%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU619^2 : 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 : n009.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 09:35:39 AM UTC 2026
% Result : Theorem 1.69s 1.42s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 47 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 547 ( 73 equ; 0 cnn)
% Maximal formula atoms : 6 ( 11 avg)
% Number of connectives : 997 ( 12 ~; 9 |; 25 &; 915 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 10 usr; 9 con; 0-2 aty)
% ( 16 !!; 11 ??; 0 @@+; 0 @@-)
% Number of variables : 87 ( 38 ^; 39 !; 10 ?; 87 :)
% 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,
iskpair: $i > $o ).
thf(func_def_8,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(f49,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
$true = $false,
inference(superposition,[status(thm)],[f39,f46]) ).
thf(f46,plain,
( ( in @ sK0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f45]) ).
thf(f45,plain,
( ( $true = $false )
| ( ( in @ sK0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(forward_demodulation,[status(thm)],[f44,f43]) ).
thf(f43,plain,
! [X2: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f23,f21]) ).
thf(f21,plain,
setukpairIL = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( setukpairIL = $true )
& ( setukpairIR = $true )
& ( $true
!= ( iskpair @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f17]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i] :
( $true
!= ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) )
=> ( $true
!= ( iskpair @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ( setukpairIL = $true )
& ( setukpairIR = $true )
& ? [X0: $i,X1: $i] :
( $true
!= ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( $true
!= ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) )
& ( setukpairIR = $true )
& ( setukpairIL = $true ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
~ ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ! [X0: $i,X1: $i] :
( $true
= ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
~ ( setukpairIL
=> ( setukpairIR
=> ! [X0: $i,X1: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( setukpairIL
=> ( setukpairIR
=> ! [X2: $i,X1: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( setukpairIL
=> ( setukpairIR
=> ! [X2: $i,X1: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UWt1AgIJAO/DTF2THF_15217.p',kpairiskpair) ).
thf(f23,plain,
( setukpairIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( setukpairIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) )
= setukpairIL ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X2: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
= setukpairIL ),
file('/export/starexec/sandbox2/tmp/tmp.UWt1AgIJAO/DTF2THF_15217.p',setukpairIL) ).
thf(f44,plain,
( ( ( in @ sK1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ sK0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(equality_resolution,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( $false
= ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i,X1: $i] :
( ( ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) )
& ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false )
| ( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) )
& ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) )
@ X2 )
= $false )
| ( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(pi_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: $i] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) )
& ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
| ( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: $i] :
( $false
= ( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) )
& ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) )
& ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( $true
!= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) )
& ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
( $true
!= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) )
@ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ),
inference(definition_unfolding,[status(thm)],[f19,f24]) ).
thf(f24,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ^ [X0: $i] :
? [X1: $i] :
( ? [X2: $i] :
( ( in @ X2 @ ( setunion @ X0 ) )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= X0 ) )
& ( in @ X1 @ ( setunion @ X0 ) ) ) )
= iskpair ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i] :
? [X1: $i] :
( ? [X2: $i] :
( ( in @ X2 @ ( setunion @ X0 ) )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= X0 ) )
& ( in @ X1 @ ( setunion @ X0 ) ) ) )
= iskpair ),
file('/export/starexec/sandbox2/tmp/tmp.UWt1AgIJAO/DTF2THF_15217.p',iskpair) ).
thf(f19,plain,
( $true
!= ( iskpair @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f39,plain,
! [X2: $i,X1: $i] :
( ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f22,f20]) ).
thf(f20,plain,
setukpairIR = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f22,plain,
( setukpairIR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( setukpairIR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) )
= setukpairIR ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X2: $i,X1: $i] :
( ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
= setukpairIR ),
file('/export/starexec/sandbox2/tmp/tmp.UWt1AgIJAO/DTF2THF_15217.p',setukpairIR) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU619^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.14 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.37 % Computer : n009.cluster.edu
% 0.19/0.37 % Model : x86_64 x86_64
% 0.19/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.37 % Memory : 8042.1875MB
% 0.19/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.37 % CPULimit : 300
% 0.19/0.37 % WCLimit : 300
% 0.19/0.37 % DateTime : Tue Feb 24 12:28:25 EST 2026
% 0.19/0.37 % CPUTime :
% 0.19/0.37 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.47 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : SEU619^2 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.47 % Domain : Set Theory
% 0.28/0.47 % Problem : Ordered Pairs - Kuratowski Pairs
% 0.28/0.47 % Version : Especial > Reduced > Especial.
