%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO539^1 : TPTP v9.2.1. Released v5.2.0.
% 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 09:54:30 AM UTC 2026
% Result : Theorem 1.54s 1.26s
% Output : Refutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 60 ( 15 unt; 0 typ; 5 def)
% Number of atoms : 675 ( 254 equ; 0 cnn)
% Maximal formula atoms : 4 ( 11 avg)
% Number of connectives : 487 ( 114 ~; 125 |; 137 &; 105 @)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 10 con; 0-3 aty)
% Number of variables : 112 ( 69 ^; 37 !; 6 ?; 112 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
eps: ( $i > $o ) > $i ).
thf(func_def_2,type,
if: $o > $i > $i > $i ).
thf(func_def_3,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_19,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f205,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f100,f101,f107,f109,f160,f204]) ).
thf(f204,plain,
~ spl3_5,
inference(avatar_contradiction_clause,[status(thm)],[f203]) ).
thf(f203,plain,
( $false
| ~ spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f166]) ).
thf(f166,plain,
( ( sK1 != sK1 )
| ~ spl3_5 ),
inference(superposition,[status(thm)],[f21,f91]) ).
thf(f91,plain,
( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f89]) ).
thf(f89,definition,
( spl3_5
<=> ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f21,plain,
( sK1
!= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
( sK1
!= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps
@ ^ [Y3: $i] :
( ( ( Y2 = Y3 )
& ~ Y0 )
| ( ( Y1 = Y3 )
& Y0 ) ) )
@ sK0
@ sK1
@ sK2 ) ),
inference(definition_unfolding,[status(thm)],[f16,f17]) ).
thf(f17,plain,
( if
= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps
@ ^ [Y3: $i] :
( ( ( Y2 = Y3 )
& ~ Y0 )
| ( ( Y1 = Y3 )
& Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( if
= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps
@ ^ [Y3: $i] :
( ( ( Y2 = Y3 )
& ~ Y0 )
| ( ( Y1 = Y3 )
& Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( if
= ( ^ [X0: $o,X1: $i,X2: $i] :
( eps
@ ^ [X3: $i] :
( ( X0
& ( X1 = X3 ) )
| ( ~ X0
& ( X2 = X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( if
= ( ^ [X2: $o,X1: $i,X3: $i] :
( eps
@ ^ [X4: $i] :
( ( X2
& ( X1 = X4 ) )
| ( ~ X2
& ( X3 = X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.3exDLK3vCm/DTF2THF_30683.p',ifd) ).
thf(f16,plain,
( ( if @ sK0 @ sK1 @ sK2 )
!= sK1 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( if @ sK0 @ sK1 @ sK2 )
!= sK1 )
& ( ( if @ sK0 @ sK1 @ sK2 )
!= sK2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f12,f13]) ).
thf(f13,plain,
( ? [X0: $o,X1: $i,X2: $i] :
( ( ( if @ X0 @ X1 @ X2 )
!= X1 )
& ( ( if @ X0 @ X1 @ X2 )
!= X2 ) )
=> ( ( ( if @ sK0 @ sK1 @ sK2 )
!= sK1 )
& ( ( if @ sK0 @ sK1 @ sK2 )
!= sK2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
? [X0: $o,X1: $i,X2: $i] :
( ( ( if @ X0 @ X1 @ X2 )
!= X1 )
& ( ( if @ X0 @ X1 @ X2 )
!= X2 ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
~ ! [X0: $o,X1: $i,X2: $i] :
( ( ( if @ X0 @ X1 @ X2 )
= X1 )
| ( ( if @ X0 @ X1 @ X2 )
= X2 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X2: $o,X1: $i,X3: $i] :
( ( ( if @ X2 @ X1 @ X3 )
= X1 )
| ( ( if @ X2 @ X1 @ X3 )
= X3 ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X2: $o,X1: $i,X3: $i] :
( ( ( if @ X2 @ X1 @ X3 )
= X1 )
| ( ( if @ X2 @ X1 @ X3 )
= X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.3exDLK3vCm/DTF2THF_30683.p',conj) ).
thf(f160,plain,
( spl3_5
| spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f159,f75,f72,f89]) ).
thf(f72,definition,
( spl3_1
<=> ! [X1: $i] : ( sK1 != X1 ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f75,definition,
( spl3_2
<=> ( sK0 = $true ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f159,plain,
( ! [X1: $i] :
( ( sK1 != X1 )
| ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) ) )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f158]) ).
thf(f158,plain,
( ! [X1: $i] :
( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
| ( sK1 != X1 )
| ( $false = $true ) )
| ~ spl3_2 ),
inference(forward_demodulation,[status(thm)],[f156,f77]) ).
thf(f77,plain,
( ( sK0 = $true )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f75]) ).
thf(f156,plain,
! [X1: $i] :
( ( sK1 != X1 )
| ( $false = sK0 )
| ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f155]) ).
thf(f155,plain,
! [X1: $i] :
( ( $false = sK0 )
| ( sK1 != X1 )
| ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f154]) ).
