%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU500^2 : 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 : 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 09:34:57 AM UTC 2026
% Result : Theorem 1.47s 1.29s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 208 ( 66 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 220 ( 27 ~; 17 |; 14 &; 147 @)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 82 ( 28 ^; 41 !; 13 ?; 82 :)
% 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_16,type,
sK4: $i > $o ).
thf(func_def_19,type,
ph6:
!>[X0: $tType] : X0 ).
thf(f37,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f36,f21]) ).
thf(f21,plain,
sK1 != $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $true
= ( in @ sK0 @ ( prop2set @ sK1 ) ) )
& ( sK1 != $true )
& ( dsetconstrER = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $o] :
( ( $true
= ( in @ X0 @ ( prop2set @ X1 ) ) )
& ( $true != X1 ) )
=> ( ( $true
= ( in @ sK0 @ ( prop2set @ sK1 ) ) )
& ( sK1 != $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X0: $i,X1: $o] :
( ( $true
= ( in @ X0 @ ( prop2set @ X1 ) ) )
& ( $true != X1 ) )
& ( dsetconstrER = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( dsetconstrER = $true )
=> ! [X0: $i,X1: $o] :
( ( $true
= ( in @ X0 @ ( prop2set @ X1 ) ) )
=> ( $true = X1 ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( dsetconstrER
=> ! [X0: $i,X1: $o] :
( ( in @ X0 @ ( prop2set @ X1 ) )
=> X1 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( dsetconstrER
=> ! [X2: $i,X1: $o] :
( ( in @ X2 @ ( prop2set @ X1 ) )
=> X1 ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( dsetconstrER
=> ! [X2: $i,X1: $o] :
( ( in @ X2 @ ( prop2set @ X1 ) )
=> X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.jivRvTfJiD/DTF2THF_600.p',prop2setE) ).
thf(f36,plain,
sK1 = $true,
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
( $true
= ( ^ [Y0: $i] : sK1
@ sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true != $true )
| ( $true
= ( ^ [Y0: $i] : sK1
@ sK0 ) ) ),
inference(superposition,[status(thm)],[f33,f31]) ).
thf(f31,plain,
( ( in @ sK0
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y0: $i] : sK1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
( $true
= ( in @ sK0
@ ( ^ [Y0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y1: $i] : Y0 )
@ sK1 ) ) ),
inference(definition_unfolding,[status(thm)],[f22,f26]) ).
thf(f26,plain,
( prop2set
= ( ^ [Y0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y1: $i] : Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( prop2set
= ( ^ [Y0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y1: $i] : Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,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.jivRvTfJiD/DTF2THF_600.p',prop2set) ).
thf(f22,plain,
( $true
= ( in @ sK0 @ ( prop2set @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f33,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( dsetconstr @ X0 @ X2 ) ) )
| ( $true
= ( X2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( $true
= ( X2 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( $true != $true )
| ( $true
= ( X2 @ X1 ) ) ),
inference(definition_unfolding,[status(thm)],[f25,f20]) ).
thf(f20,plain,
dsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f25,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( $true
= ( X2 @ X1 ) )
| ( dsetconstrER != $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( $true
= ( X2 @ X1 ) ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ( ( $true
= ( in @ sK3
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( sK4 @ Y0 ) ) ) )
& ( $true
!= ( sK4 @ sK3 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f17,f18]) ).
thf(f18,plain,
( ? [X3: $i,X4: $i,X5: $i > $o] :
( ( $true
= ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) )
& ( $true
!= ( X5 @ X4 ) ) )
=> ( ( $true
= ( in @ sK3
@ ( dsetconstr @ sK2
@ ^ [Y0: $i] : ( sK4 @ Y0 ) ) ) )
& ( $true
!= ( sK4 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( $true
= ( X2 @ X1 ) ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X3: $i,X4: $i,X5: $i > $o] :
( ( $true
= ( in @ X4
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) )
& ( $true
!= ( X5 @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( $true
= ( X2 @ X1 ) ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
& ( $true
!= ( X2 @ X1 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
| ( $true
= ( X2 @ X1 ) ) )
<=> ( dsetconstrER = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
= ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) )
=> ( $true
= ( X2 @ X1 ) ) )
<=> ( dsetconstrER = $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( dsetconstrER
= ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) ) )
=> ( X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( dsetconstrER
= ( ! [X0: $i,X2: $i,X1: $i > $o] :
( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.jivRvTfJiD/DTF2THF_600.p',dsetconstrER) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU500^2 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n009.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:24:10 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/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 : SEU500^2 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.47 % Domain : Set Theory
% 0.28/0.47 % Problem : Preliminary Notions - Propositions as Sets
% 0.28/0.47 % Version : Especial > Reduced > Especial.
