%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU618^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:39 AM UTC 2026
% Result : Theorem 1.46s 1.28s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 39 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 282 ( 51 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 444 ( 10 ~; 7 |; 6 &; 366 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 8 usr; 8 con; 0-2 aty)
% ( 23 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 78 ( 28 ^; 44 !; 6 ?; 78 :)
% 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(f44,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f42]) ).
thf(f42,plain,
$false = $true,
inference(superposition,[status(thm)],[f41,f26]) ).
thf(f26,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f19,f18]) ).
thf(f18,plain,
secondinupair = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( secondinupair = $true )
& ( ( in @ sK1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) )
!= $true )
& ( setunionI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i] :
( $true
!= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( ( in @ sK1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ( secondinupair = $true )
& ? [X0: $i,X1: $i] :
( $true
!= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( setunionI = $true ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i] :
( $true
!= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( secondinupair = $true )
& ( setunionI = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( ( setunionI = $true )
=> ( ( secondinupair = $true )
=> ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( setunionI
=> ( secondinupair
=> ! [X0: $i,X1: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( setunionI
=> ( secondinupair
=> ! [X1: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( setunionI
=> ( secondinupair
=> ! [X1: $i,X3: $i] : ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TNvdVdFY9P/DTF2THF_26009.p',setukpairIR) ).
thf(f19,plain,
( secondinupair
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( secondinupair
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
= secondinupair ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X3: $i,X1: $i] :
( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) )
= secondinupair ),
file('/export/starexec/sandbox2/tmp/tmp.TNvdVdFY9P/DTF2THF_26009.p',secondinupair) ).
thf(f41,plain,
( $false
= ( in @ sK1 @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
( ( $false
= ( in @ sK1 @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f37,f26]) ).
thf(f37,plain,
! [X0: $i] :
( ( ( in @ X0 @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( in @ sK1 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: $i] :
( ( ( in @ X0 @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( in @ sK1 @ X0 )
= $false )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f17,f34]) ).
thf(f34,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( setunion @ X2 ) )
= $true )
| ( ( in @ X3 @ X1 )
= $false )
| ( ( in @ X1 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( in @ X1 @ X2 )
=> ( in @ X3 @ ( setunion @ X2 ) ) )
= $true )
| ( ( in @ X3 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ X1 )
=> ( ( in @ X1 @ X2 )
=> ( in @ X3 @ ( setunion @ X2 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ X1 @ X2 )
=> ( in @ Y0 @ ( setunion @ X2 ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ X1 @ X2 )
=> ( in @ Y0 @ ( setunion @ X2 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ Y1 @ ( setunion @ Y0 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ Y1 @ ( setunion @ Y0 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y2 @ ( setunion @ Y1 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y2 @ ( setunion @ Y1 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f20,f16]) ).
thf(f16,plain,
setunionI = $true,
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f20,plain,
( setunionI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y2 @ ( setunion @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( setunionI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y2 @ ( setunion @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( setunionI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X2 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X0 @ ( setunion @ X1 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( setunionI
= ( ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X1 @ ( setunion @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TNvdVdFY9P/DTF2THF_26009.p',setunionI) ).
thf(f17,plain,
( ( in @ sK1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU618^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n020.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 12:28:42 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SEU618^2 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.45 % Domain : Set Theory
% 0.18/0.45 % Problem : Ordered Pairs - Kuratowski Pairs
% 0.18/0.45 % Version : Especial > Reduced > Especial.
% 0.18/0.45 % English : (! x:i.! y:i.in y (setunion (setadjoin (setadjoin x emptyset)
% 0.18/0.45 % (setadjoin (setadjoin x (setadjoin y emptyset)) emptyset))))
% 0.18/0.45
% 0.18/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.45 % Source : [Bro08]
% 0.18/0.45 % Names : ZFC120l [Bro08]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v4.1.0, 0.00 v3.7.0
% 0.18/0.45 % Syntax : Number of formulae : 9 ( 2 unt; 6 typ; 2 def)
% 0.18/0.45 % Number of atoms : 11 ( 2 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 3 ( 3 avg)
% 0.18/0.45 % Number of connectives : 30 ( 0 ~; 0 |; 0 &; 26 @)
% 0.18/0.45 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 13 ( 5 avg)
% 0.18/0.45 % Number of types : 2 ( 0 usr)
% 0.18/0.45 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 7 ( 6 usr; 3 con; 0-2 aty)
% 0.18/0.45 % Number of variables : 7 ( 0 ^; 7 !; 0 ?; 7 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : http://mathgate.info/detsetitem.php?id=173
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(in_type,type,
% 0.18/0.45 in: $i > $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(emptyset_type,type,
% 0.18/0.45 emptyset: $i ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoin_type,type,
% 0.18/0.45 setadjoin: $i > $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(setunion_type,type,
% 0.18/0.45 setunion: $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(setunionI_type,type,
% 0.18/0.45 setunionI: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setunionI,definition,
% 0.18/0.45 ( setunionI
% 0.18/0.45 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.18/0.45 ( ( in @ Xx @ B )
% 0.18/0.45 => ( ( in @ B @ A )
% 0.18/0.45 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(secondinupair_type,type,
% 0.18/0.45 secondinupair: $o ).
