%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU550^2 : 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 : n022.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 09:35:13 AM UTC 2026
% Result : Theorem 1.50s 1.26s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 12
% Syntax : Number of formulae : 137 ( 9 unt; 0 typ; 9 def)
% Number of atoms : 1105 ( 342 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 1051 ( 152 ~; 270 |; 35 &; 454 @)
% ( 15 <=>; 69 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 17 usr; 15 con; 0-2 aty)
% ( 39 !!; 17 ??; 0 @@+; 0 @@-)
% Number of variables : 217 ( 92 ^; 119 !; 6 ?; 217 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
exu: ( $i > $o ) > $o ).
thf(func_def_2,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_14,type,
sK0: $i > $o ).
thf(func_def_15,type,
sK1: $i > $o ).
thf(func_def_17,type,
sK3: $i > $i ).
thf(func_def_18,type,
sK4: $i > $i ).
thf(f253,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f74,f79,f84,f85,f92,f96,f100,f101,f126,f161,f191,f234,f251]) ).
thf(f251,plain,
( ~ spl2_1
| ~ spl2_3
| ~ spl2_6
| ~ spl2_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f250]) ).
thf(f250,plain,
( $false
| ~ spl2_1
| ~ spl2_3
| ~ spl2_6
| ~ spl2_7 ),
inference(trivial_inequality_removal,[status(thm)],[f247]) ).
thf(f247,plain,
( ( $false = $true )
| ~ spl2_1
| ~ spl2_3
| ~ spl2_6
| ~ spl2_7 ),
inference(backward_demodulation,[status(thm)],[f177,f246]) ).
thf(f246,plain,
( ( $false
= ( sK0 @ sK5 ) )
| ~ spl2_1
| ~ spl2_6
| ~ spl2_7 ),
inference(equality_resolution,[status(thm)],[f245]) ).
thf(f245,plain,
( ! [X0: $i] :
( ( sK5 != X0 )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_1
| ~ spl2_6
| ~ spl2_7 ),
inference(duplicate_literal_removal,[status(thm)],[f242]) ).
thf(f242,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 )
= $false )
| ( sK5 != X0 )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_1
| ~ spl2_6
| ~ spl2_7 ),
inference(superposition,[status(thm)],[f91,f208]) ).
thf(f208,plain,
( ! [X0: $i] :
( ( sK5
= ( sK4 @ X0 ) )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_1
| ~ spl2_7 ),
inference(trivial_inequality_removal,[status(thm)],[f207]) ).
thf(f207,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 )
= $false )
| ( $false = $true )
| ( sK5
= ( sK4 @ X0 ) ) )
| ~ spl2_1
| ~ spl2_7 ),
inference(superposition,[status(thm)],[f199,f95]) ).
thf(f95,plain,
( ! [X2: $i] :
( ( ( sK0 @ ( sK4 @ X2 ) )
= $true )
| ( $false
= ( sK0 @ X2 ) ) )
| ~ spl2_7 ),
inference(avatar_component_clause,[status(thm)],[f94]) ).
thf(f94,definition,
( spl2_7
<=> ! [X2: $i] :
( ( ( sK0 @ ( sK4 @ X2 ) )
= $true )
| ( $false
= ( sK0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_7])],[avatar_definition]) ).
thf(f199,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 )
= $false )
| ( sK5 = X0 ) )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f198]) ).
thf(f198,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 )
= $false )
| ( $false = $true )
| ( sK5 = X0 ) )
| ~ spl2_1 ),
inference(superposition,[status(thm)],[f18,f70]) ).
thf(f70,plain,
( ! [X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( sK5 = X1 ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f69]) ).
thf(f69,definition,
( spl2_1
<=> ! [X1: $i] :
( ( sK5 = X1 )
| ( ( sK1 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f18,plain,
! [X3: $i] :
( ( ( sK1 @ X3 )
= $true )
| ( ( sK0 @ X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
! [X3: $i] :
( ( sK0 @ X3 )
= ( sK1 @ X3 ) ),
inference(equality_resolution,[status(thm)],[f12]) ).
thf(f12,plain,
! [X2: $i,X3: $i] :
( ( X2 != X3 )
| ( ( sK1 @ X3 )
= ( sK0 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( exu
@ ^ [Y0: $i] : ( sK1 @ Y0 ) )
!= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
& ! [X2: $i,X3: $i] :
( ( X2 != X3 )
| ( ( sK1 @ X3 )
= ( sK0 @ X2 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f10]) ).
thf(f10,plain,
( ? [X0: $i > $o,X1: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
!= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ! [X2: $i,X3: $i] :
( ( X2 != X3 )
| ( ( X0 @ X2 )
= ( X1 @ X3 ) ) ) )
=> ( ( ( exu
@ ^ [Y0: $i] : ( sK1 @ Y0 ) )
!= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
& ! [X3: $i,X2: $i] :
( ( X2 != X3 )
| ( ( sK1 @ X3 )
= ( sK0 @ X2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: $i > $o,X1: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
!= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ! [X2: $i,X3: $i] :
( ( X2 != X3 )
| ( ( X0 @ X2 )
= ( X1 @ X3 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X0 @ X2 )
= ( X1 @ X3 ) ) )
=> ( ( exu
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ! [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X3 )
<=> ( X0 @ X2 ) ) )
=> ( ( exu
@ ^ [X4: $i] : ( X0 @ X4 ) )
<=> ( exu
@ ^ [X5: $i] : ( X1 @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X3: $i > $o,X0: $i > $o] :
( ! [X2: $i,X1: $i] :
( ( X1 = X2 )
=> ( ( X0 @ X1 )
<=> ( X3 @ X2 ) ) )
=> ( ( exu
@ ^ [X1: $i] : ( X3 @ X1 ) )
<=> ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X3: $i > $o,X0: $i > $o] :
( ! [X2: $i,X1: $i] :
( ( X1 = X2 )
=> ( ( X0 @ X1 )
<=> ( X3 @ X2 ) ) )
=> ( ( exu
@ ^ [X1: $i] : ( X3 @ X1 ) )
<=> ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.WqCf7Bvv49/DTF2THF_1945.p',exu__Cong) ).
thf(f91,plain,
( ! [X2: $i] :
( ( ( sK4 @ X2 )
!= X2 )
| ( $false
= ( sK0 @ X2 ) ) )
| ~ spl2_6 ),
inference(avatar_component_clause,[status(thm)],[f90]) ).
thf(f90,definition,
( spl2_6
<=> ! [X2: $i] :
( ( ( sK4 @ X2 )
!= X2 )
| ( $false
= ( sK0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_6])],[avatar_definition]) ).
thf(f177,plain,
( ( ( sK0 @ sK5 )
= $true )
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f176]) ).
thf(f176,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $false = $true )
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f78,f17]) ).
thf(f17,plain,
! [X3: $i] :
( ( ( sK1 @ X3 )
= $false )
| ( ( sK0 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f78,plain,
( ( ( sK1 @ sK5 )
= $true )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f76]) ).
thf(f76,definition,
( spl2_3
<=> ( ( sK1 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f234,plain,
( ~ spl2_1
| ~ spl2_3
| ~ spl2_5
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f233]) ).
thf(f233,plain,
( $false
| ~ spl2_1
| ~ spl2_3
| ~ spl2_5
| ~ spl2_8 ),
inference(trivial_inequality_removal,[status(thm)],[f229]) ).
thf(f229,plain,
( ( $false = $true )
| ~ spl2_1
| ~ spl2_3
| ~ spl2_5
| ~ spl2_8 ),
inference(backward_demodulation,[status(thm)],[f78,f222]) ).
thf(f222,plain,
( ( ( sK1 @ sK5 )
= $false )
| ~ spl2_1
| ~ spl2_5
| ~ spl2_8 ),
inference(equality_resolution,[status(thm)],[f221]) ).
thf(f221,plain,
( ! [X0: $i] :
( ( sK5 != X0 )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl2_1
| ~ spl2_5
| ~ spl2_8 ),
inference(duplicate_literal_removal,[status(thm)],[f219]) ).
thf(f219,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( $false
= ( sK1 @ X0 ) )
| ( sK5 != X0 ) )
| ~ spl2_1
| ~ spl2_5
| ~ spl2_8 ),
inference(superposition,[status(thm)],[f88,f216]) ).
thf(f216,plain,
( ! [X0: $i] :
( ( sK5
= ( sK3 @ X0 ) )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl2_1
| ~ spl2_8 ),
inference(trivial_inequality_removal,[status(thm)],[f210]) ).
thf(f210,plain,
( ! [X0: $i] :
( ( sK5
= ( sK3 @ X0 ) )
| ( $false
= ( sK1 @ X0 ) )
| ( $false = $true ) )
| ~ spl2_1
| ~ spl2_8 ),
inference(superposition,[status(thm)],[f99,f70]) ).
thf(f99,plain,
( ! [X1: $i] :
( ( ( sK1 @ ( sK3 @ X1 ) )
= $true )
| ( ( sK1 @ X1 )
= $false ) )
| ~ spl2_8 ),
inference(avatar_component_clause,[status(thm)],[f98]) ).
thf(f98,definition,
( spl2_8
<=> ! [X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( ( sK1 @ ( sK3 @ X1 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl2_8])],[avatar_definition]) ).
