%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO244^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 09:53:45 AM UTC 2026
% Result : Theorem 1.62s 1.39s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 15
% Syntax : Number of formulae : 138 ( 7 unt; 0 typ; 10 def)
% Number of atoms : 1195 ( 268 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 1578 ( 211 ~; 321 |; 91 &; 792 @)
% ( 10 <=>; 75 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 652 ( 652 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 21 usr; 15 con; 0-2 aty)
% ( 35 !!; 43 ??; 0 @@+; 0 @@-)
% Number of variables : 257 ( 110 ^; 109 !; 38 ?; 257 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_12,type,
sK0: ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_13,type,
sK1: ( ( a > $o ) > $o ) > $o ).
thf(func_def_14,type,
sK2: ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_15,type,
sK3: ( a > $o ) > $o ).
thf(func_def_17,type,
ph5:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
sK6: a ).
thf(func_def_21,type,
sK7: ( ( ( a > $o ) > $o ) > a > $o ) > ( a > $o ) > $o ).
thf(func_def_22,type,
sK8: ( a > $o ) > $o ).
thf(func_def_23,type,
sK9: ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_24,type,
sK10: ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_25,type,
sK11: ( ( a > $o ) > $o ) > a > $o ).
thf(f489,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f88,f92,f99,f103,f110,f114,f119,f120,f354,f364,f391,f432,f478,f488]) ).
thf(f488,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_7
| ~ spl4_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f487]) ).
thf(f487,plain,
( $false
| ~ spl4_2
| ~ spl4_3
| ~ spl4_7
| ~ spl4_10 ),
inference(trivial_inequality_removal,[status(thm)],[f483]) ).
thf(f483,plain,
( ( $false = $true )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_7
| ~ spl4_10 ),
inference(superposition,[status(thm)],[f482,f118]) ).
thf(f118,plain,
( ( $true
= ( sK1 @ sK8 ) )
| ~ spl4_10 ),
inference(avatar_component_clause,[status(thm)],[f116]) ).
thf(f116,definition,
( spl4_10
<=> ( $true
= ( sK1 @ sK8 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_10])],[avatar_definition]) ).
thf(f482,plain,
( ( $false
= ( sK1 @ sK8 ) )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_7
| ~ spl4_10 ),
inference(trivial_inequality_removal,[status(thm)],[f479]) ).
thf(f479,plain,
( ( $false
= ( sK1 @ sK8 ) )
| ( $false = $true )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_7
| ~ spl4_10 ),
inference(superposition,[status(thm)],[f87,f416]) ).
thf(f416,plain,
( ( $false
= ( sK11 @ sK8 @ sK6 ) )
| ~ spl4_3
| ~ spl4_7
| ~ spl4_10 ),
inference(trivial_inequality_removal,[status(thm)],[f415]) ).
thf(f415,plain,
( ( $false = $true )
| ( $false
= ( sK11 @ sK8 @ sK6 ) )
| ~ spl4_3
| ~ spl4_7
| ~ spl4_10 ),
inference(forward_demodulation,[status(thm)],[f405,f118]) ).
thf(f405,plain,
( ( $false
= ( sK1 @ sK8 ) )
| ( $false
= ( sK11 @ sK8 @ sK6 ) )
| ~ spl4_3
| ~ spl4_7 ),
inference(trivial_inequality_removal,[status(thm)],[f399]) ).
thf(f399,plain,
( ( $false
= ( sK11 @ sK8 @ sK6 ) )
| ( $false = $true )
| ( $false
= ( sK1 @ sK8 ) )
| ~ spl4_3
| ~ spl4_7 ),
inference(superposition,[status(thm)],[f91,f106]) ).
thf(f106,plain,
( ! [X2: a > $o] :
( ( $false
= ( sK8 @ X2 ) )
| ( $false
= ( X2 @ sK6 ) ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[status(thm)],[f105]) ).
thf(f105,definition,
( spl4_7
<=> ! [X2: a > $o] :
( ( $false
= ( X2 @ sK6 ) )
| ( $false
= ( sK8 @ X2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_7])],[avatar_definition]) ).
thf(f91,plain,
( ! [X2: ( a > $o ) > $o] :
( ( ( X2 @ ( sK11 @ X2 ) )
= $true )
| ( $false
= ( sK1 @ X2 ) ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f90]) ).
thf(f90,definition,
( spl4_3
<=> ! [X2: ( a > $o ) > $o] :
( ( ( X2 @ ( sK11 @ X2 ) )
= $true )
| ( $false
= ( sK1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition]) ).
thf(f87,plain,
( ! [X2: ( a > $o ) > $o] :
( ( $true
= ( sK11 @ X2 @ sK6 ) )
| ( $false
= ( sK1 @ X2 ) ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f86]) ).
thf(f86,definition,
( spl4_2
<=> ! [X2: ( a > $o ) > $o] :
( ( $false
= ( sK1 @ X2 ) )
| ( $true
= ( sK11 @ X2 @ sK6 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f478,plain,
( ~ spl4_1
| ~ spl4_5
| ~ spl4_7
| ~ spl4_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f477]) ).
thf(f477,plain,
( $false
| ~ spl4_1
| ~ spl4_5
| ~ spl4_7
| ~ spl4_10 ),
inference(trivial_inequality_removal,[status(thm)],[f473]) ).
thf(f473,plain,
( ( $false = $true )
| ~ spl4_1
| ~ spl4_5
| ~ spl4_7
| ~ spl4_10 ),
inference(superposition,[status(thm)],[f459,f118]) ).
thf(f459,plain,
( ( $false
= ( sK1 @ sK8 ) )
| ~ spl4_1
| ~ spl4_5
| ~ spl4_7
| ~ spl4_10 ),
inference(trivial_inequality_removal,[status(thm)],[f453]) ).
thf(f453,plain,
( ( $false
= ( sK1 @ sK8 ) )
| ( $false = $true )
| ~ spl4_1
| ~ spl4_5
| ~ spl4_7
| ~ spl4_10 ),
inference(superposition,[status(thm)],[f446,f84]) ).
thf(f84,plain,
( ! [X1: ( a > $o ) > $o] :
( ( ( sK9 @ X1 @ sK6 )
= $true )
| ( $false
= ( sK1 @ X1 ) ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f83]) ).
thf(f83,definition,
( spl4_1
<=> ! [X1: ( a > $o ) > $o] :
( ( ( sK9 @ X1 @ sK6 )
= $true )
| ( $false
= ( sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f446,plain,
( ( ( sK9 @ sK8 @ sK6 )
= $false )
| ~ spl4_5
| ~ spl4_7
| ~ spl4_10 ),
inference(trivial_inequality_removal,[status(thm)],[f445]) ).
thf(f445,plain,
( ( $false = $true )
| ( ( sK9 @ sK8 @ sK6 )
= $false )
| ~ spl4_5
| ~ spl4_7
| ~ spl4_10 ),
inference(forward_demodulation,[status(thm)],[f442,f118]) ).
thf(f442,plain,
( ( ( sK9 @ sK8 @ sK6 )
= $false )
| ( $false
= ( sK1 @ sK8 ) )
| ~ spl4_5
| ~ spl4_7 ),
inference(trivial_inequality_removal,[status(thm)],[f437]) ).
thf(f437,plain,
( ( $false = $true )
| ( $false
= ( sK1 @ sK8 ) )
| ( ( sK9 @ sK8 @ sK6 )
= $false )
| ~ spl4_5
| ~ spl4_7 ),
inference(superposition,[status(thm)],[f106,f98]) ).
thf(f98,plain,
( ! [X1: ( a > $o ) > $o] :
( ( ( X1 @ ( sK9 @ X1 ) )
= $true )
| ( $false
= ( sK1 @ X1 ) ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[status(thm)],[f97]) ).
thf(f97,definition,
( spl4_5
<=> ! [X1: ( a > $o ) > $o] :
( ( $false
= ( sK1 @ X1 ) )
| ( ( X1 @ ( sK9 @ X1 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition]) ).
thf(f432,plain,
( ~ spl4_4
| ~ spl4_6
| ~ spl4_7
| ~ spl4_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f431]) ).
thf(f431,plain,
( $false
| ~ spl4_4
| ~ spl4_6
| ~ spl4_7
| ~ spl4_10 ),
inference(trivial_inequality_removal,[status(thm)],[f427]) ).
thf(f427,plain,
( ( $false = $true )
| ~ spl4_4
| ~ spl4_6
| ~ spl4_7
| ~ spl4_10 ),
inference(superposition,[status(thm)],[f426,f118]) ).
thf(f426,plain,
( ( $false
= ( sK1 @ sK8 ) )
| ~ spl4_4
| ~ spl4_6
| ~ spl4_7
| ~ spl4_10 ),
inference(trivial_inequality_removal,[status(thm)],[f422]) ).
thf(f422,plain,
( ( $false
= ( sK1 @ sK8 ) )
| ( $false = $true )
| ~ spl4_4
| ~ spl4_6
| ~ spl4_7
| ~ spl4_10 ),
inference(superposition,[status(thm)],[f95,f413]) ).
thf(f413,plain,
( ( $false
= ( sK10 @ sK8 @ sK6 ) )
| ~ spl4_6
| ~ spl4_7
| ~ spl4_10 ),
inference(trivial_inequality_removal,[status(thm)],[f412]) ).
