%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU640^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n024.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 : Wed Feb 25 09:35:53 AM UTC 2026
% Result : Theorem 0.99s 0.99s
% Output : Refutation 0.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of formulae : 91 ( 15 unt; 0 typ; 5 def)
% Number of atoms : 1335 ( 429 equ; 0 cnn)
% Maximal formula atoms : 18 ( 14 avg)
% Number of connectives : 1435 ( 266 ~; 259 |; 90 &; 758 @)
% ( 10 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 13 con; 0-2 aty)
% Number of variables : 246 ( 46 ^; 154 !; 46 ?; 246 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_4,type,
singleton: $i > $o ).
thf(func_def_7,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_18,type,
sK2: $i > $o ).
thf(func_def_20,type,
sK4: ( $i > $o ) > $i > $i ).
thf(func_def_21,type,
sK5: ( $i > $o ) > $i > $i ).
thf(func_def_22,type,
sK6: $i > $o ).
thf(func_def_26,type,
ph10:
!>[X0: $tType] : X0 ).
thf(f148,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f73,f79,f112,f130,f137,f147]) ).
thf(f147,plain,
( spl9_1
| spl9_1
| ~ spl9_6
| ~ spl9_7 ),
inference(avatar_split_clause,[status(thm)],[f146,f135,f128,f67,f67]) ).
thf(f67,definition,
( spl9_1
<=> ! [X0: $i] :
( ( ( in @ X0 @ sK7 )
!= $true )
| ( ( sK6 @ X0 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl9_1])],[avatar_definition]) ).
thf(f128,definition,
( spl9_6
<=> ! [X1: $i] :
( ( ( sK6 @ X1 )
!= $true )
| ( ( sK5 @ sK6 @ sK7 )
= X1 )
| ( ( in @ X1 @ sK7 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl9_6])],[avatar_definition]) ).
thf(f135,definition,
( spl9_7
<=> ! [X0: $i] :
( ( ( sK4 @ sK6 @ sK7 )
= X0 )
| ( ( in @ X0 @ sK7 )
!= $true )
| ( ( sK6 @ X0 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl9_7])],[avatar_definition]) ).
thf(f146,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK6 @ X1 )
!= $true )
| ( ( sK6 @ X0 )
!= $true )
| ( ( in @ X1 @ sK7 )
!= $true )
| ( ( in @ X0 @ sK7 )
!= $true ) )
| ~ spl9_6
| ~ spl9_7 ),
inference(subsumption_resolution,[status(thm)],[f145,f136]) ).
thf(f136,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK7 )
!= $true )
| ( ( sK4 @ sK6 @ sK7 )
= X0 )
| ( ( sK6 @ X0 )
!= $true ) )
| ~ spl9_7 ),
inference(avatar_component_clause,[status(thm)],[f135]) ).
thf(f145,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ sK7 )
!= $true )
| ( ( sK4 @ sK6 @ sK7 )
!= X0 )
| ( ( in @ X1 @ sK7 )
!= $true )
| ( ( sK6 @ X1 )
!= $true )
| ( ( sK6 @ X0 )
!= $true ) )
| ~ spl9_6 ),
inference(subsumption_resolution,[status(thm)],[f144,f60]) ).
thf(f60,plain,
sP0 = $true,
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
( ( sP0 = $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f43,f45]) ).
thf(f45,plain,
singletonprop = $true,
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( ex1 @ sK7
@ ^ [Y0: $i] : ( sK6 @ Y0 ) )
!= $true )
& ( ( in @ sK8 @ sK7 )
= $true )
& ( ( sK6 @ sK8 )
= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ sK7 )
!= $true )
| ! [X4: $i] :
( ( ( sK6 @ X4 )
!= $true )
| ( X3 = X4 )
| ( ( in @ X4 @ sK7 )
!= $true )
| ( ( sK6 @ X3 )
!= $true ) ) )
& ( singletonprop = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f29,f31,f30]) ).
thf(f30,plain,
( ? [X0: $i > $o,X1: $i] :
( ( ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
!= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( X0 @ X2 )
= $true ) )
& ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ! [X4: $i] :
( ( ( X0 @ X4 )
!= $true )
| ( X3 = X4 )
| ( ( in @ X4 @ X1 )
!= $true )
| ( ( X0 @ X3 )
!= $true ) ) ) )
=> ( ( ( ex1 @ sK7
@ ^ [Y0: $i] : ( sK6 @ Y0 ) )
!= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ sK7 )
= $true )
& ( ( sK6 @ X2 )
= $true ) )
& ! [X3: $i] :
( ( ( in @ X3 @ sK7 )
!= $true )
| ! [X4: $i] :
( ( ( sK6 @ X4 )
!= $true )
| ( X3 = X4 )
| ( ( in @ X4 @ sK7 )
!= $true )
| ( ( sK6 @ X3 )
!= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ? [X2: $i] :
( ( ( in @ X2 @ sK7 )
= $true )
& ( ( sK6 @ X2 )
= $true ) )
=> ( ( ( in @ sK8 @ sK7 )
= $true )
& ( ( sK6 @ sK8 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f29,plain,
( ? [X0: $i > $o,X1: $i] :
( ( ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
!= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( X0 @ X2 )
= $true ) )
& ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ! [X4: $i] :
( ( ( X0 @ X4 )
!= $true )
| ( X3 = X4 )
| ( ( in @ X4 @ X1 )
!= $true )
| ( ( X0 @ X3 )
!= $true ) ) ) )
& ( singletonprop = $true ) ),
inference(rectify,[status(thm)],[f18]) ).
thf(f18,plain,
( ? [X0: $i > $o,X1: $i] :
( ( ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
!= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
& ( ( X0 @ X4 )
= $true ) )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ! [X3: $i] :
( ( ( X0 @ X3 )
!= $true )
| ( X2 = X3 )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( X0 @ X2 )
!= $true ) ) ) )
& ( singletonprop = $true ) ),
inference(flattening,[status(thm)],[f17]) ).
thf(f17,plain,
( ? [X0: $i > $o,X1: $i] :
( ( ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
!= $true )
& ? [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
& ( ( X0 @ X4 )
= $true ) )
& ! [X2: $i] :
( ! [X3: $i] :
( ( X2 = X3 )
| ( ( X0 @ X3 )
!= $true )
| ( ( X0 @ X2 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( ( in @ X2 @ X1 )
!= $true ) ) )
& ( singletonprop = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( singletonprop = $true )
=> ! [X0: $i > $o,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( X0 @ X2 )
= $true )
=> ( ( ( X0 @ X3 )
= $true )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
& ( ( X0 @ X4 )
= $true ) )
=> ( ( ex1 @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( singletonprop
=> ! [X0: $i > $o,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X0 @ X2 )
=> ( ( X0 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X4: $i] :
( ( X0 @ X4 )
& ( in @ X4 @ X1 ) )
=> ( ex1 @ X1
@ ^ [X5: $i] : ( X0 @ X5 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( singletonprop
=> ! [X2: $i > $o,X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X2 @ X1 )
=> ( ( X2 @ X3 )
=> ( X1 = X3 ) ) ) ) )
=> ( ? [X1: $i] :
( ( X2 @ X1 )
& ( in @ X1 @ X0 ) )
=> ( ex1 @ X0
@ ^ [X1: $i] : ( X2 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( singletonprop
=> ! [X2: $i > $o,X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X2 @ X1 )
=> ( ( X2 @ X3 )
=> ( X1 = X3 ) ) ) ) )
=> ( ? [X1: $i] :
( ( X2 @ X1 )
& ( in @ X1 @ X0 ) )
=> ( ex1 @ X0
@ ^ [X1: $i] : ( X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oA2HjTsKaz/DTF2THF_24605.p',ex1I2) ).
thf(f43,plain,
( ( sP0 = $true )
| ( singletonprop != $true ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( singletonprop = $true )
| ( sP0 != $true ) )
& ( ( sP0 = $true )
| ( singletonprop != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( singletonprop = $true )
<=> ( sP0 = $true ) ),
inference(definition_folding,[status(thm)],[f16,f19]) ).
thf(f19,plain,
( ( sP0 = $true )
<=> ! [X0: $i,X1: $i > $o] :
( ( ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
| ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( X1 @ X2 )
= $true )
& ( $true
= ( X1 @ X3 ) )
& ( X2 != X3 ) )
& ( ( in @ X2 @ X0 )
= $true ) )
| ! [X4: $i] :
( ( ( in @ X4 @ X0 )
!= $true )
| ( ( X1 @ X4 )
!= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f16,plain,
( ( singletonprop = $true )
<=> ! [X0: $i,X1: $i > $o] :
( ( ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
| ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( X1 @ X2 )
= $true )
& ( $true
= ( X1 @ X3 ) )
& ( X2 != X3 ) )
& ( ( in @ X2 @ X0 )
= $true ) )
| ! [X4: $i] :
( ( ( in @ X4 @ X0 )
!= $true )
| ( ( X1 @ X4 )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ( singletonprop = $true )
<=> ! [X0: $i,X1: $i > $o] :
( ( ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
| ! [X4: $i] :
( ( ( in @ X4 @ X0 )
!= $true )
| ( ( X1 @ X4 )
!= $true ) )
| ? [X2: $i] :
( ? [X3: $i] :
( ( X2 != X3 )
& ( $true
= ( X1 @ X3 ) )
& ( ( X1 @ X2 )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ X0 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( singletonprop = $true )
<=> ! [X0: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( X1 @ X2 )
= $true )
=> ( ( $true
= ( X1 @ X3 ) )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
& ( ( X1 @ X4 )
= $true ) )
=> ( ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i,X1: $i > $o] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X1 @ X2 )
=> ( ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X4: $i] :
( ( X1 @ X4 )
& ( in @ X4 @ X0 ) )
=> ( singleton
@ ( dsetconstr @ X0
@ ^ [X5: $i] : ( X1 @ X5 ) ) ) ) )
= singletonprop ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $i,X2: $i > $o] :
( ( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( X2 @ X1 )
=> ( ( X2 @ X3 )
=> ( X1 = X3 ) ) ) ) )
=> ( ? [X1: $i] :
( ( X2 @ X1 )
& ( in @ X1 @ X0 ) )
=> ( singleton
@ ( dsetconstr @ X0
@ ^ [X1: $i] : ( X2 @ X1 ) ) ) ) )
= singletonprop ),
file('/export/starexec/sandbox/tmp/tmp.oA2HjTsKaz/DTF2THF_24605.p',singletonprop) ).
thf(f144,plain,
( ! [X0: $i,X1: $i] :
( ( sP0 != $true )
| ( ( in @ X0 @ sK7 )
!= $true )
| ( ( sK4 @ sK6 @ sK7 )
!= X0 )
| ( ( sK6 @ X0 )
!= $true )
| ( ( in @ X1 @ sK7 )
!= $true )
| ( ( sK6 @ X1 )
!= $true ) )
| ~ spl9_6 ),
inference(subsumption_resolution,[status(thm)],[f142,f59]) ).
