%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU645^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 09:35:55 AM UTC 2026
% Result : Theorem 1.66s 1.39s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 14
% Syntax : Number of formulae : 106 ( 40 unt; 0 typ; 0 def)
% Number of atoms : 1211 ( 273 equ; 0 cnn)
% Maximal formula atoms : 6 ( 11 avg)
% Number of connectives : 1797 ( 112 ~; 92 |; 50 &;1496 @)
% ( 9 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 19 con; 0-4 aty)
% Number of variables : 249 ( 72 ^; 141 !; 36 ?; 249 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setunion: $i > $i ).
thf(func_def_4,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_7,type,
iskpair: $i > $o ).
thf(func_def_8,type,
kpair: $i > $i > $i ).
thf(func_def_10,type,
singleton: $i > $o ).
thf(func_def_14,type,
kfst: $i > $i ).
thf(func_def_28,type,
sK4: $i > $o ).
thf(func_def_38,type,
ph13:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
sK14: $i > $i > $i > $i > $i ).
thf(func_def_40,type,
sK15: $i > $i > $i ).
thf(f146,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f143]) ).
thf(f143,plain,
$true = $false,
inference(superposition,[status(thm)],[f140,f115]) ).
thf(f115,plain,
! [X0: $i,X1: $i] :
( $true
= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(backward_demodulation,[status(thm)],[f112,f114]) ).
thf(f114,plain,
! [X0: $i,X1: $i] :
( ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
= X0 ),
inference(trivial_inequality_removal,[status(thm)],[f113]) ).
thf(f113,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
= X0 ) ),
inference(superposition,[status(thm)],[f99,f112]) ).
thf(f99,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
| ( X0 = X2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f95]) ).
thf(f95,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( X0 = X2 )
| ( $true != $true )
| ( $true
!= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f82,f61]) ).
thf(f61,plain,
setukpairinjL1 = $true,
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
( ( kpairp = $true )
& ( dsetconstrER = $true )
& ( sK1
!= ( kfst @ ( kpair @ sK1 @ sK0 ) ) )
& ( kfstsingleton = $true )
& ( theprop = $true )
& ( setukpairinjL1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f38,f39]) ).
thf(f39,plain,
( ? [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X1 @ X0 ) )
!= X1 )
=> ( sK1
!= ( kfst @ ( kpair @ sK1 @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f38,plain,
( ( kpairp = $true )
& ( dsetconstrER = $true )
& ? [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X1 @ X0 ) )
!= X1 )
& ( kfstsingleton = $true )
& ( theprop = $true )
& ( setukpairinjL1 = $true ) ),
inference(flattening,[status(thm)],[f37]) ).
thf(f37,plain,
( ? [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X1 @ X0 ) )
!= X1 )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( kpairp = $true )
& ( dsetconstrER = $true ) ),
inference(ennf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
~ ( ( dsetconstrER = $true )
=> ( ( kpairp = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ! [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X1 @ X0 ) )
= X1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f25]) ).
thf(f25,plain,
~ ( dsetconstrER
=> ( kpairp
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ! [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X1 @ X0 ) )
= X1 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,negated_conjecture,
~ ( dsetconstrER
=> ( kpairp
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ! [X3: $i,X2: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
thf(f10,conjecture,
( dsetconstrER
=> ( kpairp
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ! [X3: $i,X2: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.FtBKtpcojT/DTF2THF_20179.p',kfstpairEq) ).
thf(f82,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( X0 = X2 )
| ( $true
!= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
| ( setukpairinjL1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f60,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( $true
!= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( setukpairinjL1 != $true ) )
& ( ( setukpairinjL1 = $true )
| ( ( sK9 != sK11 )
& ( $true
= ( in @ ( setadjoin @ sK9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK11 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK11 @ ( setadjoin @ sK10 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f58,f59]) ).
thf(f59,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( X3 != X5 )
& ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X5 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
= $true ) )
=> ( ( sK9 != sK11 )
& ( $true
= ( in @ ( setadjoin @ sK9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK11 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK11 @ ( setadjoin @ sK10 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f58,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( $true
!= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( setukpairinjL1 != $true ) )
& ( ( setukpairinjL1 = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( X3 != X5 )
& ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X5 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( $true
!= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( setukpairinjL1 != $true ) )
& ( ( setukpairinjL1 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( X0 != X2 )
& ( $true
= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( $true
!= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
<=> ( setukpairinjL1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( setukpairinjL1 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
=> ( X0 = X2 ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( X0 = X2 ) )
= setukpairinjL1 ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X4: $i,X3: $i,X2: $i] :
( ( ( in @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X4 ) )
= setukpairinjL1 ),
file('/export/starexec/sandbox2/tmp/tmp.FtBKtpcojT/DTF2THF_20179.p',setukpairinjL1) ).
thf(f112,plain,
! [X0: $i,X1: $i] :
( $true
= ( in
@ ( setadjoin
@ ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
@ emptyset )
@ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f111]) ).
thf(f111,plain,
! [X0: $i,X1: $i] :
( ( ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f110]) ).
thf(f110,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ) ),
inference(superposition,[status(thm)],[f105,f109]) ).
thf(f109,plain,
! [X0: $i,X1: $i] :
( $true
= ( in
@ ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f108]) ).
thf(f108,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
= ( in
@ ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(superposition,[status(thm)],[f100,f107]) ).
thf(f107,plain,
! [X0: $i,X1: $i] :
( ( singleton
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f106]) ).
thf(f106,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ) ),
inference(superposition,[status(thm)],[f103,f102]) ).
thf(f102,plain,
! [X0: $i,X1: $i] :
( ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f101]) ).
thf(f101,plain,
! [X0: $i,X1: $i] :
( $true
= ( iskpair
@ ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ X1
@ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f93]) ).
thf(f93,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( iskpair
@ ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ X1
@ X0 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f79,f73,f66]) ).
thf(f66,plain,
kpairp = $true,
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f73,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( kpair
= ( ^ [X0: $i,X1: $i] : ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( kpair
= ( ^ [X2: $i,X3: $i] : ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.FtBKtpcojT/DTF2THF_20179.p',kpair) ).
thf(f79,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( iskpair @ ( kpair @ X1 @ X0 ) ) )
| ( kpairp != $true ) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
thf(f56,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( iskpair @ ( kpair @ X1 @ X0 ) ) )
| ( kpairp != $true ) )
& ( ( kpairp = $true )
| ( $true
!= ( iskpair @ ( kpair @ sK8 @ sK7 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f54,f55]) ).
thf(f55,plain,
( ? [X2: $i,X3: $i] :
( ( iskpair @ ( kpair @ X3 @ X2 ) )
!= $true )
=> ( $true
!= ( iskpair @ ( kpair @ sK8 @ sK7 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f54,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( iskpair @ ( kpair @ X1 @ X0 ) ) )
| ( kpairp != $true ) )
& ( ( kpairp = $true )
| ? [X2: $i,X3: $i] :
( ( iskpair @ ( kpair @ X3 @ X2 ) )
!= $true ) ) ),
inference(rectify,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( iskpair @ ( kpair @ X1 @ X0 ) ) )
| ( kpairp != $true ) )
& ( ( kpairp = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( iskpair @ ( kpair @ X1 @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X0: $i,X1: $i] :
( $true
= ( iskpair @ ( kpair @ X1 @ X0 ) ) )
<=> ( kpairp = $true ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $i,X1: $i] :
( ( iskpair @ ( kpair @ X1 @ X0 ) )
= kpairp ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X3: $i,X2: $i] :
( ( iskpair @ ( kpair @ X2 @ X3 ) )
= kpairp ),
file('/export/starexec/sandbox2/tmp/tmp.FtBKtpcojT/DTF2THF_20179.p',kpairp) ).
thf(f103,plain,
! [X1: $i] :
( ( ( iskpair @ X1 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X1 ) ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f89]) ).
thf(f89,plain,
! [X1: $i] :
( ( $true != $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X1 ) ) )
= $true )
| ( ( iskpair @ X1 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f70,f63]) ).
thf(f63,plain,
kfstsingleton = $true,
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f70,plain,
! [X1: $i] :
( ( ( iskpair @ X1 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X1 ) ) )
= $true )
| ( kfstsingleton != $true ) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( kfstsingleton = $true )
| ( ( $true
= ( iskpair @ sK5 ) )
& ( $true
!= ( singleton
@ ( dsetconstr @ ( setunion @ sK5 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK5 ) ) ) ) ) )
& ( ! [X1: $i] :
( ( ( iskpair @ X1 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X1 ) ) )
= $true ) )
| ( kfstsingleton != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f46,f47]) ).
thf(f47,plain,
( ? [X0: $i] :
( ( ( iskpair @ X0 )
= $true )
& ( $true
!= ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X0 ) ) ) ) )
=> ( ( $true
= ( iskpair @ sK5 ) )
& ( $true
!= ( singleton
@ ( dsetconstr @ ( setunion @ sK5 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ sK5 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f46,plain,
( ( ( kfstsingleton = $true )
| ? [X0: $i] :
( ( ( iskpair @ X0 )
= $true )
& ( $true
!= ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X0 ) ) ) ) ) )
& ( ! [X1: $i] :
( ( ( iskpair @ X1 )
!= $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ X1 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X1 ) ) )
= $true ) )
| ( kfstsingleton != $true ) ) ),
inference(rectify,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ( kfstsingleton = $true )
| ? [X0: $i] :
( ( ( iskpair @ X0 )
= $true )
& ( $true
!= ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X0 ) ) ) ) ) )
& ( ! [X0: $i] :
( ( ( iskpair @ X0 )
!= $true )
| ( $true
= ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X0 ) ) ) ) )
| ( kfstsingleton != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
( ( kfstsingleton = $true )
<=> ! [X0: $i] :
( ( ( iskpair @ X0 )
!= $true )
| ( $true
= ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X0 ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( kfstsingleton = $true )
<=> ! [X0: $i] :
( ( ( iskpair @ X0 )
= $true )
=> ( $true
= ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ X0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: $i] :
( ( ( iskpair @ X0 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [X1: $i] : ( in @ ( setadjoin @ X1 @ emptyset ) @ X0 ) ) ) )
= kfstsingleton ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
! [X5: $i] :
( ( ( iskpair @ X5 )
=> ( singleton
@ ( dsetconstr @ ( setunion @ X5 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X5 ) ) ) )
= kfstsingleton ),
file('/export/starexec/sandbox2/tmp/tmp.FtBKtpcojT/DTF2THF_20179.p',kfstsingleton) ).