% 0.28/0.47 % English : (! x:i.! y:i.iskpair (setadjoin (setadjoin x emptyset) (setadjoin
% 0.28/0.47 % (setadjoin x (setadjoin y emptyset)) emptyset)))
% 0.28/0.47
% 0.28/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.28/0.47 % Source : [Bro08]
% 0.28/0.47 % Names : ZFC121l [Bro08]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.00 v3.7.0
% 0.28/0.47 % Syntax : Number of formulae : 11 ( 3 unt; 7 typ; 3 def)
% 0.28/0.47 % Number of atoms : 14 ( 4 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 3 ( 3 avg)
% 0.28/0.47 % Number of connectives : 57 ( 0 ~; 0 |; 2 &; 53 @)
% 0.28/0.47 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 12 ( 4 avg)
% 0.28/0.47 % Number of types : 2 ( 0 usr)
% 0.28/0.47 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 8 ( 7 usr; 3 con; 0-2 aty)
% 0.28/0.47 % Number of variables : 9 ( 1 ^; 6 !; 2 ?; 9 :)
% 0.28/0.47 % SPC : TH0_THM_EQU_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : http://mathgate.info/detsetitem.php?id=174
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 thf(in_type,type,
% 0.28/0.47 in: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyset_type,type,
% 0.28/0.47 emptyset: $i ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoin_type,type,
% 0.28/0.47 setadjoin: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(setunion_type,type,
% 0.28/0.47 setunion: $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(iskpair_type,type,
% 0.28/0.47 iskpair: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(iskpair,definition,
% 0.28/0.47 ( iskpair
% 0.28/0.47 = ( ^ [A: $i] :
% 0.28/0.47 ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.47 & ? [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ ( setunion @ A ) )
% 0.28/0.47 & ( A
% 0.28/0.47 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairIL_type,type,
% 0.28/0.47 setukpairIL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairIL,definition,
% 0.28/0.47 ( setukpairIL
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairIR_type,type,
% 0.28/0.47 setukpairIR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairIR,definition,
% 0.28/0.47 ( setukpairIR
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(kpairiskpair,conjecture,
% 0.28/0.47 ( setukpairIL
% 0.28/0.47 => ( setukpairIR
% 0.28/0.47 => ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 1.52/1.38 ---- Embedded in THF ---
% 1.52/1.38 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.38 %%% Generated on Tue Feb 24 12:28:26 EST 2026
% 1.52/1.38 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.38 %%% Logic specification used:
% 1.52/1.38 %%% thf(spec, logic, $$dhol).
% 1.52/1.38
% 1.52/1.38 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.UWt1AgIJAO/DTF2DTF15217.p
% See solution above
% 1.52/1.38 ------------------------
% 1.52/1.39 ---- Cleaned THF ---
% 1.52/1.39 thf(in_type,type,
% 1.52/1.39 in: $i > $i > $o ).
% 1.52/1.39
% 1.52/1.39 thf(emptyset_type,type,
% 1.52/1.39 emptyset: $i ).
% 1.52/1.39
% 1.52/1.39 thf(setadjoin_type,type,
% 1.52/1.39 setadjoin: $i > $i > $i ).
% 1.52/1.39
% 1.52/1.39 thf(setunion_type,type,
% 1.52/1.39 setunion: $i > $i ).
% 1.52/1.39
% 1.52/1.39 thf(iskpair_type,type,
% 1.52/1.39 iskpair: $i > $o ).
