%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU499^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 09:34:56 AM UTC 2026
% Result : Theorem 0.31s 1.36s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 470 ( 154 equ; 0 cnn)
% Maximal formula atoms : 19 ( 13 avg)
% Number of connectives : 329 ( 27 ~; 14 |; 70 &; 109 @)
% ( 0 <=>; 98 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 44 usr; 20 con; 0-3 aty)
% ( 7 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 71 ( 30 ^; 26 !; 15 ?; 71 :)
% 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_41,type,
sK0: $i > $o ).
thf(func_def_42,type,
sK1: $i > $i ).
thf(func_def_44,type,
sK3: $i > $i ).
thf(func_def_45,type,
sK4: $i > $i ).
thf(func_def_46,type,
sK5: $i > $i > $i ).
thf(func_def_48,type,
sK7: ( $i > $o ) > $i > $i ).
thf(func_def_49,type,
sK8: $i > ( $i > $i > $o ) > $i ).
thf(func_def_50,type,
sK9: $i > ( $i > $i > $o ) > $i ).
thf(func_def_51,type,
sK10: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_52,type,
sK11: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_53,type,
sK12: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_54,type,
sK13: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_55,type,
sK14: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_56,type,
sK15: $i > $i > $i ).
thf(func_def_57,type,
sK16: $i > $i > $i ).
thf(func_def_58,type,
sK17: $i > $i ).
thf(func_def_59,type,
sK18: $i > $i > $i > $i ).
thf(func_def_60,type,
sK19: $i > $i > $i ).
thf(func_def_61,type,
sK20: $i > $i > $i ).
thf(func_def_62,type,
sK21: $i > $i > $i ).
thf(func_def_63,type,
sK22: $i > $i > $i ).
thf(f405,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f403,f177]) ).
thf(f177,plain,
( ( sK0 @ sK6 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f175]) ).
thf(f175,plain,
( $true
= ( ( sK0 @ sK6 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK6 = Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f174]) ).
thf(f174,plain,
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ sK6 ) ),
inference(sigma_clausification,[status(thm)],[f173]) ).
thf(f173,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f92]) ).
thf(f92,plain,
( $true
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ),
inference(definition_unfolding,[status(thm)],[f64,f87]) ).
thf(f87,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f26]) ).
thf(f26,plain,
( exu
= ( ^ [X0: $i > $o] :
? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( exu
= ( ^ [X0: $i > $o] :
? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rmBBlAG7dF/DTF2THF_1626.p',exu) ).
thf(f64,plain,
( ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f57]) ).
thf(f57,plain,
( ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( foundationAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( setextAx = $true )
& ( wellorderingAx = $true )
& ( dsetconstrEL = $true )
& ( powersetAx = $true )
& ! [X1: $i] :
( ( $true
!= ( sK0 @ X1 ) )
| ( ( $true
= ( sK0 @ ( sK1 @ X1 ) ) )
& ( ( sK1 @ X1 )
!= X1 ) ) )
& ( ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
= $true )
& ( dsetconstrER = $true )
& ( setadjoinAx = $true )
& ( descrp = $true )
& ( replAx = $true )
& ( dsetconstrI = $true )
& ( emptysetAx = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f54,f56,f55]) ).
thf(f55,plain,
( ? [X0: $i > $o] :
( ! [X1: $i] :
( ( ( X0 @ X1 )
!= $true )
| ? [X2: $i] :
( ( ( X0 @ X2 )
= $true )
& ( X1 != X2 ) ) )
& ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true ) )
=> ( ! [X1: $i] :
( ( $true
!= ( sK0 @ X1 ) )
| ? [X2: $i] :
( ( $true
= ( sK0 @ X2 ) )
& ( X1 != X2 ) ) )
& ( ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f56,plain,
! [X1: $i] :
( ? [X2: $i] :
( ( $true
= ( sK0 @ X2 ) )
& ( X1 != X2 ) )
=> ( ( $true
= ( sK0 @ ( sK1 @ X1 ) ) )
& ( ( sK1 @ X1 )
!= X1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f54,plain,
( ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( foundationAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( setextAx = $true )
& ( wellorderingAx = $true )
& ( dsetconstrEL = $true )
& ( powersetAx = $true )
& ? [X0: $i > $o] :
( ! [X1: $i] :
( ( ( X0 @ X1 )
!= $true )
| ? [X2: $i] :
( ( ( X0 @ X2 )
= $true )
& ( X1 != X2 ) ) )
& ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true ) )
& ( dsetconstrER = $true )
& ( setadjoinAx = $true )
& ( descrp = $true )
& ( replAx = $true )
& ( dsetconstrI = $true )
& ( emptysetAx = $true ) ),
inference(flattening,[status(thm)],[f53]) ).
thf(f53,plain,
( ? [X0: $i > $o] :
( ! [X1: $i] :
( ( ( X0 @ X1 )
!= $true )
| ? [X2: $i] :
( ( ( X0 @ X2 )
= $true )
& ( X1 != X2 ) ) )
& ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $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)],[f52]) ).
thf(f52,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 )
=> ! [X0: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
=> ? [X1: $i] :
( ( ( X0 @ X1 )
= $true )
& ! [X2: $i] :
( ( ( X0 @ X2 )
= $true )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f25]) ).
thf(f25,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 )
=> ! [X0: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
=> ? [X2: $i] :
( ( ( X0 @ X2 )
= $true )
& ! [X3: $i] :
( ( $true
= ( X0 @ X3 ) )
=> ( X2 = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f24]) ).
thf(f24,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ? [X2: $i] :
( ( X0 @ X2 )
& ! [X3: $i] :
( ( X0 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f18]) ).
thf(f18,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ? [X1: $i] :
( ( X0 @ X1 )
& ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
thf(f17,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ? [X1: $i] :
( ( X0 @ X1 )
& ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rmBBlAG7dF/DTF2THF_1626.p',exuE1) ).
thf(f403,plain,
( ( sK0 @ sK6 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f401]) ).
thf(f401,plain,
( ( sK6 != sK6 )
| ( ( sK0 @ sK6 )
!= $true ) ),
inference(superposition,[status(thm)],[f394,f399]) ).