thf(f100,plain,
! [X1: $i] :
( ( ( singleton @ X1 )
!= $true )
| ( $true
= ( in @ ( setunion @ X1 ) @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f92]) ).
thf(f92,plain,
! [X1: $i] :
( ( $true != $true )
| ( $true
= ( in @ ( setunion @ X1 ) @ X1 ) )
| ( ( singleton @ X1 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f75,f62]) ).
thf(f62,plain,
theprop = $true,
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f75,plain,
! [X1: $i] :
( ( ( singleton @ X1 )
!= $true )
| ( $true
= ( in @ ( setunion @ X1 ) @ X1 ) )
| ( theprop != $true ) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ( theprop = $true )
| ( ( $true
= ( singleton @ sK6 ) )
& ( ( in @ ( setunion @ sK6 ) @ sK6 )
!= $true ) ) )
& ( ! [X1: $i] :
( ( ( singleton @ X1 )
!= $true )
| ( $true
= ( in @ ( setunion @ X1 ) @ X1 ) ) )
| ( theprop != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f50,f51]) ).
thf(f51,plain,
( ? [X0: $i] :
( ( ( singleton @ X0 )
= $true )
& ( ( in @ ( setunion @ X0 ) @ X0 )
!= $true ) )
=> ( ( $true
= ( singleton @ sK6 ) )
& ( ( in @ ( setunion @ sK6 ) @ sK6 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f50,plain,
( ( ( theprop = $true )
| ? [X0: $i] :
( ( ( singleton @ X0 )
= $true )
& ( ( in @ ( setunion @ X0 ) @ X0 )
!= $true ) ) )
& ( ! [X1: $i] :
( ( ( singleton @ X1 )
!= $true )
| ( $true
= ( in @ ( setunion @ X1 ) @ X1 ) ) )
| ( theprop != $true ) ) ),
inference(rectify,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ( theprop = $true )
| ? [X0: $i] :
( ( ( singleton @ X0 )
= $true )
& ( ( in @ ( setunion @ X0 ) @ X0 )
!= $true ) ) )
& ( ! [X0: $i] :
( ( ( singleton @ X0 )
!= $true )
| ( ( in @ ( setunion @ X0 ) @ X0 )
= $true ) )
| ( theprop != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
( ( theprop = $true )
<=> ! [X0: $i] :
( ( ( singleton @ X0 )
!= $true )
| ( ( in @ ( setunion @ X0 ) @ X0 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( ! [X0: $i] :
( ( ( singleton @ X0 )
= $true )
=> ( ( in @ ( setunion @ X0 ) @ X0 )
= $true ) )
<=> ( theprop = $true ) ),
inference(fool_elimination,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: $i] :
( ( ( singleton @ X0 )
=> ( in @ ( setunion @ X0 ) @ X0 ) )
= theprop ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
! [X6: $i] :
( ( ( singleton @ X6 )
=> ( in @ ( setunion @ X6 ) @ X6 ) )
= theprop ),
file('/export/starexec/sandbox2/tmp/tmp.FtBKtpcojT/DTF2THF_20179.p',theprop) ).
thf(f105,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( dsetconstr @ X0 @ X2 ) )
!= $true )
| ( ( X2 @ X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f104]) ).
thf(f104,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( X2 @ X1 )
= $true )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f84]) ).
thf(f84,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( ( X2 @ X1 )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f69,f65]) ).
thf(f65,plain,
dsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f69,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( X2 @ X1 )
= $true )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( dsetconstrER != $true ) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X1 )
= $true )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ( ( $true
!= ( sK4 @ sK3 ) )
& ( ( in @ sK3
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( sK4 @ Y0 ) ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f42,f43]) ).
thf(f43,plain,
( ? [X3: $i,X4: $i,X5: $i > $o] :
( ( $true
!= ( X5 @ X4 ) )
& ( ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
= $true ) )
=> ( ( $true
!= ( sK4 @ sK3 ) )
& ( ( in @ sK3
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( sK4 @ Y0 ) ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f42,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X1 )
= $true )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X3: $i,X4: $i,X5: $i > $o] :
( ( $true
!= ( X5 @ X4 ) )
& ( ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X1 )
= $true )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X1 )
!= $true )
& ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X1 )
= $true )
| ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) )
<=> ( dsetconstrER = $true ) ),
inference(ennf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( dsetconstrER = $true )
<=> ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
=> ( ( X2 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f23]) ).
thf(f23,plain,
( dsetconstrER
= ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) ) )
=> ( X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( dsetconstrER
= ( ! [X0: $i,X2: $i,X1: $i > $o] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.FtBKtpcojT/DTF2THF_20179.p',dsetconstrER) ).
thf(f140,plain,
( $false
= ( in @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ),
inference(forward_demodulation,[status(thm)],[f139,f135]) ).
thf(f135,plain,
( ( sK15 @ sK0 @ sK1 )
= sK1 ),
inference(trivial_inequality_removal,[status(thm)],[f134]) ).
thf(f134,plain,
( ( $true != $true )
| ( ( sK15 @ sK0 @ sK1 )
= sK1 ) ),
inference(superposition,[status(thm)],[f99,f133]) ).
thf(f133,plain,
( $true
= ( in @ ( setadjoin @ ( sK15 @ sK0 @ sK1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f132]) ).
thf(f132,plain,
( ( $true
= ( in @ ( setadjoin @ ( sK15 @ sK0 @ sK1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
| ( sK1 != sK1 ) ),
inference(duplicate_literal_removal,[status(thm)],[f131]) ).
thf(f131,plain,
( ( $true
= ( in @ ( setadjoin @ ( sK15 @ sK0 @ sK1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
| ( $true
= ( in @ ( setadjoin @ ( sK15 @ sK0 @ sK1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
| ( sK1 != sK1 ) ),
inference(equality_resolution,[status(thm)],[f129]) ).
thf(f129,plain,
! [X0: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
| ( sK1 != X0 )
| ( $true
= ( in @ ( setadjoin @ ( sK15 @ X1 @ X0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( in @ ( setadjoin @ ( sK15 @ X1 @ X0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f128]) ).
thf(f128,plain,
! [X0: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
| ( ( in @ ( setadjoin @ ( sK15 @ X1 @ X0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) )
!= ( in @ ( setadjoin @ ( sK15 @ X1 @ X0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
| ( sK1 != X0 ) ),
inference(beta_eta_normalization,[status(thm)],[f127]) ).
thf(f127,plain,
! [X0: $i,X1: $i] :
( ( sK1 != X0 )
| ( ( ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
@ ( sK15 @ X1 @ X0 ) )
!= ( ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) )
@ ( sK15 @ X1 @ X0 ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(negative_extensionality,[status(thm)],[f122]) ).
thf(f122,plain,
! [X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
!= ( ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
| ( sK1 != X0 ) ),
inference(constrained_superposition,[status(thm)],[f98,f114]) ).
thf(f98,plain,
( sK1
!= ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) )
@ ^ [Y0: $i] : ( in @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f83]) ).
thf(f83,plain,
( ( ^ [Y0: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ Y0 ) ) )
@ ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ sK1
@ sK0 ) )
!= sK1 ),
inference(definition_unfolding,[status(thm)],[f64,f74,f73]) ).
thf(f74,plain,
( kfst
= ( ^ [Y0: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
( kfst
= ( ^ [Y0: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y1: $i] : ( in @ ( setadjoin @ Y1 @ emptyset ) @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f31]) ).
thf(f31,plain,
( kfst
= ( ^ [X0: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ X0 )
@ ^ [X1: $i] : ( in @ ( setadjoin @ X1 @ emptyset ) @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
( kfst
= ( ^ [X5: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ X5 )
@ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.FtBKtpcojT/DTF2THF_20179.p',kfst) ).
thf(f64,plain,
( sK1
!= ( kfst @ ( kpair @ sK1 @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f139,plain,
( $false
= ( in @ ( setadjoin @ ( sK15 @ sK0 @ sK1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f138]) ).
thf(f138,plain,
( ( sK1 != sK1 )
| ( $false
= ( in @ ( setadjoin @ ( sK15 @ sK0 @ sK1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f137]) ).
thf(f137,plain,
( ( $false
= ( in @ ( setadjoin @ ( sK15 @ sK0 @ sK1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
| ( sK1 != sK1 )
| ( $false
= ( in @ ( setadjoin @ ( sK15 @ sK0 @ sK1 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(equality_resolution,[status(thm)],[f130]) ).
thf(f130,plain,
! [X0: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
| ( sK1 != X0 )
| ( ( in @ ( setadjoin @ ( sK15 @ X1 @ X0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( $false
= ( in @ ( setadjoin @ ( sK15 @ X1 @ X0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU645^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n016.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 12:30:21 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEU645^2 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : Ordered Pairs - Properties of Pairs
% 0.30/0.46 % Version : Especial > Reduced > Especial.
