%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU540^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n025.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 09:35:10 AM UTC 2026
% Result : Theorem 1.65s 1.31s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 55 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 340 ( 81 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 491 ( 12 ~; 15 |; 11 &; 360 @)
% ( 0 <=>; 59 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 11 usr; 7 con; 0-2 aty)
% ( 34 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 114 ( 58 ^; 53 !; 3 ?; 114 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
powerset: $i > $i ).
thf(func_def_3,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_6,type,
prop2set: $o > $i ).
thf(func_def_8,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_19,type,
sK2: $i > $i > $i ).
thf(func_def_20,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f64,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
$true = $false,
inference(superposition,[status(thm)],[f59,f51]) ).
thf(f51,plain,
! [X0: $i] :
( $true
= ( in @ X0 @ ( powerset @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( in @ X0 @ ( powerset @ X0 ) ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f49]) ).
thf(f49,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( in @ X0 @ ( powerset @ X0 ) ) )
| ( $true
= ( in @ X0 @ ( powerset @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f46,f47]) ).
thf(f47,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ X1 @ X2 ) @ X2 ) )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
| ( ( ( in @ ( sK2 @ X1 @ X2 ) @ X2 )
=> ( in @ ( sK2 @ X1 @ X2 ) @ X1 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) )
@ ( sK2 @ X1 @ X2 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
= $false )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ Y0 @ X1 ) ) )
=> ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( in @ Y0 @ ( powerset @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( in @ Y1 @ X1 ) ) )
=> ( in @ Y0 @ ( powerset @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( in @ Y1 @ ( powerset @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f24,f22]) ).
thf(f22,plain,
powersetI = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( powersetI = $true )
& ( ( in @ emptyset @ ( prop2set @ sK0 ) )
!= $true )
& ( $true = sK0 )
& ( dsetconstrI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f16,f17]) ).
thf(f17,plain,
( ? [X0: $o] :
( ( ( in @ emptyset @ ( prop2set @ X0 ) )
!= $true )
& ( $true = X0 ) )
=> ( ( ( in @ emptyset @ ( prop2set @ sK0 ) )
!= $true )
& ( $true = sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ( powersetI = $true )
& ? [X0: $o] :
( ( ( in @ emptyset @ ( prop2set @ X0 ) )
!= $true )
& ( $true = X0 ) )
& ( dsetconstrI = $true ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ? [X0: $o] :
( ( ( in @ emptyset @ ( prop2set @ X0 ) )
!= $true )
& ( $true = X0 ) )
& ( powersetI = $true )
& ( dsetconstrI = $true ) ),
inference(ennf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
~ ( ( dsetconstrI = $true )
=> ( ( powersetI = $true )
=> ! [X0: $o] :
( ( $true = X0 )
=> ( ( in @ emptyset @ ( prop2set @ X0 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
~ ( dsetconstrI
=> ( powersetI
=> ! [X0: $o] :
( X0
=> ( in @ emptyset @ ( prop2set @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( dsetconstrI
=> ( powersetI
=> ! [X1: $o] :
( X1
=> ( in @ emptyset @ ( prop2set @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( dsetconstrI
=> ( powersetI
=> ! [X1: $o] :
( X1
=> ( in @ emptyset @ ( prop2set @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YkXdK0oz2p/DTF2THF_5209.p',prop2setI) ).
thf(f24,plain,
( powersetI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( powersetI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( in @ Y2 @ Y0 ) ) )
=> ( in @ Y1 @ ( powerset @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( powersetI
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( powersetI
= ( ! [X4: $i,X0: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( in @ X2 @ X0 ) )
=> ( in @ X4 @ ( powerset @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YkXdK0oz2p/DTF2THF_5209.p',powersetI) ).
thf(f46,plain,
! [X2: $i,X1: $i] :
( ( ( in @ ( sK2 @ X1 @ X2 ) @ X1 )
= $false )
| ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f59,plain,
( ( in @ emptyset @ ( powerset @ emptyset ) )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
( ( ( in @ emptyset @ ( powerset @ emptyset ) )
= $false )
| ( $true = $false ) ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( in @ emptyset @ ( powerset @ emptyset ) )
= $false )
| ( $false
= ( ^ [Y0: $i] : $true
@ emptyset ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
( ( $true != $true )
| ( $false
= ( ^ [Y0: $i] : $true
@ emptyset ) )
| ( ( in @ emptyset @ ( powerset @ emptyset ) )
= $false ) ),
inference(superposition,[status(thm)],[f29,f38]) ).
