%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU534^2 : 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 : 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 09:35:08 AM UTC 2026
% Result : Theorem 1.48s 1.29s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 8
% Syntax : Number of formulae : 59 ( 30 unt; 0 typ; 2 def)
% Number of atoms : 380 ( 95 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 463 ( 21 ~; 21 |; 24 &; 306 @)
% ( 2 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 11 usr; 10 con; 0-2 aty)
% ( 31 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 126 ( 55 ^; 54 !; 17 ?; 126 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_15,type,
sK1: $i > $o ).
thf(func_def_19,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f73,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f50,f66,f72]) ).
thf(f72,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[status(thm)],[f71]) ).
thf(f71,plain,
( $false
| ~ spl3_1 ),
inference(equality_resolution,[status(thm)],[f68]) ).
thf(f68,plain,
( ! [X0: $o] : ( $false != X0 )
| ~ spl3_1 ),
inference(superposition,[status(thm)],[f5,f46]) ).
thf(f46,plain,
( ! [X2: $o] : ( $true = X2 )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f45,definition,
( spl3_1
<=> ! [X2: $o] : ( $true = X2 ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f5,plain,
$true != $false,
introduced(definition,[],[fool_axiom]) ).
thf(f66,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[status(thm)],[f65]) ).
thf(f65,plain,
( $false
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
( ( $true = $false )
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f60,f23]) ).
thf(f23,plain,
( $true
= ( sK1 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( emptyset
= ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) )
& ( $true
= ( sK1 @ sK2 ) )
& ( $true
= ( in @ sK2 @ sK0 ) )
& ( dsetconstrI = $true )
& ( emptysetE = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f15,f17,f16]) ).
thf(f16,plain,
( ? [X0: $i,X1: $i > $o] :
( ( emptyset
= ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
& ? [X2: $i] :
( ( ( X1 @ X2 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) )
=> ( ( emptyset
= ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) )
& ? [X2: $i] :
( ( $true
= ( sK1 @ X2 ) )
& ( $true
= ( in @ X2 @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ? [X2: $i] :
( ( $true
= ( sK1 @ X2 ) )
& ( $true
= ( in @ X2 @ sK0 ) ) )
=> ( ( $true
= ( sK1 @ sK2 ) )
& ( $true
= ( in @ sK2 @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i > $o] :
( ( emptyset
= ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
& ? [X2: $i] :
( ( ( X1 @ X2 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) )
& ( dsetconstrI = $true )
& ( emptysetE = $true ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ? [X0: $i,X1: $i > $o] :
( ( emptyset
= ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
& ? [X2: $i] :
( ( ( X1 @ X2 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) )
& ( emptysetE = $true )
& ( dsetconstrI = $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
~ ( ( dsetconstrI = $true )
=> ( ( emptysetE = $true )
=> ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( ( X1 @ X2 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
=> ( emptyset
!= ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( dsetconstrI = $true )
=> ( ( emptysetE = $true )
=> ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( ( X1 @ X2 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
=> ( emptyset
!= ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) ) ),
inference(true_and_false_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( dsetconstrI = $true )
=> ( ( emptysetE = $true )
=> ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( ( X1 @ X2 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
=> ( ( emptyset
= ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
=> $false ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( dsetconstrI
=> ( emptysetE
=> ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X0 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) )
= emptyset )
=> $false ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( dsetconstrI
=> ( emptysetE
=> ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X0 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> $false ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( dsetconstrI
=> ( emptysetE
=> ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X0 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> $false ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.u4JDJ0uL4A/DTF2THF_4790.p',emptyE1) ).
thf(f60,plain,
( ( ( sK1 @ sK2 )
= $false )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
( ( $true = $false )
| ( ( sK1 @ sK2 )
= $false )
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f22,f56]) ).
thf(f56,plain,
( ! [X0: $i] :
( ( $false
= ( in @ X0 @ sK0 ) )
| ( ( sK1 @ X0 )
= $false ) )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f51]) ).
thf(f51,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( sK1 @ X0 )
= $false )
| ( $false
= ( in @ X0 @ sK0 ) ) )
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f43,f49]) ).
