%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU506^1 : 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 : n003.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 09:34:58 AM UTC 2026
% Result : Theorem 1.98s 1.50s
% Output : Refutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 831 ( 253 equ; 0 cnn)
% Maximal formula atoms : 24 ( 18 avg)
% Number of connectives : 580 ( 70 ~; 46 |; 101 &; 222 @)
% ( 6 <=>; 135 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 82 ( 79 usr; 29 con; 0-3 aty)
% Number of variables : 93 ( 0 ^; 71 !; 22 ?; 93 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_44,type,
sP0: $i > $i > $o ).
thf(func_def_45,type,
sP1: $i > $o ).
thf(func_def_46,type,
sP2: $i > $i > $o ).
thf(func_def_47,type,
sP3: $i > $i > $o ).
thf(func_def_51,type,
sK7: $i > $i > $i ).
thf(func_def_52,type,
sK8: $i > $i > $i ).
thf(func_def_53,type,
sK9: $i > $i > $i ).
thf(func_def_54,type,
sK10: $i > $i > $i ).
thf(func_def_55,type,
sK11: $i > $i > $i > $i ).
thf(func_def_56,type,
sK12: $i > $i ).
thf(func_def_57,type,
sK13: $i > $i ).
thf(func_def_58,type,
sK14: $i > $i ).
thf(func_def_59,type,
sK15: $i > $i ).
thf(func_def_60,type,
sK16: $i > $i > $i > $i ).
thf(func_def_61,type,
sK17: $i > $i > $i > $i ).
thf(func_def_62,type,
sK18: $i > $i > $i ).
thf(func_def_63,type,
sK19: $i > $i > $i ).
thf(func_def_64,type,
sK20: $i > $i > $i ).
thf(func_def_65,type,
sK21: $i > $i ).
thf(func_def_66,type,
sK22: $i > $i > $i ).
thf(func_def_68,type,
sK24: $i > $i ).
thf(func_def_69,type,
sK25: $i > $i ).
thf(func_def_72,type,
sK28: $i > $o ).
thf(func_def_78,type,
sK34: $i > $i ).
thf(func_def_79,type,
sK35: $i > $i > $i ).
thf(func_def_83,type,
sK39: $i > $i > $i ).
thf(func_def_88,type,
sK44: $i > $o ).
thf(func_def_90,type,
sK46: ( $i > $o ) > $i ).
thf(func_def_91,type,
sK47: $i > $o ).
thf(func_def_92,type,
sK48: ( $i > $o ) > $i ).
thf(func_def_93,type,
sK49: $i > $o ).
thf(func_def_94,type,
sK50: $i > $i ).
thf(func_def_97,type,
sK53: $i > $i > $i ).
thf(func_def_98,type,
sK54: $i > $i > $i ).
thf(func_def_105,type,
sK61: $i > $i ).
thf(func_def_106,type,
sK62: $i > $i ).
thf(func_def_107,type,
sK63: $i > $o ).
thf(func_def_112,type,
sK68: $i > $i > $o ).
thf(func_def_114,type,
sK70: $i > $i ).
thf(func_def_115,type,
sK71: $i > $i ).
thf(func_def_116,type,
sK72: $i > ( $i > $i > $o ) > $i ).
thf(func_def_117,type,
sK73: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_118,type,
sK74: $i > ( $i > $i > $o ) > $i ).
thf(func_def_120,type,
ph76:
!>[X0: $tType] : X0 ).
thf(f1050,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1047,f302]) ).
thf(f302,plain,
emptyset != sK30,
inference(cnf_transformation,[status(thm)],[f155]) ).
thf(f155,plain,
( ( omegaIndAx = $true )
& ( powersetAx = $true )
& ( setunionAx = $true )
& ( emptyset != sK30 )
& ! [X1: $i] :
( ( in @ X1 @ sK30 )
!= $true )
& ( dsetconstrI = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( omegaSAx = $true )
& ( setext = $true )
& ( wellorderingAx = $true )
& ( emptysetimpfalse = $true )
& ( dsetconstrEL = $true )
& ( emptysetAx = $true )
& ( omega0Ax = $true )
& ( notinemptyset = $true )
& ( setextAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( dsetconstrER = $true )
& ( setadjoinAx = $true )
& ( descrp = $true )
& ( emptysetE = $true )
& ( exuE3e = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f91,f154]) ).
thf(f154,plain,
( ? [X0: $i] :
( ( emptyset != X0 )
& ! [X1: $i] :
( $true
!= ( in @ X1 @ X0 ) ) )
=> ( ( emptyset != sK30 )
& ! [X1: $i] :
( ( in @ X1 @ sK30 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f91,plain,
( ( omegaIndAx = $true )
& ( powersetAx = $true )
& ( setunionAx = $true )
& ? [X0: $i] :
( ( emptyset != X0 )
& ! [X1: $i] :
( $true
!= ( in @ X1 @ X0 ) ) )
& ( dsetconstrI = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( omegaSAx = $true )
& ( setext = $true )
& ( wellorderingAx = $true )
& ( emptysetimpfalse = $true )
& ( dsetconstrEL = $true )
& ( emptysetAx = $true )
& ( omega0Ax = $true )
& ( notinemptyset = $true )
& ( setextAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( dsetconstrER = $true )
& ( setadjoinAx = $true )
& ( descrp = $true )
& ( emptysetE = $true )
& ( exuE3e = $true ) ),
inference(flattening,[status(thm)],[f90]) ).
thf(f90,plain,
( ? [X0: $i] :
( ( emptyset != X0 )
& ! [X1: $i] :
( $true
!= ( in @ X1 @ X0 ) ) )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f75]) ).
thf(f75,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ! [X0: $i] :
( ! [X1: $i] :
( $true
!= ( in @ X1 @ X0 ) )
=> ( emptyset = X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f33]) ).
thf(f33,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ! [X0: $i] :
( ! [X1: $i] :
( $true
!= ( in @ X1 @ X0 ) )
=> ( emptyset = X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f32]) ).
thf(f32,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ! [X0: $i] :
( ! [X1: $i] :
~ ( in @ X1 @ X0 )
=> ( emptyset = X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f26]) ).
thf(f26,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ! [X3: $i] :
( ! [X1: $i] :
~ ( in @ X1 @ X3 )
=> ( emptyset = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
thf(f25,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ! [X3: $i] :
( ! [X1: $i] :
~ ( in @ X1 @ X3 )
=> ( emptyset = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OwlJSocWOh/DTF2THF_32624.p',emptyI) ).
thf(f1047,plain,
emptyset = sK30,
inference(trivial_inequality_removal,[status(thm)],[f1040]) ).
thf(f1040,plain,
( ( emptyset = sK30 )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f301,f1024]) ).
thf(f1024,plain,
! [X0: $i] :
( ( ( in @ ( sK53 @ X0 @ emptyset ) @ X0 )
= $true )
| ( emptyset = X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f1019]) ).
thf(f1019,plain,
! [X0: $i] :
( ( emptyset = X0 )
| ( $true != $true )
| ( ( in @ ( sK53 @ X0 @ emptyset ) @ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f486,f475]) ).
thf(f475,plain,
! [X4: $i,X5: $i] :
( ( ( in @ ( sK54 @ X5 @ X4 ) @ X4 )
= $true )
| ( ( in @ ( sK53 @ X5 @ X4 ) @ X5 )
= $true )
| ( X4 = X5 ) ),
inference(trivial_inequality_removal,[status(thm)],[f432]) ).
thf(f432,plain,
! [X4: $i,X5: $i] :
( ( $true != $true )
| ( ( in @ ( sK53 @ X5 @ X4 ) @ X5 )
= $true )
| ( ( in @ ( sK54 @ X5 @ X4 ) @ X4 )
= $true )
| ( X4 = X5 ) ),
inference(definition_unfolding,[status(thm)],[f341,f296]) ).
thf(f296,plain,
setext = $true,
inference(cnf_transformation,[status(thm)],[f155]) ).
thf(f341,plain,
! [X4: $i,X5: $i] :
( ( ( in @ ( sK53 @ X5 @ X4 ) @ X5 )
= $true )
| ( ( in @ ( sK54 @ X5 @ X4 ) @ X4 )
= $true )
| ( X4 = X5 )
| ( setext != $true ) ),
inference(cnf_transformation,[status(thm)],[f201]) ).
thf(f201,plain,
( ( ( setext = $true )
| ( ! [X2: $i] :
( ( ( in @ X2 @ sK52 )
!= $true )
| ( $true
= ( in @ X2 @ sK51 ) ) )
& ! [X3: $i] :
( ( ( in @ X3 @ sK52 )
= $true )
| ( ( in @ X3 @ sK51 )
!= $true ) )
& ( sK51 != sK52 ) ) )
& ( ! [X4: $i,X5: $i] :
( ( ( ( in @ ( sK53 @ X5 @ X4 ) @ X5 )
= $true )
& ( ( in @ ( sK53 @ X5 @ X4 ) @ X4 )
!= $true ) )
| ( ( ( in @ ( sK54 @ X5 @ X4 ) @ X5 )
!= $true )
& ( ( in @ ( sK54 @ X5 @ X4 ) @ X4 )
= $true ) )
| ( X4 = X5 ) )
| ( setext != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK51,sK52,sK53,sK54])],[f197,f200,f199,f198]) ).
thf(f198,plain,
( ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
& ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
& ( X0 != X1 ) )
=> ( ! [X2: $i] :
( ( ( in @ X2 @ sK52 )
!= $true )
| ( $true
= ( in @ X2 @ sK51 ) ) )
& ! [X3: $i] :
( ( ( in @ X3 @ sK52 )
= $true )
| ( ( in @ X3 @ sK51 )
!= $true ) )
& ( sK51 != sK52 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f199,plain,
! [X4: $i,X5: $i] :
( ? [X6: $i] :
( ( ( in @ X6 @ X5 )
= $true )
& ( ( in @ X6 @ X4 )
!= $true ) )
=> ( ( ( in @ ( sK53 @ X5 @ X4 ) @ X5 )
= $true )
& ( ( in @ ( sK53 @ X5 @ X4 ) @ X4 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f200,plain,
! [X4: $i,X5: $i] :
( ? [X7: $i] :
( ( ( in @ X7 @ X5 )
!= $true )
& ( ( in @ X7 @ X4 )
= $true ) )
=> ( ( ( in @ ( sK54 @ X5 @ X4 ) @ X5 )
!= $true )
& ( ( in @ ( sK54 @ X5 @ X4 ) @ X4 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f197,plain,
( ( ( setext = $true )
| ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
& ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
& ( X0 != X1 ) ) )
& ( ! [X4: $i,X5: $i] :
( ? [X6: $i] :
( ( ( in @ X6 @ X5 )
= $true )
& ( ( in @ X6 @ X4 )
!= $true ) )
| ? [X7: $i] :
( ( ( in @ X7 @ X5 )
!= $true )
& ( ( in @ X7 @ X4 )
= $true ) )
| ( X4 = X5 ) )
| ( setext != $true ) ) ),
inference(rectify,[status(thm)],[f196]) ).