thf(f154,plain,
! [X1: $i] :
( ( $false = sK0 )
| ( ( sK1 = X1 )
= $false )
| ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f152]) ).
thf(f152,plain,
! [X1: $i] :
( ( $false = sK0 )
| ( ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
& sK0 )
= $true )
| ( ( sK1 = X1 )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f151]) ).
thf(f151,plain,
! [X1: $i] :
( ( ( sK1 = X1 )
= $false )
| ( $false = sK0 )
| ( ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
& sK0 )
= $true )
| ( $false = sK0 ) ),
inference(not_proxy_clausification,[status(thm)],[f150]) ).
thf(f150,plain,
! [X1: $i] :
( ( ( ~ sK0 ) = $true )
| ( ( sK1 = X1 )
= $false )
| ( ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
& sK0 )
= $true )
| ( $false = sK0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f137]) ).
thf(f137,plain,
! [X1: $i] :
( ( ( ( sK1 = X1 )
& sK0 )
= $false )
| ( ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
& sK0 )
= $true )
| ( ( ~ sK0 ) = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f114]) ).
thf(f114,plain,
! [X1: $i] :
( ( ( ( ( sK2 = X1 )
& ~ sK0 )
| ( ( sK1 = X1 )
& sK0 ) )
= $false )
| ( ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
& sK0 )
= $true )
| ( ( ~ sK0 ) = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f113]) ).
thf(f113,plain,
! [X1: $i] :
( ( ( ( sK2
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
& ~ sK0 )
= $true )
| ( ( ( ( sK2 = X1 )
& ~ sK0 )
| ( ( sK1 = X1 )
& sK0 ) )
= $false )
| ( ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
& sK0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f112]) ).
thf(f112,plain,
! [X1: $i] :
( ( ( ( ( sK2
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
& ~ sK0 )
| ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
& sK0 ) )
= $true )
| ( ( ( ( sK2 = X1 )
& ~ sK0 )
| ( ( sK1 = X1 )
& sK0 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f111]) ).
thf(f111,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) )
@ ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) )
@ X1 )
= $false ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f109,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[status(thm)],[f108]) ).
thf(f108,plain,
( $false
| ~ spl3_1 ),
inference(equality_resolution,[status(thm)],[f73]) ).
thf(f73,plain,
( ! [X1: $i] : ( sK1 != X1 )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f72]) ).
thf(f107,plain,
~ spl3_6,
inference(avatar_contradiction_clause,[status(thm)],[f106]) ).
thf(f106,plain,
( $false
| ~ spl3_6 ),
inference(equality_resolution,[status(thm)],[f96]) ).
thf(f96,plain,
( ! [X1: $i] : ( sK2 != X1 )
| ~ spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f95]) ).
thf(f95,definition,
( spl3_6
<=> ! [X1: $i] : ( sK2 != X1 ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f101,plain,
~ spl3_4,
inference(avatar_split_clause,[status(thm)],[f22,f84]) ).
thf(f84,definition,
( spl3_4
<=> ( sK2
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f22,plain,
( sK2
!= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( sK2
!= ( ^ [Y0: $o,Y1: $i,Y2: $i] :
( eps
@ ^ [Y3: $i] :
( ( ( Y2 = Y3 )
& ~ Y0 )
| ( ( Y1 = Y3 )
& Y0 ) ) )
@ sK0
@ sK1
@ sK2 ) ),
inference(definition_unfolding,[status(thm)],[f15,f17]) ).
thf(f15,plain,
( ( if @ sK0 @ sK1 @ sK2 )
!= sK2 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f100,plain,
( spl3_6
| spl3_2
| spl3_4
| spl3_5 ),
inference(avatar_split_clause,[status(thm)],[f36,f89,f84,f75,f95]) ).
thf(f36,plain,
! [X1: $i] :
( ( sK2 != X1 )
| ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
| ( sK2
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
| ( sK0 = $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: $i] :
( ( sK0 = $true )
| ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
| ( ( sK2
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
= $true )
| ( sK2 != X1 ) ),
inference(not_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X1: $i] :
( ( sK2 != X1 )
| ( ( ~ sK0 ) = $false )
| ( ( sK2
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
= $true )
| ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X1: $i] :
( ( ( sK2 = X1 )
= $false )
| ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
| ( ( ~ sK0 ) = $false )
| ( ( sK2
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X1: $i] :
( ( ( ( sK2 = X1 )
& ~ sK0 )
= $false )
| ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
| ( ( sK2
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: $i] :
( ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
= $true )
| ( ( ( sK2 = X1 )
& ~ sK0 )
= $false )
| ( ( sK2
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: $i] :
( ( ( ( sK2
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
& ~ sK0 )
= $true )
| ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
= $true )
| ( ( ( sK2 = X1 )
& ~ sK0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: $i] :
( ( ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
& sK0 )
= $true )
| ( ( ( sK2
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
& ~ sK0 )
= $true )
| ( ( ( sK2 = X1 )
& ~ sK0 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $i] :
( ( ( ( ( sK2 = X1 )
& ~ sK0 )
| ( ( sK1 = X1 )
& sK0 ) )
= $false )
| ( ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
& sK0 )
= $true )
| ( ( ( sK2
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
& ~ sK0 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: $i] :
( ( ( ( ( sK2
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
& ~ sK0 )
| ( ( sK1
= ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
& sK0 ) )
= $true )
| ( ( ( ( sK2 = X1 )
& ~ sK0 )
| ( ( sK1 = X1 )
& sK0 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) )
@ ( eps
@ ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( ( sK2 = Y0 )
& ~ sK0 )
| ( ( sK1 = Y0 )
& sK0 ) )
@ X1 )
= $false ) ),
introduced(definition,[],[choice_axiom]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO539^1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n003.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 14:33:10 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.44 ---- Original DTF file ---
% 0.20/0.44 thf(spec,logic,$$dhol).
