%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU635^2 : 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 : n001.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 09:35:48 AM UTC 2026
% Result : Theorem 1.65s 1.32s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 5
% Syntax : Number of formulae : 57 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 376 ( 86 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 534 ( 10 ~; 20 |; 9 &; 399 @)
% ( 0 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 10 usr; 8 con; 0-2 aty)
% ( 39 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 122 ( 47 ^; 72 !; 3 ?; 122 :)
% 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,
subset: $i > $i > $o ).
thf(func_def_19,type,
sK2: $i > $i > $i ).
thf(f79,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f78]) ).
thf(f78,plain,
$true = $false,
inference(superposition,[status(thm)],[f40,f76]) ).
thf(f76,plain,
( ( in @ sK0 @ ( setadjoin @ sK0 @ emptyset ) )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f75]) ).
thf(f75,plain,
( ( $true != $true )
| ( ( in @ sK0 @ ( setadjoin @ sK0 @ emptyset ) )
= $false ) ),
inference(superposition,[status(thm)],[f25,f74]) ).
thf(f74,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X0 @ ( setunion @ X1 ) ) )
| ( ( in @ X0 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $false )
| ( $true
= ( subset @ X0 @ ( setunion @ X1 ) ) )
| ( $true = $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f61]) ).
thf(f61,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( subset @ X0 @ ( setunion @ X1 ) ) )
| ( ( in @ X0 @ X1 )
= $false )
| ( $true
= ( subset @ X0 @ ( setunion @ X1 ) ) ) ),
inference(superposition,[status(thm)],[f60,f49]) ).
thf(f49,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ ( sK2 @ X1 @ X2 ) @ X1 ) )
| ( $true
= ( subset @ X1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X2 ) )
| ( ( ( in @ ( sK2 @ X1 @ X2 ) @ X1 )
=> ( in @ ( sK2 @ X1 @ X2 ) @ X2 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) )
@ ( sK2 @ X1 @ X2 ) )
= $false )
| ( $true
= ( subset @ X1 @ X2 ) ) ),
inference(sigma_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
= $false )
| ( $true
= ( subset @ X1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( in @ Y0 @ X2 ) ) )
=> ( subset @ X1 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( subset @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( in @ Y1 @ Y0 ) ) )
=> ( subset @ X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f23,f21]) ).
thf(f21,plain,
( subsetI2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( subsetI2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( in @ Y2 @ Y1 ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( subset @ X1 @ X0 ) )
= subsetI2 ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X3: $i,X2: $i] :
( ( ! [X0: $i] :
( ( in @ X0 @ X2 )
=> ( in @ X0 @ X3 ) )
=> ( subset @ X2 @ X3 ) )
= subsetI2 ),
file('/export/starexec/sandbox2/tmp/tmp.G1MQ4SpQqS/DTF2THF_25039.p',subsetI2) ).
thf(f23,plain,
subsetI2 = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( $true
!= ( subset @ sK0 @ ( setunion @ ( setadjoin @ sK0 @ emptyset ) ) ) )
& ( setadjoinIL = $true )
& ( subsetI2 = $true )
& ( setunionI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f16,f17]) ).
thf(f17,plain,
( ? [X0: $i] :
( $true
!= ( subset @ X0 @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) ) )
=> ( $true
!= ( subset @ sK0 @ ( setunion @ ( setadjoin @ sK0 @ emptyset ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ? [X0: $i] :
( $true
!= ( subset @ X0 @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) ) )
& ( setadjoinIL = $true )
& ( subsetI2 = $true )
& ( setunionI = $true ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ? [X0: $i] :
( $true
!= ( subset @ X0 @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) ) )
& ( subsetI2 = $true )
& ( setunionI = $true )
& ( setadjoinIL = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( setadjoinIL = $true )
=> ( ( setunionI = $true )
=> ( ( subsetI2 = $true )
=> ! [X0: $i] :
( $true
= ( subset @ X0 @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( setadjoinIL
=> ( setunionI
=> ( subsetI2
=> ! [X0: $i] : ( subset @ X0 @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( setadjoinIL
=> ( setunionI
=> ( subsetI2
=> ! [X2: $i] : ( subset @ X2 @ ( setunion @ ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( setadjoinIL
=> ( setunionI
=> ( subsetI2
=> ! [X2: $i] : ( subset @ X2 @ ( setunion @ ( setadjoin @ X2 @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.G1MQ4SpQqS/DTF2THF_25039.p',setunionsingleton2) ).
