%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU527^2 : 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 09:35:06 AM UTC 2026
% Result : Theorem 1.66s 1.33s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 53 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 539 ( 185 equ; 0 cnn)
% Maximal formula atoms : 14 ( 10 avg)
% Number of connectives : 436 ( 85 ~; 72 |; 51 &; 186 @)
% ( 7 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 15 con; 0-2 aty)
% Number of variables : 108 ( 0 ^; 80 !; 28 ?; 108 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(f80,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f68,f73,f79]) ).
thf(f79,plain,
~ spl8_1,
inference(avatar_contradiction_clause,[status(thm)],[f78]) ).
thf(f78,plain,
( $false
| ~ spl8_1 ),
inference(equality_resolution,[status(thm)],[f75]) ).
thf(f75,plain,
( ! [X0: $o] : ( $false != X0 )
| ~ spl8_1 ),
inference(superposition,[status(thm)],[f5,f64]) ).
thf(f64,plain,
( ! [X1: $o] : ( $true = X1 )
| ~ spl8_1 ),
inference(avatar_component_clause,[status(thm)],[f63]) ).
thf(f63,definition,
( spl8_1
<=> ! [X1: $o] : ( $true = X1 ) ),
introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition]) ).
thf(f5,plain,
$false != $true,
introduced(definition,[],[fool_axiom]) ).
thf(f73,plain,
~ spl8_2,
inference(avatar_contradiction_clause,[status(thm)],[f72]) ).
thf(f72,plain,
( $false
| ~ spl8_2 ),
inference(subsumption_resolution,[status(thm)],[f71,f67]) ).
thf(f67,plain,
( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ~ spl8_2 ),
inference(avatar_component_clause,[status(thm)],[f66]) ).
thf(f66,definition,
( spl8_2
<=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition]) ).
thf(f71,plain,
( ( in @ sK3 @ emptyset )
= $true ),
inference(subsumption_resolution,[status(thm)],[f70,f32]) ).
thf(f32,plain,
sK3 != sK2,
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( setadjoinE = $true )
& ( emptysetE = $true )
& ( ( in @ sK3 @ ( setadjoin @ sK2 @ emptyset ) )
= $true )
& ( sK3 != sK2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f13,f22]) ).
thf(f22,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true )
& ( X0 != X1 ) )
=> ( ( ( in @ sK3 @ ( setadjoin @ sK2 @ emptyset ) )
= $true )
& ( sK3 != sK2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ( setadjoinE = $true )
& ( emptysetE = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true )
& ( X0 != X1 ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true )
& ( X0 != X1 ) )
& ( setadjoinE = $true )
& ( emptysetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( ( emptysetE = $true )
=> ( ( setadjoinE = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true )
=> ( X0 = X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( emptysetE
=> ( setadjoinE
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ( emptysetE
=> ( setadjoinE
=> ! [X3: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X0 = X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
( emptysetE
=> ( setadjoinE
=> ! [X3: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X3 @ emptyset ) )
=> ( X0 = X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.GfMDsW6jAf/DTF2THF_3334.p',uniqinunit) ).
thf(f70,plain,
( ( sK3 = sK2 )
| ( ( in @ sK3 @ emptyset )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ( $true != $true )
| ( ( in @ sK3 @ emptyset )
= $true )
| ( sK3 = sK2 ) ),
inference(superposition,[status(thm)],[f60,f33]) ).
thf(f33,plain,
( ( in @ sK3 @ ( setadjoin @ sK2 @ emptyset ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f60,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X2 @ X1 ) )
!= $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( X0 = X2 ) ),
inference(condensation,[status(thm)],[f59]) ).
thf(f59,plain,
! [X6: $i,X7: $o,X4: $i,X5: $i] :
( ( X5 = X6 )
| ( $true = X7 )
| ( $true
= ( in @ X6 @ X4 ) )
| ( ( in @ X6 @ ( setadjoin @ X5 @ X4 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
! [X6: $i,X7: $o,X4: $i,X5: $i] :
( ( $true != $true )
| ( ( in @ X6 @ ( setadjoin @ X5 @ X4 ) )
!= $true )
| ( $true = X7 )
| ( X5 = X6 )
| ( $true
= ( in @ X6 @ X4 ) ) ),
inference(definition_unfolding,[status(thm)],[f37,f35]) ).
thf(f35,plain,
setadjoinE = $true,
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f37,plain,
! [X6: $i,X7: $o,X4: $i,X5: $i] :
( ( $true = X7 )
| ( $true
= ( in @ X6 @ X4 ) )
| ( X5 = X6 )
| ( ( in @ X6 @ ( setadjoin @ X5 @ X4 ) )
!= $true )
| ( setadjoinE != $true ) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( setadjoinE = $true )
| ( ( sK7 != $true )
& ( ( sK7 = $true )
| ( $true
!= ( in @ sK6 @ sK4 ) ) )
& ( ( sK6 != sK5 )
| ( sK7 = $true ) )
& ( ( in @ sK6 @ ( setadjoin @ sK5 @ sK4 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i,X6: $i] :
( ! [X7: $o] :
( ( $true = X7 )
| ( ( $true != X7 )
& ( $true
= ( in @ X6 @ X4 ) ) )
| ( ( X5 = X6 )
& ( $true != X7 ) ) )
| ( ( in @ X6 @ ( setadjoin @ X5 @ X4 ) )
!= $true ) )
| ( setadjoinE != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f25,f27,f26]) ).