thf(f412,plain,
( ( $false
= ( sK10 @ sK8 @ sK6 ) )
| ( $false = $true )
| ~ spl4_6
| ~ spl4_7
| ~ spl4_10 ),
inference(forward_demodulation,[status(thm)],[f411,f118]) ).
thf(f411,plain,
( ( $false
= ( sK1 @ sK8 ) )
| ( $false
= ( sK10 @ sK8 @ sK6 ) )
| ~ spl4_6
| ~ spl4_7 ),
inference(trivial_inequality_removal,[status(thm)],[f395]) ).
thf(f395,plain,
( ( $false
= ( sK10 @ sK8 @ sK6 ) )
| ( $false = $true )
| ( $false
= ( sK1 @ sK8 ) )
| ~ spl4_6
| ~ spl4_7 ),
inference(superposition,[status(thm)],[f106,f102]) ).
thf(f102,plain,
( ! [X2: ( a > $o ) > $o] :
( ( ( X2 @ ( sK10 @ X2 ) )
= $true )
| ( $false
= ( sK1 @ X2 ) ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[status(thm)],[f101]) ).
thf(f101,definition,
( spl4_6
<=> ! [X2: ( a > $o ) > $o] :
( ( ( X2 @ ( sK10 @ X2 ) )
= $true )
| ( $false
= ( sK1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition]) ).
thf(f95,plain,
( ! [X2: ( a > $o ) > $o] :
( ( $true
= ( sK10 @ X2 @ sK6 ) )
| ( $false
= ( sK1 @ X2 ) ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[status(thm)],[f94]) ).
thf(f94,definition,
( spl4_4
<=> ! [X2: ( a > $o ) > $o] :
( ( $true
= ( sK10 @ X2 @ sK6 ) )
| ( $false
= ( sK1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition]) ).
thf(f391,plain,
( ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f390]) ).
thf(f390,plain,
( $false
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_9 ),
inference(trivial_inequality_removal,[status(thm)],[f387]) ).
thf(f387,plain,
( ( $false = $true )
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_9 ),
inference(superposition,[status(thm)],[f113,f384]) ).
thf(f384,plain,
( ( $false
= ( sK1 @ ( sK7 @ sK10 ) ) )
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_9 ),
inference(trivial_inequality_removal,[status(thm)],[f381]) ).
thf(f381,plain,
( ( $false
= ( sK1 @ ( sK7 @ sK10 ) ) )
| ( $false = $true )
| ~ spl4_4
| ~ spl4_6
| ~ spl4_8
| ~ spl4_9 ),
inference(superposition,[status(thm)],[f95,f378]) ).
thf(f378,plain,
( ( $false
= ( sK10 @ ( sK7 @ sK10 ) @ sK6 ) )
| ~ spl4_6
| ~ spl4_8
| ~ spl4_9 ),
inference(trivial_inequality_removal,[status(thm)],[f377]) ).
thf(f377,plain,
( ( $false = $true )
| ( $false
= ( sK10 @ ( sK7 @ sK10 ) @ sK6 ) )
| ~ spl4_6
| ~ spl4_8
| ~ spl4_9 ),
inference(forward_demodulation,[status(thm)],[f374,f113]) ).
thf(f374,plain,
( ( $false
= ( sK10 @ ( sK7 @ sK10 ) @ sK6 ) )
| ( $false
= ( sK1 @ ( sK7 @ sK10 ) ) )
| ~ spl4_6
| ~ spl4_8 ),
inference(trivial_inequality_removal,[status(thm)],[f368]) ).
thf(f368,plain,
( ( $false = $true )
| ( $false
= ( sK10 @ ( sK7 @ sK10 ) @ sK6 ) )
| ( $false
= ( sK1 @ ( sK7 @ sK10 ) ) )
| ~ spl4_6
| ~ spl4_8 ),
inference(superposition,[status(thm)],[f102,f109]) ).
thf(f109,plain,
( ! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( sK7 @ X1 @ ( X1 @ ( sK7 @ X1 ) ) ) )
| ( ( X1 @ ( sK7 @ X1 ) @ sK6 )
= $false ) )
| ~ spl4_8 ),
inference(avatar_component_clause,[status(thm)],[f108]) ).
thf(f108,definition,
( spl4_8
<=> ! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( sK7 @ X1 @ ( X1 @ ( sK7 @ X1 ) ) ) )
| ( ( X1 @ ( sK7 @ X1 ) @ sK6 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl4_8])],[avatar_definition]) ).
thf(f113,plain,
( ! [X1: ( ( a > $o ) > $o ) > a > $o] :
( $true
= ( sK1 @ ( sK7 @ X1 ) ) )
| ~ spl4_9 ),
inference(avatar_component_clause,[status(thm)],[f112]) ).
thf(f112,definition,
( spl4_9
<=> ! [X1: ( ( a > $o ) > $o ) > a > $o] :
( $true
= ( sK1 @ ( sK7 @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_9])],[avatar_definition]) ).
thf(f364,plain,
( ~ spl4_1
| ~ spl4_5
| ~ spl4_8
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f363]) ).
thf(f363,plain,
( $false
| ~ spl4_1
| ~ spl4_5
| ~ spl4_8
| ~ spl4_9 ),
inference(trivial_inequality_removal,[status(thm)],[f359]) ).
thf(f359,plain,
( ( $false = $true )
| ~ spl4_1
| ~ spl4_5
| ~ spl4_8
| ~ spl4_9 ),
inference(superposition,[status(thm)],[f358,f113]) ).
thf(f358,plain,
( ( ( sK1 @ ( sK7 @ sK9 ) )
= $false )
| ~ spl4_1
| ~ spl4_5
| ~ spl4_8
| ~ spl4_9 ),
inference(trivial_inequality_removal,[status(thm)],[f355]) ).
thf(f355,plain,
( ( $false = $true )
| ( ( sK1 @ ( sK7 @ sK9 ) )
= $false )
| ~ spl4_1
| ~ spl4_5
| ~ spl4_8
| ~ spl4_9 ),
inference(superposition,[status(thm)],[f84,f320]) ).
thf(f320,plain,
( ( ( sK9 @ ( sK7 @ sK9 ) @ sK6 )
= $false )
| ~ spl4_5
| ~ spl4_8
| ~ spl4_9 ),
inference(trivial_inequality_removal,[status(thm)],[f319]) ).
thf(f319,plain,
( ( $false = $true )
| ( ( sK9 @ ( sK7 @ sK9 ) @ sK6 )
= $false )
| ~ spl4_5
| ~ spl4_8
| ~ spl4_9 ),
inference(forward_demodulation,[status(thm)],[f313,f113]) ).
thf(f313,plain,
( ( ( sK1 @ ( sK7 @ sK9 ) )
= $false )
| ( ( sK9 @ ( sK7 @ sK9 ) @ sK6 )
= $false )
| ~ spl4_5
| ~ spl4_8 ),
inference(trivial_inequality_removal,[status(thm)],[f306]) ).
thf(f306,plain,
( ( ( sK1 @ ( sK7 @ sK9 ) )
= $false )
| ( ( sK9 @ ( sK7 @ sK9 ) @ sK6 )
= $false )
| ( $false = $true )
| ~ spl4_5
| ~ spl4_8 ),
inference(superposition,[status(thm)],[f98,f109]) ).
thf(f354,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_8
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f353]) ).
thf(f353,plain,
( $false
| ~ spl4_2
| ~ spl4_3
| ~ spl4_8
| ~ spl4_9 ),
inference(trivial_inequality_removal,[status(thm)],[f350]) ).
thf(f350,plain,
( ( $false = $true )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_8
| ~ spl4_9 ),
inference(superposition,[status(thm)],[f113,f335]) ).
thf(f335,plain,
( ( ( sK1 @ ( sK7 @ sK11 ) )
= $false )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_8
| ~ spl4_9 ),
inference(trivial_inequality_removal,[status(thm)],[f331]) ).
thf(f331,plain,
( ( $false = $true )
| ( ( sK1 @ ( sK7 @ sK11 ) )
= $false )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_8
| ~ spl4_9 ),
inference(superposition,[status(thm)],[f87,f322]) ).
thf(f322,plain,
( ( $false
= ( sK11 @ ( sK7 @ sK11 ) @ sK6 ) )
| ~ spl4_3
| ~ spl4_8
| ~ spl4_9 ),
inference(trivial_inequality_removal,[status(thm)],[f321]) ).
thf(f321,plain,
( ( $false = $true )
| ( $false
= ( sK11 @ ( sK7 @ sK11 ) @ sK6 ) )
| ~ spl4_3
| ~ spl4_8
| ~ spl4_9 ),
inference(forward_demodulation,[status(thm)],[f312,f113]) ).
thf(f312,plain,
( ( ( sK1 @ ( sK7 @ sK11 ) )
= $false )
| ( $false
= ( sK11 @ ( sK7 @ sK11 ) @ sK6 ) )
| ~ spl4_3
| ~ spl4_8 ),
inference(trivial_inequality_removal,[status(thm)],[f305]) ).