thf(f60,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK2 @ X0 @ ( setunion @ X1 ) ) @ X2 )
= $false )
| ( $true
= ( subset @ X0 @ ( setunion @ X1 ) ) )
| ( ( in @ X2 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( subset @ X0 @ ( setunion @ X1 ) ) )
| ( ( in @ ( sK2 @ X0 @ ( setunion @ X1 ) ) @ X2 )
= $false )
| ( $true = $false )
| ( ( in @ X2 @ X1 )
= $false ) ),
inference(superposition,[status(thm)],[f36,f48]) ).
thf(f48,plain,
! [X2: $i,X1: $i] :
( ( ( in @ ( sK2 @ X1 @ X2 ) @ X2 )
= $false )
| ( $true
= ( subset @ X1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f36,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( setunion @ X1 ) ) )
| ( ( in @ X3 @ X1 )
= $false )
| ( ( in @ X2 @ X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( in @ X3 @ X1 )
=> ( in @ X2 @ ( setunion @ X1 ) ) ) )
| ( ( in @ X2 @ X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X2 @ X3 )
=> ( ( in @ X3 @ X1 )
=> ( in @ X2 @ ( setunion @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X2 @ Y0 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ X2 @ ( setunion @ X1 ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ Y0 )
=> ( ( in @ Y0 @ X1 )
=> ( in @ X2 @ ( setunion @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( ( in @ Y1 @ X1 )
=> ( in @ Y0 @ ( setunion @ X1 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( ( in @ Y1 @ X1 )
=> ( in @ Y0 @ ( setunion @ X1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y1 @ ( setunion @ Y0 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y1 @ ( setunion @ Y0 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f22,f19]) ).
thf(f19,plain,
( setunionI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y1 @ ( setunion @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( setunionI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( in @ Y2 @ Y0 )
=> ( in @ Y1 @ ( setunion @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
=> ( ( in @ X0 @ X2 )
=> ( in @ X1 @ ( setunion @ X2 ) ) ) )
= setunionI ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X3: $i,X0: $i,X2: $i] :
( ( ( in @ X0 @ X3 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X0 @ ( setunion @ X2 ) ) ) )
= setunionI ),
file('/export/starexec/sandbox2/tmp/tmp.G1MQ4SpQqS/DTF2THF_25039.p',setunionI) ).
thf(f22,plain,
setunionI = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f25,plain,
( $true
!= ( subset @ sK0 @ ( setunion @ ( setadjoin @ sK0 @ emptyset ) ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X2 @ ( setadjoin @ X2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ ( setadjoin @ Y0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f24,f20]) ).
thf(f20,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( setadjoinIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setadjoin @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= setadjoinIL ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= setadjoinIL ),
file('/export/starexec/sandbox2/tmp/tmp.G1MQ4SpQqS/DTF2THF_25039.p',setadjoinIL) ).
thf(f24,plain,
setadjoinIL = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU635^2 : 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
% 0.16/0.34 % Computer : n001.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 12:29:50 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.32/0.47 ---- Original DTF file ---
% 0.32/0.48 thf(spec,logic,$$dhol).
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 % File : SEU635^2 : TPTP v9.2.1. Released v3.7.0.
% 0.32/0.48 % Domain : Set Theory
% 0.32/0.48 % Problem : Ordered Pairs - Singletons
% 0.32/0.48 % Version : Especial > Reduced > Especial.