thf(f26,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( ( in @ X2 @ X0 )
!= $true ) )
& ( ( X1 != X2 )
| ( $true = X3 ) ) )
& ( ( in @ X2 @ ( setadjoin @ X1 @ X0 ) )
= $true ) )
=> ( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( $true
!= ( in @ sK6 @ sK4 ) ) )
& ( ( sK6 != sK5 )
| ( $true = X3 ) ) )
& ( ( in @ sK6 @ ( setadjoin @ sK5 @ sK4 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f27,plain,
( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( $true
!= ( in @ sK6 @ sK4 ) ) )
& ( ( sK6 != sK5 )
| ( $true = X3 ) ) )
=> ( ( sK7 != $true )
& ( ( sK7 = $true )
| ( $true
!= ( in @ sK6 @ sK4 ) ) )
& ( ( sK6 != sK5 )
| ( sK7 = $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ( ( setadjoinE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( ( in @ X2 @ X0 )
!= $true ) )
& ( ( X1 != X2 )
| ( $true = X3 ) ) )
& ( ( in @ X2 @ ( setadjoin @ X1 @ X0 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i,X6: $i] :
( ! [X7: $o] :
( ( $true = X7 )
| ( ( $true != X7 )
& ( $true
= ( in @ X6 @ X4 ) ) )
| ( ( X5 = X6 )
& ( $true != X7 ) ) )
| ( ( in @ X6 @ ( setadjoin @ X5 @ X4 ) )
!= $true ) )
| ( setadjoinE != $true ) ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ( setadjoinE = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ? [X3: $o] :
( ( $true != X3 )
& ( ( $true = X3 )
| ( ( in @ X1 @ X0 )
!= $true ) )
& ( ( X1 != X2 )
| ( $true = X3 ) ) )
& ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
= $true ) ) )
& ( ! [X0: $i,X2: $i,X1: $i] :
( ! [X3: $o] :
( ( $true = X3 )
| ( ( $true != X3 )
& ( ( in @ X1 @ X0 )
= $true ) )
| ( ( X1 = X2 )
& ( $true != X3 ) ) )
| ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
!= $true ) )
| ( setadjoinE != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( setadjoinE = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ! [X3: $o] :
( ( $true = X3 )
| ( ( $true != X3 )
& ( ( in @ X1 @ X0 )
= $true ) )
| ( ( X1 = X2 )
& ( $true != X3 ) ) )
| ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
!= $true ) ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ! [X3: $o] :
( ( $true = X3 )
| ( ( $true != X3 )
& ( ( in @ X1 @ X0 )
= $true ) )
| ( ( X1 = X2 )
& ( $true != X3 ) ) )
| ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
!= $true ) )
<=> ( setadjoinE = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
= $true )
=> ! [X3: $o] :
( ( ( X1 = X2 )
=> ( $true = X3 ) )
=> ( ( ( ( in @ X1 @ X0 )
= $true )
=> ( $true = X3 ) )
=> ( $true = X3 ) ) ) )
<=> ( setadjoinE = $true ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( setadjoinE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
=> ! [X3: $o] :
( ( ( X1 = X2 )
=> X3 )
=> ( ( ( in @ X1 @ X0 )
=> X3 )
=> X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( setadjoinE
= ( ! [X2: $i,X3: $i,X0: $i] :
( ( in @ X3 @ ( setadjoin @ X0 @ X2 ) )
=> ! [X1: $o] :
( ( ( X0 = X3 )
=> X1 )
=> ( ( ( in @ X3 @ X2 )
=> X1 )
=> X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.GfMDsW6jAf/DTF2THF_3334.p',setadjoinE) ).
thf(f68,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[status(thm)],[f61,f66,f63]) ).
thf(f61,plain,
! [X0: $i,X1: $o] :
( ( $true = X1 )
| ( ( in @ X0 @ emptyset )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f44]) ).
thf(f44,plain,
! [X0: $i,X1: $o] :
( ( $true != $true )
| ( $true = X1 )
| ( ( in @ X0 @ emptyset )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f31,f34]) ).
thf(f34,plain,
emptysetE = $true,
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f31,plain,
! [X0: $i,X1: $o] :
( ( $true = X1 )
| ( ( in @ X0 @ emptyset )
!= $true )
| ( emptysetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ! [X0: $i] :
( ! [X1: $o] : ( $true = X1 )
| ( ( in @ X0 @ emptyset )
!= $true ) )
| ( emptysetE != $true ) )
& ( ( emptysetE = $true )
| ( ( sK1 != $true )
& ( ( in @ sK0 @ emptyset )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f18,f20,f19]) ).