% 0.20/0.44 %------------------------------------------------------------------------------
% 0.20/0.44 % File : SYO539^1 : TPTP v9.2.1. Released v5.2.0.
% 0.20/0.44 % Domain : Syntactic
% 0.20/0.44 % Problem : Range of if-then-else on $i defined from choice on $i
% 0.20/0.44 % Version : Especial.
% 0.20/0.44 % English : A choice operator on $i is used to define an if-then-else operator
% 0.20/0.44 % at $i. Check that it always returns the then-part or the else-part.
% 0.20/0.44
% 0.20/0.44 % Refs : [Bro11] Brown E. (2011), Email to Geoff Sutcliffe
% 0.20/0.44 % Source : [Bro11]
% 0.20/0.44 % Names : CHOICE15b [Bro11]
% 0.20/0.44
% 0.20/0.44 % Status : Theorem
% 0.20/0.44 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.57 v6.1.0, 0.43 v5.5.0, 0.33 v5.4.0, 0.40 v5.2.0
% 0.20/0.44 % Syntax : Number of formulae : 5 ( 1 unt; 2 typ; 1 def)
% 0.20/0.44 % Number of atoms : 5 ( 5 equ; 0 cnn)
% 0.20/0.44 % Maximal formula atoms : 2 ( 1 avg)
% 0.20/0.44 % Number of connectives : 16 ( 1 ~; 2 |; 2 &; 10 @)
% 0.20/0.44 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.44 % Maximal formula depth : 5 ( 4 avg)
% 0.20/0.44 % Number of types : 2 ( 0 usr)
% 0.20/0.44 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.20/0.44 % Number of symbols : 3 ( 2 usr; 0 con; 1-3 aty)
% 0.20/0.44 % Number of variables : 9 ( 4 ^; 4 !; 1 ?; 9 :)
% 0.20/0.44 % SPC : TH0_THM_EQU_NAR
% 0.20/0.44
% 0.20/0.44 % Comments :
% 0.20/0.44 %------------------------------------------------------------------------------
% 0.20/0.44 thf(eps,type,
% 0.20/0.44 eps: ( $i > $o ) > $i ).
% 0.20/0.44
% 0.20/0.44 thf(choiceax,axiom,
% 0.20/0.44 ! [P: $i > $o] :
% 0.20/0.44 ( ? [X: $i] : ( P @ X )
% 0.20/0.44 => ( P @ ( eps @ P ) ) ) ).
% 0.20/0.44
% 0.20/0.44 thf(if,type,
% 0.20/0.44 if: $o > $i > $i > $i ).
% 0.20/0.44
% 0.20/0.44 thf(ifd,definition,
% 0.20/0.44 ( if
% 0.20/0.44 = ( ^ [B: $o,X: $i,Y: $i] :
% 0.20/0.44 ( eps
% 0.20/0.44 @ ^ [Z: $i] :
% 0.20/0.44 ( ( B
% 0.20/0.44 & ( Z = X ) )
% 0.20/0.44 | ( ~ B
% 0.20/0.44 & ( Z = Y ) ) ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 thf(conj,conjecture,
% 0.20/0.44 ! [B: $o,X: $i,Y: $i] :
% 0.20/0.44 ( ( ( if @ B @ X @ Y )
% 0.20/0.44 = X )
% 0.20/0.44 | ( ( if @ B @ X @ Y )
% 0.20/0.44 = Y ) ) ).
% 0.20/0.44
% 0.20/0.44 %------------------------------------------------------------------------------
% 0.20/0.44 ------------------------
% 1.54/1.21 ---- Embedded in THF ---
% 1.54/1.21 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.54/1.21 %%% Generated on Tue Feb 24 14:33:11 EST 2026
% 1.54/1.21 %%% using '$$dhol' embedding, version 1.3.0.
% 1.54/1.21 %%% Logic specification used:
% 1.54/1.21 %%% thf(spec, logic, $$dhol).