thf(f59,plain,
( ( singleton @ ( dsetconstr @ sK7 @ sK6 ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) )
@ sK7
@ ^ [Y0: $i] : ( sK6 @ Y0 ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f49,f33]) ).
thf(f33,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ex1
= ( ^ [X0: $i,X2: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X1: $i] : ( X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.oA2HjTsKaz/DTF2THF_24605.p',ex1) ).
thf(f49,plain,
( ( ex1 @ sK7
@ ^ [Y0: $i] : ( sK6 @ Y0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f142,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK6 @ X0 )
!= $true )
| ( ( singleton @ ( dsetconstr @ sK7 @ sK6 ) )
= $true )
| ( ( sK6 @ X1 )
!= $true )
| ( ( in @ X0 @ sK7 )
!= $true )
| ( ( sK4 @ sK6 @ sK7 )
!= X0 )
| ( ( in @ X1 @ sK7 )
!= $true )
| ( sP0 != $true ) )
| ~ spl9_6 ),
inference(superposition,[status(thm)],[f58,f129]) ).
thf(f129,plain,
( ! [X1: $i] :
( ( ( sK5 @ sK6 @ sK7 )
= X1 )
| ( ( sK6 @ X1 )
!= $true )
| ( ( in @ X1 @ sK7 )
!= $true ) )
| ~ spl9_6 ),
inference(avatar_component_clause,[status(thm)],[f128]) ).
thf(f58,plain,
! [X6: $i > $o,X9: $i,X5: $i] :
( ( ( sK4 @ X6 @ X5 )
!= ( sK5 @ X6 @ X5 ) )
| ( ( singleton @ ( dsetconstr @ X5 @ X6 ) )
= $true )
| ( sP0 != $true )
| ( ( X6 @ X9 )
!= $true )
| ( ( in @ X9 @ X5 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
! [X6: $i > $o,X9: $i,X5: $i] :
( ( ( X6 @ X9 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X6 @ Y0 ) ) )
= $true )
| ( sP0 != $true )
| ( ( sK4 @ X6 @ X5 )
!= ( sK5 @ X6 @ X5 ) )
| ( ( in @ X9 @ X5 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ( sP0 = $true )
| ( ( ( singleton
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) )
!= $true )
& ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ sK1 )
!= $true )
| ( ( sK2 @ X2 )
!= $true )
| ( ( sK2 @ X3 )
!= $true )
| ( X2 = X3 ) )
| ( ( in @ X2 @ sK1 )
!= $true ) )
& ( ( in @ sK3 @ sK1 )
= $true )
& ( ( sK2 @ sK3 )
= $true ) ) )
& ( ! [X5: $i,X6: $i > $o] :
( ( ( singleton
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X6 @ Y0 ) ) )
= $true )
| ( ( ( in @ ( sK5 @ X6 @ X5 ) @ X5 )
= $true )
& ( ( X6 @ ( sK4 @ X6 @ X5 ) )
= $true )
& ( ( X6 @ ( sK5 @ X6 @ X5 ) )
= $true )
& ( ( sK4 @ X6 @ X5 )
!= ( sK5 @ X6 @ X5 ) )
& ( ( in @ ( sK4 @ X6 @ X5 ) @ X5 )
= $true ) )
| ! [X9: $i] :
( ( ( in @ X9 @ X5 )
!= $true )
| ( ( X6 @ X9 )
!= $true ) ) )
| ( sP0 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5])],[f22,f26,f25,f24,f23]) ).
thf(f23,plain,
( ? [X0: $i,X1: $i > $o] :
( ( ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true )
& ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( X1 @ X2 )
!= $true )
| ( $true
!= ( X1 @ X3 ) )
| ( X2 = X3 ) )
| ( ( in @ X2 @ X0 )
!= $true ) )
& ? [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
& ( ( X1 @ X4 )
= $true ) ) )
=> ( ( ( singleton
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) )
!= $true )
& ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ sK1 )
!= $true )
| ( ( sK2 @ X2 )
!= $true )
| ( ( sK2 @ X3 )
!= $true )
| ( X2 = X3 ) )
| ( ( in @ X2 @ sK1 )
!= $true ) )
& ? [X4: $i] :
( ( ( in @ X4 @ sK1 )
= $true )
& ( ( sK2 @ X4 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ? [X4: $i] :
( ( ( in @ X4 @ sK1 )
= $true )
& ( ( sK2 @ X4 )
= $true ) )
=> ( ( ( in @ sK3 @ sK1 )
= $true )
& ( ( sK2 @ sK3 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
! [X5: $i,X6: $i > $o] :
( ? [X7: $i] :
( ? [X8: $i] :
( ( ( in @ X8 @ X5 )
= $true )
& ( ( X6 @ X7 )
= $true )
& ( ( X6 @ X8 )
= $true )
& ( X7 != X8 ) )
& ( ( in @ X7 @ X5 )
= $true ) )
=> ( ? [X8: $i] :
( ( ( in @ X8 @ X5 )
= $true )
& ( ( X6 @ ( sK4 @ X6 @ X5 ) )
= $true )
& ( ( X6 @ X8 )
= $true )
& ( ( sK4 @ X6 @ X5 )
!= X8 ) )
& ( ( in @ ( sK4 @ X6 @ X5 ) @ X5 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f26,plain,
! [X5: $i,X6: $i > $o] :
( ? [X8: $i] :
( ( ( in @ X8 @ X5 )
= $true )
& ( ( X6 @ ( sK4 @ X6 @ X5 ) )
= $true )
& ( ( X6 @ X8 )
= $true )
& ( ( sK4 @ X6 @ X5 )
!= X8 ) )
=> ( ( ( in @ ( sK5 @ X6 @ X5 ) @ X5 )
= $true )
& ( ( X6 @ ( sK4 @ X6 @ X5 ) )
= $true )
& ( ( X6 @ ( sK5 @ X6 @ X5 ) )
= $true )
& ( ( sK4 @ X6 @ X5 )
!= ( sK5 @ X6 @ X5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ( ( sP0 = $true )
| ? [X0: $i,X1: $i > $o] :
( ( ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true )
& ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( X1 @ X2 )
!= $true )
| ( $true
!= ( X1 @ X3 ) )
| ( X2 = X3 ) )
| ( ( in @ X2 @ X0 )
!= $true ) )
& ? [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
& ( ( X1 @ X4 )
= $true ) ) ) )
& ( ! [X5: $i,X6: $i > $o] :
( ( ( singleton
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X6 @ Y0 ) ) )
= $true )
| ? [X7: $i] :
( ? [X8: $i] :
( ( ( in @ X8 @ X5 )
= $true )
& ( ( X6 @ X7 )
= $true )
& ( ( X6 @ X8 )
= $true )
& ( X7 != X8 ) )
& ( ( in @ X7 @ X5 )
= $true ) )
| ! [X9: $i] :
( ( ( in @ X9 @ X5 )
!= $true )
| ( ( X6 @ X9 )
!= $true ) ) )
| ( sP0 != $true ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( sP0 = $true )
| ? [X0: $i,X1: $i > $o] :
( ( ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
!= $true )
& ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( X1 @ X2 )
!= $true )
| ( $true
!= ( X1 @ X3 ) )
| ( X2 = X3 ) )
| ( ( in @ X2 @ X0 )
!= $true ) )
& ? [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
& ( ( X1 @ X4 )
= $true ) ) ) )
& ( ! [X0: $i,X1: $i > $o] :
( ( ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
= $true )
| ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( X1 @ X2 )
= $true )
& ( $true
= ( X1 @ X3 ) )
& ( X2 != X3 ) )
& ( ( in @ X2 @ X0 )
= $true ) )
| ! [X4: $i] :
( ( ( in @ X4 @ X0 )
!= $true )
| ( ( X1 @ X4 )
!= $true ) ) )
| ( sP0 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
thf(f137,plain,
( spl9_1
| spl9_7
| ~ spl9_3 ),
inference(avatar_split_clause,[status(thm)],[f133,f76,f135,f67]) ).
thf(f76,definition,
( spl9_3
<=> ( ( sK6 @ ( sK4 @ sK6 @ sK7 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl9_3])],[avatar_definition]) ).
thf(f133,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ sK7 )
!= $true )
| ( ( sK4 @ sK6 @ sK7 )
= X0 )
| ( ( sK6 @ X1 )
!= $true )
| ( ( sK6 @ X0 )
!= $true )
| ( ( in @ X0 @ sK7 )
!= $true ) )
| ~ spl9_3 ),
inference(subsumption_resolution,[status(thm)],[f132,f78]) ).
thf(f78,plain,
( ( ( sK6 @ ( sK4 @ sK6 @ sK7 ) )
= $true )
| ~ spl9_3 ),
inference(avatar_component_clause,[status(thm)],[f76]) ).
thf(f132,plain,
! [X0: $i,X1: $i] :
( ( ( sK6 @ X0 )
!= $true )
| ( ( in @ X1 @ sK7 )
!= $true )
| ( ( sK4 @ sK6 @ sK7 )
= X0 )
| ( ( sK6 @ ( sK4 @ sK6 @ sK7 ) )
!= $true )
| ( ( sK6 @ X1 )
!= $true )
| ( ( in @ X0 @ sK7 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f131]) ).
thf(f131,plain,
! [X0: $i,X1: $i] :
( ( ( sK6 @ ( sK4 @ sK6 @ sK7 ) )
!= $true )
| ( ( sK6 @ X0 )
!= $true )
| ( ( in @ X1 @ sK7 )
!= $true )
| ( ( in @ X0 @ sK7 )
!= $true )
| ( $true != $true )
| ( ( sK6 @ X1 )
!= $true )
| ( ( sK4 @ sK6 @ sK7 )
= X0 ) ),
inference(superposition,[status(thm)],[f59,f87]) ).
thf(f87,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( singleton @ ( dsetconstr @ sK7 @ X0 ) )
= $true )
| ( ( in @ X1 @ sK7 )
!= $true )
| ( ( in @ X2 @ sK7 )
!= $true )
| ( ( sK6 @ X1 )
!= $true )
| ( ( sK6 @ ( sK4 @ X0 @ sK7 ) )
!= $true )
| ( ( X0 @ X2 )
!= $true )
| ( ( sK4 @ X0 @ sK7 )
= X1 ) ),
inference(subsumption_resolution,[status(thm)],[f84,f60]) ).
