%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO542^1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 1.60s 1.31s
% Output : Refutation 1.60s
% 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 : 484 ( 253 equ; 0 cnn)
% Maximal formula atoms : 4 ( 8 avg)
% Number of connectives : 497 ( 117 ~; 130 |; 139 &; 105 @)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 101 ( 101 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 8 con; 0-4 aty)
% Number of variables : 112 ( 69 ^; 37 !; 6 ?; 112 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
epsii: ( ( $i > $i ) > $o ) > $i > $i ).
thf(func_def_2,type,
if: $o > ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(func_def_3,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_15,type,
sK0: $i > $i ).
thf(func_def_16,type,
sK1: $i > $i ).
thf(func_def_19,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f292,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f94,f205,f259,f264,f285,f291]) ).
thf(f291,plain,
~ spl3_6,
inference(avatar_contradiction_clause,[status(thm)],[f290]) ).
thf(f290,plain,
( $false
| ~ spl3_6 ),
inference(equality_resolution,[status(thm)],[f89]) ).
thf(f89,plain,
( ! [X1: $i > $i] : ( sK0 != X1 )
| ~ spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f88]) ).
thf(f88,definition,
( spl3_6
<=> ! [X1: $i > $i] : ( sK0 != X1 ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f285,plain,
( spl3_6
| spl3_2
| spl3_5
| spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f191,f73,f81,f69,f88]) ).
thf(f69,definition,
( spl3_2
<=> ( ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) )
= sK0 ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f81,definition,
( spl3_5
<=> ( sK2 = $true ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f73,definition,
( spl3_3
<=> ( sK1
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f191,plain,
! [X1: $i > $i] :
( ( sK2 = $true )
| ( sK1
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) )
| ( sK0 != X1 )
| ( ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) )
= sK0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f190]) ).
thf(f190,plain,
! [X1: $i > $i] :
( ( sK1
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) )
| ( ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) )
= sK0 )
| ( sK2 = $true )
| ( ( sK0 = X1 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f189]) ).
thf(f189,plain,
! [X1: $i > $i] :
( ( sK1
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) )
| ( ( ~ sK2 ) = $false )
| ( ( sK0 = X1 )
= $false )
| ( ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) )
= sK0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f188]) ).
thf(f188,plain,
! [X1: $i > $i] :
( ( ( ~ sK2
& ( sK0 = X1 ) )
= $false )
| ( ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) )
= sK0 )
| ( sK1
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f186]) ).
thf(f186,plain,
! [X1: $i > $i] :
( ( sK1
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) )
| ( ( ( ~ sK2
& ( sK0 = X1 ) )
| ( sK2
& ( sK1 = X1 ) ) )
= $false )
| ( ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) )
= sK0 ) ),
inference(equality_proxy_clausification,[status(thm)],[f174]) ).
thf(f174,plain,
! [X1: $i > $i] :
( ( ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) )
= $true )
| ( sK1
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) )
| ( ( ( ~ sK2
& ( sK0 = X1 ) )
| ( sK2
& ( sK1 = X1 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f173]) ).
thf(f173,plain,
! [X1: $i > $i] :
( ( $true
= ( ~ sK2
& ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) ) ) )
| ( sK1
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) )
| ( ( ( ~ sK2
& ( sK0 = X1 ) )
| ( sK2
& ( sK1 = X1 ) ) )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f149]) ).
thf(f149,plain,
! [X1: $i > $i] :
( ( ( sK1
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) )
= $true )
| ( $true
= ( ~ sK2
& ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) ) ) )
| ( ( ( ~ sK2
& ( sK0 = X1 ) )
| ( sK2
& ( sK1 = X1 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f148]) ).
thf(f148,plain,
! [X1: $i > $i] :
( ( ( sK2
& ( sK1
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) ) )
= $true )
| ( $true
= ( ~ sK2
& ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) ) ) )
| ( ( ( ~ sK2
& ( sK0 = X1 ) )
| ( sK2
& ( sK1 = X1 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f147]) ).
thf(f147,plain,
! [X1: $i > $i] :
( ( ( ( ~ sK2
& ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) ) )
| ( sK2
& ( sK1
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) ) ) )
= $true )
| ( ( ( ~ sK2
& ( sK0 = X1 ) )
| ( sK2
& ( sK1 = X1 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f145]) ).
thf(f145,plain,
! [X1: $i > $i] :
( ( ( ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) )
@ ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) )
= $true )
| ( ( ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) )
@ X1 )
= $false ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f264,plain,
~ spl3_4,
inference(avatar_contradiction_clause,[status(thm)],[f263]) ).
thf(f263,plain,
( $false
| ~ spl3_4 ),
inference(equality_resolution,[status(thm)],[f78]) ).
thf(f78,plain,
( ! [X1: $i > $i] : ( sK1 != X1 )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f77]) ).
thf(f77,definition,
( spl3_4
<=> ! [X1: $i > $i] : ( sK1 != X1 ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f259,plain,
( spl3_4
| spl3_3
| ~ spl3_5 ),
inference(avatar_split_clause,[status(thm)],[f258,f81,f73,f77]) ).
