%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU581^2 : 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 : n021.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 09:35:24 AM UTC 2026
% Result : Theorem 1.47s 1.29s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 178 ( 43 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 262 ( 11 ~; 2 |; 6 &; 207 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 10 usr; 6 con; 0-2 aty)
% ( 18 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 77 ( 37 ^; 34 !; 6 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_3,type,
subset: $i > $i > $o ).
thf(func_def_7,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_16,type,
sK1: $i > $o ).
thf(func_def_18,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f39,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
$true != $true,
inference(superposition,[status(thm)],[f33,f36]) ).
thf(f36,plain,
! [X0: $i,X1: $i > $o] :
( ( subset @ ( dsetconstr @ X0 @ X1 ) @ X0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f35]) ).
thf(f35,plain,
! [X0: $i,X1: $i > $o] :
( ( ( subset @ ( dsetconstr @ X0 @ X1 ) @ X0 )
= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f32,f27]) ).
thf(f27,plain,
! [X2: $i > $o,X1: $i] :
( ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] : ( in @ ( dsetconstr @ X1 @ Y0 ) @ ( powerset @ X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] : ( in @ ( dsetconstr @ X1 @ Y0 ) @ ( powerset @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] : ( in @ ( dsetconstr @ Y0 @ Y1 ) @ ( powerset @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] : ( in @ ( dsetconstr @ Y0 @ Y1 ) @ ( powerset @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( in
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ ( powerset @ Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f20,f18]) ).
thf(f18,plain,
sepInPowerset = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $true
!= ( subset
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) )
@ sK0 ) )
& ( sepInPowerset = $true )
& ( powersetE1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i > $o] :
( ( subset
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ X0 )
!= $true )
=> ( $true
!= ( subset
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) )
@ sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X0: $i,X1: $i > $o] :
( ( subset
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ X0 )
!= $true )
& ( sepInPowerset = $true )
& ( powersetE1 = $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i > $o] :
( ( subset
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ X0 )
!= $true )
& ( sepInPowerset = $true )
& ( powersetE1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( powersetE1 = $true )
=> ( ( sepInPowerset = $true )
=> ! [X0: $i,X1: $i > $o] :
( ( subset
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( powersetE1
=> ( sepInPowerset
=> ! [X0: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X0 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( powersetE1
=> ( sepInPowerset
=> ! [X0: $i,X2: $i > $o] :
( subset
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) )
@ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( powersetE1
=> ( sepInPowerset
=> ! [X0: $i,X2: $i > $o] :
( subset
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) )
@ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zqQYHvso56/DTF2THF_15369.p',sepSubset) ).
thf(f20,plain,
( sepInPowerset
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( in
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ ( powerset @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( sepInPowerset
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( in
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
@ ( powerset @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i > $o,X1: $i] :
( ( in
@ ( dsetconstr @ X1
@ ^ [X2: $i] : ( X0 @ X2 ) )
@ ( powerset @ X1 ) )
= sepInPowerset ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X2: $i > $o,X0: $i] :
( ( in
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) )
@ ( powerset @ X0 ) )
= sepInPowerset ),
file('/export/starexec/sandbox/tmp/tmp.zqQYHvso56/DTF2THF_15369.p',sepInPowerset) ).
thf(f32,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( powerset @ X2 ) ) )
| ( ( subset @ X1 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X2 ) )
=> ( subset @ X1 @ X2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( subset @ X1 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( powerset @ Y0 ) )
=> ( subset @ X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f17,f16]) ).
thf(f16,plain,
( powersetE1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( powersetE1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( powerset @ Y1 ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ X0 ) )
= powersetE1 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ X0 ) )
= powersetE1 ),
file('/export/starexec/sandbox/tmp/tmp.zqQYHvso56/DTF2THF_15369.p',powersetE1) ).
thf(f17,plain,
powersetE1 = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f33,plain,
( ( subset @ ( dsetconstr @ sK0 @ sK1 ) @ sK0 )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
( $true
!= ( subset
@ ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) )
@ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU581^2 : TPTP v9.2.1. Released v3.7.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n021.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:27:38 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SEU581^2 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.46 % Domain : Set Theory
% 0.29/0.46 % Problem : Preliminary Notions - Relations on Sets - Subsets
% 0.29/0.46 % Version : Especial > Reduced > Especial.