% 0.30/0.46 % English : (! x:i.! y:i.kfst (kpair x y) = x)
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.46 % Source : [Bro08]
% 0.30/0.46 % Names : ZFC147l [Bro08]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.40 v8.2.0, 0.46 v8.1.0, 0.55 v7.5.0, 0.43 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 0.80 v5.1.0, 0.60 v4.1.0, 0.67 v4.0.0, 1.00 v3.7.0
% 0.30/0.46 % Syntax : Number of formulae : 24 ( 9 unt; 14 typ; 9 def)
% 0.30/0.46 % Number of atoms : 37 ( 13 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 6 ( 3 avg)
% 0.30/0.46 % Number of connectives : 89 ( 0 ~; 0 |; 3 &; 77 @)
% 0.30/0.46 % ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 8 ( 2 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 15 ( 14 usr; 6 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 23 ( 8 ^; 12 !; 3 ?; 23 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : http://mathgate.info/detsetitem.php?id=202
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(in_type,type,
% 0.30/0.46 in: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyset_type,type,
% 0.30/0.46 emptyset: $i ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoin_type,type,
% 0.30/0.46 setadjoin: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(setunion_type,type,
% 0.30/0.46 setunion: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstr_type,type,
% 0.30/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrER_type,type,
% 0.30/0.46 dsetconstrER: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrER,definition,
% 0.30/0.46 ( dsetconstrER
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(iskpair_type,type,
% 0.30/0.46 iskpair: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(iskpair,definition,
% 0.30/0.46 ( iskpair
% 0.30/0.46 = ( ^ [A: $i] :
% 0.30/0.46 ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.46 & ? [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ ( setunion @ A ) )
% 0.30/0.46 & ( A
% 0.30/0.46 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(kpair_type,type,
% 0.30/0.46 kpair: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(kpair,definition,
% 0.30/0.46 ( kpair
% 0.30/0.46 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(kpairp_type,type,
% 0.30/0.46 kpairp: $o ).
% 0.30/0.46
% 0.30/0.46 thf(kpairp,definition,
% 0.30/0.46 ( kpairp
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(singleton_type,type,
% 0.30/0.46 singleton: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(singleton,definition,
% 0.30/0.46 ( singleton
% 0.30/0.46 = ( ^ [A: $i] :
% 0.30/0.46 ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( A
% 0.30/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjL1_type,type,
% 0.30/0.46 setukpairinjL1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setukpairinjL1,definition,
% 0.30/0.46 ( setukpairinjL1
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/0.46 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.30/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(kfstsingleton_type,type,
% 0.30/0.46 kfstsingleton: $o ).
% 0.30/0.46
% 0.30/0.46 thf(kfstsingleton,definition,
% 0.30/0.46 ( kfstsingleton
% 0.30/0.46 = ( ! [Xu: $i] :
% 0.30/0.46 ( ( iskpair @ Xu )
% 0.30/0.46 => ( singleton
% 0.30/0.46 @ ( dsetconstr @ ( setunion @ Xu )
% 0.30/0.46 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(theprop_type,type,
% 0.30/0.46 theprop: $o ).
% 0.30/0.46
% 0.30/0.46 thf(theprop,definition,
% 0.30/0.46 ( theprop
% 0.30/0.46 = ( ! [X: $i] :
% 0.30/0.46 ( ( singleton @ X )
% 0.30/0.46 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(kfst_type,type,
% 0.30/0.46 kfst: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(kfst,definition,
% 0.30/0.46 ( kfst
% 0.30/0.46 = ( ^ [Xu: $i] :
% 0.30/0.46 ( setunion
% 0.30/0.46 @ ( dsetconstr @ ( setunion @ Xu )
% 0.30/0.46 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(kfstpairEq,conjecture,
% 0.30/0.46 ( dsetconstrER
% 0.30/0.46 => ( kpairp
% 0.30/0.46 => ( setukpairinjL1
% 0.30/0.46 => ( kfstsingleton
% 0.30/0.46 => ( theprop
% 0.30/0.46 => ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.30/0.46 = Xx ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.45/1.29 ---- Embedded in THF ---
% 1.45/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.29 %%% Generated on Tue Feb 24 12:30:22 EST 2026
% 1.45/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.29 %%% Logic specification used:
% 1.45/1.29 %%% thf(spec, logic, $$dhol).
% 1.45/1.29
% 1.45/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.FtBKtpcojT/DTF2DTF20179.p
% See solution above
% 1.45/1.29 ------------------------
% 1.66/1.30 ---- Cleaned THF ---
% 1.66/1.30 thf(in_type,type,
% 1.66/1.30 in: $i > $i > $o ).
% 1.66/1.30
% 1.66/1.30 thf(emptyset_type,type,
% 1.66/1.30 emptyset: $i ).
% 1.66/1.30
% 1.66/1.30 thf(setadjoin_type,type,
% 1.66/1.30 setadjoin: $i > $i > $i ).
% 1.66/1.30
% 1.66/1.30 thf(setunion_type,type,
% 1.66/1.30 setunion: $i > $i ).
% 1.66/1.30
% 1.66/1.30 thf(dsetconstr_type,type,
% 1.66/1.30 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.66/1.30
% 1.66/1.30 thf(dsetconstrER_type,type,
% 1.66/1.30 dsetconstrER: $o ).
% 1.66/1.30
% 1.66/1.30 thf(dsetconstrER,definition,
% 1.66/1.30 ( dsetconstrER
% 1.66/1.30 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.66/1.30 ( ( in @ Xx
% 1.66/1.30 @ ( dsetconstr @ A
% 1.66/1.30 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.66/1.30 => ( Xphi @ Xx ) ) ) ) ).
% 1.66/1.30
% 1.66/1.30 thf(iskpair_type,type,
% 1.66/1.30 iskpair: $i > $o ).
% 1.66/1.30
% 1.66/1.30 thf(iskpair,definition,
% 1.66/1.30 ( iskpair
% 1.66/1.30 = ( ^ [A: $i] :
% 1.66/1.30 ? [Xx: $i] :
% 1.66/1.30 ( ( in @ Xx @ ( setunion @ A ) )
% 1.66/1.30 & ? [Xy: $i] :
% 1.66/1.30 ( ( in @ Xy @ ( setunion @ A ) )
% 1.66/1.30 & ( A
% 1.66/1.30 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 1.66/1.30
% 1.66/1.30 thf(kpair_type,type,
% 1.66/1.30 kpair: $i > $i > $i ).
% 1.66/1.30
% 1.66/1.30 thf(kpair,definition,
% 1.66/1.30 ( kpair
% 1.66/1.30 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 1.66/1.30
% 1.66/1.30 thf(kpairp_type,type,
% 1.66/1.30 kpairp: $o ).
% 1.66/1.30
% 1.66/1.30 thf(kpairp,definition,
% 1.66/1.30 ( kpairp
% 1.66/1.30 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 1.66/1.30
% 1.66/1.30 thf(singleton_type,type,
% 1.66/1.30 singleton: $i > $o ).
% 1.66/1.30
% 1.66/1.30 thf(singleton,definition,
% 1.66/1.30 ( singleton
% 1.66/1.30 = ( ^ [A: $i] :
% 1.66/1.30 ? [Xx: $i] :
% 1.66/1.30 ( ( in @ Xx @ A )
% 1.66/1.30 & ( A
% 1.66/1.30 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.66/1.30
% 1.66/1.30 thf(setukpairinjL1_type,type,
% 1.66/1.30 setukpairinjL1: $o ).
% 1.66/1.30
% 1.66/1.30 thf(setukpairinjL1,definition,
% 1.66/1.30 ( setukpairinjL1
% 1.66/1.30 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.66/1.30 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 1.66/1.30 => ( Xx = Xz ) ) ) ) ).
% 1.66/1.30
% 1.66/1.30 thf(kfstsingleton_type,type,
% 1.66/1.30 kfstsingleton: $o ).
% 1.66/1.30
% 1.66/1.30 thf(kfstsingleton,definition,
% 1.66/1.30 ( kfstsingleton
% 1.66/1.30 = ( ! [Xu: $i] :
% 1.66/1.30 ( ( iskpair @ Xu )
% 1.66/1.30 => ( singleton
% 1.66/1.30 @ ( dsetconstr @ ( setunion @ Xu )
% 1.66/1.30 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 1.66/1.30
% 1.66/1.30 thf(theprop_type,type,
% 1.66/1.30 theprop: $o ).
% 1.66/1.30
% 1.66/1.30 thf(theprop,definition,
% 1.66/1.30 ( theprop
% 1.66/1.30 = ( ! [X: $i] :
% 1.66/1.30 ( ( singleton @ X )
% 1.66/1.30 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 1.66/1.30
% 1.66/1.30 thf(kfst_type,type,
% 1.66/1.30 kfst: $i > $i ).
% 1.66/1.30
% 1.66/1.30 thf(kfst,definition,
% 1.66/1.30 ( kfst
% 1.66/1.30 = ( ^ [Xu: $i] :
% 1.66/1.30 ( setunion
% 1.66/1.30 @ ( dsetconstr @ ( setunion @ Xu )
% 1.66/1.30 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ).
% 1.66/1.30
% 1.66/1.30 thf(kfstpairEq,conjecture,
% 1.66/1.30 ( dsetconstrER
% 1.66/1.30 => ( kpairp
% 1.66/1.30 => ( setukpairinjL1
% 1.66/1.30 => ( kfstsingleton
% 1.66/1.30 => ( theprop
% 1.66/1.30 => ! [Xx: $i,Xy: $i] :
% 1.66/1.30 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 1.66/1.30 = Xx ) ) ) ) ) ) ).