thf(f19,plain,
( ? [X2: $i] :
( ? [X3: $o] : ( $true != X3 )
& ( $true
= ( in @ X2 @ emptyset ) ) )
=> ( ? [X3: $o] : ( $true != X3 )
& ( ( in @ sK0 @ emptyset )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
( ? [X3: $o] : ( $true != X3 )
=> ( sK1 != $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ( ! [X0: $i] :
( ! [X1: $o] : ( $true = X1 )
| ( ( in @ X0 @ emptyset )
!= $true ) )
| ( emptysetE != $true ) )
& ( ( emptysetE = $true )
| ? [X2: $i] :
( ? [X3: $o] : ( $true != X3 )
& ( $true
= ( in @ X2 @ emptyset ) ) ) ) ),
inference(rectify,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ! [X0: $i] :
( ! [X1: $o] : ( $true = X1 )
| ( ( in @ X0 @ emptyset )
!= $true ) )
| ( emptysetE != $true ) )
& ( ( emptysetE = $true )
| ? [X0: $i] :
( ? [X1: $o] : ( $true != X1 )
& ( ( in @ X0 @ emptyset )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ! [X0: $i] :
( ! [X1: $o] : ( $true = X1 )
| ( ( in @ X0 @ emptyset )
!= $true ) )
<=> ( emptysetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( emptysetE = $true )
<=> ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
= $true )
=> ! [X1: $o] : ( $true = X1 ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( emptysetE
= ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> ! [X1: $o] : X1 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( emptysetE
= ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> ! [X1: $o] : X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.GfMDsW6jAf/DTF2THF_3334.p',emptysetE) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU527^2 : 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
% 0.18/0.34 % Computer : n016.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:26:21 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.48 ---- Original DTF file ---
% 0.27/0.48 thf(spec,logic,$$dhol).
% 0.27/0.48 %------------------------------------------------------------------------------
% 0.27/0.48 % File : SEU527^2 : TPTP v9.2.1. Released v3.7.0.
% 0.27/0.48 % Domain : Set Theory
% 0.27/0.48 % Problem : Preliminary Notions - Equality Laws
% 0.27/0.48 % Version : Especial > Reduced > Especial.
% 0.27/0.48 % English : (! x:i.! y:i.in x (setadjoin y emptyset) -> x = y)
% 0.27/0.48
% 0.27/0.48 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.27/0.48 % Source : [Bro08]
% 0.27/0.48 % Names : ZFC029l [Bro08]
% 0.27/0.48
% 0.27/0.48 % Status : Theorem
% 0.27/0.48 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.1.0, 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
% 0.27/0.48 % Syntax : Number of formulae : 8 ( 2 unt; 5 typ; 2 def)
% 0.27/0.48 % Number of atoms : 12 ( 4 equ; 0 cnn)
% 0.27/0.48 % Maximal formula atoms : 4 ( 4 avg)
% 0.27/0.48 % Number of connectives : 21 ( 0 ~; 0 |; 0 &; 12 @)
% 0.27/0.48 % ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% 0.27/0.48 % Maximal formula depth : 9 ( 4 avg)
% 0.27/0.48 % Number of types : 2 ( 0 usr)
% 0.27/0.48 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.27/0.48 % Number of symbols : 6 ( 5 usr; 3 con; 0-2 aty)
% 0.27/0.48 % Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% 0.27/0.48 % SPC : TH0_THM_EQU_NAR
% 0.27/0.48
% 0.27/0.48 % Comments : http://mathgate.info/detsetitem.php?id=93
% 0.27/0.48 %------------------------------------------------------------------------------
% 0.27/0.48 thf(in_type,type,
% 0.27/0.48 in: $i > $i > $o ).
% 0.27/0.48
% 0.27/0.48 thf(emptyset_type,type,
% 0.27/0.48 emptyset: $i ).
% 0.27/0.48
% 0.27/0.48 thf(setadjoin_type,type,
% 0.27/0.48 setadjoin: $i > $i > $i ).
% 0.27/0.48
% 0.27/0.48 thf(emptysetE_type,type,
% 0.27/0.48 emptysetE: $o ).
