%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU510^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n022.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 09:35:00 AM UTC 2026
% Result : Theorem 1.64s 1.37s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 8
% Syntax : Number of formulae : 63 ( 36 unt; 0 typ; 2 def)
% Number of atoms : 367 ( 94 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 427 ( 31 ~; 23 |; 16 &; 279 @)
% ( 2 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 10 con; 0-2 aty)
% ( 27 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 117 ( 53 ^; 55 !; 9 ?; 117 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_6,type,
nonempty: $i > $o ).
thf(func_def_7,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_21,type,
sK2: $i > $o ).
thf(func_def_23,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f70,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f53,f59,f69]) ).
thf(f69,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[status(thm)],[f68]) ).
thf(f68,plain,
( $false
| ~ spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
( ( $false = $true )
| ~ spl3_1 ),
inference(backward_demodulation,[status(thm)],[f22,f65]) ).
thf(f65,plain,
( ( ( sK2 @ sK0 )
= $false )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ( ( sK2 @ sK0 )
= $false )
| ( $false = $true )
| ~ spl3_1 ),
inference(superposition,[status(thm)],[f62,f23]) ).
thf(f23,plain,
( ( in @ sK0 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( emptysetE = $true )
& ( dsetconstrI = $true )
& ( ( in @ sK0 @ sK1 )
= $true )
& ( ( sK2 @ sK0 )
= $true )
& ( ( nonempty
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f16,f17]) ).
thf(f17,plain,
( ? [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X0 @ X1 )
= $true )
& ( ( X2 @ X0 )
= $true )
& ( ( nonempty
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true ) )
=> ( ( ( in @ sK0 @ sK1 )
= $true )
& ( ( sK2 @ sK0 )
= $true )
& ( ( nonempty
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ( emptysetE = $true )
& ( dsetconstrI = $true )
& ? [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X0 @ X1 )
= $true )
& ( ( X2 @ X0 )
= $true )
& ( ( nonempty
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true ) ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i,X2: $i > $o] :
( ( ( nonempty
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true )
& ( ( X2 @ X0 )
= $true )
& ( ( in @ X0 @ X1 )
= $true ) )
& ( emptysetE = $true )
& ( dsetconstrI = $true ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
~ ( ( dsetconstrI = $true )
=> ( ( emptysetE = $true )
=> ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( ( X2 @ X0 )
= $true )
=> ( ( nonempty
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( dsetconstrI
=> ( emptysetE
=> ! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X0 @ X1 )
=> ( ( X2 @ X0 )
=> ( nonempty
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( dsetconstrI
=> ( emptysetE
=> ! [X2: $i,X0: $i,X1: $i > $o] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( dsetconstrI
=> ( emptysetE
=> ! [X2: $i,X0: $i,X1: $i > $o] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4umWNL8vtI/DTF2THF_28778.p',nonemptyI) ).
thf(f62,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK1 )
= $false )
| ( ( sK2 @ X0 )
= $false ) )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( ( in @ X0 @ sK1 )
= $false )
| ( ( sK2 @ X0 )
= $false ) )
| ~ spl3_1 ),
inference(forward_demodulation,[status(thm)],[f60,f49]) ).
thf(f49,plain,
( ! [X1: $i] :
( ( in @ X1 @ emptyset )
= $false )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f48,definition,
( spl3_1
<=> ! [X1: $i] :
( ( in @ X1 @ emptyset )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f60,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK1 )
= $false )
| ( ( in @ X0 @ emptyset )
= $true )
| ( ( sK2 @ X0 )
= $false ) ),
inference(superposition,[status(thm)],[f41,f32]) ).
thf(f32,plain,
( emptyset
= ( dsetconstr @ sK1 @ sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( ( emptyset
= ( dsetconstr @ sK1 @ sK2 ) )
= $true ),
inference(not_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( emptyset
!= ( dsetconstr @ sK1 @ sK2 ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ^ [Y0: $i] : ( emptyset != Y0 )
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f21,f20]) ).
thf(f20,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
( nonempty
= ( ^ [X0: $i] : ( emptyset != X0 ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( nonempty
= ( ^ [X2: $i] : ( emptyset != X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4umWNL8vtI/DTF2THF_28778.p',nonempty) ).