thf(f88,plain,
( ! [X1: $i] :
( ( ( sK3 @ X1 )
!= X1 )
| ( ( sK1 @ X1 )
= $false ) )
| ~ spl2_5 ),
inference(avatar_component_clause,[status(thm)],[f87]) ).
thf(f87,definition,
( spl2_5
<=> ! [X1: $i] :
( ( ( sK3 @ X1 )
!= X1 )
| ( ( sK1 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl2_5])],[avatar_definition]) ).
thf(f191,plain,
( ~ spl2_4
| spl2_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f190]) ).
thf(f190,plain,
( $false
| ~ spl2_4
| spl2_9 ),
inference(trivial_inequality_removal,[status(thm)],[f187]) ).
thf(f187,plain,
( ( $false = $true )
| ~ spl2_4
| spl2_9 ),
inference(backward_demodulation,[status(thm)],[f83,f186]) ).
thf(f186,plain,
( ( $false
= ( sK0 @ sK6 ) )
| spl2_9 ),
inference(trivial_inequality_removal,[status(thm)],[f184]) ).
thf(f184,plain,
( ( $true != $true )
| ( $false
= ( sK0 @ sK6 ) )
| spl2_9 ),
inference(superposition,[status(thm)],[f145,f18]) ).
thf(f145,plain,
( ( $true
!= ( sK1 @ sK6 ) )
| spl2_9 ),
inference(avatar_component_clause,[status(thm)],[f144]) ).
thf(f144,definition,
( spl2_9
<=> ( $true
= ( sK1 @ sK6 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_9])],[avatar_definition]) ).
thf(f83,plain,
( ( ( sK0 @ sK6 )
= $true )
| ~ spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f81]) ).
thf(f81,definition,
( spl2_4
<=> ( ( sK0 @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f161,plain,
( ~ spl2_2
| ~ spl2_5
| ~ spl2_8
| ~ spl2_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f160]) ).
thf(f160,plain,
( $false
| ~ spl2_2
| ~ spl2_5
| ~ spl2_8
| ~ spl2_9 ),
inference(trivial_inequality_removal,[status(thm)],[f156]) ).
thf(f156,plain,
( ( $false = $true )
| ~ spl2_2
| ~ spl2_5
| ~ spl2_8
| ~ spl2_9 ),
inference(backward_demodulation,[status(thm)],[f146,f155]) ).
thf(f155,plain,
( ( $false
= ( sK1 @ sK6 ) )
| ~ spl2_2
| ~ spl2_5
| ~ spl2_8 ),
inference(equality_resolution,[status(thm)],[f140]) ).
thf(f140,plain,
( ! [X0: $i] :
( ( sK6 != X0 )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl2_2
| ~ spl2_5
| ~ spl2_8 ),
inference(duplicate_literal_removal,[status(thm)],[f139]) ).
thf(f139,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( sK6 != X0 )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl2_2
| ~ spl2_5
| ~ spl2_8 ),
inference(superposition,[status(thm)],[f88,f135]) ).
thf(f135,plain,
( ! [X0: $i] :
( ( sK6
= ( sK3 @ X0 ) )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl2_2
| ~ spl2_8 ),
inference(trivial_inequality_removal,[status(thm)],[f134]) ).
thf(f134,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( $false = $true )
| ( sK6
= ( sK3 @ X0 ) ) )
| ~ spl2_2
| ~ spl2_8 ),
inference(superposition,[status(thm)],[f73,f131]) ).
thf(f131,plain,
( ! [X0: $i] :
( ( ( sK0 @ ( sK3 @ X0 ) )
= $true )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl2_8 ),
inference(trivial_inequality_removal,[status(thm)],[f130]) ).
thf(f130,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( $false = $true )
| ( ( sK0 @ ( sK3 @ X0 ) )
= $true ) )
| ~ spl2_8 ),
inference(superposition,[status(thm)],[f17,f99]) ).
thf(f73,plain,
( ! [X2: $i] :
( ( $false
= ( sK0 @ X2 ) )
| ( sK6 = X2 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f72]) ).
thf(f72,definition,
( spl2_2
<=> ! [X2: $i] :
( ( $false
= ( sK0 @ X2 ) )
| ( sK6 = X2 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f146,plain,
( ( $true
= ( sK1 @ sK6 ) )
| ~ spl2_9 ),
inference(avatar_component_clause,[status(thm)],[f144]) ).
thf(f126,plain,
( ~ spl2_2
| ~ spl2_4
| ~ spl2_6
| ~ spl2_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f125]) ).
thf(f125,plain,
( $false
| ~ spl2_2
| ~ spl2_4
| ~ spl2_6
| ~ spl2_7 ),
inference(trivial_inequality_removal,[status(thm)],[f121]) ).
thf(f121,plain,
( ( $false = $true )
| ~ spl2_2
| ~ spl2_4
| ~ spl2_6
| ~ spl2_7 ),
inference(backward_demodulation,[status(thm)],[f83,f120]) ).
thf(f120,plain,
( ( $false
= ( sK0 @ sK6 ) )
| ~ spl2_2
| ~ spl2_6
| ~ spl2_7 ),
inference(equality_resolution,[status(thm)],[f119]) ).
thf(f119,plain,
( ! [X0: $i] :
( ( sK6 != X0 )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_2
| ~ spl2_6
| ~ spl2_7 ),
inference(duplicate_literal_removal,[status(thm)],[f117]) ).
thf(f117,plain,
( ! [X0: $i] :
( ( sK6 != X0 )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_2
| ~ spl2_6
| ~ spl2_7 ),
inference(superposition,[status(thm)],[f91,f114]) ).
thf(f114,plain,
( ! [X0: $i] :
( ( sK6
= ( sK4 @ X0 ) )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl2_2
| ~ spl2_7 ),
inference(trivial_inequality_removal,[status(thm)],[f112]) ).
thf(f112,plain,
( ! [X0: $i] :
( ( sK6
= ( sK4 @ X0 ) )
| ( ( sK0 @ X0 )
= $false )
| ( $false = $true ) )
| ~ spl2_2
| ~ spl2_7 ),
inference(superposition,[status(thm)],[f95,f73]) ).
thf(f101,plain,
( spl2_8
| spl2_7 ),
inference(avatar_split_clause,[status(thm)],[f35,f94,f98]) ).
thf(f35,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ ( sK3 @ X1 ) )
= $true )
| ( ( sK0 @ ( sK4 @ X2 ) )
= $true )
| ( ( sK1 @ X1 )
= $false )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i,X1: $i] :
( ( ( ( sK0 @ ( sK4 @ X2 ) )
=> ( X2
= ( sK4 @ X2 ) ) )
= $false )
| ( ( sK1 @ ( sK3 @ X1 ) )
= $true )
| ( ( sK1 @ X1 )
= $false )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 ) )
| ( ( ( sK1 @ ( sK3 @ X1 ) )
=> ( X1
= ( sK3 @ X1 ) ) )
= $false )
| ( ( ( sK0 @ ( sK4 @ X2 ) )
=> ( X2
= ( sK4 @ X2 ) ) )
= $false )
| ( ( sK1 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 ) )
| ( ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X2 = Y0 ) )
@ ( sK4 @ X2 ) )
= $false )
| ( ( ( sK1 @ ( sK3 @ X1 ) )
=> ( X1
= ( sK3 @ X1 ) ) )
= $false )
| ( ( sK1 @ X1 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X2 = Y0 ) ) )
= $false )
| ( $false
= ( sK0 @ X2 ) )
| ( ( ( sK1 @ ( sK3 @ X1 ) )
=> ( X1
= ( sK3 @ X1 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( $false
= ( ( sK0 @ X2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( X2 = Y0 ) ) ) ) )
| ( ( ( sK1 @ ( sK3 @ X1 ) )
=> ( X1
= ( sK3 @ X1 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ X2 )
= $false )
| ( ( ( sK1 @ ( sK3 @ X1 ) )
=> ( X1
= ( sK3 @ X1 ) ) )
= $false )
| ( ( sK1 @ X1 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: $i] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) )
= $false )
| ( ( sK1 @ X1 )
= $false )
| ( ( ( sK1 @ ( sK3 @ X1 ) )
=> ( X1
= ( sK3 @ X1 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( X1 = Y0 ) )
@ ( sK3 @ X1 ) ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( X1 = Y0 ) ) ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: $i] :
( ( ( ( sK1 @ X1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( X1 = Y0 ) ) ) )
= $false )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
! [X1: $i] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) )
!= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ),
inference(definition_unfolding,[status(thm)],[f13,f14,f14]) ).
thf(f14,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,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.WqCf7Bvv49/DTF2THF_1945.p',exu_def) ).
thf(f13,plain,
( ( exu
@ ^ [Y0: $i] : ( sK1 @ Y0 ) )
!= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f100,plain,
( spl2_8
| spl2_6 ),
inference(avatar_split_clause,[status(thm)],[f36,f90,f98]) ).
thf(f36,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( $false
= ( sK0 @ X2 ) )
| ( ( sK1 @ ( sK3 @ X1 ) )
= $true )
| ( ( sK4 @ X2 )
!= X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f34]) ).
thf(f34,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ ( sK3 @ X1 ) )
= $true )
| ( $false
= ( X2
= ( sK4 @ X2 ) ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( sK1 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f96,plain,
( spl2_7
| spl2_5 ),
inference(avatar_split_clause,[status(thm)],[f39,f87,f94]) ).