% 1.52/1.39
% 1.52/1.39 thf(iskpair,definition,
% 1.52/1.39 ( iskpair
% 1.52/1.39 = ( ^ [A: $i] :
% 1.52/1.39 ? [Xx: $i] :
% 1.52/1.39 ( ( in @ Xx @ ( setunion @ A ) )
% 1.52/1.39 & ? [Xy: $i] :
% 1.52/1.39 ( ( in @ Xy @ ( setunion @ A ) )
% 1.52/1.39 & ( A
% 1.52/1.39 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 1.52/1.39
% 1.52/1.39 thf(setukpairIL_type,type,
% 1.52/1.39 setukpairIL: $o ).
% 1.52/1.39
% 1.52/1.39 thf(setukpairIL,definition,
% 1.52/1.39 ( setukpairIL
% 1.52/1.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 1.52/1.39
% 1.52/1.39 thf(setukpairIR_type,type,
% 1.52/1.39 setukpairIR: $o ).
% 1.52/1.39
% 1.52/1.39 thf(setukpairIR,definition,
% 1.52/1.39 ( setukpairIR
% 1.52/1.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 1.52/1.39
% 1.52/1.39 thf(kpairiskpair,conjecture,
% 1.52/1.39 ( setukpairIL
% 1.52/1.39 => ( setukpairIR
% 1.52/1.39 => ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 1.52/1.39 ------------------------
% 1.69/1.41 % (15317)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_15217 for (2999ds/27Mi)
% 1.69/1.41 % (15319)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_15217 for (2999ds/2Mi)
% 1.69/1.41 % (15320)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_15217 for (2999ds/275Mi)
% 1.69/1.41 % (15316)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_15217 for (2999ds/4Mi)
% 1.69/1.41 % (15318)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15217 for (2999ds/2Mi)
% 1.69/1.41 % (15321)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15217 for (2999ds/18Mi)
% 1.69/1.41 % (15315)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15217 for (2999ds/183Mi)
% 1.69/1.41 % (15318)Instruction limit reached!
% 1.69/1.41 % (15318)------------------------------
% 1.69/1.41 % (15318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.41 % (15318)Termination reason: Unknown
% 1.69/1.41 % (15318)Termination phase: Property scanning
% 1.69/1.41 % (15319)Instruction limit reached!
% 1.69/1.41 % (15319)------------------------------
% 1.69/1.41 % (15319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.41 % (15319)Termination reason: Unknown
% 1.69/1.41 % (15319)Termination phase: Property scanning
% 1.69/1.41
% 1.69/1.41 % (15319)Memory used [KB]: 895
% 1.69/1.41 % (15319)Time elapsed: 0.003 s
% 1.69/1.41 % (15319)Instructions burned: 3 (million)
% 1.69/1.41 % (15319)------------------------------
% 1.69/1.41 % (15319)------------------------------
% 1.69/1.41
% 1.69/1.41 % (15318)Memory used [KB]: 895
% 1.69/1.41 % (15318)Time elapsed: 0.003 s
% 1.69/1.41 % (15318)Instructions burned: 2 (million)
% 1.69/1.41 % (15318)------------------------------
% 1.69/1.41 % (15318)------------------------------
% 1.69/1.41 % (15316)Instruction limit reached!
% 1.69/1.41 % (15316)------------------------------
% 1.69/1.41 % (15316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.41 % (15316)Termination reason: Unknown
% 1.69/1.41 % (15316)Termination phase: Saturation
% 1.69/1.41
% 1.69/1.41 % (15316)Memory used [KB]: 5500
% 1.69/1.41 % (15316)Time elapsed: 0.004 s
% 1.69/1.41 % (15316)Instructions burned: 4 (million)
% 1.69/1.41 % (15316)------------------------------
% 1.69/1.41 % (15316)------------------------------
% 1.69/1.41 % (15320)Refutation not found, incomplete strategy
% 1.69/1.41 % (15320)------------------------------
% 1.69/1.41 % (15320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.41 % (15320)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.41
% 1.69/1.41
% 1.69/1.41 % (15320)Memory used [KB]: 5500
% 1.69/1.41 % (15320)Time elapsed: 0.004 s
% 1.69/1.41 % (15320)Instructions burned: 4 (million)
% 1.69/1.41 % (15320)------------------------------
% 1.69/1.41 % (15320)------------------------------
% 1.69/1.41 % (15317)First to succeed.