thf(f21,plain,
( ( nonempty
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( sK2 @ Y0 ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f41,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) )
= $true )
| ( ( X1 @ X3 )
= $false )
| ( ( in @ X3 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( in @ X3 @ X2 )
= $false )
| ( ( ( X1 @ X3 )
=> ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( in @ X3 @ X2 )
=> ( ( X1 @ X3 )
=> ( in @ X3 @ ( dsetconstr @ X2 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X2 @ X1 ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: $i,X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X2 @ X1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( X1 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ X1 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( X1 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y0 @ X1 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f24,f19]) ).
thf(f19,plain,
( dsetconstrI
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( dsetconstrI
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( in @ Y2
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( dsetconstrI
= ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X0 @ X1 )
=> ( ( X2 @ X0 )
=> ( in @ X0
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( dsetconstrI
= ( ! [X2: $i,X0: $i,X1: $i > $o] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4umWNL8vtI/DTF2THF_28778.p',dsetconstrI) ).
thf(f24,plain,
dsetconstrI = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f22,plain,
( ( sK2 @ sK0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f59,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[status(thm)],[f58]) ).
thf(f58,plain,
( $false
| ~ spl3_2 ),
inference(equality_resolution,[status(thm)],[f55]) ).
thf(f55,plain,
( ! [X0: $o] : ( $false != X0 )
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f6,f52]) ).
thf(f52,plain,
( ! [X2: $o] : ( $true = X2 )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f51,definition,
( spl3_2
<=> ! [X2: $o] : ( $true = X2 ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f6,plain,
$false != $true,
introduced(definition,[],[fool_axiom]) ).
thf(f53,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f46,f51,f48]) ).
thf(f46,plain,
! [X2: $o,X1: $i] :
( ( $true = X2 )
| ( ( in @ X1 @ emptyset )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: $o,X1: $i] :
( ( ( in @ X1 @ emptyset )
= $false )
| ( ( ^ [Y0: $o] : Y0
@ X2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X1: $i] :
( ( ( !! @ $o
@ ^ [Y0: $o] : Y0 )
= $true )
| ( ( in @ X1 @ emptyset )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X1: $i] :
( ( ( in @ X1 @ emptyset )
=> ( !! @ $o
@ ^ [Y0: $o] : Y0 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f26,f25]) ).
thf(f25,plain,
emptysetE = $true,
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f26,plain,
( emptysetE
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( emptysetE
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !! @ $o
@ ^ [Y1: $o] : Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( emptysetE
= ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> ! [X1: $o] : X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( emptysetE
= ( ! [X2: $i] :
( ( in @ X2 @ emptyset )
=> ! [X1: $o] : X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4umWNL8vtI/DTF2THF_28778.p',emptysetE) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU510^2 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n022.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 12:25:06 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : SEU510^2 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.47 % Domain : Set Theory
% 0.31/0.47 % Problem : Preliminary Notions - Basic Laws of Logic
% 0.31/0.47 % Version : Especial > Reduced > Especial.
% 0.31/0.47 % English : (! A:i.! phi:i>o.! x:i.in x A -> phi x -> nonempty (dsetconstr A
% 0.31/0.47 % (^ y:i.phi y)))
% 0.31/0.47
% 0.31/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.31/0.47 % Source : [Bro08]
% 0.31/0.47 % Names : ZFC012l [Bro08]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % Rating : 0.00 v9.0.0, 0.10 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, 0.33 v5.4.0, 0.20 v5.3.0, 0.60 v5.2.0, 0.40 v4.1.0, 0.33 v3.7.0
% 0.31/0.47 % Syntax : Number of formulae : 10 ( 3 unt; 6 typ; 3 def)
% 0.31/0.47 % Number of atoms : 14 ( 4 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 4 ( 3 avg)
% 0.31/0.47 % Number of connectives : 25 ( 1 ~; 0 |; 0 &; 17 @)
% 0.31/0.47 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 12 ( 4 avg)
% 0.31/0.47 % Number of types : 2 ( 0 usr)
% 0.31/0.47 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 7 ( 6 usr; 3 con; 0-2 aty)
% 0.31/0.47 % Number of variables : 11 ( 3 ^; 8 !; 0 ?; 11 :)
% 0.31/0.47 % SPC : TH0_THM_EQU_NAR
% 0.31/0.47
% 0.31/0.47 % Comments : http://mathgate.info/detsetitem.php?id=430
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 thf(in_type,type,
% 0.31/0.47 in: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyset_type,type,
% 0.31/0.47 emptyset: $i ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstr_type,type,
% 0.31/0.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrI_type,type,
% 0.31/0.47 dsetconstrI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrI,definition,
% 0.31/0.47 ( dsetconstrI
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 => ( in @ Xx
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetE_type,type,
% 0.31/0.47 emptysetE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetE,definition,
% 0.31/0.47 ( emptysetE
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ emptyset )
% 0.31/0.47 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonempty_type,type,
% 0.31/0.47 nonempty: $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonempty,definition,
% 0.31/0.47 ( nonempty
% 0.31/0.47 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyI,conjecture,
% 0.31/0.47 ( dsetconstrI
% 0.31/0.47 => ( emptysetE
% 0.31/0.47 => ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 => ( nonempty
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 1.64/1.34 ---- Embedded in THF ---
% 1.64/1.34 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.34 %%% Generated on Tue Feb 24 12:25:07 EST 2026
% 1.64/1.34 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.34 %%% Logic specification used:
% 1.64/1.34 %%% thf(spec, logic, $$dhol).