thf(f38,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( $true
= ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) ) )
| ( ( X3 @ X2 )
= $false )
| ( $false
= ( in @ X2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( ( X3 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) ) )
= $true )
| ( $false
= ( in @ X2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X2 @ X1 )
=> ( ( X3 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( ( in @ X2 @ X1 )
=> ( ( Y0 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X2 @ X1 )
=> ( ( Y0 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ X1 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ X1 )
=> ( ( Y1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f25,f19]) ).
thf(f19,plain,
dsetconstrI = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f25,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ Y0 )
=> ( ( Y2 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
=> ( ( X0 @ X1 )
=> ( in @ X1
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X0 @ X3 ) ) ) ) )
= dsetconstrI ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i > $o,X2: $i,X0: $i] :
( ( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) )
= dsetconstrI ),
file('/export/starexec/sandbox/tmp/tmp.YkXdK0oz2p/DTF2THF_5209.p',dsetconstrI) ).
thf(f29,plain,
( $true
!= ( in @ emptyset
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y0: $i] : $true ) ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
( ( in @ emptyset
@ ( ^ [Y0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y1: $i] : Y0 )
@ $true ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f21,f23,f20]) ).
thf(f20,plain,
$true = sK0,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f23,plain,
( prop2set
= ( ^ [Y0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y1: $i] : Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( prop2set
= ( ^ [Y0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y1: $i] : Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( prop2set
= ( ^ [X0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [X1: $i] : X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( prop2set
= ( ^ [X1: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [X2: $i] : X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YkXdK0oz2p/DTF2THF_5209.p',prop2set) ).
thf(f21,plain,
( ( in @ emptyset @ ( prop2set @ sK0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU540^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n025.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:26:27 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.47 ---- Original DTF file ---
% 0.29/0.47 thf(spec,logic,$$dhol).
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 % File : SEU540^2 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.47 % Domain : Set Theory
% 0.29/0.47 % Problem : Preliminary Notions - Dependent Connective Laws
% 0.29/0.47 % Version : Especial > Reduced > Especial.
% 0.29/0.47 % English : (! phi:o.phi -> in emptyset (prop2set phi))
% 0.29/0.47
% 0.29/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.47 % Source : [Bro08]
% 0.29/0.47 % Names : ZFC042l [Bro08]
% 0.29/0.47
% 0.29/0.47 % Status : Theorem
% 0.29/0.47 % Rating : 0.00 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v5.1.0, 0.20 v4.1.0, 0.00 v3.7.0
% 0.29/0.47 % Syntax : Number of formulae : 11 ( 3 unt; 7 typ; 3 def)
% 0.29/0.47 % Number of atoms : 13 ( 3 equ; 0 cnn)
% 0.29/0.47 % Maximal formula atoms : 3 ( 3 avg)
% 0.29/0.47 % Number of connectives : 28 ( 0 ~; 0 |; 0 &; 21 @)
% 0.29/0.47 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.29/0.47 % Maximal formula depth : 7 ( 3 avg)
% 0.29/0.47 % Number of types : 2 ( 0 usr)
% 0.29/0.47 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.29/0.47 % Number of symbols : 8 ( 7 usr; 3 con; 0-2 aty)
% 0.29/0.47 % Number of variables : 10 ( 3 ^; 7 !; 0 ?; 10 :)
% 0.29/0.47 % SPC : TH0_THM_EQU_NAR
% 0.29/0.47
% 0.29/0.47 % Comments : http://mathgate.info/detsetitem.php?id=101
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 thf(in_type,type,
% 0.29/0.47 in: $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(emptyset_type,type,
% 0.29/0.47 emptyset: $i ).
% 0.29/0.47
% 0.29/0.47 thf(powerset_type,type,
% 0.29/0.47 powerset: $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(dsetconstr_type,type,
% 0.29/0.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.29/0.47
% 0.29/0.47 thf(dsetconstrI_type,type,
% 0.29/0.47 dsetconstrI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(dsetconstrI,definition,
% 0.29/0.47 ( dsetconstrI
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ( Xphi @ Xx )
% 0.29/0.47 => ( in @ Xx
% 0.29/0.47 @ ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(prop2set_type,type,
% 0.29/0.47 prop2set: $o > $i ).
