%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU557^2 : TPTP v9.2.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:15 AM UTC 2026
% Result : Theorem 1.48s 1.29s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of formulae : 70 ( 27 unt; 0 typ; 4 def)
% Number of atoms : 402 ( 121 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 387 ( 46 ~; 45 |; 33 &; 199 @)
% ( 7 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 16 usr; 13 con; 0-2 aty)
% ( 11 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 112 ( 68 ^; 36 !; 8 ?; 112 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
exu: ( $i > $o ) > $o ).
thf(func_def_2,type,
descr: ( $i > $o ) > $i ).
thf(func_def_16,type,
sK0: $i > $o ).
thf(func_def_17,type,
sK1: $i > $o ).
thf(func_def_22,type,
sK5: $i > ( $i > $o ) > $i ).
thf(func_def_23,type,
sK6: ( $i > $o ) > $i > $i ).
thf(func_def_25,type,
ph7:
!>[X0: $tType] : X0 ).
thf(f185,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f98,f107,f113,f142,f179,f182]) ).
thf(f182,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f181]) ).
thf(f181,plain,
( $false
| spl2_1
| ~ spl2_2 ),
inference(subsumption_resolution,[status(thm)],[f150,f92]) ).
thf(f92,plain,
( ( ( sK1 @ sK8 )
!= $true )
| spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f91]) ).
thf(f91,definition,
( spl2_1
<=> ( ( sK1 @ sK8 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f150,plain,
( ( ( sK1 @ sK8 )
= $true )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f144]) ).
thf(f144,plain,
( ( ( sK1 @ sK8 )
= $true )
| ( $false = $true )
| ~ spl2_2 ),
inference(superposition,[status(thm)],[f97,f42]) ).
thf(f42,plain,
! [X3: $i] :
( ( $false
= ( sK0 @ X3 ) )
| ( ( sK1 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X3: $i] :
( ( sK1 @ X3 )
= ( sK0 @ X3 ) ),
inference(equality_resolution,[status(thm)],[f20]) ).
thf(f20,plain,
! [X2: $i,X3: $i] :
( ( ( sK0 @ X3 )
= ( sK1 @ X2 ) )
| ( X2 != X3 ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( descrp = $true )
& ( exuEu = $true )
& ( ( descr
@ ^ [Y0: $i] : ( sK1 @ Y0 ) )
!= ( descr
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( sK0 @ X3 )
= ( sK1 @ X2 ) )
| ( X2 != X3 ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f17]) ).
thf(f17,plain,
( ? [X0: $i > $o,X1: $i > $o] :
( ( ( descr
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
!= ( descr
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( X1 @ X2 )
= ( X0 @ X3 ) )
| ( X2 != X3 ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
=> ( ( ( descr
@ ^ [Y0: $i] : ( sK1 @ Y0 ) )
!= ( descr
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
& ! [X3: $i,X2: $i] :
( ( ( sK0 @ X3 )
= ( sK1 @ X2 ) )
| ( X2 != X3 ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ( descrp = $true )
& ( exuEu = $true )
& ? [X0: $i > $o,X1: $i > $o] :
( ( ( descr
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
!= ( descr
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( X1 @ X2 )
= ( X0 @ X3 ) )
| ( X2 != X3 ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) ),
inference(flattening,[status(thm)],[f15]) ).
thf(f15,plain,
( ? [X0: $i > $o,X1: $i > $o] :
( ( ( descr
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
!= ( descr
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ! [X2: $i,X3: $i] :
( ( ( X1 @ X2 )
= ( X0 @ X3 ) )
| ( X2 != X3 ) ) )
& ( exuEu = $true )
& ( descrp = $true ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ( ( descrp = $true )
=> ( ( exuEu = $true )
=> ! [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X2 )
= ( X0 @ X3 ) ) )
=> ( ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
=> ( ( $true
= ( exu
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
=> ( ( descr
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= ( descr
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ( descrp
=> ( exuEu
=> ! [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X0 @ X3 )
<=> ( X1 @ X2 ) ) )
=> ( ( exu
@ ^ [X4: $i] : ( X0 @ X4 ) )
=> ( ( exu
@ ^ [X5: $i] : ( X1 @ X5 ) )
=> ( ( descr
@ ^ [X6: $i] : ( X1 @ X6 ) )
= ( descr
@ ^ [X7: $i] : ( X0 @ X7 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ( descrp
=> ( exuEu
=> ! [X0: $i > $o,X3: $i > $o] :
( ! [X2: $i,X1: $i] :
( ( X1 = X2 )
=> ( ( X0 @ X1 )
<=> ( X3 @ X2 ) ) )
=> ( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ( ( exu
@ ^ [X1: $i] : ( X3 @ X1 ) )
=> ( ( descr
@ ^ [X1: $i] : ( X3 @ X1 ) )
= ( descr
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( descrp
=> ( exuEu
=> ! [X0: $i > $o,X3: $i > $o] :
( ! [X2: $i,X1: $i] :
( ( X1 = X2 )
=> ( ( X0 @ X1 )
<=> ( X3 @ X2 ) ) )
=> ( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ( ( exu
@ ^ [X1: $i] : ( X3 @ X1 ) )
=> ( ( descr
@ ^ [X1: $i] : ( X3 @ X1 ) )
= ( descr
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XUDcyInC6O/DTF2THF_13331.p',descr__Cong) ).
