%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU811^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:31:36 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 22
% Syntax : Number of formulae : 136 ( 41 unt; 0 typ; 17 def)
% Number of atoms : 868 ( 231 equ; 0 cnn)
% Maximal formula atoms : 14 ( 6 avg)
% Number of connectives : 780 ( 169 ~; 160 |; 52 &; 328 @)
% ( 24 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 39 usr; 34 con; 0-4 aty)
% Number of variables : 121 ( 0 sgn 95 !; 20 ?; 121 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setadjoinIL: $o ).
thf(func_def_5,type,
setadjoinE: $o ).
thf(func_def_6,type,
in__Cong: $o ).
thf(func_def_7,type,
notinself2: $o ).
thf(func_def_8,type,
omegaS: $i > $i ).
thf(func_def_11,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_26,type,
sK13: $o ).
thf(func_def_27,type,
vNOT: $o > $o ).
thf(f1,axiom,
( setadjoinIL
= ( ! [X1: $i,X0: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(f2,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
=> ! [X3: $o] :
( ( ( X2 = X0 )
=> X3 )
=> ( ( ( in @ X2 @ X1 )
=> X3 )
=> X3 ) ) )
= setadjoinE ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(f4,axiom,
( notinself2
= ( ! [X1: $i,X0: $i] :
( ( in @ X0 @ X1 )
=> ~ ( in @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinself2) ).
thf(f5,axiom,
( ( ^ [X0: $i] : ( setadjoin @ X0 @ X0 ) )
= omegaS ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaS) ).
thf(f6,conjecture,
( setadjoinIL
=> ( setadjoinE
=> ( in__Cong
=> ( notinself2
=> ! [X0: $i] :
( ( in @ X0 @ omega )
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ( ( ( omegaS @ X0 )
= ( omegaS @ X1 ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',peanoSinj) ).
thf(f7,negated_conjecture,
~ ( setadjoinIL
=> ( setadjoinE
=> ( in__Cong
=> ( notinself2
=> ! [X0: $i] :
( ( in @ X0 @ omega )
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ( ( ( omegaS @ X0 )
= ( omegaS @ X1 ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f10,plain,
( omegaS
= ( ^ [Y0: $i] : ( setadjoin @ Y0 @ Y0 ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f11,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
=> ! [X3: $o] :
( ( ( X0 = X1 )
=> X3 )
=> ( ( ( in @ X0 @ X2 )
=> X3 )
=> X3 ) ) )
= setadjoinE ),
inference(rectify,[],[f2]) ).
thf(f12,plain,
( ( setadjoinE = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) )
=> ! [X3: $o] :
( ( ( X0 = X1 )
=> ( $true = X3 ) )
=> ( ( ( $true
= ( in @ X0 @ X2 ) )
=> ( $true = X3 ) )
=> ( $true = X3 ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
~ ( setadjoinIL
=> ( setadjoinE
=> ( in__Cong
=> ( notinself2
=> ! [X0: $i] :
( ( in @ X0 @ omega )
=> ! [X1: $i] :
( ( in @ X1 @ omega )
=> ( ( ( omegaS @ X0 )
= ( omegaS @ X1 ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f14,plain,
~ ( ( setadjoinIL = $true )
=> ( ( setadjoinE = $true )
=> ( ( in__Cong = $true )
=> ( ( notinself2 = $true )
=> ! [X0: $i] :
( ( ( in @ X0 @ omega )
= $true )
=> ! [X1: $i] :
( ( ( in @ X1 @ omega )
= $true )
=> ( ( ( omegaS @ X0 )
= ( omegaS @ X1 ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f16,plain,
( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
<=> ( setadjoinIL = $true ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( notinself2
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ X0 )
=> ~ ( in @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f18,plain,
( ( notinself2 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( in @ X0 @ X1 )
!= $true ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( in @ X0 @ X1 )
!= $true ) )
<=> ( notinself2 = $true ) ),
inference(flattening,[],[f18]) ).