% 1.64/1.34
% 1.64/1.34 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.4umWNL8vtI/DTF2DTF28778.p
% See solution above
% 1.64/1.34 ------------------------
% 1.64/1.35 ---- Cleaned THF ---
% 1.64/1.35 thf(in_type,type,
% 1.64/1.35 in: $i > $i > $o ).
% 1.64/1.35
% 1.64/1.35 thf(emptyset_type,type,
% 1.64/1.35 emptyset: $i ).
% 1.64/1.35
% 1.64/1.35 thf(dsetconstr_type,type,
% 1.64/1.35 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.64/1.35
% 1.64/1.35 thf(dsetconstrI_type,type,
% 1.64/1.35 dsetconstrI: $o ).
% 1.64/1.35
% 1.64/1.35 thf(dsetconstrI,definition,
% 1.64/1.35 ( dsetconstrI
% 1.64/1.35 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.64/1.35 ( ( in @ Xx @ A )
% 1.64/1.35 => ( ( Xphi @ Xx )
% 1.64/1.35 => ( in @ Xx
% 1.64/1.35 @ ( dsetconstr @ A
% 1.64/1.35 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.64/1.35
% 1.64/1.35 thf(emptysetE_type,type,
% 1.64/1.35 emptysetE: $o ).
% 1.64/1.35
% 1.64/1.35 thf(emptysetE,definition,
% 1.64/1.35 ( emptysetE
% 1.64/1.35 = ( ! [Xx: $i] :
% 1.64/1.35 ( ( in @ Xx @ emptyset )
% 1.64/1.35 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.64/1.35
% 1.64/1.35 thf(nonempty_type,type,
% 1.64/1.35 nonempty: $i > $o ).
% 1.64/1.35
% 1.64/1.35 thf(nonempty,definition,
% 1.64/1.35 ( nonempty
% 1.64/1.35 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 1.64/1.35
% 1.64/1.35 thf(nonemptyI,conjecture,
% 1.64/1.35 ( dsetconstrI
% 1.64/1.35 => ( emptysetE
% 1.64/1.35 => ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.64/1.35 ( ( in @ Xx @ A )
% 1.64/1.35 => ( ( Xphi @ Xx )
% 1.64/1.35 => ( nonempty
% 1.64/1.35 @ ( dsetconstr @ A
% 1.64/1.35 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.64/1.35 ------------------------
% 1.64/1.37 % (28897)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_28778 for (2999ds/275Mi)
% 1.64/1.37 % (28894)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_28778 for (2999ds/27Mi)
% 1.64/1.37 % (28897)Refutation not found, incomplete strategy
% 1.64/1.37 % (28897)------------------------------
% 1.64/1.37 % (28897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.37 % (28897)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.37
% 1.64/1.37
% 1.64/1.37 % (28897)Memory used [KB]: 5500
% 1.64/1.37 % (28897)Time elapsed: 0.003 s
% 1.64/1.37 % (28897)Instructions burned: 4 (million)
% 1.64/1.37 % (28897)------------------------------
% 1.64/1.37 % (28897)------------------------------
% 1.64/1.37 % (28894)First to succeed.
% 1.64/1.37 % (28894)Refutation found. Thanks to Tanya!