thf(f49,plain,
( ! [X1: $i] :
( $false
= ( in @ X1 @ ( dsetconstr @ sK0 @ sK1 ) ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f48,definition,
( spl3_2
<=> ! [X1: $i] :
( $false
= ( in @ X1 @ ( dsetconstr @ sK0 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f43,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( $true
= ( in @ X1 @ ( dsetconstr @ X2 @ X3 ) ) )
| ( ( X3 @ X1 )
= $false )
| ( $false
= ( in @ X1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( $false
= ( in @ X1 @ X2 ) )
| ( ( ( X3 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ X2 @ X3 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X1 @ X2 )
=> ( ( X3 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ X2 @ X3 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( ( in @ X1 @ X2 )
=> ( ( Y0 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ X2 @ Y0 ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: $i,X1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X1 @ X2 )
=> ( ( Y0 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ X2 @ Y0 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ X1 @ Y0 )
=> ( ( Y1 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ X1 @ Y0 )
=> ( ( Y1 @ X1 )
=> ( in @ X1 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f25,f21]) ).
thf(f21,plain,
dsetconstrI = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f25,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ Y1 )
=> ( ( Y2 @ Y0 )
=> ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( dsetconstrI
= ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( X0 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X0 @ X3 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( dsetconstrI
= ( ! [X1: $i > $o,X0: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.u4JDJ0uL4A/DTF2THF_4790.p',dsetconstrI) ).
thf(f22,plain,
( $true
= ( in @ sK2 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f50,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f34,f48,f45]) ).
thf(f34,plain,
! [X2: $o,X1: $i] :
( ( $true = X2 )
| ( $false
= ( in @ X1 @ ( dsetconstr @ sK0 @ sK1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $o,X1: $i] :
( ( $true
= ( ^ [Y0: $o] : Y0
@ X2 ) )
| ( $false
= ( in @ X1 @ ( dsetconstr @ sK0 @ sK1 ) ) ) ),
inference(pi_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ ( dsetconstr @ sK0 @ sK1 ) ) )
| ( $true
= ( !! @ $o
@ ^ [Y0: $o] : Y0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ ( dsetconstr @ sK0 @ sK1 ) )
=> ( !! @ $o
@ ^ [Y0: $o] : Y0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK0 @ sK1 ) )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ sK0 @ sK1 ) )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( sK1 @ Y1 ) ) )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f20,f26]) ).
thf(f26,plain,
( emptysetE
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ sK0
@ ^ [Y1: $i] : ( sK1 @ Y1 ) ) )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f19,f24]) ).
thf(f24,plain,
( emptyset
= ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f19,plain,
( emptysetE
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( emptysetE
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i] :
( ( ( in @ X0 @ emptyset )
=> ! [X1: $o] : X1 )
= emptysetE ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X2: $i] :
( ( ( in @ X2 @ emptyset )
=> ! [X1: $o] : X1 )
= emptysetE ),
file('/export/starexec/sandbox2/tmp/tmp.u4JDJ0uL4A/DTF2THF_4790.p',emptysetE) ).
thf(f20,plain,
emptysetE = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU534^2 : 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 : n016.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 12:26:36 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SEU534^2 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.46 % Domain : Set Theory
% 0.19/0.46 % Problem : Preliminary Notions - Bounded Quantifier Laws
% 0.19/0.46 % Version : Especial > Reduced > Especial.
% 0.19/0.46 % English : (! A:i.! phi:i>o.(? x:i.in x A & phi x) -> dsetconstr A
% 0.19/0.46 % (^ x:i.phi x) = emptyset -> false)
% 0.19/0.46
% 0.19/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.46 % Source : [Bro08]
% 0.19/0.46 % Names : ZFC036l [Bro08]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.00 v8.2.0, 0.23 v8.1.0, 0.09 v7.5.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.1.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.60 v5.2.0, 0.40 v4.1.0, 0.33 v3.7.0
% 0.19/0.46 % Syntax : Number of formulae : 8 ( 2 unt; 5 typ; 2 def)
% 0.19/0.46 % Number of atoms : 12 ( 3 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 5 ( 4 avg)
% 0.19/0.46 % Number of connectives : 24 ( 0 ~; 0 |; 1 &; 16 @)
% 0.19/0.46 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 10 ( 4 avg)
% 0.19/0.46 % Number of types : 2 ( 0 usr)
% 0.19/0.46 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 7 ( 5 usr; 4 con; 0-2 aty)
% 0.19/0.46 % Number of variables : 10 ( 2 ^; 7 !; 1 ?; 10 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : http://mathgate.info/detsetitem.php?id=385
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(in_type,type,
% 0.19/0.46 in: $i > $i > $o ).