thf(f20,plain,
( ( setadjoinE = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ! [X3: $o] :
( ( $true = X3 )
| ( ( $true != X3 )
& ( $true
= ( in @ X0 @ X2 ) ) )
| ( ( $true != X3 )
& ( X0 = X1 ) ) )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) ) ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f21,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) )
| ! [X3: $o] :
( ( ( $true != X3 )
& ( $true
= ( in @ X0 @ X2 ) ) )
| ( $true = X3 )
| ( ( $true != X3 )
& ( X0 = X1 ) ) ) )
<=> ( setadjoinE = $true ) ),
inference(flattening,[],[f20]) ).
thf(f22,plain,
( ( notinself2 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( ( in @ X1 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f19]) ).
thf(f24,plain,
( ? [X0: $i] :
( ? [X1: $i] :
( ( X0 != X1 )
& ( ( omegaS @ X0 )
= ( omegaS @ X1 ) )
& ( ( in @ X1 @ omega )
= $true ) )
& ( ( in @ X0 @ omega )
= $true ) )
& ( notinself2 = $true )
& ( in__Cong = $true )
& ( setadjoinE = $true )
& ( setadjoinIL = $true ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f25,plain,
( ? [X0: $i] :
( ( ( in @ X0 @ omega )
= $true )
& ? [X1: $i] :
( ( ( omegaS @ X0 )
= ( omegaS @ X1 ) )
& ( X0 != X1 )
& ( ( in @ X1 @ omega )
= $true ) ) )
& ( notinself2 = $true )
& ( in__Cong = $true )
& ( setadjoinE = $true )
& ( setadjoinIL = $true ) ),
inference(flattening,[],[f24]) ).
thf(f29,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) ) ),
inference(nnf_transformation,[],[f16]) ).
thf(f30,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ? [X2: $i,X3: $i] :
( $true
!= ( in @ X3 @ ( setadjoin @ X3 @ X2 ) ) ) ) ),
inference(rectify,[],[f29]) ).
thf(f31,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ( $true
!= ( in @ sK5 @ ( setadjoin @ sK5 @ sK4 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X2,sK4),skolemize(X3,sK5)],[f30]) ).
thf(f32,plain,
( ( ( notinself2 = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( ( in @ X1 @ X0 )
= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( notinself2 != $true ) ) ),
inference(nnf_transformation,[],[f22]) ).
thf(f33,plain,
( ( ( notinself2 = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( ( in @ X1 @ X0 )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X2 @ X3 ) )
| ( $true
!= ( in @ X3 @ X2 ) ) )
| ( notinself2 != $true ) ) ),
inference(rectify,[],[f32]) ).
thf(f34,plain,
( ( ( notinself2 = $true )
| ( ( ( in @ sK6 @ sK7 )
= $true )
& ( ( in @ sK7 @ sK6 )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X2 @ X3 ) )
| ( $true
!= ( in @ X3 @ X2 ) ) )
| ( notinself2 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f33]) ).
thf(f35,plain,
( ( ( in @ sK8 @ omega )
= $true )
& ( ( omegaS @ sK8 )
= ( omegaS @ sK9 ) )
& ( sK9 != sK8 )
& ( $true
= ( in @ sK9 @ omega ) )
& ( notinself2 = $true )
& ( in__Cong = $true )
& ( setadjoinE = $true )
& ( setadjoinIL = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X0,sK8),skolemize(X1,sK9)],[f25]) ).
thf(f36,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) )
| ! [X3: $o] :
( ( ( $true != X3 )
& ( $true
= ( in @ X0 @ X2 ) ) )
| ( $true = X3 )
| ( ( $true != X3 )
& ( X0 = X1 ) ) ) )
| ( setadjoinE != $true ) )
& ( ( setadjoinE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) )
& ? [X3: $o] :
( ( ( $true = X3 )
| ( $true
!= ( in @ X0 @ X2 ) ) )
& ( $true != X3 )
& ( ( $true = X3 )
| ( X0 != X1 ) ) ) ) ) ),
inference(nnf_transformation,[],[f21]) ).