% 0.29/0.47
% 0.29/0.47 thf(prop2set,definition,
% 0.29/0.47 ( prop2set
% 0.29/0.47 = ( ^ [Xphi: $o] :
% 0.29/0.47 ( dsetconstr @ ( powerset @ emptyset )
% 0.29/0.47 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(powersetI_type,type,
% 0.29/0.47 powersetI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(powersetI,definition,
% 0.29/0.47 ( powersetI
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ B )
% 0.29/0.47 => ( in @ Xx @ A ) )
% 0.29/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(prop2setI,conjecture,
% 0.29/0.47 ( dsetconstrI
% 0.29/0.47 => ( powersetI
% 0.29/0.47 => ! [Xphi: $o] :
% 0.29/0.47 ( Xphi
% 0.29/0.47 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 1.50/1.26 ---- Embedded in THF ---
% 1.50/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.26 %%% Generated on Tue Feb 24 12:26:28 EST 2026
% 1.50/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.26 %%% Logic specification used:
% 1.50/1.26 %%% thf(spec, logic, $$dhol).
% 1.50/1.26
% 1.50/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.YkXdK0oz2p/DTF2DTF5209.p
% See solution above
% 1.50/1.26 ------------------------
% 1.50/1.28 ---- Cleaned THF ---
% 1.50/1.28 thf(in_type,type,
% 1.50/1.28 in: $i > $i > $o ).
% 1.50/1.28
% 1.50/1.28 thf(emptyset_type,type,
% 1.50/1.28 emptyset: $i ).
% 1.50/1.28
% 1.50/1.28 thf(powerset_type,type,
% 1.50/1.28 powerset: $i > $i ).
% 1.50/1.28
% 1.50/1.28 thf(dsetconstr_type,type,
% 1.50/1.28 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.50/1.28
% 1.50/1.28 thf(dsetconstrI_type,type,
% 1.50/1.28 dsetconstrI: $o ).
% 1.50/1.28
% 1.50/1.28 thf(dsetconstrI,definition,
% 1.50/1.28 ( dsetconstrI
% 1.50/1.28 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.50/1.28 ( ( in @ Xx @ A )
% 1.50/1.28 => ( ( Xphi @ Xx )
% 1.50/1.28 => ( in @ Xx
% 1.50/1.28 @ ( dsetconstr @ A
% 1.50/1.28 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.50/1.28
% 1.50/1.28 thf(prop2set_type,type,
% 1.50/1.28 prop2set: $o > $i ).
% 1.50/1.28
% 1.50/1.28 thf(prop2set,definition,
% 1.50/1.28 ( prop2set
% 1.50/1.28 = ( ^ [Xphi: $o] :
% 1.50/1.28 ( dsetconstr @ ( powerset @ emptyset )
% 1.50/1.28 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 1.50/1.28
% 1.50/1.28 thf(powersetI_type,type,
% 1.50/1.28 powersetI: $o ).
% 1.50/1.28
% 1.50/1.28 thf(powersetI,definition,
% 1.50/1.28 ( powersetI
% 1.50/1.28 = ( ! [A: $i,B: $i] :
% 1.50/1.28 ( ! [Xx: $i] :
% 1.50/1.28 ( ( in @ Xx @ B )
% 1.50/1.28 => ( in @ Xx @ A ) )
% 1.50/1.28 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 1.50/1.28
% 1.50/1.28 thf(prop2setI,conjecture,
% 1.50/1.28 ( dsetconstrI
% 1.50/1.28 => ( powersetI
% 1.50/1.28 => ! [Xphi: $o] :
% 1.50/1.28 ( Xphi
% 1.50/1.28 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 1.50/1.28 ------------------------
% 1.50/1.29 % (5494)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_5209 for (2999ds/2Mi)
% 1.50/1.29 % (5494)Instruction limit reached!
% 1.50/1.29 % (5494)------------------------------
% 1.50/1.29 % (5494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (5494)Termination reason: Unknown
% 1.50/1.29 % (5494)Termination phase: Saturation
% 1.50/1.29
% 1.50/1.29 % (5494)Memory used [KB]: 895
% 1.50/1.29 % (5494)Time elapsed: 0.002 s
% 1.50/1.29 % (5494)Instructions burned: 2 (million)
% 1.50/1.29 % (5494)------------------------------
% 1.50/1.29 % (5494)------------------------------
% 1.65/1.30 % (5491)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_5209 for (2999ds/4Mi)
% 1.65/1.30 % (5490)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5209 for (2999ds/183Mi)
% 1.65/1.30 % (5492)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_5209 for (2999ds/27Mi)
% 1.65/1.30 % (5493)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5209 for (2999ds/2Mi)
% 1.65/1.30 % (5495)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_5209 for (2999ds/275Mi)
% 1.65/1.30 % (5496)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5209 for (2999ds/18Mi)
% 1.65/1.30 % (5493)Instruction limit reached!