% 0.28/0.47 % English : (! phi:o.! x:i.in x (prop2set phi) -> phi)
% 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 : ZFC002l [Bro08]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % 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, 0.29 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 v3.7.0
% 0.28/0.47 % Syntax : Number of formulae : 9 ( 2 unt; 6 typ; 2 def)
% 0.28/0.47 % Number of atoms : 6 ( 2 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 2 ( 2 avg)
% 0.28/0.47 % Number of connectives : 15 ( 0 ~; 0 |; 0 &; 12 @)
% 0.28/0.47 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 7 ( 3 avg)
% 0.28/0.47 % Number of types : 2 ( 0 usr)
% 0.28/0.47 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% 0.28/0.47 % Number of variables : 8 ( 3 ^; 5 !; 0 ?; 8 :)
% 0.28/0.47 % SPC : TH0_THM_EQU_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : http://mathgate.info/detsetitem.php?id=53
% 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(powerset_type,type,
% 0.28/0.47 powerset: $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstr_type,type,
% 0.28/0.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrER_type,type,
% 0.28/0.47 dsetconstrER: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrER,definition,
% 0.28/0.47 ( dsetconstrER
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(prop2set_type,type,
% 0.28/0.47 prop2set: $o > $i ).
% 0.28/0.47
% 0.28/0.47 thf(prop2set,definition,
% 0.28/0.47 ( prop2set
% 0.28/0.47 = ( ^ [Xphi: $o] :
% 0.28/0.47 ( dsetconstr @ ( powerset @ emptyset )
% 0.28/0.47 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(prop2setE,conjecture,
% 0.28/0.47 ( dsetconstrER
% 0.28/0.47 => ! [Xphi: $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.28/0.47 => Xphi ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 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 12:24:11 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.jivRvTfJiD/DTF2DTF600.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(emptyset_type,type,
% 1.47/1.27 emptyset: $i ).
% 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(dsetconstrER_type,type,
% 1.47/1.27 dsetconstrER: $o ).
% 1.47/1.27
% 1.47/1.27 thf(dsetconstrER,definition,
% 1.47/1.27 ( dsetconstrER
% 1.47/1.27 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.47/1.27 ( ( in @ Xx
% 1.47/1.27 @ ( dsetconstr @ A
% 1.47/1.27 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.47/1.27 => ( Xphi @ Xx ) ) ) ) ).
% 1.47/1.27
% 1.47/1.27 thf(prop2set_type,type,
% 1.47/1.27 prop2set: $o > $i ).
% 1.47/1.27
% 1.47/1.27 thf(prop2set,definition,
% 1.47/1.27 ( prop2set
% 1.47/1.27 = ( ^ [Xphi: $o] :
% 1.47/1.27 ( dsetconstr @ ( powerset @ emptyset )
% 1.47/1.27 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 1.47/1.27
% 1.47/1.27 thf(prop2setE,conjecture,
% 1.47/1.27 ( dsetconstrER
% 1.47/1.27 => ! [Xphi: $o,Xx: $i] :
% 1.47/1.27 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 1.47/1.27 => Xphi ) ) ).
% 1.47/1.27 ------------------------
% 1.47/1.28 % (744)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_600 for (3000ds/18Mi)
% 1.47/1.28 % (738)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_600 for (3000ds/183Mi)
% 1.47/1.28 % (744)First to succeed.
% 1.47/1.29 % (738)Also succeeded, but the first one will report.
% 1.47/1.29 % (744)Refutation found. Thanks to Tanya!
% 1.47/1.29 % SZS status Theorem for DTF2THF_600
% 1.47/1.29 % SZS output start Proof for DTF2THF_600
% 1.47/1.29 thf(func_def_0, type, in: $i > $i > $o).
% 1.47/1.29 thf(func_def_2, type, powerset: $i > $i).
% 1.47/1.29 thf(func_def_3, type, dsetconstr: $i > ($i > $o) > $i).
% 1.47/1.29 thf(func_def_6, type, prop2set: $o > $i).
% 1.47/1.29 thf(func_def_16, type, sK4: $i > $o).
% 1.47/1.29 thf(func_def_19, type, ph6: !>[X0: $tType]:(X0)).
% 1.47/1.29 thf(f37,plain,(
% 1.47/1.29 $false),
% 1.47/1.29 inference(subsumption_resolution,[status(thm)],[f36,f21])).
% 1.47/1.29 thf(f21,plain,(
% 1.47/1.29 (sK1 != $true)),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f15])).