thf(f37,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) )
| ! [X3: $o] :
( ( ( $true != X3 )
& ( $true
= ( in @ X0 @ X2 ) ) )
| ( $true = X3 )
| ( ( $true != X3 )
& ( X0 = X1 ) ) ) )
| ( setadjoinE != $true ) )
& ( ( setadjoinE = $true )
| ? [X4: $i,X5: $i,X6: $i] :
( ( $true
= ( in @ X4 @ ( setadjoin @ X5 @ X6 ) ) )
& ? [X7: $o] :
( ( ( $true = X7 )
| ( $true
!= ( in @ X4 @ X6 ) ) )
& ( $true != X7 )
& ( ( $true = X7 )
| ( X4 != X5 ) ) ) ) ) ),
inference(rectify,[],[f36]) ).
thf(f38,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) )
| ! [X3: $o] :
( ( ( $true != X3 )
& ( $true
= ( in @ X0 @ X2 ) ) )
| ( $true = X3 )
| ( ( $true != X3 )
& ( X0 = X1 ) ) ) )
| ( setadjoinE != $true ) )
& ( ( setadjoinE = $true )
| ( ( $true
= ( in @ sK10 @ ( setadjoin @ sK11 @ sK12 ) ) )
& ( ( $true = sK13 )
| ( $true
!= ( in @ sK10 @ sK12 ) ) )
& ( $true != sK13 )
& ( ( $true = sK13 )
| ( sK10 != sK11 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13]),skolemize(X4,sK10),skolemize(X5,sK11),skolemize(X6,sK12),skolemize(X7,sK13)],[f37]) ).
thf(f43,plain,
( omegaS
= ( ^ [Y0: $i] : ( setadjoin @ Y0 @ Y0 ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f45,plain,
! [X0: $i,X1: $i] :
( ( setadjoinIL != $true )
| ( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f46,plain,
! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X3 @ X2 ) )
| ( $true
!= ( in @ X2 @ X3 ) )
| ( notinself2 != $true ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f49,plain,
setadjoinIL = $true,
inference(cnf_transformation,[],[f35]) ).
thf(f50,plain,
setadjoinE = $true,
inference(cnf_transformation,[],[f35]) ).
thf(f52,plain,
notinself2 = $true,
inference(cnf_transformation,[],[f35]) ).
thf(f53,plain,
( $true
= ( in @ sK9 @ omega ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f54,plain,
sK9 != sK8,
inference(cnf_transformation,[],[f35]) ).
thf(f55,plain,
( ( omegaS @ sK8 )
= ( omegaS @ sK9 ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f61,plain,
! [X2: $i,X3: $o,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) )
| ( $true = X3 )
| ( setadjoinE != $true )
| ( $true
= ( in @ X0 @ X2 ) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f80,definition,
( spl14_2
<=> ( setadjoinIL = $true ) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
thf(f85,definition,
( spl14_3
<=> ( notinself2 = $true ) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
thf(f88,plain,
spl14_3,
inference(avatar_split_clause,[],[f52,f85]) ).
thf(f99,definition,
( spl14_6
<=> ( setadjoinE = $true ) ),
introduced(definition,[new_symbols(definition,[spl14_6])],[avatar_definition]) ).
thf(f102,plain,
spl14_6,
inference(avatar_split_clause,[],[f50,f99]) ).
thf(f108,plain,
spl14_2,
inference(avatar_split_clause,[],[f49,f80]) ).
thf(f120,definition,
( spl14_10
<=> ! [X3: $o] : ( $true = X3 ) ),
introduced(definition,[new_symbols(definition,[spl14_10])],[avatar_definition]) ).