% 0.19/0.46
% 0.19/0.46 thf(emptyset_type,type,
% 0.19/0.46 emptyset: $i ).
% 0.19/0.46
% 0.19/0.46 thf(dsetconstr_type,type,
% 0.19/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.19/0.46
% 0.19/0.46 thf(dsetconstrI_type,type,
% 0.19/0.46 dsetconstrI: $o ).
% 0.19/0.46
% 0.19/0.46 thf(dsetconstrI,definition,
% 0.19/0.46 ( dsetconstrI
% 0.19/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 => ( ( Xphi @ Xx )
% 0.19/0.46 => ( in @ Xx
% 0.19/0.46 @ ( dsetconstr @ A
% 0.19/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(emptysetE_type,type,
% 0.19/0.46 emptysetE: $o ).
% 0.19/0.46
% 0.19/0.46 thf(emptysetE,definition,
% 0.19/0.46 ( emptysetE
% 0.19/0.46 = ( ! [Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ emptyset )
% 0.19/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(emptyE1,conjecture,
% 0.19/0.46 ( dsetconstrI
% 0.19/0.46 => ( emptysetE
% 0.19/0.46 => ! [A: $i,Xphi: $i > $o] :
% 0.19/0.46 ( ? [Xx: $i] :
% 0.19/0.46 ( ( in @ Xx @ A )
% 0.19/0.46 & ( Xphi @ Xx ) )
% 0.19/0.46 => ( ( ( dsetconstr @ A
% 0.19/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.46 = emptyset )
% 0.19/0.46 => $false ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.48/1.25 ---- Embedded in THF ---
% 1.48/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.25 %%% Generated on Tue Feb 24 12:26:37 EST 2026
% 1.48/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.25 %%% Logic specification used:
% 1.48/1.25 %%% thf(spec, logic, $$dhol).
% 1.48/1.25
% 1.48/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.u4JDJ0uL4A/DTF2DTF4790.p
% See solution above
% 1.48/1.25 ------------------------
% 1.48/1.26 ---- Cleaned THF ---
% 1.48/1.26 thf(in_type,type,
% 1.48/1.26 in: $i > $i > $o ).
% 1.48/1.26
% 1.48/1.26 thf(emptyset_type,type,
% 1.48/1.26 emptyset: $i ).
% 1.48/1.26
% 1.48/1.26 thf(dsetconstr_type,type,
% 1.48/1.26 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.48/1.26
% 1.48/1.26 thf(dsetconstrI_type,type,
% 1.48/1.26 dsetconstrI: $o ).
% 1.48/1.26
% 1.48/1.26 thf(dsetconstrI,definition,
% 1.48/1.26 ( dsetconstrI
% 1.48/1.26 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.48/1.26 ( ( in @ Xx @ A )
% 1.48/1.26 => ( ( Xphi @ Xx )
% 1.48/1.26 => ( in @ Xx
% 1.48/1.26 @ ( dsetconstr @ A
% 1.48/1.26 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.48/1.26
% 1.48/1.26 thf(emptysetE_type,type,
% 1.48/1.26 emptysetE: $o ).
% 1.48/1.26
% 1.48/1.26 thf(emptysetE,definition,
% 1.48/1.26 ( emptysetE
% 1.48/1.26 = ( ! [Xx: $i] :
% 1.48/1.26 ( ( in @ Xx @ emptyset )
% 1.48/1.26 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.48/1.26
% 1.48/1.26 thf(emptyE1,conjecture,
% 1.48/1.26 ( dsetconstrI
% 1.48/1.26 => ( emptysetE
% 1.48/1.26 => ! [A: $i,Xphi: $i > $o] :
% 1.48/1.26 ( ? [Xx: $i] :
% 1.48/1.26 ( ( in @ Xx @ A )
% 1.48/1.26 & ( Xphi @ Xx ) )
% 1.48/1.26 => ( ( ( dsetconstr @ A
% 1.48/1.26 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.48/1.26 = emptyset )
% 1.48/1.26 => $false ) ) ) ) ).