thf(f39,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( ( sK3 @ X1 )
!= X1 )
| ( ( sK0 @ ( sK4 @ X2 ) )
= $true )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X2: $i,X1: $i] :
( ( ( X1
= ( sK3 @ X1 ) )
= $false )
| ( ( sK0 @ ( sK4 @ X2 ) )
= $true )
| ( $false
= ( sK0 @ X2 ) )
| ( ( sK1 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( ( ( sK0 @ ( sK4 @ X2 ) )
=> ( X2
= ( sK4 @ X2 ) ) )
= $false )
| ( ( X1
= ( sK3 @ X1 ) )
= $false )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f92,plain,
( spl2_5
| spl2_6 ),
inference(avatar_split_clause,[status(thm)],[f41,f90,f87]) ).
thf(f41,plain,
! [X2: $i,X1: $i] :
( ( ( sK3 @ X1 )
!= X1 )
| ( ( sK4 @ X2 )
!= X2 )
| ( ( sK1 @ X1 )
= $false )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 ) )
| ( ( sK4 @ X2 )
!= X2 )
| ( ( X1
= ( sK3 @ X1 ) )
= $false )
| ( ( sK1 @ X1 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 ) )
| ( ( sK1 @ X1 )
= $false )
| ( $false
= ( X2
= ( sK4 @ X2 ) ) )
| ( ( X1
= ( sK3 @ X1 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f85,plain,
( spl2_4
| spl2_3 ),
inference(avatar_split_clause,[status(thm)],[f49,f76,f81]) ).
thf(f49,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( ( sK0 @ sK6 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( ( ( sK0 @ sK6 )
= $true )
| ( ( ( sK1 @ sK5 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ( ( sK0 @ sK6 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK6 = Y0 ) ) ) )
= $true )
| ( ( ( sK1 @ sK5 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f44]) ).
thf(f44,plain,
( ( ( ( sK1 @ sK5 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ sK6 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) )
= $true )
| ( ( ( sK1 @ sK5 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ sK5 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f84,plain,
( spl2_4
| spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f53,f69,f81]) ).
thf(f53,plain,
! [X1: $i] :
( ( sK5 = X1 )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK0 @ sK6 )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
! [X1: $i] :
( ( ( sK5 = X1 )
= $true )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK0 @ sK6 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X1: $i] :
( ( ( sK0 @ sK6 )
= $true )
| ( ( ( sK1 @ X1 )
=> ( sK5 = X1 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f50]) ).
thf(f50,plain,
! [X1: $i] :
( ( ( sK0 @ sK6 )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) )
@ X1 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) ) )
= $true )
| ( ( sK0 @ sK6 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f79,plain,
( spl2_2
| spl2_3 ),
inference(avatar_split_clause,[status(thm)],[f59,f76,f72]) ).
thf(f59,plain,
! [X1: $i] :
( ( sK6 = X1 )
| ( ( sK1 @ sK5 )
= $true )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( ( sK1 @ sK5 )
= $true )
| ( ( sK6 = X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
! [X1: $i] :
( ( ( sK1 @ sK5 )
= $true )
| ( ( ( sK0 @ X1 )
=> ( sK6 = X1 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f56]) ).
thf(f56,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK6 = Y0 ) )
@ X1 )
= $true )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ( sK1 @ sK5 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK6 = Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ( ( sK1 @ sK5 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK6 = Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f74,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f67,f72,f69]) ).
thf(f67,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 ) )
| ( sK5 = X1 )
| ( ( sK1 @ X1 )
= $false )
| ( sK6 = X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
! [X2: $i,X1: $i] :
( ( ( sK6 = X2 )
= $true )
| ( sK5 = X1 )
| ( ( sK1 @ X1 )
= $false )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
! [X2: $i,X1: $i] :
( ( ( sK5 = X1 )
= $true )
| ( ( sK6 = X2 )
= $true )
| ( $false
= ( sK0 @ X2 ) )
| ( ( sK1 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( ( ( sK0 @ X2 )
=> ( sK6 = X2 ) )
= $true )
| ( ( sK5 = X1 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f63]) ).
thf(f63,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK6 = Y0 ) )
@ X2 )
= $true )
| ( ( sK5 = X1 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f62]) ).
thf(f62,plain,
! [X1: $i] :
( ( ( sK1 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK6 = Y0 ) ) )
= $true )
| ( ( sK5 = X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X1: $i] :
( ( ( ( sK1 @ X1 )
=> ( sK5 = X1 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK6 = Y0 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK6 = Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) )
@ X1 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK6 = Y0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU550^2 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n022.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:26:51 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : SEU550^2 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.29/0.45 % Domain : Set Theory
% 0.29/0.45 % Problem : A simple congruence property of exu
% 0.29/0.45 % Version : Especial > Reduced > Especial.
% 0.29/0.45 % English : (forall phi:i>o.forall psi:i>o.(forall x:i.forall y:i.x = y ->
% 0.29/0.45 % (phi x <-> psi y)) -> (exu (lambda x:i.phi x) <->
% 0.29/0.45 % exu (lambda x:i.psi x)))
% 0.29/0.45
% 0.29/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.45 % Source : [Bro08]
% 0.29/0.45 % Names : ZFC052l [Bro08]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % 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, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0
% 0.29/0.45 % Syntax : Number of formulae : 3 ( 1 unt; 1 typ; 1 def)
% 0.29/0.45 % Number of atoms : 6 ( 3 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 3 ( 3 avg)
% 0.29/0.45 % Number of connectives : 14 ( 0 ~; 0 |; 1 &; 8 @)
% 0.29/0.45 % ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 9 ( 5 avg)
% 0.29/0.45 % Number of types : 2 ( 0 usr)
% 0.29/0.45 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 2 ( 1 usr; 0 con; 1-2 aty)
% 0.29/0.45 % Number of variables : 9 ( 3 ^; 5 !; 1 ?; 9 :)
% 0.29/0.45 % SPC : TH0_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : http://mathgate.info/detsetitem.php?id=10
% 0.29/0.45 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(exu_type,type,
% 0.29/0.45 exu: ( $i > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(exu_def,definition,
% 0.29/0.45 ( exu
% 0.29/0.45 = ( ^ [Xphi: $i > $o] :
% 0.29/0.45 ? [Xx: $i] :
% 0.29/0.45 ( ( Xphi @ Xx )
% 0.29/0.45 & ! [Xy: $i] :
% 0.29/0.45 ( ( Xphi @ Xy )
% 0.29/0.45 => ( Xx = Xy ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(exu__Cong,conjecture,
% 0.29/0.45 ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.45 ( ! [Xx: $i,Xy: $i] :
% 0.29/0.45 ( ( Xx = Xy )
% 0.29/0.45 => ( ( Xphi @ Xx )
% 0.29/0.45 <=> ( Xpsi @ Xy ) ) )
% 0.29/0.45 => ( ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.45 <=> ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 1.50/1.21 ---- Embedded in THF ---
% 1.50/1.21 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.21 %%% Generated on Tue Feb 24 12:26:52 EST 2026
% 1.50/1.21 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.21 %%% Logic specification used:
% 1.50/1.21 %%% thf(spec, logic, $$dhol).
% 1.50/1.21
% 1.50/1.21 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.WqCf7Bvv49/DTF2DTF1945.p
% See solution above
% 1.50/1.21 ------------------------
% 1.50/1.22 ---- Cleaned THF ---
% 1.50/1.22 thf(exu_type,type,
% 1.50/1.22 exu: ( $i > $o ) > $o ).
% 1.50/1.22
% 1.50/1.22 thf(exu_def,definition,
% 1.50/1.22 ( exu
% 1.50/1.22 = ( ^ [Xphi: $i > $o] :
% 1.50/1.22 ? [Xx: $i] :
% 1.50/1.22 ( ( Xphi @ Xx )
% 1.50/1.22 & ! [Xy: $i] :
% 1.50/1.22 ( ( Xphi @ Xy )
% 1.50/1.22 => ( Xx = Xy ) ) ) ) ) ).
% 1.50/1.22
% 1.50/1.22 thf(exu__Cong,conjecture,
% 1.50/1.22 ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 1.50/1.22 ( ! [Xx: $i,Xy: $i] :
% 1.50/1.22 ( ( Xx = Xy )
% 1.50/1.22 => ( ( Xphi @ Xx )
% 1.50/1.22 <=> ( Xpsi @ Xy ) ) )
% 1.50/1.22 => ( ( exu
% 1.50/1.22 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.50/1.22 <=> ( exu
% 1.50/1.22 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ).
% 1.50/1.22 ------------------------
% 1.50/1.23 % (2050)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1945 for (3000ds/18Mi)
% 1.50/1.24 % (2050)Instruction limit reached!