thf(f97,plain,
( ( $true
= ( sK0 @ sK8 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f95]) ).
thf(f95,definition,
( spl2_2
<=> ( $true
= ( sK0 @ sK8 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f179,plain,
( ~ spl2_1
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f178]) ).
thf(f178,plain,
( $false
| ~ spl2_1
| ~ spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f175]) ).
thf(f175,plain,
( ( $false = $true )
| ~ spl2_1
| ~ spl2_4 ),
inference(superposition,[status(thm)],[f93,f106]) ).
thf(f106,plain,
( ( $false
= ( sK1 @ sK8 ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f104]) ).
thf(f104,definition,
( spl2_4
<=> ( $false
= ( sK1 @ sK8 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f93,plain,
( ( ( sK1 @ sK8 )
= $true )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f91]) ).
thf(f142,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f141]) ).
thf(f141,plain,
( $false
| ~ spl2_1
| spl2_2 ),
inference(subsumption_resolution,[status(thm)],[f140,f124]) ).
thf(f124,plain,
( ( $true
!= ( sK0 @ sK3 ) )
| ~ spl2_1
| spl2_2 ),
inference(superposition,[status(thm)],[f96,f120]) ).
thf(f120,plain,
( ( sK3 = sK8 )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f118]) ).
thf(f118,plain,
( ( $false = $true )
| ( sK3 = sK8 )
| ~ spl2_1 ),
inference(superposition,[status(thm)],[f93,f41]) ).
thf(f41,plain,
! [X1: $i] :
( ( $false
= ( sK1 @ X1 ) )
| ( sK3 = X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X1: $i] :
( ( ( sK3 = X1 )
= $true )
| ( $false
= ( sK1 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X1: $i] :
( ( ( sK1 @ X1 )
=> ( sK3 = X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f38]) ).
thf(f38,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK3 = Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK3 = Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( $true
= ( ( sK1 @ sK3 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK3 = Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ sK3 )
= $true ),
inference(sigma_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK1 @ Y0 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f19,f26]) ).
thf(f26,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,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/sandbox2/tmp/tmp.XUDcyInC6O/DTF2THF_13331.p',exu_def) ).
thf(f19,plain,
( $true
= ( exu
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f96,plain,
( ( $true
!= ( sK0 @ sK8 ) )
| spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f95]) ).
thf(f140,plain,
( $true
= ( sK0 @ sK3 ) ),
inference(superposition,[status(thm)],[f49,f138]) ).
thf(f138,plain,
sK3 = sK4,
inference(trivial_inequality_removal,[status(thm)],[f135]) ).
thf(f135,plain,
( ( $false = $true )
| ( sK3 = sK4 ) ),
inference(superposition,[status(thm)],[f134,f41]) ).
thf(f134,plain,
( $true
= ( sK1 @ sK4 ) ),
inference(trivial_inequality_removal,[status(thm)],[f129]) ).
thf(f129,plain,
( ( $true
= ( sK1 @ sK4 ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f42,f49]) ).
thf(f49,plain,
( ( sK0 @ sK4 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( ( ( sK0 @ sK4 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK4 = Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,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)],[f21,f26]) ).
thf(f21,plain,
( $true
= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f113,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f112]) ).
thf(f112,plain,
( $false
| ~ spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f109]) ).
thf(f109,plain,
( ( $false = $true )
| ~ spl2_2
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f97,f102]) ).
thf(f102,plain,
( ( $false
= ( sK0 @ sK8 ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f100]) ).
thf(f100,definition,
( spl2_3
<=> ( $false
= ( sK0 @ sK8 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f107,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[status(thm)],[f89,f104,f100]) ).
thf(f89,plain,
( ( $false
= ( sK0 @ sK8 ) )
| ( $false
= ( sK1 @ sK8 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
( ( sK1 @ sK8 )
!= ( sK0 @ sK8 ) ),
inference(negative_extensionality,[status(thm)],[f86]) ).
thf(f86,plain,
sK0 != sK1,
inference(equality_resolution,[status(thm)],[f44]) ).
thf(f44,plain,
( ( descr @ sK0 )
!= ( descr @ sK1 ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
( ( descr
@ ^ [Y0: $i] : ( sK1 @ Y0 ) )
!= ( descr
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f98,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f88,f95,f91]) ).
thf(f88,plain,
( ( $true
= ( sK0 @ sK8 ) )
| ( ( sK1 @ sK8 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU557^2 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n001.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:27:20 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : SEU557^2 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.19/0.47 % Domain : Set Theory
% 0.19/0.47 % Problem : A simple congruence property of descr
% 0.19/0.47 % Version : Especial > Reduced > Especial.