% 1.65/1.30 % (5493)------------------------------
% 1.65/1.30 % (5493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.30 % (5493)Termination reason: Unknown
% 1.65/1.30 % (5493)Termination phase: Preprocessing 2
% 1.65/1.30
% 1.65/1.30 % (5493)Memory used [KB]: 895
% 1.65/1.30 % (5493)Time elapsed: 0.003 s
% 1.65/1.30 % (5493)Instructions burned: 2 (million)
% 1.65/1.30 % (5493)------------------------------
% 1.65/1.30 % (5493)------------------------------
% 1.65/1.30 % (5497)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5209 for (2999ds/3Mi)
% 1.65/1.30 % (5495)Refutation not found, incomplete strategy
% 1.65/1.30 % (5495)------------------------------
% 1.65/1.30 % (5495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.30 % (5495)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.30
% 1.65/1.30
% 1.65/1.30 % (5495)Memory used [KB]: 5500
% 1.65/1.30 % (5495)Time elapsed: 0.004 s
% 1.65/1.30 % (5495)Instructions burned: 2 (million)
% 1.65/1.30 % (5495)------------------------------
% 1.65/1.30 % (5495)------------------------------
% 1.65/1.30 % (5491)Instruction limit reached!
% 1.65/1.30 % (5491)------------------------------
% 1.65/1.30 % (5491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.30 % (5491)Termination reason: Unknown
% 1.65/1.30 % (5491)Termination phase: Saturation
% 1.65/1.30
% 1.65/1.30 % (5491)Memory used [KB]: 5500
% 1.65/1.30 % (5491)Time elapsed: 0.005 s
% 1.65/1.30 % (5491)Instructions burned: 5 (million)
% 1.65/1.30 % (5491)------------------------------
% 1.65/1.30 % (5491)------------------------------
% 1.65/1.30 % (5497)Instruction limit reached!
% 1.65/1.30 % (5497)------------------------------
% 1.65/1.30 % (5497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.30 % (5497)Termination reason: Unknown
% 1.65/1.30 % (5497)Termination phase: Saturation
% 1.65/1.30
% 1.65/1.30 % (5497)Memory used [KB]: 5500
% 1.65/1.30 % (5497)Time elapsed: 0.002 s
% 1.65/1.30 % (5497)Instructions burned: 3 (million)
% 1.65/1.30 % (5497)------------------------------
% 1.65/1.30 % (5497)------------------------------
% 1.65/1.30 % (5492)First to succeed.
% 1.65/1.30 % (5490)Also succeeded, but the first one will report.
% 1.65/1.31 % (5492)Refutation found. Thanks to Tanya!
% 1.65/1.31 % SZS status Theorem for DTF2THF_5209
% 1.65/1.31 % SZS output start Proof for DTF2THF_5209
% 1.65/1.31 thf(func_def_0, type, in: $i > $i > $o).
% 1.65/1.31 thf(func_def_2, type, powerset: $i > $i).
% 1.65/1.31 thf(func_def_3, type, dsetconstr: $i > ($i > $o) > $i).
% 1.65/1.31 thf(func_def_6, type, prop2set: $o > $i).
% 1.65/1.31 thf(func_def_8, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.65/1.31 thf(func_def_19, type, sK2: $i > $i > $i).
% 1.65/1.31 thf(func_def_20, type, ph3: !>[X0: $tType]:(X0)).
% 1.65/1.31 thf(f64,plain,(
% 1.65/1.31 $false),
% 1.65/1.31 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.65/1.31 thf(f63,plain,(
% 1.65/1.31 ($true = $false)),
% 1.65/1.31 inference(superposition,[status(thm)],[f59,f51])).
% 1.65/1.31 thf(f51,plain,(
% 1.65/1.31 ( ! [X0 : $i] : (($true = (in @ X0 @ (powerset @ X0)))) )),
% 1.65/1.31 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.65/1.31 thf(f50,plain,(
% 1.65/1.31 ( ! [X0 : $i] : (($true = $false) | ($true = (in @ X0 @ (powerset @ X0)))) )),
% 1.65/1.31 inference(duplicate_literal_removal,[status(thm)],[f49])).