thf(f121,plain,
( ! [X3: $o] : ( $true = X3 )
| ~ spl14_10 ),
inference(avatar_component_clause,[],[f120]) ).
thf(f123,definition,
( spl14_11
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) )
| ( X0 = X1 )
| ( $true
= ( in @ X0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_11])],[avatar_definition]) ).
thf(f124,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) )
| ( X0 = X1 )
| ( $true
= ( in @ X0 @ X2 ) ) )
| ~ spl14_11 ),
inference(avatar_component_clause,[],[f123]) ).
thf(f125,plain,
( ~ spl14_6
| spl14_10
| spl14_11 ),
inference(avatar_split_clause,[],[f61,f123,f120,f99]) ).
thf(f133,definition,
( spl14_13
<=> ( sK9 = sK8 ) ),
introduced(definition,[new_symbols(definition,[spl14_13])],[avatar_definition]) ).
thf(f135,plain,
( ( sK9 != sK8 )
| spl14_13 ),
inference(avatar_component_clause,[],[f133]) ).
thf(f136,plain,
~ spl14_13,
inference(avatar_split_clause,[],[f54,f133]) ).
thf(f138,definition,
( spl14_14
<=> ( ( omegaS @ sK8 )
= ( omegaS @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_14])],[avatar_definition]) ).
thf(f140,plain,
( ( ( omegaS @ sK8 )
= ( omegaS @ sK9 ) )
| ~ spl14_14 ),
inference(avatar_component_clause,[],[f138]) ).
thf(f141,plain,
spl14_14,
inference(avatar_split_clause,[],[f55,f138]) ).
thf(f143,definition,
( spl14_15
<=> ( omegaS
= ( ^ [Y0: $i] : ( setadjoin @ Y0 @ Y0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_15])],[avatar_definition]) ).
thf(f145,plain,
( ( omegaS
= ( ^ [Y0: $i] : ( setadjoin @ Y0 @ Y0 ) ) )
| ~ spl14_15 ),
inference(avatar_component_clause,[],[f143]) ).
thf(f146,plain,
spl14_15,
inference(avatar_split_clause,[],[f43,f143]) ).
thf(f171,definition,
( spl14_21
<=> ! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X3 @ X2 ) )
| ( $true
!= ( in @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_21])],[avatar_definition]) ).
thf(f172,plain,
( ! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X3 @ X2 ) )
| ( $true
!= ( in @ X2 @ X3 ) ) )
| ~ spl14_21 ),
inference(avatar_component_clause,[],[f171]) ).
thf(f173,plain,
( spl14_21
| ~ spl14_3 ),
inference(avatar_split_clause,[],[f46,f85,f171]) ).
thf(f185,definition,
( spl14_24
<=> ( $true
= ( in @ sK9 @ omega ) ) ),
introduced(definition,[new_symbols(definition,[spl14_24])],[avatar_definition]) ).
thf(f187,plain,
( ( $true
= ( in @ sK9 @ omega ) )
| ~ spl14_24 ),
inference(avatar_component_clause,[],[f185]) ).
thf(f188,plain,
spl14_24,
inference(avatar_split_clause,[],[f53,f185]) ).
thf(f195,definition,
( spl14_26
<=> ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_26])],[avatar_definition]) ).
thf(f196,plain,
( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ~ spl14_26 ),
inference(avatar_component_clause,[],[f195]) ).
thf(f197,plain,
( spl14_26
| ~ spl14_2 ),
inference(avatar_split_clause,[],[f45,f80,f195]) ).
thf(f207,plain,
( ( $true
!= ( in @ omega @ sK9 ) )
| ( $true != $true )
| ~ spl14_21
| ~ spl14_24 ),
inference(superposition,[],[f172,f187]) ).
thf(f208,plain,
( ( $true
!= ( in @ omega @ sK9 ) )
| ~ spl14_21
| ~ spl14_24 ),
inference(trivial_inequality_removal,[],[f207]) ).