thf(f84,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( sK6 @ X1 )
!= $true )
| ( ( in @ X2 @ sK7 )
!= $true )
| ( ( in @ X1 @ sK7 )
!= $true )
| ( ( sK4 @ X0 @ sK7 )
= X1 )
| ( ( sK6 @ ( sK4 @ X0 @ sK7 ) )
!= $true )
| ( ( X0 @ X2 )
!= $true )
| ( sP0 != $true )
| ( ( singleton @ ( dsetconstr @ sK7 @ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( $true != $true )
| ( ( singleton @ ( dsetconstr @ sK7 @ X0 ) )
= $true )
| ( ( sK6 @ ( sK4 @ X0 @ sK7 ) )
!= $true )
| ( ( sK4 @ X0 @ sK7 )
= X1 )
| ( ( in @ X2 @ sK7 )
!= $true )
| ( ( X0 @ X2 )
!= $true )
| ( sP0 != $true )
| ( ( sK6 @ X1 )
!= $true )
| ( ( in @ X1 @ sK7 )
!= $true ) ),
inference(superposition,[status(thm)],[f46,f53]) ).
thf(f53,plain,
! [X6: $i > $o,X9: $i,X5: $i] :
( ( ( in @ ( sK4 @ X6 @ X5 ) @ X5 )
= $true )
| ( ( X6 @ X9 )
!= $true )
| ( ( singleton @ ( dsetconstr @ X5 @ X6 ) )
= $true )
| ( sP0 != $true )
| ( ( in @ X9 @ X5 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X6: $i > $o,X9: $i,X5: $i] :
( ( sP0 != $true )
| ( ( X6 @ X9 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X6 @ Y0 ) ) )
= $true )
| ( ( in @ ( sK4 @ X6 @ X5 ) @ X5 )
= $true )
| ( ( in @ X9 @ X5 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f46,plain,
! [X3: $i,X4: $i] :
( ( ( in @ X4 @ sK7 )
!= $true )
| ( ( sK6 @ X3 )
!= $true )
| ( ( sK6 @ X4 )
!= $true )
| ( X3 = X4 )
| ( ( in @ X3 @ sK7 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f130,plain,
( spl9_1
| spl9_6
| ~ spl9_2 ),
inference(avatar_split_clause,[status(thm)],[f126,f70,f128,f67]) ).
thf(f70,definition,
( spl9_2
<=> ( ( sK6 @ ( sK5 @ sK6 @ sK7 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl9_2])],[avatar_definition]) ).
thf(f126,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ sK7 )
!= $true )
| ( ( sK6 @ X1 )
!= $true )
| ( ( in @ X1 @ sK7 )
!= $true )
| ( ( sK5 @ sK6 @ sK7 )
= X1 )
| ( ( sK6 @ X0 )
!= $true ) )
| ~ spl9_2 ),
inference(subsumption_resolution,[status(thm)],[f125,f72]) ).
thf(f72,plain,
( ( ( sK6 @ ( sK5 @ sK6 @ sK7 ) )
= $true )
| ~ spl9_2 ),
inference(avatar_component_clause,[status(thm)],[f70]) ).
thf(f125,plain,
! [X0: $i,X1: $i] :
( ( ( sK6 @ X0 )
!= $true )
| ( ( in @ X1 @ sK7 )
!= $true )
| ( ( sK6 @ ( sK5 @ sK6 @ sK7 ) )
!= $true )
| ( ( in @ X0 @ sK7 )
!= $true )
| ( ( sK5 @ sK6 @ sK7 )
= X1 )
| ( ( sK6 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f124]) ).
thf(f124,plain,
! [X0: $i,X1: $i] :
( ( ( sK5 @ sK6 @ sK7 )
= X1 )
| ( ( sK6 @ X0 )
!= $true )
| ( ( sK6 @ X1 )
!= $true )
| ( ( sK6 @ ( sK5 @ sK6 @ sK7 ) )
!= $true )
| ( ( in @ X1 @ sK7 )
!= $true )
| ( $true != $true )
| ( ( in @ X0 @ sK7 )
!= $true ) ),
inference(superposition,[status(thm)],[f59,f86]) ).
thf(f86,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( singleton @ ( dsetconstr @ sK7 @ X0 ) )
= $true )
| ( ( X0 @ X2 )
!= $true )
| ( ( sK6 @ ( sK5 @ X0 @ sK7 ) )
!= $true )
| ( ( in @ X2 @ sK7 )
!= $true )
| ( ( in @ X1 @ sK7 )
!= $true )
| ( ( sK6 @ X1 )
!= $true )
| ( ( sK5 @ X0 @ sK7 )
= X1 ) ),
inference(subsumption_resolution,[status(thm)],[f85,f60]) ).
thf(f85,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( sP0 != $true )
| ( ( in @ X2 @ sK7 )
!= $true )
| ( ( X0 @ X2 )
!= $true )
| ( ( sK6 @ ( sK5 @ X0 @ sK7 ) )
!= $true )
| ( ( sK5 @ X0 @ sK7 )
= X1 )
| ( ( sK6 @ X1 )
!= $true )
| ( ( in @ X1 @ sK7 )
!= $true )
| ( ( singleton @ ( dsetconstr @ sK7 @ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( singleton @ ( dsetconstr @ sK7 @ X0 ) )
= $true )
| ( ( sK6 @ ( sK5 @ X0 @ sK7 ) )
!= $true )
| ( ( sK6 @ X1 )
!= $true )
| ( sP0 != $true )
| ( ( in @ X1 @ sK7 )
!= $true )
| ( ( sK5 @ X0 @ sK7 )
= X1 )
| ( $true != $true )
| ( ( in @ X2 @ sK7 )
!= $true )
| ( ( X0 @ X2 )
!= $true ) ),
inference(superposition,[status(thm)],[f46,f54]) ).
thf(f54,plain,
! [X6: $i > $o,X9: $i,X5: $i] :
( ( ( in @ ( sK5 @ X6 @ X5 ) @ X5 )
= $true )
| ( sP0 != $true )
| ( ( singleton @ ( dsetconstr @ X5 @ X6 ) )
= $true )
| ( ( X6 @ X9 )
!= $true )
| ( ( in @ X9 @ X5 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
! [X6: $i > $o,X9: $i,X5: $i] :
( ( ( singleton
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X6 @ Y0 ) ) )
= $true )
| ( sP0 != $true )
| ( ( in @ ( sK5 @ X6 @ X5 ) @ X5 )
= $true )
| ( ( X6 @ X9 )
!= $true )
| ( ( in @ X9 @ X5 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f112,plain,
~ spl9_1,
inference(avatar_contradiction_clause,[status(thm)],[f111]) ).
thf(f111,plain,
( $false
| ~ spl9_1 ),
inference(subsumption_resolution,[status(thm)],[f108,f47]) ).
thf(f47,plain,
( ( sK6 @ sK8 )
= $true ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f108,plain,
( ( ( sK6 @ sK8 )
!= $true )
| ~ spl9_1 ),
inference(trivial_inequality_removal,[status(thm)],[f106]) ).
thf(f106,plain,
( ( ( sK6 @ sK8 )
!= $true )
| ( $true != $true )
| ~ spl9_1 ),
inference(superposition,[status(thm)],[f68,f48]) ).
thf(f48,plain,
( ( in @ sK8 @ sK7 )
= $true ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f68,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK7 )
!= $true )
| ( ( sK6 @ X0 )
!= $true ) )
| ~ spl9_1 ),
inference(avatar_component_clause,[status(thm)],[f67]) ).
thf(f79,plain,
( spl9_3
| spl9_1 ),
inference(avatar_split_clause,[status(thm)],[f74,f67,f76]) ).
thf(f74,plain,
! [X0: $i] :
( ( ( sK6 @ X0 )
!= $true )
| ( ( sK6 @ ( sK4 @ sK6 @ sK7 ) )
= $true )
| ( ( in @ X0 @ sK7 )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f63,f60]) ).
thf(f63,plain,
! [X0: $i] :
( ( sP0 != $true )
| ( ( sK6 @ ( sK4 @ sK6 @ sK7 ) )
= $true )
| ( ( in @ X0 @ sK7 )
!= $true )
| ( ( sK6 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( sK6 @ ( sK4 @ sK6 @ sK7 ) )
= $true )
| ( ( in @ X0 @ sK7 )
!= $true )
| ( ( sK6 @ X0 )
!= $true )
| ( sP0 != $true ) ),
inference(superposition,[status(thm)],[f59,f55]) ).
thf(f55,plain,
! [X6: $i > $o,X9: $i,X5: $i] :
( ( ( singleton @ ( dsetconstr @ X5 @ X6 ) )
= $true )
| ( ( X6 @ X9 )
!= $true )
| ( ( in @ X9 @ X5 )
!= $true )
| ( ( X6 @ ( sK4 @ X6 @ X5 ) )
= $true )
| ( sP0 != $true ) ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
! [X6: $i > $o,X9: $i,X5: $i] :
( ( ( singleton
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X6 @ Y0 ) ) )
= $true )
| ( ( X6 @ X9 )
!= $true )
| ( ( in @ X9 @ X5 )
!= $true )
| ( ( X6 @ ( sK4 @ X6 @ X5 ) )
= $true )
| ( sP0 != $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f73,plain,
( spl9_1
| spl9_2 ),
inference(avatar_split_clause,[status(thm)],[f65,f70,f67]) ).
thf(f65,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK7 )
!= $true )
| ( ( sK6 @ X0 )
!= $true )
| ( ( sK6 @ ( sK5 @ sK6 @ sK7 ) )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f64,f60]) ).
thf(f64,plain,
! [X0: $i] :
( ( sP0 != $true )
| ( ( in @ X0 @ sK7 )
!= $true )
| ( ( sK6 @ ( sK5 @ sK6 @ sK7 ) )
= $true )
| ( ( sK6 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
! [X0: $i] :
( ( sP0 != $true )
| ( ( in @ X0 @ sK7 )
!= $true )
| ( $true != $true )
| ( ( sK6 @ ( sK5 @ sK6 @ sK7 ) )
= $true )
| ( ( sK6 @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f59,f56]) ).
thf(f56,plain,
! [X6: $i > $o,X9: $i,X5: $i] :
( ( ( singleton @ ( dsetconstr @ X5 @ X6 ) )
= $true )
| ( ( in @ X9 @ X5 )
!= $true )
| ( ( X6 @ X9 )
!= $true )
| ( ( X6 @ ( sK5 @ X6 @ X5 ) )
= $true )
| ( sP0 != $true ) ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X6: $i > $o,X9: $i,X5: $i] :
( ( ( in @ X9 @ X5 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ X5
@ ^ [Y0: $i] : ( X6 @ Y0 ) ) )
= $true )
| ( ( X6 @ X9 )
!= $true )
| ( ( X6 @ ( sK5 @ X6 @ X5 ) )
= $true )
| ( sP0 != $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU640^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n024.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 07:29:10 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.32 ---- Original DTF file ---
% 0.07/0.32 thf(spec,logic,$$dhol).