% 1.69/1.41 % (15315)Also succeeded, but the first one will report.
% 1.69/1.42 % (15317)Refutation found. Thanks to Tanya!
% 1.69/1.42 % SZS status Theorem for DTF2THF_15217
% 1.69/1.42 % SZS output start Proof for DTF2THF_15217
% 1.69/1.42 thf(func_def_0, type, in: $i > $i > $o).
% 1.69/1.42 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.69/1.42 thf(func_def_3, type, setunion: $i > $i).
% 1.69/1.42 thf(func_def_4, type, iskpair: $i > $o).
% 1.69/1.42 thf(func_def_8, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.69/1.42 thf(f49,plain,(
% 1.69/1.42 $false),
% 1.69/1.42 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.69/1.42 thf(f48,plain,(
% 1.69/1.42 ($true = $false)),
% 1.69/1.42 inference(superposition,[status(thm)],[f39,f46])).
% 1.69/1.42 thf(f46,plain,(
% 1.69/1.42 ((in @ sK0 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) = $false)),
% 1.69/1.42 inference(trivial_inequality_removal,[status(thm)],[f45])).
% 1.69/1.42 thf(f45,plain,(
% 1.69/1.42 ($true = $false) | ((in @ sK0 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) = $false)),
% 1.69/1.42 inference(forward_demodulation,[status(thm)],[f44,f43])).
% 1.69/1.42 thf(f43,plain,(
% 1.69/1.42 ( ! [X2 : $i,X1 : $i] : (((in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) = $true)) )),
% 1.69/1.42 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.69/1.42 thf(f42,plain,(
% 1.69/1.42 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))) @ X2) = $true)) )),
% 1.69/1.42 inference(pi_clausification,[status(thm)],[f41])).
% 1.69/1.42 thf(f41,plain,(
% 1.69/1.42 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) )),
% 1.69/1.42 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.69/1.42 thf(f40,plain,(
% 1.69/1.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))) @ X1))) )),
% 1.69/1.42 inference(pi_clausification,[status(thm)],[f27])).
% 1.69/1.42 thf(f27,plain,(
% 1.69/1.42 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))),
% 1.69/1.42 inference(definition_unfolding,[status(thm)],[f23,f21])).
% 1.69/1.42 thf(f21,plain,(
% 1.69/1.42 (setukpairIL = $true)),
% 1.69/1.42 inference(cnf_transformation,[status(thm)],[f18])).
% 1.69/1.42 thf(f18,plain,(
% 1.69/1.42 (setukpairIL = $true) & (setukpairIR = $true) & ($true != (iskpair @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))),
% 1.69/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f17])).
% 1.69/1.42 thf(f17,plain,(
% 1.69/1.42 ? [X0 : $i,X1 : $i] : ($true != (iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))) => ($true != (iskpair @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))),
% 1.69/1.42 introduced(definition,[],[choice_axiom])).
% 1.69/1.42 thf(f16,plain,(
% 1.69/1.42 (setukpairIL = $true) & (setukpairIR = $true) & ? [X0 : $i,X1 : $i] : ($true != (iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))))),
% 1.69/1.42 inference(flattening,[status(thm)],[f15])).
% 1.69/1.42 thf(f15,plain,(
% 1.69/1.42 (? [X0 : $i,X1 : $i] : ($true != (iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))) & (setukpairIR = $true)) & (setukpairIL = $true)),
% 1.69/1.42 inference(ennf_transformation,[status(thm)],[f14])).
% 1.69/1.42 thf(f14,plain,(
% 1.69/1.42 ~((setukpairIL = $true) => ((setukpairIR = $true) => ! [X0 : $i,X1 : $i] : ($true = (iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))))))),
% 1.69/1.42 inference(fool_elimination,[status(thm)],[f13])).