thf(f305,plain,
( ( $false
= ( sK11 @ ( sK7 @ sK11 ) @ sK6 ) )
| ( ( sK1 @ ( sK7 @ sK11 ) )
= $false )
| ( $false = $true )
| ~ spl4_3
| ~ spl4_8 ),
inference(superposition,[status(thm)],[f91,f109]) ).
thf(f120,plain,
( spl4_10
| spl4_9 ),
inference(avatar_split_clause,[status(thm)],[f52,f112,f116]) ).
thf(f52,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $true
= ( sK1 @ sK8 ) )
| ( $true
= ( sK1 @ ( sK7 @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ( sK1 @ ( sK7 @ X1 ) )
=> ( ( sK7 @ X1 @ ( X1 @ ( sK7 @ X1 ) ) )
& ( X1 @ ( sK7 @ X1 ) @ sK6 ) ) )
= $false )
| ( $true
= ( sK1 @ sK8 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f48,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( ( sK1 @ sK8 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK8 @ Y0 )
& ( Y0 @ sK6 ) ) ) ) )
| ( ( ( sK1 @ ( sK7 @ X1 ) )
=> ( ( sK7 @ X1 @ ( X1 @ ( sK7 @ X1 ) ) )
& ( X1 @ ( sK7 @ X1 ) @ sK6 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f47]) ).
thf(f47,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK6 ) ) ) )
@ sK8 ) )
| ( ( ( sK1 @ ( sK7 @ X1 ) )
=> ( ( sK7 @ X1 @ ( X1 @ ( sK7 @ X1 ) ) )
& ( X1 @ ( sK7 @ X1 ) @ sK6 ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK6 ) ) ) ) )
= $false )
| ( ( ( sK1 @ ( sK7 @ X1 ) )
=> ( ( sK7 @ X1 @ ( X1 @ ( sK7 @ X1 ) ) )
& ( X1 @ ( sK7 @ X1 ) @ sK6 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f45]) ).
thf(f45,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ( Y0 @ ( X1 @ Y0 ) )
& ( X1 @ Y0 @ sK6 ) ) )
@ ( sK7 @ X1 ) ) )
| ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK6 ) ) ) ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ( Y0 @ ( X1 @ Y0 ) )
& ( X1 @ Y0 @ sK6 ) ) ) ) )
| ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK6 ) ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK6 ) ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK1 @ Y1 )
=> ( ( Y1 @ ( Y0 @ Y1 ) )
& ( Y0 @ Y1 @ sK6 ) ) ) )
@ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK1 @ Y1 )
=> ( ( Y1 @ ( Y0 @ Y1 ) )
& ( Y0 @ Y1 @ sK6 ) ) ) ) )
= $false )
| ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK6 ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK1 @ Y1 )
=> ( ( Y1 @ ( Y0 @ Y1 ) )
& ( Y0 @ Y1 @ sK6 ) ) ) ) )
!= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK6 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK1 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) )
@ sK6 )
!= ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( sK1 @ Y2 )
=> ( ( Y2 @ ( Y1 @ Y2 ) )
& ( Y1 @ Y2 @ Y0 ) ) ) ) )
@ sK6 ) ),
inference(negative_extensionality,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK1 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( sK1 @ Y2 )
=> ( ( Y2 @ ( Y1 @ Y2 ) )
& ( Y1 @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X1: ( a > $o ) > $o] :
( ( $true
= ( X1 @ ( sK0 @ X1 ) ) )
| ! [X2: a > $o] :
( ( X1 @ X2 )
!= $true ) )
& ( ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK1 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( sK1 @ Y2 )
=> ( ( Y2 @ ( Y1 @ Y2 ) )
& ( Y1 @ Y2 @ Y0 ) ) ) ) ) ) )
& ! [X4: ( a > $o ) > $o] :
( ( ( X4 @ ( sK2 @ X4 ) )
= $true )
| ( $true
!= ( sK1 @ X4 ) ) )
& ( ( sK1 @ sK3 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f7,f11,f10,f9,f8]) ).
thf(f8,plain,
( ? [X0: ( ( a > $o ) > $o ) > a > $o] :
! [X1: ( a > $o ) > $o] :
( ( ( X1 @ ( X0 @ X1 ) )
= $true )
| ! [X2: a > $o] :
( ( X1 @ X2 )
!= $true ) )
=> ! [X1: ( a > $o ) > $o] :
( ( $true
= ( X1 @ ( sK0 @ X1 ) ) )
| ! [X2: a > $o] :
( ( X1 @ X2 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X3: ( ( a > $o ) > $o ) > $o] :
( ( ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( X3 @ Y2 )
=> ( ( Y2 @ ( Y1 @ Y2 ) )
& ( Y1 @ Y2 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( X3 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) ) ) )
& ! [X4: ( a > $o ) > $o] :
( ? [X5: a > $o] :
( $true
= ( X4 @ X5 ) )
| ( $true
!= ( X3 @ X4 ) ) )
& ? [X6: ( a > $o ) > $o] :
( ( X3 @ X6 )
= $true ) )
=> ( ( ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK1 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( sK1 @ Y2 )
=> ( ( Y2 @ ( Y1 @ Y2 ) )
& ( Y1 @ Y2 @ Y0 ) ) ) ) ) ) )
& ! [X4: ( a > $o ) > $o] :
( ? [X5: a > $o] :
( $true
= ( X4 @ X5 ) )
| ( $true
!= ( sK1 @ X4 ) ) )
& ? [X6: ( a > $o ) > $o] :
( ( sK1 @ X6 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X4: ( a > $o ) > $o] :
( ? [X5: a > $o] :
( $true
= ( X4 @ X5 ) )
=> ( ( X4 @ ( sK2 @ X4 ) )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X6: ( a > $o ) > $o] :
( ( sK1 @ X6 )
= $true )
=> ( ( sK1 @ sK3 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ? [X0: ( ( a > $o ) > $o ) > a > $o] :
! [X1: ( a > $o ) > $o] :
( ( ( X1 @ ( X0 @ X1 ) )
= $true )
| ! [X2: a > $o] :
( ( X1 @ X2 )
!= $true ) )
& ? [X3: ( ( a > $o ) > $o ) > $o] :
( ( ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( X3 @ Y2 )
=> ( ( Y2 @ ( Y1 @ Y2 ) )
& ( Y1 @ Y2 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( X3 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) ) ) )
& ! [X4: ( a > $o ) > $o] :
( ? [X5: a > $o] :
( $true
= ( X4 @ X5 ) )
| ( $true
!= ( X3 @ X4 ) ) )
& ? [X6: ( a > $o ) > $o] :
( ( X3 @ X6 )
= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X3: ( ( a > $o ) > $o ) > $o] :
( ( ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( X3 @ Y2 )
=> ( ( Y2 @ ( Y1 @ Y2 ) )
& ( Y1 @ Y2 @ Y0 ) ) ) ) ) )
!= ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( X3 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) ) ) )
& ! [X4: ( a > $o ) > $o] :
( ? [X5: a > $o] :
( $true
= ( X4 @ X5 ) )
| ( $true
!= ( X3 @ X4 ) ) )
& ? [X6: ( a > $o ) > $o] :
( ( X3 @ X6 )
= $true ) )
& ? [X0: ( ( a > $o ) > $o ) > a > $o] :
! [X1: ( a > $o ) > $o] :
( ( ( X1 @ ( X0 @ X1 ) )
= $true )
| ! [X2: a > $o] :
( ( X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ? [X0: ( ( a > $o ) > $o ) > a > $o] :
! [X1: ( a > $o ) > $o] :
( ? [X2: a > $o] :
( ( X1 @ X2 )
= $true )
=> ( ( X1 @ ( X0 @ X1 ) )
= $true ) )
=> ! [X3: ( ( a > $o ) > $o ) > $o] :
( ( ! [X4: ( a > $o ) > $o] :
( ( $true
= ( X3 @ X4 ) )
=> ? [X5: a > $o] :
( $true
= ( X4 @ X5 ) ) )
& ? [X6: ( a > $o ) > $o] :
( ( X3 @ X6 )
= $true ) )
=> ( ( ^ [Y0: a] :
( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y1: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y2: ( a > $o ) > $o] :
( ( X3 @ Y2 )
=> ( ( Y2 @ ( Y1 @ Y2 ) )
& ( Y1 @ Y2 @ Y0 ) ) ) ) ) )
= ( ^ [Y0: a] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( X3 @ Y1 )
=> ( ?? @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y1 @ Y2 )
& ( Y2 @ Y0 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ? [X0: ( ( a > $o ) > $o ) > a > $o] :
! [X1: ( a > $o ) > $o] :
( ? [X2: a > $o] : ( X1 @ X2 )
=> ( X1 @ ( X0 @ X1 ) ) )
=> ! [X3: ( ( a > $o ) > $o ) > $o] :
( ( ! [X4: ( a > $o ) > $o] :
( ( X3 @ X4 )
=> ? [X5: a > $o] : ( X4 @ X5 ) )
& ? [X6: ( a > $o ) > $o] : ( X3 @ X6 ) )
=> ( ( ^ [X7: a] :
! [X8: ( a > $o ) > $o] :
( ( X3 @ X8 )
=> ? [X9: a > $o] :
( ( X9 @ X7 )
& ( X8 @ X9 ) ) ) )
= ( ^ [X10: a] :
? [X11: ( ( a > $o ) > $o ) > a > $o] :
! [X12: ( a > $o ) > $o] :
( ( X3 @ X12 )
=> ( ( X11 @ X12 @ X10 )
& ( X12 @ ( X11 @ X12 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ? [X0: ( ( a > $o ) > $o ) > a > $o] :
! [X1: ( a > $o ) > $o] :
( ? [X2: a > $o] : ( X1 @ X2 )
=> ( X1 @ ( X0 @ X1 ) ) )
=> ! [X3: ( ( a > $o ) > $o ) > $o] :
( ( ! [X1: ( a > $o ) > $o] :
( ( X3 @ X1 )
=> ? [X4: a > $o] : ( X1 @ X4 ) )
& ? [X1: ( a > $o ) > $o] : ( X3 @ X1 ) )
=> ( ( ^ [X5: a] :
! [X6: ( a > $o ) > $o] :
( ( X3 @ X6 )
=> ? [X7: a > $o] :
( ( X7 @ X5 )
& ( X6 @ X7 ) ) ) )
= ( ^ [X5: a] :
? [X0: ( ( a > $o ) > $o ) > a > $o] :
! [X6: ( a > $o ) > $o] :
( ( X3 @ X6 )
=> ( ( X0 @ X6 @ X5 )
& ( X6 @ ( X0 @ X6 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ? [X0: ( ( a > $o ) > $o ) > a > $o] :
! [X1: ( a > $o ) > $o] :
( ? [X2: a > $o] : ( X1 @ X2 )
=> ( X1 @ ( X0 @ X1 ) ) )
=> ! [X3: ( ( a > $o ) > $o ) > $o] :
( ( ! [X1: ( a > $o ) > $o] :
( ( X3 @ X1 )
=> ? [X4: a > $o] : ( X1 @ X4 ) )
& ? [X1: ( a > $o ) > $o] : ( X3 @ X1 ) )
=> ( ( ^ [X5: a] :
! [X6: ( a > $o ) > $o] :
( ( X3 @ X6 )
=> ? [X7: a > $o] :
( ( X7 @ X5 )
& ( X6 @ X7 ) ) ) )
= ( ^ [X5: a] :
? [X0: ( ( a > $o ) > $o ) > a > $o] :
! [X6: ( a > $o ) > $o] :
( ( X3 @ X6 )
=> ( ( X0 @ X6 @ X5 )
& ( X6 @ ( X0 @ X6 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9y3h8pOOCz/DTF2THF_9293.p',cTHM535B) ).
