%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU644^2 : 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 : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:54 AM UTC 2026
% Result : Theorem 1.64s 1.30s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 227 ( 68 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 199 ( 20 ~; 8 |; 22 &; 130 @)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 10 usr; 9 con; 0-2 aty)
% ( 0 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 30 ( 10 ^; 12 !; 8 ?; 30 :)
% 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_7,type,
singleton: $i > $o ).
thf(f54,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f53,f49]) ).
thf(f49,plain,
( $true
= ( in @ sK5 @ sK3 ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( $true
= ( ( in @ sK5 @ sK3 )
& ( ( setadjoin @ sK5 @ emptyset )
= sK3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
& ( ( setadjoin @ Y0 @ emptyset )
= sK3 ) )
@ sK5 ) ),
inference(sigma_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK3 )
& ( ( setadjoin @ Y0 @ emptyset )
= sK3 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) )
@ sK3 )
= $true ),
inference(definition_unfolding,[status(thm)],[f36,f27]) ).
thf(f27,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( ( setadjoin @ Y1 @ emptyset )
= Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( singleton
= ( ^ [X0: $i] :
? [X1: $i] :
( ( ( setadjoin @ X1 @ emptyset )
= X0 )
& ( in @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( singleton
= ( ^ [X2: $i] :
? [X0: $i] :
( ( ( setadjoin @ X0 @ emptyset )
= X2 )
& ( in @ X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.9JG9QquUBW/DTF2THF_20142.p',singleton) ).
thf(f36,plain,
( $true
= ( singleton @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( $true
= ( singleton @ sK3 ) )
& ( $true
!= ( in @ ( setunion @ sK3 ) @ sK3 ) )
& ( setunionsingleton = $true )
& ( eqinunit = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f15,f25]) ).
thf(f25,plain,
( ? [X0: $i] :
( ( $true
= ( singleton @ X0 ) )
& ( $true
!= ( in @ ( setunion @ X0 ) @ X0 ) ) )
=> ( ( $true
= ( singleton @ sK3 ) )
& ( $true
!= ( in @ ( setunion @ sK3 ) @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ? [X0: $i] :
( ( $true
= ( singleton @ X0 ) )
& ( $true
!= ( in @ ( setunion @ X0 ) @ X0 ) ) )
& ( setunionsingleton = $true )
& ( eqinunit = $true ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ? [X0: $i] :
( ( $true
= ( singleton @ X0 ) )
& ( $true
!= ( in @ ( setunion @ X0 ) @ X0 ) ) )
& ( setunionsingleton = $true )
& ( eqinunit = $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( ( eqinunit = $true )
=> ( ( setunionsingleton = $true )
=> ! [X0: $i] :
( ( $true
= ( singleton @ X0 ) )
=> ( $true
= ( in @ ( setunion @ X0 ) @ X0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( eqinunit
=> ( setunionsingleton
=> ! [X0: $i] :
( ( singleton @ X0 )
=> ( in @ ( setunion @ X0 ) @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( eqinunit
=> ( setunionsingleton
=> ! [X3: $i] :
( ( singleton @ X3 )
=> ( in @ ( setunion @ X3 ) @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( eqinunit
=> ( setunionsingleton
=> ! [X3: $i] :
( ( singleton @ X3 )
=> ( in @ ( setunion @ X3 ) @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.9JG9QquUBW/DTF2THF_20142.p',theprop) ).
thf(f53,plain,
( $true
!= ( in @ sK5 @ sK3 ) ),
inference(backward_demodulation,[status(thm)],[f35,f52]) ).
thf(f52,plain,
( sK5
= ( setunion @ sK3 ) ),
inference(superposition,[status(thm)],[f44,f50]) ).
thf(f50,plain,
( ( setadjoin @ sK5 @ emptyset )
= sK3 ),
inference(equality_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( $true
= ( ( setadjoin @ sK5 @ emptyset )
= sK3 ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f44,plain,
! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: $i] :
( ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f32,f34]) ).
thf(f34,plain,
setunionsingleton = $true,
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f32,plain,
! [X0: $i] :
( ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( setunionsingleton != $true ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( setunionsingleton != $true ) )
& ( ( setunionsingleton = $true )
| ( sK2
!= ( setunion @ ( setadjoin @ sK2 @ emptyset ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f22,f23]) ).