thf(f258,plain,
( ! [X1: $i > $i] :
( ( sK1 != X1 )
| ( sK1
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) ) )
| ~ spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f257]) ).
thf(f257,plain,
( ! [X1: $i > $i] :
( ( sK1 != X1 )
| ( $false = $true )
| ( sK1
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) ) )
| ~ spl3_5 ),
inference(forward_demodulation,[status(thm)],[f233,f83]) ).
thf(f83,plain,
( ( sK2 = $true )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f81]) ).
thf(f233,plain,
! [X1: $i > $i] :
( ( sK1 != X1 )
| ( sK1
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) )
| ( sK2 = $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f232]) ).
thf(f232,plain,
! [X1: $i > $i] :
( ( sK2 = $false )
| ( ( sK1
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) )
= $true )
| ( sK1 != X1 ) ),
inference(duplicate_literal_removal,[status(thm)],[f231]) ).
thf(f231,plain,
! [X1: $i > $i] :
( ( sK2 = $false )
| ( sK1 != X1 )
| ( sK2 = $false )
| ( ( sK1
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f230]) ).
thf(f230,plain,
! [X1: $i > $i] :
( ( sK2 = $false )
| ( sK1 != X1 )
| ( ( ~ sK2 ) = $true )
| ( ( sK1
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f229]) ).
thf(f229,plain,
! [X1: $i > $i] :
( ( $false
= ( sK1 = X1 ) )
| ( sK2 = $false )
| ( ( sK1
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) )
= $true )
| ( ( ~ sK2 ) = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f222]) ).
thf(f222,plain,
! [X1: $i > $i] :
( ( ( sK2
& ( sK1 = X1 ) )
= $false )
| ( ( sK1
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) )
= $true )
| ( ( ~ sK2 ) = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f210]) ).
thf(f210,plain,
! [X1: $i > $i] :
( ( ( ( ~ sK2
& ( sK0 = X1 ) )
| ( sK2
& ( sK1 = X1 ) ) )
= $false )
| ( ( ~ sK2 ) = $true )
| ( ( sK1
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f209]) ).
thf(f209,plain,
! [X1: $i > $i] :
( ( ( sK2
& ( sK1
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) ) )
= $true )
| ( ( ( ~ sK2
& ( sK0 = X1 ) )
| ( sK2
& ( sK1 = X1 ) ) )
= $false )
| ( ( ~ sK2 ) = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f207]) ).
thf(f207,plain,
! [X1: $i > $i] :
( ( $true
= ( ~ sK2
& ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) ) ) )
| ( ( sK2
& ( sK1
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) ) )
= $true )
| ( ( ( ~ sK2
& ( sK0 = X1 ) )
| ( sK2
& ( sK1 = X1 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f206]) ).
thf(f206,plain,
! [X1: $i > $i] :
( ( ( ( ~ sK2
& ( sK0
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) ) )
| ( sK2
& ( sK1
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) ) ) )
= $true )
| ( ( ( ~ sK2
& ( sK0 = X1 ) )
| ( sK2
& ( sK1 = X1 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f200]) ).
thf(f200,plain,
! [X1: $i > $i] :
( ( ( ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) )
@ ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) )
= $true )
| ( ( ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) )
@ X1 )
= $false ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f205,plain,
~ spl3_3,
inference(avatar_contradiction_clause,[status(thm)],[f204]) ).
thf(f204,plain,
( $false
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f203]) ).
thf(f203,plain,
( ( sK1 != sK1 )
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f21,f75]) ).
thf(f75,plain,
( ( sK1
= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f73]) ).
thf(f21,plain,
( sK1
!= ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
( sK1
!= ( ^ [Y0: $o,Y1: $i > $i,Y2: $i > $i] :
( epsii
@ ^ [Y3: $i > $i] :
( ( ~ Y0
& ( Y2 = Y3 ) )
| ( Y0
& ( Y1 = Y3 ) ) ) )
@ sK2
@ sK1
@ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f17,f18]) ).
thf(f18,plain,
( if
= ( ^ [Y0: $o,Y1: $i > $i,Y2: $i > $i] :
( epsii
@ ^ [Y3: $i > $i] :
( ( ~ Y0
& ( Y2 = Y3 ) )
| ( Y0
& ( Y1 = Y3 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( if
= ( ^ [Y0: $o,Y1: $i > $i,Y2: $i > $i] :
( epsii
@ ^ [Y3: $i > $i] :
( ( ~ Y0
& ( Y2 = Y3 ) )
| ( Y0
& ( Y1 = Y3 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
( if
= ( ^ [X0: $o,X1: $i > $i,X2: $i > $i] :
( epsii
@ ^ [X3: $i > $i] :
( ( ( X1 = X3 )
& X0 )
| ( ( X2 = X3 )
& ~ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( if
= ( ^ [X2: $o,X1: $i > $i,X3: $i > $i] :
( epsii
@ ^ [X4: $i > $i] :
( ( ( X1 = X4 )
& X2 )
| ( ( X3 = X4 )
& ~ X2 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WzCueA1QXu/DTF2THF_18593.p',ifd) ).