% 1.65/1.31 thf(f49,plain,(
% 1.65/1.31 ( ! [X0 : $i] : (($true = $false) | ($true = (in @ X0 @ (powerset @ X0))) | ($true = (in @ X0 @ (powerset @ X0)))) )),
% 1.65/1.31 inference(superposition,[status(thm)],[f46,f47])).
% 1.65/1.31 thf(f47,plain,(
% 1.65/1.31 ( ! [X2 : $i,X1 : $i] : (($true = (in @ (sK2 @ X1 @ X2) @ X2)) | ((in @ X2 @ (powerset @ X1)) = $true)) )),
% 1.65/1.31 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.65/1.31 thf(f45,plain,(
% 1.65/1.31 ( ! [X2 : $i,X1 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) | (((in @ (sK2 @ X1 @ X2) @ X2) => (in @ (sK2 @ X1 @ X2) @ X1)) = $false)) )),
% 1.65/1.31 inference(beta_eta_normalization,[status(thm)],[f44])).
% 1.65/1.31 thf(f44,plain,(
% 1.65/1.31 ( ! [X2 : $i,X1 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) | (((^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1))) @ (sK2 @ X1 @ X2)) = $false)) )),
% 1.65/1.31 inference(sigma_clausification,[status(thm)],[f43])).
% 1.65/1.31 thf(f43,plain,(
% 1.65/1.31 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) = $false) | ((in @ X2 @ (powerset @ X1)) = $true)) )),
% 1.65/1.31 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.65/1.31 thf(f42,plain,(
% 1.65/1.31 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (in @ Y0 @ X1)))) => (in @ X2 @ (powerset @ X1))))) )),
% 1.65/1.31 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.65/1.31 thf(f41,plain,(
% 1.65/1.31 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => (in @ Y0 @ (powerset @ X1)))) @ X2) = $true)) )),
% 1.65/1.31 inference(pi_clausification,[status(thm)],[f40])).
% 1.65/1.31 thf(f40,plain,(
% 1.65/1.31 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ X1)))) => (in @ Y0 @ (powerset @ X1))))))) )),
% 1.65/1.31 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.65/1.31 thf(f39,plain,(
% 1.65/1.31 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0)))))) @ X1) = $true)) )),
% 1.65/1.31 inference(pi_clausification,[status(thm)],[f27])).
% 1.65/1.31 thf(f27,plain,(
% 1.65/1.31 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))))),
% 1.65/1.31 inference(definition_unfolding,[status(thm)],[f24,f22])).
% 1.65/1.31 thf(f22,plain,(
% 1.65/1.31 (powersetI = $true)),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f18])).
% 1.65/1.31 thf(f18,plain,(
% 1.65/1.31 (powersetI = $true) & (((in @ emptyset @ (prop2set @ sK0)) != $true) & ($true = sK0)) & (dsetconstrI = $true)),
% 1.65/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f16,f17])).
% 1.65/1.31 thf(f17,plain,(
% 1.65/1.31 ? [X0 : $o] : (((in @ emptyset @ (prop2set @ X0)) != $true) & ($true = X0)) => (((in @ emptyset @ (prop2set @ sK0)) != $true) & ($true = sK0))),
% 1.65/1.31 introduced(definition,[],[choice_axiom])).
% 1.65/1.31 thf(f16,plain,(
% 1.65/1.31 (powersetI = $true) & ? [X0 : $o] : (((in @ emptyset @ (prop2set @ X0)) != $true) & ($true = X0)) & (dsetconstrI = $true)),
% 1.65/1.31 inference(flattening,[status(thm)],[f15])).
% 1.65/1.31 thf(f15,plain,(
% 1.65/1.31 (? [X0 : $o] : (((in @ emptyset @ (prop2set @ X0)) != $true) & ($true = X0)) & (powersetI = $true)) & (dsetconstrI = $true)),
% 1.65/1.31 inference(ennf_transformation,[status(thm)],[f14])).
% 1.65/1.31 thf(f14,plain,(
% 1.65/1.31 ~((dsetconstrI = $true) => ((powersetI = $true) => ! [X0 : $o] : (($true = X0) => ((in @ emptyset @ (prop2set @ X0)) = $true))))),
% 1.65/1.31 inference(fool_elimination,[status(thm)],[f13])).