% 0.29/0.46 % English : (! A:i.! phi:i>o.subset (dsetconstr A (^ x:i.phi x)) A)
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.46 % Source : [Bro08]
% 0.29/0.46 % Names : ZFC083l [Bro08]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.00 v8.2.0, 0.23 v8.1.0, 0.09 v7.5.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v3.7.0
% 0.29/0.46 % Syntax : Number of formulae : 9 ( 2 unt; 6 typ; 2 def)
% 0.29/0.46 % Number of atoms : 10 ( 2 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 3 ( 3 avg)
% 0.29/0.46 % Number of connectives : 19 ( 0 ~; 0 |; 0 &; 16 @)
% 0.29/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 10 ( 4 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% 0.29/0.46 % Number of variables : 8 ( 2 ^; 6 !; 0 ?; 8 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : http://mathgate.info/detsetitem.php?id=259
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(in_type,type,
% 0.29/0.46 in: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(powerset_type,type,
% 0.29/0.46 powerset: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstr_type,type,
% 0.29/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(subset_type,type,
% 0.29/0.46 subset: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE1_type,type,
% 0.29/0.46 powersetE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE1,definition,
% 0.29/0.46 ( powersetE1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sepInPowerset_type,type,
% 0.29/0.46 sepInPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(sepInPowerset,definition,
% 0.29/0.46 ( sepInPowerset
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( in
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sepSubset,conjecture,
% 0.29/0.46 ( powersetE1
% 0.29/0.46 => ( sepInPowerset
% 0.29/0.46 => ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( subset
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.47/1.26 ---- Embedded in THF ---
% 1.47/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.26 %%% Generated on Tue Feb 24 12:27:39 EST 2026
% 1.47/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.26 %%% Logic specification used:
% 1.47/1.26 %%% thf(spec, logic, $$dhol).
% 1.47/1.26
% 1.47/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.zqQYHvso56/DTF2DTF15369.p
% See solution above
% 1.47/1.26 ------------------------
% 1.47/1.27 ---- Cleaned THF ---
% 1.47/1.27 thf(in_type,type,
% 1.47/1.27 in: $i > $i > $o ).
% 1.47/1.27
% 1.47/1.27 thf(powerset_type,type,
% 1.47/1.27 powerset: $i > $i ).
% 1.47/1.27
% 1.47/1.27 thf(dsetconstr_type,type,
% 1.47/1.27 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.47/1.27
% 1.47/1.27 thf(subset_type,type,
% 1.47/1.27 subset: $i > $i > $o ).
% 1.47/1.27
% 1.47/1.27 thf(powersetE1_type,type,
% 1.47/1.27 powersetE1: $o ).
% 1.47/1.27
% 1.47/1.27 thf(powersetE1,definition,
% 1.47/1.27 ( powersetE1
% 1.47/1.27 = ( ! [A: $i,B: $i] :
% 1.47/1.27 ( ( in @ B @ ( powerset @ A ) )
% 1.47/1.27 => ( subset @ B @ A ) ) ) ) ).
% 1.47/1.27
% 1.47/1.27 thf(sepInPowerset_type,type,
% 1.47/1.27 sepInPowerset: $o ).
% 1.47/1.27
% 1.47/1.27 thf(sepInPowerset,definition,
% 1.47/1.27 ( sepInPowerset
% 1.47/1.27 = ( ! [A: $i,Xphi: $i > $o] :
% 1.47/1.27 ( in
% 1.47/1.27 @ ( dsetconstr @ A
% 1.47/1.27 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.47/1.27 @ ( powerset @ A ) ) ) ) ).
% 1.47/1.27
% 1.47/1.27 thf(sepSubset,conjecture,
% 1.47/1.27 ( powersetE1
% 1.47/1.27 => ( sepInPowerset
% 1.47/1.27 => ! [A: $i,Xphi: $i > $o] :
% 1.47/1.27 ( subset
% 1.47/1.27 @ ( dsetconstr @ A
% 1.47/1.27 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.47/1.27 @ A ) ) ) ).
% 1.47/1.27 ------------------------
% 1.47/1.29 % (15661)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_15369 for (2999ds/27Mi)
% 1.47/1.29 % (15661)First to succeed.
% 1.47/1.29 % (15661)Refutation found. Thanks to Tanya!
% 1.47/1.29 % SZS status Theorem for DTF2THF_15369
% 1.47/1.29 % SZS output start Proof for DTF2THF_15369
% 1.47/1.29 thf(func_def_0, type, in: $i > $i > $o).
% 1.47/1.29 thf(func_def_1, type, powerset: $i > $i).
% 1.47/1.29 thf(func_def_2, type, dsetconstr: $i > ($i > $o) > $i).
% 1.47/1.29 thf(func_def_3, type, subset: $i > $i > $o).
% 1.47/1.29 thf(func_def_7, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.47/1.29 thf(func_def_16, type, sK1: $i > $o).
% 1.47/1.29 thf(func_def_18, type, ph3: !>[X0: $tType]:(X0)).