% 0.19/0.47 % English : (forall phi:i>o.forall psi:i>o.(forall x:i.forall y:i.x = y ->
% 0.19/0.47 % (phi x <-> psi y)) -> exu (lambda x:i.phi x) ->
% 0.19/0.47 % exu (lambda x:i.psi x) -> descr (lambda x:i.phi x) =
% 0.19/0.47 % descr (lambda x:i.psi x))
% 0.19/0.47
% 0.19/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.47 % Source : [Bro08]
% 0.19/0.47 % Names : ZFC059l [Bro08]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.80 v5.2.0
% 0.19/0.47 % Syntax : Number of formulae : 8 ( 3 unt; 4 typ; 3 def)
% 0.19/0.47 % Number of atoms : 16 ( 7 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 6 ( 4 avg)
% 0.19/0.47 % Number of connectives : 34 ( 0 ~; 0 |; 1 &; 21 @)
% 0.19/0.47 % ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 11 ( 4 avg)
% 0.19/0.47 % Number of types : 2 ( 0 usr)
% 0.19/0.47 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.19/0.47 % Number of variables : 18 ( 8 ^; 9 !; 1 ?; 18 :)
% 0.19/0.47 % SPC : TH0_THM_EQU_NAR
% 0.19/0.47
% 0.19/0.47 % Comments : http://mathgate.info/detsetitem.php?id=43
% 0.19/0.47 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 thf(exu_type,type,
% 0.19/0.47 exu: ( $i > $o ) > $o ).
% 0.19/0.47
% 0.19/0.47 thf(exuEu_type,type,
% 0.19/0.47 exuEu: $o ).
% 0.19/0.47
% 0.19/0.47 thf(descr_type,type,
% 0.19/0.47 descr: ( $i > $o ) > $i ).
% 0.19/0.47
% 0.19/0.47 thf(descrp_type,type,
% 0.19/0.47 descrp: $o ).
% 0.19/0.47
% 0.19/0.47 thf(exu_def,definition,
% 0.19/0.47 ( exu
% 0.19/0.47 = ( ^ [Xphi: $i > $o] :
% 0.19/0.47 ? [Xx: $i] :
% 0.19/0.47 ( ( Xphi @ Xx )
% 0.19/0.47 & ! [Xy: $i] :
% 0.19/0.47 ( ( Xphi @ Xy )
% 0.19/0.47 => ( Xx = Xy ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(exuEu_def,definition,
% 0.19/0.47 ( exuEu
% 0.19/0.47 = ( ! [Xphi: $i > $o] :
% 0.19/0.47 ( ( exu
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.47 => ! [Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( Xphi @ Xx )
% 0.19/0.47 => ( ( Xphi @ Xy )
% 0.19/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(descrp_def,definition,
% 0.19/0.47 ( descrp
% 0.19/0.47 = ( ! [Xphi: $i > $o] :
% 0.19/0.47 ( ( exu
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.47 => ( Xphi
% 0.19/0.47 @ ( descr
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 thf(descr__Cong,conjecture,
% 0.19/0.47 ( descrp
% 0.19/0.47 => ( exuEu
% 0.19/0.47 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.19/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.19/0.47 ( ( Xx = Xy )
% 0.19/0.47 => ( ( Xphi @ Xx )
% 0.19/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.19/0.47 => ( ( exu
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.47 => ( ( exu
% 0.19/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.19/0.47 => ( ( descr
% 0.19/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.47 = ( descr
% 0.19/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 1.48/1.25 ---- Embedded in THF ---
% 1.48/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.25 %%% Generated on Tue Feb 24 12:27:21 EST 2026
% 1.48/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.25 %%% Logic specification used:
% 1.48/1.25 %%% thf(spec, logic, $$dhol).
% 1.48/1.25
% 1.48/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.XUDcyInC6O/DTF2DTF13331.p
% See solution above
% 1.48/1.25 ------------------------
% 1.48/1.26 ---- Cleaned THF ---
% 1.48/1.27 thf(exu_type,type,
% 1.48/1.27 exu: ( $i > $o ) > $o ).
% 1.48/1.27
% 1.48/1.27 thf(exuEu_type,type,
% 1.48/1.27 exuEu: $o ).
% 1.48/1.27
% 1.48/1.27 thf(descr_type,type,
% 1.48/1.27 descr: ( $i > $o ) > $i ).
% 1.48/1.27
% 1.48/1.27 thf(descrp_type,type,
% 1.48/1.27 descrp: $o ).