% 1.69/1.42 thf(f13,plain,(
% 1.69/1.42 ~(setukpairIL => (setukpairIR => ! [X0 : $i,X1 : $i] : (iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))))),
% 1.69/1.42 inference(rectify,[status(thm)],[f5])).
% 1.69/1.42 thf(f5,negated_conjecture,(
% 1.69/1.42 ~(setukpairIL => (setukpairIR => ! [X2 : $i,X1 : $i] : (iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))))),
% 1.69/1.42 inference(negated_conjecture,[status(cth)],[f4])).
% 1.69/1.42 thf(f4,conjecture,(
% 1.69/1.42 setukpairIL => (setukpairIR => ! [X2 : $i,X1 : $i] : (iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))))),
% 1.69/1.42 file('/export/starexec/sandbox2/tmp/tmp.UWt1AgIJAO/DTF2THF_15217.p',kpairiskpair)).
% 1.69/1.42 thf(f23,plain,(
% 1.69/1.42 (setukpairIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))),
% 1.69/1.42 inference(cnf_transformation,[status(thm)],[f12])).
% 1.69/1.42 thf(f12,plain,(
% 1.69/1.42 (setukpairIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))),
% 1.69/1.42 inference(fool_elimination,[status(thm)],[f11])).
% 1.69/1.42 thf(f11,plain,(
% 1.69/1.42 (! [X0 : $i,X1 : $i] : (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))) = setukpairIL)),
% 1.69/1.42 inference(rectify,[status(thm)],[f2])).
% 1.69/1.42 thf(f2,axiom,(
% 1.69/1.42 (! [X2 : $i,X1 : $i] : (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) = setukpairIL)),
% 1.69/1.42 file('/export/starexec/sandbox2/tmp/tmp.UWt1AgIJAO/DTF2THF_15217.p',setukpairIL)).
% 1.69/1.42 thf(f44,plain,(
% 1.69/1.42 ((in @ sK1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) = $false) | ((in @ sK0 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) = $false)),
% 1.69/1.42 inference(equality_resolution,[status(thm)],[f35])).
% 1.69/1.42 thf(f35,plain,(
% 1.69/1.42 ( ! [X2 : $i,X1 : $i] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) | ($false = (in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))) | ((in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) = $false)) )),
% 1.69/1.42 inference(equality_proxy_clausification,[status(thm)],[f34])).
% 1.69/1.42 thf(f34,plain,(
% 1.69/1.42 ( ! [X2 : $i,X1 : $i] : (($false = (in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))) | ($false = ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) | ((in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) = $false)) )),
% 1.69/1.42 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.69/1.42 thf(f33,plain,(
% 1.69/1.42 ( ! [X2 : $i,X1 : $i] : (((((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) & (in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))) = $false) | ((in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) = $false)) )),
% 1.69/1.42 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.69/1.42 thf(f32,plain,(
% 1.69/1.42 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) & (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))))) @ X2) = $false) | ((in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) = $false)) )),
% 1.69/1.42 inference(pi_clausification,[status(thm)],[f31])).
% 1.69/1.42 thf(f31,plain,(
% 1.69/1.42 ( ! [X1 : $i] : (($false = (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) & (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))))))) | ((in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) = $false)) )),
% 1.69/1.42 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.69/1.42 thf(f30,plain,(
% 1.69/1.42 ( ! [X1 : $i] : (($false = ((in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) & (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))))))))) )),
% 1.69/1.42 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.69/1.42 thf(f29,plain,(
% 1.69/1.42 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) & (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))))))) @ X1))) )),
% 1.69/1.42 inference(pi_clausification,[status(thm)],[f28])).
% 1.69/1.42 thf(f28,plain,(
% 1.69/1.42 ($true != (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) & (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))))))))))),
% 1.69/1.42 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.69/1.42 thf(f25,plain,(
% 1.69/1.42 ($true != ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0))))))))) @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))),
% 1.69/1.42 inference(definition_unfolding,[status(thm)],[f19,f24])).