thf(f17,plain,
( ( if @ sK2 @ sK1 @ sK0 )
!= sK1 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( if @ sK2 @ sK1 @ sK0 )
!= sK1 )
& ( ( if @ sK2 @ sK1 @ sK0 )
!= sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f12,f13]) ).
thf(f13,plain,
( ? [X0: $i > $i,X1: $i > $i,X2: $o] :
( ( ( if @ X2 @ X1 @ X0 )
!= X1 )
& ( ( if @ X2 @ X1 @ X0 )
!= X0 ) )
=> ( ( ( if @ sK2 @ sK1 @ sK0 )
!= sK1 )
& ( ( if @ sK2 @ sK1 @ sK0 )
!= sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
? [X0: $i > $i,X1: $i > $i,X2: $o] :
( ( ( if @ X2 @ X1 @ X0 )
!= X1 )
& ( ( if @ X2 @ X1 @ X0 )
!= X0 ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
~ ! [X0: $i > $i,X1: $i > $i,X2: $o] :
( ( ( if @ X2 @ X1 @ X0 )
= X1 )
| ( ( if @ X2 @ X1 @ X0 )
= X0 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X3: $i > $i,X1: $i > $i,X2: $o] :
( ( ( if @ X2 @ X1 @ X3 )
= X3 )
| ( ( if @ X2 @ X1 @ X3 )
= X1 ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X3: $i > $i,X1: $i > $i,X2: $o] :
( ( ( if @ X2 @ X1 @ X3 )
= X3 )
| ( ( if @ X2 @ X1 @ X3 )
= X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.WzCueA1QXu/DTF2THF_18593.p',conj) ).
thf(f94,plain,
~ spl3_2,
inference(avatar_split_clause,[status(thm)],[f22,f69]) ).
thf(f22,plain,
( ( epsii
@ ^ [Y0: $i > $i] :
( ( ~ sK2
& ( sK0 = Y0 ) )
| ( sK2
& ( sK1 = Y0 ) ) ) )
!= sK0 ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ^ [Y0: $o,Y1: $i > $i,Y2: $i > $i] :
( epsii
@ ^ [Y3: $i > $i] :
( ( ~ Y0
& ( Y2 = Y3 ) )
| ( Y0
& ( Y1 = Y3 ) ) ) )
@ sK2
@ sK1
@ sK0 )
!= sK0 ),
inference(definition_unfolding,[status(thm)],[f16,f18]) ).
thf(f16,plain,
( ( if @ sK2 @ sK1 @ sK0 )
!= sK0 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO542^1 : TPTP v9.2.1. Released v5.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n010.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 14:33:18 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
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SYO542^1 : TPTP v9.2.1. Released v5.2.0.
% 0.29/0.46 % Domain : Syntactic
% 0.29/0.46 % Problem : If-then-else on $i>$i defined from choice on $i>$i
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English : A choice operator on ($i>$i) is used to define an if-then-else
% 0.29/0.46 % operator at ($i>$i). Check that it always returns the then-part
% 0.29/0.46 % or the else-part.
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro11] Brown E. (2011), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Bro11]
% 0.29/0.46 % Names : CHOICE16b [Bro11]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % 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
% 0.29/0.46 % Syntax : Number of formulae : 5 ( 1 unt; 2 typ; 1 def)
% 0.29/0.46 % Number of atoms : 5 ( 5 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 2 ( 1 avg)
% 0.29/0.46 % Number of connectives : 16 ( 1 ~; 2 |; 2 &; 10 @)
% 0.29/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 5 ( 4 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 3 ( 2 usr; 0 con; 2-4 aty)
% 0.29/0.46 % Number of variables : 9 ( 4 ^; 4 !; 1 ?; 9 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments :
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(epsii,type,
% 0.29/0.46 epsii: ( ( $i > $i ) > $o ) > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(choiceaxii,axiom,
% 0.29/0.46 ! [P: ( $i > $i ) > $o] :
% 0.29/0.46 ( ? [X: $i > $i] : ( P @ X )
% 0.29/0.46 => ( P @ ( epsii @ P ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(if,type,
% 0.29/0.46 if: $o > ( $i > $i ) > ( $i > $i ) > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(ifd,definition,
% 0.29/0.46 ( if
% 0.29/0.46 = ( ^ [B: $o,X: $i > $i,Y: $i > $i] :
% 0.29/0.46 ( epsii
% 0.29/0.46 @ ^ [Z: $i > $i] :
% 0.29/0.46 ( ( B
% 0.29/0.46 & ( Z = X ) )
% 0.29/0.46 | ( ~ B
% 0.29/0.46 & ( Z = Y ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(conj,conjecture,
% 0.29/0.46 ! [B: $o,X: $i > $i,Y: $i > $i] :
% 0.29/0.46 ( ( ( if @ B @ X @ Y )
% 0.29/0.46 = X )
% 0.29/0.46 | ( ( if @ B @ X @ Y )
% 0.29/0.46 = Y ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.47/1.26 ---- Embedded in THF ---
% 1.47/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.26 %%% Generated on Tue Feb 24 14:33:19 EST 2026
% 1.47/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.26 %%% Logic specification used:
% 1.47/1.26 %%% thf(spec, logic, $$dhol).