% 1.66/1.30 ------------------------
% 1.66/1.32 % (20350)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_20179 for (3000ds/27Mi)
% 1.66/1.32 % (20348)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20179 for (3000ds/183Mi)
% 1.66/1.32 % (20349)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_20179 for (3000ds/4Mi)
% 1.66/1.32 % (20351)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20179 for (3000ds/2Mi)
% 1.66/1.32 % (20352)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_20179 for (3000ds/2Mi)
% 1.66/1.32 % (20354)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20179 for (3000ds/18Mi)
% 1.66/1.32 % (20353)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_20179 for (3000ds/275Mi)
% 1.66/1.33 % (20350)Instruction limit reached!
% 1.66/1.33 % (20350)------------------------------
% 1.66/1.33 % (20350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (20350)Termination reason: Unknown
% 1.66/1.33 % (20350)Termination phase: Saturation
% 1.66/1.33
% 1.66/1.33 % (20350)Memory used [KB]: 5756
% 1.66/1.33 % (20350)Time elapsed: 0.010 s
% 1.66/1.33 % (20350)Instructions burned: 28 (million)
% 1.66/1.33 % (20350)------------------------------
% 1.66/1.33 % (20350)------------------------------
% 1.66/1.33 % (20351)Instruction limit reached!
% 1.66/1.33 % (20351)------------------------------
% 1.66/1.33 % (20351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (20351)Termination reason: Unknown
% 1.66/1.33 % (20351)Termination phase: shuffling
% 1.66/1.33
% 1.66/1.33 % (20351)Memory used [KB]: 1023
% 1.66/1.33 % (20351)Time elapsed: 0.003 s
% 1.66/1.33 % (20351)Instructions burned: 2 (million)
% 1.66/1.33 % (20351)------------------------------
% 1.66/1.33 % (20351)------------------------------
% 1.66/1.33 % (20352)Instruction limit reached!
% 1.66/1.33 % (20352)------------------------------
% 1.66/1.33 % (20352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (20352)Termination reason: Unknown
% 1.66/1.33 % (20352)Termination phase: shuffling
% 1.66/1.33
% 1.66/1.33 % (20352)Memory used [KB]: 1023
% 1.66/1.33 % (20352)Time elapsed: 0.003 s
% 1.66/1.33 % (20352)Instructions burned: 2 (million)
% 1.66/1.33 % (20352)------------------------------
% 1.66/1.33 % (20352)------------------------------
% 1.66/1.33 % (20349)Instruction limit reached!
% 1.66/1.33 % (20349)------------------------------
% 1.66/1.33 % (20349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (20349)Termination reason: Unknown
% 1.66/1.33 % (20349)Termination phase: Property scanning
% 1.66/1.33
% 1.66/1.33 % (20349)Memory used [KB]: 1023
% 1.66/1.33 % (20349)Time elapsed: 0.004 s
% 1.66/1.33 % (20349)Instructions burned: 4 (million)
% 1.66/1.33 % (20349)------------------------------
% 1.66/1.33 % (20349)------------------------------
% 1.66/1.33 % (20353)Refutation not found, incomplete strategy
% 1.66/1.33 % (20353)------------------------------
% 1.66/1.33 % (20353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (20353)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.33
% 1.66/1.33
% 1.66/1.33 % (20353)Memory used [KB]: 5628
% 1.66/1.33 % (20353)Time elapsed: 0.009 s
% 1.66/1.33 % (20353)Instructions burned: 10 (million)
% 1.66/1.33 % (20353)------------------------------
% 1.66/1.33 % (20353)------------------------------
% 1.66/1.34 % (20355)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20179 for (2999ds/3Mi)
% 1.66/1.34 % (20354)Instruction limit reached!
% 1.66/1.34 % (20354)------------------------------
% 1.66/1.34 % (20354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.34 % (20354)Termination reason: Unknown
% 1.66/1.34 % (20354)Termination phase: Saturation
% 1.66/1.34
% 1.66/1.34 % (20354)Memory used [KB]: 5628
% 1.66/1.34 % (20354)Time elapsed: 0.013 s
% 1.66/1.34 % (20354)Instructions burned: 18 (million)
% 1.66/1.34 % (20354)------------------------------
% 1.66/1.34 % (20354)------------------------------
% 1.66/1.34 % (20355)Instruction limit reached!
% 1.66/1.34 % (20355)------------------------------
% 1.66/1.34 % (20355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.34 % (20355)Termination reason: Unknown
% 1.66/1.34 % (20355)Termination phase: Property scanning
% 1.66/1.34
% 1.66/1.34 % (20355)Memory used [KB]: 1023
% 1.66/1.34 % (20355)Time elapsed: 0.002 s
% 1.66/1.34 % (20355)Instructions burned: 3 (million)
% 1.66/1.34 % (20355)------------------------------
% 1.66/1.34 % (20355)------------------------------
% 1.66/1.34 % (20356)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_20179 for (2999ds/37Mi)
% 1.66/1.34 % (20358)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20179 for (2999ds/3Mi)
% 1.66/1.35 % (20361)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_20179 for (2999ds/16Mi)
% 1.66/1.35 % (20358)Instruction limit reached!
% 1.66/1.35 % (20358)------------------------------
% 1.66/1.35 % (20358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (20358)Termination reason: Unknown
% 1.66/1.35 % (20358)Termination phase: Function definition elimination
% 1.66/1.35
% 1.66/1.35 % (20358)Memory used [KB]: 1023
% 1.66/1.35 % (20358)Time elapsed: 0.004 s
% 1.66/1.35 % (20358)Instructions burned: 4 (million)
% 1.66/1.35 % (20358)------------------------------
% 1.66/1.35 % (20358)------------------------------
% 1.66/1.35 % (20359)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_20179 for (2999ds/1041Mi)
% 1.66/1.35 % (20361)Instruction limit reached!
% 1.66/1.35 % (20361)------------------------------
% 1.66/1.35 % (20361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (20361)Termination reason: Unknown
% 1.66/1.35 % (20361)Termination phase: Saturation
% 1.66/1.35
% 1.66/1.35 % (20361)Memory used [KB]: 5884
% 1.66/1.35 % (20361)Time elapsed: 0.007 s
% 1.66/1.35 % (20361)Instructions burned: 18 (million)
% 1.66/1.35 % (20361)------------------------------
% 1.66/1.35 % (20361)------------------------------
% 1.66/1.35 % (20357)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_20179 for (2999ds/15Mi)
% 1.66/1.35 % (20360)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_20179 for (2999ds/7Mi)
% 1.66/1.36 % (20360)Instruction limit reached!
% 1.66/1.36 % (20360)------------------------------
% 1.66/1.36 % (20360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.36 % (20360)Termination reason: Unknown
% 1.66/1.36 % (20360)Termination phase: Saturation
% 1.66/1.36
% 1.66/1.36 % (20360)Memory used [KB]: 1023
% 1.66/1.36 % (20360)Time elapsed: 0.006 s
% 1.66/1.36 % (20360)Instructions burned: 8 (million)
% 1.66/1.36 % (20360)------------------------------
% 1.66/1.36 % (20360)------------------------------
% 1.66/1.36 % (20363)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_20179 for (2999ds/3Mi)
% 1.66/1.36 % (20363)Instruction limit reached!
% 1.66/1.36 % (20363)------------------------------
% 1.66/1.36 % (20363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.36 % (20363)Termination reason: Unknown
% 1.66/1.36 % (20363)Termination phase: Property scanning
% 1.66/1.36
% 1.66/1.36 % (20363)Memory used [KB]: 1023
% 1.66/1.36 % (20363)Time elapsed: 0.002 s
% 1.66/1.36 % (20363)Instructions burned: 4 (million)
% 1.66/1.36 % (20363)------------------------------
% 1.66/1.36 % (20363)------------------------------
% 1.66/1.36 % (20362)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_20179 for (2999ds/3Mi)
% 1.66/1.36 % (20356)Instruction limit reached!
% 1.66/1.36 % (20356)------------------------------
% 1.66/1.36 % (20356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.36 % (20356)Termination reason: Unknown
% 1.66/1.36 % (20356)Termination phase: Saturation
% 1.66/1.36
% 1.66/1.36 % (20356)Memory used [KB]: 5756
% 1.66/1.36 % (20356)Time elapsed: 0.023 s
% 1.66/1.36 % (20356)Instructions burned: 38 (million)
% 1.66/1.36 % (20356)------------------------------
% 1.66/1.36 % (20356)------------------------------
% 1.66/1.37 % (20362)Instruction limit reached!
% 1.66/1.37 % (20362)------------------------------
% 1.66/1.37 % (20362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.37 % (20362)Termination reason: Unknown
% 1.66/1.37 % (20362)Termination phase: Property scanning
% 1.66/1.37
% 1.66/1.37 % (20362)Memory used [KB]: 1023
% 1.66/1.37 % (20362)Time elapsed: 0.004 s
% 1.66/1.37 % (20362)Instructions burned: 4 (million)
% 1.66/1.37 % (20362)------------------------------
% 1.66/1.37 % (20362)------------------------------
% 1.66/1.37 % (20357)Instruction limit reached!
% 1.66/1.37 % (20357)------------------------------
% 1.66/1.37 % (20357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.37 % (20357)Termination reason: Unknown
% 1.66/1.37 % (20357)Termination phase: Saturation
% 1.66/1.37
% 1.66/1.37 % (20357)Memory used [KB]: 5628
% 1.66/1.37 % (20357)Time elapsed: 0.017 s
% 1.66/1.37 % (20357)Instructions burned: 15 (million)
% 1.66/1.37 % (20357)------------------------------
% 1.66/1.37 % (20357)------------------------------
% 1.66/1.37 % (20365)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_20179 for (2999ds/3Mi)
% 1.66/1.37 % (20365)Instruction limit reached!