% 1.48/1.26 ------------------------
% 1.48/1.27 % (4949)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4790 for (2999ds/2Mi)
% 1.48/1.27 % (4947)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_4790 for (2999ds/4Mi)
% 1.48/1.27 % (4949)Instruction limit reached!
% 1.48/1.27 % (4949)------------------------------
% 1.48/1.27 % (4949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.27 % (4949)Termination reason: Unknown
% 1.48/1.27 % (4949)Termination phase: Saturation
% 1.48/1.27
% 1.48/1.27 % (4949)Memory used [KB]: 1023
% 1.48/1.27 % (4949)Time elapsed: 0.002 s
% 1.48/1.27 % (4949)Instructions burned: 2 (million)
% 1.48/1.27 % (4949)------------------------------
% 1.48/1.27 % (4949)------------------------------
% 1.48/1.28 % (4947)Instruction limit reached!
% 1.48/1.28 % (4947)------------------------------
% 1.48/1.28 % (4947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (4947)Termination reason: Unknown
% 1.48/1.28 % (4947)Termination phase: Saturation
% 1.48/1.28
% 1.48/1.28 % (4947)Memory used [KB]: 5500
% 1.48/1.28 % (4947)Time elapsed: 0.003 s
% 1.48/1.28 % (4947)Instructions burned: 4 (million)
% 1.48/1.28 % (4947)------------------------------
% 1.48/1.28 % (4947)------------------------------
% 1.48/1.28 % (4946)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4790 for (2999ds/183Mi)
% 1.48/1.28 % (4950)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_4790 for (2999ds/2Mi)
% 1.48/1.28 % (4948)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_4790 for (2999ds/27Mi)
% 1.48/1.28 % (4951)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_4790 for (2999ds/275Mi)
% 1.48/1.28 % (4952)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4790 for (2999ds/18Mi)
% 1.48/1.28 % (4950)Instruction limit reached!
% 1.48/1.28 % (4950)------------------------------
% 1.48/1.28 % (4950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (4950)Termination reason: Unknown
% 1.48/1.28 % (4950)Termination phase: Property scanning
% 1.48/1.28
% 1.48/1.28 % (4950)Memory used [KB]: 895
% 1.48/1.28 % (4950)Time elapsed: 0.003 s
% 1.48/1.28 % (4950)Instructions burned: 2 (million)
% 1.48/1.28 % (4950)------------------------------
% 1.48/1.28 % (4950)------------------------------
% 1.48/1.28 % (4951)Refutation not found, incomplete strategy
% 1.48/1.28 % (4951)------------------------------
% 1.48/1.28 % (4951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (4951)Termination reason: Refutation not found, incomplete strategy
% 1.48/1.28
% 1.48/1.28
% 1.48/1.28 % (4951)Memory used [KB]: 5500
% 1.48/1.28 % (4951)Time elapsed: 0.005 s
% 1.48/1.28 % (4951)Instructions burned: 4 (million)
% 1.48/1.28 % (4951)------------------------------
% 1.48/1.28 % (4951)------------------------------
% 1.48/1.28 % (4954)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4790 for (2999ds/3Mi)
% 1.48/1.28 % (4946)First to succeed.
% 1.48/1.29 % (4954)Instruction limit reached!
% 1.48/1.29 % (4954)------------------------------
% 1.48/1.29 % (4954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (4954)Termination reason: Unknown
% 1.48/1.29 % (4954)Termination phase: Saturation
% 1.48/1.29
% 1.48/1.29 % (4954)Memory used [KB]: 5500
% 1.48/1.29 % (4954)Time elapsed: 0.002 s
% 1.48/1.29 % (4954)Instructions burned: 3 (million)
% 1.48/1.29 % (4954)------------------------------
% 1.48/1.29 % (4954)------------------------------
% 1.48/1.29 % (4955)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_4790 for (2999ds/37Mi)
% 1.48/1.29 % (4952)Also succeeded, but the first one will report.