thf(f399,plain,
! [X0: $i] :
( ( sK6
= ( sK1 @ X0 ) )
| ( $true
!= ( sK0 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f397]) ).
thf(f397,plain,
! [X0: $i] :
( ( $true = $false )
| ( sK6
= ( sK1 @ X0 ) )
| ( $true
!= ( sK0 @ X0 ) ) ),
inference(superposition,[status(thm)],[f181,f66]) ).
thf(f66,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ ( sK1 @ X1 ) ) )
| ( $true
!= ( sK0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
thf(f181,plain,
! [X1: $i] :
( ( ( sK0 @ X1 )
= $false )
| ( sK6 = X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f180]) ).
thf(f180,plain,
! [X1: $i] :
( ( ( sK0 @ X1 )
= $false )
| ( $true
= ( sK6 = X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f179]) ).
thf(f179,plain,
! [X1: $i] :
( $true
= ( ( sK0 @ X1 )
=> ( sK6 = X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f178]) ).
thf(f178,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK6 = Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f176]) ).
thf(f176,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK6 = Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f175]) ).
thf(f394,plain,
( sK6
!= ( sK1 @ sK6 ) ),
inference(trivial_inequality_removal,[status(thm)],[f392]) ).
thf(f392,plain,
( ( sK6
!= ( sK1 @ sK6 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f65,f177]) ).
thf(f65,plain,
! [X1: $i] :
( ( $true
!= ( sK0 @ X1 ) )
| ( ( sK1 @ X1 )
!= X1 ) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU499^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n009.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:24:25 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEU499^1 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : Foundation - Axioms - Logical Axioms
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English : (!phi:i>o.exu(^x:i.phi x)->(?x:i.phi x & (!y:i.phi y -> x = y)))
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.46 % Source : [Bro08]
% 0.30/0.46 % Names : ZFC001g [Bro08]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % 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, 0.00 v6.2.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0, 0.00 v3.7.0
% 0.30/0.46 % Syntax : Number of formulae : 41 ( 16 unt; 24 typ; 16 def)
% 0.30/0.46 % Number of atoms : 112 ( 21 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 17 ( 6 avg)
% 0.30/0.46 % Number of connectives : 223 ( 3 ~; 3 |; 18 &; 149 @)
% 0.30/0.46 % ( 6 <=>; 44 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 23 ( 2 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 25 ( 24 usr; 17 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 69 ( 8 ^; 48 !; 13 ?; 69 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : http://mathgate.info/detsetitem.php?id=404
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(in_type,type,
% 0.30/0.46 in: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(exu_type,type,
% 0.30/0.46 exu: ( $i > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(exu,definition,
% 0.30/0.46 ( exu
% 0.30/0.46 = ( ^ [Xphi: $i > $o] :
% 0.30/0.46 ? [Xx: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 & ! [Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setextAx_type,type,
% 0.30/0.46 setextAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setextAx,definition,
% 0.30/0.46 ( setextAx
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 <=> ( in @ Xx @ B ) )
% 0.30/0.46 => ( A = B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyset_type,type,
% 0.30/0.46 emptyset: $i ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetAx_type,type,
% 0.30/0.46 emptysetAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetAx,definition,
% 0.30/0.46 ( emptysetAx
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoin_type,type,
% 0.30/0.46 setadjoin: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinAx_type,type,
% 0.30/0.46 setadjoinAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinAx,definition,
% 0.30/0.46 ( setadjoinAx
% 0.30/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.46 <=> ( ( Xy = Xx )
% 0.30/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powerset_type,type,
% 0.30/0.46 powerset: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(powersetAx_type,type,
% 0.30/0.46 powersetAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powersetAx,definition,
% 0.30/0.46 ( powersetAx
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.46 <=> ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunion_type,type,
% 0.30/0.46 setunion: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(setunionAx_type,type,
% 0.30/0.46 setunionAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunionAx,definition,
% 0.30/0.46 ( setunionAx
% 0.30/0.46 = ( ! [A: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.46 <=> ? [B: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(omega_type,type,
% 0.30/0.46 omega: $i ).
% 0.30/0.46
% 0.30/0.46 thf(omega0Ax_type,type,
% 0.30/0.46 omega0Ax: $o ).
% 0.30/0.46
% 0.30/0.46 thf(omega0Ax,definition,
% 0.30/0.46 ( omega0Ax
% 0.30/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(omegaSAx_type,type,
% 0.30/0.46 omegaSAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(omegaSAx,definition,
% 0.30/0.46 ( omegaSAx
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ omega )
% 0.30/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(omegaIndAx_type,type,
% 0.30/0.46 omegaIndAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(omegaIndAx,definition,
% 0.30/0.46 ( omegaIndAx
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ( ( in @ emptyset @ A )
% 0.30/0.46 & ! [Xx: $i] :
% 0.30/0.46 ( ( ( in @ Xx @ omega )
% 0.30/0.46 & ( in @ Xx @ A ) )
% 0.30/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ omega )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(replAx_type,type,
% 0.30/0.46 replAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(replAx,definition,
% 0.30/0.46 ( replAx
% 0.30/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( exu
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.30/0.46 => ? [B: $i] :
% 0.30/0.46 ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 <=> ? [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ A )
% 0.30/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(foundationAx_type,type,
% 0.30/0.46 foundationAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(foundationAx,definition,
% 0.30/0.46 ( foundationAx
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.30/0.46 => ? [B: $i] :
% 0.30/0.46 ( ( in @ B @ A )
% 0.30/0.46 & ~ ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(wellorderingAx_type,type,
% 0.30/0.46 wellorderingAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(wellorderingAx,definition,
% 0.30/0.46 ( wellorderingAx
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ? [B: $i] :
% 0.30/0.46 ( ! [C: $i] :
% 0.30/0.46 ( ( in @ C @ B )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ C )
% 0.30/0.46 => ( in @ Xx @ A ) ) )
% 0.30/0.46 & ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( ( in @ Xx @ A )
% 0.30/0.46 & ( in @ Xy @ A ) )
% 0.30/0.46 => ( ! [C: $i] :
% 0.30/0.46 ( ( in @ C @ B )
% 0.30/0.46 => ( ( in @ Xx @ C )
% 0.30/0.46 <=> ( in @ Xy @ C ) ) )
% 0.30/0.46 => ( Xx = Xy ) ) )
% 0.30/0.46 & ! [C: $i,D: $i] :
% 0.30/0.46 ( ( ( in @ C @ B )
% 0.30/0.46 & ( in @ D @ B ) )
% 0.30/0.46 => ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ C )
% 0.30/0.46 => ( in @ Xx @ D ) )
% 0.30/0.46 | ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ D )
% 0.30/0.46 => ( in @ Xx @ C ) ) ) )
% 0.30/0.46 & ! [C: $i] :
% 0.30/0.46 ( ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ C )
% 0.30/0.46 => ( in @ Xx @ A ) )
% 0.30/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.30/0.46 => ? [D: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ D @ B )
% 0.30/0.46 & ( in @ Xx @ C )
% 0.30/0.46 & ~ ? [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ D )
% 0.30/0.46 & ( in @ Xy @ C ) )
% 0.30/0.46 & ! [E: $i] :
% 0.30/0.46 ( ( in @ E @ B )
% 0.30/0.46 => ( ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ E )
% 0.30/0.46 => ( in @ Xy @ D ) )
% 0.30/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(descr_type,type,
% 0.30/0.46 descr: ( $i > $o ) > $i ).