thf(f119,plain,
( spl4_8
| spl4_10 ),
inference(avatar_split_clause,[status(thm)],[f53,f116,f108]) ).
thf(f53,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $true
= ( sK1 @ sK8 ) )
| ( ( X1 @ ( sK7 @ X1 ) @ sK6 )
= $false )
| ( $false
= ( sK7 @ X1 @ ( X1 @ ( sK7 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f51]) ).
thf(f51,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $true
= ( sK1 @ sK8 ) )
| ( $false
= ( ( sK7 @ X1 @ ( X1 @ ( sK7 @ X1 ) ) )
& ( X1 @ ( sK7 @ X1 ) @ sK6 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f50]) ).
thf(f114,plain,
( spl4_7
| spl4_9 ),
inference(avatar_split_clause,[status(thm)],[f58,f112,f105]) ).
thf(f58,plain,
! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $true
= ( sK1 @ ( sK7 @ X1 ) ) )
| ( $false
= ( X2 @ sK6 ) )
| ( $false
= ( sK8 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $true
= ( sK1 @ ( sK7 @ X1 ) ) )
| ( $false
= ( ( sK8 @ X2 )
& ( X2 @ sK6 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f56]) ).
thf(f56,plain,
! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( ^ [Y0: a > $o] :
( ( sK8 @ Y0 )
& ( Y0 @ sK6 ) )
@ X2 ) )
| ( $true
= ( sK1 @ ( sK7 @ X1 ) ) ) ),
inference(pi_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $true
= ( sK1 @ ( sK7 @ X1 ) ) )
| ( $false
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK8 @ Y0 )
& ( Y0 @ sK6 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( ( ( sK1 @ ( sK7 @ X1 ) )
=> ( ( sK7 @ X1 @ ( X1 @ ( sK7 @ X1 ) ) )
& ( X1 @ ( sK7 @ X1 ) @ sK6 ) ) )
= $false )
| ( $false
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK8 @ Y0 )
& ( Y0 @ sK6 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f48]) ).
thf(f110,plain,
( spl4_7
| spl4_8 ),
inference(avatar_split_clause,[status(thm)],[f62,f108,f105]) ).
thf(f62,plain,
! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( X2 @ sK6 ) )
| ( $false
= ( sK7 @ X1 @ ( X1 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( sK8 @ X2 ) )
| ( ( X1 @ ( sK7 @ X1 ) @ sK6 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( ( sK8 @ X2 )
& ( X2 @ sK6 ) ) )
| ( ( X1 @ ( sK7 @ X1 ) @ sK6 )
= $false )
| ( $false
= ( sK7 @ X1 @ ( X1 @ ( sK7 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,plain,
! [X2: a > $o,X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( ^ [Y0: a > $o] :
( ( sK8 @ Y0 )
& ( Y0 @ sK6 ) )
@ X2 ) )
| ( ( X1 @ ( sK7 @ X1 ) @ sK6 )
= $false )
| ( $false
= ( sK7 @ X1 @ ( X1 @ ( sK7 @ X1 ) ) ) ) ),
inference(pi_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( sK7 @ X1 @ ( X1 @ ( sK7 @ X1 ) ) ) )
| ( ( X1 @ ( sK7 @ X1 ) @ sK6 )
= $false )
| ( $false
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK8 @ Y0 )
& ( Y0 @ sK6 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
! [X1: ( ( a > $o ) > $o ) > a > $o] :
( ( $false
= ( ( sK7 @ X1 @ ( X1 @ ( sK7 @ X1 ) ) )
& ( X1 @ ( sK7 @ X1 ) @ sK6 ) ) )
| ( $false
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK8 @ Y0 )
& ( Y0 @ sK6 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f103,plain,
( spl4_5
| spl4_6 ),
inference(avatar_split_clause,[status(thm)],[f76,f101,f97]) ).
thf(f76,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( X1 @ ( sK9 @ X1 ) )
= $true )
| ( ( X2 @ ( sK10 @ X2 ) )
= $true )
| ( $false
= ( sK1 @ X2 ) )
| ( $false
= ( sK1 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( X1 @ ( sK9 @ X1 ) )
= $true )
| ( $false
= ( sK1 @ X1 ) )
| ( ( ( X2 @ ( sK10 @ X2 ) )
& ( sK10 @ X2 @ sK6 ) )
= $true )
| ( $false
= ( sK1 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f73]) ).
thf(f73,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( X1 @ ( sK9 @ X1 ) )
= $true )
| ( $false
= ( sK1 @ X1 ) )
| ( $false
= ( sK1 @ X2 ) )
| ( ( ^ [Y0: a > $o] :
( ( X2 @ Y0 )
& ( Y0 @ sK6 ) )
@ ( sK10 @ X2 ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( $false
= ( sK1 @ X2 ) )
| ( $false
= ( sK1 @ X1 ) )
| ( $true
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( X2 @ Y0 )
& ( Y0 @ sK6 ) ) ) )
| ( ( X1 @ ( sK9 @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( X1 @ ( sK9 @ X1 ) )
= $true )
| ( $false
= ( sK1 @ X1 ) )
| ( ( ( sK1 @ X2 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( X2 @ Y0 )
& ( Y0 @ sK6 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f69]) ).
thf(f69,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( $true
= ( ( X1 @ ( sK9 @ X1 ) )
& ( sK9 @ X1 @ sK6 ) ) )
| ( ( ( sK1 @ X2 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( X2 @ Y0 )
& ( Y0 @ sK6 ) ) ) )
= $true )
| ( $false
= ( sK1 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f68]) ).
thf(f68,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK6 ) ) ) )
@ X2 )
= $true )
| ( $true
= ( ( X1 @ ( sK9 @ X1 ) )
& ( sK9 @ X1 @ sK6 ) ) )
| ( $false
= ( sK1 @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
! [X1: ( a > $o ) > $o] :
( ( $false
= ( sK1 @ X1 ) )
| ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK6 ) ) ) ) )
= $true )
| ( $true
= ( ( X1 @ ( sK9 @ X1 ) )
& ( sK9 @ X1 @ sK6 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
! [X1: ( a > $o ) > $o] :
( ( ( ( sK1 @ X1 )
=> ( ( X1 @ ( sK9 @ X1 ) )
& ( sK9 @ X1 @ sK6 ) ) )
= $true )
| ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK6 ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f65]) ).
thf(f65,plain,
! [X1: ( a > $o ) > $o] :
( ( ( ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ( Y0 @ ( sK9 @ Y0 ) )
& ( sK9 @ Y0 @ sK6 ) ) )
@ X1 )
= $true )
| ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK6 ) ) ) ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f64]) ).
thf(f64,plain,
( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ( Y0 @ ( sK9 @ Y0 ) )
& ( sK9 @ Y0 @ sK6 ) ) ) )
= $true )
| ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK6 ) ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f63]) ).