% 1.48/1.29 % (4946)Refutation found. Thanks to Tanya!
% 1.48/1.29 % SZS status Theorem for DTF2THF_4790
% 1.48/1.29 % SZS output start Proof for DTF2THF_4790
% 1.48/1.29 thf(func_def_0, type, in: $i > $i > $o).
% 1.48/1.29 thf(func_def_2, type, dsetconstr: $i > ($i > $o) > $i).
% 1.48/1.29 thf(func_def_15, type, sK1: $i > $o).
% 1.48/1.29 thf(func_def_19, type, ph4: !>[X0: $tType]:(X0)).
% 1.48/1.29 thf(f73,plain,(
% 1.48/1.29 $false),
% 1.48/1.29 inference(avatar_sat_refutation,[status(thm)],[f50,f66,f72])).
% 1.48/1.29 thf(f72,plain,(
% 1.48/1.29 ~spl3_1),
% 1.48/1.29 inference(avatar_contradiction_clause,[status(thm)],[f71])).
% 1.48/1.29 thf(f71,plain,(
% 1.48/1.29 $false | ~spl3_1),
% 1.48/1.29 inference(equality_resolution,[status(thm)],[f68])).
% 1.48/1.29 thf(f68,plain,(
% 1.48/1.29 ( ! [X0 : $o] : (($false != X0)) ) | ~spl3_1),
% 1.48/1.29 inference(superposition,[status(thm)],[f5,f46])).
% 1.48/1.29 thf(f46,plain,(
% 1.48/1.29 ( ! [X2 : $o] : (($true = X2)) ) | ~spl3_1),
% 1.48/1.29 inference(avatar_component_clause,[status(thm)],[f45])).
% 1.48/1.29 thf(f45,definition,(
% 1.48/1.29 spl3_1 <=> ! [X2 : $o] : ($true = X2)),
% 1.48/1.29 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.48/1.29 thf(f5,plain,(
% 1.48/1.29 ($true != $false)),
% 1.48/1.29 introduced(definition,[],[fool_axiom])).
% 1.48/1.29 thf(f66,plain,(
% 1.48/1.29 ~spl3_2),
% 1.48/1.29 inference(avatar_contradiction_clause,[status(thm)],[f65])).
% 1.48/1.29 thf(f65,plain,(
% 1.48/1.29 $false | ~spl3_2),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 1.48/1.29 thf(f61,plain,(
% 1.48/1.29 ($true = $false) | ~spl3_2),
% 1.48/1.29 inference(superposition,[status(thm)],[f60,f23])).
% 1.48/1.29 thf(f23,plain,(
% 1.48/1.29 ($true = (sK1 @ sK2))),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f18])).
% 1.48/1.29 thf(f18,plain,(
% 1.48/1.29 ((emptyset = (dsetconstr @ sK0 @ (^[Y0 : $i]: (sK1 @ Y0)))) & (($true = (sK1 @ sK2)) & ($true = (in @ sK2 @ sK0)))) & (dsetconstrI = $true) & (emptysetE = $true)),
% 1.48/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f15,f17,f16])).
% 1.48/1.29 thf(f16,plain,(
% 1.48/1.29 ? [X0 : $i,X1 : $i > $o] : ((emptyset = (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) & ? [X2 : $i] : (((X1 @ X2) = $true) & ((in @ X2 @ X0) = $true))) => ((emptyset = (dsetconstr @ sK0 @ (^[Y0 : $i]: (sK1 @ Y0)))) & ? [X2 : $i] : (($true = (sK1 @ X2)) & ($true = (in @ X2 @ sK0))))),
% 1.48/1.29 introduced(definition,[],[choice_axiom])).
% 1.48/1.29 thf(f17,plain,(
% 1.48/1.29 ? [X2 : $i] : (($true = (sK1 @ X2)) & ($true = (in @ X2 @ sK0))) => (($true = (sK1 @ sK2)) & ($true = (in @ sK2 @ sK0)))),
% 1.48/1.29 introduced(definition,[],[choice_axiom])).