% 0.30/0.46
% 0.30/0.46 thf(descrp_type,type,
% 0.30/0.46 descrp: $o ).
% 0.30/0.46
% 0.30/0.46 thf(descrp,definition,
% 0.30/0.46 ( descrp
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ( Xphi
% 0.30/0.46 @ ( descr
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstr_type,type,
% 0.30/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrI_type,type,
% 0.30/0.46 dsetconstrI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrI,definition,
% 0.30/0.46 ( dsetconstrI
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 => ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrEL_type,type,
% 0.30/0.46 dsetconstrEL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrEL,definition,
% 0.30/0.46 ( dsetconstrEL
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrER_type,type,
% 0.30/0.46 dsetconstrER: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrER,definition,
% 0.30/0.46 ( dsetconstrER
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuE1,conjecture,
% 0.30/0.46 ( setextAx
% 0.30/0.46 => ( emptysetAx
% 0.30/0.46 => ( setadjoinAx
% 0.30/0.46 => ( powersetAx
% 0.30/0.46 => ( setunionAx
% 0.30/0.46 => ( omega0Ax
% 0.30/0.46 => ( omegaSAx
% 0.30/0.46 => ( omegaIndAx
% 0.30/0.46 => ( replAx
% 0.30/0.46 => ( foundationAx
% 0.30/0.46 => ( wellorderingAx
% 0.30/0.46 => ( descrp
% 0.30/0.46 => ( dsetconstrI
% 0.30/0.46 => ( dsetconstrEL
% 0.30/0.46 => ( dsetconstrER
% 0.30/0.46 => ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 & ! [Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 0.31/1.30 ---- Embedded in THF ---
% 0.31/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.31/1.30 %%% Generated on Tue Feb 24 12:24:26 EST 2026
% 0.31/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.31/1.30 %%% Logic specification used:
% 0.31/1.30 %%% thf(spec, logic, $$dhol).
% 0.31/1.30
% 0.31/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.rmBBlAG7dF/DTF2DTF1626.p
% See solution above
% 0.31/1.30 ------------------------
% 0.31/1.31 ---- Cleaned THF ---
% 0.31/1.31 thf(in_type,type,
% 0.31/1.31 in: $i > $i > $o ).
% 0.31/1.31
% 0.31/1.31 thf(exu_type,type,
% 0.31/1.31 exu: ( $i > $o ) > $o ).
% 0.31/1.31
% 0.31/1.31 thf(exu,definition,
% 0.31/1.31 ( exu
% 0.31/1.31 = ( ^ [Xphi: $i > $o] :
% 0.31/1.31 ? [Xx: $i] :
% 0.31/1.31 ( ( Xphi @ Xx )
% 0.31/1.31 & ! [Xy: $i] :
% 0.31/1.31 ( ( Xphi @ Xy )
% 0.31/1.31 => ( Xx = Xy ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(setextAx_type,type,
% 0.31/1.31 setextAx: $o ).
% 0.31/1.31
% 0.31/1.31 thf(setextAx,definition,
% 0.31/1.31 ( setextAx
% 0.31/1.31 = ( ! [A: $i,B: $i] :
% 0.31/1.31 ( ! [Xx: $i] :
% 0.31/1.31 ( ( in @ Xx @ A )
% 0.31/1.31 <=> ( in @ Xx @ B ) )
% 0.31/1.31 => ( A = B ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(emptyset_type,type,
% 0.31/1.31 emptyset: $i ).
% 0.31/1.31
% 0.31/1.31 thf(emptysetAx_type,type,
% 0.31/1.31 emptysetAx: $o ).
% 0.31/1.31
% 0.31/1.31 thf(emptysetAx,definition,
% 0.31/1.31 ( emptysetAx
% 0.31/1.31 = ( ! [Xx: $i] :
% 0.31/1.31 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(setadjoin_type,type,
% 0.31/1.31 setadjoin: $i > $i > $i ).
% 0.31/1.31
% 0.31/1.31 thf(setadjoinAx_type,type,
% 0.31/1.31 setadjoinAx: $o ).
% 0.31/1.31
% 0.31/1.31 thf(setadjoinAx,definition,
% 0.31/1.31 ( setadjoinAx
% 0.31/1.31 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/1.31 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.31/1.31 <=> ( ( Xy = Xx )
% 0.31/1.31 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(powerset_type,type,
% 0.31/1.31 powerset: $i > $i ).
% 0.31/1.31
% 0.31/1.31 thf(powersetAx_type,type,
% 0.31/1.31 powersetAx: $o ).