% 1.64/1.37 % SZS status Theorem for DTF2THF_28778
% 1.64/1.37 % SZS output start Proof for DTF2THF_28778
% 1.64/1.37 thf(func_def_0, type, in: $i > $i > $o).
% 1.64/1.37 thf(func_def_2, type, dsetconstr: $i > ($i > $o) > $i).
% 1.64/1.37 thf(func_def_6, type, nonempty: $i > $o).
% 1.64/1.37 thf(func_def_7, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.64/1.37 thf(func_def_21, type, sK2: $i > $o).
% 1.64/1.37 thf(func_def_23, type, ph4: !>[X0: $tType]:(X0)).
% 1.64/1.37 thf(f70,plain,(
% 1.64/1.37 $false),
% 1.64/1.37 inference(avatar_sat_refutation,[status(thm)],[f53,f59,f69])).
% 1.64/1.37 thf(f69,plain,(
% 1.64/1.37 ~spl3_1),
% 1.64/1.37 inference(avatar_contradiction_clause,[status(thm)],[f68])).
% 1.64/1.37 thf(f68,plain,(
% 1.64/1.37 $false | ~spl3_1),
% 1.64/1.37 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 1.64/1.37 thf(f67,plain,(
% 1.64/1.37 ($false = $true) | ~spl3_1),
% 1.64/1.37 inference(backward_demodulation,[status(thm)],[f22,f65])).
% 1.64/1.37 thf(f65,plain,(
% 1.64/1.37 ((sK2 @ sK0) = $false) | ~spl3_1),
% 1.64/1.37 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.64/1.37 thf(f63,plain,(
% 1.64/1.37 ((sK2 @ sK0) = $false) | ($false = $true) | ~spl3_1),
% 1.64/1.37 inference(superposition,[status(thm)],[f62,f23])).
% 1.64/1.37 thf(f23,plain,(
% 1.64/1.37 ((in @ sK0 @ sK1) = $true)),
% 1.64/1.37 inference(cnf_transformation,[status(thm)],[f18])).
% 1.64/1.37 thf(f18,plain,(
% 1.64/1.37 (emptysetE = $true) & (dsetconstrI = $true) & (((in @ sK0 @ sK1) = $true) & ((sK2 @ sK0) = $true) & ((nonempty @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (sK2 @ Y0)))) != $true))),
% 1.64/1.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f16,f17])).
% 1.64/1.37 thf(f17,plain,(
% 1.64/1.37 ? [X0 : $i,X1 : $i,X2 : $i > $o] : (((in @ X0 @ X1) = $true) & ((X2 @ X0) = $true) & ((nonempty @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true)) => (((in @ sK0 @ sK1) = $true) & ((sK2 @ sK0) = $true) & ((nonempty @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (sK2 @ Y0)))) != $true))),
% 1.64/1.37 introduced(definition,[],[choice_axiom])).
% 1.64/1.37 thf(f16,plain,(
% 1.64/1.37 (emptysetE = $true) & (dsetconstrI = $true) & ? [X0 : $i,X1 : $i,X2 : $i > $o] : (((in @ X0 @ X1) = $true) & ((X2 @ X0) = $true) & ((nonempty @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true))),
% 1.64/1.37 inference(flattening,[status(thm)],[f15])).
% 1.64/1.37 thf(f15,plain,(
% 1.64/1.37 (? [X0 : $i,X1 : $i,X2 : $i > $o] : ((((nonempty @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true) & ((X2 @ X0) = $true)) & ((in @ X0 @ X1) = $true)) & (emptysetE = $true)) & (dsetconstrI = $true)),
% 1.64/1.37 inference(ennf_transformation,[status(thm)],[f10])).
% 1.64/1.37 thf(f10,plain,(
% 1.64/1.37 ~((dsetconstrI = $true) => ((emptysetE = $true) => ! [X0 : $i,X1 : $i,X2 : $i > $o] : (((in @ X0 @ X1) = $true) => (((X2 @ X0) = $true) => ((nonempty @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true)))))),
% 1.64/1.37 inference(fool_elimination,[status(thm)],[f9])).
% 1.64/1.37 thf(f9,plain,(
% 1.64/1.37 ~(dsetconstrI => (emptysetE => ! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X0 @ X1) => ((X2 @ X0) => (nonempty @ (dsetconstr @ X1 @ (^[X3 : $i] : (X2 @ X3))))))))),
% 1.64/1.37 inference(rectify,[status(thm)],[f5])).