% 0.18/0.45
% 0.18/0.45 thf(secondinupair,definition,
% 0.18/0.45 ( secondinupair
% 0.18/0.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setukpairIR,conjecture,
% 0.18/0.45 ( setunionI
% 0.18/0.45 => ( secondinupair
% 0.18/0.45 => ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.46/1.25 ---- Embedded in THF ---
% 1.46/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.25 %%% Generated on Tue Feb 24 12:28:43 EST 2026
% 1.46/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.25 %%% Logic specification used:
% 1.46/1.25 %%% thf(spec, logic, $$dhol).
% 1.46/1.25
% 1.46/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.TNvdVdFY9P/DTF2DTF26009.p
% See solution above
% 1.46/1.25 ------------------------
% 1.46/1.26 ---- Cleaned THF ---
% 1.46/1.26 thf(in_type,type,
% 1.46/1.26 in: $i > $i > $o ).
% 1.46/1.26
% 1.46/1.26 thf(emptyset_type,type,
% 1.46/1.26 emptyset: $i ).
% 1.46/1.26
% 1.46/1.26 thf(setadjoin_type,type,
% 1.46/1.26 setadjoin: $i > $i > $i ).
% 1.46/1.26
% 1.46/1.26 thf(setunion_type,type,
% 1.46/1.26 setunion: $i > $i ).
% 1.46/1.26
% 1.46/1.26 thf(setunionI_type,type,
% 1.46/1.26 setunionI: $o ).
% 1.46/1.26
% 1.46/1.26 thf(setunionI,definition,
% 1.46/1.26 ( setunionI
% 1.46/1.26 = ( ! [A: $i,Xx: $i,B: $i] :
% 1.46/1.26 ( ( in @ Xx @ B )
% 1.46/1.26 => ( ( in @ B @ A )
% 1.46/1.26 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 1.46/1.26
% 1.46/1.26 thf(secondinupair_type,type,
% 1.46/1.26 secondinupair: $o ).
% 1.46/1.26
% 1.46/1.26 thf(secondinupair,definition,
% 1.46/1.26 ( secondinupair
% 1.46/1.26 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 1.46/1.26
% 1.46/1.26 thf(setukpairIR,conjecture,
% 1.46/1.26 ( setunionI
% 1.46/1.26 => ( secondinupair
% 1.46/1.26 => ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 1.46/1.26 ------------------------
% 1.46/1.27 % (26162)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26009 for (3000ds/183Mi)
% 1.46/1.28 % (26163)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_26009 for (3000ds/4Mi)
% 1.46/1.28 % (26162)First to succeed.
% 1.46/1.28 % (26163)Instruction limit reached!
% 1.46/1.28 % (26163)------------------------------
% 1.46/1.28 % (26163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.28 % (26163)Termination reason: Unknown
% 1.46/1.28 % (26163)Termination phase: Saturation
% 1.46/1.28
% 1.46/1.28 % (26163)Memory used [KB]: 5500
% 1.46/1.28 % (26163)Time elapsed: 0.004 s
% 1.46/1.28 % (26163)Instructions burned: 5 (million)
% 1.46/1.28 % (26163)------------------------------
% 1.46/1.28 % (26163)------------------------------
% 1.46/1.28 % (26162)Refutation found. Thanks to Tanya!
% 1.46/1.28 % SZS status Theorem for DTF2THF_26009
% 1.46/1.28 % SZS output start Proof for DTF2THF_26009
% 1.46/1.28 thf(func_def_0, type, in: $i > $i > $o).
% 1.46/1.28 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.46/1.28 thf(func_def_3, type, setunion: $i > $i).
% 1.46/1.28 thf(f44,plain,(
% 1.46/1.28 $false),
% 1.46/1.28 inference(trivial_inequality_removal,[status(thm)],[f42])).
% 1.46/1.28 thf(f42,plain,(
% 1.46/1.28 ($false = $true)),
% 1.46/1.28 inference(superposition,[status(thm)],[f41,f26])).