% 0.32/0.48 % English : (! A:i.subset A (setunion (setadjoin A emptyset)))
% 0.32/0.48
% 0.32/0.48 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.32/0.48 % Source : [Bro08]
% 0.32/0.48 % Names : ZFC137l [Bro08]
% 0.32/0.48
% 0.32/0.48 % Status : Theorem
% 0.32/0.48 % 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 v3.7.0
% 0.32/0.48 % Syntax : Number of formulae : 12 ( 3 unt; 8 typ; 3 def)
% 0.32/0.48 % Number of atoms : 17 ( 3 equ; 0 cnn)
% 0.32/0.48 % Maximal formula atoms : 4 ( 4 avg)
% 0.32/0.48 % Number of connectives : 29 ( 0 ~; 0 |; 0 &; 22 @)
% 0.32/0.48 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.32/0.48 % Maximal formula depth : 9 ( 3 avg)
% 0.32/0.48 % Number of types : 2 ( 0 usr)
% 0.32/0.48 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.32/0.48 % Number of symbols : 9 ( 8 usr; 4 con; 0-2 aty)
% 0.32/0.48 % Number of variables : 9 ( 0 ^; 9 !; 0 ?; 9 :)
% 0.32/0.48 % SPC : TH0_THM_EQU_NAR
% 0.32/0.48
% 0.32/0.48 % Comments : http://mathgate.info/detsetitem.php?id=192
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 thf(in_type,type,
% 0.32/0.48 in: $i > $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(emptyset_type,type,
% 0.32/0.48 emptyset: $i ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoin_type,type,
% 0.32/0.48 setadjoin: $i > $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(setunion_type,type,
% 0.32/0.48 setunion: $i > $i ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoinIL_type,type,
% 0.32/0.48 setadjoinIL: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setadjoinIL,definition,
% 0.32/0.48 ( setadjoinIL
% 0.32/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setunionI_type,type,
% 0.32/0.48 setunionI: $o ).
% 0.32/0.48
% 0.32/0.48 thf(setunionI,definition,
% 0.32/0.48 ( setunionI
% 0.32/0.48 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.32/0.48 ( ( in @ Xx @ B )
% 0.32/0.48 => ( ( in @ B @ A )
% 0.32/0.48 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(subset_type,type,
% 0.32/0.48 subset: $i > $i > $o ).
% 0.32/0.48
% 0.32/0.48 thf(subsetI2_type,type,
% 0.32/0.48 subsetI2: $o ).
% 0.32/0.48
% 0.32/0.48 thf(subsetI2,definition,
% 0.32/0.48 ( subsetI2
% 0.32/0.48 = ( ! [A: $i,B: $i] :
% 0.32/0.48 ( ! [Xx: $i] :
% 0.32/0.48 ( ( in @ Xx @ A )
% 0.32/0.48 => ( in @ Xx @ B ) )
% 0.32/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(setunionsingleton2,conjecture,
% 0.32/0.48 ( setadjoinIL
% 0.32/0.48 => ( setunionI
% 0.32/0.48 => ( subsetI2
% 0.32/0.48 => ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 ------------------------
% 1.45/1.29 ---- Embedded in THF ---
% 1.45/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.29 %%% Generated on Tue Feb 24 12:29:51 EST 2026
% 1.45/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.29 %%% Logic specification used:
% 1.45/1.29 %%% thf(spec, logic, $$dhol).
% 1.45/1.29
% 1.45/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.G1MQ4SpQqS/DTF2DTF25039.p
% See solution above
% 1.45/1.29 ------------------------
% 1.65/1.30 ---- Cleaned THF ---
% 1.65/1.30 thf(in_type,type,
% 1.65/1.30 in: $i > $i > $o ).
% 1.65/1.30
% 1.65/1.30 thf(emptyset_type,type,
% 1.65/1.30 emptyset: $i ).
% 1.65/1.30
% 1.65/1.30 thf(setadjoin_type,type,
% 1.65/1.30 setadjoin: $i > $i > $i ).
% 1.65/1.30
% 1.65/1.30 thf(setunion_type,type,
% 1.65/1.30 setunion: $i > $i ).
% 1.65/1.30
% 1.65/1.30 thf(setadjoinIL_type,type,
% 1.65/1.30 setadjoinIL: $o ).
% 1.65/1.30
% 1.65/1.30 thf(setadjoinIL,definition,
% 1.65/1.30 ( setadjoinIL
% 1.65/1.30 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.65/1.30
% 1.65/1.30 thf(setunionI_type,type,
% 1.65/1.30 setunionI: $o ).
% 1.65/1.30
% 1.65/1.30 thf(setunionI,definition,
% 1.65/1.30 ( setunionI
% 1.65/1.30 = ( ! [A: $i,Xx: $i,B: $i] :
% 1.65/1.30 ( ( in @ Xx @ B )
% 1.65/1.30 => ( ( in @ B @ A )
% 1.65/1.30 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 1.65/1.30
% 1.65/1.30 thf(subset_type,type,
% 1.65/1.30 subset: $i > $i > $o ).