% 1.48/1.27
% 1.48/1.27 thf(exu_def,definition,
% 1.48/1.27 ( exu
% 1.48/1.27 = ( ^ [Xphi: $i > $o] :
% 1.48/1.27 ? [Xx: $i] :
% 1.48/1.27 ( ( Xphi @ Xx )
% 1.48/1.27 & ! [Xy: $i] :
% 1.48/1.27 ( ( Xphi @ Xy )
% 1.48/1.27 => ( Xx = Xy ) ) ) ) ) ).
% 1.48/1.27
% 1.48/1.27 thf(exuEu_def,definition,
% 1.48/1.27 ( exuEu
% 1.48/1.27 = ( ! [Xphi: $i > $o] :
% 1.48/1.27 ( ( exu
% 1.48/1.27 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.48/1.27 => ! [Xx: $i,Xy: $i] :
% 1.48/1.27 ( ( Xphi @ Xx )
% 1.48/1.27 => ( ( Xphi @ Xy )
% 1.48/1.27 => ( Xx = Xy ) ) ) ) ) ) ).
% 1.48/1.27
% 1.48/1.27 thf(descrp_def,definition,
% 1.48/1.27 ( descrp
% 1.48/1.27 = ( ! [Xphi: $i > $o] :
% 1.48/1.27 ( ( exu
% 1.48/1.27 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.48/1.27 => ( Xphi
% 1.48/1.27 @ ( descr
% 1.48/1.27 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 1.48/1.27
% 1.48/1.27 thf(descr__Cong,conjecture,
% 1.48/1.27 ( descrp
% 1.48/1.27 => ( exuEu
% 1.48/1.27 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 1.48/1.27 ( ! [Xx: $i,Xy: $i] :
% 1.48/1.27 ( ( Xx = Xy )
% 1.48/1.27 => ( ( Xphi @ Xx )
% 1.48/1.27 <=> ( Xpsi @ Xy ) ) )
% 1.48/1.27 => ( ( exu
% 1.48/1.27 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.48/1.27 => ( ( exu
% 1.48/1.27 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 1.48/1.27 => ( ( descr
% 1.48/1.27 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.48/1.27 = ( descr
% 1.48/1.27 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 1.48/1.27 ------------------------
% 1.48/1.28 % (13475)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_13331 for (2999ds/2Mi)
% 1.48/1.28 % (13474)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13331 for (2999ds/2Mi)
% 1.48/1.28 % (13471)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13331 for (2999ds/183Mi)
% 1.48/1.28 % (13474)Instruction limit reached!
% 1.48/1.28 % (13474)------------------------------
% 1.48/1.28 % (13474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (13474)Termination reason: Unknown
% 1.48/1.28 % (13474)Termination phase: Saturation
% 1.48/1.28
% 1.48/1.28 % (13474)Memory used [KB]: 5500
% 1.48/1.28 % (13474)Time elapsed: 0.002 s
% 1.48/1.28 % (13474)Instructions burned: 3 (million)
% 1.48/1.28 % (13474)------------------------------
% 1.48/1.28 % (13474)------------------------------
% 1.48/1.28 % (13477)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13331 for (2999ds/18Mi)
% 1.48/1.28 % (13475)Instruction limit reached!
% 1.48/1.28 % (13475)------------------------------
% 1.48/1.28 % (13475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (13475)Termination reason: Unknown
% 1.48/1.28 % (13475)Termination phase: shuffling
% 1.48/1.28
% 1.48/1.28 % (13475)Memory used [KB]: 895
% 1.48/1.28 % (13475)Time elapsed: 0.003 s
% 1.48/1.28 % (13475)Instructions burned: 2 (million)
% 1.48/1.28 % (13475)------------------------------
% 1.48/1.28 % (13475)------------------------------
% 1.48/1.28 % (13471)First to succeed.
% 1.48/1.29 % (13471)Refutation found. Thanks to Tanya!
% 1.48/1.29 % SZS status Theorem for DTF2THF_13331
% 1.48/1.29 % SZS output start Proof for DTF2THF_13331
% 1.48/1.29 thf(func_def_0, type, exu: ($i > $o) > $o).
% 1.48/1.29 thf(func_def_2, type, descr: ($i > $o) > $i).
% 1.48/1.29 thf(func_def_16, type, sK0: $i > $o).
% 1.48/1.29 thf(func_def_17, type, sK1: $i > $o).
% 1.48/1.29 thf(func_def_22, type, sK5: $i > ($i > $o) > $i).
% 1.48/1.29 thf(func_def_23, type, sK6: ($i > $o) > $i > $i).
% 1.48/1.29 thf(func_def_25, type, ph7: !>[X0: $tType]:(X0)).
% 1.48/1.29 thf(f185,plain,(
% 1.48/1.29 $false),
% 1.48/1.29 inference(avatar_sat_refutation,[status(thm)],[f98,f107,f113,f142,f179,f182])).
% 1.48/1.29 thf(f182,plain,(
% 1.48/1.29 spl2_1 | ~spl2_2),
% 1.48/1.29 inference(avatar_contradiction_clause,[status(thm)],[f181])).