% 0.27/0.48
% 0.27/0.48 thf(emptysetE,definition,
% 0.27/0.48 ( emptysetE
% 0.27/0.48 = ( ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ emptyset )
% 0.27/0.48 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setadjoinE_type,type,
% 0.27/0.48 setadjoinE: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setadjoinE,definition,
% 0.27/0.48 ( setadjoinE
% 0.27/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.27/0.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.27/0.48 => ! [Xphi: $o] :
% 0.27/0.48 ( ( ( Xy = Xx )
% 0.27/0.48 => Xphi )
% 0.27/0.48 => ( ( ( in @ Xy @ A )
% 0.27/0.48 => Xphi )
% 0.27/0.48 => Xphi ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(uniqinunit,conjecture,
% 0.27/0.48 ( emptysetE
% 0.27/0.48 => ( setadjoinE
% 0.27/0.48 => ! [Xx: $i,Xy: $i] :
% 0.27/0.48 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.27/0.48 => ( Xx = Xy ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 %------------------------------------------------------------------------------
% 0.27/0.48 ------------------------
% 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 12:26:21 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.GfMDsW6jAf/DTF2DTF3334.p
% See solution above
% 1.45/1.29 ------------------------
% 1.66/1.31 ---- Cleaned THF ---
% 1.66/1.31 thf(in_type,type,
% 1.66/1.31 in: $i > $i > $o ).
% 1.66/1.31
% 1.66/1.31 thf(emptyset_type,type,
% 1.66/1.31 emptyset: $i ).
% 1.66/1.31
% 1.66/1.31 thf(setadjoin_type,type,
% 1.66/1.31 setadjoin: $i > $i > $i ).
% 1.66/1.31
% 1.66/1.31 thf(emptysetE_type,type,
% 1.66/1.31 emptysetE: $o ).
% 1.66/1.31
% 1.66/1.31 thf(emptysetE,definition,
% 1.66/1.31 ( emptysetE
% 1.66/1.31 = ( ! [Xx: $i] :
% 1.66/1.31 ( ( in @ Xx @ emptyset )
% 1.66/1.31 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.66/1.31
% 1.66/1.31 thf(setadjoinE_type,type,
% 1.66/1.31 setadjoinE: $o ).
% 1.66/1.31
% 1.66/1.31 thf(setadjoinE,definition,
% 1.66/1.31 ( setadjoinE
% 1.66/1.31 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.66/1.31 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.66/1.31 => ! [Xphi: $o] :
% 1.66/1.31 ( ( ( Xy = Xx )
% 1.66/1.31 => Xphi )
% 1.66/1.31 => ( ( ( in @ Xy @ A )
% 1.66/1.31 => Xphi )
% 1.66/1.31 => Xphi ) ) ) ) ) ).
% 1.66/1.31
% 1.66/1.31 thf(uniqinunit,conjecture,
% 1.66/1.31 ( emptysetE
% 1.66/1.31 => ( setadjoinE
% 1.66/1.31 => ! [Xx: $i,Xy: $i] :
% 1.66/1.31 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.66/1.31 => ( Xx = Xy ) ) ) ) ).
% 1.66/1.31 ------------------------
% 1.66/1.32 % (3453)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_3334 for (2999ds/2Mi)
% 1.66/1.32 % (3453)Instruction limit reached!
% 1.66/1.32 % (3453)------------------------------
% 1.66/1.32 % (3453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (3453)Termination reason: Unknown
% 1.66/1.32 % (3453)Termination phase: Saturation
% 1.66/1.32
% 1.66/1.32 % (3453)Memory used [KB]: 895
% 1.66/1.32 % (3453)Time elapsed: 0.002 s
% 1.66/1.32 % (3453)Instructions burned: 2 (million)
% 1.66/1.32 % (3453)------------------------------
% 1.66/1.32 % (3453)------------------------------
% 1.66/1.32 % (3452)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3334 for (2999ds/2Mi)
% 1.66/1.32 % (3452)Instruction limit reached!
% 1.66/1.32 % (3452)------------------------------
% 1.66/1.32 % (3452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (3452)Termination reason: Unknown
% 1.66/1.32 % (3452)Termination phase: Saturation
% 1.66/1.32
% 1.66/1.32 % (3452)Memory used [KB]: 5500
% 1.66/1.32 % (3452)Time elapsed: 0.003 s
% 1.66/1.32 % (3452)Instructions burned: 3 (million)
% 1.66/1.32 % (3452)------------------------------
% 1.66/1.32 % (3452)------------------------------
% 1.66/1.33 % (3450)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_3334 for (2999ds/4Mi)
% 1.66/1.33 % (3449)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3334 for (2999ds/183Mi)
% 1.66/1.33 % (3451)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_3334 for (2999ds/27Mi)
% 1.66/1.33 % (3454)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_3334 for (2999ds/275Mi)
% 1.66/1.33 % (3455)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3334 for (2999ds/18Mi)
% 1.66/1.33 % (3456)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3334 for (2999ds/3Mi)
% 1.66/1.33 % (3450)Instruction limit reached!