% 1.65/1.30
% 1.65/1.30 thf(subsetI2_type,type,
% 1.65/1.30 subsetI2: $o ).
% 1.65/1.30
% 1.65/1.30 thf(subsetI2,definition,
% 1.65/1.30 ( subsetI2
% 1.65/1.30 = ( ! [A: $i,B: $i] :
% 1.65/1.30 ( ! [Xx: $i] :
% 1.65/1.30 ( ( in @ Xx @ A )
% 1.65/1.30 => ( in @ Xx @ B ) )
% 1.65/1.30 => ( subset @ A @ B ) ) ) ) ).
% 1.65/1.30
% 1.65/1.30 thf(setunionsingleton2,conjecture,
% 1.65/1.30 ( setadjoinIL
% 1.65/1.30 => ( setunionI
% 1.65/1.30 => ( subsetI2
% 1.65/1.30 => ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ) ).
% 1.65/1.30 ------------------------
% 1.65/1.32 % (25185)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25039 for (2999ds/2Mi)
% 1.65/1.32 % (25185)Instruction limit reached!
% 1.65/1.32 % (25185)------------------------------
% 1.65/1.32 % (25185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (25182)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25039 for (2999ds/183Mi)
% 1.65/1.32 % (25185)Termination reason: Unknown
% 1.65/1.32 % (25185)Termination phase: Saturation
% 1.65/1.32
% 1.65/1.32 % (25185)Memory used [KB]: 5500
% 1.65/1.32 % (25185)Time elapsed: 0.002 s
% 1.65/1.32 % (25185)Instructions burned: 2 (million)
% 1.65/1.32 % (25185)------------------------------
% 1.65/1.32 % (25185)------------------------------
% 1.65/1.32 % (25182)First to succeed.
% 1.65/1.32 % (25182)Refutation found. Thanks to Tanya!
% 1.65/1.32 % SZS status Theorem for DTF2THF_25039
% 1.65/1.32 % SZS output start Proof for DTF2THF_25039
% 1.65/1.32 thf(func_def_0, type, in: $i > $i > $o).
% 1.65/1.32 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.65/1.32 thf(func_def_3, type, setunion: $i > $i).
% 1.65/1.32 thf(func_def_7, type, subset: $i > $i > $o).
% 1.65/1.32 thf(func_def_19, type, sK2: $i > $i > $i).
% 1.65/1.32 thf(f79,plain,(
% 1.65/1.32 $false),
% 1.65/1.32 inference(trivial_inequality_removal,[status(thm)],[f78])).
% 1.65/1.32 thf(f78,plain,(
% 1.65/1.32 ($true = $false)),
% 1.65/1.32 inference(superposition,[status(thm)],[f40,f76])).
% 1.65/1.32 thf(f76,plain,(
% 1.65/1.32 ((in @ sK0 @ (setadjoin @ sK0 @ emptyset)) = $false)),
% 1.65/1.32 inference(trivial_inequality_removal,[status(thm)],[f75])).
% 1.65/1.32 thf(f75,plain,(
% 1.65/1.32 ($true != $true) | ((in @ sK0 @ (setadjoin @ sK0 @ emptyset)) = $false)),
% 1.65/1.32 inference(superposition,[status(thm)],[f25,f74])).
% 1.65/1.32 thf(f74,plain,(
% 1.65/1.32 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X0 @ (setunion @ X1))) | ((in @ X0 @ X1) = $false)) )),
% 1.65/1.32 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.65/1.32 thf(f73,plain,(
% 1.65/1.32 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ X1) = $false) | ($true = (subset @ X0 @ (setunion @ X1))) | ($true = $false)) )),
% 1.65/1.32 inference(duplicate_literal_removal,[status(thm)],[f61])).
% 1.65/1.32 thf(f61,plain,(
% 1.65/1.32 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($true = (subset @ X0 @ (setunion @ X1))) | ((in @ X0 @ X1) = $false) | ($true = (subset @ X0 @ (setunion @ X1)))) )),
% 1.65/1.32 inference(superposition,[status(thm)],[f60,f49])).