thf(f63,plain,
( ( ( ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK1 @ Y1 )
=> ( ( Y1 @ ( Y0 @ Y1 ) )
& ( Y0 @ Y1 @ sK6 ) ) ) )
@ sK9 )
= $true )
| ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK6 ) ) ) ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ( ?? @ ( ( ( a > $o ) > $o ) > a > $o )
@ ^ [Y0: ( ( a > $o ) > $o ) > a > $o] :
( !! @ ( ( a > $o ) > $o )
@ ^ [Y1: ( a > $o ) > $o] :
( ( sK1 @ Y1 )
=> ( ( Y1 @ ( Y0 @ Y1 ) )
& ( Y0 @ Y1 @ sK6 ) ) ) ) )
= $true )
| ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( sK1 @ Y0 )
=> ( ?? @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
& ( Y1 @ sK6 ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f99,plain,
( spl4_4
| spl4_5 ),
inference(avatar_split_clause,[status(thm)],[f75,f97,f94]) ).
thf(f75,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( $false
= ( sK1 @ X1 ) )
| ( $true
= ( sK10 @ X2 @ sK6 ) )
| ( $false
= ( sK1 @ X2 ) )
| ( ( X1 @ ( sK9 @ X1 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f74]) ).
thf(f92,plain,
( spl4_3
| spl4_1 ),
inference(avatar_split_clause,[status(thm)],[f81,f83,f90]) ).
thf(f81,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( X2 @ ( sK11 @ X2 ) )
= $true )
| ( $false
= ( sK1 @ X1 ) )
| ( ( sK9 @ X1 @ sK6 )
= $true )
| ( $false
= ( sK1 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( $false
= ( sK1 @ X1 ) )
| ( $false
= ( sK1 @ X2 ) )
| ( ( ( X2 @ ( sK11 @ X2 ) )
& ( sK11 @ X2 @ sK6 ) )
= $true )
| ( ( sK9 @ X1 @ sK6 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f78]) ).
thf(f78,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( sK9 @ X1 @ sK6 )
= $true )
| ( $false
= ( sK1 @ X2 ) )
| ( $false
= ( sK1 @ X1 ) )
| ( ( ^ [Y0: a > $o] :
( ( X2 @ Y0 )
& ( Y0 @ sK6 ) )
@ ( sK11 @ X2 ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( $false
= ( sK1 @ X2 ) )
| ( ( sK9 @ X1 @ sK6 )
= $true )
| ( $false
= ( sK1 @ X1 ) )
| ( $true
= ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( X2 @ Y0 )
& ( Y0 @ sK6 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( $false
= ( sK1 @ X1 ) )
| ( ( sK9 @ X1 @ sK6 )
= $true )
| ( ( ( sK1 @ X2 )
=> ( ?? @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( X2 @ Y0 )
& ( Y0 @ sK6 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f69]) ).
thf(f88,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f80,f86,f83]) ).
thf(f80,plain,
! [X2: ( a > $o ) > $o,X1: ( a > $o ) > $o] :
( ( ( sK9 @ X1 @ sK6 )
= $true )
| ( $false
= ( sK1 @ X2 ) )
| ( $true
= ( sK11 @ X2 @ sK6 ) )
| ( $false
= ( sK1 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO244^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n016.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 14:27:21 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SYO244^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.46 % Domain : Syntactic
% 0.19/0.46 % Problem : TPS problem from BASIC-HO-EQ-THMS
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bro09]
% 0.19/0.46 % Names : tps_0994 [Bro09]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.56 v9.1.0, 0.50 v8.2.0, 0.54 v8.1.0, 0.45 v7.5.0, 0.57 v7.4.0, 0.67 v7.2.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.86 v6.1.0, 0.71 v5.5.0, 1.00 v4.0.0
% 0.19/0.46 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.19/0.46 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.19/0.46 % Number of connectives : 23 ( 0 ~; 0 |; 3 &; 14 @)
% 0.19/0.46 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 9 ( 9 avg)
% 0.19/0.46 % Number of types : 2 ( 1 usr)
% 0.19/0.46 % Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.19/0.46 % Number of variables : 13 ( 2 ^; 5 !; 6 ?; 13 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(a_type,type,
% 0.19/0.46 a: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(cTHM535B,conjecture,
% 0.19/0.46 ( ? [Xf: ( ( a > $o ) > $o ) > a > $o] :
% 0.19/0.46 ! [X: ( a > $o ) > $o] :
% 0.19/0.46 ( ? [Xt: a > $o] : ( X @ Xt )
% 0.19/0.46 => ( X @ ( Xf @ X ) ) )
% 0.19/0.46 => ! [A: ( ( a > $o ) > $o ) > $o] :
% 0.19/0.46 ( ( ? [X: ( a > $o ) > $o] : ( A @ X )
% 0.19/0.46 & ! [X: ( a > $o ) > $o] :
% 0.19/0.46 ( ( A @ X )
% 0.19/0.46 => ? [Xu: a > $o] : ( X @ Xu ) ) )
% 0.19/0.46 => ( ( ^ [Xx: a] :
% 0.19/0.46 ! [Xa: ( a > $o ) > $o] :
% 0.19/0.46 ( ( A @ Xa )
% 0.19/0.46 => ? [Xb: a > $o] :
% 0.19/0.46 ( ( Xa @ Xb )
% 0.19/0.46 & ( Xb @ Xx ) ) ) )
% 0.19/0.46 = ( ^ [Xx: a] :
% 0.19/0.46 ? [Xf: ( ( a > $o ) > $o ) > a > $o] :
% 0.19/0.46 ! [Xa: ( a > $o ) > $o] :
% 0.19/0.46 ( ( A @ Xa )
% 0.19/0.46 => ( ( Xa @ ( Xf @ Xa ) )
% 0.19/0.46 & ( Xf @ Xa @ Xx ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.62/1.32 ---- Embedded in THF ---
% 1.62/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.62/1.32 %%% Generated on Tue Feb 24 14:27:22 EST 2026
% 1.62/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.62/1.32 %%% Logic specification used:
% 1.62/1.32 %%% thf(spec, logic, $$dhol).
% 1.62/1.32
% 1.62/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.9y3h8pOOCz/DTF2DTF9293.p
% See solution above
% 1.62/1.32 ------------------------
% 1.62/1.33 ---- Cleaned THF ---
% 1.62/1.33 thf(a_type,type,
% 1.62/1.33 a: $tType ).
% 1.62/1.33
% 1.62/1.33 thf(cTHM535B,conjecture,
% 1.62/1.33 ( ? [Xf: ( ( a > $o ) > $o ) > a > $o] :
% 1.62/1.33 ! [X: ( a > $o ) > $o] :
% 1.62/1.33 ( ? [Xt: a > $o] : ( X @ Xt )
% 1.62/1.33 => ( X @ ( Xf @ X ) ) )
% 1.62/1.33 => ! [A: ( ( a > $o ) > $o ) > $o] :
% 1.62/1.33 ( ( ? [X: ( a > $o ) > $o] : ( A @ X )
% 1.62/1.33 & ! [X: ( a > $o ) > $o] :
% 1.62/1.33 ( ( A @ X )
% 1.62/1.33 => ? [Xu: a > $o] : ( X @ Xu ) ) )
% 1.62/1.33 => ( ( ^ [Xx: a] :
% 1.62/1.33 ! [Xa: ( a > $o ) > $o] :
% 1.62/1.33 ( ( A @ Xa )
% 1.62/1.33 => ? [Xb: a > $o] :
% 1.62/1.33 ( ( Xa @ Xb )
% 1.62/1.33 & ( Xb @ Xx ) ) ) )
% 1.62/1.33 = ( ^ [Xx: a] :
% 1.62/1.33 ? [Xf: ( ( a > $o ) > $o ) > a > $o] :
% 1.62/1.33 ! [Xa: ( a > $o ) > $o] :
% 1.62/1.33 ( ( A @ Xa )
% 1.62/1.33 => ( ( Xa @ ( Xf @ Xa ) )
% 1.62/1.33 & ( Xf @ Xa @ Xx ) ) ) ) ) ) ) ).
% 1.62/1.33 ------------------------
% 1.62/1.35 % (9453)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9293 for (2999ds/183Mi)
% 1.62/1.35 % (9456)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9293 for (2999ds/2Mi)
% 1.62/1.35 % (9454)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_9293 for (2999ds/4Mi)
% 1.62/1.35 % (9456)Instruction limit reached!
% 1.62/1.35 % (9456)------------------------------
% 1.62/1.35 % (9456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.35 % (9456)Termination reason: Unknown
% 1.62/1.35 % (9456)Termination phase: Saturation
% 1.62/1.35
% 1.62/1.35 % (9456)Memory used [KB]: 5500
% 1.62/1.35 % (9456)Time elapsed: 0.002 s
% 1.62/1.35 % (9456)Instructions burned: 2 (million)
% 1.62/1.35 % (9456)------------------------------
% 1.62/1.35 % (9456)------------------------------
% 1.62/1.35 % (9454)Instruction limit reached!