% 1.64/1.37 thf(f5,negated_conjecture,(
% 1.64/1.37 ~(dsetconstrI => (emptysetE => ! [X2 : $i,X0 : $i,X1 : $i > $o] : ((in @ X2 @ X0) => ((X1 @ X2) => (nonempty @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3))))))))),
% 1.64/1.37 inference(negated_conjecture,[status(cth)],[f4])).
% 1.64/1.37 thf(f4,conjecture,(
% 1.64/1.37 dsetconstrI => (emptysetE => ! [X2 : $i,X0 : $i,X1 : $i > $o] : ((in @ X2 @ X0) => ((X1 @ X2) => (nonempty @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))))),
% 1.64/1.37 file('/export/starexec/sandbox/tmp/tmp.4umWNL8vtI/DTF2THF_28778.p',nonemptyI)).
% 1.64/1.37 thf(f62,plain,(
% 1.64/1.37 ( ! [X0 : $i] : (((in @ X0 @ sK1) = $false) | ((sK2 @ X0) = $false)) ) | ~spl3_1),
% 1.64/1.37 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 1.64/1.37 thf(f61,plain,(
% 1.64/1.37 ( ! [X0 : $i] : (($false = $true) | ((in @ X0 @ sK1) = $false) | ((sK2 @ X0) = $false)) ) | ~spl3_1),
% 1.64/1.37 inference(forward_demodulation,[status(thm)],[f60,f49])).
% 1.64/1.37 thf(f49,plain,(
% 1.64/1.37 ( ! [X1 : $i] : (((in @ X1 @ emptyset) = $false)) ) | ~spl3_1),
% 1.64/1.37 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.64/1.37 thf(f48,definition,(
% 1.64/1.37 spl3_1 <=> ! [X1 : $i] : ((in @ X1 @ emptyset) = $false)),
% 1.64/1.37 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.64/1.37 thf(f60,plain,(
% 1.64/1.37 ( ! [X0 : $i] : (((in @ X0 @ sK1) = $false) | ((in @ X0 @ emptyset) = $true) | ((sK2 @ X0) = $false)) )),
% 1.64/1.37 inference(superposition,[status(thm)],[f41,f32])).
% 1.64/1.37 thf(f32,plain,(
% 1.64/1.37 (emptyset = (dsetconstr @ sK1 @ sK2))),
% 1.64/1.37 inference(equality_proxy_clausification,[status(thm)],[f31])).
% 1.64/1.37 thf(f31,plain,(
% 1.64/1.37 ((emptyset = (dsetconstr @ sK1 @ sK2)) = $true)),
% 1.64/1.37 inference(not_proxy_clausification,[status(thm)],[f30])).
% 1.64/1.37 thf(f30,plain,(
% 1.64/1.37 ((~ (emptyset = (dsetconstr @ sK1 @ sK2))) != $true)),
% 1.64/1.37 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.64/1.37 thf(f28,plain,(
% 1.64/1.37 (((^[Y0 : $i]: (~ (emptyset = Y0))) @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (sK2 @ Y0)))) != $true)),
% 1.64/1.37 inference(definition_unfolding,[status(thm)],[f21,f20])).
% 1.64/1.37 thf(f20,plain,(
% 1.64/1.37 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 1.64/1.37 inference(cnf_transformation,[status(thm)],[f12])).
% 1.64/1.37 thf(f12,plain,(
% 1.64/1.37 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 1.64/1.37 inference(fool_elimination,[status(thm)],[f11])).
% 1.64/1.37 thf(f11,plain,(
% 1.64/1.37 (nonempty = (^[X0 : $i] : ((emptyset != X0))))),
% 1.64/1.37 inference(rectify,[status(thm)],[f3])).
% 1.64/1.37 thf(f3,axiom,(
% 1.64/1.37 (nonempty = (^[X2 : $i] : ((emptyset != X2))))),
% 1.64/1.37 file('/export/starexec/sandbox/tmp/tmp.4umWNL8vtI/DTF2THF_28778.p',nonempty)).
% 1.64/1.37 thf(f21,plain,(
% 1.64/1.37 ((nonempty @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (sK2 @ Y0)))) != $true)),
% 1.64/1.37 inference(cnf_transformation,[status(thm)],[f18])).