% 1.65/1.32 thf(f49,plain,(
% 1.65/1.32 ( ! [X2 : $i,X1 : $i] : (($true = (in @ (sK2 @ X1 @ X2) @ X1)) | ($true = (subset @ X1 @ X2))) )),
% 1.65/1.32 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.65/1.32 thf(f47,plain,(
% 1.65/1.32 ( ! [X2 : $i,X1 : $i] : (($true = (subset @ X1 @ X2)) | (((in @ (sK2 @ X1 @ X2) @ X1) => (in @ (sK2 @ X1 @ X2) @ X2)) = $false)) )),
% 1.65/1.32 inference(beta_eta_normalization,[status(thm)],[f46])).
% 1.65/1.32 thf(f46,plain,(
% 1.65/1.32 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2))) @ (sK2 @ X1 @ X2)) = $false) | ($true = (subset @ X1 @ X2))) )),
% 1.65/1.32 inference(sigma_clausification,[status(thm)],[f45])).
% 1.65/1.32 thf(f45,plain,(
% 1.65/1.32 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) = $false) | ($true = (subset @ X1 @ X2))) )),
% 1.65/1.32 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.65/1.32 thf(f44,plain,(
% 1.65/1.32 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => (subset @ X1 @ X2)))) )),
% 1.65/1.32 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.65/1.32 thf(f43,plain,(
% 1.65/1.32 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (subset @ X1 @ Y0))) @ X2))) )),
% 1.65/1.32 inference(pi_clausification,[status(thm)],[f42])).
% 1.65/1.32 thf(f42,plain,(
% 1.65/1.32 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (subset @ X1 @ Y0)))))) )),
% 1.65/1.32 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.65/1.32 thf(f41,plain,(
% 1.65/1.32 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1))))) @ X1))) )),
% 1.65/1.32 inference(pi_clausification,[status(thm)],[f27])).
% 1.65/1.32 thf(f27,plain,(
% 1.65/1.32 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))),
% 1.65/1.32 inference(definition_unfolding,[status(thm)],[f23,f21])).
% 1.65/1.32 thf(f21,plain,(
% 1.65/1.32 (subsetI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f8])).
% 1.65/1.32 thf(f8,plain,(
% 1.65/1.32 (subsetI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))),
% 1.65/1.32 inference(fool_elimination,[status(thm)],[f7])).
% 1.65/1.32 thf(f7,plain,(
% 1.65/1.32 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)) = subsetI2)),
% 1.65/1.32 inference(rectify,[status(thm)],[f3])).
% 1.65/1.32 thf(f3,axiom,(
% 1.65/1.32 (! [X3 : $i,X2 : $i] : (! [X0 : $i] : ((in @ X0 @ X2) => (in @ X0 @ X3)) => (subset @ X2 @ X3)) = subsetI2)),
% 1.65/1.32 file('/export/starexec/sandbox2/tmp/tmp.G1MQ4SpQqS/DTF2THF_25039.p',subsetI2)).
% 1.65/1.32 thf(f23,plain,(
% 1.65/1.32 (subsetI2 = $true)),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f18])).
% 1.65/1.32 thf(f18,plain,(
% 1.65/1.32 ($true != (subset @ sK0 @ (setunion @ (setadjoin @ sK0 @ emptyset)))) & (setadjoinIL = $true) & (subsetI2 = $true) & (setunionI = $true)),
% 1.65/1.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f16,f17])).
% 1.65/1.32 thf(f17,plain,(
% 1.65/1.32 ? [X0 : $i] : ($true != (subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset)))) => ($true != (subset @ sK0 @ (setunion @ (setadjoin @ sK0 @ emptyset))))),
% 1.65/1.32 introduced(definition,[],[choice_axiom])).
% 1.65/1.32 thf(f16,plain,(
% 1.65/1.32 ? [X0 : $i] : ($true != (subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset)))) & (setadjoinIL = $true) & (subsetI2 = $true) & (setunionI = $true)),
% 1.65/1.32 inference(flattening,[status(thm)],[f15])).
% 1.65/1.32 thf(f15,plain,(
% 1.65/1.32 ((? [X0 : $i] : ($true != (subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset)))) & (subsetI2 = $true)) & (setunionI = $true)) & (setadjoinIL = $true)),
% 1.65/1.32 inference(ennf_transformation,[status(thm)],[f12])).