thf(f196,plain,
( ( ( setext = $true )
| ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true ) )
& ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
& ( X0 != X1 ) ) )
& ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) )
| ? [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
| ( X0 = X1 ) )
| ( setext != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f89]) ).
thf(f89,plain,
( ( setext = $true )
<=> ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) )
| ? [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
| ( X0 = X1 ) ) ),
inference(flattening,[status(thm)],[f88]) ).
thf(f88,plain,
( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ? [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true ) ) )
<=> ( setext = $true ) ),
inference(ennf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) )
=> ( ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( in @ X3 @ X1 )
= $true ) )
=> ( X0 = X1 ) ) )
<=> ( setext = $true ) ),
inference(fool_elimination,[status(thm)],[f40]) ).
thf(f40,plain,
( setext
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ X3 @ X1 ) )
=> ( X0 = X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,axiom,
( setext
= ( ! [X4: $i,X3: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( in @ X1 @ X4 ) )
=> ( ! [X1: $i] :
( ( in @ X1 @ X4 )
=> ( in @ X1 @ X3 ) )
=> ( X3 = X4 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OwlJSocWOh/DTF2THF_32624.p',setext) ).
thf(f486,plain,
! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f396]) ).
thf(f396,plain,
! [X1: $i] :
( ( $true != $true )
| ( ( in @ X1 @ emptyset )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f306,f294]) ).
thf(f294,plain,
emptysetimpfalse = $true,
inference(cnf_transformation,[status(thm)],[f155]) ).
thf(f306,plain,
! [X1: $i] :
( ( ( in @ X1 @ emptyset )
!= $true )
| ( emptysetimpfalse != $true ) ),
inference(cnf_transformation,[status(thm)],[f159]) ).
thf(f159,plain,
( ( ( emptysetimpfalse = $true )
| ( ( in @ sK31 @ emptyset )
= $true ) )
& ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true )
| ( emptysetimpfalse != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f157,f158]) ).
thf(f158,plain,
( ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $true )
=> ( ( in @ sK31 @ emptyset )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f157,plain,
( ( ( emptysetimpfalse = $true )
| ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $true ) )
& ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true )
| ( emptysetimpfalse != $true ) ) ),
inference(rectify,[status(thm)],[f156]) ).
thf(f156,plain,
( ( ( emptysetimpfalse = $true )
| ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $true ) )
& ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ( emptysetimpfalse != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f80]) ).
thf(f80,plain,
( ( emptysetimpfalse = $true )
<=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ) ),
inference(flattening,[status(thm)],[f79]) ).
thf(f79,plain,
( ( emptysetimpfalse = $true )
<=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ) ),
inference(true_and_false_elimination,[status(thm)],[f72]) ).
thf(f72,plain,
( ( emptysetimpfalse = $true )
<=> ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
= $true )
=> $false ) ),
inference(fool_elimination,[status(thm)],[f71]) ).
thf(f71,plain,
( emptysetimpfalse
= ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> $false ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,axiom,
( emptysetimpfalse
= ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> $false ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OwlJSocWOh/DTF2THF_32624.p',emptysetimpfalse) ).
thf(f301,plain,
! [X1: $i] :
( ( in @ X1 @ sK30 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU506^1 : 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
% 0.17/0.34 % Computer : n003.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:24:25 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.47 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : SEU506^1 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.47 % Domain : Set Theory
% 0.20/0.47 % Problem : Preliminary Notions - Basic Laws of Logic
% 0.20/0.47 % Version : Especial.
% 0.20/0.47 % English : (! A:i.(! x:i.~(in x A)) -> A = emptyset)
% 0.20/0.47
% 0.20/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.47 % Source : [Bro08]
% 0.20/0.47 % Names : ZFC008g [Bro08]
% 0.20/0.47
% 0.20/0.47 % Status : Theorem
% 0.20/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.67 v4.0.1, 1.00 v3.7.0
% 0.20/0.47 % Syntax : Number of formulae : 57 ( 24 unt; 32 typ; 24 def)
% 0.20/0.47 % Number of atoms : 147 ( 31 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 24 ( 5 avg)
% 0.20/0.47 % Number of connectives : 266 ( 5 ~; 3 |; 18 &; 174 @)
% 0.20/0.47 % ( 6 <=>; 60 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 29 ( 2 avg)
% 0.20/0.47 % Number of types : 2 ( 0 usr)
% 0.20/0.47 % Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 34 ( 32 usr; 25 con; 0-2 aty)
% 0.20/0.47 % Number of variables : 86 ( 11 ^; 61 !; 14 ?; 86 :)
% 0.20/0.47 % SPC : TH0_THM_EQU_NAR
% 0.20/0.47
% 0.20/0.47 % Comments : http://mathgate.info/detsetitem.php?id=386
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 thf(in_type,type,
% 0.20/0.47 in: $i > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(exu_type,type,
% 0.20/0.47 exu: ( $i > $o ) > $o ).
% 0.20/0.47
% 0.20/0.47 thf(exu,definition,
% 0.20/0.47 ( exu
% 0.20/0.47 = ( ^ [Xphi: $i > $o] :
% 0.20/0.47 ? [Xx: $i] :
% 0.20/0.47 ( ( Xphi @ Xx )
% 0.20/0.47 & ! [Xy: $i] :
% 0.20/0.47 ( ( Xphi @ Xy )
% 0.20/0.47 => ( Xx = Xy ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setextAx_type,type,
% 0.20/0.47 setextAx: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setextAx,definition,
% 0.20/0.47 ( setextAx
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 <=> ( in @ Xx @ B ) )
% 0.20/0.47 => ( A = B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(emptyset_type,type,
% 0.20/0.47 emptyset: $i ).
% 0.20/0.47
% 0.20/0.47 thf(emptysetAx_type,type,
% 0.20/0.47 emptysetAx: $o ).
% 0.20/0.47
% 0.20/0.47 thf(emptysetAx,definition,
% 0.20/0.47 ( emptysetAx
% 0.20/0.47 = ( ! [Xx: $i] :
% 0.20/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoin_type,type,
% 0.20/0.47 setadjoin: $i > $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinAx_type,type,
% 0.20/0.47 setadjoinAx: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinAx,definition,
% 0.20/0.47 ( setadjoinAx
% 0.20/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.47 <=> ( ( Xy = Xx )
% 0.20/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(powerset_type,type,
% 0.20/0.47 powerset: $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(powersetAx_type,type,
% 0.20/0.47 powersetAx: $o ).
% 0.20/0.47
% 0.20/0.47 thf(powersetAx,definition,
% 0.20/0.47 ( powersetAx
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.20/0.47 <=> ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ B )
% 0.20/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setunion_type,type,
% 0.20/0.47 setunion: $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(setunionAx_type,type,
% 0.20/0.47 setunionAx: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setunionAx,definition,
% 0.20/0.47 ( setunionAx
% 0.20/0.47 = ( ! [A: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.20/0.47 <=> ? [B: $i] :
% 0.20/0.47 ( ( in @ Xx @ B )
% 0.20/0.47 & ( in @ B @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(omega_type,type,
% 0.20/0.47 omega: $i ).
% 0.20/0.47
% 0.20/0.47 thf(omega0Ax_type,type,
% 0.20/0.47 omega0Ax: $o ).
% 0.20/0.47
% 0.20/0.47 thf(omega0Ax,definition,
% 0.20/0.47 ( omega0Ax
% 0.20/0.47 = ( in @ emptyset @ omega ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(omegaSAx_type,type,
% 0.20/0.47 omegaSAx: $o ).
% 0.20/0.47
% 0.20/0.47 thf(omegaSAx,definition,
% 0.20/0.47 ( omegaSAx
% 0.20/0.47 = ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ omega )
% 0.20/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(omegaIndAx_type,type,
% 0.20/0.47 omegaIndAx: $o ).
% 0.20/0.47
% 0.20/0.47 thf(omegaIndAx,definition,
% 0.20/0.47 ( omegaIndAx
% 0.20/0.47 = ( ! [A: $i] :
% 0.20/0.47 ( ( ( in @ emptyset @ A )
% 0.20/0.47 & ! [Xx: $i] :
% 0.20/0.47 ( ( ( in @ Xx @ omega )
% 0.20/0.47 & ( in @ Xx @ A ) )
% 0.20/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.20/0.47 => ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ omega )
% 0.20/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(replAx_type,type,
% 0.20/0.47 replAx: $o ).
% 0.20/0.47
% 0.20/0.47 thf(replAx,definition,
% 0.20/0.47 ( replAx
% 0.20/0.47 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( exu
% 0.20/0.47 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.20/0.47 => ? [B: $i] :
% 0.20/0.47 ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ B )
% 0.20/0.47 <=> ? [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ A )
% 0.20/0.47 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(foundationAx_type,type,
% 0.20/0.47 foundationAx: $o ).
% 0.20/0.47
% 0.20/0.47 thf(foundationAx,definition,
% 0.20/0.47 ( foundationAx
% 0.20/0.47 = ( ! [A: $i] :
% 0.20/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.20/0.47 => ? [B: $i] :
% 0.20/0.47 ( ( in @ B @ A )
% 0.20/0.47 & ~ ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ B )
% 0.20/0.47 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(wellorderingAx_type,type,
% 0.20/0.47 wellorderingAx: $o ).