% 1.54/1.21
% 1.54/1.21 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.3exDLK3vCm/DTF2DTF30683.p
% See solution above
% 1.54/1.21 ------------------------
% 1.54/1.22 ---- Cleaned THF ---
% 1.54/1.22 thf(eps,type,
% 1.54/1.22 eps: ( $i > $o ) > $i ).
% 1.54/1.22
% 1.54/1.22 thf(choiceax,axiom,
% 1.54/1.22 ! [P: $i > $o] :
% 1.54/1.22 ( ? [X: $i] : ( P @ X )
% 1.54/1.22 => ( P @ ( eps @ P ) ) ) ).
% 1.54/1.22
% 1.54/1.22 thf(if,type,
% 1.54/1.22 if: $o > $i > $i > $i ).
% 1.54/1.22
% 1.54/1.22 thf(ifd,definition,
% 1.54/1.22 ( if
% 1.54/1.22 = ( ^ [B: $o,X: $i,Y: $i] :
% 1.54/1.22 ( eps
% 1.54/1.22 @ ^ [Z: $i] :
% 1.54/1.22 ( ( B
% 1.54/1.22 & ( Z = X ) )
% 1.54/1.22 | ( ~ B
% 1.54/1.22 & ( Z = Y ) ) ) ) ) ) ).
% 1.54/1.22
% 1.54/1.22 thf(conj,conjecture,
% 1.54/1.22 ! [B: $o,X: $i,Y: $i] :
% 1.54/1.22 ( ( ( if @ B @ X @ Y )
% 1.54/1.22 = X )
% 1.54/1.22 | ( ( if @ B @ X @ Y )
% 1.54/1.22 = Y ) ) ).
% 1.54/1.22 ------------------------
% 1.54/1.23 % (30840)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_30683 for (3000ds/275Mi)
% 1.54/1.23 % (30840)Refutation not found, incomplete strategy
% 1.54/1.23 % (30840)------------------------------
% 1.54/1.23 % (30840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.23 % (30840)Termination reason: Refutation not found, incomplete strategy
% 1.54/1.23
% 1.54/1.23
% 1.54/1.23 % (30840)Memory used [KB]: 5500
% 1.54/1.23 % (30840)Time elapsed: 0.002 s
% 1.54/1.23 % (30840)Instructions burned: 2 (million)
% 1.54/1.23 % (30840)------------------------------
% 1.54/1.23 % (30840)------------------------------
% 1.54/1.23 % (30841)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30683 for (3000ds/18Mi)
% 1.54/1.24 % (30839)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_30683 for (3000ds/2Mi)
% 1.54/1.24 % (30839)Instruction limit reached!
% 1.54/1.24 % (30839)------------------------------
% 1.54/1.24 % (30839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.24 % (30839)Termination reason: Unknown
% 1.54/1.24 % (30839)Termination phase: Saturation
% 1.54/1.24
% 1.54/1.24 % (30839)Memory used [KB]: 895
% 1.54/1.24 % (30839)Time elapsed: 0.002 s
% 1.54/1.24 % (30839)Instructions burned: 2 (million)
% 1.54/1.24 % (30839)------------------------------
% 1.54/1.24 % (30839)------------------------------
% 1.54/1.24 % (30835)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30683 for (3000ds/183Mi)
% 1.54/1.24 % (30846)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30683 for (2999ds/3Mi)
% 1.54/1.24 % (30841)Instruction limit reached!
% 1.54/1.24 % (30841)------------------------------
% 1.54/1.24 % (30841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.24 % (30841)Termination reason: Unknown
% 1.54/1.24 % (30841)Termination phase: Saturation
% 1.54/1.24
% 1.54/1.24 % (30841)Memory used [KB]: 5628
% 1.54/1.24 % (30841)Time elapsed: 0.011 s
% 1.54/1.24 % (30841)Instructions burned: 19 (million)
% 1.54/1.24 % (30841)------------------------------
% 1.54/1.24 % (30841)------------------------------
% 1.54/1.24 % (30837)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_30683 for (3000ds/27Mi)
% 1.54/1.24 % (30838)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30683 for (3000ds/2Mi)
% 1.54/1.24 % (30846)Instruction limit reached!
% 1.54/1.24 % (30846)------------------------------
% 1.54/1.24 % (30846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.24 % (30846)Termination reason: Unknown
% 1.54/1.24 % (30846)Termination phase: Saturation
% 1.54/1.24
% 1.54/1.24 % (30846)Memory used [KB]: 5500
% 1.54/1.24 % (30846)Time elapsed: 0.002 s
% 1.54/1.24 % (30846)Instructions burned: 3 (million)
% 1.54/1.24 % (30846)------------------------------
% 1.54/1.24 % (30846)------------------------------
% 1.54/1.25 % (30836)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_30683 for (3000ds/4Mi)
% 1.54/1.25 % (30838)Instruction limit reached!