thf(f23,plain,
( ? [X1: $i] :
( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
!= X1 )
=> ( sK2
!= ( setunion @ ( setadjoin @ sK2 @ emptyset ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ( ! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( setunionsingleton != $true ) )
& ( ( setunionsingleton = $true )
| ? [X1: $i] :
( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
!= X1 ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( setunionsingleton != $true ) )
& ( ( setunionsingleton = $true )
| ? [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
!= X0 ) ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
<=> ( setunionsingleton = $true ) ),
inference(fool_elimination,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $i] :
( ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
= setunionsingleton ),
file('/export/starexec/sandbox/tmp/tmp.9JG9QquUBW/DTF2THF_20142.p',setunionsingleton) ).
thf(f35,plain,
( $true
!= ( in @ ( setunion @ sK3 ) @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU644^2 : 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 : n016.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 12:30:21 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
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEU644^2 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : Ordered Pairs - Properties of Pairs
% 0.30/0.46 % Version : Especial > Reduced > Especial.
% 0.30/0.46 % English : (! X:i.singleton X -> in (setunion X) X)
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.46 % Source : [Bro08]
% 0.30/0.46 % Names : ZFC146l [Bro08]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 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 v4.0.0, 0.33 v3.7.0
% 0.30/0.46 % Syntax : Number of formulae : 11 ( 3 unt; 7 typ; 3 def)
% 0.30/0.46 % Number of atoms : 15 ( 6 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 4 ( 3 avg)
% 0.30/0.46 % Number of connectives : 20 ( 0 ~; 0 |; 1 &; 15 @)
% 0.30/0.46 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 8 ( 3 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 8 ( 7 usr; 3 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 6 ( 1 ^; 4 !; 1 ?; 6 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : http://mathgate.info/detsetitem.php?id=200
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(in_type,type,
% 0.30/0.46 in: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyset_type,type,
% 0.30/0.46 emptyset: $i ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoin_type,type,
% 0.30/0.46 setadjoin: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(setunion_type,type,
% 0.30/0.46 setunion: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(eqinunit_type,type,
% 0.30/0.46 eqinunit: $o ).
% 0.30/0.46
% 0.30/0.46 thf(eqinunit,definition,
% 0.30/0.46 ( eqinunit
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunionsingleton_type,type,
% 0.30/0.46 setunionsingleton: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunionsingleton,definition,
% 0.30/0.46 ( setunionsingleton
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.30/0.46 = Xx ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(singleton_type,type,
% 0.30/0.46 singleton: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(singleton,definition,
% 0.30/0.46 ( singleton
% 0.30/0.46 = ( ^ [A: $i] :
% 0.30/0.46 ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( A
% 0.30/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(theprop,conjecture,
% 0.30/0.46 ( eqinunit
% 0.30/0.46 => ( setunionsingleton
% 0.30/0.46 => ! [X: $i] :
% 0.30/0.46 ( ( singleton @ X )
% 0.30/0.46 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.47/1.27 ---- Embedded in THF ---
% 1.47/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.27 %%% Generated on Tue Feb 24 12:30:22 EST 2026
% 1.47/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.27 %%% Logic specification used:
% 1.47/1.27 %%% thf(spec, logic, $$dhol).
% 1.47/1.27
% 1.47/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.9JG9QquUBW/DTF2DTF20142.p
% See solution above
% 1.47/1.27 ------------------------
% 1.47/1.28 ---- Cleaned THF ---
% 1.47/1.28 thf(in_type,type,
% 1.47/1.28 in: $i > $i > $o ).
% 1.47/1.28
% 1.47/1.28 thf(emptyset_type,type,
% 1.47/1.28 emptyset: $i ).
% 1.47/1.28
% 1.47/1.28 thf(setadjoin_type,type,
% 1.47/1.28 setadjoin: $i > $i > $i ).
% 1.47/1.28
% 1.47/1.28 thf(setunion_type,type,
% 1.47/1.28 setunion: $i > $i ).
% 1.47/1.28
% 1.47/1.28 thf(eqinunit_type,type,
% 1.47/1.28 eqinunit: $o ).
% 1.47/1.28
% 1.47/1.28 thf(eqinunit,definition,
% 1.47/1.28 ( eqinunit
% 1.47/1.28 = ( ! [Xx: $i,Xy: $i] :
% 1.47/1.28 ( ( Xx = Xy )
% 1.47/1.28 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 1.47/1.28
% 1.47/1.28 thf(setunionsingleton_type,type,
% 1.47/1.28 setunionsingleton: $o ).