% 1.47/1.26
% 1.47/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.WzCueA1QXu/DTF2DTF18593.p
% See solution above
% 1.47/1.26 ------------------------
% 1.47/1.27 ---- Cleaned THF ---
% 1.47/1.27 thf(epsii,type,
% 1.47/1.27 epsii: ( ( $i > $i ) > $o ) > $i > $i ).
% 1.47/1.27
% 1.47/1.27 thf(choiceaxii,axiom,
% 1.47/1.27 ! [P: ( $i > $i ) > $o] :
% 1.47/1.27 ( ? [X: $i > $i] : ( P @ X )
% 1.47/1.27 => ( P @ ( epsii @ P ) ) ) ).
% 1.47/1.27
% 1.47/1.27 thf(if,type,
% 1.47/1.27 if: $o > ( $i > $i ) > ( $i > $i ) > $i > $i ).
% 1.47/1.27
% 1.47/1.27 thf(ifd,definition,
% 1.47/1.27 ( if
% 1.47/1.27 = ( ^ [B: $o,X: $i > $i,Y: $i > $i] :
% 1.47/1.27 ( epsii
% 1.47/1.27 @ ^ [Z: $i > $i] :
% 1.47/1.27 ( ( B
% 1.47/1.27 & ( Z = X ) )
% 1.47/1.27 | ( ~ B
% 1.47/1.27 & ( Z = Y ) ) ) ) ) ) ).
% 1.47/1.27
% 1.47/1.27 thf(conj,conjecture,
% 1.47/1.27 ! [B: $o,X: $i > $i,Y: $i > $i] :
% 1.47/1.27 ( ( ( if @ B @ X @ Y )
% 1.47/1.27 = X )
% 1.47/1.27 | ( ( if @ B @ X @ Y )
% 1.47/1.27 = Y ) ) ).
% 1.47/1.27 ------------------------
% 1.47/1.29 % (18781)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18593 for (2999ds/183Mi)
% 1.47/1.29 % (18785)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_18593 for (2999ds/2Mi)
% 1.47/1.29 % (18784)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18593 for (2999ds/2Mi)
% 1.47/1.29 % (18785)Instruction limit reached!
% 1.47/1.29 % (18785)------------------------------
% 1.47/1.29 % (18785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (18785)Termination reason: Unknown
% 1.47/1.29 % (18785)Termination phase: Saturation
% 1.47/1.29
% 1.47/1.29 % (18785)Memory used [KB]: 5500
% 1.47/1.29 % (18785)Time elapsed: 0.002 s
% 1.47/1.29 % (18785)Instructions burned: 3 (million)
% 1.47/1.29 % (18785)------------------------------
% 1.47/1.29 % (18785)------------------------------
% 1.47/1.29 % (18784)Instruction limit reached!
% 1.47/1.29 % (18784)------------------------------
% 1.47/1.29 % (18784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (18784)Termination reason: Unknown
% 1.47/1.29 % (18784)Termination phase: Saturation
% 1.47/1.29
% 1.47/1.29 % (18784)Memory used [KB]: 5500
% 1.47/1.29 % (18784)Time elapsed: 0.003 s
% 1.47/1.29 % (18784)Instructions burned: 3 (million)
% 1.47/1.29 % (18784)------------------------------
% 1.47/1.29 % (18784)------------------------------
% 1.47/1.29 % (18786)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_18593 for (2999ds/275Mi)
% 1.47/1.29 % (18786)Refutation not found, incomplete strategy
% 1.47/1.29 % (18786)------------------------------
% 1.47/1.29 % (18786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (18786)Termination reason: Refutation not found, incomplete strategy
% 1.47/1.29
% 1.47/1.29
% 1.47/1.29 % (18786)Memory used [KB]: 5500
% 1.47/1.29 % (18786)Time elapsed: 0.002 s
% 1.47/1.29 % (18786)Instructions burned: 1 (million)
% 1.47/1.29 % (18786)------------------------------
% 1.47/1.29 % (18786)------------------------------
% 1.47/1.29 % (18783)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_18593 for (2999ds/27Mi)
% 1.47/1.29 % (18787)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18593 for (2999ds/18Mi)
% 1.47/1.30 % (18788)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_18593 for (2999ds/3Mi)
% 1.60/1.30 % (18788)Instruction limit reached!
% 1.60/1.30 % (18788)------------------------------
% 1.60/1.30 % (18788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.30 % (18788)Termination reason: Unknown
% 1.60/1.30 % (18788)Termination phase: Saturation
% 1.60/1.30
% 1.60/1.30 % (18788)Memory used [KB]: 5500
% 1.60/1.30 % (18788)Time elapsed: 0.002 s
% 1.60/1.30 % (18788)Instructions burned: 3 (million)
% 1.60/1.30 % (18788)------------------------------
% 1.60/1.30 % (18788)------------------------------
% 1.60/1.30 % (18789)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_18593 for (2999ds/37Mi)
% 1.60/1.30 % (18782)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_18593 for (2999ds/4Mi)
% 1.60/1.30 % (18782)Instruction limit reached!