% 1.54/1.25 % (30838)------------------------------
% 1.54/1.25 % (30838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.25 % (30838)Termination reason: Unknown
% 1.54/1.25 % (30838)Termination phase: Property scanning
% 1.54/1.25
% 1.54/1.25 % (30838)Memory used [KB]: 895
% 1.54/1.25 % (30838)Time elapsed: 0.004 s
% 1.54/1.25 % (30838)Instructions burned: 2 (million)
% 1.54/1.25 % (30838)------------------------------
% 1.54/1.25 % (30838)------------------------------
% 1.54/1.25 % (30836)Instruction limit reached!
% 1.54/1.25 % (30836)------------------------------
% 1.54/1.25 % (30836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.25 % (30836)Termination reason: Unknown
% 1.54/1.25 % (30836)Termination phase: Saturation
% 1.54/1.25
% 1.54/1.25 % (30836)Memory used [KB]: 5500
% 1.54/1.25 % (30836)Time elapsed: 0.007 s
% 1.54/1.25 % (30836)Instructions burned: 4 (million)
% 1.54/1.25 % (30836)------------------------------
% 1.54/1.25 % (30836)------------------------------
% 1.54/1.25 % (30850)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_30683 for (2999ds/37Mi)
% 1.54/1.25 % (30855)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_30683 for (2999ds/15Mi)
% 1.54/1.25 % (30855)Refutation not found, incomplete strategy
% 1.54/1.25 % (30855)------------------------------
% 1.54/1.25 % (30855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.25 % (30855)Termination reason: Refutation not found, incomplete strategy
% 1.54/1.25
% 1.54/1.25
% 1.54/1.25 % (30855)Memory used [KB]: 5500
% 1.54/1.25 % (30855)Time elapsed: 0.002 s
% 1.54/1.25 % (30855)Instructions burned: 1 (million)
% 1.54/1.25 % (30855)------------------------------
% 1.54/1.25 % (30855)------------------------------
% 1.54/1.26 % (30837)First to succeed.
% 1.54/1.26 % (30837)Refutation found. Thanks to Tanya!
% 1.54/1.26 % SZS status Theorem for DTF2THF_30683
% 1.54/1.26 % SZS output start Proof for DTF2THF_30683
% 1.54/1.26 thf(func_def_0, type, eps: ($i > $o) > $i).
% 1.54/1.26 thf(func_def_2, type, if: $o > $i > $i > $i).
% 1.54/1.26 thf(func_def_3, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.54/1.26 thf(func_def_19, type, ph4: !>[X0: $tType]:(X0)).
% 1.54/1.26 thf(f205,plain,(
% 1.54/1.26 $false),
% 1.54/1.26 inference(avatar_sat_refutation,[status(thm)],[f100,f101,f107,f109,f160,f204])).
% 1.54/1.26 thf(f204,plain,(
% 1.54/1.26 ~spl3_5),
% 1.54/1.26 inference(avatar_contradiction_clause,[status(thm)],[f203])).
% 1.54/1.26 thf(f203,plain,(
% 1.54/1.26 $false | ~spl3_5),
% 1.54/1.26 inference(trivial_inequality_removal,[status(thm)],[f166])).
% 1.54/1.26 thf(f166,plain,(
% 1.54/1.26 (sK1 != sK1) | ~spl3_5),
% 1.54/1.26 inference(superposition,[status(thm)],[f21,f91])).
% 1.54/1.26 thf(f91,plain,(
% 1.54/1.26 (sK1 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) | ~spl3_5),
% 1.54/1.26 inference(avatar_component_clause,[status(thm)],[f89])).
% 1.54/1.26 thf(f89,definition,(
% 1.54/1.26 spl3_5 <=> (sK1 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0)))))),
% 1.54/1.26 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.54/1.26 thf(f21,plain,(
% 1.54/1.26 (sK1 != (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0)))))),
% 1.54/1.26 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.54/1.26 thf(f19,plain,(
% 1.54/1.26 (sK1 != ((^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((Y2 = Y3) & (~ Y0)) | ((Y1 = Y3) & Y0))))))))) @ sK0 @ sK1 @ sK2))),
% 1.54/1.26 inference(definition_unfolding,[status(thm)],[f16,f17])).
% 1.54/1.26 thf(f17,plain,(
% 1.54/1.26 (if = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((Y2 = Y3) & (~ Y0)) | ((Y1 = Y3) & Y0))))))))))),
% 1.54/1.26 inference(cnf_transformation,[status(thm)],[f7])).
% 1.54/1.26 thf(f7,plain,(
% 1.54/1.26 (if = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((Y2 = Y3) & (~ Y0)) | ((Y1 = Y3) & Y0))))))))))),
% 1.54/1.26 inference(fool_elimination,[status(thm)],[f6])).
% 1.54/1.26 thf(f6,plain,(
% 1.54/1.26 (if = (^[X0 : $o, X1 : $i, X2 : $i] : (eps @ (^[X3 : $i] : ((X0 & (X1 = X3)) | (~X0 & (X2 = X3)))))))),
% 1.54/1.26 inference(rectify,[status(thm)],[f2])).