% 1.69/1.42 thf(f24,plain,(
% 1.69/1.42 (iskpair = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0))))))))))),
% 1.69/1.42 inference(cnf_transformation,[status(thm)],[f10])).
% 1.69/1.42 thf(f10,plain,(
% 1.69/1.42 (iskpair = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0))))))))))),
% 1.69/1.42 inference(fool_elimination,[status(thm)],[f9])).
% 1.69/1.42 thf(f9,plain,(
% 1.69/1.42 ((^[X0 : $i] : (? [X1 : $i] : (? [X2 : $i] : ((in @ X2 @ (setunion @ X0)) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = X0)) & (in @ X1 @ (setunion @ X0))))) = iskpair)),
% 1.69/1.42 inference(rectify,[status(thm)],[f1])).
% 1.69/1.42 thf(f1,axiom,(
% 1.69/1.42 ((^[X0 : $i] : (? [X1 : $i] : (? [X2 : $i] : ((in @ X2 @ (setunion @ X0)) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = X0)) & (in @ X1 @ (setunion @ X0))))) = iskpair)),
% 1.69/1.42 file('/export/starexec/sandbox2/tmp/tmp.UWt1AgIJAO/DTF2THF_15217.p',iskpair)).
% 1.69/1.42 thf(f19,plain,(
% 1.69/1.42 ($true != (iskpair @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))),
% 1.69/1.42 inference(cnf_transformation,[status(thm)],[f18])).
% 1.69/1.42 thf(f39,plain,(
% 1.69/1.42 ( ! [X2 : $i,X1 : $i] : (((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) = $true)) )),
% 1.69/1.42 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.69/1.42 thf(f38,plain,(
% 1.69/1.42 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))) @ X2))) )),
% 1.69/1.42 inference(pi_clausification,[status(thm)],[f37])).
% 1.69/1.42 thf(f37,plain,(
% 1.69/1.42 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) )),
% 1.69/1.42 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.69/1.42 thf(f36,plain,(
% 1.69/1.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))) @ X1))) )),
% 1.69/1.42 inference(pi_clausification,[status(thm)],[f26])).
% 1.69/1.42 thf(f26,plain,(
% 1.69/1.42 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))),
% 1.69/1.42 inference(definition_unfolding,[status(thm)],[f22,f20])).
% 1.69/1.42 thf(f20,plain,(
% 1.69/1.42 (setukpairIR = $true)),
% 1.69/1.42 inference(cnf_transformation,[status(thm)],[f18])).
% 1.69/1.42 thf(f22,plain,(
% 1.69/1.42 (setukpairIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))),
% 1.69/1.42 inference(cnf_transformation,[status(thm)],[f8])).
% 1.69/1.42 thf(f8,plain,(
% 1.69/1.42 (setukpairIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))),
% 1.69/1.42 inference(fool_elimination,[status(thm)],[f7])).
% 1.69/1.42 thf(f7,plain,(
% 1.69/1.42 (! [X0 : $i,X1 : $i] : (in @ X0 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))) = setukpairIR)),
% 1.69/1.42 inference(rectify,[status(thm)],[f3])).
% 1.69/1.42 thf(f3,axiom,(
% 1.69/1.42 (! [X2 : $i,X1 : $i] : (in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) = setukpairIR)),
% 1.69/1.42 file('/export/starexec/sandbox2/tmp/tmp.UWt1AgIJAO/DTF2THF_15217.p',setukpairIR)).
% 1.69/1.42 % SZS output end Proof for DTF2THF_15217
% 1.69/1.42 % (15317)------------------------------
% 1.69/1.42 % (15317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.42 % (15317)Termination reason: Refutation
% 1.69/1.42
% 1.69/1.42 % (15317)Memory used [KB]: 5500
% 1.69/1.42 % (15317)Time elapsed: 0.008 s
% 1.69/1.42 % (15317)Instructions burned: 8 (million)
% 1.69/1.42 % (15317)------------------------------
% 1.69/1.42 % (15317)------------------------------
% 1.69/1.42 % (15314)Success in time 0.022 s
%------------------------------------------------------------------------------