thf(f210,definition,
( spl14_28
<=> ( $true
= ( in @ omega @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_28])],[avatar_definition]) ).
thf(f212,plain,
( ( $true
!= ( in @ omega @ sK9 ) )
| spl14_28 ),
inference(avatar_component_clause,[],[f210]) ).
thf(f213,plain,
( ~ spl14_28
| ~ spl14_21
| ~ spl14_24 ),
inference(avatar_split_clause,[],[f208,f185,f171,f210]) ).
thf(f219,plain,
( ! [X1: $i] :
( ( omegaS @ X1 )
= ( ^ [Y0: $i] : ( setadjoin @ Y0 @ Y0 )
@ X1 ) )
| ~ spl14_15 ),
inference(argument_congruence,[],[f145]) ).
thf(f220,plain,
( ! [X1: $i] :
( ( omegaS @ X1 )
= ( setadjoin @ X1 @ X1 ) )
| ~ spl14_15 ),
inference(beta-eta_normalization,[],[f219]) ).
thf(f221,plain,
( ( ( setadjoin @ sK9 @ sK9 )
= ( omegaS @ sK8 ) )
| ~ spl14_14
| ~ spl14_15 ),
inference(superposition,[],[f220,f140]) ).
thf(f224,definition,
( spl14_29
<=> ( ( setadjoin @ sK9 @ sK9 )
= ( omegaS @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_29])],[avatar_definition]) ).
thf(f226,plain,
( ( ( setadjoin @ sK9 @ sK9 )
= ( omegaS @ sK8 ) )
| ~ spl14_29 ),
inference(avatar_component_clause,[],[f224]) ).
thf(f227,plain,
( spl14_29
| ~ spl14_14
| ~ spl14_15 ),
inference(avatar_split_clause,[],[f221,f143,f138,f224]) ).
thf(f228,plain,
( $false
| ~ spl14_10
| spl14_28 ),
inference(forward_subsumption_resolution,[],[f212,f121]) ).
thf(f229,plain,
( ~ spl14_10
| spl14_28 ),
inference(avatar_contradiction_clause,[],[f228]) ).
thf(f235,plain,
( ( ( setadjoin @ sK9 @ sK9 )
= ( setadjoin @ sK8 @ sK8 ) )
| ~ spl14_15
| ~ spl14_29 ),
inference(superposition,[],[f220,f226]) ).
thf(f237,definition,
( spl14_30
<=> ( ( setadjoin @ sK9 @ sK9 )
= ( setadjoin @ sK8 @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_30])],[avatar_definition]) ).
thf(f239,plain,
( ( ( setadjoin @ sK9 @ sK9 )
= ( setadjoin @ sK8 @ sK8 ) )
| ~ spl14_30 ),
inference(avatar_component_clause,[],[f237]) ).
thf(f240,plain,
( spl14_30
| ~ spl14_15
| ~ spl14_29 ),
inference(avatar_split_clause,[],[f235,f224,f143,f237]) ).
thf(f256,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ X0 @ ( setadjoin @ sK8 @ sK8 ) ) )
| ( sK9 = X0 )
| ( $true
= ( in @ X0 @ sK9 ) ) )
| ~ spl14_11
| ~ spl14_30 ),
inference(superposition,[],[f124,f239]) ).
thf(f257,plain,
( ( $true
= ( in @ sK9 @ ( setadjoin @ sK8 @ sK8 ) ) )
| ~ spl14_26
| ~ spl14_30 ),
inference(superposition,[],[f196,f239]) ).
thf(f259,definition,
( spl14_32
<=> ( $true
= ( in @ sK9 @ ( setadjoin @ sK8 @ sK8 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_32])],[avatar_definition]) ).
thf(f261,plain,
( ( $true
= ( in @ sK9 @ ( setadjoin @ sK8 @ sK8 ) ) )
| ~ spl14_32 ),
inference(avatar_component_clause,[],[f259]) ).