% 1.47/1.28
% 1.47/1.28 thf(setunionsingleton,definition,
% 1.47/1.28 ( setunionsingleton
% 1.47/1.28 = ( ! [Xx: $i] :
% 1.47/1.28 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 1.47/1.28 = Xx ) ) ) ).
% 1.47/1.28
% 1.47/1.28 thf(singleton_type,type,
% 1.47/1.28 singleton: $i > $o ).
% 1.47/1.28
% 1.47/1.28 thf(singleton,definition,
% 1.47/1.28 ( singleton
% 1.47/1.28 = ( ^ [A: $i] :
% 1.47/1.28 ? [Xx: $i] :
% 1.47/1.28 ( ( in @ Xx @ A )
% 1.47/1.28 & ( A
% 1.47/1.28 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.47/1.28
% 1.47/1.28 thf(theprop,conjecture,
% 1.47/1.28 ( eqinunit
% 1.47/1.28 => ( setunionsingleton
% 1.47/1.28 => ! [X: $i] :
% 1.47/1.28 ( ( singleton @ X )
% 1.47/1.28 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 1.47/1.28 ------------------------
% 1.47/1.29 % (20332)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_20142 for (3000ds/4Mi)
% 1.47/1.29 % (20332)Instruction limit reached!
% 1.47/1.29 % (20332)------------------------------
% 1.47/1.29 % (20332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (20332)Termination reason: Unknown
% 1.47/1.29 % (20332)Termination phase: Saturation
% 1.47/1.29
% 1.47/1.29 % (20332)Memory used [KB]: 5500
% 1.47/1.29 % (20332)Time elapsed: 0.003 s
% 1.47/1.29 % (20332)Instructions burned: 4 (million)
% 1.47/1.29 % (20332)------------------------------
% 1.47/1.29 % (20332)------------------------------
% 1.47/1.30 % (20336)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_20142 for (3000ds/275Mi)
% 1.64/1.30 % (20337)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20142 for (3000ds/18Mi)
% 1.64/1.30 % (20336)Refutation not found, incomplete strategy
% 1.64/1.30 % (20336)------------------------------
% 1.64/1.30 % (20336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (20336)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.30
% 1.64/1.30
% 1.64/1.30 % (20336)Memory used [KB]: 5500
% 1.64/1.30 % (20336)Time elapsed: 0.002 s
% 1.64/1.30 % (20336)Instructions burned: 2 (million)
% 1.64/1.30 % (20336)------------------------------
% 1.64/1.30 % (20336)------------------------------
% 1.64/1.30 % (20337)First to succeed.
% 1.64/1.30 % (20337)Refutation found. Thanks to Tanya!
% 1.64/1.30 % SZS status Theorem for DTF2THF_20142
% 1.64/1.30 % SZS output start Proof for DTF2THF_20142
% 1.64/1.30 thf(func_def_0, type, in: $i > $i > $o).
% 1.64/1.30 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.64/1.30 thf(func_def_3, type, setunion: $i > $i).
% 1.64/1.30 thf(func_def_7, type, singleton: $i > $o).
% 1.64/1.30 thf(f54,plain,(
% 1.64/1.30 $false),
% 1.64/1.30 inference(subsumption_resolution,[status(thm)],[f53,f49])).
% 1.64/1.30 thf(f49,plain,(
% 1.64/1.30 ($true = (in @ sK5 @ sK3))),
% 1.64/1.30 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.64/1.30 thf(f47,plain,(
% 1.64/1.30 ($true = ((in @ sK5 @ sK3) & ((setadjoin @ sK5 @ emptyset) = sK3)))),
% 1.64/1.30 inference(beta_eta_normalization,[status(thm)],[f46])).
% 1.64/1.30 thf(f46,plain,(
% 1.64/1.30 ($true = ((^[Y0 : $i]: ((in @ Y0 @ sK3) & ((setadjoin @ Y0 @ emptyset) = sK3))) @ sK5))),
% 1.64/1.30 inference(sigma_clausification,[status(thm)],[f45])).