% 1.47/1.29 thf(f15,plain,(
% 1.47/1.29 (($true = (in @ sK0 @ (prop2set @ sK1))) & (sK1 != $true)) & (dsetconstrER = $true)),
% 1.47/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f14])).
% 1.47/1.29 thf(f14,plain,(
% 1.47/1.29 ? [X0 : $i,X1 : $o] : (($true = (in @ X0 @ (prop2set @ X1))) & ($true != X1)) => (($true = (in @ sK0 @ (prop2set @ sK1))) & (sK1 != $true))),
% 1.47/1.29 introduced(definition,[],[choice_axiom])).
% 1.47/1.29 thf(f12,plain,(
% 1.47/1.29 ? [X0 : $i,X1 : $o] : (($true = (in @ X0 @ (prop2set @ X1))) & ($true != X1)) & (dsetconstrER = $true)),
% 1.47/1.29 inference(ennf_transformation,[status(thm)],[f7])).
% 1.47/1.29 thf(f7,plain,(
% 1.47/1.29 ~((dsetconstrER = $true) => ! [X0 : $i,X1 : $o] : (($true = (in @ X0 @ (prop2set @ X1))) => ($true = X1)))),
% 1.47/1.29 inference(fool_elimination,[status(thm)],[f6])).
% 1.47/1.29 thf(f6,plain,(
% 1.47/1.29 ~(dsetconstrER => ! [X0 : $i,X1 : $o] : ((in @ X0 @ (prop2set @ X1)) => X1))),
% 1.47/1.29 inference(rectify,[status(thm)],[f4])).
% 1.47/1.29 thf(f4,negated_conjecture,(
% 1.47/1.29 ~(dsetconstrER => ! [X2 : $i,X1 : $o] : ((in @ X2 @ (prop2set @ X1)) => X1))),
% 1.47/1.29 inference(negated_conjecture,[status(cth)],[f3])).
% 1.47/1.29 thf(f3,conjecture,(
% 1.47/1.29 dsetconstrER => ! [X2 : $i,X1 : $o] : ((in @ X2 @ (prop2set @ X1)) => X1)),
% 1.47/1.29 file('/export/starexec/sandbox/tmp/tmp.jivRvTfJiD/DTF2THF_600.p',prop2setE)).
% 1.47/1.29 thf(f36,plain,(
% 1.47/1.29 (sK1 = $true)),
% 1.47/1.29 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.47/1.29 thf(f35,plain,(
% 1.47/1.29 ($true = ((^[Y0 : $i]: (sK1)) @ sK0))),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.47/1.29 thf(f34,plain,(
% 1.47/1.29 ($true != $true) | ($true = ((^[Y0 : $i]: (sK1)) @ sK0))),
% 1.47/1.29 inference(superposition,[status(thm)],[f33,f31])).
% 1.47/1.29 thf(f31,plain,(
% 1.47/1.29 ((in @ sK0 @ (dsetconstr @ (powerset @ emptyset) @ (^[Y0 : $i]: (sK1)))) = $true)),
% 1.47/1.29 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.47/1.29 thf(f27,plain,(
% 1.47/1.29 ($true = (in @ sK0 @ ((^[Y0 : $o]: (dsetconstr @ (powerset @ emptyset) @ (^[Y1 : $i]: (Y0)))) @ sK1)))),
% 1.47/1.29 inference(definition_unfolding,[status(thm)],[f22,f26])).
% 1.47/1.29 thf(f26,plain,(
% 1.47/1.29 (prop2set = (^[Y0 : $o]: (dsetconstr @ (powerset @ emptyset) @ (^[Y1 : $i]: (Y0)))))),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.47/1.29 thf(f9,plain,(
% 1.47/1.29 (prop2set = (^[Y0 : $o]: (dsetconstr @ (powerset @ emptyset) @ (^[Y1 : $i]: (Y0)))))),
% 1.47/1.29 inference(fool_elimination,[status(thm)],[f8])).
% 1.47/1.29 thf(f8,plain,(
% 1.47/1.29 (prop2set = (^[X0 : $o] : (dsetconstr @ (powerset @ emptyset) @ (^[X1 : $i] : (X0)))))),
% 1.47/1.29 inference(rectify,[status(thm)],[f2])).
% 1.47/1.29 thf(f2,axiom,(
% 1.47/1.29 (prop2set = (^[X1 : $o] : (dsetconstr @ (powerset @ emptyset) @ (^[X2 : $i] : (X1)))))),
% 1.47/1.29 file('/export/starexec/sandbox/tmp/tmp.jivRvTfJiD/DTF2THF_600.p',prop2set)).
% 1.47/1.29 thf(f22,plain,(
% 1.47/1.29 ($true = (in @ sK0 @ (prop2set @ sK1)))),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f15])).