% 1.66/1.33 % (3450)------------------------------
% 1.66/1.33 % (3450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (3450)Termination reason: Unknown
% 1.66/1.33 % (3450)Termination phase: Saturation
% 1.66/1.33
% 1.66/1.33 % (3450)Memory used [KB]: 5500
% 1.66/1.33 % (3450)Time elapsed: 0.005 s
% 1.66/1.33 % (3454)Refutation not found, incomplete strategy
% 1.66/1.33 % (3454)------------------------------
% 1.66/1.33 % (3454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (3450)Instructions burned: 4 (million)
% 1.66/1.33 % (3450)------------------------------
% 1.66/1.33 % (3450)------------------------------
% 1.66/1.33 % (3454)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.33
% 1.66/1.33
% 1.66/1.33 % (3454)Memory used [KB]: 5500
% 1.66/1.33 % (3454)Time elapsed: 0.004 s
% 1.66/1.33 % (3454)Instructions burned: 3 (million)
% 1.66/1.33 % (3454)------------------------------
% 1.66/1.33 % (3454)------------------------------
% 1.66/1.33 % (3456)Instruction limit reached!
% 1.66/1.33 % (3456)------------------------------
% 1.66/1.33 % (3456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (3456)Termination reason: Unknown
% 1.66/1.33 % (3456)Termination phase: Saturation
% 1.66/1.33
% 1.66/1.33 % (3456)Memory used [KB]: 5500
% 1.66/1.33 % (3456)Time elapsed: 0.002 s
% 1.66/1.33 % (3456)Instructions burned: 3 (million)
% 1.66/1.33 % (3456)------------------------------
% 1.66/1.33 % (3456)------------------------------
% 1.66/1.33 % (3455)First to succeed.
% 1.66/1.33 % (3449)Also succeeded, but the first one will report.
% 1.66/1.33 % (3455)Refutation found. Thanks to Tanya!
% 1.66/1.33 % SZS status Theorem for DTF2THF_3334
% 1.66/1.33 % SZS output start Proof for DTF2THF_3334
% 1.66/1.33 thf(func_def_0, type, in: $i > $i > $o).
% 1.66/1.33 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 1.66/1.33 thf(f80,plain,(
% 1.66/1.33 $false),
% 1.66/1.33 inference(avatar_sat_refutation,[status(thm)],[f68,f73,f79])).
% 1.66/1.33 thf(f79,plain,(
% 1.66/1.33 ~spl8_1),
% 1.66/1.33 inference(avatar_contradiction_clause,[status(thm)],[f78])).
% 1.66/1.33 thf(f78,plain,(
% 1.66/1.33 $false | ~spl8_1),
% 1.66/1.33 inference(equality_resolution,[status(thm)],[f75])).
% 1.66/1.33 thf(f75,plain,(
% 1.66/1.33 ( ! [X0 : $o] : (($false != X0)) ) | ~spl8_1),
% 1.66/1.33 inference(superposition,[status(thm)],[f5,f64])).
% 1.66/1.33 thf(f64,plain,(
% 1.66/1.33 ( ! [X1 : $o] : (($true = X1)) ) | ~spl8_1),
% 1.66/1.33 inference(avatar_component_clause,[status(thm)],[f63])).
% 1.66/1.33 thf(f63,definition,(
% 1.66/1.33 spl8_1 <=> ! [X1 : $o] : ($true = X1)),
% 1.66/1.33 introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition])).
% 1.66/1.33 thf(f5,plain,(
% 1.66/1.33 ($false != $true)),
% 1.66/1.33 introduced(definition,[],[fool_axiom])).
% 1.66/1.33 thf(f73,plain,(
% 1.66/1.33 ~spl8_2),
% 1.66/1.33 inference(avatar_contradiction_clause,[status(thm)],[f72])).
% 1.66/1.34 thf(f72,plain,(
% 1.66/1.34 $false | ~spl8_2),
% 1.66/1.34 inference(subsumption_resolution,[status(thm)],[f71,f67])).
% 1.66/1.34 thf(f67,plain,(
% 1.66/1.34 ( ! [X0 : $i] : (((in @ X0 @ emptyset) != $true)) ) | ~spl8_2),
% 1.66/1.34 inference(avatar_component_clause,[status(thm)],[f66])).
% 1.66/1.34 thf(f66,definition,(
% 1.66/1.34 spl8_2 <=> ! [X0 : $i] : ((in @ X0 @ emptyset) != $true)),
% 1.66/1.34 introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition])).
% 1.66/1.34 thf(f71,plain,(
% 1.66/1.34 ((in @ sK3 @ emptyset) = $true)),
% 1.66/1.34 inference(subsumption_resolution,[status(thm)],[f70,f32])).
% 1.66/1.34 thf(f32,plain,(
% 1.66/1.34 (sK3 != sK2)),
% 1.66/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 1.66/1.34 thf(f23,plain,(
% 1.66/1.34 (setadjoinE = $true) & (emptysetE = $true) & (((in @ sK3 @ (setadjoin @ sK2 @ emptyset)) = $true) & (sK3 != sK2))),
% 1.66/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f13,f22])).
% 1.66/1.34 thf(f22,plain,(
% 1.66/1.34 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) = $true) & (X0 != X1)) => (((in @ sK3 @ (setadjoin @ sK2 @ emptyset)) = $true) & (sK3 != sK2))),
% 1.66/1.34 introduced(definition,[],[choice_axiom])).