% 1.64/1.30 thf(f45,plain,(
% 1.64/1.30 ($true = (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) & ((setadjoin @ Y0 @ emptyset) = sK3)))))),
% 1.64/1.30 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.64/1.30 thf(f42,plain,(
% 1.64/1.30 (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))) @ sK3) = $true)),
% 1.64/1.30 inference(definition_unfolding,[status(thm)],[f36,f27])).
% 1.64/1.30 thf(f27,plain,(
% 1.64/1.30 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f13])).
% 1.64/1.30 thf(f13,plain,(
% 1.64/1.30 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 1.64/1.30 inference(fool_elimination,[status(thm)],[f12])).
% 1.64/1.30 thf(f12,plain,(
% 1.64/1.30 (singleton = (^[X0 : $i] : (? [X1 : $i] : (((setadjoin @ X1 @ emptyset) = X0) & (in @ X1 @ X0)))))),
% 1.64/1.30 inference(rectify,[status(thm)],[f3])).
% 1.64/1.30 thf(f3,axiom,(
% 1.64/1.30 (singleton = (^[X2 : $i] : (? [X0 : $i] : (((setadjoin @ X0 @ emptyset) = X2) & (in @ X0 @ X2)))))),
% 1.64/1.30 file('/export/starexec/sandbox/tmp/tmp.9JG9QquUBW/DTF2THF_20142.p',singleton)).
% 1.64/1.30 thf(f36,plain,(
% 1.64/1.30 ($true = (singleton @ sK3))),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f26])).
% 1.64/1.30 thf(f26,plain,(
% 1.64/1.30 (($true = (singleton @ sK3)) & ($true != (in @ (setunion @ sK3) @ sK3))) & (setunionsingleton = $true) & (eqinunit = $true)),
% 1.64/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f15,f25])).
% 1.64/1.30 thf(f25,plain,(
% 1.64/1.30 ? [X0 : $i] : (($true = (singleton @ X0)) & ($true != (in @ (setunion @ X0) @ X0))) => (($true = (singleton @ sK3)) & ($true != (in @ (setunion @ sK3) @ sK3)))),
% 1.64/1.30 introduced(definition,[],[choice_axiom])).
% 1.64/1.30 thf(f15,plain,(
% 1.64/1.30 ? [X0 : $i] : (($true = (singleton @ X0)) & ($true != (in @ (setunion @ X0) @ X0))) & (setunionsingleton = $true) & (eqinunit = $true)),
% 1.64/1.30 inference(flattening,[status(thm)],[f14])).
% 1.64/1.30 thf(f14,plain,(
% 1.64/1.30 (? [X0 : $i] : (($true = (singleton @ X0)) & ($true != (in @ (setunion @ X0) @ X0))) & (setunionsingleton = $true)) & (eqinunit = $true)),
% 1.64/1.30 inference(ennf_transformation,[status(thm)],[f10])).
% 1.64/1.30 thf(f10,plain,(
% 1.64/1.30 ~((eqinunit = $true) => ((setunionsingleton = $true) => ! [X0 : $i] : (($true = (singleton @ X0)) => ($true = (in @ (setunion @ X0) @ X0)))))),
% 1.64/1.30 inference(fool_elimination,[status(thm)],[f9])).
% 1.64/1.30 thf(f9,plain,(
% 1.64/1.30 ~(eqinunit => (setunionsingleton => ! [X0 : $i] : ((singleton @ X0) => (in @ (setunion @ X0) @ X0))))),
% 1.64/1.30 inference(rectify,[status(thm)],[f5])).
% 1.64/1.30 thf(f5,negated_conjecture,(
% 1.64/1.30 ~(eqinunit => (setunionsingleton => ! [X3 : $i] : ((singleton @ X3) => (in @ (setunion @ X3) @ X3))))),
% 1.64/1.30 inference(negated_conjecture,[status(cth)],[f4])).
% 1.64/1.30 thf(f4,conjecture,(
% 1.64/1.30 eqinunit => (setunionsingleton => ! [X3 : $i] : ((singleton @ X3) => (in @ (setunion @ X3) @ X3)))),
% 1.64/1.30 file('/export/starexec/sandbox/tmp/tmp.9JG9QquUBW/DTF2THF_20142.p',theprop)).
% 1.64/1.30 thf(f53,plain,(
% 1.64/1.30 ($true != (in @ sK5 @ sK3))),
% 1.64/1.30 inference(backward_demodulation,[status(thm)],[f35,f52])).