% 1.62/1.35 % (9454)------------------------------
% 1.62/1.35 % (9454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.35 % (9454)Termination reason: Unknown
% 1.62/1.35 % (9454)Termination phase: Saturation
% 1.62/1.35
% 1.62/1.35 % (9454)Memory used [KB]: 5500
% 1.62/1.35 % (9454)Time elapsed: 0.003 s
% 1.62/1.35 % (9454)Instructions burned: 5 (million)
% 1.62/1.35 % (9454)------------------------------
% 1.62/1.35 % (9454)------------------------------
% 1.62/1.35 % (9455)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_9293 for (2999ds/27Mi)
% 1.62/1.35 % (9457)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_9293 for (2999ds/2Mi)
% 1.62/1.35 % (9458)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_9293 for (2999ds/275Mi)
% 1.62/1.35 % (9457)Instruction limit reached!
% 1.62/1.35 % (9457)------------------------------
% 1.62/1.35 % (9457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.35 % (9457)Termination reason: Unknown
% 1.62/1.35 % (9457)Termination phase: Unused predicate definition removal
% 1.62/1.35
% 1.62/1.35 % (9457)Memory used [KB]: 895
% 1.62/1.35 % (9457)Time elapsed: 0.003 s
% 1.62/1.35 % (9457)Instructions burned: 2 (million)
% 1.62/1.35 % (9457)------------------------------
% 1.62/1.35 % (9457)------------------------------
% 1.62/1.35 % (9459)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9293 for (2999ds/18Mi)
% 1.62/1.36 % (9460)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_9293 for (2999ds/3Mi)
% 1.62/1.36 % (9460)Instruction limit reached!
% 1.62/1.36 % (9460)------------------------------
% 1.62/1.36 % (9460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.36 % (9460)Termination reason: Unknown
% 1.62/1.36 % (9460)Termination phase: Saturation
% 1.62/1.36
% 1.62/1.36 % (9460)Memory used [KB]: 5500
% 1.62/1.36 % (9460)Time elapsed: 0.002 s
% 1.62/1.36 % (9460)Instructions burned: 3 (million)
% 1.62/1.36 % (9460)------------------------------
% 1.62/1.36 % (9460)------------------------------
% 1.62/1.36 % (9461)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_9293 for (2999ds/37Mi)
% 1.62/1.37 % (9459)Instruction limit reached!
% 1.62/1.37 % (9459)------------------------------
% 1.62/1.37 % (9459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.37 % (9459)Termination reason: Unknown
% 1.62/1.37 % (9459)Termination phase: Saturation
% 1.62/1.37
% 1.62/1.37 % (9459)Memory used [KB]: 5628
% 1.62/1.37 % (9459)Time elapsed: 0.013 s
% 1.62/1.37 % (9459)Instructions burned: 18 (million)
% 1.62/1.37 % (9459)------------------------------
% 1.62/1.37 % (9459)------------------------------
% 1.62/1.37 % (9463)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_9293 for (2999ds/3Mi)
% 1.62/1.37 % (9463)Instruction limit reached!
% 1.62/1.37 % (9463)------------------------------
% 1.62/1.37 % (9463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.37 % (9463)Termination reason: Unknown
% 1.62/1.37 % (9463)Termination phase: Saturation
% 1.62/1.37
% 1.62/1.37 % (9463)Memory used [KB]: 5500
% 1.62/1.37 % (9463)Time elapsed: 0.002 s
% 1.62/1.37 % (9463)Instructions burned: 3 (million)
% 1.62/1.37 % (9463)------------------------------
% 1.62/1.37 % (9463)------------------------------
% 1.62/1.37 % (9461)Instruction limit reached!
% 1.62/1.37 % (9461)------------------------------
% 1.62/1.37 % (9461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.37 % (9461)Termination reason: Unknown
% 1.62/1.37 % (9461)Termination phase: Saturation
% 1.62/1.37
% 1.62/1.37 % (9461)Memory used [KB]: 6012
% 1.62/1.37 % (9461)Time elapsed: 0.013 s
% 1.62/1.37 % (9461)Instructions burned: 37 (million)
% 1.62/1.37 % (9461)------------------------------
% 1.62/1.37 % (9461)------------------------------
% 1.62/1.37 % (9455)Instruction limit reached!
% 1.62/1.37 % (9455)------------------------------
% 1.62/1.37 % (9455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.37 % (9455)Termination reason: Unknown
% 1.62/1.37 % (9455)Termination phase: Saturation
% 1.62/1.37
% 1.62/1.37 % (9455)Memory used [KB]: 5628
% 1.62/1.37 % (9455)Time elapsed: 0.020 s
% 1.62/1.37 % (9455)Instructions burned: 27 (million)
% 1.62/1.37 % (9455)------------------------------
% 1.62/1.37 % (9455)------------------------------
% 1.62/1.37 % (9462)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_9293 for (2999ds/15Mi)
% 1.62/1.38 % (9465)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_9293 for (2999ds/7Mi)
% 1.62/1.38 % (9465)Instruction limit reached!
% 1.62/1.38 % (9465)------------------------------
% 1.62/1.38 % (9465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.38 % (9465)Termination reason: Unknown
% 1.62/1.38 % (9465)Termination phase: Saturation
% 1.62/1.38
% 1.62/1.38 % (9465)Memory used [KB]: 1023
% 1.62/1.38 % (9465)Time elapsed: 0.003 s
% 1.62/1.38 % (9465)Instructions burned: 7 (million)
% 1.62/1.38 % (9465)------------------------------
% 1.62/1.38 % (9465)------------------------------
% 1.62/1.38 % (9466)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_9293 for (2999ds/16Mi)
% 1.62/1.38 % (9462)Instruction limit reached!
% 1.62/1.38 % (9462)------------------------------
% 1.62/1.38 % (9462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.38 % (9462)Termination reason: Unknown
% 1.62/1.38 % (9462)Termination phase: Saturation
% 1.62/1.38
% 1.62/1.38 % (9462)Memory used [KB]: 5628
% 1.62/1.38 % (9462)Time elapsed: 0.012 s
% 1.62/1.38 % (9462)Instructions burned: 16 (million)
% 1.62/1.38 % (9462)------------------------------
% 1.62/1.38 % (9462)------------------------------
% 1.62/1.38 % (9458)First to succeed.
% 1.62/1.38 % (9464)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_9293 for (2999ds/1041Mi)
% 1.62/1.39 % (9466)Instruction limit reached!
% 1.62/1.39 % (9466)------------------------------
% 1.62/1.39 % (9466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.39 % (9466)Termination reason: Unknown
% 1.62/1.39 % (9466)Termination phase: Saturation
% 1.62/1.39
% 1.62/1.39 % (9466)Memory used [KB]: 5756
% 1.62/1.39 % (9466)Time elapsed: 0.008 s
% 1.62/1.39 % (9466)Instructions burned: 18 (million)
% 1.62/1.39 % (9466)------------------------------
% 1.62/1.39 % (9466)------------------------------
% 1.62/1.39 % (9468)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_9293 for (2999ds/3Mi)
% 1.62/1.39 % (9467)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_9293 for (2999ds/3Mi)
% 1.62/1.39 % (9468)Instruction limit reached!
% 1.62/1.39 % (9468)------------------------------
% 1.62/1.39 % (9468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.39 % (9458)Refutation found. Thanks to Tanya!
% 1.62/1.39 % SZS status Theorem for DTF2THF_9293
% 1.62/1.39 % SZS output start Proof for DTF2THF_9293
% 1.62/1.39 thf(type_def_5, type, a: $tType).
% 1.62/1.39 thf(func_def_0, type, a: $tType).
% 1.62/1.39 thf(func_def_12, type, sK0: ((a > $o) > $o) > a > $o).
% 1.62/1.39 thf(func_def_13, type, sK1: ((a > $o) > $o) > $o).
% 1.62/1.39 thf(func_def_14, type, sK2: ((a > $o) > $o) > a > $o).
% 1.62/1.39 thf(func_def_15, type, sK3: (a > $o) > $o).
% 1.62/1.39 thf(func_def_17, type, ph5: !>[X0: $tType]:(X0)).
% 1.62/1.39 thf(func_def_20, type, sK6: a).
% 1.62/1.39 thf(func_def_21, type, sK7: (((a > $o) > $o) > a > $o) > (a > $o) > $o).
% 1.62/1.39 thf(func_def_22, type, sK8: (a > $o) > $o).
% 1.62/1.39 thf(func_def_23, type, sK9: ((a > $o) > $o) > a > $o).
% 1.62/1.39 thf(func_def_24, type, sK10: ((a > $o) > $o) > a > $o).
% 1.62/1.39 thf(func_def_25, type, sK11: ((a > $o) > $o) > a > $o).
% 1.62/1.39 thf(f489,plain,(
% 1.62/1.39 $false),
% 1.62/1.39 inference(avatar_sat_refutation,[status(thm)],[f88,f92,f99,f103,f110,f114,f119,f120,f354,f364,f391,f432,f478,f488])).
% 1.62/1.39 thf(f488,plain,(
% 1.62/1.39 ~spl4_2 | ~spl4_3 | ~spl4_7 | ~spl4_10),
% 1.62/1.39 inference(avatar_contradiction_clause,[status(thm)],[f487])).
% 1.62/1.39 thf(f487,plain,(
% 1.62/1.39 $false | (~spl4_2 | ~spl4_3 | ~spl4_7 | ~spl4_10)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f483])).