% 0.31/1.31
% 0.31/1.31 thf(powersetAx,definition,
% 0.31/1.31 ( powersetAx
% 0.31/1.31 = ( ! [A: $i,B: $i] :
% 0.31/1.31 ( ( in @ B @ ( powerset @ A ) )
% 0.31/1.31 <=> ! [Xx: $i] :
% 0.31/1.31 ( ( in @ Xx @ B )
% 0.31/1.31 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(setunion_type,type,
% 0.31/1.31 setunion: $i > $i ).
% 0.31/1.31
% 0.31/1.31 thf(setunionAx_type,type,
% 0.31/1.31 setunionAx: $o ).
% 0.31/1.31
% 0.31/1.31 thf(setunionAx,definition,
% 0.31/1.31 ( setunionAx
% 0.31/1.31 = ( ! [A: $i,Xx: $i] :
% 0.31/1.31 ( ( in @ Xx @ ( setunion @ A ) )
% 0.31/1.31 <=> ? [B: $i] :
% 0.31/1.31 ( ( in @ Xx @ B )
% 0.31/1.31 & ( in @ B @ A ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(omega_type,type,
% 0.31/1.31 omega: $i ).
% 0.31/1.31
% 0.31/1.31 thf(omega0Ax_type,type,
% 0.31/1.31 omega0Ax: $o ).
% 0.31/1.31
% 0.31/1.31 thf(omega0Ax,definition,
% 0.31/1.31 ( omega0Ax
% 0.31/1.31 = ( in @ emptyset @ omega ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(omegaSAx_type,type,
% 0.31/1.31 omegaSAx: $o ).
% 0.31/1.31
% 0.31/1.31 thf(omegaSAx,definition,
% 0.31/1.31 ( omegaSAx
% 0.31/1.31 = ( ! [Xx: $i] :
% 0.31/1.31 ( ( in @ Xx @ omega )
% 0.31/1.31 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(omegaIndAx_type,type,
% 0.31/1.31 omegaIndAx: $o ).
% 0.31/1.31
% 0.31/1.31 thf(omegaIndAx,definition,
% 0.31/1.31 ( omegaIndAx
% 0.31/1.31 = ( ! [A: $i] :
% 0.31/1.31 ( ( ( in @ emptyset @ A )
% 0.31/1.31 & ! [Xx: $i] :
% 0.31/1.31 ( ( ( in @ Xx @ omega )
% 0.31/1.31 & ( in @ Xx @ A ) )
% 0.31/1.31 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.31/1.31 => ! [Xx: $i] :
% 0.31/1.31 ( ( in @ Xx @ omega )
% 0.31/1.31 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(replAx_type,type,
% 0.31/1.31 replAx: $o ).
% 0.31/1.31
% 0.31/1.31 thf(replAx,definition,
% 0.31/1.31 ( replAx
% 0.31/1.31 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.31/1.31 ( ! [Xx: $i] :
% 0.31/1.31 ( ( in @ Xx @ A )
% 0.31/1.31 => ( exu
% 0.31/1.31 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.31/1.31 => ? [B: $i] :
% 0.31/1.31 ! [Xx: $i] :
% 0.31/1.31 ( ( in @ Xx @ B )
% 0.31/1.31 <=> ? [Xy: $i] :
% 0.31/1.31 ( ( in @ Xy @ A )
% 0.31/1.31 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(foundationAx_type,type,
% 0.31/1.31 foundationAx: $o ).
% 0.31/1.31
% 0.31/1.31 thf(foundationAx,definition,
% 0.31/1.31 ( foundationAx
% 0.31/1.31 = ( ! [A: $i] :
% 0.31/1.31 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.31/1.31 => ? [B: $i] :
% 0.31/1.31 ( ( in @ B @ A )
% 0.31/1.31 & ~ ? [Xx: $i] :
% 0.31/1.31 ( ( in @ Xx @ B )
% 0.31/1.31 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(wellorderingAx_type,type,
% 0.31/1.31 wellorderingAx: $o ).
% 0.31/1.31
% 0.31/1.31 thf(wellorderingAx,definition,
% 0.31/1.31 ( wellorderingAx
% 0.31/1.31 = ( ! [A: $i] :
% 0.31/1.31 ? [B: $i] :
% 0.31/1.31 ( ! [C: $i] :
% 0.31/1.31 ( ( in @ C @ B )
% 0.31/1.31 => ! [Xx: $i] :
% 0.31/1.31 ( ( in @ Xx @ C )
% 0.31/1.31 => ( in @ Xx @ A ) ) )
% 0.31/1.31 & ! [Xx: $i,Xy: $i] :
% 0.31/1.31 ( ( ( in @ Xx @ A )
% 0.31/1.31 & ( in @ Xy @ A ) )
% 0.31/1.31 => ( ! [C: $i] :
% 0.31/1.31 ( ( in @ C @ B )
% 0.31/1.31 => ( ( in @ Xx @ C )
% 0.31/1.31 <=> ( in @ Xy @ C ) ) )
% 0.31/1.31 => ( Xx = Xy ) ) )
% 0.31/1.31 & ! [C: $i,D: $i] :
% 0.31/1.31 ( ( ( in @ C @ B )
% 0.31/1.31 & ( in @ D @ B ) )
% 0.31/1.31 => ( ! [Xx: $i] :
% 0.31/1.31 ( ( in @ Xx @ C )
% 0.31/1.31 => ( in @ Xx @ D ) )
% 0.31/1.31 | ! [Xx: $i] :
% 0.31/1.31 ( ( in @ Xx @ D )
% 0.31/1.31 => ( in @ Xx @ C ) ) ) )
% 0.31/1.31 & ! [C: $i] :
% 0.31/1.31 ( ( ! [Xx: $i] :
% 0.31/1.31 ( ( in @ Xx @ C )
% 0.31/1.31 => ( in @ Xx @ A ) )
% 0.31/1.31 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.31/1.31 => ? [D: $i,Xx: $i] :
% 0.31/1.31 ( ( in @ D @ B )
% 0.31/1.31 & ( in @ Xx @ C )
% 0.31/1.31 & ~ ? [Xy: $i] :
% 0.31/1.31 ( ( in @ Xy @ D )
% 0.31/1.31 & ( in @ Xy @ C ) )
% 0.31/1.31 & ! [E: $i] :
% 0.31/1.31 ( ( in @ E @ B )
% 0.31/1.31 => ( ! [Xy: $i] :
% 0.31/1.31 ( ( in @ Xy @ E )
% 0.31/1.31 => ( in @ Xy @ D ) )
% 0.31/1.31 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(descr_type,type,
% 0.31/1.31 descr: ( $i > $o ) > $i ).