% 1.64/1.30 thf(f52,plain,(
% 1.64/1.30 (sK5 = (setunion @ sK3))),
% 1.64/1.30 inference(superposition,[status(thm)],[f44,f50])).
% 1.64/1.30 thf(f50,plain,(
% 1.64/1.30 ((setadjoin @ sK5 @ emptyset) = sK3)),
% 1.64/1.30 inference(equality_proxy_clausification,[status(thm)],[f48])).
% 1.64/1.30 thf(f48,plain,(
% 1.64/1.30 ($true = ((setadjoin @ sK5 @ emptyset) = sK3))),
% 1.64/1.30 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.64/1.30 thf(f44,plain,(
% 1.64/1.30 ( ! [X0 : $i] : (((setunion @ (setadjoin @ X0 @ emptyset)) = X0)) )),
% 1.64/1.30 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.64/1.30 thf(f40,plain,(
% 1.64/1.30 ( ! [X0 : $i] : (((setunion @ (setadjoin @ X0 @ emptyset)) = X0) | ($true != $true)) )),
% 1.64/1.30 inference(definition_unfolding,[status(thm)],[f32,f34])).
% 1.64/1.30 thf(f34,plain,(
% 1.64/1.30 (setunionsingleton = $true)),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f26])).
% 1.64/1.30 thf(f32,plain,(
% 1.64/1.30 ( ! [X0 : $i] : (((setunion @ (setadjoin @ X0 @ emptyset)) = X0) | (setunionsingleton != $true)) )),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f24])).
% 1.64/1.30 thf(f24,plain,(
% 1.64/1.30 (! [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) = X0) | (setunionsingleton != $true)) & ((setunionsingleton = $true) | (sK2 != (setunion @ (setadjoin @ sK2 @ emptyset))))),
% 1.64/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f22,f23])).
% 1.64/1.30 thf(f23,plain,(
% 1.64/1.30 ? [X1 : $i] : ((setunion @ (setadjoin @ X1 @ emptyset)) != X1) => (sK2 != (setunion @ (setadjoin @ sK2 @ emptyset)))),
% 1.64/1.30 introduced(definition,[],[choice_axiom])).
% 1.64/1.30 thf(f22,plain,(
% 1.64/1.30 (! [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) = X0) | (setunionsingleton != $true)) & ((setunionsingleton = $true) | ? [X1 : $i] : ((setunion @ (setadjoin @ X1 @ emptyset)) != X1))),
% 1.64/1.30 inference(rectify,[status(thm)],[f21])).
% 1.64/1.30 thf(f21,plain,(
% 1.64/1.30 (! [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) = X0) | (setunionsingleton != $true)) & ((setunionsingleton = $true) | ? [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) != X0))),
% 1.64/1.30 inference(nnf_transformation,[status(thm)],[f11])).
% 1.64/1.30 thf(f11,plain,(
% 1.64/1.30 ! [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) = X0) <=> (setunionsingleton = $true)),
% 1.64/1.30 inference(fool_elimination,[status(thm)],[f2])).
% 1.64/1.30 thf(f2,axiom,(
% 1.64/1.30 (! [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) = X0) = setunionsingleton)),
% 1.64/1.30 file('/export/starexec/sandbox/tmp/tmp.9JG9QquUBW/DTF2THF_20142.p',setunionsingleton)).
% 1.64/1.30 thf(f35,plain,(
% 1.64/1.30 ($true != (in @ (setunion @ sK3) @ sK3))),
% 1.64/1.30 inference(cnf_transformation,[status(thm)],[f26])).
% 1.64/1.30 % SZS output end Proof for DTF2THF_20142
% 1.64/1.30 % (20337)------------------------------
% 1.64/1.30 % (20337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (20337)Termination reason: Refutation
% 1.64/1.30
% 1.64/1.30 % (20337)Memory used [KB]: 5500
% 1.64/1.30 % (20337)Time elapsed: 0.003 s
% 1.64/1.30 % (20337)Instructions burned: 2 (million)
% 1.64/1.30 % (20337)------------------------------
% 1.64/1.30 % (20337)------------------------------
% 1.64/1.30 % (20330)Success in time 0.016 s
%------------------------------------------------------------------------------