% 1.50/1.24 % (2050)------------------------------
% 1.50/1.24 % (2050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.24 % (2050)Termination reason: Unknown
% 1.50/1.24 % (2050)Termination phase: Saturation
% 1.50/1.24
% 1.50/1.24 % (2050)Memory used [KB]: 5628
% 1.50/1.24 % (2050)Time elapsed: 0.008 s
% 1.50/1.24 % (2050)Instructions burned: 18 (million)
% 1.50/1.24 % (2050)------------------------------
% 1.50/1.24 % (2050)------------------------------
% 1.50/1.24 % (2044)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1945 for (3000ds/183Mi)
% 1.50/1.24 % (2045)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_1945 for (3000ds/4Mi)
% 1.50/1.24 % (2046)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_1945 for (3000ds/27Mi)
% 1.50/1.24 % (2049)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_1945 for (3000ds/275Mi)
% 1.50/1.24 % (2047)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1945 for (3000ds/2Mi)
% 1.50/1.24 % (2048)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_1945 for (3000ds/2Mi)
% 1.50/1.24 % (2048)Instruction limit reached!
% 1.50/1.24 % (2048)------------------------------
% 1.50/1.24 % (2048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.24 % (2048)Termination reason: Unknown
% 1.50/1.24 % (2048)Termination phase: Property scanning
% 1.50/1.24
% 1.50/1.24 % (2048)Memory used [KB]: 895
% 1.50/1.24 % (2048)Time elapsed: 0.003 s
% 1.50/1.24 % (2048)Instructions burned: 2 (million)
% 1.50/1.24 % (2048)------------------------------
% 1.50/1.24 % (2048)------------------------------
% 1.50/1.24 % (2047)Instruction limit reached!
% 1.50/1.24 % (2047)------------------------------
% 1.50/1.24 % (2047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.24 % (2047)Termination reason: Unknown
% 1.50/1.24 % (2047)Termination phase: Saturation
% 1.50/1.24
% 1.50/1.24 % (2047)Memory used [KB]: 5500
% 1.50/1.24 % (2047)Time elapsed: 0.004 s
% 1.50/1.24 % (2047)Instructions burned: 3 (million)
% 1.50/1.24 % (2047)------------------------------
% 1.50/1.24 % (2047)------------------------------
% 1.50/1.24 % (2049)Refutation not found, incomplete strategy
% 1.50/1.24 % (2049)------------------------------
% 1.50/1.24 % (2049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.24 % (2049)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.24
% 1.50/1.24
% 1.50/1.24 % (2049)Memory used [KB]: 5500
% 1.50/1.24 % (2049)Time elapsed: 0.004 s
% 1.50/1.24 % (2049)Instructions burned: 2 (million)
% 1.50/1.24 % (2049)------------------------------
% 1.50/1.24 % (2049)------------------------------
% 1.50/1.24 % (2045)Instruction limit reached!
% 1.50/1.24 % (2045)------------------------------
% 1.50/1.24 % (2045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.24 % (2045)Termination reason: Unknown
% 1.50/1.24 % (2045)Termination phase: Saturation
% 1.50/1.24
% 1.50/1.24 % (2045)Memory used [KB]: 5500
% 1.50/1.24 % (2045)Time elapsed: 0.005 s
% 1.50/1.24 % (2045)Instructions burned: 4 (million)
% 1.50/1.24 % (2045)------------------------------
% 1.50/1.24 % (2045)------------------------------
% 1.50/1.25 % (2046)First to succeed.
% 1.50/1.26 % (2051)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1945 for (2999ds/3Mi)
% 1.50/1.26 % (2051)Instruction limit reached!
% 1.50/1.26 % (2051)------------------------------
% 1.50/1.26 % (2051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.26 % (2051)Termination reason: Unknown
% 1.50/1.26 % (2051)Termination phase: Saturation
% 1.50/1.26
% 1.50/1.26 % (2051)Memory used [KB]: 5500
% 1.50/1.26 % (2051)Time elapsed: 0.003 s
% 1.50/1.26 % (2051)Instructions burned: 3 (million)
% 1.50/1.26 % (2051)------------------------------
% 1.50/1.26 % (2051)------------------------------
% 1.50/1.26 % (2052)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_1945 for (2999ds/37Mi)
% 1.50/1.26 % (2046)Refutation found. Thanks to Tanya!
% 1.50/1.26 % SZS status Theorem for DTF2THF_1945
% 1.50/1.26 % SZS output start Proof for DTF2THF_1945
% 1.50/1.26 thf(func_def_0, type, exu: ($i > $o) > $o).
% 1.50/1.26 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.50/1.26 thf(func_def_14, type, sK0: $i > $o).
% 1.50/1.26 thf(func_def_15, type, sK1: $i > $o).
% 1.50/1.26 thf(func_def_17, type, sK3: $i > $i).
% 1.50/1.26 thf(func_def_18, type, sK4: $i > $i).
% 1.50/1.26 thf(f253,plain,(
% 1.50/1.26 $false),
% 1.50/1.26 inference(avatar_sat_refutation,[status(thm)],[f74,f79,f84,f85,f92,f96,f100,f101,f126,f161,f191,f234,f251])).
% 1.50/1.26 thf(f251,plain,(
% 1.50/1.26 ~spl2_1 | ~spl2_3 | ~spl2_6 | ~spl2_7),
% 1.50/1.26 inference(avatar_contradiction_clause,[status(thm)],[f250])).
% 1.50/1.26 thf(f250,plain,(
% 1.50/1.26 $false | (~spl2_1 | ~spl2_3 | ~spl2_6 | ~spl2_7)),
% 1.50/1.26 inference(trivial_inequality_removal,[status(thm)],[f247])).
% 1.50/1.26 thf(f247,plain,(
% 1.50/1.26 ($false = $true) | (~spl2_1 | ~spl2_3 | ~spl2_6 | ~spl2_7)),
% 1.50/1.26 inference(backward_demodulation,[status(thm)],[f177,f246])).
% 1.50/1.26 thf(f246,plain,(
% 1.50/1.26 ($false = (sK0 @ sK5)) | (~spl2_1 | ~spl2_6 | ~spl2_7)),
% 1.50/1.26 inference(equality_resolution,[status(thm)],[f245])).
% 1.50/1.26 thf(f245,plain,(
% 1.50/1.26 ( ! [X0 : $i] : ((sK5 != X0) | ((sK0 @ X0) = $false)) ) | (~spl2_1 | ~spl2_6 | ~spl2_7)),
% 1.50/1.26 inference(duplicate_literal_removal,[status(thm)],[f242])).
% 1.50/1.26 thf(f242,plain,(
% 1.50/1.26 ( ! [X0 : $i] : (((sK0 @ X0) = $false) | (sK5 != X0) | ((sK0 @ X0) = $false)) ) | (~spl2_1 | ~spl2_6 | ~spl2_7)),
% 1.50/1.26 inference(superposition,[status(thm)],[f91,f208])).
% 1.50/1.26 thf(f208,plain,(
% 1.50/1.26 ( ! [X0 : $i] : ((sK5 = (sK4 @ X0)) | ((sK0 @ X0) = $false)) ) | (~spl2_1 | ~spl2_7)),
% 1.50/1.26 inference(trivial_inequality_removal,[status(thm)],[f207])).
% 1.50/1.26 thf(f207,plain,(
% 1.50/1.26 ( ! [X0 : $i] : (((sK0 @ X0) = $false) | ($false = $true) | (sK5 = (sK4 @ X0))) ) | (~spl2_1 | ~spl2_7)),
% 1.50/1.26 inference(superposition,[status(thm)],[f199,f95])).
% 1.50/1.26 thf(f95,plain,(
% 1.50/1.26 ( ! [X2 : $i] : (((sK0 @ (sK4 @ X2)) = $true) | ($false = (sK0 @ X2))) ) | ~spl2_7),
% 1.50/1.26 inference(avatar_component_clause,[status(thm)],[f94])).
% 1.50/1.26 thf(f94,definition,(
% 1.50/1.26 spl2_7 <=> ! [X2 : $i] : (((sK0 @ (sK4 @ X2)) = $true) | ($false = (sK0 @ X2)))),
% 1.50/1.26 introduced(definition,[new_symbols(naming,[spl2_7])],[avatar_definition])).
% 1.50/1.26 thf(f199,plain,(
% 1.50/1.26 ( ! [X0 : $i] : (((sK0 @ X0) = $false) | (sK5 = X0)) ) | ~spl2_1),
% 1.50/1.26 inference(trivial_inequality_removal,[status(thm)],[f198])).
% 1.50/1.26 thf(f198,plain,(
% 1.50/1.26 ( ! [X0 : $i] : (((sK0 @ X0) = $false) | ($false = $true) | (sK5 = X0)) ) | ~spl2_1),
% 1.50/1.26 inference(superposition,[status(thm)],[f18,f70])).
% 1.50/1.26 thf(f70,plain,(
% 1.50/1.26 ( ! [X1 : $i] : (((sK1 @ X1) = $false) | (sK5 = X1)) ) | ~spl2_1),
% 1.50/1.26 inference(avatar_component_clause,[status(thm)],[f69])).
% 1.50/1.26 thf(f69,definition,(
% 1.50/1.26 spl2_1 <=> ! [X1 : $i] : ((sK5 = X1) | ((sK1 @ X1) = $false))),
% 1.50/1.26 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.50/1.26 thf(f18,plain,(
% 1.50/1.26 ( ! [X3 : $i] : (((sK1 @ X3) = $true) | ((sK0 @ X3) = $false)) )),
% 1.50/1.26 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.50/1.26 thf(f16,plain,(
% 1.50/1.26 ( ! [X3 : $i] : (((sK0 @ X3) = (sK1 @ X3))) )),
% 1.50/1.26 inference(equality_resolution,[status(thm)],[f12])).