% 1.60/1.30 % (18782)------------------------------
% 1.60/1.30 % (18782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.30 % (18782)Termination reason: Unknown
% 1.60/1.30 % (18782)Termination phase: Saturation
% 1.60/1.30
% 1.60/1.30 % (18782)Memory used [KB]: 5500
% 1.60/1.30 % (18782)Time elapsed: 0.004 s
% 1.60/1.30 % (18782)Instructions burned: 4 (million)
% 1.60/1.30 % (18782)------------------------------
% 1.60/1.30 % (18782)------------------------------
% 1.60/1.30 % (18783)First to succeed.
% 1.60/1.31 % (18787)Instruction limit reached!
% 1.60/1.31 % (18787)------------------------------
% 1.60/1.31 % (18787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (18787)Termination reason: Unknown
% 1.60/1.31 % (18787)Termination phase: Saturation
% 1.60/1.31
% 1.60/1.31 % (18787)Memory used [KB]: 5628
% 1.60/1.31 % (18787)Time elapsed: 0.014 s
% 1.60/1.31 % (18787)Instructions burned: 18 (million)
% 1.60/1.31 % (18787)------------------------------
% 1.60/1.31 % (18787)------------------------------
% 1.60/1.31 % (18790)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_18593 for (2999ds/15Mi)
% 1.60/1.31 % (18791)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_18593 for (2999ds/3Mi)
% 1.60/1.31 % (18791)Refutation not found, incomplete strategy
% 1.60/1.31 % (18791)------------------------------
% 1.60/1.31 % (18791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (18791)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.31
% 1.60/1.31
% 1.60/1.31 % (18791)Memory used [KB]: 5500
% 1.60/1.31 % (18791)Time elapsed: 0.001 s
% 1.60/1.31 % (18791)Instructions burned: 1 (million)
% 1.60/1.31 % (18791)------------------------------
% 1.60/1.31 % (18791)------------------------------
% 1.60/1.31 % (18790)Refutation not found, incomplete strategy
% 1.60/1.31 % (18790)------------------------------
% 1.60/1.31 % (18790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (18790)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.31
% 1.60/1.31
% 1.60/1.31 % (18790)Memory used [KB]: 5500
% 1.60/1.31 % (18790)Time elapsed: 0.003 s
% 1.60/1.31 % (18790)Instructions burned: 2 (million)
% 1.60/1.31 % (18790)------------------------------
% 1.60/1.31 % (18790)------------------------------
% 1.60/1.31 % (18783)Refutation found. Thanks to Tanya!
% 1.60/1.31 % SZS status Theorem for DTF2THF_18593
% 1.60/1.31 % SZS output start Proof for DTF2THF_18593
% 1.60/1.31 thf(func_def_0, type, epsii: (($i > $i) > $o) > $i > $i).
% 1.60/1.31 thf(func_def_2, type, if: $o > ($i > $i) > ($i > $i) > $i > $i).
% 1.60/1.31 thf(func_def_3, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.60/1.31 thf(func_def_15, type, sK0: $i > $i).
% 1.60/1.31 thf(func_def_16, type, sK1: $i > $i).
% 1.60/1.31 thf(func_def_19, type, ph4: !>[X0: $tType]:(X0)).
% 1.60/1.31 thf(f292,plain,(
% 1.60/1.31 $false),
% 1.60/1.31 inference(avatar_sat_refutation,[status(thm)],[f94,f205,f259,f264,f285,f291])).
% 1.60/1.31 thf(f291,plain,(
% 1.60/1.31 ~spl3_6),
% 1.60/1.31 inference(avatar_contradiction_clause,[status(thm)],[f290])).
% 1.60/1.31 thf(f290,plain,(
% 1.60/1.31 $false | ~spl3_6),
% 1.60/1.31 inference(equality_resolution,[status(thm)],[f89])).
% 1.60/1.31 thf(f89,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : ((sK0 != X1)) ) | ~spl3_6),
% 1.60/1.31 inference(avatar_component_clause,[status(thm)],[f88])).
% 1.60/1.31 thf(f88,definition,(
% 1.60/1.31 spl3_6 <=> ! [X1 : $i > $i] : (sK0 != X1)),
% 1.60/1.31 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 1.60/1.31 thf(f285,plain,(
% 1.60/1.31 spl3_6 | spl3_2 | spl3_5 | spl3_3),
% 1.60/1.31 inference(avatar_split_clause,[status(thm)],[f191,f73,f81,f69,f88])).
% 1.60/1.31 thf(f69,definition,(
% 1.60/1.31 spl3_2 <=> ((epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0))))) = sK0)),
% 1.60/1.31 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.60/1.31 thf(f81,definition,(
% 1.60/1.31 spl3_5 <=> (sK2 = $true)),
% 1.60/1.31 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.60/1.31 thf(f73,definition,(
% 1.60/1.31 spl3_3 <=> (sK1 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0))))))),
% 1.60/1.31 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.60/1.31 thf(f191,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : ((sK2 = $true) | (sK1 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))))) | (sK0 != X1) | ((epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0))))) = sK0)) )),
% 1.60/1.31 inference(equality_proxy_clausification,[status(thm)],[f190])).