% 1.66/1.34 thf(f13,plain,(
% 1.66/1.34 (setadjoinE = $true) & (emptysetE = $true) & ? [X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) = $true) & (X0 != X1))),
% 1.66/1.34 inference(flattening,[status(thm)],[f12])).
% 1.66/1.34 thf(f12,plain,(
% 1.66/1.34 (? [X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) = $true) & (X0 != X1)) & (setadjoinE = $true)) & (emptysetE = $true)),
% 1.66/1.34 inference(ennf_transformation,[status(thm)],[f7])).
% 1.66/1.34 thf(f7,plain,(
% 1.66/1.34 ~((emptysetE = $true) => ((setadjoinE = $true) => ! [X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X0 @ emptyset)) = $true) => (X0 = X1))))),
% 1.66/1.34 inference(fool_elimination,[status(thm)],[f6])).
% 1.66/1.34 thf(f6,plain,(
% 1.66/1.34 ~(emptysetE => (setadjoinE => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (setadjoin @ X0 @ emptyset)) => (X0 = X1))))),
% 1.66/1.34 inference(rectify,[status(thm)],[f4])).
% 1.66/1.34 thf(f4,negated_conjecture,(
% 1.66/1.34 ~(emptysetE => (setadjoinE => ! [X3 : $i,X0 : $i] : ((in @ X0 @ (setadjoin @ X3 @ emptyset)) => (X0 = X3))))),
% 1.66/1.34 inference(negated_conjecture,[status(cth)],[f3])).
% 1.66/1.34 thf(f3,conjecture,(
% 1.66/1.34 emptysetE => (setadjoinE => ! [X3 : $i,X0 : $i] : ((in @ X0 @ (setadjoin @ X3 @ emptyset)) => (X0 = X3)))),
% 1.66/1.34 file('/export/starexec/sandbox2/tmp/tmp.GfMDsW6jAf/DTF2THF_3334.p',uniqinunit)).
% 1.66/1.34 thf(f70,plain,(
% 1.66/1.34 (sK3 = sK2) | ((in @ sK3 @ emptyset) = $true)),
% 1.66/1.34 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.66/1.34 thf(f69,plain,(
% 1.66/1.34 ($true != $true) | ((in @ sK3 @ emptyset) = $true) | (sK3 = sK2)),
% 1.66/1.34 inference(superposition,[status(thm)],[f60,f33])).
% 1.66/1.34 thf(f33,plain,(
% 1.66/1.34 ((in @ sK3 @ (setadjoin @ sK2 @ emptyset)) = $true)),
% 1.66/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 1.66/1.34 thf(f60,plain,(
% 1.66/1.34 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X2 @ X1)) != $true) | ((in @ X0 @ X1) = $true) | (X0 = X2)) )),
% 1.66/1.34 inference(condensation,[status(thm)],[f59])).
% 1.66/1.34 thf(f59,plain,(
% 1.66/1.34 ( ! [X6 : $i,X7 : $o,X4 : $i,X5 : $i] : ((X5 = X6) | ($true = X7) | ($true = (in @ X6 @ X4)) | ((in @ X6 @ (setadjoin @ X5 @ X4)) != $true)) )),
% 1.66/1.34 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.66/1.34 thf(f53,plain,(
% 1.66/1.34 ( ! [X6 : $i,X7 : $o,X4 : $i,X5 : $i] : (($true != $true) | ((in @ X6 @ (setadjoin @ X5 @ X4)) != $true) | ($true = X7) | (X5 = X6) | ($true = (in @ X6 @ X4))) )),
% 1.66/1.34 inference(definition_unfolding,[status(thm)],[f37,f35])).
% 1.66/1.34 thf(f35,plain,(
% 1.66/1.34 (setadjoinE = $true)),
% 1.66/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 1.66/1.34 thf(f37,plain,(
% 1.66/1.34 ( ! [X6 : $i,X7 : $o,X4 : $i,X5 : $i] : (($true = X7) | ($true = (in @ X6 @ X4)) | (X5 = X6) | ((in @ X6 @ (setadjoin @ X5 @ X4)) != $true) | (setadjoinE != $true)) )),
% 1.66/1.34 inference(cnf_transformation,[status(thm)],[f28])).
% 1.66/1.34 thf(f28,plain,(
% 1.66/1.34 ((setadjoinE = $true) | (((sK7 != $true) & ((sK7 = $true) | ($true != (in @ sK6 @ sK4))) & ((sK6 != sK5) | (sK7 = $true))) & ((in @ sK6 @ (setadjoin @ sK5 @ sK4)) = $true))) & (! [X4 : $i,X5 : $i,X6 : $i] : (! [X7 : $o] : (($true = X7) | (($true != X7) & ($true = (in @ X6 @ X4))) | ((X5 = X6) & ($true != X7))) | ((in @ X6 @ (setadjoin @ X5 @ X4)) != $true)) | (setadjoinE != $true))),
% 1.66/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f25,f27,f26])).