% 0.20/0.47
% 0.20/0.47 thf(wellorderingAx,definition,
% 0.20/0.47 ( wellorderingAx
% 0.20/0.47 = ( ! [A: $i] :
% 0.20/0.47 ? [B: $i] :
% 0.20/0.47 ( ! [C: $i] :
% 0.20/0.47 ( ( in @ C @ B )
% 0.20/0.47 => ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ C )
% 0.20/0.47 => ( in @ Xx @ A ) ) )
% 0.20/0.47 & ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( ( in @ Xx @ A )
% 0.20/0.47 & ( in @ Xy @ A ) )
% 0.20/0.47 => ( ! [C: $i] :
% 0.20/0.47 ( ( in @ C @ B )
% 0.20/0.47 => ( ( in @ Xx @ C )
% 0.20/0.47 <=> ( in @ Xy @ C ) ) )
% 0.20/0.47 => ( Xx = Xy ) ) )
% 0.20/0.47 & ! [C: $i,D: $i] :
% 0.20/0.47 ( ( ( in @ C @ B )
% 0.20/0.47 & ( in @ D @ B ) )
% 0.20/0.47 => ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ C )
% 0.20/0.47 => ( in @ Xx @ D ) )
% 0.20/0.47 | ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ D )
% 0.20/0.47 => ( in @ Xx @ C ) ) ) )
% 0.20/0.47 & ! [C: $i] :
% 0.20/0.47 ( ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ C )
% 0.20/0.47 => ( in @ Xx @ A ) )
% 0.20/0.47 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.20/0.47 => ? [D: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ D @ B )
% 0.20/0.47 & ( in @ Xx @ C )
% 0.20/0.47 & ~ ? [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ D )
% 0.20/0.47 & ( in @ Xy @ C ) )
% 0.20/0.47 & ! [E: $i] :
% 0.20/0.47 ( ( in @ E @ B )
% 0.20/0.47 => ( ! [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ E )
% 0.20/0.47 => ( in @ Xy @ D ) )
% 0.20/0.47 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(descr_type,type,
% 0.20/0.47 descr: ( $i > $o ) > $i ).
% 0.20/0.47
% 0.20/0.47 thf(descrp_type,type,
% 0.20/0.47 descrp: $o ).
% 0.20/0.47
% 0.20/0.47 thf(descrp,definition,
% 0.20/0.47 ( descrp
% 0.20/0.47 = ( ! [Xphi: $i > $o] :
% 0.20/0.47 ( ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 => ( Xphi
% 0.20/0.47 @ ( descr
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(dsetconstr_type,type,
% 0.20/0.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.20/0.47
% 0.20/0.47 thf(dsetconstrI_type,type,
% 0.20/0.47 dsetconstrI: $o ).
% 0.20/0.47
% 0.20/0.47 thf(dsetconstrI,definition,
% 0.20/0.47 ( dsetconstrI
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( ( Xphi @ Xx )
% 0.20/0.47 => ( in @ Xx
% 0.20/0.47 @ ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(dsetconstrEL_type,type,
% 0.20/0.47 dsetconstrEL: $o ).
% 0.20/0.47
% 0.20/0.47 thf(dsetconstrEL,definition,
% 0.20/0.47 ( dsetconstrEL
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx
% 0.20/0.47 @ ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(dsetconstrER_type,type,
% 0.20/0.47 dsetconstrER: $o ).
% 0.20/0.47
% 0.20/0.47 thf(dsetconstrER,definition,
% 0.20/0.47 ( dsetconstrER
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx
% 0.20/0.47 @ ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(exuE1_type,type,
% 0.20/0.47 exuE1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(exuE1,definition,
% 0.20/0.47 ( exuE1
% 0.20/0.47 = ( ! [Xphi: $i > $o] :
% 0.20/0.47 ( ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 => ? [Xx: $i] :
% 0.20/0.47 ( ( Xphi @ Xx )
% 0.20/0.47 & ! [Xy: $i] :
% 0.20/0.47 ( ( Xphi @ Xy )
% 0.20/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(prop2set_type,type,
% 0.20/0.47 prop2set: $o > $i ).
% 0.20/0.47
% 0.20/0.47 thf(prop2set,definition,
% 0.20/0.47 ( prop2set
% 0.20/0.47 = ( ^ [Xphi: $o] :
% 0.20/0.47 ( dsetconstr @ ( powerset @ emptyset )
% 0.20/0.47 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(prop2setE_type,type,
% 0.20/0.47 prop2setE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(prop2setE,definition,
% 0.20/0.47 ( prop2setE
% 0.20/0.47 = ( ! [Xphi: $o,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.20/0.47 => Xphi ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(emptysetE_type,type,
% 0.20/0.47 emptysetE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(emptysetE,definition,
% 0.20/0.47 ( emptysetE
% 0.20/0.47 = ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ emptyset )
% 0.20/0.47 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(emptysetimpfalse_type,type,
% 0.20/0.47 emptysetimpfalse: $o ).
% 0.20/0.47
% 0.20/0.47 thf(emptysetimpfalse,definition,
% 0.20/0.47 ( emptysetimpfalse
% 0.20/0.47 = ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ emptyset )
% 0.20/0.47 => $false ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(notinemptyset_type,type,
% 0.20/0.47 notinemptyset: $o ).
% 0.20/0.47
% 0.20/0.47 thf(notinemptyset,definition,
% 0.20/0.47 ( notinemptyset
% 0.20/0.47 = ( ! [Xx: $i] :
% 0.20/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(exuE3e_type,type,
% 0.20/0.47 exuE3e: $o ).
% 0.20/0.47
% 0.20/0.47 thf(exuE3e,definition,
% 0.20/0.47 ( exuE3e
% 0.20/0.47 = ( ! [Xphi: $i > $o] :
% 0.20/0.47 ( ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setext_type,type,
% 0.20/0.47 setext: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setext,definition,
% 0.20/0.47 ( setext
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( in @ Xx @ B ) )
% 0.20/0.47 => ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ B )
% 0.20/0.47 => ( in @ Xx @ A ) )
% 0.20/0.47 => ( A = B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(emptyI,conjecture,
% 0.20/0.47 ( setextAx
% 0.20/0.47 => ( emptysetAx
% 0.20/0.47 => ( setadjoinAx
% 0.20/0.47 => ( powersetAx
% 0.20/0.47 => ( setunionAx
% 0.20/0.47 => ( omega0Ax
% 0.20/0.47 => ( omegaSAx
% 0.20/0.47 => ( omegaIndAx
% 0.20/0.47 => ( replAx
% 0.20/0.47 => ( foundationAx
% 0.20/0.47 => ( wellorderingAx
% 0.20/0.47 => ( descrp
% 0.20/0.47 => ( dsetconstrI
% 0.20/0.47 => ( dsetconstrEL
% 0.20/0.47 => ( dsetconstrER
% 0.20/0.47 => ( exuE1
% 0.20/0.47 => ( prop2setE
% 0.20/0.47 => ( emptysetE
% 0.20/0.47 => ( emptysetimpfalse
% 0.20/0.47 => ( notinemptyset
% 0.20/0.47 => ( exuE3e
% 0.20/0.47 => ( setext
% 0.20/0.47 => ! [A: $i] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ~ ( in @ Xx @ A )
% 0.20/0.47 => ( A = emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 1.79/1.37 ---- Embedded in THF ---
% 1.79/1.37 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.79/1.37 %%% Generated on Tue Feb 24 12:24:26 EST 2026
% 1.79/1.37 %%% using '$$dhol' embedding, version 1.3.0.
% 1.79/1.37 %%% Logic specification used:
% 1.79/1.37 %%% thf(spec, logic, $$dhol).
% 1.79/1.37
% 1.79/1.37 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.OwlJSocWOh/DTF2DTF32624.p
% See solution above
% 1.79/1.37 ------------------------
% 1.79/1.38 ---- Cleaned THF ---
% 1.79/1.39 thf(in_type,type,
% 1.79/1.39 in: $i > $i > $o ).
% 1.79/1.39
% 1.79/1.39 thf(exu_type,type,
% 1.79/1.39 exu: ( $i > $o ) > $o ).
% 1.79/1.39
% 1.79/1.39 thf(exu,definition,
% 1.79/1.39 ( exu
% 1.79/1.39 = ( ^ [Xphi: $i > $o] :
% 1.79/1.39 ? [Xx: $i] :
% 1.79/1.39 ( ( Xphi @ Xx )
% 1.79/1.39 & ! [Xy: $i] :
% 1.79/1.39 ( ( Xphi @ Xy )
% 1.79/1.39 => ( Xx = Xy ) ) ) ) ) ).
% 1.79/1.39
% 1.79/1.39 thf(setextAx_type,type,
% 1.79/1.39 setextAx: $o ).
% 1.79/1.39
% 1.79/1.39 thf(setextAx,definition,
% 1.79/1.39 ( setextAx
% 1.79/1.39 = ( ! [A: $i,B: $i] :
% 1.79/1.39 ( ! [Xx: $i] :
% 1.79/1.39 ( ( in @ Xx @ A )
% 1.79/1.39 <=> ( in @ Xx @ B ) )
% 1.79/1.39 => ( A = B ) ) ) ) ).
% 1.79/1.39
% 1.79/1.39 thf(emptyset_type,type,
% 1.79/1.39 emptyset: $i ).
% 1.79/1.39
% 1.79/1.39 thf(emptysetAx_type,type,
% 1.79/1.39 emptysetAx: $o ).
% 1.79/1.39
% 1.79/1.39 thf(emptysetAx,definition,
% 1.79/1.39 ( emptysetAx
% 1.79/1.39 = ( ! [Xx: $i] :
% 1.79/1.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.79/1.39
% 1.79/1.39 thf(setadjoin_type,type,
% 1.79/1.39 setadjoin: $i > $i > $i ).
% 1.79/1.39
% 1.79/1.39 thf(setadjoinAx_type,type,
% 1.79/1.39 setadjoinAx: $o ).
% 1.79/1.39
% 1.79/1.39 thf(setadjoinAx,definition,
% 1.79/1.39 ( setadjoinAx
% 1.79/1.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.79/1.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.79/1.39 <=> ( ( Xy = Xx )
% 1.79/1.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.79/1.39
% 1.79/1.39 thf(powerset_type,type,
% 1.79/1.39 powerset: $i > $i ).