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 % File : SEU640^2 : TPTP v9.2.1. Released v3.7.0.
% 0.07/0.32 % Domain : Set Theory
% 0.07/0.32 % Problem : Ordered Pairs - Singletons
% 0.07/0.32 % Version : Especial > Reduced > Especial.
% 0.07/0.32 % English : (! A:i.! phi:i>o.(! x:i.in x A -> (! y:i.in y A -> phi x ->
% 0.07/0.32 % phi y -> x = y)) -> (? x:i.in x A & phi x) -> ex1 A (^ x:i.phi x))
% 0.07/0.32
% 0.07/0.32 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.07/0.32 % Source : [Bro08]
% 0.07/0.32 % Names : ZFC142l [Bro08]
% 0.07/0.32
% 0.07/0.32 % Status : Theorem
% 0.07/0.32 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v4.1.0, 0.33 v4.0.0, 0.67 v3.7.0
% 0.07/0.32 % Syntax : Number of formulae : 11 ( 3 unt; 7 typ; 3 def)
% 0.07/0.32 % Number of atoms : 20 ( 6 equ; 0 cnn)
% 0.07/0.32 % Maximal formula atoms : 6 ( 5 avg)
% 0.07/0.32 % Number of connectives : 49 ( 0 ~; 0 |; 3 &; 33 @)
% 0.07/0.32 % ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% 0.07/0.32 % Maximal formula depth : 12 ( 4 avg)
% 0.07/0.32 % Number of types : 2 ( 0 usr)
% 0.07/0.32 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.07/0.32 % Number of symbols : 8 ( 7 usr; 2 con; 0-2 aty)
% 0.07/0.32 % Number of variables : 17 ( 6 ^; 8 !; 3 ?; 17 :)
% 0.07/0.32 % SPC : TH0_THM_EQU_NAR
% 0.07/0.32
% 0.07/0.32 % Comments : http://mathgate.info/detsetitem.php?id=470
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 thf(in_type,type,
% 0.07/0.32 in: $i > $i > $o ).
% 0.07/0.32
% 0.07/0.32 thf(emptyset_type,type,
% 0.07/0.32 emptyset: $i ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoin_type,type,
% 0.07/0.32 setadjoin: $i > $i > $i ).
% 0.07/0.32
% 0.07/0.32 thf(dsetconstr_type,type,
% 0.07/0.32 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.07/0.32
% 0.07/0.32 thf(singleton_type,type,
% 0.07/0.32 singleton: $i > $o ).
% 0.07/0.32
% 0.07/0.32 thf(singleton,definition,
% 0.07/0.32 ( singleton
% 0.07/0.32 = ( ^ [A: $i] :
% 0.07/0.32 ? [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ A )
% 0.07/0.32 & ( A
% 0.07/0.32 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(singletonprop_type,type,
% 0.07/0.32 singletonprop: $o ).
% 0.07/0.32
% 0.07/0.32 thf(singletonprop,definition,
% 0.07/0.32 ( singletonprop
% 0.07/0.32 = ( ! [A: $i,Xphi: $i > $o] :
% 0.07/0.32 ( ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ A )
% 0.07/0.32 => ! [Xy: $i] :
% 0.07/0.32 ( ( in @ Xy @ A )
% 0.07/0.32 => ( ( Xphi @ Xx )
% 0.07/0.32 => ( ( Xphi @ Xy )
% 0.07/0.32 => ( Xx = Xy ) ) ) ) )
% 0.07/0.32 => ( ? [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ A )
% 0.07/0.32 & ( Xphi @ Xx ) )
% 0.07/0.32 => ( singleton
% 0.07/0.32 @ ( dsetconstr @ A
% 0.07/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(ex1_type,type,
% 0.07/0.32 ex1: $i > ( $i > $o ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(ex1,definition,
% 0.07/0.32 ( ex1
% 0.07/0.32 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.07/0.32 ( singleton
% 0.07/0.32 @ ( dsetconstr @ A
% 0.07/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(ex1I2,conjecture,
% 0.07/0.32 ( singletonprop
% 0.07/0.32 => ! [A: $i,Xphi: $i > $o] :
% 0.07/0.32 ( ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ A )
% 0.07/0.32 => ! [Xy: $i] :
% 0.07/0.32 ( ( in @ Xy @ A )
% 0.07/0.32 => ( ( Xphi @ Xx )
% 0.07/0.32 => ( ( Xphi @ Xy )
% 0.07/0.32 => ( Xx = Xy ) ) ) ) )
% 0.07/0.32 => ( ? [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ A )
% 0.07/0.32 & ( Xphi @ Xx ) )
% 0.07/0.32 => ( ex1 @ A
% 0.07/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 ------------------------
% 0.99/0.95 ---- Embedded in THF ---
% 0.99/0.95 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.99/0.95 %%% Generated on Tue Feb 24 07:29:11 EST 2026
% 0.99/0.95 %%% using '$$dhol' embedding, version 1.3.0.
% 0.99/0.95 %%% Logic specification used:
% 0.99/0.95 %%% thf(spec, logic, $$dhol).
% 0.99/0.95
% 0.99/0.95 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.oA2HjTsKaz/DTF2DTF24605.p
% See solution above
% 0.99/0.95 ------------------------
% 0.99/0.96 ---- Cleaned THF ---
% 0.99/0.96 thf(in_type,type,
% 0.99/0.96 in: $i > $i > $o ).
% 0.99/0.96
% 0.99/0.96 thf(emptyset_type,type,
% 0.99/0.96 emptyset: $i ).
% 0.99/0.96
% 0.99/0.96 thf(setadjoin_type,type,
% 0.99/0.96 setadjoin: $i > $i > $i ).
% 0.99/0.96
% 0.99/0.96 thf(dsetconstr_type,type,
% 0.99/0.96 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.99/0.96
% 0.99/0.96 thf(singleton_type,type,
% 0.99/0.96 singleton: $i > $o ).
% 0.99/0.96
% 0.99/0.96 thf(singleton,definition,
% 0.99/0.96 ( singleton
% 0.99/0.96 = ( ^ [A: $i] :
% 0.99/0.96 ? [Xx: $i] :
% 0.99/0.96 ( ( in @ Xx @ A )
% 0.99/0.96 & ( A
% 0.99/0.96 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.99/0.96
% 0.99/0.96 thf(singletonprop_type,type,
% 0.99/0.96 singletonprop: $o ).
% 0.99/0.96
% 0.99/0.96 thf(singletonprop,definition,
% 0.99/0.96 ( singletonprop
% 0.99/0.96 = ( ! [A: $i,Xphi: $i > $o] :
% 0.99/0.96 ( ! [Xx: $i] :
% 0.99/0.96 ( ( in @ Xx @ A )
% 0.99/0.96 => ! [Xy: $i] :
% 0.99/0.96 ( ( in @ Xy @ A )
% 0.99/0.96 => ( ( Xphi @ Xx )
% 0.99/0.96 => ( ( Xphi @ Xy )
% 0.99/0.96 => ( Xx = Xy ) ) ) ) )
% 0.99/0.96 => ( ? [Xx: $i] :
% 0.99/0.96 ( ( in @ Xx @ A )
% 0.99/0.96 & ( Xphi @ Xx ) )
% 0.99/0.96 => ( singleton
% 0.99/0.96 @ ( dsetconstr @ A
% 0.99/0.96 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.99/0.96
% 0.99/0.96 thf(ex1_type,type,
% 0.99/0.96 ex1: $i > ( $i > $o ) > $o ).
% 0.99/0.96
% 0.99/0.96 thf(ex1,definition,
% 0.99/0.96 ( ex1
% 0.99/0.96 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.99/0.96 ( singleton
% 0.99/0.96 @ ( dsetconstr @ A
% 0.99/0.96 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.99/0.96
% 0.99/0.96 thf(ex1I2,conjecture,
% 0.99/0.96 ( singletonprop
% 0.99/0.96 => ! [A: $i,Xphi: $i > $o] :
% 0.99/0.96 ( ! [Xx: $i] :
% 0.99/0.96 ( ( in @ Xx @ A )
% 0.99/0.96 => ! [Xy: $i] :
% 0.99/0.96 ( ( in @ Xy @ A )
% 0.99/0.96 => ( ( Xphi @ Xx )
% 0.99/0.96 => ( ( Xphi @ Xy )
% 0.99/0.96 => ( Xx = Xy ) ) ) ) )
% 0.99/0.96 => ( ? [Xx: $i] :
% 0.99/0.96 ( ( in @ Xx @ A )
% 0.99/0.96 & ( Xphi @ Xx ) )
% 0.99/0.96 => ( ex1 @ A
% 0.99/0.96 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.99/0.96 ------------------------
% 0.99/0.97 % (24795)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_24605 for (3000ds/4Mi)
% 0.99/0.97 % (24794)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24605 for (3000ds/183Mi)
% 0.99/0.97 % (24800)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_24605 for (3000ds/18Mi)
% 0.99/0.98 % (24796)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_24605 for (3000ds/27Mi)
% 0.99/0.98 % (24797)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_24605 for (3000ds/2Mi)
% 0.99/0.98 % (24800)Instruction limit reached!
% 0.99/0.98 % (24800)------------------------------
% 0.99/0.98 % (24800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.99/0.98 % (24798)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_24605 for (3000ds/2Mi)
% 0.99/0.98 % (24800)Termination reason: Unknown
% 0.99/0.98 % (24800)Termination phase: Saturation
% 0.99/0.98
% 0.99/0.98 % (24800)Memory used [KB]: 5628
% 0.99/0.98 % (24800)Time elapsed: 0.009 s
% 0.99/0.98 % (24800)Instructions burned: 18 (million)
% 0.99/0.98 % (24800)------------------------------
% 0.99/0.98 % (24800)------------------------------
% 0.99/0.98 % (24797)Instruction limit reached!
% 0.99/0.98 % (24797)------------------------------
% 0.99/0.98 % (24797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.99/0.98 % (24797)Termination reason: Unknown
% 0.99/0.98 % (24797)Termination phase: Saturation
% 0.99/0.98
% 0.99/0.98 % (24798)Instruction limit reached!
% 0.99/0.98 % (24798)------------------------------
% 0.99/0.98 % (24798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.99/0.98 % (24797)Memory used [KB]: 1023
% 0.99/0.98 % (24798)Termination reason: Unknown
% 0.99/0.98 % (24798)Termination phase: Saturation
% 0.99/0.98
% 0.99/0.98 % (24798)Memory used [KB]: 1023
% 0.99/0.98 % (24798)Time elapsed: 0.002 s
% 0.99/0.98 % (24798)Instructions burned: 4 (million)
% 0.99/0.98 % (24798)------------------------------
% 0.99/0.98 % (24798)------------------------------
% 0.99/0.98 % (24797)Time elapsed: 0.002 s
% 0.99/0.98 % (24797)Instructions burned: 3 (million)
% 0.99/0.98 % (24797)------------------------------
% 0.99/0.98 % (24797)------------------------------
% 0.99/0.98 % (24799)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_24605 for (3000ds/275Mi)
% 0.99/0.98 % (24795)Instruction limit reached!