% 1.54/1.26 thf(f2,axiom,(
% 1.54/1.26 (if = (^[X2 : $o, X1 : $i, X3 : $i] : (eps @ (^[X4 : $i] : ((X2 & (X1 = X4)) | (~X2 & (X3 = X4)))))))),
% 1.54/1.26 file('/export/starexec/sandbox2/tmp/tmp.3exDLK3vCm/DTF2THF_30683.p',ifd)).
% 1.54/1.26 thf(f16,plain,(
% 1.54/1.26 ((if @ sK0 @ sK1 @ sK2) != sK1)),
% 1.54/1.26 inference(cnf_transformation,[status(thm)],[f14])).
% 1.54/1.26 thf(f14,plain,(
% 1.54/1.26 ((if @ sK0 @ sK1 @ sK2) != sK1) & ((if @ sK0 @ sK1 @ sK2) != sK2)),
% 1.54/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f12,f13])).
% 1.54/1.26 thf(f13,plain,(
% 1.54/1.26 ? [X0 : $o,X1 : $i,X2 : $i] : (((if @ X0 @ X1 @ X2) != X1) & ((if @ X0 @ X1 @ X2) != X2)) => (((if @ sK0 @ sK1 @ sK2) != sK1) & ((if @ sK0 @ sK1 @ sK2) != sK2))),
% 1.54/1.26 introduced(definition,[],[choice_axiom])).
% 1.54/1.26 thf(f12,plain,(
% 1.54/1.26 ? [X0 : $o,X1 : $i,X2 : $i] : (((if @ X0 @ X1 @ X2) != X1) & ((if @ X0 @ X1 @ X2) != X2))),
% 1.54/1.26 inference(ennf_transformation,[status(thm)],[f10])).
% 1.54/1.26 thf(f10,plain,(
% 1.54/1.26 ~! [X0 : $o,X1 : $i,X2 : $i] : (((if @ X0 @ X1 @ X2) = X1) | ((if @ X0 @ X1 @ X2) = X2))),
% 1.54/1.26 inference(rectify,[status(thm)],[f4])).
% 1.54/1.26 thf(f4,negated_conjecture,(
% 1.54/1.26 ~! [X2 : $o,X1 : $i,X3 : $i] : (((if @ X2 @ X1 @ X3) = X1) | ((if @ X2 @ X1 @ X3) = X3))),
% 1.54/1.26 inference(negated_conjecture,[status(cth)],[f3])).
% 1.54/1.26 thf(f3,conjecture,(
% 1.54/1.26 ! [X2 : $o,X1 : $i,X3 : $i] : (((if @ X2 @ X1 @ X3) = X1) | ((if @ X2 @ X1 @ X3) = X3))),
% 1.54/1.26 file('/export/starexec/sandbox2/tmp/tmp.3exDLK3vCm/DTF2THF_30683.p',conj)).
% 1.54/1.26 thf(f160,plain,(
% 1.54/1.26 spl3_5 | spl3_1 | ~spl3_2),
% 1.54/1.26 inference(avatar_split_clause,[status(thm)],[f159,f75,f72,f89])).
% 1.54/1.26 thf(f72,definition,(
% 1.54/1.26 spl3_1 <=> ! [X1 : $i] : (sK1 != X1)),
% 1.54/1.26 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.54/1.26 thf(f75,definition,(
% 1.54/1.26 spl3_2 <=> (sK0 = $true)),
% 1.54/1.26 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.54/1.26 thf(f159,plain,(
% 1.54/1.26 ( ! [X1 : $i] : ((sK1 != X1) | (sK1 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0)))))) ) | ~spl3_2),
% 1.54/1.26 inference(trivial_inequality_removal,[status(thm)],[f158])).
% 1.54/1.26 thf(f158,plain,(
% 1.54/1.26 ( ! [X1 : $i] : ((sK1 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) | (sK1 != X1) | ($false = $true)) ) | ~spl3_2),
% 1.54/1.26 inference(forward_demodulation,[status(thm)],[f156,f77])).
% 1.54/1.26 thf(f77,plain,(
% 1.54/1.26 (sK0 = $true) | ~spl3_2),
% 1.54/1.26 inference(avatar_component_clause,[status(thm)],[f75])).
% 1.54/1.26 thf(f156,plain,(
% 1.54/1.26 ( ! [X1 : $i] : ((sK1 != X1) | ($false = sK0) | (sK1 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0)))))) )),
% 1.54/1.26 inference(equality_proxy_clausification,[status(thm)],[f155])).
% 1.54/1.26 thf(f155,plain,(
% 1.54/1.26 ( ! [X1 : $i] : (($false = sK0) | (sK1 != X1) | ((sK1 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) = $true)) )),
% 1.54/1.26 inference(equality_proxy_clausification,[status(thm)],[f154])).
% 1.54/1.26 thf(f154,plain,(
% 1.54/1.26 ( ! [X1 : $i] : (($false = sK0) | ((sK1 = X1) = $false) | ((sK1 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) = $true)) )),
% 1.54/1.26 inference(binary_proxy_clausification,[status(thm)],[f152])).