% 1.79/1.39
% 1.79/1.39 thf(powersetAx_type,type,
% 1.79/1.39 powersetAx: $o ).
% 1.79/1.39
% 1.79/1.39 thf(powersetAx,definition,
% 1.79/1.39 ( powersetAx
% 1.79/1.39 = ( ! [A: $i,B: $i] :
% 1.79/1.39 ( ( in @ B @ ( powerset @ A ) )
% 1.79/1.39 <=> ! [Xx: $i] :
% 1.79/1.39 ( ( in @ Xx @ B )
% 1.79/1.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.79/1.39
% 1.79/1.39 thf(setunion_type,type,
% 1.79/1.39 setunion: $i > $i ).
% 1.79/1.39
% 1.79/1.39 thf(setunionAx_type,type,
% 1.79/1.39 setunionAx: $o ).
% 1.79/1.39
% 1.79/1.39 thf(setunionAx,definition,
% 1.79/1.39 ( setunionAx
% 1.79/1.39 = ( ! [A: $i,Xx: $i] :
% 1.79/1.39 ( ( in @ Xx @ ( setunion @ A ) )
% 1.79/1.39 <=> ? [B: $i] :
% 1.79/1.39 ( ( in @ Xx @ B )
% 1.79/1.39 & ( in @ B @ A ) ) ) ) ) ).
% 1.79/1.39
% 1.79/1.39 thf(omega_type,type,
% 1.79/1.39 omega: $i ).
% 1.79/1.39
% 1.79/1.39 thf(omega0Ax_type,type,
% 1.79/1.39 omega0Ax: $o ).
% 1.79/1.39
% 1.79/1.39 thf(omega0Ax,definition,
% 1.79/1.39 ( omega0Ax
% 1.79/1.39 = ( in @ emptyset @ omega ) ) ).
% 1.79/1.39
% 1.79/1.39 thf(omegaSAx_type,type,
% 1.79/1.39 omegaSAx: $o ).
% 1.79/1.39
% 1.79/1.39 thf(omegaSAx,definition,
% 1.79/1.39 ( omegaSAx
% 1.79/1.39 = ( ! [Xx: $i] :
% 1.79/1.39 ( ( in @ Xx @ omega )
% 1.79/1.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 1.79/1.39
% 1.79/1.39 thf(omegaIndAx_type,type,
% 1.79/1.39 omegaIndAx: $o ).
% 1.79/1.39
% 1.79/1.39 thf(omegaIndAx,definition,
% 1.79/1.39 ( omegaIndAx
% 1.79/1.39 = ( ! [A: $i] :
% 1.79/1.39 ( ( ( in @ emptyset @ A )
% 1.79/1.39 & ! [Xx: $i] :
% 1.79/1.39 ( ( ( in @ Xx @ omega )
% 1.79/1.39 & ( in @ Xx @ A ) )
% 1.79/1.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 1.79/1.39 => ! [Xx: $i] :
% 1.79/1.39 ( ( in @ Xx @ omega )
% 1.79/1.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.79/1.39
% 1.79/1.39 thf(replAx_type,type,
% 1.79/1.39 replAx: $o ).
% 1.79/1.39
% 1.79/1.39 thf(replAx,definition,
% 1.79/1.39 ( replAx
% 1.79/1.39 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 1.79/1.39 ( ! [Xx: $i] :
% 1.79/1.39 ( ( in @ Xx @ A )
% 1.79/1.39 => ( exu
% 1.79/1.39 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 1.79/1.39 => ? [B: $i] :
% 1.79/1.39 ! [Xx: $i] :
% 1.79/1.39 ( ( in @ Xx @ B )
% 1.79/1.39 <=> ? [Xy: $i] :
% 1.79/1.39 ( ( in @ Xy @ A )
% 1.79/1.39 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 1.79/1.39
% 1.79/1.39 thf(foundationAx_type,type,
% 1.79/1.39 foundationAx: $o ).
% 1.79/1.39
% 1.79/1.39 thf(foundationAx,definition,
% 1.79/1.39 ( foundationAx
% 1.79/1.39 = ( ! [A: $i] :
% 1.79/1.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.79/1.39 => ? [B: $i] :
% 1.79/1.39 ( ( in @ B @ A )
% 1.79/1.39 & ~ ? [Xx: $i] :
% 1.79/1.39 ( ( in @ Xx @ B )
% 1.79/1.39 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 1.79/1.39
% 1.79/1.39 thf(wellorderingAx_type,type,
% 1.79/1.39 wellorderingAx: $o ).
% 1.79/1.39
% 1.79/1.39 thf(wellorderingAx,definition,
% 1.79/1.39 ( wellorderingAx
% 1.79/1.39 = ( ! [A: $i] :
% 1.79/1.39 ? [B: $i] :
% 1.79/1.39 ( ! [C: $i] :
% 1.79/1.39 ( ( in @ C @ B )
% 1.79/1.39 => ! [Xx: $i] :
% 1.79/1.39 ( ( in @ Xx @ C )
% 1.79/1.39 => ( in @ Xx @ A ) ) )
% 1.79/1.39 & ! [Xx: $i,Xy: $i] :
% 1.79/1.39 ( ( ( in @ Xx @ A )
% 1.79/1.39 & ( in @ Xy @ A ) )
% 1.79/1.39 => ( ! [C: $i] :
% 1.79/1.39 ( ( in @ C @ B )
% 1.79/1.39 => ( ( in @ Xx @ C )
% 1.79/1.39 <=> ( in @ Xy @ C ) ) )
% 1.79/1.39 => ( Xx = Xy ) ) )
% 1.79/1.39 & ! [C: $i,D: $i] :
% 1.79/1.39 ( ( ( in @ C @ B )
% 1.79/1.39 & ( in @ D @ B ) )
% 1.79/1.39 => ( ! [Xx: $i] :
% 1.79/1.39 ( ( in @ Xx @ C )
% 1.79/1.39 => ( in @ Xx @ D ) )
% 1.79/1.39 | ! [Xx: $i] :
% 1.79/1.39 ( ( in @ Xx @ D )
% 1.79/1.39 => ( in @ Xx @ C ) ) ) )
% 1.79/1.39 & ! [C: $i] :
% 1.79/1.39 ( ( ! [Xx: $i] :
% 1.79/1.39 ( ( in @ Xx @ C )
% 1.79/1.39 => ( in @ Xx @ A ) )
% 1.79/1.39 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 1.79/1.39 => ? [D: $i,Xx: $i] :
% 1.79/1.39 ( ( in @ D @ B )
% 1.79/1.39 & ( in @ Xx @ C )
% 1.79/1.39 & ~ ? [Xy: $i] :
% 1.79/1.39 ( ( in @ Xy @ D )
% 1.79/1.39 & ( in @ Xy @ C ) )
% 1.79/1.39 & ! [E: $i] :
% 1.79/1.39 ( ( in @ E @ B )
% 1.79/1.39 => ( ! [Xy: $i] :
% 1.79/1.39 ( ( in @ Xy @ E )
% 1.79/1.39 => ( in @ Xy @ D ) )
% 1.79/1.39 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 1.79/1.39
% 1.79/1.39 thf(descr_type,type,
% 1.79/1.39 descr: ( $i > $o ) > $i ).
% 1.79/1.39
% 1.79/1.39 thf(descrp_type,type,
% 1.79/1.39 descrp: $o ).
% 1.79/1.39
% 1.79/1.39 thf(descrp,definition,
% 1.79/1.39 ( descrp
% 1.79/1.39 = ( ! [Xphi: $i > $o] :
% 1.79/1.39 ( ( exu
% 1.79/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.79/1.39 => ( Xphi
% 1.79/1.39 @ ( descr
% 1.79/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 1.79/1.39
% 1.79/1.39 thf(dsetconstr_type,type,
% 1.79/1.39 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.79/1.39
% 1.79/1.39 thf(dsetconstrI_type,type,
% 1.79/1.39 dsetconstrI: $o ).
% 1.79/1.39
% 1.79/1.39 thf(dsetconstrI,definition,
% 1.79/1.39 ( dsetconstrI
% 1.79/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.79/1.39 ( ( in @ Xx @ A )
% 1.79/1.39 => ( ( Xphi @ Xx )
% 1.79/1.39 => ( in @ Xx
% 1.79/1.39 @ ( dsetconstr @ A
% 1.79/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.79/1.39
% 1.79/1.39 thf(dsetconstrEL_type,type,
% 1.79/1.39 dsetconstrEL: $o ).
% 1.79/1.39
% 1.79/1.39 thf(dsetconstrEL,definition,
% 1.79/1.39 ( dsetconstrEL
% 1.79/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.79/1.39 ( ( in @ Xx
% 1.79/1.39 @ ( dsetconstr @ A
% 1.79/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.79/1.39 => ( in @ Xx @ A ) ) ) ) ).
% 1.79/1.39
% 1.79/1.39 thf(dsetconstrER_type,type,
% 1.79/1.39 dsetconstrER: $o ).
% 1.79/1.39
% 1.79/1.39 thf(dsetconstrER,definition,
% 1.79/1.39 ( dsetconstrER
% 1.79/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.79/1.39 ( ( in @ Xx
% 1.79/1.39 @ ( dsetconstr @ A
% 1.79/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.79/1.39 => ( Xphi @ Xx ) ) ) ) ).
% 1.79/1.39
% 1.79/1.39 thf(exuE1_type,type,
% 1.79/1.39 exuE1: $o ).
% 1.79/1.39
% 1.79/1.39 thf(exuE1,definition,
% 1.79/1.39 ( exuE1
% 1.79/1.39 = ( ! [Xphi: $i > $o] :
% 1.79/1.39 ( ( exu
% 1.79/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.79/1.39 => ? [Xx: $i] :
% 1.79/1.39 ( ( Xphi @ Xx )
% 1.79/1.39 & ! [Xy: $i] :
% 1.79/1.39 ( ( Xphi @ Xy )
% 1.79/1.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 1.79/1.39
% 1.79/1.39 thf(prop2set_type,type,
% 1.79/1.39 prop2set: $o > $i ).