% 1.66/1.34 thf(f26,plain,(
% 1.66/1.34 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $o] : (($true != X3) & (($true = X3) | ((in @ X2 @ X0) != $true)) & ((X1 != X2) | ($true = X3))) & ((in @ X2 @ (setadjoin @ X1 @ X0)) = $true)) => (? [X3 : $o] : (($true != X3) & (($true = X3) | ($true != (in @ sK6 @ sK4))) & ((sK6 != sK5) | ($true = X3))) & ((in @ sK6 @ (setadjoin @ sK5 @ sK4)) = $true))),
% 1.66/1.34 introduced(definition,[],[choice_axiom])).
% 1.66/1.34 thf(f27,plain,(
% 1.66/1.34 ? [X3 : $o] : (($true != X3) & (($true = X3) | ($true != (in @ sK6 @ sK4))) & ((sK6 != sK5) | ($true = X3))) => ((sK7 != $true) & ((sK7 = $true) | ($true != (in @ sK6 @ sK4))) & ((sK6 != sK5) | (sK7 = $true)))),
% 1.66/1.34 introduced(definition,[],[choice_axiom])).
% 1.66/1.34 thf(f25,plain,(
% 1.66/1.34 ((setadjoinE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $o] : (($true != X3) & (($true = X3) | ((in @ X2 @ X0) != $true)) & ((X1 != X2) | ($true = X3))) & ((in @ X2 @ (setadjoin @ X1 @ X0)) = $true))) & (! [X4 : $i,X5 : $i,X6 : $i] : (! [X7 : $o] : (($true = X7) | (($true != X7) & ($true = (in @ X6 @ X4))) | ((X5 = X6) & ($true != X7))) | ((in @ X6 @ (setadjoin @ X5 @ X4)) != $true)) | (setadjoinE != $true))),
% 1.66/1.34 inference(rectify,[status(thm)],[f24])).
% 1.66/1.34 thf(f24,plain,(
% 1.66/1.34 ((setadjoinE = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : (? [X3 : $o] : (($true != X3) & (($true = X3) | ((in @ X1 @ X0) != $true)) & ((X1 != X2) | ($true = X3))) & ((in @ X1 @ (setadjoin @ X2 @ X0)) = $true))) & (! [X0 : $i,X2 : $i,X1 : $i] : (! [X3 : $o] : (($true = X3) | (($true != X3) & ((in @ X1 @ X0) = $true)) | ((X1 = X2) & ($true != X3))) | ((in @ X1 @ (setadjoin @ X2 @ X0)) != $true)) | (setadjoinE != $true))),
% 1.66/1.34 inference(nnf_transformation,[status(thm)],[f15])).
% 1.66/1.34 thf(f15,plain,(
% 1.66/1.34 (setadjoinE = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (! [X3 : $o] : (($true = X3) | (($true != X3) & ((in @ X1 @ X0) = $true)) | ((X1 = X2) & ($true != X3))) | ((in @ X1 @ (setadjoin @ X2 @ X0)) != $true))),
% 1.66/1.34 inference(flattening,[status(thm)],[f14])).
% 1.66/1.34 thf(f14,plain,(
% 1.66/1.34 ! [X2 : $i,X0 : $i,X1 : $i] : (! [X3 : $o] : ((($true = X3) | (($true != X3) & ((in @ X1 @ X0) = $true))) | ((X1 = X2) & ($true != X3))) | ((in @ X1 @ (setadjoin @ X2 @ X0)) != $true)) <=> (setadjoinE = $true)),
% 1.66/1.34 inference(ennf_transformation,[status(thm)],[f9])).
% 1.66/1.34 thf(f9,plain,(
% 1.66/1.34 ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X2 @ X0)) = $true) => ! [X3 : $o] : (((X1 = X2) => ($true = X3)) => ((((in @ X1 @ X0) = $true) => ($true = X3)) => ($true = X3)))) <=> (setadjoinE = $true)),
% 1.66/1.34 inference(fool_elimination,[status(thm)],[f8])).
% 1.66/1.34 thf(f8,plain,(
% 1.66/1.34 (setadjoinE = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (setadjoin @ X2 @ X0)) => ! [X3 : $o] : (((X1 = X2) => X3) => (((in @ X1 @ X0) => X3) => X3))))),
% 1.66/1.34 inference(rectify,[status(thm)],[f2])).
% 1.66/1.34 thf(f2,axiom,(
% 1.66/1.34 (setadjoinE = ! [X2 : $i,X3 : $i,X0 : $i] : ((in @ X3 @ (setadjoin @ X0 @ X2)) => ! [X1 : $o] : (((X0 = X3) => X1) => (((in @ X3 @ X2) => X1) => X1))))),
% 1.66/1.34 file('/export/starexec/sandbox2/tmp/tmp.GfMDsW6jAf/DTF2THF_3334.p',setadjoinE)).