% 1.64/1.37 thf(f41,plain,(
% 1.64/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (((in @ X3 @ (dsetconstr @ X2 @ X1)) = $true) | ((X1 @ X3) = $false) | ((in @ X3 @ X2) = $false)) )),
% 1.64/1.37 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.64/1.37 thf(f40,plain,(
% 1.64/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (((in @ X3 @ X2) = $false) | (((X1 @ X3) => (in @ X3 @ (dsetconstr @ X2 @ X1))) = $true)) )),
% 1.64/1.37 inference(binary_proxy_clausification,[status(thm)],[f39])).
% 1.64/1.37 thf(f39,plain,(
% 1.64/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : ((((in @ X3 @ X2) => ((X1 @ X3) => (in @ X3 @ (dsetconstr @ X2 @ X1)))) = $true)) )),
% 1.64/1.37 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.64/1.37 thf(f38,plain,(
% 1.64/1.37 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: ((in @ Y0 @ X2) => ((X1 @ Y0) => (in @ Y0 @ (dsetconstr @ X2 @ X1))))) @ X3) = $true)) )),
% 1.64/1.37 inference(pi_clausification,[status(thm)],[f37])).
% 1.64/1.37 thf(f37,plain,(
% 1.64/1.37 ( ! [X2 : $i,X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((X1 @ Y0) => (in @ Y0 @ (dsetconstr @ X2 @ X1)))))) = $true)) )),
% 1.64/1.37 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.64/1.37 thf(f36,plain,(
% 1.64/1.37 ( ! [X2 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((X1 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ X1))))))) @ X2) = $true)) )),
% 1.64/1.37 inference(pi_clausification,[status(thm)],[f35])).
% 1.64/1.37 thf(f35,plain,(
% 1.64/1.37 ( ! [X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((X1 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ X1)))))))) = $true)) )),
% 1.64/1.37 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.64/1.37 thf(f34,plain,(
% 1.64/1.37 ( ! [X1 : $i > $o] : ((((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))) @ X1) = $true)) )),
% 1.64/1.37 inference(pi_clausification,[status(thm)],[f33])).
% 1.64/1.37 thf(f33,plain,(
% 1.64/1.37 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) = $true)),
% 1.64/1.37 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.64/1.37 thf(f27,plain,(
% 1.64/1.37 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))) = $true)),
% 1.64/1.37 inference(definition_unfolding,[status(thm)],[f24,f19])).
% 1.64/1.37 thf(f19,plain,(
% 1.64/1.37 (dsetconstrI = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
% 1.64/1.37 inference(cnf_transformation,[status(thm)],[f14])).
% 1.64/1.37 thf(f14,plain,(
% 1.64/1.37 (dsetconstrI = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
% 1.64/1.37 inference(fool_elimination,[status(thm)],[f13])).
% 1.64/1.37 thf(f13,plain,(
% 1.64/1.37 (dsetconstrI = ! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X0 @ X1) => ((X2 @ X0) => (in @ X0 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X2 @ X3)))))))),
% 1.64/1.37 inference(rectify,[status(thm)],[f1])).
% 1.64/1.37 thf(f1,axiom,(
% 1.64/1.37 (dsetconstrI = ! [X2 : $i,X0 : $i,X1 : $i > $o] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))))),
% 1.64/1.37 file('/export/starexec/sandbox/tmp/tmp.4umWNL8vtI/DTF2THF_28778.p',dsetconstrI)).
% 1.64/1.37 thf(f24,plain,(
% 1.64/1.37 (dsetconstrI = $true)),
% 1.64/1.37 inference(cnf_transformation,[status(thm)],[f18])).
% 1.64/1.37 thf(f22,plain,(
% 1.64/1.37 ((sK2 @ sK0) = $true)),
% 1.64/1.37 inference(cnf_transformation,[status(thm)],[f18])).
% 1.64/1.37 thf(f59,plain,(
% 1.64/1.37 ~spl3_2),
% 1.64/1.37 inference(avatar_contradiction_clause,[status(thm)],[f58])).
% 1.64/1.37 thf(f58,plain,(
% 1.64/1.37 $false | ~spl3_2),
% 1.64/1.37 inference(equality_resolution,[status(thm)],[f55])).