% 1.50/1.26 thf(f12,plain,(
% 1.50/1.26 ( ! [X2 : $i,X3 : $i] : ((X2 != X3) | ((sK1 @ X3) = (sK0 @ X2))) )),
% 1.50/1.26 inference(cnf_transformation,[status(thm)],[f11])).
% 1.50/1.26 thf(f11,plain,(
% 1.50/1.26 ((exu @ (^[Y0 : $i]: (sK1 @ Y0))) != (exu @ (^[Y0 : $i]: (sK0 @ Y0)))) & ! [X2 : $i,X3 : $i] : ((X2 != X3) | ((sK1 @ X3) = (sK0 @ X2)))),
% 1.50/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f10])).
% 1.50/1.26 thf(f10,plain,(
% 1.50/1.26 ? [X0 : $i > $o,X1 : $i > $o] : (((exu @ (^[Y0 : $i]: (X1 @ Y0))) != (exu @ (^[Y0 : $i]: (X0 @ Y0)))) & ! [X2 : $i,X3 : $i] : ((X2 != X3) | ((X0 @ X2) = (X1 @ X3)))) => (((exu @ (^[Y0 : $i]: (sK1 @ Y0))) != (exu @ (^[Y0 : $i]: (sK0 @ Y0)))) & ! [X3 : $i,X2 : $i] : ((X2 != X3) | ((sK1 @ X3) = (sK0 @ X2))))),
% 1.50/1.26 introduced(definition,[],[choice_axiom])).
% 1.50/1.26 thf(f9,plain,(
% 1.50/1.26 ? [X0 : $i > $o,X1 : $i > $o] : (((exu @ (^[Y0 : $i]: (X1 @ Y0))) != (exu @ (^[Y0 : $i]: (X0 @ Y0)))) & ! [X2 : $i,X3 : $i] : ((X2 != X3) | ((X0 @ X2) = (X1 @ X3))))),
% 1.50/1.26 inference(ennf_transformation,[status(thm)],[f8])).
% 1.50/1.26 thf(f8,plain,(
% 1.50/1.26 ~! [X0 : $i > $o,X1 : $i > $o] : (! [X2 : $i,X3 : $i] : ((X2 = X3) => ((X0 @ X2) = (X1 @ X3))) => ((exu @ (^[Y0 : $i]: (X1 @ Y0))) = (exu @ (^[Y0 : $i]: (X0 @ Y0)))))),
% 1.50/1.26 inference(fool_elimination,[status(thm)],[f7])).
% 1.50/1.26 thf(f7,plain,(
% 1.50/1.26 ~! [X0 : $i > $o,X1 : $i > $o] : (! [X2 : $i,X3 : $i] : ((X2 = X3) => ((X1 @ X3) <=> (X0 @ X2))) => ((exu @ (^[X4 : $i] : (X0 @ X4))) <=> (exu @ (^[X5 : $i] : (X1 @ X5)))))),
% 1.50/1.26 inference(rectify,[status(thm)],[f3])).
% 1.50/1.26 thf(f3,negated_conjecture,(
% 1.50/1.26 ~! [X3 : $i > $o,X0 : $i > $o] : (! [X2 : $i,X1 : $i] : ((X1 = X2) => ((X0 @ X1) <=> (X3 @ X2))) => ((exu @ (^[X1 : $i] : (X3 @ X1))) <=> (exu @ (^[X1 : $i] : (X0 @ X1)))))),
% 1.50/1.26 inference(negated_conjecture,[status(cth)],[f2])).
% 1.50/1.26 thf(f2,conjecture,(
% 1.50/1.26 ! [X3 : $i > $o,X0 : $i > $o] : (! [X2 : $i,X1 : $i] : ((X1 = X2) => ((X0 @ X1) <=> (X3 @ X2))) => ((exu @ (^[X1 : $i] : (X3 @ X1))) <=> (exu @ (^[X1 : $i] : (X0 @ X1)))))),
% 1.50/1.26 file('/export/starexec/sandbox2/tmp/tmp.WqCf7Bvv49/DTF2THF_1945.p',exu__Cong)).
% 1.50/1.26 thf(f91,plain,(
% 1.50/1.26 ( ! [X2 : $i] : (((sK4 @ X2) != X2) | ($false = (sK0 @ X2))) ) | ~spl2_6),
% 1.50/1.26 inference(avatar_component_clause,[status(thm)],[f90])).
% 1.50/1.26 thf(f90,definition,(
% 1.50/1.26 spl2_6 <=> ! [X2 : $i] : (((sK4 @ X2) != X2) | ($false = (sK0 @ X2)))),
% 1.50/1.26 introduced(definition,[new_symbols(naming,[spl2_6])],[avatar_definition])).
% 1.50/1.26 thf(f177,plain,(
% 1.50/1.26 ((sK0 @ sK5) = $true) | ~spl2_3),
% 1.50/1.26 inference(trivial_inequality_removal,[status(thm)],[f176])).
% 1.50/1.26 thf(f176,plain,(
% 1.50/1.26 ((sK0 @ sK5) = $true) | ($false = $true) | ~spl2_3),
% 1.50/1.26 inference(superposition,[status(thm)],[f78,f17])).
% 1.50/1.26 thf(f17,plain,(
% 1.50/1.26 ( ! [X3 : $i] : (((sK1 @ X3) = $false) | ((sK0 @ X3) = $true)) )),
% 1.50/1.26 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.50/1.26 thf(f78,plain,(
% 1.50/1.26 ((sK1 @ sK5) = $true) | ~spl2_3),
% 1.50/1.26 inference(avatar_component_clause,[status(thm)],[f76])).
% 1.50/1.26 thf(f76,definition,(
% 1.50/1.26 spl2_3 <=> ((sK1 @ sK5) = $true)),
% 1.50/1.26 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.50/1.26 thf(f234,plain,(
% 1.50/1.26 ~spl2_1 | ~spl2_3 | ~spl2_5 | ~spl2_8),
% 1.50/1.26 inference(avatar_contradiction_clause,[status(thm)],[f233])).
% 1.50/1.26 thf(f233,plain,(
% 1.50/1.26 $false | (~spl2_1 | ~spl2_3 | ~spl2_5 | ~spl2_8)),
% 1.50/1.26 inference(trivial_inequality_removal,[status(thm)],[f229])).
% 1.50/1.26 thf(f229,plain,(
% 1.50/1.26 ($false = $true) | (~spl2_1 | ~spl2_3 | ~spl2_5 | ~spl2_8)),
% 1.50/1.26 inference(backward_demodulation,[status(thm)],[f78,f222])).
% 1.50/1.26 thf(f222,plain,(
% 1.50/1.26 ((sK1 @ sK5) = $false) | (~spl2_1 | ~spl2_5 | ~spl2_8)),
% 1.50/1.26 inference(equality_resolution,[status(thm)],[f221])).
% 1.50/1.26 thf(f221,plain,(
% 1.50/1.26 ( ! [X0 : $i] : ((sK5 != X0) | ($false = (sK1 @ X0))) ) | (~spl2_1 | ~spl2_5 | ~spl2_8)),
% 1.50/1.26 inference(duplicate_literal_removal,[status(thm)],[f219])).
% 1.50/1.26 thf(f219,plain,(
% 1.50/1.26 ( ! [X0 : $i] : (($false = (sK1 @ X0)) | ($false = (sK1 @ X0)) | (sK5 != X0)) ) | (~spl2_1 | ~spl2_5 | ~spl2_8)),
% 1.50/1.26 inference(superposition,[status(thm)],[f88,f216])).
% 1.50/1.26 thf(f216,plain,(
% 1.50/1.26 ( ! [X0 : $i] : ((sK5 = (sK3 @ X0)) | ($false = (sK1 @ X0))) ) | (~spl2_1 | ~spl2_8)),
% 1.50/1.26 inference(trivial_inequality_removal,[status(thm)],[f210])).
% 1.50/1.26 thf(f210,plain,(
% 1.50/1.26 ( ! [X0 : $i] : ((sK5 = (sK3 @ X0)) | ($false = (sK1 @ X0)) | ($false = $true)) ) | (~spl2_1 | ~spl2_8)),
% 1.50/1.26 inference(superposition,[status(thm)],[f99,f70])).
% 1.50/1.26 thf(f99,plain,(
% 1.50/1.26 ( ! [X1 : $i] : (((sK1 @ (sK3 @ X1)) = $true) | ((sK1 @ X1) = $false)) ) | ~spl2_8),
% 1.50/1.26 inference(avatar_component_clause,[status(thm)],[f98])).
% 1.50/1.26 thf(f98,definition,(
% 1.50/1.26 spl2_8 <=> ! [X1 : $i] : (((sK1 @ X1) = $false) | ((sK1 @ (sK3 @ X1)) = $true))),
% 1.50/1.26 introduced(definition,[new_symbols(naming,[spl2_8])],[avatar_definition])).
% 1.50/1.26 thf(f88,plain,(
% 1.50/1.26 ( ! [X1 : $i] : (((sK3 @ X1) != X1) | ((sK1 @ X1) = $false)) ) | ~spl2_5),
% 1.50/1.26 inference(avatar_component_clause,[status(thm)],[f87])).