% 1.66/1.34 thf(f68,plain,(
% 1.66/1.34 spl8_1 | spl8_2),
% 1.66/1.34 inference(avatar_split_clause,[status(thm)],[f61,f66,f63])).
% 1.66/1.34 thf(f61,plain,(
% 1.66/1.34 ( ! [X0 : $i,X1 : $o] : (($true = X1) | ((in @ X0 @ emptyset) != $true)) )),
% 1.66/1.34 inference(trivial_inequality_removal,[status(thm)],[f44])).
% 1.66/1.34 thf(f44,plain,(
% 1.66/1.34 ( ! [X0 : $i,X1 : $o] : (($true != $true) | ($true = X1) | ((in @ X0 @ emptyset) != $true)) )),
% 1.66/1.34 inference(definition_unfolding,[status(thm)],[f31,f34])).
% 1.66/1.34 thf(f34,plain,(
% 1.66/1.34 (emptysetE = $true)),
% 1.66/1.34 inference(cnf_transformation,[status(thm)],[f23])).
% 1.66/1.34 thf(f31,plain,(
% 1.66/1.34 ( ! [X0 : $i,X1 : $o] : (($true = X1) | ((in @ X0 @ emptyset) != $true) | (emptysetE != $true)) )),
% 1.66/1.34 inference(cnf_transformation,[status(thm)],[f21])).
% 1.66/1.34 thf(f21,plain,(
% 1.66/1.34 (! [X0 : $i] : (! [X1 : $o] : ($true = X1) | ((in @ X0 @ emptyset) != $true)) | (emptysetE != $true)) & ((emptysetE = $true) | ((sK1 != $true) & ((in @ sK0 @ emptyset) = $true)))),
% 1.66/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f18,f20,f19])).
% 1.66/1.34 thf(f19,plain,(
% 1.66/1.34 ? [X2 : $i] : (? [X3 : $o] : ($true != X3) & ($true = (in @ X2 @ emptyset))) => (? [X3 : $o] : ($true != X3) & ((in @ sK0 @ emptyset) = $true))),
% 1.66/1.34 introduced(definition,[],[choice_axiom])).
% 1.66/1.34 thf(f20,plain,(
% 1.66/1.34 ? [X3 : $o] : ($true != X3) => (sK1 != $true)),
% 1.66/1.34 introduced(definition,[],[choice_axiom])).
% 1.66/1.34 thf(f18,plain,(
% 1.66/1.34 (! [X0 : $i] : (! [X1 : $o] : ($true = X1) | ((in @ X0 @ emptyset) != $true)) | (emptysetE != $true)) & ((emptysetE = $true) | ? [X2 : $i] : (? [X3 : $o] : ($true != X3) & ($true = (in @ X2 @ emptyset))))),
% 1.66/1.34 inference(rectify,[status(thm)],[f17])).
% 1.66/1.34 thf(f17,plain,(
% 1.66/1.34 (! [X0 : $i] : (! [X1 : $o] : ($true = X1) | ((in @ X0 @ emptyset) != $true)) | (emptysetE != $true)) & ((emptysetE = $true) | ? [X0 : $i] : (? [X1 : $o] : ($true != X1) & ((in @ X0 @ emptyset) = $true)))),
% 1.66/1.34 inference(nnf_transformation,[status(thm)],[f16])).
% 1.66/1.34 thf(f16,plain,(
% 1.66/1.34 ! [X0 : $i] : (! [X1 : $o] : ($true = X1) | ((in @ X0 @ emptyset) != $true)) <=> (emptysetE = $true)),
% 1.66/1.34 inference(ennf_transformation,[status(thm)],[f11])).
% 1.66/1.34 thf(f11,plain,(
% 1.66/1.34 (emptysetE = $true) <=> ! [X0 : $i] : (((in @ X0 @ emptyset) = $true) => ! [X1 : $o] : ($true = X1))),
% 1.66/1.34 inference(fool_elimination,[status(thm)],[f10])).
% 1.66/1.34 thf(f10,plain,(
% 1.66/1.34 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 1.66/1.34 inference(rectify,[status(thm)],[f1])).
% 1.66/1.34 thf(f1,axiom,(
% 1.66/1.34 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 1.66/1.34 file('/export/starexec/sandbox2/tmp/tmp.GfMDsW6jAf/DTF2THF_3334.p',emptysetE)).
% 1.66/1.34 % SZS output end Proof for DTF2THF_3334
% 1.66/1.34 % (3455)------------------------------
% 1.66/1.34 % (3455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.34 % (3455)Termination reason: Refutation
% 1.66/1.34
% 1.66/1.34 % (3455)Memory used [KB]: 5500
% 1.66/1.34 % (3455)Time elapsed: 0.007 s
% 1.66/1.34 % (3455)Instructions burned: 4 (million)
% 1.66/1.34 % (3455)------------------------------
% 1.66/1.34 % (3455)------------------------------
% 1.66/1.34 % (3448)Success in time 0.014 s
%------------------------------------------------------------------------------