% 0.99/0.98 % (24795)------------------------------
% 0.99/0.98 % (24795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.99/0.98 % (24795)Termination reason: Unknown
% 0.99/0.98 % (24795)Termination phase: Saturation
% 0.99/0.98
% 0.99/0.98 % (24795)Memory used [KB]: 5500
% 0.99/0.98 % (24795)Time elapsed: 0.004 s
% 0.99/0.98 % (24795)Instructions burned: 5 (million)
% 0.99/0.98 % (24795)------------------------------
% 0.99/0.98 % (24795)------------------------------
% 0.99/0.99 % (24799)First to succeed.
% 0.99/0.99 % (24796)Instruction limit reached!
% 0.99/0.99 % (24796)------------------------------
% 0.99/0.99 % (24796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.99/0.99 % (24796)Termination reason: Unknown
% 0.99/0.99 % (24796)Termination phase: Saturation
% 0.99/0.99
% 0.99/0.99 % (24796)Memory used [KB]: 5628
% 0.99/0.99 % (24796)Time elapsed: 0.015 s
% 0.99/0.99 % (24796)Instructions burned: 28 (million)
% 0.99/0.99 % (24796)------------------------------
% 0.99/0.99 % (24796)------------------------------
% 0.99/0.99 % (24801)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_24605 for (2999ds/3Mi)
% 0.99/0.99 % (24802)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_24605 for (2999ds/37Mi)
% 0.99/0.99 % (24799)Refutation found. Thanks to Tanya!
% 0.99/0.99 % SZS status Theorem for DTF2THF_24605
% 0.99/0.99 % SZS output start Proof for DTF2THF_24605
% 0.99/0.99 thf(func_def_0, type, in: $i > $i > $o).
% 0.99/0.99 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.99/0.99 thf(func_def_3, type, dsetconstr: $i > ($i > $o) > $i).
% 0.99/0.99 thf(func_def_4, type, singleton: $i > $o).
% 0.99/0.99 thf(func_def_7, type, ex1: $i > ($i > $o) > $o).
% 0.99/0.99 thf(func_def_18, type, sK2: $i > $o).
% 0.99/0.99 thf(func_def_20, type, sK4: ($i > $o) > $i > $i).
% 0.99/0.99 thf(func_def_21, type, sK5: ($i > $o) > $i > $i).
% 0.99/0.99 thf(func_def_22, type, sK6: $i > $o).
% 0.99/0.99 thf(func_def_26, type, ph10: !>[X0: $tType]:(X0)).
% 0.99/0.99 thf(f148,plain,(
% 0.99/0.99 $false),
% 0.99/0.99 inference(avatar_sat_refutation,[status(thm)],[f73,f79,f112,f130,f137,f147])).
% 0.99/0.99 thf(f147,plain,(
% 0.99/0.99 spl9_1 | spl9_1 | ~spl9_6 | ~spl9_7),
% 0.99/0.99 inference(avatar_split_clause,[status(thm)],[f146,f135,f128,f67,f67])).
% 0.99/0.99 thf(f67,definition,(
% 0.99/0.99 spl9_1 <=> ! [X0 : $i] : (((in @ X0 @ sK7) != $true) | ((sK6 @ X0) != $true))),
% 0.99/0.99 introduced(definition,[new_symbols(naming,[spl9_1])],[avatar_definition])).
% 0.99/0.99 thf(f128,definition,(
% 0.99/0.99 spl9_6 <=> ! [X1 : $i] : (((sK6 @ X1) != $true) | ((sK5 @ sK6 @ sK7) = X1) | ((in @ X1 @ sK7) != $true))),
% 0.99/0.99 introduced(definition,[new_symbols(naming,[spl9_6])],[avatar_definition])).
% 0.99/0.99 thf(f135,definition,(
% 0.99/0.99 spl9_7 <=> ! [X0 : $i] : (((sK4 @ sK6 @ sK7) = X0) | ((in @ X0 @ sK7) != $true) | ((sK6 @ X0) != $true))),
% 0.99/0.99 introduced(definition,[new_symbols(naming,[spl9_7])],[avatar_definition])).
% 0.99/0.99 thf(f146,plain,(
% 0.99/0.99 ( ! [X0 : $i,X1 : $i] : (((sK6 @ X1) != $true) | ((sK6 @ X0) != $true) | ((in @ X1 @ sK7) != $true) | ((in @ X0 @ sK7) != $true)) ) | (~spl9_6 | ~spl9_7)),
% 0.99/0.99 inference(subsumption_resolution,[status(thm)],[f145,f136])).
% 0.99/0.99 thf(f136,plain,(
% 0.99/0.99 ( ! [X0 : $i] : (((in @ X0 @ sK7) != $true) | ((sK4 @ sK6 @ sK7) = X0) | ((sK6 @ X0) != $true)) ) | ~spl9_7),
% 0.99/0.99 inference(avatar_component_clause,[status(thm)],[f135])).
% 0.99/0.99 thf(f145,plain,(
% 0.99/0.99 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ sK7) != $true) | ((sK4 @ sK6 @ sK7) != X0) | ((in @ X1 @ sK7) != $true) | ((sK6 @ X1) != $true) | ((sK6 @ X0) != $true)) ) | ~spl9_6),
% 0.99/0.99 inference(subsumption_resolution,[status(thm)],[f144,f60])).
% 0.99/0.99 thf(f60,plain,(
% 0.99/0.99 (sP0 = $true)),
% 0.99/0.99 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 0.99/0.99 thf(f51,plain,(
% 0.99/0.99 (sP0 = $true) | ($true != $true)),
% 0.99/0.99 inference(definition_unfolding,[status(thm)],[f43,f45])).
% 0.99/0.99 thf(f45,plain,(
% 0.99/0.99 (singletonprop = $true)),
% 0.99/0.99 inference(cnf_transformation,[status(thm)],[f32])).
% 0.99/0.99 thf(f32,plain,(
% 0.99/0.99 (((ex1 @ sK7 @ (^[Y0 : $i]: (sK6 @ Y0))) != $true) & (((in @ sK8 @ sK7) = $true) & ((sK6 @ sK8) = $true)) & ! [X3 : $i] : (((in @ X3 @ sK7) != $true) | ! [X4 : $i] : (((sK6 @ X4) != $true) | (X3 = X4) | ((in @ X4 @ sK7) != $true) | ((sK6 @ X3) != $true)))) & (singletonprop = $true)),
% 0.99/0.99 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f29,f31,f30])).
% 0.99/0.99 thf(f30,plain,(
% 0.99/0.99 ? [X0 : $i > $o,X1 : $i] : (((ex1 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) != $true) & ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((X0 @ X2) = $true)) & ! [X3 : $i] : (((in @ X3 @ X1) != $true) | ! [X4 : $i] : (((X0 @ X4) != $true) | (X3 = X4) | ((in @ X4 @ X1) != $true) | ((X0 @ X3) != $true)))) => (((ex1 @ sK7 @ (^[Y0 : $i]: (sK6 @ Y0))) != $true) & ? [X2 : $i] : (((in @ X2 @ sK7) = $true) & ((sK6 @ X2) = $true)) & ! [X3 : $i] : (((in @ X3 @ sK7) != $true) | ! [X4 : $i] : (((sK6 @ X4) != $true) | (X3 = X4) | ((in @ X4 @ sK7) != $true) | ((sK6 @ X3) != $true))))),
% 0.99/0.99 introduced(definition,[],[choice_axiom])).
% 0.99/0.99 thf(f31,plain,(
% 0.99/0.99 ? [X2 : $i] : (((in @ X2 @ sK7) = $true) & ((sK6 @ X2) = $true)) => (((in @ sK8 @ sK7) = $true) & ((sK6 @ sK8) = $true))),
% 0.99/0.99 introduced(definition,[],[choice_axiom])).
% 0.99/0.99 thf(f29,plain,(
% 0.99/0.99 ? [X0 : $i > $o,X1 : $i] : (((ex1 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) != $true) & ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((X0 @ X2) = $true)) & ! [X3 : $i] : (((in @ X3 @ X1) != $true) | ! [X4 : $i] : (((X0 @ X4) != $true) | (X3 = X4) | ((in @ X4 @ X1) != $true) | ((X0 @ X3) != $true)))) & (singletonprop = $true)),
% 0.99/0.99 inference(rectify,[status(thm)],[f18])).
% 0.99/0.99 thf(f18,plain,(
% 0.99/0.99 ? [X0 : $i > $o,X1 : $i] : (((ex1 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) != $true) & ? [X4 : $i] : (((in @ X4 @ X1) = $true) & ((X0 @ X4) = $true)) & ! [X2 : $i] : (((in @ X2 @ X1) != $true) | ! [X3 : $i] : (((X0 @ X3) != $true) | (X2 = X3) | ((in @ X3 @ X1) != $true) | ((X0 @ X2) != $true)))) & (singletonprop = $true)),
% 0.99/0.99 inference(flattening,[status(thm)],[f17])).
% 0.99/0.99 thf(f17,plain,(
% 0.99/0.99 ? [X0 : $i > $o,X1 : $i] : ((((ex1 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) != $true) & ? [X4 : $i] : (((in @ X4 @ X1) = $true) & ((X0 @ X4) = $true))) & ! [X2 : $i] : (! [X3 : $i] : ((((X2 = X3) | ((X0 @ X3) != $true)) | ((X0 @ X2) != $true)) | ((in @ X3 @ X1) != $true)) | ((in @ X2 @ X1) != $true))) & (singletonprop = $true)),
% 0.99/0.99 inference(ennf_transformation,[status(thm)],[f12])).
% 0.99/0.99 thf(f12,plain,(
% 0.99/0.99 ~((singletonprop = $true) => ! [X0 : $i > $o,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) = $true) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => (((X0 @ X2) = $true) => (((X0 @ X3) = $true) => (X2 = X3))))) => (? [X4 : $i] : (((in @ X4 @ X1) = $true) & ((X0 @ X4) = $true)) => ((ex1 @ X1 @ (^[Y0 : $i]: (X0 @ Y0))) = $true))))),
% 0.99/0.99 inference(fool_elimination,[status(thm)],[f11])).
% 0.99/0.99 thf(f11,plain,(
% 0.99/0.99 ~(singletonprop => ! [X0 : $i > $o,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => ! [X3 : $i] : ((in @ X3 @ X1) => ((X0 @ X2) => ((X0 @ X3) => (X2 = X3))))) => (? [X4 : $i] : ((X0 @ X4) & (in @ X4 @ X1)) => (ex1 @ X1 @ (^[X5 : $i] : (X0 @ X5))))))),
% 0.99/0.99 inference(rectify,[status(thm)],[f5])).