% 1.66/1.37 % (20365)------------------------------
% 1.66/1.37 % (20365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.37 % (20365)Termination reason: Unknown
% 1.66/1.37 % (20365)Termination phase: Function definition elimination
% 1.66/1.37
% 1.66/1.37 % (20365)Memory used [KB]: 1023
% 1.66/1.37 % (20365)Time elapsed: 0.002 s
% 1.66/1.37 % (20365)Instructions burned: 4 (million)
% 1.66/1.37 % (20365)------------------------------
% 1.66/1.37 % (20365)------------------------------
% 1.66/1.37 % (20348)Instruction limit reached!
% 1.66/1.37 % (20348)------------------------------
% 1.66/1.37 % (20348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.37 % (20348)Termination reason: Unknown
% 1.66/1.37 % (20348)Termination phase: Saturation
% 1.66/1.37
% 1.66/1.37 % (20348)Memory used [KB]: 6268
% 1.66/1.37 % (20348)Time elapsed: 0.057 s
% 1.66/1.37 % (20348)Instructions burned: 184 (million)
% 1.66/1.37 % (20348)------------------------------
% 1.66/1.37 % (20348)------------------------------
% 1.66/1.37 % (20364)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_20179 for (2999ds/7Mi)
% 1.66/1.38 % (20368)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_20179 for (2999ds/710Mi)
% 1.66/1.38 % (20364)Instruction limit reached!
% 1.66/1.38 % (20364)------------------------------
% 1.66/1.38 % (20364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.38 % (20364)Termination reason: Unknown
% 1.66/1.38 % (20364)Termination phase: Saturation
% 1.66/1.38
% 1.66/1.38 % (20364)Memory used [KB]: 5500
% 1.66/1.38 % (20364)Time elapsed: 0.006 s
% 1.66/1.38 % (20364)Instructions burned: 7 (million)
% 1.66/1.38 % (20364)------------------------------
% 1.66/1.38 % (20364)------------------------------
% 1.66/1.38 % (20369)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_20179 for (2999ds/6Mi)
% 1.66/1.38 % (20366)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_20179 for (2999ds/4Mi)
% 1.66/1.38 % (20367)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_20179 for (2999ds/18Mi)
% 1.66/1.38 % (20369)Instruction limit reached!
% 1.66/1.38 % (20369)------------------------------
% 1.66/1.38 % (20369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.38 % (20369)Termination reason: Unknown
% 1.66/1.38 % (20369)Termination phase: Saturation
% 1.66/1.38
% 1.66/1.38 % (20369)Memory used [KB]: 5500
% 1.66/1.38 % (20369)Time elapsed: 0.003 s
% 1.66/1.38 % (20369)Instructions burned: 7 (million)
% 1.66/1.38 % (20369)------------------------------
% 1.66/1.38 % (20369)------------------------------
% 1.66/1.38 % (20366)Instruction limit reached!
% 1.66/1.38 % (20366)------------------------------
% 1.66/1.38 % (20366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.38 % (20366)Termination reason: Unknown
% 1.66/1.38 % (20366)Termination phase: Function definition elimination
% 1.66/1.38
% 1.66/1.38 % (20366)Memory used [KB]: 1023
% 1.66/1.38 % (20366)Time elapsed: 0.004 s
% 1.66/1.38 % (20366)Instructions burned: 4 (million)
% 1.66/1.38 % (20366)------------------------------
% 1.66/1.38 % (20366)------------------------------
% 1.66/1.38 % (20370)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_20179 for (2999ds/902Mi)
% 1.66/1.39 % (20370)Refutation not found, incomplete strategy
% 1.66/1.39 % (20370)------------------------------
% 1.66/1.39 % (20370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.39 % (20370)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.39
% 1.66/1.39
% 1.66/1.39 % (20370)Memory used [KB]: 5500
% 1.66/1.39 % (20370)Time elapsed: 0.004 s
% 1.66/1.39 % (20370)Instructions burned: 4 (million)
% 1.66/1.39 % (20370)------------------------------
% 1.66/1.39 % (20370)------------------------------
% 1.66/1.39 % (20368)First to succeed.
% 1.66/1.39 % (20372)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_20179 for (2999ds/5Mi)
% 1.66/1.39 % (20368)Refutation found. Thanks to Tanya!
% 1.66/1.39 % SZS status Theorem for DTF2THF_20179
% 1.66/1.39 % SZS output start Proof for DTF2THF_20179
% 1.66/1.39 thf(func_def_0, type, in: $i > $i > $o).
% 1.66/1.39 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.66/1.39 thf(func_def_3, type, setunion: $i > $i).
% 1.66/1.39 thf(func_def_4, type, dsetconstr: $i > ($i > $o) > $i).
% 1.66/1.39 thf(func_def_7, type, iskpair: $i > $o).
% 1.66/1.39 thf(func_def_8, type, kpair: $i > $i > $i).
% 1.66/1.39 thf(func_def_10, type, singleton: $i > $o).
% 1.66/1.39 thf(func_def_14, type, kfst: $i > $i).
% 1.66/1.39 thf(func_def_28, type, sK4: $i > $o).
% 1.66/1.39 thf(func_def_38, type, ph13: !>[X0: $tType]:(X0)).
% 1.66/1.39 thf(func_def_39, type, sK14: $i > $i > $i > $i > $i).
% 1.66/1.39 thf(func_def_40, type, sK15: $i > $i > $i).
% 1.66/1.39 thf(f146,plain,(
% 1.66/1.39 $false),
% 1.66/1.39 inference(trivial_inequality_removal,[status(thm)],[f143])).
% 1.66/1.39 thf(f143,plain,(
% 1.66/1.39 ($true = $false)),
% 1.66/1.39 inference(superposition,[status(thm)],[f140,f115])).
% 1.66/1.39 thf(f115,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))) )),
% 1.66/1.39 inference(backward_demodulation,[status(thm)],[f112,f114])).
% 1.66/1.39 thf(f114,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : (((setunion @ (dsetconstr @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) @ (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))))) = X0)) )),
% 1.66/1.39 inference(trivial_inequality_removal,[status(thm)],[f113])).
% 1.66/1.39 thf(f113,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((setunion @ (dsetconstr @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) @ (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))))) = X0)) )),
% 1.66/1.39 inference(superposition,[status(thm)],[f99,f112])).
% 1.66/1.39 thf(f99,plain,(
% 1.66/1.39 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) | (X0 = X2)) )),
% 1.66/1.39 inference(trivial_inequality_removal,[status(thm)],[f95])).
% 1.66/1.39 thf(f95,plain,(
% 1.66/1.39 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((X0 = X2) | ($true != $true) | ($true != (in @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))) )),
% 1.66/1.39 inference(definition_unfolding,[status(thm)],[f82,f61])).
% 1.66/1.39 thf(f61,plain,(
% 1.66/1.39 (setukpairinjL1 = $true)),
% 1.66/1.39 inference(cnf_transformation,[status(thm)],[f40])).
% 1.66/1.39 thf(f40,plain,(
% 1.66/1.39 (kpairp = $true) & (dsetconstrER = $true) & (sK1 != (kfst @ (kpair @ sK1 @ sK0))) & (kfstsingleton = $true) & (theprop = $true) & (setukpairinjL1 = $true)),
% 1.66/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f38,f39])).
% 1.66/1.39 thf(f39,plain,(
% 1.66/1.39 ? [X0 : $i,X1 : $i] : ((kfst @ (kpair @ X1 @ X0)) != X1) => (sK1 != (kfst @ (kpair @ sK1 @ sK0)))),
% 1.66/1.39 introduced(definition,[],[choice_axiom])).
% 1.66/1.39 thf(f38,plain,(
% 1.66/1.39 (kpairp = $true) & (dsetconstrER = $true) & ? [X0 : $i,X1 : $i] : ((kfst @ (kpair @ X1 @ X0)) != X1) & (kfstsingleton = $true) & (theprop = $true) & (setukpairinjL1 = $true)),
% 1.66/1.39 inference(flattening,[status(thm)],[f37])).
% 1.66/1.39 thf(f37,plain,(
% 1.66/1.39 ((((? [X0 : $i,X1 : $i] : ((kfst @ (kpair @ X1 @ X0)) != X1) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (kpairp = $true)) & (dsetconstrER = $true)),
% 1.66/1.39 inference(ennf_transformation,[status(thm)],[f26])).
% 1.66/1.39 thf(f26,plain,(
% 1.66/1.39 ~((dsetconstrER = $true) => ((kpairp = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ! [X0 : $i,X1 : $i] : ((kfst @ (kpair @ X1 @ X0)) = X1))))))),
% 1.66/1.39 inference(fool_elimination,[status(thm)],[f25])).
% 1.66/1.39 thf(f25,plain,(
% 1.66/1.39 ~(dsetconstrER => (kpairp => (setukpairinjL1 => (kfstsingleton => (theprop => ! [X0 : $i,X1 : $i] : ((kfst @ (kpair @ X1 @ X0)) = X1))))))),
% 1.66/1.39 inference(rectify,[status(thm)],[f11])).
% 1.66/1.39 thf(f11,negated_conjecture,(
% 1.66/1.39 ~(dsetconstrER => (kpairp => (setukpairinjL1 => (kfstsingleton => (theprop => ! [X3 : $i,X2 : $i] : ((kfst @ (kpair @ X2 @ X3)) = X2))))))),
% 1.66/1.39 inference(negated_conjecture,[status(cth)],[f10])).
% 1.66/1.39 thf(f10,conjecture,(
% 1.66/1.39 dsetconstrER => (kpairp => (setukpairinjL1 => (kfstsingleton => (theprop => ! [X3 : $i,X2 : $i] : ((kfst @ (kpair @ X2 @ X3)) = X2)))))),
% 1.66/1.39 file('/export/starexec/sandbox2/tmp/tmp.FtBKtpcojT/DTF2THF_20179.p',kfstpairEq)).