% 1.65/1.32 thf(f12,plain,(
% 1.65/1.32 ~((setadjoinIL = $true) => ((setunionI = $true) => ((subsetI2 = $true) => ! [X0 : $i] : ($true = (subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset)))))))),
% 1.65/1.32 inference(fool_elimination,[status(thm)],[f11])).
% 1.65/1.32 thf(f11,plain,(
% 1.65/1.32 ~(setadjoinIL => (setunionI => (subsetI2 => ! [X0 : $i] : (subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset))))))),
% 1.65/1.32 inference(rectify,[status(thm)],[f5])).
% 1.65/1.32 thf(f5,negated_conjecture,(
% 1.65/1.32 ~(setadjoinIL => (setunionI => (subsetI2 => ! [X2 : $i] : (subset @ X2 @ (setunion @ (setadjoin @ X2 @ emptyset))))))),
% 1.65/1.32 inference(negated_conjecture,[status(cth)],[f4])).
% 1.65/1.32 thf(f4,conjecture,(
% 1.65/1.32 setadjoinIL => (setunionI => (subsetI2 => ! [X2 : $i] : (subset @ X2 @ (setunion @ (setadjoin @ X2 @ emptyset)))))),
% 1.65/1.32 file('/export/starexec/sandbox2/tmp/tmp.G1MQ4SpQqS/DTF2THF_25039.p',setunionsingleton2)).
% 1.65/1.32 thf(f60,plain,(
% 1.65/1.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK2 @ X0 @ (setunion @ X1)) @ X2) = $false) | ($true = (subset @ X0 @ (setunion @ X1))) | ((in @ X2 @ X1) = $false)) )),
% 1.65/1.32 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 1.65/1.32 thf(f56,plain,(
% 1.65/1.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (subset @ X0 @ (setunion @ X1))) | ((in @ (sK2 @ X0 @ (setunion @ X1)) @ X2) = $false) | ($true = $false) | ((in @ X2 @ X1) = $false)) )),
% 1.65/1.32 inference(superposition,[status(thm)],[f36,f48])).
% 1.65/1.32 thf(f48,plain,(
% 1.65/1.32 ( ! [X2 : $i,X1 : $i] : (((in @ (sK2 @ X1 @ X2) @ X2) = $false) | ($true = (subset @ X1 @ X2))) )),
% 1.65/1.32 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.65/1.32 thf(f36,plain,(
% 1.65/1.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (in @ X2 @ (setunion @ X1))) | ((in @ X3 @ X1) = $false) | ((in @ X2 @ X3) = $false)) )),
% 1.65/1.32 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.65/1.32 thf(f35,plain,(
% 1.65/1.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X3 @ X1) => (in @ X2 @ (setunion @ X1)))) | ((in @ X2 @ X3) = $false)) )),
% 1.65/1.32 inference(binary_proxy_clausification,[status(thm)],[f34])).
% 1.65/1.32 thf(f34,plain,(
% 1.65/1.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X2 @ X3) => ((in @ X3 @ X1) => (in @ X2 @ (setunion @ X1)))))) )),
% 1.65/1.32 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.65/1.32 thf(f33,plain,(
% 1.65/1.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ X2 @ Y0) => ((in @ Y0 @ X1) => (in @ X2 @ (setunion @ X1))))) @ X3))) )),
% 1.65/1.32 inference(pi_clausification,[status(thm)],[f32])).
% 1.65/1.32 thf(f32,plain,(
% 1.65/1.32 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ Y0) => ((in @ Y0 @ X1) => (in @ X2 @ (setunion @ X1)))))))) )),
% 1.65/1.32 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.65/1.32 thf(f31,plain,(
% 1.65/1.32 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ X1) => (in @ Y0 @ (setunion @ X1))))))) @ X2))) )),
% 1.65/1.32 inference(pi_clausification,[status(thm)],[f30])).
% 1.65/1.32 thf(f30,plain,(
% 1.65/1.32 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ X1) => (in @ Y0 @ (setunion @ X1)))))))))) )),
% 1.65/1.32 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.65/1.32 thf(f29,plain,(
% 1.65/1.32 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y2 @ Y0) => (in @ Y1 @ (setunion @ Y0))))))))) @ X1))) )),
% 1.65/1.32 inference(pi_clausification,[status(thm)],[f28])).