% 1.50/1.26 thf(f87,definition,(
% 1.50/1.26 spl2_5 <=> ! [X1 : $i] : (((sK3 @ X1) != X1) | ((sK1 @ X1) = $false))),
% 1.50/1.26 introduced(definition,[new_symbols(naming,[spl2_5])],[avatar_definition])).
% 1.50/1.26 thf(f191,plain,(
% 1.50/1.26 ~spl2_4 | spl2_9),
% 1.50/1.26 inference(avatar_contradiction_clause,[status(thm)],[f190])).
% 1.50/1.26 thf(f190,plain,(
% 1.50/1.26 $false | (~spl2_4 | spl2_9)),
% 1.50/1.26 inference(trivial_inequality_removal,[status(thm)],[f187])).
% 1.50/1.26 thf(f187,plain,(
% 1.50/1.26 ($false = $true) | (~spl2_4 | spl2_9)),
% 1.50/1.26 inference(backward_demodulation,[status(thm)],[f83,f186])).
% 1.50/1.26 thf(f186,plain,(
% 1.50/1.26 ($false = (sK0 @ sK6)) | spl2_9),
% 1.50/1.26 inference(trivial_inequality_removal,[status(thm)],[f184])).
% 1.50/1.26 thf(f184,plain,(
% 1.50/1.26 ($true != $true) | ($false = (sK0 @ sK6)) | spl2_9),
% 1.50/1.26 inference(superposition,[status(thm)],[f145,f18])).
% 1.50/1.26 thf(f145,plain,(
% 1.50/1.26 ($true != (sK1 @ sK6)) | spl2_9),
% 1.50/1.26 inference(avatar_component_clause,[status(thm)],[f144])).
% 1.50/1.26 thf(f144,definition,(
% 1.50/1.26 spl2_9 <=> ($true = (sK1 @ sK6))),
% 1.50/1.26 introduced(definition,[new_symbols(naming,[spl2_9])],[avatar_definition])).
% 1.50/1.26 thf(f83,plain,(
% 1.50/1.26 ((sK0 @ sK6) = $true) | ~spl2_4),
% 1.50/1.26 inference(avatar_component_clause,[status(thm)],[f81])).
% 1.50/1.26 thf(f81,definition,(
% 1.50/1.26 spl2_4 <=> ((sK0 @ sK6) = $true)),
% 1.50/1.26 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.50/1.26 thf(f161,plain,(
% 1.50/1.26 ~spl2_2 | ~spl2_5 | ~spl2_8 | ~spl2_9),
% 1.50/1.26 inference(avatar_contradiction_clause,[status(thm)],[f160])).
% 1.50/1.26 thf(f160,plain,(
% 1.50/1.26 $false | (~spl2_2 | ~spl2_5 | ~spl2_8 | ~spl2_9)),
% 1.50/1.26 inference(trivial_inequality_removal,[status(thm)],[f156])).
% 1.50/1.26 thf(f156,plain,(
% 1.50/1.26 ($false = $true) | (~spl2_2 | ~spl2_5 | ~spl2_8 | ~spl2_9)),
% 1.50/1.26 inference(backward_demodulation,[status(thm)],[f146,f155])).
% 1.50/1.26 thf(f155,plain,(
% 1.50/1.26 ($false = (sK1 @ sK6)) | (~spl2_2 | ~spl2_5 | ~spl2_8)),
% 1.50/1.26 inference(equality_resolution,[status(thm)],[f140])).
% 1.50/1.26 thf(f140,plain,(
% 1.50/1.26 ( ! [X0 : $i] : ((sK6 != X0) | ($false = (sK1 @ X0))) ) | (~spl2_2 | ~spl2_5 | ~spl2_8)),
% 1.50/1.26 inference(duplicate_literal_removal,[status(thm)],[f139])).
% 1.50/1.26 thf(f139,plain,(
% 1.50/1.26 ( ! [X0 : $i] : (($false = (sK1 @ X0)) | (sK6 != X0) | ($false = (sK1 @ X0))) ) | (~spl2_2 | ~spl2_5 | ~spl2_8)),
% 1.50/1.26 inference(superposition,[status(thm)],[f88,f135])).
% 1.50/1.26 thf(f135,plain,(
% 1.50/1.26 ( ! [X0 : $i] : ((sK6 = (sK3 @ X0)) | ($false = (sK1 @ X0))) ) | (~spl2_2 | ~spl2_8)),
% 1.50/1.26 inference(trivial_inequality_removal,[status(thm)],[f134])).
% 1.50/1.26 thf(f134,plain,(
% 1.50/1.26 ( ! [X0 : $i] : (($false = (sK1 @ X0)) | ($false = $true) | (sK6 = (sK3 @ X0))) ) | (~spl2_2 | ~spl2_8)),
% 1.50/1.26 inference(superposition,[status(thm)],[f73,f131])).
% 1.50/1.26 thf(f131,plain,(
% 1.50/1.26 ( ! [X0 : $i] : (((sK0 @ (sK3 @ X0)) = $true) | ($false = (sK1 @ X0))) ) | ~spl2_8),
% 1.50/1.26 inference(trivial_inequality_removal,[status(thm)],[f130])).
% 1.50/1.26 thf(f130,plain,(
% 1.50/1.26 ( ! [X0 : $i] : (($false = (sK1 @ X0)) | ($false = $true) | ((sK0 @ (sK3 @ X0)) = $true)) ) | ~spl2_8),
% 1.50/1.26 inference(superposition,[status(thm)],[f17,f99])).
% 1.50/1.26 thf(f73,plain,(
% 1.50/1.26 ( ! [X2 : $i] : (($false = (sK0 @ X2)) | (sK6 = X2)) ) | ~spl2_2),
% 1.50/1.26 inference(avatar_component_clause,[status(thm)],[f72])).
% 1.50/1.26 thf(f72,definition,(
% 1.50/1.26 spl2_2 <=> ! [X2 : $i] : (($false = (sK0 @ X2)) | (sK6 = X2))),
% 1.50/1.26 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.50/1.26 thf(f146,plain,(
% 1.50/1.26 ($true = (sK1 @ sK6)) | ~spl2_9),
% 1.50/1.26 inference(avatar_component_clause,[status(thm)],[f144])).
% 1.50/1.26 thf(f126,plain,(
% 1.50/1.26 ~spl2_2 | ~spl2_4 | ~spl2_6 | ~spl2_7),
% 1.50/1.26 inference(avatar_contradiction_clause,[status(thm)],[f125])).
% 1.50/1.26 thf(f125,plain,(
% 1.50/1.26 $false | (~spl2_2 | ~spl2_4 | ~spl2_6 | ~spl2_7)),
% 1.50/1.26 inference(trivial_inequality_removal,[status(thm)],[f121])).
% 1.50/1.26 thf(f121,plain,(
% 1.50/1.26 ($false = $true) | (~spl2_2 | ~spl2_4 | ~spl2_6 | ~spl2_7)),
% 1.50/1.26 inference(backward_demodulation,[status(thm)],[f83,f120])).
% 1.50/1.26 thf(f120,plain,(
% 1.50/1.26 ($false = (sK0 @ sK6)) | (~spl2_2 | ~spl2_6 | ~spl2_7)),
% 1.50/1.26 inference(equality_resolution,[status(thm)],[f119])).
% 1.50/1.26 thf(f119,plain,(
% 1.50/1.26 ( ! [X0 : $i] : ((sK6 != X0) | ((sK0 @ X0) = $false)) ) | (~spl2_2 | ~spl2_6 | ~spl2_7)),
% 1.50/1.26 inference(duplicate_literal_removal,[status(thm)],[f117])).
% 1.50/1.26 thf(f117,plain,(
% 1.50/1.26 ( ! [X0 : $i] : ((sK6 != X0) | ((sK0 @ X0) = $false) | ((sK0 @ X0) = $false)) ) | (~spl2_2 | ~spl2_6 | ~spl2_7)),
% 1.50/1.26 inference(superposition,[status(thm)],[f91,f114])).
% 1.50/1.26 thf(f114,plain,(
% 1.50/1.26 ( ! [X0 : $i] : ((sK6 = (sK4 @ X0)) | ((sK0 @ X0) = $false)) ) | (~spl2_2 | ~spl2_7)),
% 1.50/1.26 inference(trivial_inequality_removal,[status(thm)],[f112])).
% 1.50/1.26 thf(f112,plain,(
% 1.50/1.26 ( ! [X0 : $i] : ((sK6 = (sK4 @ X0)) | ((sK0 @ X0) = $false) | ($false = $true)) ) | (~spl2_2 | ~spl2_7)),
% 1.50/1.26 inference(superposition,[status(thm)],[f95,f73])).
% 1.50/1.26 thf(f101,plain,(
% 1.50/1.26 spl2_8 | spl2_7),
% 1.50/1.26 inference(avatar_split_clause,[status(thm)],[f35,f94,f98])).