% 1.62/1.39 thf(f483,plain,(
% 1.62/1.39 ($false = $true) | (~spl4_2 | ~spl4_3 | ~spl4_7 | ~spl4_10)),
% 1.62/1.39 inference(superposition,[status(thm)],[f482,f118])).
% 1.62/1.39 thf(f118,plain,(
% 1.62/1.39 ($true = (sK1 @ sK8)) | ~spl4_10),
% 1.62/1.39 inference(avatar_component_clause,[status(thm)],[f116])).
% 1.62/1.39 thf(f116,definition,(
% 1.62/1.39 spl4_10 <=> ($true = (sK1 @ sK8))),
% 1.62/1.39 introduced(definition,[new_symbols(naming,[spl4_10])],[avatar_definition])).
% 1.62/1.39 thf(f482,plain,(
% 1.62/1.39 ($false = (sK1 @ sK8)) | (~spl4_2 | ~spl4_3 | ~spl4_7 | ~spl4_10)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f479])).
% 1.62/1.39 thf(f479,plain,(
% 1.62/1.39 ($false = (sK1 @ sK8)) | ($false = $true) | (~spl4_2 | ~spl4_3 | ~spl4_7 | ~spl4_10)),
% 1.62/1.39 inference(superposition,[status(thm)],[f87,f416])).
% 1.62/1.39 thf(f416,plain,(
% 1.62/1.39 ($false = (sK11 @ sK8 @ sK6)) | (~spl4_3 | ~spl4_7 | ~spl4_10)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f415])).
% 1.62/1.39 thf(f415,plain,(
% 1.62/1.39 ($false = $true) | ($false = (sK11 @ sK8 @ sK6)) | (~spl4_3 | ~spl4_7 | ~spl4_10)),
% 1.62/1.39 inference(forward_demodulation,[status(thm)],[f405,f118])).
% 1.62/1.39 thf(f405,plain,(
% 1.62/1.39 ($false = (sK1 @ sK8)) | ($false = (sK11 @ sK8 @ sK6)) | (~spl4_3 | ~spl4_7)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f399])).
% 1.62/1.39 thf(f399,plain,(
% 1.62/1.39 ($false = (sK11 @ sK8 @ sK6)) | ($false = $true) | ($false = (sK1 @ sK8)) | (~spl4_3 | ~spl4_7)),
% 1.62/1.39 inference(superposition,[status(thm)],[f91,f106])).
% 1.62/1.39 thf(f106,plain,(
% 1.62/1.39 ( ! [X2 : a > $o] : (($false = (sK8 @ X2)) | ($false = (X2 @ sK6))) ) | ~spl4_7),
% 1.62/1.39 inference(avatar_component_clause,[status(thm)],[f105])).
% 1.62/1.39 thf(f105,definition,(
% 1.62/1.39 spl4_7 <=> ! [X2 : a > $o] : (($false = (X2 @ sK6)) | ($false = (sK8 @ X2)))),
% 1.62/1.39 introduced(definition,[new_symbols(naming,[spl4_7])],[avatar_definition])).
% 1.62/1.39 thf(f91,plain,(
% 1.62/1.39 ( ! [X2 : (a > $o) > $o] : (((X2 @ (sK11 @ X2)) = $true) | ($false = (sK1 @ X2))) ) | ~spl4_3),
% 1.62/1.39 inference(avatar_component_clause,[status(thm)],[f90])).
% 1.62/1.39 thf(f90,definition,(
% 1.62/1.39 spl4_3 <=> ! [X2 : (a > $o) > $o] : (((X2 @ (sK11 @ X2)) = $true) | ($false = (sK1 @ X2)))),
% 1.62/1.39 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 1.62/1.39 thf(f87,plain,(
% 1.62/1.39 ( ! [X2 : (a > $o) > $o] : (($true = (sK11 @ X2 @ sK6)) | ($false = (sK1 @ X2))) ) | ~spl4_2),
% 1.62/1.39 inference(avatar_component_clause,[status(thm)],[f86])).
% 1.62/1.39 thf(f86,definition,(
% 1.62/1.39 spl4_2 <=> ! [X2 : (a > $o) > $o] : (($false = (sK1 @ X2)) | ($true = (sK11 @ X2 @ sK6)))),
% 1.62/1.39 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.62/1.39 thf(f478,plain,(
% 1.62/1.39 ~spl4_1 | ~spl4_5 | ~spl4_7 | ~spl4_10),
% 1.62/1.39 inference(avatar_contradiction_clause,[status(thm)],[f477])).
% 1.62/1.39 thf(f477,plain,(
% 1.62/1.39 $false | (~spl4_1 | ~spl4_5 | ~spl4_7 | ~spl4_10)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f473])).
% 1.62/1.39 thf(f473,plain,(
% 1.62/1.39 ($false = $true) | (~spl4_1 | ~spl4_5 | ~spl4_7 | ~spl4_10)),
% 1.62/1.39 inference(superposition,[status(thm)],[f459,f118])).
% 1.62/1.39 thf(f459,plain,(
% 1.62/1.39 ($false = (sK1 @ sK8)) | (~spl4_1 | ~spl4_5 | ~spl4_7 | ~spl4_10)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f453])).
% 1.62/1.39 thf(f453,plain,(
% 1.62/1.39 ($false = (sK1 @ sK8)) | ($false = $true) | (~spl4_1 | ~spl4_5 | ~spl4_7 | ~spl4_10)),
% 1.62/1.39 inference(superposition,[status(thm)],[f446,f84])).
% 1.62/1.39 thf(f84,plain,(
% 1.62/1.39 ( ! [X1 : (a > $o) > $o] : (((sK9 @ X1 @ sK6) = $true) | ($false = (sK1 @ X1))) ) | ~spl4_1),
% 1.62/1.39 inference(avatar_component_clause,[status(thm)],[f83])).
% 1.62/1.39 thf(f83,definition,(
% 1.62/1.39 spl4_1 <=> ! [X1 : (a > $o) > $o] : (((sK9 @ X1 @ sK6) = $true) | ($false = (sK1 @ X1)))),
% 1.62/1.39 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.62/1.39 thf(f446,plain,(
% 1.62/1.39 ((sK9 @ sK8 @ sK6) = $false) | (~spl4_5 | ~spl4_7 | ~spl4_10)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f445])).
% 1.62/1.39 thf(f445,plain,(
% 1.62/1.39 ($false = $true) | ((sK9 @ sK8 @ sK6) = $false) | (~spl4_5 | ~spl4_7 | ~spl4_10)),
% 1.62/1.39 inference(forward_demodulation,[status(thm)],[f442,f118])).
% 1.62/1.39 thf(f442,plain,(
% 1.62/1.39 ((sK9 @ sK8 @ sK6) = $false) | ($false = (sK1 @ sK8)) | (~spl4_5 | ~spl4_7)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f437])).
% 1.62/1.39 thf(f437,plain,(
% 1.62/1.39 ($false = $true) | ($false = (sK1 @ sK8)) | ((sK9 @ sK8 @ sK6) = $false) | (~spl4_5 | ~spl4_7)),
% 1.62/1.39 inference(superposition,[status(thm)],[f106,f98])).
% 1.62/1.39 thf(f98,plain,(
% 1.62/1.39 ( ! [X1 : (a > $o) > $o] : (((X1 @ (sK9 @ X1)) = $true) | ($false = (sK1 @ X1))) ) | ~spl4_5),
% 1.62/1.39 inference(avatar_component_clause,[status(thm)],[f97])).
% 1.62/1.39 thf(f97,definition,(
% 1.62/1.39 spl4_5 <=> ! [X1 : (a > $o) > $o] : (($false = (sK1 @ X1)) | ((X1 @ (sK9 @ X1)) = $true))),
% 1.62/1.39 introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition])).
% 1.62/1.39 thf(f432,plain,(
% 1.62/1.39 ~spl4_4 | ~spl4_6 | ~spl4_7 | ~spl4_10),
% 1.62/1.39 inference(avatar_contradiction_clause,[status(thm)],[f431])).
% 1.62/1.39 thf(f431,plain,(
% 1.62/1.39 $false | (~spl4_4 | ~spl4_6 | ~spl4_7 | ~spl4_10)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f427])).
% 1.62/1.39 thf(f427,plain,(
% 1.62/1.39 ($false = $true) | (~spl4_4 | ~spl4_6 | ~spl4_7 | ~spl4_10)),
% 1.62/1.39 inference(superposition,[status(thm)],[f426,f118])).
% 1.62/1.39 thf(f426,plain,(
% 1.62/1.39 ($false = (sK1 @ sK8)) | (~spl4_4 | ~spl4_6 | ~spl4_7 | ~spl4_10)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f422])).
% 1.62/1.39 thf(f422,plain,(
% 1.62/1.39 ($false = (sK1 @ sK8)) | ($false = $true) | (~spl4_4 | ~spl4_6 | ~spl4_7 | ~spl4_10)),
% 1.62/1.39 inference(superposition,[status(thm)],[f95,f413])).
% 1.62/1.39 thf(f413,plain,(
% 1.62/1.39 ($false = (sK10 @ sK8 @ sK6)) | (~spl4_6 | ~spl4_7 | ~spl4_10)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f412])).