% 1.60/1.31 thf(f190,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : ((sK1 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))))) | ((epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0))))) = sK0) | (sK2 = $true) | ((sK0 = X1) = $false)) )),
% 1.60/1.31 inference(not_proxy_clausification,[status(thm)],[f189])).
% 1.60/1.31 thf(f189,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : ((sK1 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))))) | ((~ sK2) = $false) | ((sK0 = X1) = $false) | ((epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0))))) = sK0)) )),
% 1.60/1.31 inference(binary_proxy_clausification,[status(thm)],[f188])).
% 1.60/1.31 thf(f188,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : ((((~ sK2) & (sK0 = X1)) = $false) | ((epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0))))) = sK0) | (sK1 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0))))))) )),
% 1.60/1.31 inference(binary_proxy_clausification,[status(thm)],[f186])).
% 1.60/1.31 thf(f186,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : ((sK1 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))))) | ((((~ sK2) & (sK0 = X1)) | (sK2 & (sK1 = X1))) = $false) | ((epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0))))) = sK0)) )),
% 1.60/1.31 inference(equality_proxy_clausification,[status(thm)],[f174])).
% 1.60/1.31 thf(f174,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : (((sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))))) = $true) | (sK1 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))))) | ((((~ sK2) & (sK0 = X1)) | (sK2 & (sK1 = X1))) = $false)) )),
% 1.60/1.31 inference(binary_proxy_clausification,[status(thm)],[f173])).
% 1.60/1.31 thf(f173,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : (($true = ((~ sK2) & (sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))))))) | (sK1 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))))) | ((((~ sK2) & (sK0 = X1)) | (sK2 & (sK1 = X1))) = $false)) )),
% 1.60/1.31 inference(equality_proxy_clausification,[status(thm)],[f149])).
% 1.60/1.31 thf(f149,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : (((sK1 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))))) = $true) | ($true = ((~ sK2) & (sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))))))) | ((((~ sK2) & (sK0 = X1)) | (sK2 & (sK1 = X1))) = $false)) )),
% 1.60/1.31 inference(binary_proxy_clausification,[status(thm)],[f148])).
% 1.60/1.31 thf(f148,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : (((sK2 & (sK1 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0))))))) = $true) | ($true = ((~ sK2) & (sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))))))) | ((((~ sK2) & (sK0 = X1)) | (sK2 & (sK1 = X1))) = $false)) )),
% 1.60/1.31 inference(binary_proxy_clausification,[status(thm)],[f147])).
% 1.60/1.31 thf(f147,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : (((((~ sK2) & (sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0))))))) | (sK2 & (sK1 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))))))) = $true) | ((((~ sK2) & (sK0 = X1)) | (sK2 & (sK1 = X1))) = $false)) )),
% 1.60/1.31 inference(beta_eta_normalization,[status(thm)],[f145])).
% 1.60/1.31 thf(f145,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : ((((^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))) @ (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))))) = $true) | (((^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))) @ X1) = $false)) )),
% 1.60/1.31 introduced(definition,[],[choice_axiom])).
% 1.60/1.31 thf(f264,plain,(
% 1.60/1.31 ~spl3_4),
% 1.60/1.31 inference(avatar_contradiction_clause,[status(thm)],[f263])).
% 1.60/1.31 thf(f263,plain,(
% 1.60/1.31 $false | ~spl3_4),
% 1.60/1.31 inference(equality_resolution,[status(thm)],[f78])).
% 1.60/1.31 thf(f78,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : ((sK1 != X1)) ) | ~spl3_4),
% 1.60/1.31 inference(avatar_component_clause,[status(thm)],[f77])).
% 1.60/1.31 thf(f77,definition,(
% 1.60/1.31 spl3_4 <=> ! [X1 : $i > $i] : (sK1 != X1)),
% 1.60/1.31 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.60/1.31 thf(f259,plain,(
% 1.60/1.31 spl3_4 | spl3_3 | ~spl3_5),
% 1.60/1.31 inference(avatar_split_clause,[status(thm)],[f258,f81,f73,f77])).
% 1.60/1.31 thf(f258,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : ((sK1 != X1) | (sK1 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0))))))) ) | ~spl3_5),
% 1.60/1.31 inference(trivial_inequality_removal,[status(thm)],[f257])).
% 1.60/1.31 thf(f257,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : ((sK1 != X1) | ($false = $true) | (sK1 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0))))))) ) | ~spl3_5),
% 1.60/1.31 inference(forward_demodulation,[status(thm)],[f233,f83])).
% 1.60/1.31 thf(f83,plain,(
% 1.60/1.31 (sK2 = $true) | ~spl3_5),
% 1.60/1.31 inference(avatar_component_clause,[status(thm)],[f81])).
% 1.60/1.31 thf(f233,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : ((sK1 != X1) | (sK1 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))))) | (sK2 = $false)) )),
% 1.60/1.31 inference(equality_proxy_clausification,[status(thm)],[f232])).
% 1.60/1.31 thf(f232,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : ((sK2 = $false) | ((sK1 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))))) = $true) | (sK1 != X1)) )),
% 1.60/1.31 inference(duplicate_literal_removal,[status(thm)],[f231])).