% 1.79/1.39
% 1.79/1.39 thf(prop2set,definition,
% 1.79/1.39 ( prop2set
% 1.79/1.39 = ( ^ [Xphi: $o] :
% 1.79/1.39 ( dsetconstr @ ( powerset @ emptyset )
% 1.79/1.39 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 1.79/1.39
% 1.79/1.39 thf(prop2setE_type,type,
% 1.79/1.39 prop2setE: $o ).
% 1.79/1.39
% 1.79/1.39 thf(prop2setE,definition,
% 1.79/1.39 ( prop2setE
% 1.79/1.39 = ( ! [Xphi: $o,Xx: $i] :
% 1.79/1.39 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 1.79/1.39 => Xphi ) ) ) ).
% 1.79/1.39
% 1.79/1.39 thf(emptysetE_type,type,
% 1.79/1.39 emptysetE: $o ).
% 1.79/1.39
% 1.79/1.39 thf(emptysetE,definition,
% 1.79/1.39 ( emptysetE
% 1.79/1.39 = ( ! [Xx: $i] :
% 1.79/1.39 ( ( in @ Xx @ emptyset )
% 1.79/1.39 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.79/1.39
% 1.79/1.39 thf(emptysetimpfalse_type,type,
% 1.79/1.39 emptysetimpfalse: $o ).
% 1.79/1.39
% 1.79/1.39 thf(emptysetimpfalse,definition,
% 1.79/1.39 ( emptysetimpfalse
% 1.79/1.39 = ( ! [Xx: $i] :
% 1.79/1.39 ( ( in @ Xx @ emptyset )
% 1.79/1.39 => $false ) ) ) ).
% 1.79/1.39
% 1.79/1.39 thf(notinemptyset_type,type,
% 1.79/1.39 notinemptyset: $o ).
% 1.79/1.39
% 1.79/1.39 thf(notinemptyset,definition,
% 1.79/1.39 ( notinemptyset
% 1.79/1.39 = ( ! [Xx: $i] :
% 1.79/1.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.79/1.39
% 1.79/1.39 thf(exuE3e_type,type,
% 1.79/1.39 exuE3e: $o ).
% 1.79/1.39
% 1.79/1.39 thf(exuE3e,definition,
% 1.79/1.39 ( exuE3e
% 1.79/1.39 = ( ! [Xphi: $i > $o] :
% 1.79/1.39 ( ( exu
% 1.79/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.79/1.39 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 1.79/1.39
% 1.79/1.39 thf(setext_type,type,
% 1.79/1.39 setext: $o ).
% 1.79/1.39
% 1.79/1.39 thf(setext,definition,
% 1.79/1.39 ( setext
% 1.79/1.39 = ( ! [A: $i,B: $i] :
% 1.79/1.39 ( ! [Xx: $i] :
% 1.79/1.39 ( ( in @ Xx @ A )
% 1.79/1.39 => ( in @ Xx @ B ) )
% 1.79/1.39 => ( ! [Xx: $i] :
% 1.79/1.39 ( ( in @ Xx @ B )
% 1.79/1.39 => ( in @ Xx @ A ) )
% 1.79/1.39 => ( A = B ) ) ) ) ) ).
% 1.79/1.39
% 1.79/1.39 thf(emptyI,conjecture,
% 1.79/1.39 ( setextAx
% 1.79/1.39 => ( emptysetAx
% 1.79/1.39 => ( setadjoinAx
% 1.79/1.39 => ( powersetAx
% 1.79/1.39 => ( setunionAx
% 1.79/1.39 => ( omega0Ax
% 1.79/1.39 => ( omegaSAx
% 1.79/1.39 => ( omegaIndAx
% 1.79/1.39 => ( replAx
% 1.79/1.39 => ( foundationAx
% 1.79/1.39 => ( wellorderingAx
% 1.79/1.39 => ( descrp
% 1.79/1.39 => ( dsetconstrI
% 1.79/1.39 => ( dsetconstrEL
% 1.79/1.39 => ( dsetconstrER
% 1.79/1.39 => ( exuE1
% 1.79/1.39 => ( prop2setE
% 1.79/1.39 => ( emptysetE
% 1.79/1.39 => ( emptysetimpfalse
% 1.79/1.39 => ( notinemptyset
% 1.79/1.39 => ( exuE3e
% 1.79/1.39 => ( setext
% 1.79/1.39 => ! [A: $i] :
% 1.79/1.39 ( ! [Xx: $i] :
% 1.79/1.39 ~ ( in @ Xx @ A )
% 1.79/1.39 => ( A = emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.79/1.39 ------------------------
% 1.98/1.40 % (32746)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32624 for (2999ds/18Mi)
% 1.98/1.40 % (32744)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_32624 for (2999ds/2Mi)
% 1.98/1.40 % (32744)Instruction limit reached!
% 1.98/1.40 % (32744)------------------------------
% 1.98/1.40 % (32744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.40 % (32744)Termination reason: Unknown
% 1.98/1.40 % (32744)Termination phase: shuffling
% 1.98/1.40
% 1.98/1.40 % (32744)Memory used [KB]: 1023
% 1.98/1.40 % (32744)Time elapsed: 0.003 s
% 1.98/1.40 % (32744)Instructions burned: 4 (million)
% 1.98/1.40 % (32744)------------------------------
% 1.98/1.40 % (32744)------------------------------
% 1.98/1.41 % (32746)Instruction limit reached!
% 1.98/1.41 % (32746)------------------------------
% 1.98/1.41 % (32746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.41 % (32746)Termination reason: Unknown
% 1.98/1.41 % (32746)Termination phase: Property scanning
% 1.98/1.41
% 1.98/1.41 % (32746)Memory used [KB]: 1407
% 1.98/1.41 % (32746)Time elapsed: 0.007 s
% 1.98/1.41 % (32746)Instructions burned: 18 (million)
% 1.98/1.41 % (32746)------------------------------
% 1.98/1.41 % (32746)------------------------------
% 1.98/1.41 % (32740)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32624 for (2999ds/183Mi)
% 1.98/1.41 % (32743)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32624 for (2999ds/2Mi)
% 1.98/1.41 % (32745)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_32624 for (2999ds/275Mi)
% 1.98/1.41 % (32742)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_32624 for (2999ds/27Mi)
% 1.98/1.41 % (32741)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_32624 for (2999ds/4Mi)
% 1.98/1.41 % (32743)Instruction limit reached!
% 1.98/1.41 % (32743)------------------------------
% 1.98/1.41 % (32743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.41 % (32743)Termination reason: Unknown
% 1.98/1.41 % (32743)Termination phase: shuffling
% 1.98/1.41
% 1.98/1.41 % (32743)Memory used [KB]: 1023
% 1.98/1.41 % (32743)Time elapsed: 0.003 s
% 1.98/1.41 % (32743)Instructions burned: 2 (million)
% 1.98/1.41 % (32743)------------------------------
% 1.98/1.41 % (32743)------------------------------
% 1.98/1.41 % (32741)Instruction limit reached!
% 1.98/1.41 % (32741)------------------------------
% 1.98/1.41 % (32741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.41 % (32741)Termination reason: Unknown
% 1.98/1.41 % (32741)Termination phase: shuffling
% 1.98/1.41
% 1.98/1.41 % (32741)Memory used [KB]: 1023
% 1.98/1.41 % (32741)Time elapsed: 0.004 s
% 1.98/1.41 % (32741)Instructions burned: 5 (million)
% 1.98/1.41 % (32741)------------------------------
% 1.98/1.41 % (32741)------------------------------
% 1.98/1.42 % (32747)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_32624 for (2999ds/3Mi)
% 1.98/1.42 % (32748)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_32624 for (2999ds/37Mi)
% 1.98/1.42 % (32747)Instruction limit reached!
% 1.98/1.42 % (32747)------------------------------
% 1.98/1.42 % (32747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.42 % (32747)Termination reason: Unknown
% 1.98/1.42 % (32747)Termination phase: shuffling
% 1.98/1.42
% 1.98/1.42 % (32747)Memory used [KB]: 1023
% 1.98/1.42 % (32747)Time elapsed: 0.003 s
% 1.98/1.42 % (32747)Instructions burned: 3 (million)
% 1.98/1.42 % (32747)------------------------------
% 1.98/1.42 % (32747)------------------------------
% 1.98/1.42 % (32742)Instruction limit reached!
% 1.98/1.42 % (32742)------------------------------
% 1.98/1.42 % (32742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.42 % (32742)Termination reason: Unknown
% 1.98/1.42 % (32742)Termination phase: Saturation
% 1.98/1.42
% 1.98/1.42 % (32742)Memory used [KB]: 5756
% 1.98/1.42 % (32742)Time elapsed: 0.017 s
% 1.98/1.42 % (32742)Instructions burned: 28 (million)
% 1.98/1.42 % (32742)------------------------------
% 1.98/1.42 % (32742)------------------------------
% 1.98/1.43 % (32749)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_32624 for (2999ds/15Mi)
% 1.98/1.43 % (32748)Instruction limit reached!
% 1.98/1.43 % (32748)------------------------------
% 1.98/1.43 % (32748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.43 % (32748)Termination reason: Unknown
% 1.98/1.43 % (32748)Termination phase: Saturation
% 1.98/1.43
% 1.98/1.43 % (32748)Memory used [KB]: 5756
% 1.98/1.43 % (32748)Time elapsed: 0.013 s
% 1.98/1.43 % (32748)Instructions burned: 40 (million)
% 1.98/1.43 % (32748)------------------------------
% 1.98/1.43 % (32748)------------------------------
% 1.98/1.43 % (32751)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_32624 for (2999ds/1041Mi)
% 1.98/1.43 % (32750)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_32624 for (2999ds/3Mi)
% 1.98/1.43 % (32750)Instruction limit reached!
% 1.98/1.43 % (32750)------------------------------
% 1.98/1.43 % (32750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.43 % (32750)Termination reason: Unknown
% 1.98/1.43 % (32750)Termination phase: shuffling
% 1.98/1.43
% 1.98/1.43 % (32750)Memory used [KB]: 1023
% 1.98/1.43 % (32750)Time elapsed: 0.004 s
% 1.98/1.43 % (32750)Instructions burned: 3 (million)
% 1.98/1.43 % (32750)------------------------------
% 1.98/1.43 % (32750)------------------------------
% 1.98/1.43 % (32749)Instruction limit reached!