% 0.31/1.31
% 0.31/1.31 thf(descrp_type,type,
% 0.31/1.31 descrp: $o ).
% 0.31/1.31
% 0.31/1.31 thf(descrp,definition,
% 0.31/1.31 ( descrp
% 0.31/1.31 = ( ! [Xphi: $i > $o] :
% 0.31/1.31 ( ( exu
% 0.31/1.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/1.31 => ( Xphi
% 0.31/1.31 @ ( descr
% 0.31/1.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(dsetconstr_type,type,
% 0.31/1.31 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.31/1.31
% 0.31/1.31 thf(dsetconstrI_type,type,
% 0.31/1.31 dsetconstrI: $o ).
% 0.31/1.31
% 0.31/1.31 thf(dsetconstrI,definition,
% 0.31/1.31 ( dsetconstrI
% 0.31/1.31 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/1.31 ( ( in @ Xx @ A )
% 0.31/1.31 => ( ( Xphi @ Xx )
% 0.31/1.31 => ( in @ Xx
% 0.31/1.31 @ ( dsetconstr @ A
% 0.31/1.31 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(dsetconstrEL_type,type,
% 0.31/1.31 dsetconstrEL: $o ).
% 0.31/1.31
% 0.31/1.31 thf(dsetconstrEL,definition,
% 0.31/1.31 ( dsetconstrEL
% 0.31/1.31 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/1.31 ( ( in @ Xx
% 0.31/1.31 @ ( dsetconstr @ A
% 0.31/1.31 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/1.31 => ( in @ Xx @ A ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(dsetconstrER_type,type,
% 0.31/1.31 dsetconstrER: $o ).
% 0.31/1.31
% 0.31/1.31 thf(dsetconstrER,definition,
% 0.31/1.31 ( dsetconstrER
% 0.31/1.31 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/1.31 ( ( in @ Xx
% 0.31/1.31 @ ( dsetconstr @ A
% 0.31/1.31 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/1.31 => ( Xphi @ Xx ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(exuE1,conjecture,
% 0.31/1.31 ( setextAx
% 0.31/1.31 => ( emptysetAx
% 0.31/1.31 => ( setadjoinAx
% 0.31/1.31 => ( powersetAx
% 0.31/1.31 => ( setunionAx
% 0.31/1.31 => ( omega0Ax
% 0.31/1.31 => ( omegaSAx
% 0.31/1.31 => ( omegaIndAx
% 0.31/1.31 => ( replAx
% 0.31/1.31 => ( foundationAx
% 0.31/1.31 => ( wellorderingAx
% 0.31/1.31 => ( descrp
% 0.31/1.31 => ( dsetconstrI
% 0.31/1.31 => ( dsetconstrEL
% 0.31/1.31 => ( dsetconstrER
% 0.31/1.31 => ! [Xphi: $i > $o] :
% 0.31/1.31 ( ( exu
% 0.31/1.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/1.31 => ? [Xx: $i] :
% 0.31/1.31 ( ( Xphi @ Xx )
% 0.31/1.31 & ! [Xy: $i] :
% 0.31/1.31 ( ( Xphi @ Xy )
% 0.31/1.31 => ( Xx = Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/1.31 ------------------------
% 0.31/1.33 % (1756)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1626 for (2999ds/18Mi)
% 0.31/1.33 % (1750)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1626 for (2999ds/2Mi)
% 0.31/1.33 % (1749)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_1626 for (2999ds/27Mi)
% 0.31/1.33 % (1750)Instruction limit reached!
% 0.31/1.33 % (1750)------------------------------
% 0.31/1.33 % (1750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.33 % (1750)Termination reason: Unknown
% 0.31/1.33 % (1750)Termination phase: shuffling
% 0.31/1.33
% 0.31/1.33 % (1750)Memory used [KB]: 1023
% 0.31/1.33 % (1750)Time elapsed: 0.002 s
% 0.31/1.33 % (1750)Instructions burned: 3 (million)
% 0.31/1.33 % (1750)------------------------------
% 0.31/1.33 % (1750)------------------------------
% 0.31/1.33 % (1756)Instruction limit reached!
% 0.31/1.33 % (1756)------------------------------
% 0.31/1.33 % (1756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.33 % (1756)Termination reason: Unknown
% 0.31/1.33 % (1756)Termination phase: Saturation
% 0.31/1.33
% 0.31/1.33 % (1756)Memory used [KB]: 5756
% 0.31/1.33 % (1756)Time elapsed: 0.007 s
% 0.31/1.33 % (1756)Instructions burned: 20 (million)
% 0.31/1.33 % (1756)------------------------------
% 0.31/1.33 % (1756)------------------------------
% 0.31/1.33 % (1747)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1626 for (2999ds/183Mi)
% 0.31/1.33 % (1748)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_1626 for (2999ds/4Mi)
% 0.31/1.33 % (1751)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_1626 for (2999ds/2Mi)
% 0.31/1.33 % (1755)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_1626 for (2999ds/275Mi)
% 0.31/1.33 % (1751)Instruction limit reached!
% 0.31/1.33 % (1751)------------------------------
% 0.31/1.33 % (1751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.33 % (1751)Termination reason: Unknown
% 0.31/1.33 % (1751)Termination phase: shuffling
% 0.31/1.33
% 0.31/1.33 % (1751)Memory used [KB]: 1023
% 0.31/1.33 % (1751)Time elapsed: 0.003 s
% 0.31/1.33 % (1751)Instructions burned: 2 (million)
% 0.31/1.33 % (1751)------------------------------
% 0.31/1.33 % (1751)------------------------------
% 0.31/1.34 % (1748)Instruction limit reached!