% 1.60/1.31 thf(f231,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : ((sK2 = $false) | (sK1 != X1) | (sK2 = $false) | ((sK1 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))))) = $true)) )),
% 1.60/1.31 inference(not_proxy_clausification,[status(thm)],[f230])).
% 1.60/1.31 thf(f230,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : ((sK2 = $false) | (sK1 != X1) | ((~ sK2) = $true) | ((sK1 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))))) = $true)) )),
% 1.60/1.31 inference(equality_proxy_clausification,[status(thm)],[f229])).
% 1.60/1.31 thf(f229,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : (($false = (sK1 = X1)) | (sK2 = $false) | ((sK1 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))))) = $true) | ((~ sK2) = $true)) )),
% 1.60/1.31 inference(binary_proxy_clausification,[status(thm)],[f222])).
% 1.60/1.31 thf(f222,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : (((sK2 & (sK1 = X1)) = $false) | ((sK1 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))))) = $true) | ((~ sK2) = $true)) )),
% 1.60/1.31 inference(binary_proxy_clausification,[status(thm)],[f210])).
% 1.60/1.31 thf(f210,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : (((((~ sK2) & (sK0 = X1)) | (sK2 & (sK1 = X1))) = $false) | ((~ sK2) = $true) | ((sK1 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))))) = $true)) )),
% 1.60/1.31 inference(binary_proxy_clausification,[status(thm)],[f209])).
% 1.60/1.31 thf(f209,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : (((sK2 & (sK1 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0))))))) = $true) | ((((~ sK2) & (sK0 = X1)) | (sK2 & (sK1 = X1))) = $false) | ((~ sK2) = $true)) )),
% 1.60/1.31 inference(binary_proxy_clausification,[status(thm)],[f207])).
% 1.60/1.31 thf(f207,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : (($true = ((~ sK2) & (sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))))))) | ((sK2 & (sK1 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0))))))) = $true) | ((((~ sK2) & (sK0 = X1)) | (sK2 & (sK1 = X1))) = $false)) )),
% 1.60/1.31 inference(binary_proxy_clausification,[status(thm)],[f206])).
% 1.60/1.31 thf(f206,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : (((((~ sK2) & (sK0 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0))))))) | (sK2 & (sK1 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))))))) = $true) | ((((~ sK2) & (sK0 = X1)) | (sK2 & (sK1 = X1))) = $false)) )),
% 1.60/1.31 inference(beta_eta_normalization,[status(thm)],[f200])).
% 1.60/1.31 thf(f200,plain,(
% 1.60/1.31 ( ! [X1 : $i > $i] : ((((^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))) @ (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))))) = $true) | (((^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))) @ X1) = $false)) )),
% 1.60/1.31 introduced(definition,[],[choice_axiom])).
% 1.60/1.31 thf(f205,plain,(
% 1.60/1.31 ~spl3_3),
% 1.60/1.31 inference(avatar_contradiction_clause,[status(thm)],[f204])).
% 1.60/1.31 thf(f204,plain,(
% 1.60/1.31 $false | ~spl3_3),
% 1.60/1.31 inference(trivial_inequality_removal,[status(thm)],[f203])).
% 1.60/1.31 thf(f203,plain,(
% 1.60/1.31 (sK1 != sK1) | ~spl3_3),
% 1.60/1.31 inference(superposition,[status(thm)],[f21,f75])).
% 1.60/1.31 thf(f75,plain,(
% 1.60/1.31 (sK1 = (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0)))))) | ~spl3_3),
% 1.60/1.31 inference(avatar_component_clause,[status(thm)],[f73])).
% 1.60/1.31 thf(f21,plain,(
% 1.60/1.31 (sK1 != (epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0))))))),
% 1.60/1.31 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.60/1.31 thf(f19,plain,(
% 1.60/1.31 (sK1 != ((^[Y0 : $o]: ((^[Y1 : $i > $i]: ((^[Y2 : $i > $i]: (epsii @ (^[Y3 : $i > $i]: (((~ Y0) & (Y2 = Y3)) | (Y0 & (Y1 = Y3)))))))))) @ sK2 @ sK1 @ sK0))),
% 1.60/1.31 inference(definition_unfolding,[status(thm)],[f17,f18])).
% 1.60/1.31 thf(f18,plain,(
% 1.60/1.31 (if = (^[Y0 : $o]: ((^[Y1 : $i > $i]: ((^[Y2 : $i > $i]: (epsii @ (^[Y3 : $i > $i]: (((~ Y0) & (Y2 = Y3)) | (Y0 & (Y1 = Y3)))))))))))),
% 1.60/1.31 inference(cnf_transformation,[status(thm)],[f7])).
% 1.60/1.31 thf(f7,plain,(
% 1.60/1.31 (if = (^[Y0 : $o]: ((^[Y1 : $i > $i]: ((^[Y2 : $i > $i]: (epsii @ (^[Y3 : $i > $i]: (((~ Y0) & (Y2 = Y3)) | (Y0 & (Y1 = Y3)))))))))))),
% 1.60/1.31 inference(fool_elimination,[status(thm)],[f6])).