thf(f262,plain,
( spl14_32
| ~ spl14_26
| ~ spl14_30 ),
inference(avatar_split_clause,[],[f257,f237,f195,f259]) ).
thf(f265,plain,
( ( ( in @ sK9 @ sK8 )
= $true )
| ( $true != $true )
| ( sK9 = sK8 )
| ~ spl14_11
| ~ spl14_32 ),
inference(superposition,[],[f124,f261]) ).
thf(f267,plain,
( ( ( in @ sK9 @ sK8 )
= $true )
| ( sK9 = sK8 )
| ~ spl14_11
| ~ spl14_32 ),
inference(trivial_inequality_removal,[],[f265]) ).
thf(f269,plain,
( ( ( in @ sK9 @ sK8 )
= $true )
| ~ spl14_11
| spl14_13
| ~ spl14_32 ),
inference(forward_subsumption_resolution,[],[f267,f135]) ).
thf(f276,definition,
( spl14_34
<=> ( ( in @ sK9 @ sK8 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl14_34])],[avatar_definition]) ).
thf(f278,plain,
( ( ( in @ sK9 @ sK8 )
= $true )
| ~ spl14_34 ),
inference(avatar_component_clause,[],[f276]) ).
thf(f279,plain,
( spl14_34
| ~ spl14_11
| spl14_13
| ~ spl14_32 ),
inference(avatar_split_clause,[],[f269,f259,f133,f123,f276]) ).
thf(f280,plain,
( ( ( in @ sK8 @ sK9 )
= $true )
| ( sK9 = sK8 )
| ( $true != $true )
| ~ spl14_11
| ~ spl14_26
| ~ spl14_30 ),
inference(superposition,[],[f256,f196]) ).
thf(f281,plain,
( ( ( in @ sK8 @ sK9 )
= $true )
| ( sK9 = sK8 )
| ~ spl14_11
| ~ spl14_26
| ~ spl14_30 ),
inference(trivial_inequality_removal,[],[f280]) ).
thf(f282,plain,
( ( ( in @ sK8 @ sK9 )
= $true )
| ~ spl14_11
| spl14_13
| ~ spl14_26
| ~ spl14_30 ),
inference(forward_subsumption_resolution,[],[f281,f135]) ).
thf(f284,definition,
( spl14_35
<=> ( ( in @ sK8 @ sK9 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl14_35])],[avatar_definition]) ).
thf(f287,plain,
( spl14_35
| ~ spl14_11
| spl14_13
| ~ spl14_26
| ~ spl14_30 ),
inference(avatar_split_clause,[],[f282,f237,f195,f133,f123,f284]) ).
thf(f291,plain,
( ( $true != $true )
| ( ( in @ sK8 @ sK9 )
!= $true )
| ~ spl14_21
| ~ spl14_34 ),
inference(superposition,[],[f172,f278]) ).
thf(f292,plain,
( ( ( in @ sK8 @ sK9 )
!= $true )
| ~ spl14_21
| ~ spl14_34 ),
inference(trivial_inequality_removal,[],[f291]) ).
thf(f293,plain,
( ~ spl14_35
| ~ spl14_21
| ~ spl14_34 ),
inference(avatar_split_clause,[],[f292,f276,f171,f284]) ).
cnf(s2,plain,
spl14_3,
inference(sat_conversion,[],[f88]) ).
cnf(s4,plain,
spl14_6,
inference(sat_conversion,[],[f102]) ).
cnf(s6,plain,
spl14_2,
inference(sat_conversion,[],[f108]) ).
cnf(s9,plain,
( ~ spl14_6
| spl14_10
| spl14_11 ),
inference(sat_conversion,[],[f125]) ).
cnf(s12,plain,
~ spl14_13,
inference(sat_conversion,[],[f136]) ).
cnf(s13,plain,
spl14_14,
inference(sat_conversion,[],[f141]) ).