% 1.65/1.31 thf(f13,plain,(
% 1.65/1.31 ~(dsetconstrI => (powersetI => ! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0)))))),
% 1.65/1.31 inference(rectify,[status(thm)],[f5])).
% 1.65/1.31 thf(f5,negated_conjecture,(
% 1.65/1.31 ~(dsetconstrI => (powersetI => ! [X1 : $o] : (X1 => (in @ emptyset @ (prop2set @ X1)))))),
% 1.65/1.31 inference(negated_conjecture,[status(cth)],[f4])).
% 1.65/1.31 thf(f4,conjecture,(
% 1.65/1.31 dsetconstrI => (powersetI => ! [X1 : $o] : (X1 => (in @ emptyset @ (prop2set @ X1))))),
% 1.65/1.31 file('/export/starexec/sandbox/tmp/tmp.YkXdK0oz2p/DTF2THF_5209.p',prop2setI)).
% 1.65/1.31 thf(f24,plain,(
% 1.65/1.31 (powersetI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))))),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f10])).
% 1.65/1.31 thf(f10,plain,(
% 1.65/1.31 (powersetI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))))),
% 1.65/1.31 inference(fool_elimination,[status(thm)],[f9])).
% 1.65/1.31 thf(f9,plain,(
% 1.65/1.31 (powersetI = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (in @ X0 @ (powerset @ X1))))),
% 1.65/1.31 inference(rectify,[status(thm)],[f3])).
% 1.65/1.31 thf(f3,axiom,(
% 1.65/1.31 (powersetI = ! [X4 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X4) => (in @ X2 @ X0)) => (in @ X4 @ (powerset @ X0))))),
% 1.65/1.31 file('/export/starexec/sandbox/tmp/tmp.YkXdK0oz2p/DTF2THF_5209.p',powersetI)).
% 1.65/1.31 thf(f46,plain,(
% 1.65/1.31 ( ! [X2 : $i,X1 : $i] : (((in @ (sK2 @ X1 @ X2) @ X1) = $false) | ((in @ X2 @ (powerset @ X1)) = $true)) )),
% 1.65/1.31 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.65/1.31 thf(f59,plain,(
% 1.65/1.31 ((in @ emptyset @ (powerset @ emptyset)) = $false)),
% 1.65/1.31 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.65/1.31 thf(f58,plain,(
% 1.65/1.31 ((in @ emptyset @ (powerset @ emptyset)) = $false) | ($true = $false)),
% 1.65/1.31 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.65/1.31 thf(f57,plain,(
% 1.65/1.31 ((in @ emptyset @ (powerset @ emptyset)) = $false) | ($false = ((^[Y0 : $i]: ($true)) @ emptyset))),
% 1.65/1.31 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 1.65/1.31 thf(f56,plain,(
% 1.65/1.31 ($true != $true) | ($false = ((^[Y0 : $i]: ($true)) @ emptyset)) | ((in @ emptyset @ (powerset @ emptyset)) = $false)),
% 1.65/1.31 inference(superposition,[status(thm)],[f29,f38])).
% 1.65/1.31 thf(f38,plain,(
% 1.65/1.31 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = (in @ X2 @ (dsetconstr @ X1 @ X3))) | ((X3 @ X2) = $false) | ($false = (in @ X2 @ X1))) )),
% 1.65/1.31 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.65/1.31 thf(f37,plain,(
% 1.65/1.31 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((X3 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ X3))) = $true) | ($false = (in @ X2 @ X1))) )),
% 1.65/1.31 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.65/1.31 thf(f36,plain,(
% 1.65/1.31 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((in @ X2 @ X1) => ((X3 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ X3)))) = $true)) )),
% 1.65/1.31 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.65/1.31 thf(f35,plain,(
% 1.65/1.31 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: ((in @ X2 @ X1) => ((Y0 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ Y0))))) @ X3))) )),
% 1.65/1.31 inference(pi_clausification,[status(thm)],[f34])).
% 1.65/1.31 thf(f34,plain,(
% 1.65/1.31 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X2 @ X1) => ((Y0 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ Y0)))))))) )),
% 1.65/1.31 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.65/1.31 thf(f33,plain,(
% 1.65/1.31 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ X1) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ X1 @ Y1))))))) @ X2))) )),
% 1.65/1.31 inference(pi_clausification,[status(thm)],[f32])).