% 1.66/1.39 thf(f82,plain,(
% 1.66/1.39 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((X0 = X2) | ($true != (in @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) | (setukpairinjL1 != $true)) )),
% 1.66/1.39 inference(cnf_transformation,[status(thm)],[f60])).
% 1.66/1.39 thf(f60,plain,(
% 1.66/1.39 (! [X0 : $i,X1 : $i,X2 : $i] : ((X0 = X2) | ($true != (in @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))) | (setukpairinjL1 != $true)) & ((setukpairinjL1 = $true) | ((sK9 != sK11) & ($true = (in @ (setadjoin @ sK9 @ emptyset) @ (setadjoin @ (setadjoin @ sK11 @ emptyset) @ (setadjoin @ (setadjoin @ sK11 @ (setadjoin @ sK10 @ emptyset)) @ emptyset))))))),
% 1.66/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f58,f59])).
% 1.66/1.39 thf(f59,plain,(
% 1.66/1.39 ? [X3 : $i,X4 : $i,X5 : $i] : ((X3 != X5) & ((in @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X5 @ emptyset) @ (setadjoin @ (setadjoin @ X5 @ (setadjoin @ X4 @ emptyset)) @ emptyset))) = $true)) => ((sK9 != sK11) & ($true = (in @ (setadjoin @ sK9 @ emptyset) @ (setadjoin @ (setadjoin @ sK11 @ emptyset) @ (setadjoin @ (setadjoin @ sK11 @ (setadjoin @ sK10 @ emptyset)) @ emptyset)))))),
% 1.66/1.39 introduced(definition,[],[choice_axiom])).
% 1.66/1.39 thf(f58,plain,(
% 1.66/1.39 (! [X0 : $i,X1 : $i,X2 : $i] : ((X0 = X2) | ($true != (in @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))) | (setukpairinjL1 != $true)) & ((setukpairinjL1 = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : ((X3 != X5) & ((in @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X5 @ emptyset) @ (setadjoin @ (setadjoin @ X5 @ (setadjoin @ X4 @ emptyset)) @ emptyset))) = $true)))),
% 1.66/1.39 inference(rectify,[status(thm)],[f57])).
% 1.66/1.39 thf(f57,plain,(
% 1.66/1.39 (! [X0 : $i,X1 : $i,X2 : $i] : ((X0 = X2) | ($true != (in @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))) | (setukpairinjL1 != $true)) & ((setukpairinjL1 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((X0 != X2) & ($true = (in @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))))),
% 1.66/1.39 inference(nnf_transformation,[status(thm)],[f33])).
% 1.66/1.39 thf(f33,plain,(
% 1.66/1.39 ! [X0 : $i,X1 : $i,X2 : $i] : ((X0 = X2) | ($true != (in @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))) <=> (setukpairinjL1 = $true)),
% 1.66/1.39 inference(ennf_transformation,[status(thm)],[f20])).
% 1.66/1.39 thf(f20,plain,(
% 1.66/1.39 (setukpairinjL1 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) => (X0 = X2))),
% 1.66/1.39 inference(fool_elimination,[status(thm)],[f19])).
% 1.66/1.39 thf(f19,plain,(
% 1.66/1.39 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (X0 = X2)) = setukpairinjL1)),
% 1.66/1.39 inference(rectify,[status(thm)],[f6])).
% 1.66/1.39 thf(f6,axiom,(
% 1.66/1.39 (! [X4 : $i,X3 : $i,X2 : $i] : ((in @ (setadjoin @ X4 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))) => (X2 = X4)) = setukpairinjL1)),
% 1.66/1.39 file('/export/starexec/sandbox2/tmp/tmp.FtBKtpcojT/DTF2THF_20179.p',setukpairinjL1)).
% 1.66/1.39 thf(f112,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (setadjoin @ (setunion @ (dsetconstr @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) @ (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))))) @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))) )),
% 1.66/1.39 inference(beta_eta_normalization,[status(thm)],[f111])).
% 1.66/1.39 thf(f111,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : ((((^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) @ (setunion @ (dsetconstr @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) @ (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))))) = $true)) )),
% 1.66/1.39 inference(trivial_inequality_removal,[status(thm)],[f110])).
% 1.66/1.39 thf(f110,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) @ (setunion @ (dsetconstr @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) @ (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))))) = $true)) )),
% 1.66/1.39 inference(superposition,[status(thm)],[f105,f109])).
% 1.66/1.39 thf(f109,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (setunion @ (dsetconstr @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) @ (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))))) @ (dsetconstr @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) @ (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))))))) )),
% 1.66/1.39 inference(trivial_inequality_removal,[status(thm)],[f108])).
% 1.66/1.39 thf(f108,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = (in @ (setunion @ (dsetconstr @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) @ (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))))) @ (dsetconstr @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) @ (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))))))) )),
% 1.66/1.39 inference(superposition,[status(thm)],[f100,f107])).
% 1.66/1.39 thf(f107,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : (((singleton @ (dsetconstr @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) @ (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))))) = $true)) )),
% 1.66/1.39 inference(trivial_inequality_removal,[status(thm)],[f106])).
% 1.66/1.39 thf(f106,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((singleton @ (dsetconstr @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) @ (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))))) = $true)) )),
% 1.66/1.39 inference(superposition,[status(thm)],[f103,f102])).
% 1.66/1.39 thf(f102,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : (((iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) = $true)) )),
% 1.66/1.39 inference(beta_eta_normalization,[status(thm)],[f101])).
% 1.66/1.39 thf(f101,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : (($true = (iskpair @ ((^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))) @ X1 @ X0)))) )),
% 1.66/1.39 inference(trivial_inequality_removal,[status(thm)],[f93])).
% 1.66/1.39 thf(f93,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : (($true = (iskpair @ ((^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))) @ X1 @ X0))) | ($true != $true)) )),
% 1.66/1.39 inference(definition_unfolding,[status(thm)],[f79,f73,f66])).
% 1.66/1.39 thf(f66,plain,(
% 1.66/1.39 (kpairp = $true)),
% 1.66/1.39 inference(cnf_transformation,[status(thm)],[f40])).
% 1.66/1.39 thf(f73,plain,(
% 1.66/1.39 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 1.66/1.39 inference(cnf_transformation,[status(thm)],[f14])).
% 1.66/1.39 thf(f14,plain,(
% 1.66/1.39 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 1.66/1.39 inference(fool_elimination,[status(thm)],[f13])).
% 1.66/1.39 thf(f13,plain,(
% 1.66/1.39 (kpair = (^[X0 : $i, X1 : $i] : (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))),
% 1.66/1.39 inference(rectify,[status(thm)],[f3])).
% 1.66/1.39 thf(f3,axiom,(
% 1.66/1.39 (kpair = (^[X2 : $i, X3 : $i] : (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))),
% 1.66/1.39 file('/export/starexec/sandbox2/tmp/tmp.FtBKtpcojT/DTF2THF_20179.p',kpair)).
% 1.66/1.39 thf(f79,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : (($true = (iskpair @ (kpair @ X1 @ X0))) | (kpairp != $true)) )),
% 1.66/1.39 inference(cnf_transformation,[status(thm)],[f56])).
% 1.66/1.39 thf(f56,plain,(
% 1.66/1.39 (! [X0 : $i,X1 : $i] : ($true = (iskpair @ (kpair @ X1 @ X0))) | (kpairp != $true)) & ((kpairp = $true) | ($true != (iskpair @ (kpair @ sK8 @ sK7))))),
% 1.66/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f54,f55])).
% 1.66/1.39 thf(f55,plain,(
% 1.66/1.39 ? [X2 : $i,X3 : $i] : ((iskpair @ (kpair @ X3 @ X2)) != $true) => ($true != (iskpair @ (kpair @ sK8 @ sK7)))),
% 1.66/1.39 introduced(definition,[],[choice_axiom])).
% 1.66/1.39 thf(f54,plain,(
% 1.66/1.39 (! [X0 : $i,X1 : $i] : ($true = (iskpair @ (kpair @ X1 @ X0))) | (kpairp != $true)) & ((kpairp = $true) | ? [X2 : $i,X3 : $i] : ((iskpair @ (kpair @ X3 @ X2)) != $true))),
% 1.66/1.39 inference(rectify,[status(thm)],[f53])).
% 1.66/1.39 thf(f53,plain,(
% 1.66/1.39 (! [X0 : $i,X1 : $i] : ($true = (iskpair @ (kpair @ X1 @ X0))) | (kpairp != $true)) & ((kpairp = $true) | ? [X0 : $i,X1 : $i] : ($true != (iskpair @ (kpair @ X1 @ X0))))),
% 1.66/1.39 inference(nnf_transformation,[status(thm)],[f18])).
% 1.66/1.39 thf(f18,plain,(
% 1.66/1.39 ! [X0 : $i,X1 : $i] : ($true = (iskpair @ (kpair @ X1 @ X0))) <=> (kpairp = $true)),
% 1.66/1.39 inference(fool_elimination,[status(thm)],[f17])).
% 1.66/1.39 thf(f17,plain,(
% 1.66/1.39 (! [X0 : $i,X1 : $i] : (iskpair @ (kpair @ X1 @ X0)) = kpairp)),
% 1.66/1.39 inference(rectify,[status(thm)],[f4])).
% 1.66/1.39 thf(f4,axiom,(
% 1.66/1.39 (! [X3 : $i,X2 : $i] : (iskpair @ (kpair @ X2 @ X3)) = kpairp)),
% 1.66/1.39 file('/export/starexec/sandbox2/tmp/tmp.FtBKtpcojT/DTF2THF_20179.p',kpairp)).
% 1.66/1.39 thf(f103,plain,(
% 1.66/1.39 ( ! [X1 : $i] : (((iskpair @ X1) != $true) | ((singleton @ (dsetconstr @ (setunion @ X1) @ (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ X1)))) = $true)) )),
% 1.66/1.39 inference(trivial_inequality_removal,[status(thm)],[f89])).