% 1.47/1.29 thf(f33,plain,(
% 1.47/1.29 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (($true != (in @ X1 @ (dsetconstr @ X0 @ X2))) | ($true = (X2 @ X1))) )),
% 1.47/1.29 inference(beta_eta_normalization,[status(thm)],[f32])).
% 1.47/1.29 thf(f32,plain,(
% 1.47/1.29 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (($true != (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) | ($true = (X2 @ X1))) )),
% 1.47/1.29 inference(trivial_inequality_removal,[status(thm)],[f28])).
% 1.47/1.29 thf(f28,plain,(
% 1.47/1.29 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (($true != (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) | ($true != $true) | ($true = (X2 @ X1))) )),
% 1.47/1.29 inference(definition_unfolding,[status(thm)],[f25,f20])).
% 1.47/1.29 thf(f20,plain,(
% 1.47/1.29 (dsetconstrER = $true)),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f15])).
% 1.47/1.29 thf(f25,plain,(
% 1.47/1.29 ( ! [X2 : $i > $o,X0 : $i,X1 : $i] : (($true != (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) | ($true = (X2 @ X1)) | (dsetconstrER != $true)) )),
% 1.47/1.29 inference(cnf_transformation,[status(thm)],[f19])).
% 1.47/1.29 thf(f19,plain,(
% 1.47/1.29 (! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true != (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) | ($true = (X2 @ X1))) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | (($true = (in @ sK3 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (sK4 @ Y0))))) & ($true != (sK4 @ sK3))))),
% 1.47/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f17,f18])).
% 1.47/1.29 thf(f18,plain,(
% 1.47/1.29 ? [X3 : $i,X4 : $i,X5 : $i > $o] : (($true = (in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0))))) & ($true != (X5 @ X4))) => (($true = (in @ sK3 @ (dsetconstr @ sK2 @ (^[Y0 : $i]: (sK4 @ Y0))))) & ($true != (sK4 @ sK3)))),
% 1.47/1.29 introduced(definition,[],[choice_axiom])).
% 1.47/1.29 thf(f17,plain,(
% 1.47/1.29 (! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true != (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) | ($true = (X2 @ X1))) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X3 : $i,X4 : $i,X5 : $i > $o] : (($true = (in @ X4 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X5 @ Y0))))) & ($true != (X5 @ X4))))),
% 1.47/1.29 inference(rectify,[status(thm)],[f16])).
% 1.47/1.29 thf(f16,plain,(
% 1.47/1.29 (! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true != (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) | ($true = (X2 @ X1))) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X0 : $i,X1 : $i,X2 : $i > $o] : (($true = (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) & ($true != (X2 @ X1))))),
% 1.47/1.29 inference(nnf_transformation,[status(thm)],[f13])).
% 1.47/1.29 thf(f13,plain,(
% 1.47/1.29 ! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true != (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) | ($true = (X2 @ X1))) <=> (dsetconstrER = $true)),
% 1.47/1.29 inference(ennf_transformation,[status(thm)],[f11])).
% 1.47/1.29 thf(f11,plain,(
% 1.47/1.29 ! [X0 : $i,X1 : $i,X2 : $i > $o] : (($true = (in @ X1 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) => ($true = (X2 @ X1))) <=> (dsetconstrER = $true)),
% 1.47/1.29 inference(fool_elimination,[status(thm)],[f10])).
% 1.47/1.29 thf(f10,plain,(
% 1.47/1.29 (dsetconstrER = ! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X1 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X2 @ X3)))) => (X2 @ X1)))),
% 1.47/1.29 inference(rectify,[status(thm)],[f1])).
% 1.47/1.29 thf(f1,axiom,(
% 1.47/1.29 (dsetconstrER = ! [X0 : $i,X2 : $i,X1 : $i > $o] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)))),
% 1.47/1.29 file('/export/starexec/sandbox/tmp/tmp.jivRvTfJiD/DTF2THF_600.p',dsetconstrER)).
% 1.47/1.29 % SZS output end Proof for DTF2THF_600
% 1.47/1.29 % (744)------------------------------
% 1.47/1.29 % (744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (744)Termination reason: Refutation
% 1.47/1.29
% 1.47/1.29 % (744)Memory used [KB]: 5500
% 1.47/1.29 % (744)Time elapsed: 0.003 s
% 1.47/1.29 % (744)Instructions burned: 2 (million)
% 1.47/1.29 % (744)------------------------------
% 1.47/1.29 % (744)------------------------------
% 1.47/1.29 % (737)Success in time 0.004 s
%------------------------------------------------------------------------------