% 1.48/1.29 thf(f181,plain,(
% 1.48/1.29 $false | (spl2_1 | ~spl2_2)),
% 1.48/1.29 inference(subsumption_resolution,[status(thm)],[f150,f92])).
% 1.48/1.29 thf(f92,plain,(
% 1.48/1.29 ((sK1 @ sK8) != $true) | spl2_1),
% 1.48/1.29 inference(avatar_component_clause,[status(thm)],[f91])).
% 1.48/1.29 thf(f91,definition,(
% 1.48/1.29 spl2_1 <=> ((sK1 @ sK8) = $true)),
% 1.48/1.29 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.48/1.29 thf(f150,plain,(
% 1.48/1.29 ((sK1 @ sK8) = $true) | ~spl2_2),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f144])).
% 1.48/1.29 thf(f144,plain,(
% 1.48/1.29 ((sK1 @ sK8) = $true) | ($false = $true) | ~spl2_2),
% 1.48/1.29 inference(superposition,[status(thm)],[f97,f42])).
% 1.48/1.29 thf(f42,plain,(
% 1.48/1.29 ( ! [X3 : $i] : (($false = (sK0 @ X3)) | ((sK1 @ X3) = $true)) )),
% 1.48/1.29 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.48/1.29 thf(f32,plain,(
% 1.48/1.29 ( ! [X3 : $i] : (((sK1 @ X3) = (sK0 @ X3))) )),
% 1.48/1.29 inference(equality_resolution,[status(thm)],[f20])).
% 1.48/1.29 thf(f20,plain,(
% 1.48/1.29 ( ! [X2 : $i,X3 : $i] : (((sK0 @ X3) = (sK1 @ X2)) | (X2 != X3)) )),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f18])).
% 1.48/1.29 thf(f18,plain,(
% 1.48/1.29 (descrp = $true) & (exuEu = $true) & (((descr @ (^[Y0 : $i]: (sK1 @ Y0))) != (descr @ (^[Y0 : $i]: (sK0 @ Y0)))) & ($true = (exu @ (^[Y0 : $i]: (sK0 @ Y0)))) & ! [X2 : $i,X3 : $i] : (((sK0 @ X3) = (sK1 @ X2)) | (X2 != X3)) & ($true = (exu @ (^[Y0 : $i]: (sK1 @ Y0)))))),
% 1.48/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f17])).
% 1.48/1.29 thf(f17,plain,(
% 1.48/1.29 ? [X0 : $i > $o,X1 : $i > $o] : (((descr @ (^[Y0 : $i]: (X0 @ Y0))) != (descr @ (^[Y0 : $i]: (X1 @ Y0)))) & ($true = (exu @ (^[Y0 : $i]: (X0 @ Y0)))) & ! [X2 : $i,X3 : $i] : (((X1 @ X2) = (X0 @ X3)) | (X2 != X3)) & ($true = (exu @ (^[Y0 : $i]: (X1 @ Y0))))) => (((descr @ (^[Y0 : $i]: (sK1 @ Y0))) != (descr @ (^[Y0 : $i]: (sK0 @ Y0)))) & ($true = (exu @ (^[Y0 : $i]: (sK0 @ Y0)))) & ! [X3 : $i,X2 : $i] : (((sK0 @ X3) = (sK1 @ X2)) | (X2 != X3)) & ($true = (exu @ (^[Y0 : $i]: (sK1 @ Y0)))))),
% 1.48/1.29 introduced(definition,[],[choice_axiom])).
% 1.48/1.29 thf(f16,plain,(
% 1.48/1.29 (descrp = $true) & (exuEu = $true) & ? [X0 : $i > $o,X1 : $i > $o] : (((descr @ (^[Y0 : $i]: (X0 @ Y0))) != (descr @ (^[Y0 : $i]: (X1 @ Y0)))) & ($true = (exu @ (^[Y0 : $i]: (X0 @ Y0)))) & ! [X2 : $i,X3 : $i] : (((X1 @ X2) = (X0 @ X3)) | (X2 != X3)) & ($true = (exu @ (^[Y0 : $i]: (X1 @ Y0)))))),
% 1.48/1.29 inference(flattening,[status(thm)],[f15])).
% 1.48/1.29 thf(f15,plain,(
% 1.48/1.29 (? [X0 : $i > $o,X1 : $i > $o] : (((((descr @ (^[Y0 : $i]: (X0 @ Y0))) != (descr @ (^[Y0 : $i]: (X1 @ Y0)))) & ($true = (exu @ (^[Y0 : $i]: (X1 @ Y0))))) & ($true = (exu @ (^[Y0 : $i]: (X0 @ Y0))))) & ! [X2 : $i,X3 : $i] : (((X1 @ X2) = (X0 @ X3)) | (X2 != X3))) & (exuEu = $true)) & (descrp = $true)),
% 1.48/1.29 inference(ennf_transformation,[status(thm)],[f12])).