% 1.60/1.31 thf(f6,plain,(
% 1.60/1.31 (if = (^[X0 : $o, X1 : $i > $i, X2 : $i > $i] : (epsii @ (^[X3 : $i > $i] : (((X1 = X3) & X0) | ((X2 = X3) & ~X0))))))),
% 1.60/1.31 inference(rectify,[status(thm)],[f2])).
% 1.60/1.31 thf(f2,axiom,(
% 1.60/1.31 (if = (^[X2 : $o, X1 : $i > $i, X3 : $i > $i] : (epsii @ (^[X4 : $i > $i] : (((X1 = X4) & X2) | ((X3 = X4) & ~X2))))))),
% 1.60/1.31 file('/export/starexec/sandbox/tmp/tmp.WzCueA1QXu/DTF2THF_18593.p',ifd)).
% 1.60/1.31 thf(f17,plain,(
% 1.60/1.31 ((if @ sK2 @ sK1 @ sK0) != sK1)),
% 1.60/1.31 inference(cnf_transformation,[status(thm)],[f14])).
% 1.60/1.31 thf(f14,plain,(
% 1.60/1.31 ((if @ sK2 @ sK1 @ sK0) != sK1) & ((if @ sK2 @ sK1 @ sK0) != sK0)),
% 1.60/1.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f12,f13])).
% 1.60/1.31 thf(f13,plain,(
% 1.60/1.31 ? [X0 : $i > $i,X1 : $i > $i,X2 : $o] : (((if @ X2 @ X1 @ X0) != X1) & ((if @ X2 @ X1 @ X0) != X0)) => (((if @ sK2 @ sK1 @ sK0) != sK1) & ((if @ sK2 @ sK1 @ sK0) != sK0))),
% 1.60/1.31 introduced(definition,[],[choice_axiom])).
% 1.60/1.31 thf(f12,plain,(
% 1.60/1.31 ? [X0 : $i > $i,X1 : $i > $i,X2 : $o] : (((if @ X2 @ X1 @ X0) != X1) & ((if @ X2 @ X1 @ X0) != X0))),
% 1.60/1.31 inference(ennf_transformation,[status(thm)],[f10])).
% 1.60/1.31 thf(f10,plain,(
% 1.60/1.31 ~! [X0 : $i > $i,X1 : $i > $i,X2 : $o] : (((if @ X2 @ X1 @ X0) = X1) | ((if @ X2 @ X1 @ X0) = X0))),
% 1.60/1.31 inference(rectify,[status(thm)],[f4])).
% 1.60/1.31 thf(f4,negated_conjecture,(
% 1.60/1.31 ~! [X3 : $i > $i,X1 : $i > $i,X2 : $o] : (((if @ X2 @ X1 @ X3) = X3) | ((if @ X2 @ X1 @ X3) = X1))),
% 1.60/1.31 inference(negated_conjecture,[status(cth)],[f3])).
% 1.60/1.31 thf(f3,conjecture,(
% 1.60/1.31 ! [X3 : $i > $i,X1 : $i > $i,X2 : $o] : (((if @ X2 @ X1 @ X3) = X3) | ((if @ X2 @ X1 @ X3) = X1))),
% 1.60/1.31 file('/export/starexec/sandbox/tmp/tmp.WzCueA1QXu/DTF2THF_18593.p',conj)).
% 1.60/1.31 thf(f94,plain,(
% 1.60/1.31 ~spl3_2),
% 1.60/1.31 inference(avatar_split_clause,[status(thm)],[f22,f69])).
% 1.60/1.31 thf(f22,plain,(
% 1.60/1.31 ((epsii @ (^[Y0 : $i > $i]: (((~ sK2) & (sK0 = Y0)) | (sK2 & (sK1 = Y0))))) != sK0)),
% 1.60/1.31 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.60/1.31 thf(f20,plain,(
% 1.60/1.31 (((^[Y0 : $o]: ((^[Y1 : $i > $i]: ((^[Y2 : $i > $i]: (epsii @ (^[Y3 : $i > $i]: (((~ Y0) & (Y2 = Y3)) | (Y0 & (Y1 = Y3)))))))))) @ sK2 @ sK1 @ sK0) != sK0)),
% 1.60/1.31 inference(definition_unfolding,[status(thm)],[f16,f18])).
% 1.60/1.31 thf(f16,plain,(
% 1.60/1.31 ((if @ sK2 @ sK1 @ sK0) != sK0)),
% 1.60/1.31 inference(cnf_transformation,[status(thm)],[f14])).
% 1.60/1.31 % SZS output end Proof for DTF2THF_18593
% 1.60/1.31 % (18783)------------------------------
% 1.60/1.31 % (18783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (18783)Termination reason: Refutation
% 1.60/1.31
% 1.60/1.31 % (18783)Memory used [KB]: 5628
% 1.60/1.31 % (18783)Time elapsed: 0.015 s
% 1.60/1.31 % (18783)Instructions burned: 17 (million)
% 1.60/1.31 % (18783)------------------------------
% 1.60/1.31 % (18783)------------------------------
% 1.60/1.31 % (18780)Success in time 0.029 s
%------------------------------------------------------------------------------