% 1.98/1.43 % (32749)------------------------------
% 1.98/1.43 % (32749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.43 % (32749)Termination reason: Unknown
% 1.98/1.43 % (32749)Termination phase: Property scanning
% 1.98/1.43
% 1.98/1.43 % (32749)Memory used [KB]: 1407
% 1.98/1.43 % (32749)Time elapsed: 0.010 s
% 1.98/1.43 % (32749)Instructions burned: 15 (million)
% 1.98/1.43 % (32749)------------------------------
% 1.98/1.43 % (32749)------------------------------
% 1.98/1.44 % (32753)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_32624 for (2999ds/16Mi)
% 1.98/1.44 % (32752)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_32624 for (2999ds/7Mi)
% 1.98/1.44 % (32753)Instruction limit reached!
% 1.98/1.44 % (32753)------------------------------
% 1.98/1.44 % (32753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.44 % (32753)Termination reason: Unknown
% 1.98/1.44 % (32753)Termination phase: Saturation
% 1.98/1.44
% 1.98/1.44 % (32753)Memory used [KB]: 5628
% 1.98/1.44 % (32753)Time elapsed: 0.007 s
% 1.98/1.44 % (32753)Instructions burned: 18 (million)
% 1.98/1.44 % (32753)------------------------------
% 1.98/1.44 % (32753)------------------------------
% 1.98/1.44 % (32752)Instruction limit reached!
% 1.98/1.44 % (32752)------------------------------
% 1.98/1.44 % (32752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.44 % (32752)Termination reason: Unknown
% 1.98/1.44 % (32752)Termination phase: Property scanning
% 1.98/1.44
% 1.98/1.44 % (32752)Memory used [KB]: 1151
% 1.98/1.44 % (32752)Time elapsed: 0.006 s
% 1.98/1.44 % (32752)Instructions burned: 7 (million)
% 1.98/1.44 % (32752)------------------------------
% 1.98/1.44 % (32752)------------------------------
% 1.98/1.45 % (32754)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_32624 for (2999ds/3Mi)
% 1.98/1.45 % (32754)Instruction limit reached!
% 1.98/1.45 % (32754)------------------------------
% 1.98/1.45 % (32754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.45 % (32754)Termination reason: Unknown
% 1.98/1.45 % (32754)Termination phase: shuffling
% 1.98/1.45
% 1.98/1.45 % (32754)Memory used [KB]: 1023
% 1.98/1.45 % (32754)Time elapsed: 0.003 s
% 1.98/1.45 % (32754)Instructions burned: 3 (million)
% 1.98/1.45 % (32754)------------------------------
% 1.98/1.45 % (32754)------------------------------
% 1.98/1.45 % (32755)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_32624 for (2999ds/3Mi)
% 1.98/1.45 % (32755)Instruction limit reached!
% 1.98/1.45 % (32755)------------------------------
% 1.98/1.45 % (32755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.45 % (32755)Termination reason: Unknown
% 1.98/1.45 % (32755)Termination phase: shuffling
% 1.98/1.45
% 1.98/1.45 % (32755)Memory used [KB]: 1023
% 1.98/1.45 % (32755)Time elapsed: 0.004 s
% 1.98/1.45 % (32755)Instructions burned: 3 (million)
% 1.98/1.45 % (32755)------------------------------
% 1.98/1.45 % (32755)------------------------------
% 1.98/1.45 % (32756)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_32624 for (2999ds/7Mi)
% 1.98/1.46 % (32756)Instruction limit reached!
% 1.98/1.46 % (32756)------------------------------
% 1.98/1.46 % (32756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.46 % (32756)Termination reason: Unknown
% 1.98/1.46 % (32756)Termination phase: Property scanning
% 1.98/1.46
% 1.98/1.46 % (32756)Memory used [KB]: 1151
% 1.98/1.46 % (32756)Time elapsed: 0.004 s
% 1.98/1.46 % (32756)Instructions burned: 7 (million)
% 1.98/1.46 % (32756)------------------------------
% 1.98/1.46 % (32756)------------------------------
% 1.98/1.46 % (32757)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_32624 for (2999ds/3Mi)
% 1.98/1.46 % (32757)Instruction limit reached!
% 1.98/1.46 % (32757)------------------------------
% 1.98/1.46 % (32757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.46 % (32757)Termination reason: Unknown
% 1.98/1.46 % (32757)Termination phase: shuffling
% 1.98/1.46
% 1.98/1.46 % (32757)Memory used [KB]: 1023
% 1.98/1.46 % (32757)Time elapsed: 0.004 s
% 1.98/1.46 % (32757)Instructions burned: 3 (million)
% 1.98/1.46 % (32757)------------------------------
% 1.98/1.46 % (32757)------------------------------
% 1.98/1.47 % (32758)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_32624 for (2999ds/4Mi)
% 1.98/1.47 % (32758)Instruction limit reached!
% 1.98/1.47 % (32758)------------------------------
% 1.98/1.47 % (32758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.47 % (32758)Termination reason: Unknown
% 1.98/1.47 % (32758)Termination phase: shuffling
% 1.98/1.47
% 1.98/1.47 % (32758)Memory used [KB]: 1023
% 1.98/1.47 % (32758)Time elapsed: 0.003 s
% 1.98/1.47 % (32758)Instructions burned: 4 (million)
% 1.98/1.47 % (32758)------------------------------
% 1.98/1.47 % (32758)------------------------------
% 1.98/1.47 % (32760)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_32624 for (2999ds/710Mi)
% 1.98/1.47 % (32759)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_32624 for (2999ds/18Mi)
% 1.98/1.48 % (32762)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_32624 for (2999ds/902Mi)
% 1.98/1.48 % (32740)Instruction limit reached!
% 1.98/1.48 % (32740)------------------------------
% 1.98/1.48 % (32740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.48 % (32740)Termination reason: Unknown
% 1.98/1.48 % (32740)Termination phase: Saturation
% 1.98/1.48
% 1.98/1.48 % (32740)Memory used [KB]: 6780
% 1.98/1.48 % (32740)Time elapsed: 0.075 s
% 1.98/1.48 % (32740)Instructions burned: 184 (million)
% 1.98/1.48 % (32740)------------------------------
% 1.98/1.48 % (32740)------------------------------
% 1.98/1.48 % (32759)Instruction limit reached!
% 1.98/1.48 % (32759)------------------------------
% 1.98/1.48 % (32759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.48 % (32759)Termination reason: Unknown
% 1.98/1.48 % (32759)Termination phase: Saturation
% 1.98/1.48
% 1.98/1.48 % (32759)Memory used [KB]: 5628
% 1.98/1.48 % (32759)Time elapsed: 0.012 s
% 1.98/1.48 % (32759)Instructions burned: 19 (million)
% 1.98/1.48 % (32759)------------------------------
% 1.98/1.48 % (32759)------------------------------
% 1.98/1.48 % (32761)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_32624 for (2999ds/6Mi)
% 1.98/1.48 % (32761)Instruction limit reached!
% 1.98/1.48 % (32761)------------------------------
% 1.98/1.48 % (32761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.48 % (32761)Termination reason: Unknown
% 1.98/1.48 % (32761)Termination phase: Property scanning
% 1.98/1.48
% 1.98/1.48 % (32761)Memory used [KB]: 1023
% 1.98/1.48 % (32761)Time elapsed: 0.005 s
% 1.98/1.49 % (32761)Instructions burned: 6 (million)
% 1.98/1.49 % (32761)------------------------------
% 1.98/1.49 % (32761)------------------------------
% 1.98/1.49 % (32763)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_32624 for (2999ds/21Mi)
% 1.98/1.50 % (32763)Instruction limit reached!
% 1.98/1.50 % (32763)------------------------------
% 1.98/1.50 % (32763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.50 % (32763)Termination reason: Unknown
% 1.98/1.50 % (32763)Termination phase: Saturation
% 1.98/1.50
% 1.98/1.50 % (32763)Memory used [KB]: 5628
% 1.98/1.50 % (32763)Time elapsed: 0.031 s
% 1.98/1.50 % (32763)Instructions burned: 23 (million)
% 1.98/1.50 % (32763)------------------------------
% 1.98/1.50 % (32763)------------------------------
% 1.98/1.50 % (32764)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_32624 for (2999ds/5Mi)
% 1.98/1.50 % (32745)First to succeed.
% 1.98/1.50 % (32764)Instruction limit reached!
% 1.98/1.50 % (32764)------------------------------
% 1.98/1.50 % (32764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.50 % (32764)Termination reason: Unknown
% 1.98/1.50 % (32764)Termination phase: shuffling
% 1.98/1.50
% 1.98/1.50 % (32764)Memory used [KB]: 1023
% 1.98/1.50 % (32764)Time elapsed: 0.004 s
% 1.98/1.50 % (32764)Instructions burned: 5 (million)
% 1.98/1.50 % (32764)------------------------------
% 1.98/1.50 % (32764)------------------------------
% 1.98/1.50 % (32765)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_32624 for (2999ds/6Mi)
% 1.98/1.50 % (32762)Also succeeded, but the first one will report.
% 1.98/1.50 % (32745)Refutation found. Thanks to Tanya!
% 1.98/1.50 % SZS status Theorem for DTF2THF_32624
% 1.98/1.50 % SZS output start Proof for DTF2THF_32624
% 1.98/1.50 thf(func_def_0, type, in: $i > $i > $o).
% 1.98/1.50 thf(func_def_1, type, exu: ($i > $o) > $o).
% 1.98/1.50 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 1.98/1.50 thf(func_def_8, type, powerset: $i > $i).
% 1.98/1.50 thf(func_def_10, type, setunion: $i > $i).
% 1.98/1.50 thf(func_def_19, type, descr: ($i > $o) > $i).
% 1.98/1.50 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 1.98/1.50 thf(func_def_26, type, prop2set: $o > $i).
% 1.98/1.50 thf(func_def_44, type, sP0: $i > $i > $o).
% 1.98/1.50 thf(func_def_45, type, sP1: $i > $o).
% 1.98/1.50 thf(func_def_46, type, sP2: $i > $i > $o).
% 1.98/1.50 thf(func_def_47, type, sP3: $i > $i > $o).
% 1.98/1.50 thf(func_def_51, type, sK7: $i > $i > $i).