% 1.48/1.29 thf(f12,plain,(
% 1.48/1.29 ~((descrp = $true) => ((exuEu = $true) => ! [X0 : $i > $o,X1 : $i > $o] : (! [X2 : $i,X3 : $i] : ((X2 = X3) => ((X1 @ X2) = (X0 @ X3))) => (($true = (exu @ (^[Y0 : $i]: (X0 @ Y0)))) => (($true = (exu @ (^[Y0 : $i]: (X1 @ Y0)))) => ((descr @ (^[Y0 : $i]: (X0 @ Y0))) = (descr @ (^[Y0 : $i]: (X1 @ Y0)))))))))),
% 1.48/1.29 inference(fool_elimination,[status(thm)],[f11])).
% 1.48/1.29 thf(f11,plain,(
% 1.48/1.29 ~(descrp => (exuEu => ! [X0 : $i > $o,X1 : $i > $o] : (! [X2 : $i,X3 : $i] : ((X2 = X3) => ((X0 @ X3) <=> (X1 @ X2))) => ((exu @ (^[X4 : $i] : (X0 @ X4))) => ((exu @ (^[X5 : $i] : (X1 @ X5))) => ((descr @ (^[X6 : $i] : (X1 @ X6))) = (descr @ (^[X7 : $i] : (X0 @ X7)))))))))),
% 1.48/1.29 inference(rectify,[status(thm)],[f5])).
% 1.48/1.29 thf(f5,negated_conjecture,(
% 1.48/1.29 ~(descrp => (exuEu => ! [X0 : $i > $o,X3 : $i > $o] : (! [X2 : $i,X1 : $i] : ((X1 = X2) => ((X0 @ X1) <=> (X3 @ X2))) => ((exu @ (^[X1 : $i] : (X0 @ X1))) => ((exu @ (^[X1 : $i] : (X3 @ X1))) => ((descr @ (^[X1 : $i] : (X3 @ X1))) = (descr @ (^[X1 : $i] : (X0 @ X1)))))))))),
% 1.48/1.29 inference(negated_conjecture,[status(cth)],[f4])).
% 1.48/1.29 thf(f4,conjecture,(
% 1.48/1.29 descrp => (exuEu => ! [X0 : $i > $o,X3 : $i > $o] : (! [X2 : $i,X1 : $i] : ((X1 = X2) => ((X0 @ X1) <=> (X3 @ X2))) => ((exu @ (^[X1 : $i] : (X0 @ X1))) => ((exu @ (^[X1 : $i] : (X3 @ X1))) => ((descr @ (^[X1 : $i] : (X3 @ X1))) = (descr @ (^[X1 : $i] : (X0 @ X1))))))))),
% 1.48/1.29 file('/export/starexec/sandbox2/tmp/tmp.XUDcyInC6O/DTF2THF_13331.p',descr__Cong)).
% 1.48/1.29 thf(f97,plain,(
% 1.48/1.29 ($true = (sK0 @ sK8)) | ~spl2_2),
% 1.48/1.29 inference(avatar_component_clause,[status(thm)],[f95])).
% 1.48/1.29 thf(f95,definition,(
% 1.48/1.29 spl2_2 <=> ($true = (sK0 @ sK8))),
% 1.48/1.29 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.48/1.29 thf(f179,plain,(
% 1.48/1.29 ~spl2_1 | ~spl2_4),
% 1.48/1.29 inference(avatar_contradiction_clause,[status(thm)],[f178])).
% 1.48/1.29 thf(f178,plain,(
% 1.48/1.29 $false | (~spl2_1 | ~spl2_4)),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f175])).
% 1.48/1.29 thf(f175,plain,(
% 1.48/1.29 ($false = $true) | (~spl2_1 | ~spl2_4)),
% 1.48/1.29 inference(superposition,[status(thm)],[f93,f106])).
% 1.48/1.29 thf(f106,plain,(
% 1.48/1.29 ($false = (sK1 @ sK8)) | ~spl2_4),
% 1.48/1.29 inference(avatar_component_clause,[status(thm)],[f104])).
% 1.48/1.29 thf(f104,definition,(
% 1.48/1.29 spl2_4 <=> ($false = (sK1 @ sK8))),
% 1.48/1.29 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.48/1.29 thf(f93,plain,(
% 1.48/1.29 ((sK1 @ sK8) = $true) | ~spl2_1),
% 1.48/1.29 inference(avatar_component_clause,[status(thm)],[f91])).
% 1.48/1.29 thf(f142,plain,(
% 1.48/1.29 ~spl2_1 | spl2_2),
% 1.48/1.29 inference(avatar_contradiction_clause,[status(thm)],[f141])).
% 1.48/1.29 thf(f141,plain,(
% 1.48/1.29 $false | (~spl2_1 | spl2_2)),
% 1.48/1.29 inference(subsumption_resolution,[status(thm)],[f140,f124])).