% 0.99/0.99 thf(f5,negated_conjecture,(
% 0.99/0.99 ~(singletonprop => ! [X2 : $i > $o,X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X2 @ X1) => ((X2 @ X3) => (X1 = X3))))) => (? [X1 : $i] : ((X2 @ X1) & (in @ X1 @ X0)) => (ex1 @ X0 @ (^[X1 : $i] : (X2 @ X1))))))),
% 0.99/0.99 inference(negated_conjecture,[status(cth)],[f4])).
% 0.99/0.99 thf(f4,conjecture,(
% 0.99/0.99 singletonprop => ! [X2 : $i > $o,X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X2 @ X1) => ((X2 @ X3) => (X1 = X3))))) => (? [X1 : $i] : ((X2 @ X1) & (in @ X1 @ X0)) => (ex1 @ X0 @ (^[X1 : $i] : (X2 @ X1)))))),
% 0.99/0.99 file('/export/starexec/sandbox/tmp/tmp.oA2HjTsKaz/DTF2THF_24605.p',ex1I2)).
% 0.99/0.99 thf(f43,plain,(
% 0.99/0.99 (sP0 = $true) | (singletonprop != $true)),
% 0.99/0.99 inference(cnf_transformation,[status(thm)],[f28])).
% 0.99/0.99 thf(f28,plain,(
% 0.99/0.99 ((singletonprop = $true) | (sP0 != $true)) & ((sP0 = $true) | (singletonprop != $true))),
% 0.99/0.99 inference(nnf_transformation,[status(thm)],[f20])).
% 0.99/0.99 thf(f20,plain,(
% 0.99/0.99 (singletonprop = $true) <=> (sP0 = $true)),
% 0.99/0.99 inference(definition_folding,[status(thm)],[f16,f19])).
% 0.99/0.99 thf(f19,plain,(
% 0.99/0.99 (sP0 = $true) <=> ! [X0 : $i,X1 : $i > $o] : (((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true) | ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((X1 @ X2) = $true) & ($true = (X1 @ X3)) & (X2 != X3)) & ((in @ X2 @ X0) = $true)) | ! [X4 : $i] : (((in @ X4 @ X0) != $true) | ((X1 @ X4) != $true)))),
% 0.99/0.99 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 0.99/0.99 thf(f16,plain,(
% 0.99/0.99 (singletonprop = $true) <=> ! [X0 : $i,X1 : $i > $o] : (((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true) | ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((X1 @ X2) = $true) & ($true = (X1 @ X3)) & (X2 != X3)) & ((in @ X2 @ X0) = $true)) | ! [X4 : $i] : (((in @ X4 @ X0) != $true) | ((X1 @ X4) != $true)))),
% 0.99/0.99 inference(flattening,[status(thm)],[f15])).
% 0.99/0.99 thf(f15,plain,(
% 0.99/0.99 (singletonprop = $true) <=> ! [X0 : $i,X1 : $i > $o] : ((((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true) | ! [X4 : $i] : (((in @ X4 @ X0) != $true) | ((X1 @ X4) != $true))) | ? [X2 : $i] : (? [X3 : $i] : ((((X2 != X3) & ($true = (X1 @ X3))) & ((X1 @ X2) = $true)) & ((in @ X3 @ X0) = $true)) & ((in @ X2 @ X0) = $true)))),
% 0.99/0.99 inference(ennf_transformation,[status(thm)],[f10])).
% 0.99/0.99 thf(f10,plain,(
% 0.99/0.99 (singletonprop = $true) <=> ! [X0 : $i,X1 : $i > $o] : (! [X2 : $i] : (((in @ X2 @ X0) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (((X1 @ X2) = $true) => (($true = (X1 @ X3)) => (X2 = X3))))) => (? [X4 : $i] : (((in @ X4 @ X0) = $true) & ((X1 @ X4) = $true)) => ((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true)))),
% 0.99/0.99 inference(fool_elimination,[status(thm)],[f9])).
% 0.99/0.99 thf(f9,plain,(
% 0.99/0.99 (! [X0 : $i,X1 : $i > $o] : (! [X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (? [X4 : $i] : ((X1 @ X4) & (in @ X4 @ X0)) => (singleton @ (dsetconstr @ X0 @ (^[X5 : $i] : (X1 @ X5)))))) = singletonprop)),
% 0.99/0.99 inference(rectify,[status(thm)],[f2])).
% 0.99/0.99 thf(f2,axiom,(
% 0.99/0.99 (! [X0 : $i,X2 : $i > $o] : (! [X1 : $i] : ((in @ X1 @ X0) => ! [X3 : $i] : ((in @ X3 @ X0) => ((X2 @ X1) => ((X2 @ X3) => (X1 = X3))))) => (? [X1 : $i] : ((X2 @ X1) & (in @ X1 @ X0)) => (singleton @ (dsetconstr @ X0 @ (^[X1 : $i] : (X2 @ X1)))))) = singletonprop)),
% 0.99/0.99 file('/export/starexec/sandbox/tmp/tmp.oA2HjTsKaz/DTF2THF_24605.p',singletonprop)).
% 0.99/0.99 thf(f144,plain,(
% 0.99/0.99 ( ! [X0 : $i,X1 : $i] : ((sP0 != $true) | ((in @ X0 @ sK7) != $true) | ((sK4 @ sK6 @ sK7) != X0) | ((sK6 @ X0) != $true) | ((in @ X1 @ sK7) != $true) | ((sK6 @ X1) != $true)) ) | ~spl9_6),
% 0.99/0.99 inference(subsumption_resolution,[status(thm)],[f142,f59])).
% 0.99/0.99 thf(f59,plain,(
% 0.99/0.99 ((singleton @ (dsetconstr @ sK7 @ sK6)) != $true)),
% 0.99/0.99 inference(beta_eta_normalization,[status(thm)],[f52])).
% 0.99/0.99 thf(f52,plain,(
% 0.99/0.99 (((^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))) @ sK7 @ (^[Y0 : $i]: (sK6 @ Y0))) != $true)),
% 0.99/0.99 inference(definition_unfolding,[status(thm)],[f49,f33])).
% 0.99/0.99 thf(f33,plain,(
% 0.99/0.99 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 0.99/0.99 inference(cnf_transformation,[status(thm)],[f14])).
% 0.99/0.99 thf(f14,plain,(
% 0.99/0.99 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 0.99/0.99 inference(fool_elimination,[status(thm)],[f13])).
% 0.99/0.99 thf(f13,plain,(
% 0.99/0.99 (ex1 = (^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))))),
% 0.99/0.99 inference(rectify,[status(thm)],[f3])).
% 0.99/0.99 thf(f3,axiom,(
% 0.99/0.99 (ex1 = (^[X0 : $i, X2 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X1 : $i] : (X2 @ X1))))))),
% 0.99/0.99 file('/export/starexec/sandbox/tmp/tmp.oA2HjTsKaz/DTF2THF_24605.p',ex1)).
% 0.99/0.99 thf(f49,plain,(
% 0.99/0.99 ((ex1 @ sK7 @ (^[Y0 : $i]: (sK6 @ Y0))) != $true)),
% 0.99/0.99 inference(cnf_transformation,[status(thm)],[f32])).
% 0.99/0.99 thf(f142,plain,(
% 0.99/0.99 ( ! [X0 : $i,X1 : $i] : (((sK6 @ X0) != $true) | ((singleton @ (dsetconstr @ sK7 @ sK6)) = $true) | ((sK6 @ X1) != $true) | ((in @ X0 @ sK7) != $true) | ((sK4 @ sK6 @ sK7) != X0) | ((in @ X1 @ sK7) != $true) | (sP0 != $true)) ) | ~spl9_6),
% 0.99/0.99 inference(superposition,[status(thm)],[f58,f129])).
% 0.99/0.99 thf(f129,plain,(
% 0.99/0.99 ( ! [X1 : $i] : (((sK5 @ sK6 @ sK7) = X1) | ((sK6 @ X1) != $true) | ((in @ X1 @ sK7) != $true)) ) | ~spl9_6),
% 0.99/0.99 inference(avatar_component_clause,[status(thm)],[f128])).
% 0.99/0.99 thf(f58,plain,(
% 0.99/0.99 ( ! [X6 : $i > $o,X9 : $i,X5 : $i] : (((sK4 @ X6 @ X5) != (sK5 @ X6 @ X5)) | ((singleton @ (dsetconstr @ X5 @ X6)) = $true) | (sP0 != $true) | ((X6 @ X9) != $true) | ((in @ X9 @ X5) != $true)) )),
% 0.99/0.99 inference(beta_eta_normalization,[status(thm)],[f35])).
% 0.99/0.99 thf(f35,plain,(
% 0.99/0.99 ( ! [X6 : $i > $o,X9 : $i,X5 : $i] : (((X6 @ X9) != $true) | ((singleton @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X6 @ Y0)))) = $true) | (sP0 != $true) | ((sK4 @ X6 @ X5) != (sK5 @ X6 @ X5)) | ((in @ X9 @ X5) != $true)) )),
% 0.99/0.99 inference(cnf_transformation,[status(thm)],[f27])).
% 0.99/0.99 thf(f27,plain,(
% 0.99/0.99 ((sP0 = $true) | (((singleton @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (sK2 @ Y0)))) != $true) & ! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ sK1) != $true) | ((sK2 @ X2) != $true) | ((sK2 @ X3) != $true) | (X2 = X3)) | ((in @ X2 @ sK1) != $true)) & (((in @ sK3 @ sK1) = $true) & ((sK2 @ sK3) = $true)))) & (! [X5 : $i,X6 : $i > $o] : (((singleton @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X6 @ Y0)))) = $true) | ((((in @ (sK5 @ X6 @ X5) @ X5) = $true) & ((X6 @ (sK4 @ X6 @ X5)) = $true) & ((X6 @ (sK5 @ X6 @ X5)) = $true) & ((sK4 @ X6 @ X5) != (sK5 @ X6 @ X5))) & ((in @ (sK4 @ X6 @ X5) @ X5) = $true)) | ! [X9 : $i] : (((in @ X9 @ X5) != $true) | ((X6 @ X9) != $true))) | (sP0 != $true))),
% 0.99/0.99 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5])],[f22,f26,f25,f24,f23])).