% 1.48/1.29 thf(f15,plain,(
% 1.48/1.29 ? [X0 : $i,X1 : $i > $o] : ((emptyset = (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) & ? [X2 : $i] : (((X1 @ X2) = $true) & ((in @ X2 @ X0) = $true))) & (dsetconstrI = $true) & (emptysetE = $true)),
% 1.48/1.29 inference(flattening,[status(thm)],[f14])).
% 1.48/1.29 thf(f14,plain,(
% 1.48/1.29 (? [X0 : $i,X1 : $i > $o] : ((emptyset = (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) & ? [X2 : $i] : (((X1 @ X2) = $true) & ((in @ X2 @ X0) = $true))) & (emptysetE = $true)) & (dsetconstrI = $true)),
% 1.48/1.29 inference(ennf_transformation,[status(thm)],[f13])).
% 1.48/1.29 thf(f13,plain,(
% 1.48/1.29 ~((dsetconstrI = $true) => ((emptysetE = $true) => ! [X0 : $i,X1 : $i > $o] : (? [X2 : $i] : (((X1 @ X2) = $true) & ((in @ X2 @ X0) = $true)) => (emptyset != (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))))),
% 1.48/1.29 inference(flattening,[status(thm)],[f12])).
% 1.48/1.29 thf(f12,plain,(
% 1.48/1.29 ~((dsetconstrI = $true) => ((emptysetE = $true) => ! [X0 : $i,X1 : $i > $o] : (? [X2 : $i] : (((X1 @ X2) = $true) & ((in @ X2 @ X0) = $true)) => ~(emptyset = (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))))),
% 1.48/1.29 inference(true_and_false_elimination,[status(thm)],[f7])).
% 1.48/1.29 thf(f7,plain,(
% 1.48/1.29 ~((dsetconstrI = $true) => ((emptysetE = $true) => ! [X0 : $i,X1 : $i > $o] : (? [X2 : $i] : (((X1 @ X2) = $true) & ((in @ X2 @ X0) = $true)) => ((emptyset = (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) => $false))))),
% 1.48/1.29 inference(fool_elimination,[status(thm)],[f6])).
% 1.48/1.29 thf(f6,plain,(
% 1.48/1.29 ~(dsetconstrI => (emptysetE => ! [X0 : $i,X1 : $i > $o] : (? [X2 : $i] : ((in @ X2 @ X0) & (X1 @ X2)) => (((dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3))) = emptyset) => $false))))),
% 1.48/1.29 inference(rectify,[status(thm)],[f4])).
% 1.48/1.29 thf(f4,negated_conjecture,(
% 1.48/1.29 ~(dsetconstrI => (emptysetE => ! [X0 : $i,X1 : $i > $o] : (? [X2 : $i] : ((in @ X2 @ X0) & (X1 @ X2)) => (((dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))) = emptyset) => $false))))),
% 1.48/1.29 inference(negated_conjecture,[status(cth)],[f3])).
% 1.48/1.29 thf(f3,conjecture,(
% 1.48/1.29 dsetconstrI => (emptysetE => ! [X0 : $i,X1 : $i > $o] : (? [X2 : $i] : ((in @ X2 @ X0) & (X1 @ X2)) => (((dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))) = emptyset) => $false)))),
% 1.48/1.29 file('/export/starexec/sandbox2/tmp/tmp.u4JDJ0uL4A/DTF2THF_4790.p',emptyE1)).
% 1.48/1.29 thf(f60,plain,(
% 1.48/1.29 ((sK1 @ sK2) = $false) | ~spl3_2),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.48/1.29 thf(f58,plain,(
% 1.48/1.29 ($true = $false) | ((sK1 @ sK2) = $false) | ~spl3_2),
% 1.48/1.29 inference(superposition,[status(thm)],[f22,f56])).
% 1.48/1.29 thf(f56,plain,(
% 1.48/1.29 ( ! [X0 : $i] : (($false = (in @ X0 @ sK0)) | ((sK1 @ X0) = $false)) ) | ~spl3_2),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f51])).