cnf(s14,plain,
spl14_15,
inference(sat_conversion,[],[f146]) ).
cnf(s18,plain,
( ~ spl14_3
| spl14_21 ),
inference(sat_conversion,[],[f173]) ).
cnf(s21,plain,
spl14_24,
inference(sat_conversion,[],[f188]) ).
cnf(s23,plain,
( ~ spl14_2
| spl14_26 ),
inference(sat_conversion,[],[f197]) ).
cnf(s25,plain,
( ~ spl14_21
| ~ spl14_24
| ~ spl14_28 ),
inference(sat_conversion,[],[f213]) ).
cnf(s26,plain,
( ~ spl14_14
| ~ spl14_15
| spl14_29 ),
inference(sat_conversion,[],[f227]) ).
cnf(s28,plain,
( ~ spl14_10
| spl14_28 ),
inference(sat_conversion,[],[f229]) ).
cnf(s29,plain,
( ~ spl14_15
| ~ spl14_29
| spl14_30 ),
inference(sat_conversion,[],[f240]) ).
cnf(s32,plain,
( ~ spl14_26
| ~ spl14_30
| spl14_32 ),
inference(sat_conversion,[],[f262]) ).
cnf(s34,plain,
( ~ spl14_11
| spl14_13
| ~ spl14_32
| spl14_34 ),
inference(sat_conversion,[],[f279]) ).
cnf(s35,plain,
( ~ spl14_11
| spl14_13
| ~ spl14_26
| ~ spl14_30
| spl14_35 ),
inference(sat_conversion,[],[f287]) ).
cnf(s37,plain,
( ~ spl14_21
| ~ spl14_34
| ~ spl14_35 ),
inference(sat_conversion,[],[f293]) ).
cnf(s38,plain,
spl14_29,
inference(rat,[],[s26,s14,s13]) ).
cnf(s39,plain,
spl14_30,
inference(rat,[],[s29,s14,s38]) ).
cnf(s40,plain,
spl14_26,
inference(rat,[],[s23,s6]) ).
cnf(s41,plain,
spl14_32,
inference(rat,[],[s32,s39,s40]) ).
cnf(s43,plain,
spl14_21,
inference(rat,[],[s18,s2]) ).
cnf(s45,plain,
~ spl14_28,
inference(rat,[],[s25,s21,s43]) ).
cnf(s47,plain,
~ spl14_10,
inference(rat,[],[s28,s45]) ).
cnf(s48,plain,
spl14_11,
inference(rat,[],[s9,s4,s47]) ).
cnf(s49,plain,
spl14_35,
inference(rat,[],[s35,s40,s39,s12,s48]) ).
cnf(s50,plain,
spl14_34,
inference(rat,[],[s34,s41,s12,s48]) ).
cnf(s51,plain,
$false,
inference(rat,[],[s37,s43,s49,s50]) ).
thf(f294,plain,
$false,
inference(avatar_sat_refutation,[],[s51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU811^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n020.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 14:34:19 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.27 % (1136337)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (1136345)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1965787306:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.27 % (1136345) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1136337-1136345"...
% 0.20/0.27 % (1136346)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=96419026:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.27 % (1136343)lrs+10_16_si=on:nwc=1.5:random_seed=1797975916:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.27 % (1136342)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=298626628:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.27 % (1136345)...printing done.
% 0.20/0.27 % (1136344)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=998004201:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.27 % (1136345)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (1136345)------------------------------
% 0.20/0.27 % (1136345)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (1136345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (1136345)CaDiCaL version: 2.1.3
% 0.20/0.27 % (1136345)Termination reason: Refutation
% 0.20/0.27 % (1136345)Time elapsed: 0.006 s
% 0.20/0.27 % (1136345)Peak memory usage: 13 MB
% 0.20/0.27 % (1136345)Instructions burned: 13 (million)
% 0.20/0.27 % (1136337)Success in time 0.037 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------