
& aElementOf0(X0,xI) )
=> ( xy = sdtpldt0(sK4,sK5)
& aElementOf0(sK5,xJ)
& aElementOf0(sK4,xI) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
( ? [X2,X3] :
( xx = sdtpldt0(X2,X3)
& aElementOf0(X3,xJ)
& aElementOf0(X2,xI) )
=> ( xx = sdtpldt0(sK6,sK7)
& aElementOf0(sK7,xJ)
& aElementOf0(sK6,xI) ) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xy
& aElementOf0(X1,xJ)
& aElementOf0(X0,xI) )
& aElementOf0(xx,sdtpldt1(xI,xJ))
& ? [X2,X3] :
( xx = sdtpldt0(X2,X3)
& aElementOf0(X3,xJ)
& aElementOf0(X2,xI) ) ),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xy
& aElementOf0(X1,xJ)
& aElementOf0(X0,xI) )
& aElementOf0(xx,sdtpldt1(xI,xJ))
& ? [X0,X1] :
( sdtpldt0(X0,X1) = xx
& aElementOf0(X1,xJ)
& aElementOf0(X0,xI) ) ),
file('/export/starexec/sandbox/tmp/tmp.x8c0eKl87C/Vampire---4.8_26890',m__901) ).
fof(f309,plain,
spl19_24,
inference(avatar_split_clause,[],[f128,f306]) ).
fof(f306,plain,
( spl19_24
<=> xy = sdtpldt0(sK4,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_24])]) ).
fof(f128,plain,
xy = sdtpldt0(sK4,sK5),
inference(cnf_transformation,[],[f78]) ).
fof(f304,plain,
spl19_23,
inference(avatar_split_clause,[],[f125,f301]) ).
fof(f301,plain,
( spl19_23
<=> aElementOf0(xx,sdtpldt1(xI,xJ)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_23])]) ).
fof(f125,plain,
aElementOf0(xx,sdtpldt1(xI,xJ)),
inference(cnf_transformation,[],[f78]) ).
fof(f299,plain,
spl19_22,
inference(avatar_split_clause,[],[f124,f296]) ).
fof(f296,plain,
( spl19_22
<=> xx = sdtpldt0(sK6,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_22])]) ).
fof(f124,plain,
xx = sdtpldt0(sK6,sK7),
inference(cnf_transformation,[],[f78]) ).
fof(f294,plain,
spl19_21,
inference(avatar_split_clause,[],[f121,f291]) ).
fof(f291,plain,
( spl19_21
<=> xy = sdtpldt0(xm,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_21])]) ).
fof(f121,plain,
xy = sdtpldt0(xm,xn),
inference(cnf_transformation,[],[f28]) ).
fof(f28,axiom,
( xy = sdtpldt0(xm,xn)
& aElementOf0(xn,xJ)
& aElementOf0(xm,xI) ),
file('/export/starexec/sandbox/tmp/tmp.x8c0eKl87C/Vampire---4.8_26890',m__967) ).
fof(f289,plain,
spl19_20,
inference(avatar_split_clause,[],[f118,f286]) ).
fof(f286,plain,
( spl19_20
<=> xx = sdtpldt0(xk,xl) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_20])]) ).
fof(f118,plain,
xx = sdtpldt0(xk,xl),
inference(cnf_transformation,[],[f27]) ).
fof(f27,axiom,
( xx = sdtpldt0(xk,xl)
& aElementOf0(xl,xJ)
& aElementOf0(xk,xI) ),
file('/export/starexec/sandbox/tmp/tmp.x8c0eKl87C/Vampire---4.8_26890',m__934) ).
fof(f282,plain,
spl19_19,
inference(avatar_split_clause,[],[f152,f280]) ).
fof(f280,plain,
( spl19_19
<=> ! [X0] :
( aSet0(X0)
| ~ aIdeal0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_19])]) ).
fof(f152,plain,
! [X0] :
( aSet0(X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f278,plain,
~ spl19_18,
inference(avatar_split_clause,[],[f133,f275]) ).
fof(f275,plain,
( spl19_18
<=> sz00 = sz10 ),
introduced(avatar_definition,[new_symbols(naming,[spl19_18])]) ).
fof(f133,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f18]) ).
fof(f18,axiom,
sz00 != sz10,
file('/export/starexec/sandbox/tmp/tmp.x8c0eKl87C/Vampire---4.8_26890',mUnNeZr) ).
fof(f273,plain,
spl19_17,
inference(avatar_split_clause,[],[f127,f270]) ).
fof(f270,plain,
( spl19_17
<=> aElementOf0(sK5,xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_17])]) ).
fof(f127,plain,
aElementOf0(sK5,xJ),
inference(cnf_transformation,[],[f78]) ).
fof(f268,plain,
spl19_16,
inference(avatar_split_clause,[],[f126,f265]) ).
fof(f265,plain,
( spl19_16
<=> aElementOf0(sK4,xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_16])]) ).
fof(f126,plain,
aElementOf0(sK4,xI),
inference(cnf_transformation,[],[f78]) ).
fof(f263,plain,
spl19_15,
inference(avatar_split_clause,[],[f123,f260]) ).
fof(f260,plain,
( spl19_15
<=> aElementOf0(sK7,xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_15])]) ).
fof(f123,plain,
aElementOf0(sK7,xJ),
inference(cnf_transformation,[],[f78]) ).
fof(f258,plain,
spl19_14,
inference(avatar_split_clause,[],[f122,f255]) ).
fof(f255,plain,
( spl19_14
<=> aElementOf0(sK6,xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_14])]) ).
fof(f122,plain,
aElementOf0(sK6,xI),
inference(cnf_transformation,[],[f78]) ).