% 1.65/1.31 thf(f32,plain,(
% 1.65/1.31 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ X1) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ X1 @ Y1)))))))))) )),
% 1.65/1.31 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.65/1.31 thf(f31,plain,(
% 1.65/1.31 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2))))))))) @ X1))) )),
% 1.65/1.31 inference(pi_clausification,[status(thm)],[f30])).
% 1.65/1.31 thf(f30,plain,(
% 1.65/1.31 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) = $true)),
% 1.65/1.31 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.65/1.31 thf(f28,plain,(
% 1.65/1.31 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 1.65/1.31 inference(definition_unfolding,[status(thm)],[f25,f19])).
% 1.65/1.31 thf(f19,plain,(
% 1.65/1.31 (dsetconstrI = $true)),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f18])).
% 1.65/1.31 thf(f25,plain,(
% 1.65/1.31 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f8])).
% 1.65/1.31 thf(f8,plain,(
% 1.65/1.31 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 1.65/1.31 inference(fool_elimination,[status(thm)],[f7])).
% 1.65/1.31 thf(f7,plain,(
% 1.65/1.31 (! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ((X0 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X0 @ X3)))))) = dsetconstrI)),
% 1.65/1.31 inference(rectify,[status(thm)],[f1])).
% 1.65/1.31 thf(f1,axiom,(
% 1.65/1.31 (! [X1 : $i > $o,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))) = dsetconstrI)),
% 1.65/1.31 file('/export/starexec/sandbox/tmp/tmp.YkXdK0oz2p/DTF2THF_5209.p',dsetconstrI)).
% 1.65/1.31 thf(f29,plain,(
% 1.65/1.31 ($true != (in @ emptyset @ (dsetconstr @ (powerset @ emptyset) @ (^[Y0 : $i]: ($true)))))),
% 1.65/1.31 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.65/1.31 thf(f26,plain,(
% 1.65/1.31 ((in @ emptyset @ ((^[Y0 : $o]: (dsetconstr @ (powerset @ emptyset) @ (^[Y1 : $i]: (Y0)))) @ $true)) != $true)),
% 1.65/1.31 inference(definition_unfolding,[status(thm)],[f21,f23,f20])).
% 1.65/1.31 thf(f20,plain,(
% 1.65/1.31 ($true = sK0)),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f18])).
% 1.65/1.31 thf(f23,plain,(
% 1.65/1.31 (prop2set = (^[Y0 : $o]: (dsetconstr @ (powerset @ emptyset) @ (^[Y1 : $i]: (Y0)))))),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f12])).
% 1.65/1.31 thf(f12,plain,(
% 1.65/1.31 (prop2set = (^[Y0 : $o]: (dsetconstr @ (powerset @ emptyset) @ (^[Y1 : $i]: (Y0)))))),
% 1.65/1.31 inference(fool_elimination,[status(thm)],[f11])).
% 1.65/1.31 thf(f11,plain,(
% 1.65/1.31 (prop2set = (^[X0 : $o] : (dsetconstr @ (powerset @ emptyset) @ (^[X1 : $i] : (X0)))))),
% 1.65/1.31 inference(rectify,[status(thm)],[f2])).
% 1.65/1.31 thf(f2,axiom,(
% 1.65/1.31 (prop2set = (^[X1 : $o] : (dsetconstr @ (powerset @ emptyset) @ (^[X2 : $i] : (X1)))))),
% 1.65/1.31 file('/export/starexec/sandbox/tmp/tmp.YkXdK0oz2p/DTF2THF_5209.p',prop2set)).
% 1.65/1.31 thf(f21,plain,(
% 1.65/1.31 ((in @ emptyset @ (prop2set @ sK0)) != $true)),
% 1.65/1.31 inference(cnf_transformation,[status(thm)],[f18])).
% 1.65/1.31 % SZS output end Proof for DTF2THF_5209
% 1.65/1.31 % (5492)------------------------------
% 1.65/1.31 % (5492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.31 % (5492)Termination reason: Refutation
% 1.65/1.31
% 1.65/1.31 % (5492)Memory used [KB]: 5500
% 1.65/1.31 % (5492)Time elapsed: 0.008 s
% 1.65/1.31 % (5492)Instructions burned: 6 (million)
% 1.65/1.31 % (5492)------------------------------
% 1.65/1.31 % (5492)------------------------------
% 1.65/1.31 % (5489)Success in time 0.022 s
%------------------------------------------------------------------------------