% 1.47/1.29 thf(f39,plain,(
% 1.47/1.29 $false),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.47/1.29 thf(f38,plain,(
% 1.47/1.29 ($true != $true)),
% 1.47/1.29 inference(superposition,[status(thm)],[f33,f36])).
% 1.47/1.29 thf(f36,plain,(
% 1.47/1.29 ( ! [X0 : $i,X1 : $i > $o] : (((subset @ (dsetconstr @ X0 @ X1) @ X0) = $true)) )),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f35])).
% 1.47/1.29 thf(f35,plain,(
% 1.47/1.29 ( ! [X0 : $i,X1 : $i > $o] : (((subset @ (dsetconstr @ X0 @ X1) @ X0) = $true) | ($false = $true)) )),
% 1.47/1.29 inference(superposition,[status(thm)],[f32,f27])).
% 1.47/1.29 thf(f27,plain,(
% 1.47/1.29 ( ! [X2 : $i > $o,X1 : $i] : (((in @ (dsetconstr @ X1 @ X2) @ (powerset @ X1)) = $true)) )),
% 1.47/1.29 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.47/1.29 thf(f26,plain,(
% 1.47/1.29 ( ! [X2 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: (in @ (dsetconstr @ X1 @ Y0) @ (powerset @ X1))) @ X2) = $true)) )),
% 1.47/1.29 inference(pi_clausification,[status(thm)],[f25])).
% 1.47/1.29 thf(f25,plain,(
% 1.47/1.29 ( ! [X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (in @ (dsetconstr @ X1 @ Y0) @ (powerset @ X1)))) = $true)) )),
% 1.47/1.29 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.47/1.29 thf(f24,plain,(
% 1.47/1.29 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0))))) @ X1) = $true)) )),
% 1.47/1.29 inference(pi_clausification,[status(thm)],[f23])).
% 1.47/1.29 thf(f23,plain,(
% 1.47/1.29 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))))),
% 1.47/1.29 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.47/1.29 thf(f22,plain,(
% 1.47/1.29 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) @ (powerset @ Y0)))))))),
% 1.47/1.29 inference(definition_unfolding,[status(thm)],[f20,f18])).
% 1.47/1.29 thf(f18,plain,(
% 1.47/1.29 (sepInPowerset = $true)),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f15])).
% 1.47/1.29 thf(f15,plain,(
% 1.47/1.29 ($true != (subset @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (sK1 @ Y0))) @ sK0)) & (sepInPowerset = $true) & (powersetE1 = $true)),
% 1.47/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f14])).
% 1.47/1.29 thf(f14,plain,(
% 1.47/1.29 ? [X0 : $i,X1 : $i > $o] : ((subset @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ X0) != $true) => ($true != (subset @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (sK1 @ Y0))) @ sK0))),
% 1.47/1.29 introduced(definition,[],[choice_axiom])).
% 1.47/1.29 thf(f13,plain,(
% 1.47/1.29 ? [X0 : $i,X1 : $i > $o] : ((subset @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ X0) != $true) & (sepInPowerset = $true) & (powersetE1 = $true)),
% 1.47/1.29 inference(flattening,[status(thm)],[f12])).
% 1.47/1.29 thf(f12,plain,(
% 1.47/1.29 (? [X0 : $i,X1 : $i > $o] : ((subset @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ X0) != $true) & (sepInPowerset = $true)) & (powersetE1 = $true)),
% 1.47/1.29 inference(ennf_transformation,[status(thm)],[f9])).
% 1.47/1.29 thf(f9,plain,(
% 1.47/1.29 ~((powersetE1 = $true) => ((sepInPowerset = $true) => ! [X0 : $i,X1 : $i > $o] : ((subset @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ X0) = $true)))),
% 1.47/1.29 inference(fool_elimination,[status(thm)],[f8])).
% 1.47/1.29 thf(f8,plain,(
% 1.47/1.29 ~(powersetE1 => (sepInPowerset => ! [X0 : $i,X1 : $i > $o] : (subset @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))) @ X0)))),
% 1.47/1.29 inference(rectify,[status(thm)],[f4])).
% 1.47/1.29 thf(f4,negated_conjecture,(
% 1.47/1.29 ~(powersetE1 => (sepInPowerset => ! [X0 : $i,X2 : $i > $o] : (subset @ (dsetconstr @ X0 @ (^[X3 : $i] : (X2 @ X3))) @ X0)))),
% 1.47/1.29 inference(negated_conjecture,[status(cth)],[f3])).