% 1.98/1.50 thf(func_def_52, type, sK8: $i > $i > $i).
% 1.98/1.50 thf(func_def_53, type, sK9: $i > $i > $i).
% 1.98/1.50 thf(func_def_54, type, sK10: $i > $i > $i).
% 1.98/1.50 thf(func_def_55, type, sK11: $i > $i > $i > $i).
% 1.98/1.50 thf(func_def_56, type, sK12: $i > $i).
% 1.98/1.50 thf(func_def_57, type, sK13: $i > $i).
% 1.98/1.50 thf(func_def_58, type, sK14: $i > $i).
% 1.98/1.50 thf(func_def_59, type, sK15: $i > $i).
% 1.98/1.50 thf(func_def_60, type, sK16: $i > $i > $i > $i).
% 1.98/1.50 thf(func_def_61, type, sK17: $i > $i > $i > $i).
% 1.98/1.50 thf(func_def_62, type, sK18: $i > $i > $i).
% 1.98/1.50 thf(func_def_63, type, sK19: $i > $i > $i).
% 1.98/1.50 thf(func_def_64, type, sK20: $i > $i > $i).
% 1.98/1.50 thf(func_def_65, type, sK21: $i > $i).
% 1.98/1.50 thf(func_def_66, type, sK22: $i > $i > $i).
% 1.98/1.50 thf(func_def_68, type, sK24: $i > $i).
% 1.98/1.50 thf(func_def_69, type, sK25: $i > $i).
% 1.98/1.50 thf(func_def_72, type, sK28: $i > $o).
% 1.98/1.50 thf(func_def_78, type, sK34: $i > $i).
% 1.98/1.50 thf(func_def_79, type, sK35: $i > $i > $i).
% 1.98/1.50 thf(func_def_83, type, sK39: $i > $i > $i).
% 1.98/1.50 thf(func_def_88, type, sK44: $i > $o).
% 1.98/1.50 thf(func_def_90, type, sK46: ($i > $o) > $i).
% 1.98/1.50 thf(func_def_91, type, sK47: $i > $o).
% 1.98/1.50 thf(func_def_92, type, sK48: ($i > $o) > $i).
% 1.98/1.50 thf(func_def_93, type, sK49: $i > $o).
% 1.98/1.50 thf(func_def_94, type, sK50: $i > $i).
% 1.98/1.50 thf(func_def_97, type, sK53: $i > $i > $i).
% 1.98/1.50 thf(func_def_98, type, sK54: $i > $i > $i).
% 1.98/1.50 thf(func_def_105, type, sK61: $i > $i).
% 1.98/1.50 thf(func_def_106, type, sK62: $i > $i).
% 1.98/1.50 thf(func_def_107, type, sK63: $i > $o).
% 1.98/1.50 thf(func_def_112, type, sK68: $i > $i > $o).
% 1.98/1.50 thf(func_def_114, type, sK70: $i > $i).
% 1.98/1.50 thf(func_def_115, type, sK71: $i > $i).
% 1.98/1.50 thf(func_def_116, type, sK72: $i > ($i > $i > $o) > $i).
% 1.98/1.50 thf(func_def_117, type, sK73: $i > $i > ($i > $i > $o) > $i).
% 1.98/1.50 thf(func_def_118, type, sK74: $i > ($i > $i > $o) > $i).
% 1.98/1.50 thf(func_def_120, type, ph76: !>[X0: $tType]:(X0)).
% 1.98/1.50 thf(f1050,plain,(
% 1.98/1.50 $false),
% 1.98/1.50 inference(subsumption_resolution,[status(thm)],[f1047,f302])).
% 1.98/1.50 thf(f302,plain,(
% 1.98/1.50 (emptyset != sK30)),
% 1.98/1.50 inference(cnf_transformation,[status(thm)],[f155])).
% 1.98/1.50 thf(f155,plain,(
% 1.98/1.50 (omegaIndAx = $true) & (powersetAx = $true) & (setunionAx = $true) & ((emptyset != sK30) & ! [X1 : $i] : ((in @ X1 @ sK30) != $true)) & (dsetconstrI = $true) & (prop2setE = $true) & (exuE1 = $true) & (omegaSAx = $true) & (setext = $true) & (wellorderingAx = $true) & (emptysetimpfalse = $true) & (dsetconstrEL = $true) & (emptysetAx = $true) & (omega0Ax = $true) & (notinemptyset = $true) & (setextAx = $true) & (foundationAx = $true) & (replAx = $true) & (dsetconstrER = $true) & (setadjoinAx = $true) & (descrp = $true) & (emptysetE = $true) & (exuE3e = $true)),
% 1.98/1.50 inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f91,f154])).
% 1.98/1.50 thf(f154,plain,(
% 1.98/1.50 ? [X0 : $i] : ((emptyset != X0) & ! [X1 : $i] : ($true != (in @ X1 @ X0))) => ((emptyset != sK30) & ! [X1 : $i] : ((in @ X1 @ sK30) != $true))),
% 1.98/1.50 introduced(definition,[],[choice_axiom])).
% 1.98/1.50 thf(f91,plain,(
% 1.98/1.50 (omegaIndAx = $true) & (powersetAx = $true) & (setunionAx = $true) & ? [X0 : $i] : ((emptyset != X0) & ! [X1 : $i] : ($true != (in @ X1 @ X0))) & (dsetconstrI = $true) & (prop2setE = $true) & (exuE1 = $true) & (omegaSAx = $true) & (setext = $true) & (wellorderingAx = $true) & (emptysetimpfalse = $true) & (dsetconstrEL = $true) & (emptysetAx = $true) & (omega0Ax = $true) & (notinemptyset = $true) & (setextAx = $true) & (foundationAx = $true) & (replAx = $true) & (dsetconstrER = $true) & (setadjoinAx = $true) & (descrp = $true) & (emptysetE = $true) & (exuE3e = $true)),
% 1.98/1.50 inference(flattening,[status(thm)],[f90])).
% 1.98/1.50 thf(f90,plain,(
% 1.98/1.50 (((((((((((((((((((((? [X0 : $i] : ((emptyset != X0) & ! [X1 : $i] : ($true != (in @ X1 @ X0))) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 1.98/1.50 inference(ennf_transformation,[status(thm)],[f75])).
% 1.98/1.50 thf(f75,plain,(
% 1.98/1.50 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ! [X0 : $i] : (! [X1 : $i] : ($true != (in @ X1 @ X0)) => (emptyset = X0))))))))))))))))))))))))),
% 1.98/1.50 inference(flattening,[status(thm)],[f33])).
% 1.98/1.50 thf(f33,plain,(
% 1.98/1.50 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ! [X0 : $i] : (! [X1 : $i] : ~($true = (in @ X1 @ X0)) => (emptyset = X0))))))))))))))))))))))))),
% 1.98/1.50 inference(fool_elimination,[status(thm)],[f32])).
% 1.98/1.50 thf(f32,plain,(
% 1.98/1.50 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => ! [X0 : $i] : (! [X1 : $i] : ~(in @ X1 @ X0) => (emptyset = X0))))))))))))))))))))))))),
% 1.98/1.50 inference(rectify,[status(thm)],[f26])).
% 1.98/1.50 thf(f26,negated_conjecture,(
% 1.98/1.50 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => ! [X3 : $i] : (! [X1 : $i] : ~(in @ X1 @ X3) => (emptyset = X3))))))))))))))))))))))))),
% 1.98/1.50 inference(negated_conjecture,[status(cth)],[f25])).
% 1.98/1.50 thf(f25,conjecture,(
% 1.98/1.50 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => ! [X3 : $i] : (! [X1 : $i] : ~(in @ X1 @ X3) => (emptyset = X3)))))))))))))))))))))))),
% 1.98/1.50 file('/export/starexec/sandbox2/tmp/tmp.OwlJSocWOh/DTF2THF_32624.p',emptyI)).
% 1.98/1.50 thf(f1047,plain,(
% 1.98/1.50 (emptyset = sK30)),
% 1.98/1.50 inference(trivial_inequality_removal,[status(thm)],[f1040])).
% 1.98/1.50 thf(f1040,plain,(
% 1.98/1.50 (emptyset = sK30) | ($true != $true)),
% 1.98/1.50 inference(superposition,[status(thm)],[f301,f1024])).
% 1.98/1.50 thf(f1024,plain,(
% 1.98/1.50 ( ! [X0 : $i] : (((in @ (sK53 @ X0 @ emptyset) @ X0) = $true) | (emptyset = X0)) )),
% 1.98/1.50 inference(trivial_inequality_removal,[status(thm)],[f1019])).
% 1.98/1.50 thf(f1019,plain,(
% 1.98/1.50 ( ! [X0 : $i] : ((emptyset = X0) | ($true != $true) | ((in @ (sK53 @ X0 @ emptyset) @ X0) = $true)) )),
% 1.98/1.50 inference(superposition,[status(thm)],[f486,f475])).
% 1.98/1.50 thf(f475,plain,(
% 1.98/1.50 ( ! [X4 : $i,X5 : $i] : (((in @ (sK54 @ X5 @ X4) @ X4) = $true) | ((in @ (sK53 @ X5 @ X4) @ X5) = $true) | (X4 = X5)) )),
% 1.98/1.50 inference(trivial_inequality_removal,[status(thm)],[f432])).
% 1.98/1.50 thf(f432,plain,(
% 1.98/1.50 ( ! [X4 : $i,X5 : $i] : (($true != $true) | ((in @ (sK53 @ X5 @ X4) @ X5) = $true) | ((in @ (sK54 @ X5 @ X4) @ X4) = $true) | (X4 = X5)) )),
% 1.98/1.50 inference(definition_unfolding,[status(thm)],[f341,f296])).
% 1.98/1.50 thf(f296,plain,(
% 1.98/1.50 (setext = $true)),
% 1.98/1.50 inference(cnf_transformation,[status(thm)],[f155])).
% 1.98/1.50 thf(f341,plain,(
% 1.98/1.50 ( ! [X4 : $i,X5 : $i] : (((in @ (sK53 @ X5 @ X4) @ X5) = $true) | ((in @ (sK54 @ X5 @ X4) @ X4) = $true) | (X4 = X5) | (setext != $true)) )),
% 1.98/1.50 inference(cnf_transformation,[status(thm)],[f201])).