% 1.54/1.26 thf(f152,plain,(
% 1.54/1.26 ( ! [X1 : $i] : (($false = sK0) | (((sK1 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) & sK0) = $true) | ((sK1 = X1) = $false)) )),
% 1.54/1.26 inference(duplicate_literal_removal,[status(thm)],[f151])).
% 1.54/1.26 thf(f151,plain,(
% 1.54/1.26 ( ! [X1 : $i] : (((sK1 = X1) = $false) | ($false = sK0) | (((sK1 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) & sK0) = $true) | ($false = sK0)) )),
% 1.54/1.26 inference(not_proxy_clausification,[status(thm)],[f150])).
% 1.54/1.26 thf(f150,plain,(
% 1.54/1.26 ( ! [X1 : $i] : (((~ sK0) = $true) | ((sK1 = X1) = $false) | (((sK1 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) & sK0) = $true) | ($false = sK0)) )),
% 1.54/1.26 inference(binary_proxy_clausification,[status(thm)],[f137])).
% 1.54/1.26 thf(f137,plain,(
% 1.54/1.26 ( ! [X1 : $i] : ((((sK1 = X1) & sK0) = $false) | (((sK1 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) & sK0) = $true) | ((~ sK0) = $true)) )),
% 1.54/1.26 inference(binary_proxy_clausification,[status(thm)],[f114])).
% 1.54/1.26 thf(f114,plain,(
% 1.54/1.26 ( ! [X1 : $i] : (((((sK2 = X1) & (~ sK0)) | ((sK1 = X1) & sK0)) = $false) | (((sK1 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) & sK0) = $true) | ((~ sK0) = $true)) )),
% 1.54/1.26 inference(binary_proxy_clausification,[status(thm)],[f113])).
% 1.54/1.26 thf(f113,plain,(
% 1.54/1.26 ( ! [X1 : $i] : ((((sK2 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) & (~ sK0)) = $true) | ((((sK2 = X1) & (~ sK0)) | ((sK1 = X1) & sK0)) = $false) | (((sK1 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) & sK0) = $true)) )),
% 1.54/1.26 inference(binary_proxy_clausification,[status(thm)],[f112])).
% 1.54/1.26 thf(f112,plain,(
% 1.54/1.26 ( ! [X1 : $i] : (((((sK2 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) & (~ sK0)) | ((sK1 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) & sK0)) = $true) | ((((sK2 = X1) & (~ sK0)) | ((sK1 = X1) & sK0)) = $false)) )),
% 1.54/1.26 inference(beta_eta_normalization,[status(thm)],[f111])).
% 1.54/1.26 thf(f111,plain,(
% 1.54/1.26 ( ! [X1 : $i] : ((((^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))) @ (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) = $true) | (((^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))) @ X1) = $false)) )),
% 1.54/1.26 introduced(definition,[],[choice_axiom])).
% 1.54/1.26 thf(f109,plain,(
% 1.54/1.26 ~spl3_1),
% 1.54/1.26 inference(avatar_contradiction_clause,[status(thm)],[f108])).
% 1.54/1.26 thf(f108,plain,(
% 1.54/1.26 $false | ~spl3_1),
% 1.54/1.26 inference(equality_resolution,[status(thm)],[f73])).
% 1.54/1.26 thf(f73,plain,(
% 1.54/1.26 ( ! [X1 : $i] : ((sK1 != X1)) ) | ~spl3_1),
% 1.54/1.26 inference(avatar_component_clause,[status(thm)],[f72])).
% 1.54/1.26 thf(f107,plain,(
% 1.54/1.26 ~spl3_6),
% 1.54/1.26 inference(avatar_contradiction_clause,[status(thm)],[f106])).
% 1.54/1.26 thf(f106,plain,(
% 1.54/1.26 $false | ~spl3_6),
% 1.54/1.26 inference(equality_resolution,[status(thm)],[f96])).
% 1.54/1.26 thf(f96,plain,(
% 1.54/1.26 ( ! [X1 : $i] : ((sK2 != X1)) ) | ~spl3_6),
% 1.54/1.26 inference(avatar_component_clause,[status(thm)],[f95])).
% 1.54/1.26 thf(f95,definition,(
% 1.54/1.26 spl3_6 <=> ! [X1 : $i] : (sK2 != X1)),
% 1.54/1.26 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 1.54/1.26 thf(f101,plain,(
% 1.54/1.26 ~spl3_4),
% 1.54/1.26 inference(avatar_split_clause,[status(thm)],[f22,f84])).