% 0.99/0.99 thf(f23,plain,(
% 0.99/0.99 ? [X0 : $i,X1 : $i > $o] : (((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true) & ! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X0) != $true) | ((X1 @ X2) != $true) | ($true != (X1 @ X3)) | (X2 = X3)) | ((in @ X2 @ X0) != $true)) & ? [X4 : $i] : (((in @ X4 @ X0) = $true) & ((X1 @ X4) = $true))) => (((singleton @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (sK2 @ Y0)))) != $true) & ! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ sK1) != $true) | ((sK2 @ X2) != $true) | ((sK2 @ X3) != $true) | (X2 = X3)) | ((in @ X2 @ sK1) != $true)) & ? [X4 : $i] : (((in @ X4 @ sK1) = $true) & ((sK2 @ X4) = $true)))),
% 0.99/0.99 introduced(definition,[],[choice_axiom])).
% 0.99/0.99 thf(f24,plain,(
% 0.99/0.99 ? [X4 : $i] : (((in @ X4 @ sK1) = $true) & ((sK2 @ X4) = $true)) => (((in @ sK3 @ sK1) = $true) & ((sK2 @ sK3) = $true))),
% 0.99/0.99 introduced(definition,[],[choice_axiom])).
% 0.99/0.99 thf(f25,plain,(
% 0.99/0.99 ! [X5 : $i,X6 : $i > $o] : (? [X7 : $i] : (? [X8 : $i] : (((in @ X8 @ X5) = $true) & ((X6 @ X7) = $true) & ((X6 @ X8) = $true) & (X7 != X8)) & ((in @ X7 @ X5) = $true)) => (? [X8 : $i] : (((in @ X8 @ X5) = $true) & ((X6 @ (sK4 @ X6 @ X5)) = $true) & ((X6 @ X8) = $true) & ((sK4 @ X6 @ X5) != X8)) & ((in @ (sK4 @ X6 @ X5) @ X5) = $true)))),
% 0.99/0.99 introduced(definition,[],[choice_axiom])).
% 0.99/0.99 thf(f26,plain,(
% 0.99/0.99 ! [X5 : $i,X6 : $i > $o] : (? [X8 : $i] : (((in @ X8 @ X5) = $true) & ((X6 @ (sK4 @ X6 @ X5)) = $true) & ((X6 @ X8) = $true) & ((sK4 @ X6 @ X5) != X8)) => (((in @ (sK5 @ X6 @ X5) @ X5) = $true) & ((X6 @ (sK4 @ X6 @ X5)) = $true) & ((X6 @ (sK5 @ X6 @ X5)) = $true) & ((sK4 @ X6 @ X5) != (sK5 @ X6 @ X5))))),
% 0.99/0.99 introduced(definition,[],[choice_axiom])).
% 0.99/0.99 thf(f22,plain,(
% 0.99/0.99 ((sP0 = $true) | ? [X0 : $i,X1 : $i > $o] : (((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true) & ! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X0) != $true) | ((X1 @ X2) != $true) | ($true != (X1 @ X3)) | (X2 = X3)) | ((in @ X2 @ X0) != $true)) & ? [X4 : $i] : (((in @ X4 @ X0) = $true) & ((X1 @ X4) = $true)))) & (! [X5 : $i,X6 : $i > $o] : (((singleton @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X6 @ Y0)))) = $true) | ? [X7 : $i] : (? [X8 : $i] : (((in @ X8 @ X5) = $true) & ((X6 @ X7) = $true) & ((X6 @ X8) = $true) & (X7 != X8)) & ((in @ X7 @ X5) = $true)) | ! [X9 : $i] : (((in @ X9 @ X5) != $true) | ((X6 @ X9) != $true))) | (sP0 != $true))),
% 0.99/0.99 inference(rectify,[status(thm)],[f21])).
% 0.99/0.99 thf(f21,plain,(
% 0.99/0.99 ((sP0 = $true) | ? [X0 : $i,X1 : $i > $o] : (((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) != $true) & ! [X2 : $i] : (! [X3 : $i] : (((in @ X3 @ X0) != $true) | ((X1 @ X2) != $true) | ($true != (X1 @ X3)) | (X2 = X3)) | ((in @ X2 @ X0) != $true)) & ? [X4 : $i] : (((in @ X4 @ X0) = $true) & ((X1 @ X4) = $true)))) & (! [X0 : $i,X1 : $i > $o] : (((singleton @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) = $true) | ? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((X1 @ X2) = $true) & ($true = (X1 @ X3)) & (X2 != X3)) & ((in @ X2 @ X0) = $true)) | ! [X4 : $i] : (((in @ X4 @ X0) != $true) | ((X1 @ X4) != $true))) | (sP0 != $true))),
% 0.99/0.99 inference(nnf_transformation,[status(thm)],[f19])).
% 0.99/0.99 thf(f137,plain,(
% 0.99/0.99 spl9_1 | spl9_7 | ~spl9_3),
% 0.99/0.99 inference(avatar_split_clause,[status(thm)],[f133,f76,f135,f67])).
% 0.99/0.99 thf(f76,definition,(
% 0.99/0.99 spl9_3 <=> ((sK6 @ (sK4 @ sK6 @ sK7)) = $true)),
% 0.99/0.99 introduced(definition,[new_symbols(naming,[spl9_3])],[avatar_definition])).
% 0.99/0.99 thf(f133,plain,(
% 0.99/0.99 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ sK7) != $true) | ((sK4 @ sK6 @ sK7) = X0) | ((sK6 @ X1) != $true) | ((sK6 @ X0) != $true) | ((in @ X0 @ sK7) != $true)) ) | ~spl9_3),
% 0.99/0.99 inference(subsumption_resolution,[status(thm)],[f132,f78])).
% 0.99/0.99 thf(f78,plain,(
% 0.99/0.99 ((sK6 @ (sK4 @ sK6 @ sK7)) = $true) | ~spl9_3),
% 0.99/0.99 inference(avatar_component_clause,[status(thm)],[f76])).
% 0.99/0.99 thf(f132,plain,(
% 0.99/0.99 ( ! [X0 : $i,X1 : $i] : (((sK6 @ X0) != $true) | ((in @ X1 @ sK7) != $true) | ((sK4 @ sK6 @ sK7) = X0) | ((sK6 @ (sK4 @ sK6 @ sK7)) != $true) | ((sK6 @ X1) != $true) | ((in @ X0 @ sK7) != $true)) )),
% 0.99/0.99 inference(trivial_inequality_removal,[status(thm)],[f131])).
% 0.99/0.99 thf(f131,plain,(
% 0.99/0.99 ( ! [X0 : $i,X1 : $i] : (((sK6 @ (sK4 @ sK6 @ sK7)) != $true) | ((sK6 @ X0) != $true) | ((in @ X1 @ sK7) != $true) | ((in @ X0 @ sK7) != $true) | ($true != $true) | ((sK6 @ X1) != $true) | ((sK4 @ sK6 @ sK7) = X0)) )),
% 0.99/0.99 inference(superposition,[status(thm)],[f59,f87])).
% 0.99/0.99 thf(f87,plain,(
% 0.99/0.99 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((singleton @ (dsetconstr @ sK7 @ X0)) = $true) | ((in @ X1 @ sK7) != $true) | ((in @ X2 @ sK7) != $true) | ((sK6 @ X1) != $true) | ((sK6 @ (sK4 @ X0 @ sK7)) != $true) | ((X0 @ X2) != $true) | ((sK4 @ X0 @ sK7) = X1)) )),
% 0.99/0.99 inference(subsumption_resolution,[status(thm)],[f84,f60])).
% 0.99/0.99 thf(f84,plain,(
% 0.99/0.99 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((sK6 @ X1) != $true) | ((in @ X2 @ sK7) != $true) | ((in @ X1 @ sK7) != $true) | ((sK4 @ X0 @ sK7) = X1) | ((sK6 @ (sK4 @ X0 @ sK7)) != $true) | ((X0 @ X2) != $true) | (sP0 != $true) | ((singleton @ (dsetconstr @ sK7 @ X0)) = $true)) )),
% 0.99/0.99 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 0.99/0.99 thf(f80,plain,(
% 0.99/0.99 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (($true != $true) | ((singleton @ (dsetconstr @ sK7 @ X0)) = $true) | ((sK6 @ (sK4 @ X0 @ sK7)) != $true) | ((sK4 @ X0 @ sK7) = X1) | ((in @ X2 @ sK7) != $true) | ((X0 @ X2) != $true) | (sP0 != $true) | ((sK6 @ X1) != $true) | ((in @ X1 @ sK7) != $true)) )),
% 0.99/0.99 inference(superposition,[status(thm)],[f46,f53])).
% 0.99/0.99 thf(f53,plain,(
% 0.99/0.99 ( ! [X6 : $i > $o,X9 : $i,X5 : $i] : (((in @ (sK4 @ X6 @ X5) @ X5) = $true) | ((X6 @ X9) != $true) | ((singleton @ (dsetconstr @ X5 @ X6)) = $true) | (sP0 != $true) | ((in @ X9 @ X5) != $true)) )),
% 0.99/0.99 inference(beta_eta_normalization,[status(thm)],[f34])).
% 0.99/0.99 thf(f34,plain,(
% 0.99/0.99 ( ! [X6 : $i > $o,X9 : $i,X5 : $i] : ((sP0 != $true) | ((X6 @ X9) != $true) | ((singleton @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X6 @ Y0)))) = $true) | ((in @ (sK4 @ X6 @ X5) @ X5) = $true) | ((in @ X9 @ X5) != $true)) )),
% 0.99/0.99 inference(cnf_transformation,[status(thm)],[f27])).
% 0.99/0.99 thf(f46,plain,(
% 0.99/0.99 ( ! [X3 : $i,X4 : $i] : (((in @ X4 @ sK7) != $true) | ((sK6 @ X3) != $true) | ((sK6 @ X4) != $true) | (X3 = X4) | ((in @ X3 @ sK7) != $true)) )),
% 0.99/0.99 inference(cnf_transformation,[status(thm)],[f32])).
% 0.99/0.99 thf(f130,plain,(
% 0.99/0.99 spl9_1 | spl9_6 | ~spl9_2),
% 0.99/0.99 inference(avatar_split_clause,[status(thm)],[f126,f70,f128,f67])).
% 0.99/0.99 thf(f70,definition,(
% 0.99/0.99 spl9_2 <=> ((sK6 @ (sK5 @ sK6 @ sK7)) = $true)),
% 0.99/0.99 introduced(definition,[new_symbols(naming,[spl9_2])],[avatar_definition])).
% 0.99/0.99 thf(f126,plain,(
% 0.99/0.99 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ sK7) != $true) | ((sK6 @ X1) != $true) | ((in @ X1 @ sK7) != $true) | ((sK5 @ sK6 @ sK7) = X1) | ((sK6 @ X0) != $true)) ) | ~spl9_2),
% 0.99/0.99 inference(subsumption_resolution,[status(thm)],[f125,f72])).