% 1.46/1.28 thf(f26,plain,(
% 1.46/1.28 ( ! [X2 : $i,X1 : $i] : (($true = (in @ X2 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))))) )),
% 1.46/1.28 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.46/1.28 thf(f25,plain,(
% 1.46/1.28 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (in @ Y0 @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)))) @ X2) = $true)) )),
% 1.46/1.28 inference(pi_clausification,[status(thm)],[f24])).
% 1.46/1.28 thf(f24,plain,(
% 1.46/1.28 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset))))) = $true)) )),
% 1.46/1.28 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.46/1.28 thf(f23,plain,(
% 1.46/1.28 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))) @ X1) = $true)) )),
% 1.46/1.28 inference(pi_clausification,[status(thm)],[f21])).
% 1.46/1.28 thf(f21,plain,(
% 1.46/1.28 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) = $true)),
% 1.46/1.28 inference(definition_unfolding,[status(thm)],[f19,f18])).
% 1.46/1.28 thf(f18,plain,(
% 1.46/1.28 (secondinupair = $true)),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f15])).
% 1.46/1.28 thf(f15,plain,(
% 1.46/1.28 (secondinupair = $true) & ((in @ sK1 @ (setunion @ (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset)) @ emptyset)))) != $true) & (setunionI = $true)),
% 1.46/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f14])).
% 1.46/1.28 thf(f14,plain,(
% 1.46/1.28 ? [X0 : $i,X1 : $i] : ($true != (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))) => ((in @ sK1 @ (setunion @ (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset)) @ emptyset)))) != $true)),
% 1.46/1.28 introduced(definition,[],[choice_axiom])).
% 1.46/1.28 thf(f13,plain,(
% 1.46/1.28 (secondinupair = $true) & ? [X0 : $i,X1 : $i] : ($true != (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))) & (setunionI = $true)),
% 1.46/1.28 inference(flattening,[status(thm)],[f12])).
% 1.46/1.28 thf(f12,plain,(
% 1.46/1.28 (? [X0 : $i,X1 : $i] : ($true != (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))) & (secondinupair = $true)) & (setunionI = $true)),
% 1.46/1.28 inference(ennf_transformation,[status(thm)],[f11])).
% 1.46/1.28 thf(f11,plain,(
% 1.46/1.28 ~((setunionI = $true) => ((secondinupair = $true) => ! [X0 : $i,X1 : $i] : ($true = (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))))))),
% 1.46/1.28 inference(fool_elimination,[status(thm)],[f10])).
% 1.46/1.28 thf(f10,plain,(
% 1.46/1.28 ~(setunionI => (secondinupair => ! [X0 : $i,X1 : $i] : (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))))),
% 1.46/1.28 inference(rectify,[status(thm)],[f4])).
% 1.46/1.28 thf(f4,negated_conjecture,(
% 1.46/1.28 ~(setunionI => (secondinupair => ! [X1 : $i,X3 : $i] : (in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))))),
% 1.46/1.28 inference(negated_conjecture,[status(cth)],[f3])).
% 1.46/1.28 thf(f3,conjecture,(
% 1.46/1.28 setunionI => (secondinupair => ! [X1 : $i,X3 : $i] : (in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))),
% 1.46/1.28 file('/export/starexec/sandbox2/tmp/tmp.TNvdVdFY9P/DTF2THF_26009.p',setukpairIR)).
% 1.46/1.28 thf(f19,plain,(
% 1.46/1.28 (secondinupair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f7])).
% 1.46/1.28 thf(f7,plain,(
% 1.46/1.28 (secondinupair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))),
% 1.46/1.28 inference(fool_elimination,[status(thm)],[f6])).
% 1.46/1.28 thf(f6,plain,(
% 1.46/1.28 (! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))) = secondinupair)),
% 1.46/1.28 inference(rectify,[status(thm)],[f2])).
% 1.46/1.28 thf(f2,axiom,(
% 1.46/1.28 (! [X3 : $i,X1 : $i] : (in @ X3 @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset))) = secondinupair)),
% 1.46/1.28 file('/export/starexec/sandbox2/tmp/tmp.TNvdVdFY9P/DTF2THF_26009.p',secondinupair)).
% 1.46/1.28 thf(f41,plain,(
% 1.46/1.28 ($false = (in @ sK1 @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset))))),
% 1.46/1.28 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.46/1.28 thf(f38,plain,(
% 1.46/1.28 ($false = (in @ sK1 @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset)))) | ($false = $true)),
% 1.46/1.28 inference(superposition,[status(thm)],[f37,f26])).
% 1.46/1.28 thf(f37,plain,(
% 1.46/1.28 ( ! [X0 : $i] : (((in @ X0 @ (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset)) @ emptyset))) = $false) | ((in @ sK1 @ X0) = $false)) )),
% 1.46/1.28 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.46/1.28 thf(f36,plain,(
% 1.46/1.28 ( ! [X0 : $i] : (((in @ X0 @ (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset)) @ emptyset))) = $false) | ((in @ sK1 @ X0) = $false) | ($true != $true)) )),
% 1.46/1.28 inference(superposition,[status(thm)],[f17,f34])).