% 1.50/1.26 thf(f35,plain,(
% 1.50/1.26 ( ! [X2 : $i,X1 : $i] : (((sK1 @ (sK3 @ X1)) = $true) | ((sK0 @ (sK4 @ X2)) = $true) | ((sK1 @ X1) = $false) | ($false = (sK0 @ X2))) )),
% 1.50/1.26 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.50/1.26 thf(f33,plain,(
% 1.50/1.26 ( ! [X2 : $i,X1 : $i] : ((((sK0 @ (sK4 @ X2)) => (X2 = (sK4 @ X2))) = $false) | ((sK1 @ (sK3 @ X1)) = $true) | ((sK1 @ X1) = $false) | ($false = (sK0 @ X2))) )),
% 1.50/1.26 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.50/1.26 thf(f31,plain,(
% 1.50/1.26 ( ! [X2 : $i,X1 : $i] : (($false = (sK0 @ X2)) | (((sK1 @ (sK3 @ X1)) => (X1 = (sK3 @ X1))) = $false) | (((sK0 @ (sK4 @ X2)) => (X2 = (sK4 @ X2))) = $false) | ((sK1 @ X1) = $false)) )),
% 1.50/1.26 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.50/1.26 thf(f30,plain,(
% 1.50/1.26 ( ! [X2 : $i,X1 : $i] : (($false = (sK0 @ X2)) | (((^[Y0 : $i]: ((sK0 @ Y0) => (X2 = Y0))) @ (sK4 @ X2)) = $false) | (((sK1 @ (sK3 @ X1)) => (X1 = (sK3 @ X1))) = $false) | ((sK1 @ X1) = $false)) )),
% 1.50/1.26 inference(sigma_clausification,[status(thm)],[f29])).
% 1.50/1.26 thf(f29,plain,(
% 1.50/1.26 ( ! [X2 : $i,X1 : $i] : (((sK1 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X2 = Y0)))) = $false) | ($false = (sK0 @ X2)) | (((sK1 @ (sK3 @ X1)) => (X1 = (sK3 @ X1))) = $false)) )),
% 1.50/1.26 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.50/1.26 thf(f28,plain,(
% 1.50/1.26 ( ! [X2 : $i,X1 : $i] : (((sK1 @ X1) = $false) | ($false = ((sK0 @ X2) & (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (X2 = Y0)))))) | (((sK1 @ (sK3 @ X1)) => (X1 = (sK3 @ X1))) = $false)) )),
% 1.50/1.26 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.50/1.26 thf(f27,plain,(
% 1.50/1.26 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))))) @ X2) = $false) | (((sK1 @ (sK3 @ X1)) => (X1 = (sK3 @ X1))) = $false) | ((sK1 @ X1) = $false)) )),
% 1.50/1.26 inference(pi_clausification,[status(thm)],[f26])).
% 1.50/1.26 thf(f26,plain,(
% 1.50/1.26 ( ! [X1 : $i] : (((?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1))))))) = $false) | ((sK1 @ X1) = $false) | (((sK1 @ (sK3 @ X1)) => (X1 = (sK3 @ X1))) = $false)) )),
% 1.50/1.26 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.50/1.26 thf(f25,plain,(
% 1.50/1.26 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((sK1 @ Y0) => (X1 = Y0))) @ (sK3 @ X1))) | ((sK1 @ X1) = $false) | ((?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1))))))) = $false)) )),
% 1.50/1.26 inference(sigma_clausification,[status(thm)],[f24])).
% 1.50/1.26 thf(f24,plain,(
% 1.50/1.26 ( ! [X1 : $i] : (((sK1 @ X1) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (X1 = Y0))))) | ((?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1))))))) = $false)) )),
% 1.50/1.26 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.50/1.26 thf(f23,plain,(
% 1.50/1.26 ( ! [X1 : $i] : ((((sK1 @ X1) & (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (X1 = Y0))))) = $false) | ((?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1))))))) = $false)) )),
% 1.50/1.26 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.50/1.26 thf(f22,plain,(
% 1.50/1.26 ( ! [X1 : $i] : (((?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1))))))) = $false) | ($false = ((^[Y0 : $i]: ((sK1 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) => (Y0 = Y1)))))) @ X1))) )),
% 1.50/1.26 inference(pi_clausification,[status(thm)],[f21])).
% 1.50/1.26 thf(f21,plain,(
% 1.50/1.26 ($false = (?? @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) => (Y0 = Y1)))))))) | ((?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1))))))) = $false)),
% 1.50/1.26 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.50/1.26 thf(f19,plain,(
% 1.50/1.26 ((?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1))))))) != (?? @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) => (Y0 = Y1))))))))),
% 1.50/1.26 inference(beta_eta_normalization,[status(thm)],[f15])).
% 1.50/1.26 thf(f15,plain,(
% 1.50/1.26 (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))) @ (^[Y0 : $i]: (sK0 @ Y0))) != ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))) @ (^[Y0 : $i]: (sK1 @ Y0))))),
% 1.50/1.26 inference(definition_unfolding,[status(thm)],[f13,f14,f14])).
% 1.50/1.26 thf(f14,plain,(
% 1.50/1.26 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 1.50/1.26 inference(cnf_transformation,[status(thm)],[f6])).
% 1.50/1.26 thf(f6,plain,(
% 1.50/1.26 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 1.50/1.26 inference(fool_elimination,[status(thm)],[f5])).
% 1.50/1.26 thf(f5,plain,(
% 1.50/1.26 (exu = (^[X0 : $i > $o] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 1.50/1.26 inference(rectify,[status(thm)],[f1])).
% 1.50/1.26 thf(f1,axiom,(
% 1.50/1.26 (exu = (^[X0 : $i > $o] : (? [X1 : $i] : (! [X2 : $i] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))),
% 1.50/1.26 file('/export/starexec/sandbox2/tmp/tmp.WqCf7Bvv49/DTF2THF_1945.p',exu_def)).
% 1.50/1.26 thf(f13,plain,(
% 1.50/1.26 ((exu @ (^[Y0 : $i]: (sK1 @ Y0))) != (exu @ (^[Y0 : $i]: (sK0 @ Y0))))),
% 1.50/1.26 inference(cnf_transformation,[status(thm)],[f11])).
% 1.50/1.26 thf(f100,plain,(
% 1.50/1.26 spl2_8 | spl2_6),
% 1.50/1.26 inference(avatar_split_clause,[status(thm)],[f36,f90,f98])).
% 1.50/1.26 thf(f36,plain,(
% 1.50/1.26 ( ! [X2 : $i,X1 : $i] : (((sK1 @ X1) = $false) | ($false = (sK0 @ X2)) | ((sK1 @ (sK3 @ X1)) = $true) | ((sK4 @ X2) != X2)) )),
% 1.50/1.26 inference(equality_proxy_clausification,[status(thm)],[f34])).
% 1.50/1.26 thf(f34,plain,(
% 1.50/1.26 ( ! [X2 : $i,X1 : $i] : (((sK1 @ (sK3 @ X1)) = $true) | ($false = (X2 = (sK4 @ X2))) | ($false = (sK0 @ X2)) | ((sK1 @ X1) = $false)) )),
% 1.50/1.26 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.50/1.26 thf(f96,plain,(
% 1.50/1.26 spl2_7 | spl2_5),
% 1.50/1.26 inference(avatar_split_clause,[status(thm)],[f39,f87,f94])).
% 1.50/1.26 thf(f39,plain,(
% 1.50/1.26 ( ! [X2 : $i,X1 : $i] : (((sK1 @ X1) = $false) | ((sK3 @ X1) != X1) | ((sK0 @ (sK4 @ X2)) = $true) | ($false = (sK0 @ X2))) )),
% 1.50/1.26 inference(equality_proxy_clausification,[status(thm)],[f38])).
% 1.50/1.26 thf(f38,plain,(
% 1.50/1.26 ( ! [X2 : $i,X1 : $i] : (((X1 = (sK3 @ X1)) = $false) | ((sK0 @ (sK4 @ X2)) = $true) | ($false = (sK0 @ X2)) | ((sK1 @ X1) = $false)) )),
% 1.50/1.26 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.50/1.26 thf(f32,plain,(
% 1.50/1.26 ( ! [X2 : $i,X1 : $i] : (((sK1 @ X1) = $false) | (((sK0 @ (sK4 @ X2)) => (X2 = (sK4 @ X2))) = $false) | ((X1 = (sK3 @ X1)) = $false) | ($false = (sK0 @ X2))) )),
% 1.50/1.26 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.50/1.26 thf(f92,plain,(
% 1.50/1.26 spl2_5 | spl2_6),
% 1.50/1.26 inference(avatar_split_clause,[status(thm)],[f41,f90,f87])).
% 1.50/1.26 thf(f41,plain,(
% 1.50/1.26 ( ! [X2 : $i,X1 : $i] : (((sK3 @ X1) != X1) | ((sK4 @ X2) != X2) | ((sK1 @ X1) = $false) | ($false = (sK0 @ X2))) )),
% 1.50/1.26 inference(equality_proxy_clausification,[status(thm)],[f40])).
% 1.50/1.26 thf(f40,plain,(
% 1.50/1.26 ( ! [X2 : $i,X1 : $i] : (($false = (sK0 @ X2)) | ((sK4 @ X2) != X2) | ((X1 = (sK3 @ X1)) = $false) | ((sK1 @ X1) = $false)) )),
% 1.50/1.26 inference(equality_proxy_clausification,[status(thm)],[f37])).