% 1.66/1.39 thf(f89,plain,(
% 1.66/1.39 ( ! [X1 : $i] : (($true != $true) | ((singleton @ (dsetconstr @ (setunion @ X1) @ (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ X1)))) = $true) | ((iskpair @ X1) != $true)) )),
% 1.66/1.39 inference(definition_unfolding,[status(thm)],[f70,f63])).
% 1.66/1.39 thf(f63,plain,(
% 1.66/1.39 (kfstsingleton = $true)),
% 1.66/1.39 inference(cnf_transformation,[status(thm)],[f40])).
% 1.66/1.39 thf(f70,plain,(
% 1.66/1.39 ( ! [X1 : $i] : (((iskpair @ X1) != $true) | ((singleton @ (dsetconstr @ (setunion @ X1) @ (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ X1)))) = $true) | (kfstsingleton != $true)) )),
% 1.66/1.39 inference(cnf_transformation,[status(thm)],[f48])).
% 1.66/1.39 thf(f48,plain,(
% 1.66/1.39 ((kfstsingleton = $true) | (($true = (iskpair @ sK5)) & ($true != (singleton @ (dsetconstr @ (setunion @ sK5) @ (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ sK5))))))) & (! [X1 : $i] : (((iskpair @ X1) != $true) | ((singleton @ (dsetconstr @ (setunion @ X1) @ (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ X1)))) = $true)) | (kfstsingleton != $true))),
% 1.66/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f46,f47])).
% 1.66/1.39 thf(f47,plain,(
% 1.66/1.39 ? [X0 : $i] : (((iskpair @ X0) = $true) & ($true != (singleton @ (dsetconstr @ (setunion @ X0) @ (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ X0)))))) => (($true = (iskpair @ sK5)) & ($true != (singleton @ (dsetconstr @ (setunion @ sK5) @ (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ sK5))))))),
% 1.66/1.39 introduced(definition,[],[choice_axiom])).
% 1.66/1.39 thf(f46,plain,(
% 1.66/1.39 ((kfstsingleton = $true) | ? [X0 : $i] : (((iskpair @ X0) = $true) & ($true != (singleton @ (dsetconstr @ (setunion @ X0) @ (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ X0))))))) & (! [X1 : $i] : (((iskpair @ X1) != $true) | ((singleton @ (dsetconstr @ (setunion @ X1) @ (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ X1)))) = $true)) | (kfstsingleton != $true))),
% 1.66/1.39 inference(rectify,[status(thm)],[f45])).
% 1.66/1.39 thf(f45,plain,(
% 1.66/1.39 ((kfstsingleton = $true) | ? [X0 : $i] : (((iskpair @ X0) = $true) & ($true != (singleton @ (dsetconstr @ (setunion @ X0) @ (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ X0))))))) & (! [X0 : $i] : (((iskpair @ X0) != $true) | ($true = (singleton @ (dsetconstr @ (setunion @ X0) @ (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ X0)))))) | (kfstsingleton != $true))),
% 1.66/1.39 inference(nnf_transformation,[status(thm)],[f36])).
% 1.66/1.39 thf(f36,plain,(
% 1.66/1.39 (kfstsingleton = $true) <=> ! [X0 : $i] : (((iskpair @ X0) != $true) | ($true = (singleton @ (dsetconstr @ (setunion @ X0) @ (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ X0))))))),
% 1.66/1.39 inference(ennf_transformation,[status(thm)],[f22])).
% 1.66/1.39 thf(f22,plain,(
% 1.66/1.39 (kfstsingleton = $true) <=> ! [X0 : $i] : (((iskpair @ X0) = $true) => ($true = (singleton @ (dsetconstr @ (setunion @ X0) @ (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ X0))))))),
% 1.66/1.39 inference(fool_elimination,[status(thm)],[f21])).
% 1.66/1.39 thf(f21,plain,(
% 1.66/1.39 (! [X0 : $i] : ((iskpair @ X0) => (singleton @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : (in @ (setadjoin @ X1 @ emptyset) @ X0))))) = kfstsingleton)),
% 1.66/1.39 inference(rectify,[status(thm)],[f7])).
% 1.66/1.39 thf(f7,axiom,(
% 1.66/1.39 (! [X5 : $i] : ((iskpair @ X5) => (singleton @ (dsetconstr @ (setunion @ X5) @ (^[X2 : $i] : (in @ (setadjoin @ X2 @ emptyset) @ X5))))) = kfstsingleton)),
% 1.66/1.39 file('/export/starexec/sandbox2/tmp/tmp.FtBKtpcojT/DTF2THF_20179.p',kfstsingleton)).
% 1.66/1.39 thf(f100,plain,(
% 1.66/1.39 ( ! [X1 : $i] : (((singleton @ X1) != $true) | ($true = (in @ (setunion @ X1) @ X1))) )),
% 1.66/1.39 inference(trivial_inequality_removal,[status(thm)],[f92])).
% 1.66/1.39 thf(f92,plain,(
% 1.66/1.39 ( ! [X1 : $i] : (($true != $true) | ($true = (in @ (setunion @ X1) @ X1)) | ((singleton @ X1) != $true)) )),
% 1.66/1.39 inference(definition_unfolding,[status(thm)],[f75,f62])).
% 1.66/1.39 thf(f62,plain,(
% 1.66/1.39 (theprop = $true)),
% 1.66/1.39 inference(cnf_transformation,[status(thm)],[f40])).
% 1.66/1.39 thf(f75,plain,(
% 1.66/1.39 ( ! [X1 : $i] : (((singleton @ X1) != $true) | ($true = (in @ (setunion @ X1) @ X1)) | (theprop != $true)) )),
% 1.66/1.39 inference(cnf_transformation,[status(thm)],[f52])).
% 1.66/1.39 thf(f52,plain,(
% 1.66/1.39 ((theprop = $true) | (($true = (singleton @ sK6)) & ((in @ (setunion @ sK6) @ sK6) != $true))) & (! [X1 : $i] : (((singleton @ X1) != $true) | ($true = (in @ (setunion @ X1) @ X1))) | (theprop != $true))),
% 1.66/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f50,f51])).
% 1.66/1.39 thf(f51,plain,(
% 1.66/1.39 ? [X0 : $i] : (((singleton @ X0) = $true) & ((in @ (setunion @ X0) @ X0) != $true)) => (($true = (singleton @ sK6)) & ((in @ (setunion @ sK6) @ sK6) != $true))),
% 1.66/1.39 introduced(definition,[],[choice_axiom])).
% 1.66/1.39 thf(f50,plain,(
% 1.66/1.39 ((theprop = $true) | ? [X0 : $i] : (((singleton @ X0) = $true) & ((in @ (setunion @ X0) @ X0) != $true))) & (! [X1 : $i] : (((singleton @ X1) != $true) | ($true = (in @ (setunion @ X1) @ X1))) | (theprop != $true))),
% 1.66/1.39 inference(rectify,[status(thm)],[f49])).
% 1.66/1.39 thf(f49,plain,(
% 1.66/1.39 ((theprop = $true) | ? [X0 : $i] : (((singleton @ X0) = $true) & ((in @ (setunion @ X0) @ X0) != $true))) & (! [X0 : $i] : (((singleton @ X0) != $true) | ((in @ (setunion @ X0) @ X0) = $true)) | (theprop != $true))),
% 1.66/1.39 inference(nnf_transformation,[status(thm)],[f34])).
% 1.66/1.39 thf(f34,plain,(
% 1.66/1.39 (theprop = $true) <=> ! [X0 : $i] : (((singleton @ X0) != $true) | ((in @ (setunion @ X0) @ X0) = $true))),
% 1.66/1.39 inference(ennf_transformation,[status(thm)],[f30])).
% 1.66/1.39 thf(f30,plain,(
% 1.66/1.39 ! [X0 : $i] : (((singleton @ X0) = $true) => ((in @ (setunion @ X0) @ X0) = $true)) <=> (theprop = $true)),
% 1.66/1.39 inference(fool_elimination,[status(thm)],[f29])).
% 1.66/1.39 thf(f29,plain,(
% 1.66/1.39 (! [X0 : $i] : ((singleton @ X0) => (in @ (setunion @ X0) @ X0)) = theprop)),
% 1.66/1.39 inference(rectify,[status(thm)],[f8])).
% 1.66/1.39 thf(f8,axiom,(
% 1.66/1.39 (! [X6 : $i] : ((singleton @ X6) => (in @ (setunion @ X6) @ X6)) = theprop)),
% 1.66/1.39 file('/export/starexec/sandbox2/tmp/tmp.FtBKtpcojT/DTF2THF_20179.p',theprop)).
% 1.66/1.39 thf(f105,plain,(
% 1.66/1.39 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (((in @ X1 @ (dsetconstr @ X0 @ X2)) != $true) | ((X2 @ X1) = $true)) )),
% 1.66/1.39 inference(beta_eta_normalization,[status(thm)],[f104])).
% 1.66/1.39 thf(f104,plain,(
% 1.66/1.39 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (((X2 @ X1) = $true) | ($true != (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))))) )),
% 1.66/1.39 inference(trivial_inequality_removal,[status(thm)],[f84])).
% 1.66/1.39 thf(f84,plain,(
% 1.66/1.39 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (($true != (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) | ((X2 @ X1) = $true) | ($true != $true)) )),
% 1.66/1.39 inference(definition_unfolding,[status(thm)],[f69,f65])).
% 1.66/1.39 thf(f65,plain,(
% 1.66/1.39 (dsetconstrER = $true)),
% 1.66/1.39 inference(cnf_transformation,[status(thm)],[f40])).