% 1.98/1.50 thf(f201,plain,(
% 1.98/1.50 ((setext = $true) | (! [X2 : $i] : (((in @ X2 @ sK52) != $true) | ($true = (in @ X2 @ sK51))) & ! [X3 : $i] : (((in @ X3 @ sK52) = $true) | ((in @ X3 @ sK51) != $true)) & (sK51 != sK52))) & (! [X4 : $i,X5 : $i] : ((((in @ (sK53 @ X5 @ X4) @ X5) = $true) & ((in @ (sK53 @ X5 @ X4) @ X4) != $true)) | (((in @ (sK54 @ X5 @ X4) @ X5) != $true) & ((in @ (sK54 @ X5 @ X4) @ X4) = $true)) | (X4 = X5)) | (setext != $true))),
% 1.98/1.50 inference(skolemisation,[status(esa),new_symbols(skolem,[sK51,sK52,sK53,sK54])],[f197,f200,f199,f198])).
% 1.98/1.50 thf(f198,plain,(
% 1.98/1.50 ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)) & ! [X3 : $i] : (((in @ X3 @ X1) = $true) | ((in @ X3 @ X0) != $true)) & (X0 != X1)) => (! [X2 : $i] : (((in @ X2 @ sK52) != $true) | ($true = (in @ X2 @ sK51))) & ! [X3 : $i] : (((in @ X3 @ sK52) = $true) | ((in @ X3 @ sK51) != $true)) & (sK51 != sK52))),
% 1.98/1.50 introduced(definition,[],[choice_axiom])).
% 1.98/1.50 thf(f199,plain,(
% 1.98/1.50 ! [X4 : $i,X5 : $i] : (? [X6 : $i] : (((in @ X6 @ X5) = $true) & ((in @ X6 @ X4) != $true)) => (((in @ (sK53 @ X5 @ X4) @ X5) = $true) & ((in @ (sK53 @ X5 @ X4) @ X4) != $true)))),
% 1.98/1.50 introduced(definition,[],[choice_axiom])).
% 1.98/1.50 thf(f200,plain,(
% 1.98/1.50 ! [X4 : $i,X5 : $i] : (? [X7 : $i] : (((in @ X7 @ X5) != $true) & ((in @ X7 @ X4) = $true)) => (((in @ (sK54 @ X5 @ X4) @ X5) != $true) & ((in @ (sK54 @ X5 @ X4) @ X4) = $true)))),
% 1.98/1.50 introduced(definition,[],[choice_axiom])).
% 1.98/1.50 thf(f197,plain,(
% 1.98/1.50 ((setext = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)) & ! [X3 : $i] : (((in @ X3 @ X1) = $true) | ((in @ X3 @ X0) != $true)) & (X0 != X1))) & (! [X4 : $i,X5 : $i] : (? [X6 : $i] : (((in @ X6 @ X5) = $true) & ((in @ X6 @ X4) != $true)) | ? [X7 : $i] : (((in @ X7 @ X5) != $true) & ((in @ X7 @ X4) = $true)) | (X4 = X5)) | (setext != $true))),
% 1.98/1.50 inference(rectify,[status(thm)],[f196])).
% 1.98/1.50 thf(f196,plain,(
% 1.98/1.50 ((setext = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)) & ! [X3 : $i] : (((in @ X3 @ X1) = $true) | ((in @ X3 @ X0) != $true)) & (X0 != X1))) & (! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true)) | ? [X3 : $i] : (((in @ X3 @ X1) != $true) & ((in @ X3 @ X0) = $true)) | (X0 = X1)) | (setext != $true))),
% 1.98/1.50 inference(nnf_transformation,[status(thm)],[f89])).
% 1.98/1.50 thf(f89,plain,(
% 1.98/1.50 (setext = $true) <=> ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true)) | ? [X3 : $i] : (((in @ X3 @ X1) != $true) & ((in @ X3 @ X0) = $true)) | (X0 = X1))),
% 1.98/1.50 inference(flattening,[status(thm)],[f88])).
% 1.98/1.50 thf(f88,plain,(
% 1.98/1.50 ! [X0 : $i,X1 : $i] : (((X0 = X1) | ? [X3 : $i] : (((in @ X3 @ X1) != $true) & ((in @ X3 @ X0) = $true))) | ? [X2 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true))) <=> (setext = $true)),
% 1.98/1.50 inference(ennf_transformation,[status(thm)],[f41])).
% 1.98/1.50 thf(f41,plain,(
% 1.98/1.50 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true)) => (! [X3 : $i] : (((in @ X3 @ X0) = $true) => ((in @ X3 @ X1) = $true)) => (X0 = X1))) <=> (setext = $true)),
% 1.98/1.50 inference(fool_elimination,[status(thm)],[f40])).
% 1.98/1.50 thf(f40,plain,(
% 1.98/1.50 (setext = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => (in @ X3 @ X1)) => (X0 = X1))))),
% 1.98/1.50 inference(rectify,[status(thm)],[f24])).
% 1.98/1.50 thf(f24,axiom,(
% 1.98/1.50 (setext = ! [X4 : $i,X3 : $i] : (! [X1 : $i] : ((in @ X1 @ X3) => (in @ X1 @ X4)) => (! [X1 : $i] : ((in @ X1 @ X4) => (in @ X1 @ X3)) => (X3 = X4))))),
% 1.98/1.50 file('/export/starexec/sandbox2/tmp/tmp.OwlJSocWOh/DTF2THF_32624.p',setext)).
% 1.98/1.50 thf(f486,plain,(
% 1.98/1.50 ( ! [X1 : $i] : (((in @ X1 @ emptyset) != $true)) )),
% 1.98/1.50 inference(trivial_inequality_removal,[status(thm)],[f396])).
% 1.98/1.50 thf(f396,plain,(
% 1.98/1.50 ( ! [X1 : $i] : (($true != $true) | ((in @ X1 @ emptyset) != $true)) )),
% 1.98/1.50 inference(definition_unfolding,[status(thm)],[f306,f294])).
% 1.98/1.50 thf(f294,plain,(
% 1.98/1.50 (emptysetimpfalse = $true)),
% 1.98/1.50 inference(cnf_transformation,[status(thm)],[f155])).
% 1.98/1.50 thf(f306,plain,(
% 1.98/1.50 ( ! [X1 : $i] : (((in @ X1 @ emptyset) != $true) | (emptysetimpfalse != $true)) )),
% 1.98/1.50 inference(cnf_transformation,[status(thm)],[f159])).
% 1.98/1.50 thf(f159,plain,(
% 1.98/1.50 ((emptysetimpfalse = $true) | ((in @ sK31 @ emptyset) = $true)) & (! [X1 : $i] : ((in @ X1 @ emptyset) != $true) | (emptysetimpfalse != $true))),
% 1.98/1.50 inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f157,f158])).
% 1.98/1.50 thf(f158,plain,(
% 1.98/1.50 ? [X0 : $i] : ((in @ X0 @ emptyset) = $true) => ((in @ sK31 @ emptyset) = $true)),
% 1.98/1.50 introduced(definition,[],[choice_axiom])).
% 1.98/1.50 thf(f157,plain,(
% 1.98/1.50 ((emptysetimpfalse = $true) | ? [X0 : $i] : ((in @ X0 @ emptyset) = $true)) & (! [X1 : $i] : ((in @ X1 @ emptyset) != $true) | (emptysetimpfalse != $true))),
% 1.98/1.50 inference(rectify,[status(thm)],[f156])).
% 1.98/1.50 thf(f156,plain,(
% 1.98/1.50 ((emptysetimpfalse = $true) | ? [X0 : $i] : ((in @ X0 @ emptyset) = $true)) & (! [X0 : $i] : ((in @ X0 @ emptyset) != $true) | (emptysetimpfalse != $true))),
% 1.98/1.50 inference(nnf_transformation,[status(thm)],[f80])).
% 1.98/1.50 thf(f80,plain,(
% 1.98/1.50 (emptysetimpfalse = $true) <=> ! [X0 : $i] : ((in @ X0 @ emptyset) != $true)),
% 1.98/1.50 inference(flattening,[status(thm)],[f79])).
% 1.98/1.50 thf(f79,plain,(
% 1.98/1.50 (emptysetimpfalse = $true) <=> ! [X0 : $i] : ~((in @ X0 @ emptyset) = $true)),
% 1.98/1.50 inference(true_and_false_elimination,[status(thm)],[f72])).
% 1.98/1.50 thf(f72,plain,(
% 1.98/1.50 (emptysetimpfalse = $true) <=> ! [X0 : $i] : (((in @ X0 @ emptyset) = $true) => $false)),
% 1.98/1.50 inference(fool_elimination,[status(thm)],[f71])).
% 1.98/1.50 thf(f71,plain,(
% 1.98/1.50 (emptysetimpfalse = ! [X0 : $i] : ((in @ X0 @ emptyset) => $false))),
% 1.98/1.50 inference(rectify,[status(thm)],[f21])).
% 1.98/1.50 thf(f21,axiom,(
% 1.98/1.50 (emptysetimpfalse = ! [X1 : $i] : ((in @ X1 @ emptyset) => $false))),
% 1.98/1.50 file('/export/starexec/sandbox2/tmp/tmp.OwlJSocWOh/DTF2THF_32624.p',emptysetimpfalse)).
% 1.98/1.50 thf(f301,plain,(
% 1.98/1.50 ( ! [X1 : $i] : (((in @ X1 @ sK30) != $true)) )),
% 1.98/1.50 inference(cnf_transformation,[status(thm)],[f155])).
% 1.98/1.50 % SZS output end Proof for DTF2THF_32624
% 1.98/1.50 % (32745)------------------------------
% 1.98/1.50 % (32745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.98/1.50 % (32745)Termination reason: Refutation
% 1.98/1.50
% 1.98/1.50 % (32745)Memory used [KB]: 6780
% 1.98/1.50 % (32745)Time elapsed: 0.095 s
% 1.98/1.50 % (32745)Instructions burned: 239 (million)
% 1.98/1.50 % (32745)------------------------------
% 1.98/1.50 % (32745)------------------------------
% 1.98/1.50 % (32739)Success in time 0.113 s
%------------------------------------------------------------------------------