% 1.48/1.29 thf(f124,plain,(
% 1.48/1.29 ($true != (sK0 @ sK3)) | (~spl2_1 | spl2_2)),
% 1.48/1.29 inference(superposition,[status(thm)],[f96,f120])).
% 1.48/1.29 thf(f120,plain,(
% 1.48/1.29 (sK3 = sK8) | ~spl2_1),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f118])).
% 1.48/1.29 thf(f118,plain,(
% 1.48/1.29 ($false = $true) | (sK3 = sK8) | ~spl2_1),
% 1.48/1.29 inference(superposition,[status(thm)],[f93,f41])).
% 1.48/1.29 thf(f41,plain,(
% 1.48/1.29 ( ! [X1 : $i] : (($false = (sK1 @ X1)) | (sK3 = X1)) )),
% 1.48/1.29 inference(equality_proxy_clausification,[status(thm)],[f40])).
% 1.48/1.29 thf(f40,plain,(
% 1.48/1.29 ( ! [X1 : $i] : (((sK3 = X1) = $true) | ($false = (sK1 @ X1))) )),
% 1.48/1.29 inference(binary_proxy_clausification,[status(thm)],[f39])).
% 1.48/1.29 thf(f39,plain,(
% 1.48/1.29 ( ! [X1 : $i] : ((((sK1 @ X1) => (sK3 = X1)) = $true)) )),
% 1.48/1.29 inference(beta_eta_normalization,[status(thm)],[f38])).
% 1.48/1.29 thf(f38,plain,(
% 1.48/1.29 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK1 @ Y0) => (sK3 = Y0))) @ X1) = $true)) )),
% 1.48/1.29 inference(pi_clausification,[status(thm)],[f36])).
% 1.48/1.29 thf(f36,plain,(
% 1.48/1.29 ($true = (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK3 = Y0)))))),
% 1.48/1.29 inference(binary_proxy_clausification,[status(thm)],[f35])).
% 1.48/1.29 thf(f35,plain,(
% 1.48/1.29 ($true = ((sK1 @ sK3) & (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK3 = Y0))))))),
% 1.48/1.29 inference(beta_eta_normalization,[status(thm)],[f34])).
% 1.48/1.29 thf(f34,plain,(
% 1.48/1.29 (((^[Y0 : $i]: ((sK1 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) => (Y0 = Y1)))))) @ sK3) = $true)),
% 1.48/1.29 inference(sigma_clausification,[status(thm)],[f33])).
% 1.48/1.29 thf(f33,plain,(
% 1.48/1.29 ((?? @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) => (Y0 = Y1))))))) = $true)),
% 1.48/1.29 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.48/1.29 thf(f29,plain,(
% 1.48/1.29 (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))) @ (^[Y0 : $i]: (sK1 @ Y0))) = $true)),
% 1.48/1.29 inference(definition_unfolding,[status(thm)],[f19,f26])).
% 1.48/1.29 thf(f26,plain,(
% 1.48/1.29 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f10])).
% 1.48/1.29 thf(f10,plain,(
% 1.48/1.29 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 1.48/1.29 inference(fool_elimination,[status(thm)],[f9])).
% 1.48/1.29 thf(f9,plain,(
% 1.48/1.29 (exu = (^[X0 : $i > $o] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 1.48/1.29 inference(rectify,[status(thm)],[f1])).
% 1.48/1.29 thf(f1,axiom,(
% 1.48/1.29 (exu = (^[X0 : $i > $o] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 1.48/1.29 file('/export/starexec/sandbox2/tmp/tmp.XUDcyInC6O/DTF2THF_13331.p',exu_def)).
% 1.48/1.29 thf(f19,plain,(
% 1.48/1.29 ($true = (exu @ (^[Y0 : $i]: (sK1 @ Y0))))),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f18])).
% 1.48/1.29 thf(f96,plain,(
% 1.48/1.29 ($true != (sK0 @ sK8)) | spl2_2),
% 1.48/1.29 inference(avatar_component_clause,[status(thm)],[f95])).
% 1.48/1.29 thf(f140,plain,(
% 1.48/1.29 ($true = (sK0 @ sK3))),
% 1.48/1.29 inference(superposition,[status(thm)],[f49,f138])).
% 1.48/1.29 thf(f138,plain,(
% 1.48/1.29 (sK3 = sK4)),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f135])).
% 1.48/1.29 thf(f135,plain,(
% 1.48/1.29 ($false = $true) | (sK3 = sK4)),
% 1.48/1.29 inference(superposition,[status(thm)],[f134,f41])).
% 1.48/1.29 thf(f134,plain,(
% 1.48/1.29 ($true = (sK1 @ sK4))),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f129])).