% 0.99/0.99 thf(f72,plain,(
% 0.99/0.99 ((sK6 @ (sK5 @ sK6 @ sK7)) = $true) | ~spl9_2),
% 0.99/0.99 inference(avatar_component_clause,[status(thm)],[f70])).
% 0.99/0.99 thf(f125,plain,(
% 0.99/0.99 ( ! [X0 : $i,X1 : $i] : (((sK6 @ X0) != $true) | ((in @ X1 @ sK7) != $true) | ((sK6 @ (sK5 @ sK6 @ sK7)) != $true) | ((in @ X0 @ sK7) != $true) | ((sK5 @ sK6 @ sK7) = X1) | ((sK6 @ X1) != $true)) )),
% 0.99/0.99 inference(trivial_inequality_removal,[status(thm)],[f124])).
% 0.99/0.99 thf(f124,plain,(
% 0.99/0.99 ( ! [X0 : $i,X1 : $i] : (((sK5 @ sK6 @ sK7) = X1) | ((sK6 @ X0) != $true) | ((sK6 @ X1) != $true) | ((sK6 @ (sK5 @ sK6 @ sK7)) != $true) | ((in @ X1 @ sK7) != $true) | ($true != $true) | ((in @ X0 @ sK7) != $true)) )),
% 0.99/0.99 inference(superposition,[status(thm)],[f59,f86])).
% 0.99/0.99 thf(f86,plain,(
% 0.99/0.99 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((singleton @ (dsetconstr @ sK7 @ X0)) = $true) | ((X0 @ X2) != $true) | ((sK6 @ (sK5 @ X0 @ sK7)) != $true) | ((in @ X2 @ sK7) != $true) | ((in @ X1 @ sK7) != $true) | ((sK6 @ X1) != $true) | ((sK5 @ X0 @ sK7) = X1)) )),
% 0.99/0.99 inference(subsumption_resolution,[status(thm)],[f85,f60])).
% 0.99/0.99 thf(f85,plain,(
% 0.99/0.99 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : ((sP0 != $true) | ((in @ X2 @ sK7) != $true) | ((X0 @ X2) != $true) | ((sK6 @ (sK5 @ X0 @ sK7)) != $true) | ((sK5 @ X0 @ sK7) = X1) | ((sK6 @ X1) != $true) | ((in @ X1 @ sK7) != $true) | ((singleton @ (dsetconstr @ sK7 @ X0)) = $true)) )),
% 0.99/0.99 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 0.99/0.99 thf(f81,plain,(
% 0.99/0.99 ( ! [X2 : $i,X0 : $i > $o,X1 : $i] : (((singleton @ (dsetconstr @ sK7 @ X0)) = $true) | ((sK6 @ (sK5 @ X0 @ sK7)) != $true) | ((sK6 @ X1) != $true) | (sP0 != $true) | ((in @ X1 @ sK7) != $true) | ((sK5 @ X0 @ sK7) = X1) | ($true != $true) | ((in @ X2 @ sK7) != $true) | ((X0 @ X2) != $true)) )),
% 0.99/0.99 inference(superposition,[status(thm)],[f46,f54])).
% 0.99/0.99 thf(f54,plain,(
% 0.99/0.99 ( ! [X6 : $i > $o,X9 : $i,X5 : $i] : (((in @ (sK5 @ X6 @ X5) @ X5) = $true) | (sP0 != $true) | ((singleton @ (dsetconstr @ X5 @ X6)) = $true) | ((X6 @ X9) != $true) | ((in @ X9 @ X5) != $true)) )),
% 0.99/0.99 inference(beta_eta_normalization,[status(thm)],[f38])).
% 0.99/0.99 thf(f38,plain,(
% 0.99/0.99 ( ! [X6 : $i > $o,X9 : $i,X5 : $i] : (((singleton @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X6 @ Y0)))) = $true) | (sP0 != $true) | ((in @ (sK5 @ X6 @ X5) @ X5) = $true) | ((X6 @ X9) != $true) | ((in @ X9 @ X5) != $true)) )),
% 0.99/0.99 inference(cnf_transformation,[status(thm)],[f27])).
% 0.99/0.99 thf(f112,plain,(
% 0.99/0.99 ~spl9_1),
% 0.99/0.99 inference(avatar_contradiction_clause,[status(thm)],[f111])).
% 0.99/0.99 thf(f111,plain,(
% 0.99/0.99 $false | ~spl9_1),
% 0.99/0.99 inference(subsumption_resolution,[status(thm)],[f108,f47])).
% 0.99/0.99 thf(f47,plain,(
% 0.99/0.99 ((sK6 @ sK8) = $true)),
% 0.99/0.99 inference(cnf_transformation,[status(thm)],[f32])).
% 0.99/0.99 thf(f108,plain,(
% 0.99/0.99 ((sK6 @ sK8) != $true) | ~spl9_1),
% 0.99/0.99 inference(trivial_inequality_removal,[status(thm)],[f106])).
% 0.99/0.99 thf(f106,plain,(
% 0.99/0.99 ((sK6 @ sK8) != $true) | ($true != $true) | ~spl9_1),
% 0.99/0.99 inference(superposition,[status(thm)],[f68,f48])).
% 0.99/0.99 thf(f48,plain,(
% 0.99/0.99 ((in @ sK8 @ sK7) = $true)),
% 0.99/0.99 inference(cnf_transformation,[status(thm)],[f32])).
% 0.99/0.99 thf(f68,plain,(
% 0.99/0.99 ( ! [X0 : $i] : (((in @ X0 @ sK7) != $true) | ((sK6 @ X0) != $true)) ) | ~spl9_1),
% 0.99/0.99 inference(avatar_component_clause,[status(thm)],[f67])).
% 0.99/0.99 thf(f79,plain,(
% 0.99/0.99 spl9_3 | spl9_1),
% 0.99/0.99 inference(avatar_split_clause,[status(thm)],[f74,f67,f76])).
% 0.99/0.99 thf(f74,plain,(
% 0.99/0.99 ( ! [X0 : $i] : (((sK6 @ X0) != $true) | ((sK6 @ (sK4 @ sK6 @ sK7)) = $true) | ((in @ X0 @ sK7) != $true)) )),
% 0.99/0.99 inference(subsumption_resolution,[status(thm)],[f63,f60])).
% 0.99/0.99 thf(f63,plain,(
% 0.99/0.99 ( ! [X0 : $i] : ((sP0 != $true) | ((sK6 @ (sK4 @ sK6 @ sK7)) = $true) | ((in @ X0 @ sK7) != $true) | ((sK6 @ X0) != $true)) )),
% 0.99/0.99 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 0.99/0.99 thf(f62,plain,(
% 0.99/0.99 ( ! [X0 : $i] : (($true != $true) | ((sK6 @ (sK4 @ sK6 @ sK7)) = $true) | ((in @ X0 @ sK7) != $true) | ((sK6 @ X0) != $true) | (sP0 != $true)) )),
% 0.99/0.99 inference(superposition,[status(thm)],[f59,f55])).
% 0.99/0.99 thf(f55,plain,(
% 0.99/0.99 ( ! [X6 : $i > $o,X9 : $i,X5 : $i] : (((singleton @ (dsetconstr @ X5 @ X6)) = $true) | ((X6 @ X9) != $true) | ((in @ X9 @ X5) != $true) | ((X6 @ (sK4 @ X6 @ X5)) = $true) | (sP0 != $true)) )),
% 0.99/0.99 inference(beta_eta_normalization,[status(thm)],[f37])).
% 0.99/0.99 thf(f37,plain,(
% 0.99/0.99 ( ! [X6 : $i > $o,X9 : $i,X5 : $i] : (((singleton @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X6 @ Y0)))) = $true) | ((X6 @ X9) != $true) | ((in @ X9 @ X5) != $true) | ((X6 @ (sK4 @ X6 @ X5)) = $true) | (sP0 != $true)) )),
% 0.99/0.99 inference(cnf_transformation,[status(thm)],[f27])).
% 0.99/0.99 thf(f73,plain,(
% 0.99/0.99 spl9_1 | spl9_2),
% 0.99/0.99 inference(avatar_split_clause,[status(thm)],[f65,f70,f67])).
% 0.99/0.99 thf(f65,plain,(
% 0.99/0.99 ( ! [X0 : $i] : (((in @ X0 @ sK7) != $true) | ((sK6 @ X0) != $true) | ((sK6 @ (sK5 @ sK6 @ sK7)) = $true)) )),
% 0.99/0.99 inference(subsumption_resolution,[status(thm)],[f64,f60])).
% 0.99/0.99 thf(f64,plain,(
% 0.99/0.99 ( ! [X0 : $i] : ((sP0 != $true) | ((in @ X0 @ sK7) != $true) | ((sK6 @ (sK5 @ sK6 @ sK7)) = $true) | ((sK6 @ X0) != $true)) )),
% 0.99/0.99 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 0.99/0.99 thf(f61,plain,(
% 0.99/0.99 ( ! [X0 : $i] : ((sP0 != $true) | ((in @ X0 @ sK7) != $true) | ($true != $true) | ((sK6 @ (sK5 @ sK6 @ sK7)) = $true) | ((sK6 @ X0) != $true)) )),
% 0.99/0.99 inference(superposition,[status(thm)],[f59,f56])).
% 0.99/0.99 thf(f56,plain,(
% 0.99/0.99 ( ! [X6 : $i > $o,X9 : $i,X5 : $i] : (((singleton @ (dsetconstr @ X5 @ X6)) = $true) | ((in @ X9 @ X5) != $true) | ((X6 @ X9) != $true) | ((X6 @ (sK5 @ X6 @ X5)) = $true) | (sP0 != $true)) )),
% 0.99/0.99 inference(beta_eta_normalization,[status(thm)],[f36])).
% 0.99/0.99 thf(f36,plain,(
% 0.99/0.99 ( ! [X6 : $i > $o,X9 : $i,X5 : $i] : (((in @ X9 @ X5) != $true) | ((singleton @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X6 @ Y0)))) = $true) | ((X6 @ X9) != $true) | ((X6 @ (sK5 @ X6 @ X5)) = $true) | (sP0 != $true)) )),
% 0.99/0.99 inference(cnf_transformation,[status(thm)],[f27])).
% 0.99/0.99 % SZS output end Proof for DTF2THF_24605
% 0.99/0.99 % (24799)------------------------------
% 0.99/0.99 % (24799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.99/0.99 % (24799)Termination reason: Refutation
% 0.99/0.99
% 0.99/0.99 % (24799)Memory used [KB]: 5628
% 0.99/0.99 % (24799)Time elapsed: 0.010 s
% 0.99/0.99 % (24799)Instructions burned: 20 (million)
% 0.99/0.99 % (24799)------------------------------
% 0.99/0.99 % (24799)------------------------------
% 0.99/0.99 % (24793)Success in time 0.027 s
%------------------------------------------------------------------------------