% 1.48/1.29 thf(f51,plain,(
% 1.48/1.29 ( ! [X0 : $i] : (($true = $false) | ((sK1 @ X0) = $false) | ($false = (in @ X0 @ sK0))) ) | ~spl3_2),
% 1.48/1.29 inference(superposition,[status(thm)],[f43,f49])).
% 1.48/1.29 thf(f49,plain,(
% 1.48/1.29 ( ! [X1 : $i] : (($false = (in @ X1 @ (dsetconstr @ sK0 @ sK1)))) ) | ~spl3_2),
% 1.48/1.29 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.48/1.29 thf(f48,definition,(
% 1.48/1.29 spl3_2 <=> ! [X1 : $i] : ($false = (in @ X1 @ (dsetconstr @ sK0 @ sK1)))),
% 1.48/1.29 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.48/1.29 thf(f43,plain,(
% 1.48/1.29 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = (in @ X1 @ (dsetconstr @ X2 @ X3))) | ((X3 @ X1) = $false) | ($false = (in @ X1 @ X2))) )),
% 1.48/1.29 inference(binary_proxy_clausification,[status(thm)],[f42])).
% 1.48/1.29 thf(f42,plain,(
% 1.48/1.29 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($false = (in @ X1 @ X2)) | (((X3 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ X3))) = $true)) )),
% 1.48/1.29 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.48/1.29 thf(f41,plain,(
% 1.48/1.29 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((in @ X1 @ X2) => ((X3 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ X3)))) = $true)) )),
% 1.48/1.29 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.48/1.29 thf(f40,plain,(
% 1.48/1.29 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: ((in @ X1 @ X2) => ((Y0 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ Y0))))) @ X3))) )),
% 1.48/1.29 inference(pi_clausification,[status(thm)],[f39])).
% 1.48/1.29 thf(f39,plain,(
% 1.48/1.29 ( ! [X2 : $i,X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X1 @ X2) => ((Y0 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ Y0)))))) = $true)) )),
% 1.48/1.29 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.48/1.29 thf(f38,plain,(
% 1.48/1.29 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ X1 @ Y0) => ((Y1 @ X1) => (in @ X1 @ (dsetconstr @ Y0 @ Y1))))))) @ X2))) )),
% 1.48/1.29 inference(pi_clausification,[status(thm)],[f37])).
% 1.48/1.29 thf(f37,plain,(
% 1.48/1.29 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ X1 @ Y0) => ((Y1 @ X1) => (in @ X1 @ (dsetconstr @ Y0 @ Y1)))))))))) )),
% 1.48/1.29 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.48/1.29 thf(f36,plain,(
% 1.48/1.29 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2))))))))) @ X1) = $true)) )),
% 1.48/1.29 inference(pi_clausification,[status(thm)],[f35])).
% 1.48/1.29 thf(f35,plain,(
% 1.48/1.29 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))))),
% 1.48/1.29 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.48/1.29 thf(f28,plain,(
% 1.48/1.29 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))) = $true)),
% 1.48/1.29 inference(definition_unfolding,[status(thm)],[f25,f21])).
% 1.48/1.29 thf(f21,plain,(
% 1.48/1.29 (dsetconstrI = $true)),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f18])).
% 1.48/1.29 thf(f25,plain,(
% 1.48/1.29 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.48/1.29 thf(f11,plain,(
% 1.48/1.29 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 1.48/1.29 inference(fool_elimination,[status(thm)],[f10])).
% 1.48/1.29 thf(f10,plain,(
% 1.48/1.29 (dsetconstrI = ! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => ((X0 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X0 @ X3)))))))),
% 1.48/1.29 inference(rectify,[status(thm)],[f1])).
% 1.48/1.29 thf(f1,axiom,(
% 1.48/1.29 (dsetconstrI = ! [X1 : $i > $o,X0 : $i,X2 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))))),
% 1.48/1.29 file('/export/starexec/sandbox2/tmp/tmp.u4JDJ0uL4A/DTF2THF_4790.p',dsetconstrI)).
% 1.48/1.29 thf(f22,plain,(
% 1.48/1.29 ($true = (in @ sK2 @ sK0))),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f18])).
% 1.48/1.29 thf(f50,plain,(
% 1.48/1.29 spl3_1 | spl3_2),
% 1.48/1.29 inference(avatar_split_clause,[status(thm)],[f34,f48,f45])).