fof(f253,plain,
spl19_13,
inference(avatar_split_clause,[],[f120,f250]) ).
fof(f120,plain,
aElementOf0(xn,xJ),
inference(cnf_transformation,[],[f28]) ).
fof(f248,plain,
spl19_12,
inference(avatar_split_clause,[],[f119,f245]) ).
fof(f119,plain,
aElementOf0(xm,xI),
inference(cnf_transformation,[],[f28]) ).
fof(f243,plain,
spl19_11,
inference(avatar_split_clause,[],[f117,f240]) ).
fof(f117,plain,
aElementOf0(xl,xJ),
inference(cnf_transformation,[],[f27]) ).
fof(f238,plain,
spl19_10,
inference(avatar_split_clause,[],[f116,f235]) ).
fof(f116,plain,
aElementOf0(xk,xI),
inference(cnf_transformation,[],[f27]) ).
fof(f233,plain,
( ~ spl19_8
| ~ spl19_9 ),
inference(avatar_split_clause,[],[f107,f230,f226]) ).
fof(f107,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,negated_conjecture,
~ ( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(negated_conjecture,[],[f29]) ).
fof(f29,conjecture,
( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
file('/export/starexec/sandbox/tmp/tmp.x8c0eKl87C/Vampire---4.8_26890',m__) ).
fof(f224,plain,
spl19_7,
inference(avatar_split_clause,[],[f132,f221]) ).
fof(f221,plain,
( spl19_7
<=> aElement0(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_7])]) ).
fof(f132,plain,
aElement0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
aElement0(sz00),
file('/export/starexec/sandbox/tmp/tmp.x8c0eKl87C/Vampire---4.8_26890',mSortsC) ).
fof(f219,plain,
spl19_6,
inference(avatar_split_clause,[],[f131,f216]) ).
fof(f216,plain,
( spl19_6
<=> aElement0(sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_6])]) ).
fof(f131,plain,
aElement0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/tmp/tmp.x8c0eKl87C/Vampire---4.8_26890',mSortsC_01) ).
fof(f214,plain,
spl19_5,
inference(avatar_split_clause,[],[f130,f211]) ).
fof(f211,plain,
( spl19_5
<=> aElement0(xz) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_5])]) ).
fof(f130,plain,
aElement0(xz),
inference(cnf_transformation,[],[f78]) ).
fof(f209,plain,
spl19_4,
inference(avatar_split_clause,[],[f115,f206]) ).
fof(f206,plain,
( spl19_4
<=> aIdeal0(xJ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_4])]) ).
fof(f115,plain,
aIdeal0(xJ),
inference(cnf_transformation,[],[f38]) ).
fof(f204,plain,
spl19_3,
inference(avatar_split_clause,[],[f112,f201]) ).
fof(f112,plain,
aSet0(xJ),
inference(cnf_transformation,[],[f38]) ).
fof(f199,plain,
spl19_2,
inference(avatar_split_clause,[],[f111,f196]) ).
fof(f196,plain,
( spl19_2
<=> aIdeal0(xI) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_2])]) ).
fof(f111,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f38]) ).
fof(f194,plain,
spl19_1,
inference(avatar_split_clause,[],[f108,f191]) ).
fof(f108,plain,
aSet0(xI),
inference(cnf_transformation,[],[f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : RNG088+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n014.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Aug 30 16:00:44 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.42 % (26997)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42 % (27000)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 Vampire---4 for (569ds/0Mi)
% 0.22/0.43 % (26998)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.22/0.43 % (26999)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.22/0.43 % (27001)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.22/0.43 % (27004)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 Vampire---4 for (522ds/0Mi)
% 0.22/0.43 % (27002)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 Vampire---4 for (531ds/0Mi)
% 0.22/0.43 % (27005)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 Vampire---4 for (497ds/0Mi)
% 0.22/0.43 TRYING [1]
% 0.22/0.43 TRYING [1]
% 0.22/0.43 TRYING [2]
% 0.22/0.43 TRYING [2]
% 0.22/0.44 % (27002)First to succeed.
% 0.22/0.44 TRYING [3]
% 0.22/0.44 TRYING [1]
% 0.22/0.44 TRYING [3]
% 0.22/0.44 TRYING [2]
% 0.22/0.44 % (27002)Refutation found. Thanks to Tanya!
% 0.22/0.44 % SZS status Theorem for Vampire---4
% 0.22/0.44 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.44 % (27002)------------------------------
% 0.22/0.44 % (27002)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.44 % (27002)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.44 % (27002)Termination reason: Refutation
% 0.22/0.44
% 0.22/0.44 % (27002)Memory used [KB]: 5884
% 0.22/0.44 % (27002)Time elapsed: 0.016 s
% 0.22/0.44 % (27002)------------------------------
% 0.22/0.44 % (27002)------------------------------
% 0.22/0.44 % (26997)Success in time 0.078 s
% 0.22/0.45 27000 Aborted by signal SIGHUP on /export/starexec/sandbox/tmp/tmp.x8c0eKl87C/Vampire---4.8_26890
% 0.22/0.45 % (27000)------------------------------
% 0.22/0.45 % (27000)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.45 % (27000)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.45 % (27000)Termination reason: Unknown
% 0.22/0.45 % (27000)Termination phase: Saturation
% 0.22/0.45
% 0.22/0.45 % (27000)Memory used [KB]: 5373
% 0.22/0.45 % (27000)Time elapsed: 0.022 s
% 0.22/0.45 % (27000)------------------------------
% 0.22/0.45 % (27000)------------------------------
% 0.22/0.45 % Vampire---4.8 exiting
%------------------------------------------------------------------------------