% 1.50/1.26 thf(f37,plain,(
% 1.50/1.26 ( ! [X2 : $i,X1 : $i] : (($false = (sK0 @ X2)) | ((sK1 @ X1) = $false) | ($false = (X2 = (sK4 @ X2))) | ((X1 = (sK3 @ X1)) = $false)) )),
% 1.50/1.26 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.50/1.26 thf(f85,plain,(
% 1.50/1.26 spl2_4 | spl2_3),
% 1.50/1.26 inference(avatar_split_clause,[status(thm)],[f49,f76,f81])).
% 1.50/1.26 thf(f49,plain,(
% 1.50/1.26 ((sK1 @ sK5) = $true) | ((sK0 @ sK6) = $true)),
% 1.50/1.26 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.50/1.26 thf(f47,plain,(
% 1.50/1.26 ((sK0 @ sK6) = $true) | (((sK1 @ sK5) & (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK5 = Y0))))) = $true)),
% 1.50/1.26 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.50/1.26 thf(f45,plain,(
% 1.50/1.26 (((sK0 @ sK6) & (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK6 = Y0))))) = $true) | (((sK1 @ sK5) & (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK5 = Y0))))) = $true)),
% 1.50/1.26 inference(beta_eta_normalization,[status(thm)],[f44])).
% 1.50/1.26 thf(f44,plain,(
% 1.50/1.26 (((sK1 @ sK5) & (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK5 = Y0))))) = $true) | (((^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))))) @ sK6) = $true)),
% 1.50/1.26 inference(sigma_clausification,[status(thm)],[f43])).
% 1.50/1.26 thf(f43,plain,(
% 1.50/1.26 ((?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1))))))) = $true) | (((sK1 @ sK5) & (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK5 = Y0))))) = $true)),
% 1.50/1.26 inference(beta_eta_normalization,[status(thm)],[f42])).
% 1.50/1.26 thf(f42,plain,(
% 1.50/1.26 ((?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1))))))) = $true) | (((^[Y0 : $i]: ((sK1 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) => (Y0 = Y1)))))) @ sK5) = $true)),
% 1.50/1.26 inference(sigma_clausification,[status(thm)],[f20])).
% 1.50/1.26 thf(f20,plain,(
% 1.50/1.26 ($true = (?? @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) => (Y0 = Y1)))))))) | ((?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1))))))) = $true)),
% 1.50/1.26 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.50/1.26 thf(f84,plain,(
% 1.50/1.26 spl2_4 | spl2_1),
% 1.50/1.26 inference(avatar_split_clause,[status(thm)],[f53,f69,f81])).
% 1.50/1.26 thf(f53,plain,(
% 1.50/1.26 ( ! [X1 : $i] : ((sK5 = X1) | ((sK1 @ X1) = $false) | ((sK0 @ sK6) = $true)) )),
% 1.50/1.26 inference(equality_proxy_clausification,[status(thm)],[f52])).
% 1.50/1.26 thf(f52,plain,(
% 1.50/1.26 ( ! [X1 : $i] : (((sK5 = X1) = $true) | ((sK1 @ X1) = $false) | ((sK0 @ sK6) = $true)) )),
% 1.50/1.26 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 1.50/1.26 thf(f51,plain,(
% 1.50/1.26 ( ! [X1 : $i] : (((sK0 @ sK6) = $true) | (((sK1 @ X1) => (sK5 = X1)) = $true)) )),
% 1.50/1.26 inference(beta_eta_normalization,[status(thm)],[f50])).
% 1.50/1.26 thf(f50,plain,(
% 1.50/1.26 ( ! [X1 : $i] : (((sK0 @ sK6) = $true) | (((^[Y0 : $i]: ((sK1 @ Y0) => (sK5 = Y0))) @ X1) = $true)) )),
% 1.50/1.26 inference(pi_clausification,[status(thm)],[f48])).
% 1.50/1.26 thf(f48,plain,(
% 1.50/1.26 ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK5 = Y0)))) = $true) | ((sK0 @ sK6) = $true)),
% 1.50/1.26 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.50/1.26 thf(f79,plain,(
% 1.50/1.26 spl2_2 | spl2_3),
% 1.50/1.26 inference(avatar_split_clause,[status(thm)],[f59,f76,f72])).
% 1.50/1.26 thf(f59,plain,(
% 1.50/1.26 ( ! [X1 : $i] : ((sK6 = X1) | ((sK1 @ sK5) = $true) | ($false = (sK0 @ X1))) )),
% 1.50/1.26 inference(equality_proxy_clausification,[status(thm)],[f58])).
% 1.50/1.26 thf(f58,plain,(
% 1.50/1.26 ( ! [X1 : $i] : (($false = (sK0 @ X1)) | ((sK1 @ sK5) = $true) | ((sK6 = X1) = $true)) )),
% 1.50/1.26 inference(binary_proxy_clausification,[status(thm)],[f57])).
% 1.50/1.26 thf(f57,plain,(
% 1.50/1.26 ( ! [X1 : $i] : (((sK1 @ sK5) = $true) | (((sK0 @ X1) => (sK6 = X1)) = $true)) )),
% 1.50/1.26 inference(beta_eta_normalization,[status(thm)],[f56])).
% 1.50/1.26 thf(f56,plain,(
% 1.50/1.26 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK0 @ Y0) => (sK6 = Y0))) @ X1) = $true) | ((sK1 @ sK5) = $true)) )),
% 1.50/1.26 inference(pi_clausification,[status(thm)],[f55])).
% 1.50/1.26 thf(f55,plain,(
% 1.50/1.26 ((sK1 @ sK5) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK6 = Y0)))) = $true)),
% 1.50/1.26 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.50/1.26 thf(f46,plain,(
% 1.50/1.26 (((sK1 @ sK5) & (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK5 = Y0))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK6 = Y0)))) = $true)),
% 1.50/1.26 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.50/1.26 thf(f74,plain,(
% 1.50/1.26 spl2_1 | spl2_2),
% 1.50/1.26 inference(avatar_split_clause,[status(thm)],[f67,f72,f69])).
% 1.50/1.26 thf(f67,plain,(
% 1.50/1.26 ( ! [X2 : $i,X1 : $i] : (($false = (sK0 @ X2)) | (sK5 = X1) | ((sK1 @ X1) = $false) | (sK6 = X2)) )),
% 1.50/1.26 inference(equality_proxy_clausification,[status(thm)],[f66])).
% 1.50/1.26 thf(f66,plain,(
% 1.50/1.26 ( ! [X2 : $i,X1 : $i] : (((sK6 = X2) = $true) | (sK5 = X1) | ((sK1 @ X1) = $false) | ($false = (sK0 @ X2))) )),
% 1.50/1.26 inference(equality_proxy_clausification,[status(thm)],[f65])).
% 1.50/1.26 thf(f65,plain,(
% 1.50/1.26 ( ! [X2 : $i,X1 : $i] : (((sK5 = X1) = $true) | ((sK6 = X2) = $true) | ($false = (sK0 @ X2)) | ((sK1 @ X1) = $false)) )),
% 1.50/1.26 inference(binary_proxy_clausification,[status(thm)],[f64])).
% 1.50/1.26 thf(f64,plain,(
% 1.50/1.26 ( ! [X2 : $i,X1 : $i] : (((sK1 @ X1) = $false) | (((sK0 @ X2) => (sK6 = X2)) = $true) | ((sK5 = X1) = $true)) )),
% 1.50/1.26 inference(beta_eta_normalization,[status(thm)],[f63])).
% 1.50/1.26 thf(f63,plain,(
% 1.50/1.26 ( ! [X2 : $i,X1 : $i] : (((sK1 @ X1) = $false) | (((^[Y0 : $i]: ((sK0 @ Y0) => (sK6 = Y0))) @ X2) = $true) | ((sK5 = X1) = $true)) )),
% 1.50/1.26 inference(pi_clausification,[status(thm)],[f62])).
% 1.50/1.26 thf(f62,plain,(
% 1.50/1.26 ( ! [X1 : $i] : (((sK1 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK6 = Y0)))) = $true) | ((sK5 = X1) = $true)) )),
% 1.50/1.26 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.50/1.26 thf(f61,plain,(
% 1.50/1.26 ( ! [X1 : $i] : ((((sK1 @ X1) => (sK5 = X1)) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK6 = Y0)))) = $true)) )),
% 1.50/1.26 inference(beta_eta_normalization,[status(thm)],[f60])).
% 1.50/1.26 thf(f60,plain,(
% 1.50/1.26 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK6 = Y0)))) = $true) | (((^[Y0 : $i]: ((sK1 @ Y0) => (sK5 = Y0))) @ X1) = $true)) )),
% 1.50/1.26 inference(pi_clausification,[status(thm)],[f54])).
% 1.50/1.26 thf(f54,plain,(
% 1.50/1.26 ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) => (sK5 = Y0)))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK6 = Y0)))) = $true)),
% 1.50/1.26 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.50/1.26 % SZS output end Proof for DTF2THF_1945
% 1.50/1.26 % (2046)------------------------------
% 1.50/1.26 % (2046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.26 % (2046)Termination reason: Refutation
% 1.50/1.26
% 1.50/1.26 % (2046)Memory used [KB]: 5628
% 1.50/1.26 % (2046)Time elapsed: 0.020 s
% 1.50/1.26 % (2046)Instructions burned: 20 (million)
% 1.50/1.26 % (2046)------------------------------
% 1.50/1.26 % (2046)------------------------------
% 1.50/1.26 % (2043)Success in time 0.021 s
%------------------------------------------------------------------------------