% 1.48/1.29 thf(f129,plain,(
% 1.48/1.29 ($true = (sK1 @ sK4)) | ($false = $true)),
% 1.48/1.29 inference(superposition,[status(thm)],[f42,f49])).
% 1.48/1.29 thf(f49,plain,(
% 1.48/1.29 ((sK0 @ sK4) = $true)),
% 1.48/1.29 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.48/1.29 thf(f47,plain,(
% 1.48/1.29 (((sK0 @ sK4) & (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK4 = Y0))))) = $true)),
% 1.48/1.29 inference(beta_eta_normalization,[status(thm)],[f46])).
% 1.48/1.29 thf(f46,plain,(
% 1.48/1.29 ($true = ((^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))))) @ sK4))),
% 1.48/1.29 inference(sigma_clausification,[status(thm)],[f45])).
% 1.48/1.29 thf(f45,plain,(
% 1.48/1.29 ((?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1))))))) = $true)),
% 1.48/1.29 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.48/1.29 thf(f28,plain,(
% 1.48/1.29 ($true = ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))) @ (^[Y0 : $i]: (sK0 @ Y0))))),
% 1.48/1.29 inference(definition_unfolding,[status(thm)],[f21,f26])).
% 1.48/1.29 thf(f21,plain,(
% 1.48/1.29 ($true = (exu @ (^[Y0 : $i]: (sK0 @ Y0))))),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f18])).
% 1.48/1.29 thf(f113,plain,(
% 1.48/1.29 ~spl2_2 | ~spl2_3),
% 1.48/1.29 inference(avatar_contradiction_clause,[status(thm)],[f112])).
% 1.48/1.29 thf(f112,plain,(
% 1.48/1.29 $false | (~spl2_2 | ~spl2_3)),
% 1.48/1.29 inference(trivial_inequality_removal,[status(thm)],[f109])).
% 1.48/1.29 thf(f109,plain,(
% 1.48/1.29 ($false = $true) | (~spl2_2 | ~spl2_3)),
% 1.48/1.29 inference(superposition,[status(thm)],[f97,f102])).
% 1.48/1.29 thf(f102,plain,(
% 1.48/1.29 ($false = (sK0 @ sK8)) | ~spl2_3),
% 1.48/1.29 inference(avatar_component_clause,[status(thm)],[f100])).
% 1.48/1.29 thf(f100,definition,(
% 1.48/1.29 spl2_3 <=> ($false = (sK0 @ sK8))),
% 1.48/1.29 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.48/1.29 thf(f107,plain,(
% 1.48/1.29 spl2_3 | spl2_4),
% 1.48/1.29 inference(avatar_split_clause,[status(thm)],[f89,f104,f100])).
% 1.48/1.29 thf(f89,plain,(
% 1.48/1.29 ($false = (sK0 @ sK8)) | ($false = (sK1 @ sK8))),
% 1.48/1.29 inference(binary_proxy_clausification,[status(thm)],[f87])).
% 1.48/1.29 thf(f87,plain,(
% 1.48/1.29 ((sK1 @ sK8) != (sK0 @ sK8))),
% 1.48/1.29 inference(negative_extensionality,[status(thm)],[f86])).
% 1.48/1.29 thf(f86,plain,(
% 1.48/1.29 (sK0 != sK1)),
% 1.48/1.29 inference(equality_resolution,[status(thm)],[f44])).
% 1.48/1.29 thf(f44,plain,(
% 1.48/1.29 ((descr @ sK0) != (descr @ sK1))),
% 1.48/1.29 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.48/1.29 thf(f22,plain,(
% 1.48/1.29 ((descr @ (^[Y0 : $i]: (sK1 @ Y0))) != (descr @ (^[Y0 : $i]: (sK0 @ Y0))))),
% 1.48/1.29 inference(cnf_transformation,[status(thm)],[f18])).
% 1.48/1.29 thf(f98,plain,(
% 1.48/1.29 spl2_1 | spl2_2),
% 1.48/1.29 inference(avatar_split_clause,[status(thm)],[f88,f95,f91])).
% 1.48/1.29 thf(f88,plain,(
% 1.48/1.29 ($true = (sK0 @ sK8)) | ((sK1 @ sK8) = $true)),
% 1.48/1.29 inference(binary_proxy_clausification,[status(thm)],[f87])).
% 1.48/1.29 % SZS output end Proof for DTF2THF_13331
% 1.48/1.29 % (13471)------------------------------
% 1.48/1.29 % (13471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (13471)Termination reason: Refutation
% 1.48/1.29
% 1.48/1.29 % (13471)Memory used [KB]: 5628
% 1.48/1.29 % (13471)Time elapsed: 0.007 s
% 1.48/1.29 % (13471)Instructions burned: 12 (million)
% 1.48/1.29 % (13471)------------------------------
% 1.48/1.29 % (13471)------------------------------
% 1.48/1.29 % (13470)Success in time 0.007 s
%------------------------------------------------------------------------------