% 0.31/1.34 % (1748)------------------------------
% 0.31/1.34 % (1748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (1749)Instruction limit reached!
% 0.31/1.34 % (1749)------------------------------
% 0.31/1.34 % (1749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (1748)Termination reason: Unknown
% 0.31/1.34 % (1748)Termination phase: shuffling
% 0.31/1.34
% 0.31/1.34 % (1748)Memory used [KB]: 1023
% 0.31/1.34 % (1748)Time elapsed: 0.004 s
% 0.31/1.34 % (1748)Instructions burned: 4 (million)
% 0.31/1.34 % (1748)------------------------------
% 0.31/1.34 % (1748)------------------------------
% 0.31/1.34 % (1749)Termination reason: Unknown
% 0.31/1.34 % (1749)Termination phase: Saturation
% 0.31/1.34
% 0.31/1.34 % (1749)Memory used [KB]: 5756
% 0.31/1.34 % (1749)Time elapsed: 0.010 s
% 0.31/1.34 % (1749)Instructions burned: 29 (million)
% 0.31/1.34 % (1749)------------------------------
% 0.31/1.34 % (1749)------------------------------
% 0.31/1.34 % (1758)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1626 for (2999ds/3Mi)
% 0.31/1.34 % (1758)Instruction limit reached!
% 0.31/1.34 % (1758)------------------------------
% 0.31/1.34 % (1758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (1758)Termination reason: Unknown
% 0.31/1.34 % (1758)Termination phase: shuffling
% 0.31/1.34
% 0.31/1.34 % (1758)Memory used [KB]: 1023
% 0.31/1.34 % (1758)Time elapsed: 0.003 s
% 0.31/1.34 % (1758)Instructions burned: 4 (million)
% 0.31/1.34 % (1758)------------------------------
% 0.31/1.34 % (1758)------------------------------
% 0.31/1.34 % (1759)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_1626 for (2999ds/37Mi)
% 0.31/1.35 % (1761)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_1626 for (2999ds/3Mi)
% 0.31/1.35 % (1761)Instruction limit reached!
% 0.31/1.35 % (1761)------------------------------
% 0.31/1.35 % (1761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.35 % (1761)Termination reason: Unknown
% 0.31/1.35 % (1761)Termination phase: shuffling
% 0.31/1.35
% 0.31/1.35 % (1761)Memory used [KB]: 1023
% 0.31/1.35 % (1761)Time elapsed: 0.003 s
% 0.31/1.35 % (1761)Instructions burned: 4 (million)
% 0.31/1.35 % (1761)------------------------------
% 0.31/1.35 % (1761)------------------------------
% 0.31/1.35 % (1763)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_1626 for (2999ds/7Mi)
% 0.31/1.35 % (1759)Instruction limit reached!
% 0.31/1.35 % (1759)------------------------------
% 0.31/1.35 % (1759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.35 % (1759)Termination reason: Unknown
% 0.31/1.35 % (1759)Termination phase: Saturation
% 0.31/1.35
% 0.31/1.35 % (1759)Memory used [KB]: 5756
% 0.31/1.35 % (1759)Time elapsed: 0.011 s
% 0.31/1.35 % (1759)Instructions burned: 38 (million)
% 0.31/1.35 % (1759)------------------------------
% 0.31/1.35 % (1759)------------------------------
% 0.31/1.35 % (1763)Instruction limit reached!
% 0.31/1.35 % (1763)------------------------------
% 0.31/1.35 % (1763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.35 % (1763)Termination reason: Unknown
% 0.31/1.35 % (1763)Termination phase: SInE selection
% 0.31/1.35
% 0.31/1.35 % (1763)Memory used [KB]: 1023
% 0.31/1.35 % (1763)Time elapsed: 0.004 s
% 0.31/1.35 % (1763)Instructions burned: 7 (million)
% 0.31/1.35 % (1763)------------------------------
% 0.31/1.35 % (1763)------------------------------
% 0.31/1.35 % (1760)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_1626 for (2999ds/15Mi)
% 0.31/1.35 % (1762)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_1626 for (2999ds/1041Mi)
% 0.31/1.36 % (1747)First to succeed.
% 0.31/1.36 % (1764)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_1626 for (2999ds/16Mi)
% 0.31/1.36 % (1747)Refutation found. Thanks to Tanya!
% 0.31/1.36 % SZS status Theorem for DTF2THF_1626
% 0.31/1.36 % SZS output start Proof for DTF2THF_1626
% 0.31/1.36 thf(func_def_0, type, in: $i > $i > $o).
% 0.31/1.36 thf(func_def_1, type, exu: ($i > $o) > $o).
% 0.31/1.36 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 0.31/1.36 thf(func_def_8, type, powerset: $i > $i).
% 0.31/1.36 thf(func_def_10, type, setunion: $i > $i).
% 0.31/1.36 thf(func_def_19, type, descr: ($i > $o) > $i).
% 0.31/1.36 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 0.31/1.36 thf(func_def_41, type, sK0: $i > $o).
% 0.31/1.36 thf(func_def_42, type, sK1: $i > $i).
% 0.31/1.36 thf(func_def_44, type, sK3: $i > $i).
% 0.31/1.36 thf(func_def_45, type, sK4: $i > $i).
% 0.31/1.36 thf(func_def_46, type, sK5: $i > $i > $i).
% 0.31/1.36 thf(func_def_48, type, sK7: ($i > $o) > $i > $i).
% 0.31/1.36 thf(func_def_49, type, sK8: $i > ($i > $i > $o) > $i).
% 0.31/1.36 thf(func_def_50, type, sK9: $i > ($i > $i > $o) > $i).
% 0.31/1.36 thf(func_def_51, type, sK10: $i > $i > ($i > $i > $o) > $i).
% 0.31/1.36 thf(func_def_52, type, sK11: $i > $i > ($i > $i > $o) > $i).
% 0.31/1.36 thf(func_def_53, type, sK12: $i > $i > ($i > $i > $o) > $i).
% 0.31/1.36 thf(func_def_54, type, sK13: $i > $i > ($i > $i > $o) > $i).