% 1.64/1.37 thf(f55,plain,(
% 1.64/1.37 ( ! [X0 : $o] : (($false != X0)) ) | ~spl3_2),
% 1.64/1.37 inference(superposition,[status(thm)],[f6,f52])).
% 1.64/1.37 thf(f52,plain,(
% 1.64/1.37 ( ! [X2 : $o] : (($true = X2)) ) | ~spl3_2),
% 1.64/1.37 inference(avatar_component_clause,[status(thm)],[f51])).
% 1.64/1.37 thf(f51,definition,(
% 1.64/1.37 spl3_2 <=> ! [X2 : $o] : ($true = X2)),
% 1.64/1.37 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.64/1.37 thf(f6,plain,(
% 1.64/1.37 ($false != $true)),
% 1.64/1.37 introduced(definition,[],[fool_axiom])).
% 1.64/1.37 thf(f53,plain,(
% 1.64/1.37 spl3_1 | spl3_2),
% 1.64/1.37 inference(avatar_split_clause,[status(thm)],[f46,f51,f48])).
% 1.64/1.37 thf(f46,plain,(
% 1.64/1.37 ( ! [X2 : $o,X1 : $i] : (($true = X2) | ((in @ X1 @ emptyset) = $false)) )),
% 1.64/1.37 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.64/1.37 thf(f45,plain,(
% 1.64/1.37 ( ! [X2 : $o,X1 : $i] : (((in @ X1 @ emptyset) = $false) | (((^[Y0 : $o]: (Y0)) @ X2) = $true)) )),
% 1.64/1.37 inference(pi_clausification,[status(thm)],[f44])).
% 1.64/1.37 thf(f44,plain,(
% 1.64/1.37 ( ! [X1 : $i] : (((!! @ $o @ (^[Y0 : $o]: (Y0))) = $true) | ((in @ X1 @ emptyset) = $false)) )),
% 1.64/1.37 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.64/1.37 thf(f43,plain,(
% 1.64/1.37 ( ! [X1 : $i] : ((((in @ X1 @ emptyset) => (!! @ $o @ (^[Y0 : $o]: (Y0)))) = $true)) )),
% 1.64/1.37 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.64/1.37 thf(f42,plain,(
% 1.64/1.37 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1))))) @ X1) = $true)) )),
% 1.64/1.37 inference(pi_clausification,[status(thm)],[f29])).
% 1.64/1.37 thf(f29,plain,(
% 1.64/1.37 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) = $true)),
% 1.64/1.37 inference(definition_unfolding,[status(thm)],[f26,f25])).
% 1.64/1.37 thf(f25,plain,(
% 1.64/1.37 (emptysetE = $true)),
% 1.64/1.37 inference(cnf_transformation,[status(thm)],[f18])).
% 1.64/1.37 thf(f26,plain,(
% 1.64/1.37 (emptysetE = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))))),
% 1.64/1.37 inference(cnf_transformation,[status(thm)],[f8])).
% 1.64/1.37 thf(f8,plain,(
% 1.64/1.37 (emptysetE = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))))),
% 1.64/1.37 inference(fool_elimination,[status(thm)],[f7])).
% 1.64/1.37 thf(f7,plain,(
% 1.64/1.37 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 1.64/1.37 inference(rectify,[status(thm)],[f2])).
% 1.64/1.37 thf(f2,axiom,(
% 1.64/1.37 (emptysetE = ! [X2 : $i] : ((in @ X2 @ emptyset) => ! [X1 : $o] : X1))),
% 1.64/1.37 file('/export/starexec/sandbox/tmp/tmp.4umWNL8vtI/DTF2THF_28778.p',emptysetE)).
% 1.64/1.37 % SZS output end Proof for DTF2THF_28778
% 1.64/1.37 % (28894)------------------------------
% 1.64/1.37 % (28894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.37 % (28894)Termination reason: Refutation
% 1.64/1.37
% 1.64/1.37 % (28894)Memory used [KB]: 5500
% 1.64/1.37 % (28894)Time elapsed: 0.004 s
% 1.64/1.37 % (28894)Instructions burned: 4 (million)
% 1.64/1.37 % (28894)------------------------------
% 1.64/1.37 % (28894)------------------------------
% 1.64/1.37 % (28891)Success in time 0.006 s
%------------------------------------------------------------------------------