% 1.65/1.32 thf(f28,plain,(
% 1.65/1.32 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y2 @ Y0) => (in @ Y1 @ (setunion @ Y0)))))))))))),
% 1.65/1.32 inference(definition_unfolding,[status(thm)],[f22,f19])).
% 1.65/1.32 thf(f19,plain,(
% 1.65/1.32 (setunionI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y2 @ Y0) => (in @ Y1 @ (setunion @ Y0)))))))))))),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f14])).
% 1.65/1.32 thf(f14,plain,(
% 1.65/1.32 (setunionI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y2 @ Y0) => (in @ Y1 @ (setunion @ Y0)))))))))))),
% 1.65/1.32 inference(fool_elimination,[status(thm)],[f13])).
% 1.65/1.32 thf(f13,plain,(
% 1.65/1.32 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => ((in @ X0 @ X2) => (in @ X1 @ (setunion @ X2)))) = setunionI)),
% 1.65/1.32 inference(rectify,[status(thm)],[f2])).
% 1.65/1.32 thf(f2,axiom,(
% 1.65/1.32 (! [X3 : $i,X0 : $i,X2 : $i] : ((in @ X0 @ X3) => ((in @ X3 @ X2) => (in @ X0 @ (setunion @ X2)))) = setunionI)),
% 1.65/1.32 file('/export/starexec/sandbox2/tmp/tmp.G1MQ4SpQqS/DTF2THF_25039.p',setunionI)).
% 1.65/1.32 thf(f22,plain,(
% 1.65/1.32 (setunionI = $true)),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f18])).
% 1.65/1.32 thf(f25,plain,(
% 1.65/1.32 ($true != (subset @ sK0 @ (setunion @ (setadjoin @ sK0 @ emptyset))))),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f18])).
% 1.65/1.32 thf(f40,plain,(
% 1.65/1.32 ( ! [X2 : $i,X1 : $i] : (($true = (in @ X2 @ (setadjoin @ X2 @ X1)))) )),
% 1.65/1.32 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.65/1.32 thf(f39,plain,(
% 1.65/1.32 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ X1))) @ X2) = $true)) )),
% 1.65/1.32 inference(pi_clausification,[status(thm)],[f38])).
% 1.65/1.32 thf(f38,plain,(
% 1.65/1.32 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ X1)))))) )),
% 1.65/1.32 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.65/1.32 thf(f37,plain,(
% 1.65/1.32 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0))))) @ X1) = $true)) )),
% 1.65/1.32 inference(pi_clausification,[status(thm)],[f26])).
% 1.65/1.32 thf(f26,plain,(
% 1.65/1.32 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))))),
% 1.65/1.32 inference(definition_unfolding,[status(thm)],[f24,f20])).
% 1.65/1.32 thf(f20,plain,(
% 1.65/1.32 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))))),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f10])).
% 1.65/1.32 thf(f10,plain,(
% 1.65/1.32 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))))),
% 1.65/1.32 inference(fool_elimination,[status(thm)],[f9])).
% 1.65/1.32 thf(f9,plain,(
% 1.65/1.32 (! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)) = setadjoinIL)),
% 1.65/1.32 inference(rectify,[status(thm)],[f1])).
% 1.65/1.32 thf(f1,axiom,(
% 1.65/1.32 (! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)) = setadjoinIL)),
% 1.65/1.32 file('/export/starexec/sandbox2/tmp/tmp.G1MQ4SpQqS/DTF2THF_25039.p',setadjoinIL)).
% 1.65/1.32 thf(f24,plain,(
% 1.65/1.32 (setadjoinIL = $true)),
% 1.65/1.32 inference(cnf_transformation,[status(thm)],[f18])).
% 1.65/1.32 % SZS output end Proof for DTF2THF_25039
% 1.65/1.32 % (25182)------------------------------
% 1.65/1.32 % (25182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (25182)Termination reason: Refutation
% 1.65/1.32
% 1.65/1.32 % (25182)Memory used [KB]: 5500
% 1.65/1.32 % (25182)Time elapsed: 0.005 s
% 1.65/1.32 % (25182)Instructions burned: 8 (million)
% 1.65/1.32 % (25182)------------------------------
% 1.65/1.32 % (25182)------------------------------
% 1.65/1.32 % (25181)Success in time 0.015 s
%------------------------------------------------------------------------------