% 1.46/1.28 thf(f34,plain,(
% 1.46/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X3 @ (setunion @ X2)) = $true) | ((in @ X3 @ X1) = $false) | ((in @ X1 @ X2) = $false)) )),
% 1.46/1.28 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.46/1.28 thf(f33,plain,(
% 1.46/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ X2) => (in @ X3 @ (setunion @ X2))) = $true) | ((in @ X3 @ X1) = $false)) )),
% 1.46/1.28 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.46/1.28 thf(f32,plain,(
% 1.46/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X3 @ X1) => ((in @ X1 @ X2) => (in @ X3 @ (setunion @ X2)))) = $true)) )),
% 1.46/1.28 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.46/1.28 thf(f31,plain,(
% 1.46/1.28 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ X1) => ((in @ X1 @ X2) => (in @ Y0 @ (setunion @ X2))))) @ X3) = $true)) )),
% 1.46/1.28 inference(pi_clausification,[status(thm)],[f30])).
% 1.46/1.28 thf(f30,plain,(
% 1.46/1.28 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((in @ X1 @ X2) => (in @ Y0 @ (setunion @ X2)))))) = $true)) )),
% 1.46/1.28 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.46/1.28 thf(f29,plain,(
% 1.46/1.28 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((in @ X1 @ Y0) => (in @ Y1 @ (setunion @ Y0))))))) @ X2) = $true)) )),
% 1.46/1.28 inference(pi_clausification,[status(thm)],[f28])).
% 1.46/1.28 thf(f28,plain,(
% 1.46/1.28 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((in @ X1 @ Y0) => (in @ Y1 @ (setunion @ Y0)))))))) = $true)) )),
% 1.46/1.28 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.46/1.28 thf(f27,plain,(
% 1.46/1.28 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y0 @ Y1) => (in @ Y2 @ (setunion @ Y1))))))))) @ X1) = $true)) )),
% 1.46/1.28 inference(pi_clausification,[status(thm)],[f22])).
% 1.46/1.28 thf(f22,plain,(
% 1.46/1.28 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y0 @ Y1) => (in @ Y2 @ (setunion @ Y1)))))))))) = $true)),
% 1.46/1.28 inference(definition_unfolding,[status(thm)],[f20,f16])).
% 1.46/1.28 thf(f16,plain,(
% 1.46/1.28 (setunionI = $true)),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f15])).
% 1.46/1.28 thf(f20,plain,(
% 1.46/1.28 (setunionI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y0 @ Y1) => (in @ Y2 @ (setunion @ Y1)))))))))))),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f9])).
% 1.46/1.28 thf(f9,plain,(
% 1.46/1.28 (setunionI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y0 @ Y1) => (in @ Y2 @ (setunion @ Y1)))))))))))),
% 1.46/1.28 inference(fool_elimination,[status(thm)],[f8])).
% 1.46/1.28 thf(f8,plain,(
% 1.46/1.28 (setunionI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => ((in @ X2 @ X1) => (in @ X0 @ (setunion @ X1)))))),
% 1.46/1.28 inference(rectify,[status(thm)],[f1])).
% 1.46/1.28 thf(f1,axiom,(
% 1.46/1.28 (setunionI = ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X1 @ X2) => ((in @ X2 @ X0) => (in @ X1 @ (setunion @ X0)))))),
% 1.46/1.28 file('/export/starexec/sandbox2/tmp/tmp.TNvdVdFY9P/DTF2THF_26009.p',setunionI)).
% 1.46/1.28 thf(f17,plain,(
% 1.46/1.28 ((in @ sK1 @ (setunion @ (setadjoin @ (setadjoin @ sK0 @ emptyset) @ (setadjoin @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset)) @ emptyset)))) != $true)),
% 1.46/1.28 inference(cnf_transformation,[status(thm)],[f15])).
% 1.46/1.28 % SZS output end Proof for DTF2THF_26009
% 1.46/1.28 % (26162)------------------------------
% 1.46/1.28 % (26162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.28 % (26162)Termination reason: Refutation
% 1.46/1.28
% 1.46/1.28 % (26162)Memory used [KB]: 5500
% 1.46/1.28 % (26162)Time elapsed: 0.004 s
% 1.46/1.28 % (26162)Instructions burned: 4 (million)
% 1.46/1.28 % (26162)------------------------------
% 1.46/1.28 % (26162)------------------------------
% 1.46/1.28 % (26161)Success in time 0.006 s
%------------------------------------------------------------------------------