% 0.31/1.36 thf(func_def_55, type, sK14: $i > $i > ($i > $i > $o) > $i).
% 0.31/1.36 thf(func_def_56, type, sK15: $i > $i > $i).
% 0.31/1.36 thf(func_def_57, type, sK16: $i > $i > $i).
% 0.31/1.36 thf(func_def_58, type, sK17: $i > $i).
% 0.31/1.36 thf(func_def_59, type, sK18: $i > $i > $i > $i).
% 0.31/1.36 thf(func_def_60, type, sK19: $i > $i > $i).
% 0.31/1.36 thf(func_def_61, type, sK20: $i > $i > $i).
% 0.31/1.36 thf(func_def_62, type, sK21: $i > $i > $i).
% 0.31/1.36 thf(func_def_63, type, sK22: $i > $i > $i).
% 0.31/1.36 thf(f405,plain,(
% 0.31/1.36 $false),
% 0.31/1.36 inference(subsumption_resolution,[status(thm)],[f403,f177])).
% 0.31/1.36 thf(f177,plain,(
% 0.31/1.36 ((sK0 @ sK6) = $true)),
% 0.31/1.36 inference(binary_proxy_clausification,[status(thm)],[f175])).
% 0.31/1.36 thf(f175,plain,(
% 0.31/1.36 ($true = ((sK0 @ sK6) & (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK6 = Y0))))))),
% 0.31/1.36 inference(beta_eta_normalization,[status(thm)],[f174])).
% 0.31/1.36 thf(f174,plain,(
% 0.31/1.36 ($true = ((^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))))) @ sK6))),
% 0.31/1.36 inference(sigma_clausification,[status(thm)],[f173])).
% 0.31/1.36 thf(f173,plain,(
% 0.31/1.36 ($true = (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1))))))))),
% 0.31/1.36 inference(beta_eta_normalization,[status(thm)],[f92])).
% 0.31/1.36 thf(f92,plain,(
% 0.31/1.36 ($true = ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))) @ (^[Y0 : $i]: (sK0 @ Y0))))),
% 0.31/1.36 inference(definition_unfolding,[status(thm)],[f64,f87])).
% 0.31/1.36 thf(f87,plain,(
% 0.31/1.36 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 0.31/1.36 inference(cnf_transformation,[status(thm)],[f27])).
% 0.31/1.36 thf(f27,plain,(
% 0.31/1.36 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 0.31/1.36 inference(fool_elimination,[status(thm)],[f26])).
% 0.31/1.36 thf(f26,plain,(
% 0.31/1.36 (exu = (^[X0 : $i > $o] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 0.31/1.36 inference(rectify,[status(thm)],[f1])).
% 0.31/1.36 thf(f1,axiom,(
% 0.31/1.36 (exu = (^[X0 : $i > $o] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 0.31/1.36 file('/export/starexec/sandbox/tmp/tmp.rmBBlAG7dF/DTF2THF_1626.p',exu)).
% 0.31/1.36 thf(f64,plain,(
% 0.31/1.36 ((exu @ (^[Y0 : $i]: (sK0 @ Y0))) = $true)),
% 0.31/1.36 inference(cnf_transformation,[status(thm)],[f57])).
% 0.31/1.36 thf(f57,plain,(
% 0.31/1.36 (omegaIndAx = $true) & (omegaSAx = $true) & (foundationAx = $true) & (omega0Ax = $true) & (setunionAx = $true) & (setextAx = $true) & (wellorderingAx = $true) & (dsetconstrEL = $true) & (powersetAx = $true) & (! [X1 : $i] : (($true != (sK0 @ X1)) | (($true = (sK0 @ (sK1 @ X1))) & ((sK1 @ X1) != X1))) & ((exu @ (^[Y0 : $i]: (sK0 @ Y0))) = $true)) & (dsetconstrER = $true) & (setadjoinAx = $true) & (descrp = $true) & (replAx = $true) & (dsetconstrI = $true) & (emptysetAx = $true)),
% 0.31/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f54,f56,f55])).
% 0.31/1.36 thf(f55,plain,(
% 0.31/1.36 ? [X0 : $i > $o] : (! [X1 : $i] : (((X0 @ X1) != $true) | ? [X2 : $i] : (((X0 @ X2) = $true) & (X1 != X2))) & ((exu @ (^[Y0 : $i]: (X0 @ Y0))) = $true)) => (! [X1 : $i] : (($true != (sK0 @ X1)) | ? [X2 : $i] : (($true = (sK0 @ X2)) & (X1 != X2))) & ((exu @ (^[Y0 : $i]: (sK0 @ Y0))) = $true))),
% 0.31/1.36 introduced(definition,[],[choice_axiom])).
% 0.31/1.36 thf(f56,plain,(
% 0.31/1.36 ! [X1 : $i] : (? [X2 : $i] : (($true = (sK0 @ X2)) & (X1 != X2)) => (($true = (sK0 @ (sK1 @ X1))) & ((sK1 @ X1) != X1)))),
% 0.31/1.36 introduced(definition,[],[choice_axiom])).
% 0.31/1.36 thf(f54,plain,(
% 0.31/1.36 (omegaIndAx = $true) & (omegaSAx = $true) & (foundationAx = $true) & (omega0Ax = $true) & (setunionAx = $true) & (setextAx = $true) & (wellorderingAx = $true) & (dsetconstrEL = $true) & (powersetAx = $true) & ? [X0 : $i > $o] : (! [X1 : $i] : (((X0 @ X1) != $true) | ? [X2 : $i] : (((X0 @ X2) = $true) & (X1 != X2))) & ((exu @ (^[Y0 : $i]: (X0 @ Y0))) = $true)) & (dsetconstrER = $true) & (setadjoinAx = $true) & (descrp = $true) & (replAx = $true) & (dsetconstrI = $true) & (emptysetAx = $true)),
% 0.31/1.36 inference(flattening,[status(thm)],[f53])).