% 1.47/1.29 thf(f3,conjecture,(
% 1.47/1.29 powersetE1 => (sepInPowerset => ! [X0 : $i,X2 : $i > $o] : (subset @ (dsetconstr @ X0 @ (^[X3 : $i] : (X2 @ X3))) @ X0))),
% 1.47/1.29 file('/export/starexec/sandbox/tmp/tmp.zqQYHvso56/DTF2THF_15369.p',sepSubset)).
% 1.47/1.29 thf(f20,plain,(
% 1.47/1.29 (sepInPowerset = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) @ (powerset @ Y0)))))))),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f7])).
% 1.47/1.29 thf(f7,plain,(
% 1.47/1.29 (sepInPowerset = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) @ (powerset @ Y0)))))))),
% 1.47/1.29 inference(fool_elimination,[status(thm)],[f6])).
% 1.47/1.29 thf(f6,plain,(
% 1.47/1.29 (! [X0 : $i > $o,X1 : $i] : (in @ (dsetconstr @ X1 @ (^[X2 : $i] : (X0 @ X2))) @ (powerset @ X1)) = sepInPowerset)),
% 1.47/1.29 inference(rectify,[status(thm)],[f2])).
% 1.47/1.29 thf(f2,axiom,(
% 1.47/1.29 (! [X2 : $i > $o,X0 : $i] : (in @ (dsetconstr @ X0 @ (^[X3 : $i] : (X2 @ X3))) @ (powerset @ X0)) = sepInPowerset)),
% 1.47/1.29 file('/export/starexec/sandbox/tmp/tmp.zqQYHvso56/DTF2THF_15369.p',sepInPowerset)).
% 1.47/1.29 thf(f32,plain,(
% 1.47/1.29 ( ! [X2 : $i,X1 : $i] : (($false = (in @ X1 @ (powerset @ X2))) | ((subset @ X1 @ X2) = $true)) )),
% 1.47/1.29 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.47/1.29 thf(f31,plain,(
% 1.47/1.29 ( ! [X2 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2)) => (subset @ X1 @ X2)) = $true)) )),
% 1.47/1.29 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.47/1.29 thf(f30,plain,(
% 1.47/1.29 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (subset @ X1 @ Y0))) @ X2) = $true)) )),
% 1.47/1.29 inference(pi_clausification,[status(thm)],[f29])).
% 1.47/1.29 thf(f29,plain,(
% 1.47/1.29 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (subset @ X1 @ Y0)))))) )),
% 1.47/1.29 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.47/1.29 thf(f28,plain,(
% 1.47/1.29 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1))))) @ X1) = $true)) )),
% 1.47/1.29 inference(pi_clausification,[status(thm)],[f21])).
% 1.47/1.29 thf(f21,plain,(
% 1.47/1.29 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1)))))))),
% 1.47/1.29 inference(definition_unfolding,[status(thm)],[f17,f16])).
% 1.47/1.29 thf(f16,plain,(
% 1.47/1.29 (powersetE1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1)))))))),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.47/1.29 thf(f11,plain,(
% 1.47/1.29 (powersetE1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1)))))))),
% 1.47/1.29 inference(fool_elimination,[status(thm)],[f10])).
% 1.47/1.29 thf(f10,plain,(
% 1.47/1.29 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ X0)) = powersetE1)),
% 1.47/1.29 inference(rectify,[status(thm)],[f1])).
% 1.47/1.29 thf(f1,axiom,(
% 1.47/1.29 (! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ X0)) = powersetE1)),
% 1.47/1.29 file('/export/starexec/sandbox/tmp/tmp.zqQYHvso56/DTF2THF_15369.p',powersetE1)).
% 1.47/1.29 thf(f17,plain,(
% 1.47/1.29 (powersetE1 = $true)),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f15])).
% 1.47/1.29 thf(f33,plain,(
% 1.47/1.29 ((subset @ (dsetconstr @ sK0 @ sK1) @ sK0) != $true)),
% 1.47/1.29 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.47/1.29 thf(f19,plain,(
% 1.47/1.29 ($true != (subset @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (sK1 @ Y0))) @ sK0))),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f15])).
% 1.47/1.29 % SZS output end Proof for DTF2THF_15369
% 1.47/1.29 % (15661)------------------------------
% 1.47/1.29 % (15661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (15661)Termination reason: Refutation
% 1.47/1.29
% 1.47/1.29 % (15661)Memory used [KB]: 5500
% 1.47/1.29 % (15661)Time elapsed: 0.003 s
% 1.47/1.29 % (15661)Instructions burned: 3 (million)
% 1.47/1.29 % (15661)------------------------------
% 1.47/1.29 % (15661)------------------------------
% 1.47/1.29 % (15658)Success in time 0.013 s
%------------------------------------------------------------------------------