% 1.48/1.29 thf(f34,plain,(
% 1.48/1.29 ( ! [X2 : $o,X1 : $i] : (($true = X2) | ($false = (in @ X1 @ (dsetconstr @ sK0 @ sK1)))) )),
% 1.48/1.29 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.48/1.29 thf(f33,plain,(
% 1.48/1.29 ( ! [X2 : $o,X1 : $i] : (($true = ((^[Y0 : $o]: (Y0)) @ X2)) | ($false = (in @ X1 @ (dsetconstr @ sK0 @ sK1)))) )),
% 1.48/1.29 inference(pi_clausification,[status(thm)],[f32])).
% 1.48/1.29 thf(f32,plain,(
% 1.48/1.29 ( ! [X1 : $i] : (($false = (in @ X1 @ (dsetconstr @ sK0 @ sK1))) | ($true = (!! @ $o @ (^[Y0 : $o]: (Y0))))) )),
% 1.48/1.29 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.48/1.29 thf(f31,plain,(
% 1.48/1.29 ( ! [X1 : $i] : (($true = ((in @ X1 @ (dsetconstr @ sK0 @ sK1)) => (!! @ $o @ (^[Y0 : $o]: (Y0)))))) )),
% 1.48/1.29 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.48/1.29 thf(f30,plain,(
% 1.48/1.29 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK0 @ sK1)) => (!! @ $o @ (^[Y1 : $o]: (Y1))))) @ X1))) )),
% 1.48/1.29 inference(pi_clausification,[status(thm)],[f29])).
% 1.48/1.29 thf(f29,plain,(
% 1.48/1.29 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK0 @ sK1)) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))))),
% 1.48/1.29 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.48/1.29 thf(f27,plain,(
% 1.48/1.29 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK0 @ (^[Y1 : $i]: (sK1 @ Y1)))) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) = $true)),
% 1.48/1.29 inference(definition_unfolding,[status(thm)],[f20,f26])).
% 1.48/1.29 thf(f26,plain,(
% 1.48/1.29 (emptysetE = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ sK0 @ (^[Y1 : $i]: (sK1 @ Y1)))) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))))),
% 1.48/1.29 inference(definition_unfolding,[status(thm)],[f19,f24])).
% 1.48/1.29 thf(f24,plain,(
% 1.48/1.29 (emptyset = (dsetconstr @ sK0 @ (^[Y0 : $i]: (sK1 @ Y0))))),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f18])).
% 1.48/1.29 thf(f19,plain,(
% 1.48/1.29 (emptysetE = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))))),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f9])).
% 1.48/1.29 thf(f9,plain,(
% 1.48/1.29 (emptysetE = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))))),
% 1.48/1.29 inference(fool_elimination,[status(thm)],[f8])).
% 1.48/1.29 thf(f8,plain,(
% 1.48/1.29 (! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1) = emptysetE)),
% 1.48/1.29 inference(rectify,[status(thm)],[f2])).
% 1.48/1.29 thf(f2,axiom,(
% 1.48/1.29 (! [X2 : $i] : ((in @ X2 @ emptyset) => ! [X1 : $o] : X1) = emptysetE)),
% 1.48/1.29 file('/export/starexec/sandbox2/tmp/tmp.u4JDJ0uL4A/DTF2THF_4790.p',emptysetE)).
% 1.48/1.29 thf(f20,plain,(
% 1.48/1.29 (emptysetE = $true)),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f18])).
% 1.48/1.29 % SZS output end Proof for DTF2THF_4790
% 1.48/1.29 % (4946)------------------------------
% 1.48/1.29 % (4946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (4946)Termination reason: Refutation
% 1.48/1.29
% 1.48/1.29 % (4946)Memory used [KB]: 5500
% 1.48/1.29 % (4946)Time elapsed: 0.009 s
% 1.48/1.29 % (4946)Instructions burned: 5 (million)
% 1.48/1.29 % (4946)------------------------------
% 1.48/1.29 % (4946)------------------------------
% 1.48/1.29 % (4945)Success in time 0.014 s
%------------------------------------------------------------------------------