% 1.54/1.26 thf(f84,definition,(
% 1.54/1.26 spl3_4 <=> (sK2 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0)))))),
% 1.54/1.26 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.54/1.26 thf(f22,plain,(
% 1.54/1.26 (sK2 != (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0)))))),
% 1.54/1.26 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.54/1.26 thf(f20,plain,(
% 1.54/1.26 (sK2 != ((^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((Y2 = Y3) & (~ Y0)) | ((Y1 = Y3) & Y0))))))))) @ sK0 @ sK1 @ sK2))),
% 1.54/1.26 inference(definition_unfolding,[status(thm)],[f15,f17])).
% 1.54/1.26 thf(f15,plain,(
% 1.54/1.26 ((if @ sK0 @ sK1 @ sK2) != sK2)),
% 1.54/1.26 inference(cnf_transformation,[status(thm)],[f14])).
% 1.54/1.26 thf(f100,plain,(
% 1.54/1.26 spl3_6 | spl3_2 | spl3_4 | spl3_5),
% 1.54/1.26 inference(avatar_split_clause,[status(thm)],[f36,f89,f84,f75,f95])).
% 1.54/1.26 thf(f36,plain,(
% 1.54/1.26 ( ! [X1 : $i] : ((sK2 != X1) | (sK1 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) | (sK2 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) | (sK0 = $true)) )),
% 1.54/1.26 inference(equality_proxy_clausification,[status(thm)],[f35])).
% 1.54/1.26 thf(f35,plain,(
% 1.54/1.26 ( ! [X1 : $i] : ((sK0 = $true) | (sK1 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) | ((sK2 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) = $true) | (sK2 != X1)) )),
% 1.54/1.26 inference(not_proxy_clausification,[status(thm)],[f34])).
% 1.54/1.26 thf(f34,plain,(
% 1.54/1.26 ( ! [X1 : $i] : ((sK2 != X1) | ((~ sK0) = $false) | ((sK2 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) = $true) | (sK1 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0)))))) )),
% 1.54/1.26 inference(equality_proxy_clausification,[status(thm)],[f33])).
% 1.54/1.26 thf(f33,plain,(
% 1.54/1.26 ( ! [X1 : $i] : (((sK2 = X1) = $false) | (sK1 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) | ((~ sK0) = $false) | ((sK2 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) = $true)) )),
% 1.54/1.26 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.54/1.26 thf(f32,plain,(
% 1.54/1.26 ( ! [X1 : $i] : ((((sK2 = X1) & (~ sK0)) = $false) | (sK1 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) | ((sK2 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) = $true)) )),
% 1.54/1.26 inference(equality_proxy_clausification,[status(thm)],[f31])).
% 1.54/1.26 thf(f31,plain,(
% 1.54/1.26 ( ! [X1 : $i] : (((sK1 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) = $true) | (((sK2 = X1) & (~ sK0)) = $false) | ((sK2 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) = $true)) )),
% 1.54/1.26 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.54/1.26 thf(f29,plain,(
% 1.54/1.26 ( ! [X1 : $i] : ((((sK2 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) & (~ sK0)) = $true) | ((sK1 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) = $true) | (((sK2 = X1) & (~ sK0)) = $false)) )),
% 1.54/1.26 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.54/1.26 thf(f27,plain,(
% 1.54/1.26 ( ! [X1 : $i] : ((((sK1 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) & sK0) = $true) | (((sK2 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) & (~ sK0)) = $true) | (((sK2 = X1) & (~ sK0)) = $false)) )),
% 1.54/1.26 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.54/1.26 thf(f25,plain,(
% 1.54/1.26 ( ! [X1 : $i] : (((((sK2 = X1) & (~ sK0)) | ((sK1 = X1) & sK0)) = $false) | (((sK1 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) & sK0) = $true) | (((sK2 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) & (~ sK0)) = $true)) )),
% 1.54/1.26 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.54/1.26 thf(f24,plain,(
% 1.54/1.26 ( ! [X1 : $i] : (((((sK2 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) & (~ sK0)) | ((sK1 = (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) & sK0)) = $true) | ((((sK2 = X1) & (~ sK0)) | ((sK1 = X1) & sK0)) = $false)) )),
% 1.54/1.26 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.54/1.26 thf(f23,plain,(
% 1.54/1.26 ( ! [X1 : $i] : ((((^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))) @ (eps @ (^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))))) = $true) | (((^[Y0 : $i]: (((sK2 = Y0) & (~ sK0)) | ((sK1 = Y0) & sK0))) @ X1) = $false)) )),
% 1.54/1.26 introduced(definition,[],[choice_axiom])).
% 1.54/1.26 % SZS output end Proof for DTF2THF_30683
% 1.54/1.26 % (30837)------------------------------
% 1.54/1.26 % (30837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.26 % (30837)Termination reason: Refutation
% 1.54/1.26
% 1.54/1.26 % (30837)Memory used [KB]: 5500
% 1.54/1.26 % (30837)Time elapsed: 0.017 s
% 1.54/1.26 % (30837)Instructions burned: 11 (million)
% 1.54/1.26 % (30837)------------------------------
% 1.54/1.26 % (30837)------------------------------
% 1.54/1.26 % (30833)Success in time 0.022 s
%------------------------------------------------------------------------------