% 0.31/1.36 thf(f53,plain,(
% 0.31/1.36 ((((((((((((((? [X0 : $i > $o] : (! [X1 : $i] : (((X0 @ X1) != $true) | ? [X2 : $i] : (((X0 @ X2) = $true) & (X1 != X2))) & ((exu @ (^[Y0 : $i]: (X0 @ Y0))) = $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)),
% 0.31/1.36 inference(ennf_transformation,[status(thm)],[f52])).
% 0.31/1.36 thf(f52,plain,(
% 0.31/1.36 ~((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) => ! [X0 : $i > $o] : (((exu @ (^[Y0 : $i]: (X0 @ Y0))) = $true) => ? [X1 : $i] : (((X0 @ X1) = $true) & ! [X2 : $i] : (((X0 @ X2) = $true) => (X1 = X2)))))))))))))))))))),
% 0.31/1.36 inference(rectify,[status(thm)],[f25])).
% 0.31/1.36 thf(f25,plain,(
% 0.31/1.36 ~((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) => ! [X0 : $i > $o] : (((exu @ (^[Y0 : $i]: (X0 @ Y0))) = $true) => ? [X2 : $i] : (((X0 @ X2) = $true) & ! [X3 : $i] : (($true = (X0 @ X3)) => (X2 = X3)))))))))))))))))))),
% 0.31/1.36 inference(fool_elimination,[status(thm)],[f24])).
% 0.31/1.36 thf(f24,plain,(
% 0.31/1.36 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X2 : $i] : ((X0 @ X2) & ! [X3 : $i] : ((X0 @ X3) => (X2 = X3)))))))))))))))))))),
% 0.31/1.36 inference(rectify,[status(thm)],[f18])).
% 0.31/1.36 thf(f18,negated_conjecture,(
% 0.31/1.36 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2)))))))))))))))))))),
% 0.31/1.36 inference(negated_conjecture,[status(cth)],[f17])).
% 0.31/1.36 thf(f17,conjecture,(
% 0.31/1.36 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))))))))))))))))))),
% 0.31/1.36 file('/export/starexec/sandbox/tmp/tmp.rmBBlAG7dF/DTF2THF_1626.p',exuE1)).
% 0.31/1.36 thf(f403,plain,(
% 0.31/1.36 ((sK0 @ sK6) != $true)),
% 0.31/1.36 inference(trivial_inequality_removal,[status(thm)],[f401])).
% 0.31/1.36 thf(f401,plain,(
% 0.31/1.36 (sK6 != sK6) | ((sK0 @ sK6) != $true)),
% 0.31/1.36 inference(superposition,[status(thm)],[f394,f399])).
% 0.31/1.36 thf(f399,plain,(
% 0.31/1.36 ( ! [X0 : $i] : ((sK6 = (sK1 @ X0)) | ($true != (sK0 @ X0))) )),
% 0.31/1.36 inference(trivial_inequality_removal,[status(thm)],[f397])).
% 0.31/1.36 thf(f397,plain,(
% 0.31/1.36 ( ! [X0 : $i] : (($true = $false) | (sK6 = (sK1 @ X0)) | ($true != (sK0 @ X0))) )),
% 0.31/1.36 inference(superposition,[status(thm)],[f181,f66])).
% 0.31/1.36 thf(f66,plain,(
% 0.31/1.36 ( ! [X1 : $i] : (($true = (sK0 @ (sK1 @ X1))) | ($true != (sK0 @ X1))) )),
% 0.31/1.36 inference(cnf_transformation,[status(thm)],[f57])).
% 0.31/1.36 thf(f181,plain,(
% 0.31/1.36 ( ! [X1 : $i] : (((sK0 @ X1) = $false) | (sK6 = X1)) )),
% 0.31/1.36 inference(equality_proxy_clausification,[status(thm)],[f180])).
% 0.31/1.36 thf(f180,plain,(
% 0.31/1.36 ( ! [X1 : $i] : (((sK0 @ X1) = $false) | ($true = (sK6 = X1))) )),
% 0.31/1.36 inference(binary_proxy_clausification,[status(thm)],[f179])).
% 0.31/1.36 thf(f179,plain,(
% 0.31/1.36 ( ! [X1 : $i] : (($true = ((sK0 @ X1) => (sK6 = X1)))) )),
% 0.31/1.36 inference(beta_eta_normalization,[status(thm)],[f178])).
% 0.31/1.36 thf(f178,plain,(
% 0.31/1.36 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK0 @ Y0) => (sK6 = Y0))) @ X1) = $true)) )),
% 0.31/1.36 inference(pi_clausification,[status(thm)],[f176])).
% 0.31/1.36 thf(f176,plain,(
% 0.31/1.36 ($true = (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK6 = Y0)))))),
% 0.31/1.36 inference(binary_proxy_clausification,[status(thm)],[f175])).
% 0.31/1.36 thf(f394,plain,(
% 0.31/1.36 (sK6 != (sK1 @ sK6))),
% 0.31/1.36 inference(trivial_inequality_removal,[status(thm)],[f392])).
% 0.31/1.36 thf(f392,plain,(
% 0.31/1.36 (sK6 != (sK1 @ sK6)) | ($true != $true)),
% 0.31/1.36 inference(superposition,[status(thm)],[f65,f177])).
% 0.31/1.36 thf(f65,plain,(
% 0.31/1.36 ( ! [X1 : $i] : (($true != (sK0 @ X1)) | ((sK1 @ X1) != X1)) )),
% 0.31/1.36 inference(cnf_transformation,[status(thm)],[f57])).
% 0.31/1.36 % SZS output end Proof for DTF2THF_1626
% 0.31/1.36 % (1747)------------------------------
% 0.31/1.36 % (1747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.36 % (1747)Termination reason: Refutation
% 0.31/1.36
% 0.31/1.36 % (1747)Memory used [KB]: 5884
% 0.31/1.36 % (1747)Time elapsed: 0.026 s
% 0.31/1.36 % (1747)Instructions burned: 41 (million)
% 0.31/1.36 % (1747)------------------------------
% 0.31/1.36 % (1747)------------------------------
% 0.31/1.36 % (1746)Success in time 0.03 s
%------------------------------------------------------------------------------