% 1.66/1.39 thf(f69,plain,(
% 1.66/1.39 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (((X2 @ X1) = $true) | ($true != (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) | (dsetconstrER != $true)) )),
% 1.66/1.39 inference(cnf_transformation,[status(thm)],[f44])).
% 1.66/1.39 thf(f44,plain,(
% 1.66/1.39 (! [X0 : $i,X1 : $i,X2 : $i > $o] : (((X2 @ X1) = $true) | ($true != (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))))) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | (($true != (sK4 @ sK3)) & ((in @ sK3 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (sK4 @ Y0)))) = $true)))),
% 1.66/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f42,f43])).
% 1.66/1.39 thf(f43,plain,(
% 1.66/1.39 ? [X3 : $i,X4 : $i,X5 : $i > $o] : (($true != (X5 @ X4)) & ((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))) = $true)) => (($true != (sK4 @ sK3)) & ((in @ sK3 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (sK4 @ Y0)))) = $true))),
% 1.66/1.39 introduced(definition,[],[choice_axiom])).
% 1.66/1.39 thf(f42,plain,(
% 1.66/1.39 (! [X0 : $i,X1 : $i,X2 : $i > $o] : (((X2 @ X1) = $true) | ($true != (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))))) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X3 : $i,X4 : $i,X5 : $i > $o] : (($true != (X5 @ X4)) & ((in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0)))) = $true)))),
% 1.66/1.39 inference(rectify,[status(thm)],[f41])).
% 1.66/1.39 thf(f41,plain,(
% 1.66/1.39 (! [X0 : $i,X1 : $i,X2 : $i > $o] : (((X2 @ X1) = $true) | ($true != (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))))) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X0 : $i,X1 : $i,X2 : $i > $o] : (((X2 @ X1) != $true) & ($true = (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))))))),
% 1.66/1.39 inference(nnf_transformation,[status(thm)],[f35])).
% 1.66/1.39 thf(f35,plain,(
% 1.66/1.39 ! [X0 : $i,X1 : $i,X2 : $i > $o] : (((X2 @ X1) = $true) | ($true != (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0)))))) <=> (dsetconstrER = $true)),
% 1.66/1.39 inference(ennf_transformation,[status(thm)],[f24])).
% 1.66/1.39 thf(f24,plain,(
% 1.66/1.39 (dsetconstrER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true = (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) => ((X2 @ X1) = $true))),
% 1.66/1.39 inference(fool_elimination,[status(thm)],[f23])).
% 1.66/1.39 thf(f23,plain,(
% 1.66/1.39 (dsetconstrER = ! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X1 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X2 @ X3)))) => (X2 @ X1)))),
% 1.66/1.39 inference(rectify,[status(thm)],[f1])).
% 1.66/1.39 thf(f1,axiom,(
% 1.66/1.39 (dsetconstrER = ! [X0 : $i,X2 : $i,X1 : $i > $o] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)))),
% 1.66/1.39 file('/export/starexec/sandbox2/tmp/tmp.FtBKtpcojT/DTF2THF_20179.p',dsetconstrER)).
% 1.66/1.39 thf(f140,plain,(
% 1.66/1.39 ($false = (in @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))),
% 1.66/1.39 inference(forward_demodulation,[status(thm)],[f139,f135])).
% 1.66/1.39 thf(f135,plain,(
% 1.66/1.39 ((sK15 @ sK0 @ sK1) = sK1)),
% 1.66/1.39 inference(trivial_inequality_removal,[status(thm)],[f134])).
% 1.66/1.39 thf(f134,plain,(
% 1.66/1.39 ($true != $true) | ((sK15 @ sK0 @ sK1) = sK1)),
% 1.66/1.39 inference(superposition,[status(thm)],[f99,f133])).
% 1.66/1.39 thf(f133,plain,(
% 1.66/1.39 ($true = (in @ (setadjoin @ (sK15 @ sK0 @ sK1) @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))),
% 1.66/1.39 inference(trivial_inequality_removal,[status(thm)],[f132])).
% 1.66/1.39 thf(f132,plain,(
% 1.66/1.39 ($true = (in @ (setadjoin @ (sK15 @ sK0 @ sK1) @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) | (sK1 != sK1)),
% 1.66/1.39 inference(duplicate_literal_removal,[status(thm)],[f131])).
% 1.66/1.39 thf(f131,plain,(
% 1.66/1.39 ($true = (in @ (setadjoin @ (sK15 @ sK0 @ sK1) @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) | ($true = (in @ (setadjoin @ (sK15 @ sK0 @ sK1) @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) | (sK1 != sK1)),
% 1.66/1.39 inference(equality_resolution,[status(thm)],[f129])).
% 1.66/1.39 thf(f129,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : (((setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) | (sK1 != X0) | ($true = (in @ (setadjoin @ (sK15 @ X1 @ X0) @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) | ((in @ (setadjoin @ (sK15 @ X1 @ X0) @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) = $true)) )),
% 1.66/1.39 inference(binary_proxy_clausification,[status(thm)],[f128])).
% 1.66/1.39 thf(f128,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : (((setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) | ((in @ (setadjoin @ (sK15 @ X1 @ X0) @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) != (in @ (setadjoin @ (sK15 @ X1 @ X0) @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) | (sK1 != X0)) )),
% 1.66/1.39 inference(beta_eta_normalization,[status(thm)],[f127])).
% 1.66/1.39 thf(f127,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : ((sK1 != X0) | (((^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) @ (sK15 @ X1 @ X0)) != ((^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) @ (sK15 @ X1 @ X0))) | ((setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) )),
% 1.66/1.39 inference(negative_extensionality,[status(thm)],[f122])).
% 1.66/1.39 thf(f122,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : (((^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) != (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))) | ((setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) | (sK1 != X0)) )),
% 1.66/1.39 inference(constrained_superposition,[status(thm)],[f98,f114])).
% 1.66/1.39 thf(f98,plain,(
% 1.66/1.39 (sK1 != (setunion @ (dsetconstr @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) @ (^[Y0 : $i]: (in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))))))),
% 1.66/1.39 inference(beta_eta_normalization,[status(thm)],[f83])).
% 1.66/1.39 thf(f83,plain,(
% 1.66/1.39 (((^[Y0 : $i]: (setunion @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0))))) @ ((^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))) @ sK1 @ sK0)) != sK1)),
% 1.66/1.39 inference(definition_unfolding,[status(thm)],[f64,f74,f73])).
% 1.66/1.39 thf(f74,plain,(
% 1.66/1.39 (kfst = (^[Y0 : $i]: (setunion @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0))))))),
% 1.66/1.39 inference(cnf_transformation,[status(thm)],[f32])).
% 1.66/1.39 thf(f32,plain,(
% 1.66/1.39 (kfst = (^[Y0 : $i]: (setunion @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0))))))),
% 1.66/1.39 inference(fool_elimination,[status(thm)],[f31])).
% 1.66/1.39 thf(f31,plain,(
% 1.66/1.39 (kfst = (^[X0 : $i] : (setunion @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : (in @ (setadjoin @ X1 @ emptyset) @ X0))))))),
% 1.66/1.39 inference(rectify,[status(thm)],[f9])).
% 1.66/1.39 thf(f9,axiom,(
% 1.66/1.39 (kfst = (^[X5 : $i] : (setunion @ (dsetconstr @ (setunion @ X5) @ (^[X2 : $i] : (in @ (setadjoin @ X2 @ emptyset) @ X5))))))),
% 1.66/1.39 file('/export/starexec/sandbox2/tmp/tmp.FtBKtpcojT/DTF2THF_20179.p',kfst)).
% 1.66/1.39 thf(f64,plain,(
% 1.66/1.39 (sK1 != (kfst @ (kpair @ sK1 @ sK0)))),
% 1.66/1.39 inference(cnf_transformation,[status(thm)],[f40])).
% 1.66/1.39 thf(f139,plain,(
% 1.66/1.39 ($false = (in @ (setadjoin @ (sK15 @ sK0 @ sK1) @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))),
% 1.66/1.39 inference(trivial_inequality_removal,[status(thm)],[f138])).
% 1.66/1.39 thf(f138,plain,(
% 1.66/1.39 (sK1 != sK1) | ($false = (in @ (setadjoin @ (sK15 @ sK0 @ sK1) @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))),
% 1.66/1.39 inference(duplicate_literal_removal,[status(thm)],[f137])).
% 1.66/1.39 thf(f137,plain,(
% 1.66/1.39 ($false = (in @ (setadjoin @ (sK15 @ sK0 @ sK1) @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) | (sK1 != sK1) | ($false = (in @ (setadjoin @ (sK15 @ sK0 @ sK1) @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))),
% 1.66/1.39 inference(equality_resolution,[status(thm)],[f130])).
% 1.66/1.39 thf(f130,plain,(
% 1.66/1.39 ( ! [X0 : $i,X1 : $i] : (((setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) | (sK1 != X0) | ((in @ (setadjoin @ (sK15 @ X1 @ X0) @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) = $false) | ($false = (in @ (setadjoin @ (sK15 @ X1 @ X0) @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))) )),
% 1.66/1.39 inference(binary_proxy_clausification,[status(thm)],[f128])).
% 1.66/1.39 % SZS output end Proof for DTF2THF_20179
% 1.66/1.39 % (20368)------------------------------
% 1.66/1.39 % (20368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.39 % (20368)Termination reason: Refutation
% 1.66/1.39
% 1.66/1.39 % (20368)Memory used [KB]: 5756
% 1.66/1.39 % (20368)Time elapsed: 0.015 s
% 1.66/1.39 % (20368)Instructions burned: 35 (million)
% 1.66/1.39 % (20368)------------------------------
% 1.66/1.39 % (20368)------------------------------
% 1.66/1.39 % (20347)Success in time 0.075 s
%------------------------------------------------------------------------------