% 1.62/1.39 thf(f412,plain,(
% 1.62/1.39 ($false = (sK10 @ sK8 @ sK6)) | ($false = $true) | (~spl4_6 | ~spl4_7 | ~spl4_10)),
% 1.62/1.39 inference(forward_demodulation,[status(thm)],[f411,f118])).
% 1.62/1.39 thf(f411,plain,(
% 1.62/1.39 ($false = (sK1 @ sK8)) | ($false = (sK10 @ sK8 @ sK6)) | (~spl4_6 | ~spl4_7)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f395])).
% 1.62/1.39 thf(f395,plain,(
% 1.62/1.39 ($false = (sK10 @ sK8 @ sK6)) | ($false = $true) | ($false = (sK1 @ sK8)) | (~spl4_6 | ~spl4_7)),
% 1.62/1.39 inference(superposition,[status(thm)],[f106,f102])).
% 1.62/1.39 thf(f102,plain,(
% 1.62/1.39 ( ! [X2 : (a > $o) > $o] : (((X2 @ (sK10 @ X2)) = $true) | ($false = (sK1 @ X2))) ) | ~spl4_6),
% 1.62/1.39 inference(avatar_component_clause,[status(thm)],[f101])).
% 1.62/1.39 thf(f101,definition,(
% 1.62/1.39 spl4_6 <=> ! [X2 : (a > $o) > $o] : (((X2 @ (sK10 @ X2)) = $true) | ($false = (sK1 @ X2)))),
% 1.62/1.39 introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition])).
% 1.62/1.39 thf(f95,plain,(
% 1.62/1.39 ( ! [X2 : (a > $o) > $o] : (($true = (sK10 @ X2 @ sK6)) | ($false = (sK1 @ X2))) ) | ~spl4_4),
% 1.62/1.39 inference(avatar_component_clause,[status(thm)],[f94])).
% 1.62/1.39 thf(f94,definition,(
% 1.62/1.39 spl4_4 <=> ! [X2 : (a > $o) > $o] : (($true = (sK10 @ X2 @ sK6)) | ($false = (sK1 @ X2)))),
% 1.62/1.39 introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition])).
% 1.62/1.39 thf(f391,plain,(
% 1.62/1.39 ~spl4_4 | ~spl4_6 | ~spl4_8 | ~spl4_9),
% 1.62/1.39 inference(avatar_contradiction_clause,[status(thm)],[f390])).
% 1.62/1.39 thf(f390,plain,(
% 1.62/1.39 $false | (~spl4_4 | ~spl4_6 | ~spl4_8 | ~spl4_9)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f387])).
% 1.62/1.39 thf(f387,plain,(
% 1.62/1.39 ($false = $true) | (~spl4_4 | ~spl4_6 | ~spl4_8 | ~spl4_9)),
% 1.62/1.39 inference(superposition,[status(thm)],[f113,f384])).
% 1.62/1.39 thf(f384,plain,(
% 1.62/1.39 ($false = (sK1 @ (sK7 @ sK10))) | (~spl4_4 | ~spl4_6 | ~spl4_8 | ~spl4_9)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f381])).
% 1.62/1.39 thf(f381,plain,(
% 1.62/1.39 ($false = (sK1 @ (sK7 @ sK10))) | ($false = $true) | (~spl4_4 | ~spl4_6 | ~spl4_8 | ~spl4_9)),
% 1.62/1.39 inference(superposition,[status(thm)],[f95,f378])).
% 1.62/1.39 thf(f378,plain,(
% 1.62/1.39 ($false = (sK10 @ (sK7 @ sK10) @ sK6)) | (~spl4_6 | ~spl4_8 | ~spl4_9)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f377])).
% 1.62/1.39 thf(f377,plain,(
% 1.62/1.39 ($false = $true) | ($false = (sK10 @ (sK7 @ sK10) @ sK6)) | (~spl4_6 | ~spl4_8 | ~spl4_9)),
% 1.62/1.39 inference(forward_demodulation,[status(thm)],[f374,f113])).
% 1.62/1.39 thf(f374,plain,(
% 1.62/1.39 ($false = (sK10 @ (sK7 @ sK10) @ sK6)) | ($false = (sK1 @ (sK7 @ sK10))) | (~spl4_6 | ~spl4_8)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f368])).
% 1.62/1.39 thf(f368,plain,(
% 1.62/1.39 ($false = $true) | ($false = (sK10 @ (sK7 @ sK10) @ sK6)) | ($false = (sK1 @ (sK7 @ sK10))) | (~spl4_6 | ~spl4_8)),
% 1.62/1.39 inference(superposition,[status(thm)],[f102,f109])).
% 1.62/1.39 thf(f109,plain,(
% 1.62/1.39 ( ! [X1 : ((a > $o) > $o) > a > $o] : (($false = (sK7 @ X1 @ (X1 @ (sK7 @ X1)))) | ((X1 @ (sK7 @ X1) @ sK6) = $false)) ) | ~spl4_8),
% 1.62/1.39 inference(avatar_component_clause,[status(thm)],[f108])).
% 1.62/1.39 thf(f108,definition,(
% 1.62/1.39 spl4_8 <=> ! [X1 : ((a > $o) > $o) > a > $o] : (($false = (sK7 @ X1 @ (X1 @ (sK7 @ X1)))) | ((X1 @ (sK7 @ X1) @ sK6) = $false))),
% 1.62/1.39 introduced(definition,[new_symbols(naming,[spl4_8])],[avatar_definition])).
% 1.62/1.39 thf(f113,plain,(
% 1.62/1.39 ( ! [X1 : ((a > $o) > $o) > a > $o] : (($true = (sK1 @ (sK7 @ X1)))) ) | ~spl4_9),
% 1.62/1.39 inference(avatar_component_clause,[status(thm)],[f112])).
% 1.62/1.39 thf(f112,definition,(
% 1.62/1.39 spl4_9 <=> ! [X1 : ((a > $o) > $o) > a > $o] : ($true = (sK1 @ (sK7 @ X1)))),
% 1.62/1.39 introduced(definition,[new_symbols(naming,[spl4_9])],[avatar_definition])).
% 1.62/1.39 thf(f364,plain,(
% 1.62/1.39 ~spl4_1 | ~spl4_5 | ~spl4_8 | ~spl4_9),
% 1.62/1.39 inference(avatar_contradiction_clause,[status(thm)],[f363])).
% 1.62/1.39 thf(f363,plain,(
% 1.62/1.39 $false | (~spl4_1 | ~spl4_5 | ~spl4_8 | ~spl4_9)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f359])).
% 1.62/1.39 thf(f359,plain,(
% 1.62/1.39 ($false = $true) | (~spl4_1 | ~spl4_5 | ~spl4_8 | ~spl4_9)),
% 1.62/1.39 inference(superposition,[status(thm)],[f358,f113])).
% 1.62/1.39 thf(f358,plain,(
% 1.62/1.39 ((sK1 @ (sK7 @ sK9)) = $false) | (~spl4_1 | ~spl4_5 | ~spl4_8 | ~spl4_9)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f355])).
% 1.62/1.39 thf(f355,plain,(
% 1.62/1.39 ($false = $true) | ((sK1 @ (sK7 @ sK9)) = $false) | (~spl4_1 | ~spl4_5 | ~spl4_8 | ~spl4_9)),
% 1.62/1.39 inference(superposition,[status(thm)],[f84,f320])).
% 1.62/1.39 thf(f320,plain,(
% 1.62/1.39 ((sK9 @ (sK7 @ sK9) @ sK6) = $false) | (~spl4_5 | ~spl4_8 | ~spl4_9)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f319])).
% 1.62/1.39 thf(f319,plain,(
% 1.62/1.39 ($false = $true) | ((sK9 @ (sK7 @ sK9) @ sK6) = $false) | (~spl4_5 | ~spl4_8 | ~spl4_9)),
% 1.62/1.39 inference(forward_demodulation,[status(thm)],[f313,f113])).
% 1.62/1.39 thf(f313,plain,(
% 1.62/1.39 ((sK1 @ (sK7 @ sK9)) = $false) | ((sK9 @ (sK7 @ sK9) @ sK6) = $false) | (~spl4_5 | ~spl4_8)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f306])).
% 1.62/1.39 thf(f306,plain,(
% 1.62/1.39 ((sK1 @ (sK7 @ sK9)) = $false) | ((sK9 @ (sK7 @ sK9) @ sK6) = $false) | ($false = $true) | (~spl4_5 | ~spl4_8)),
% 1.62/1.39 inference(superposition,[status(thm)],[f98,f109])).
% 1.62/1.39 thf(f354,plain,(
% 1.62/1.39 ~spl4_2 | ~spl4_3 | ~spl4_8 | ~spl4_9),
% 1.62/1.39 inference(avatar_contradiction_clause,[status(thm)],[f353])).
% 1.62/1.39 thf(f353,plain,(
% 1.62/1.39 $false | (~spl4_2 | ~spl4_3 | ~spl4_8 | ~spl4_9)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f350])).
% 1.62/1.39 thf(f350,plain,(
% 1.62/1.39 ($false = $true) | (~spl4_2 | ~spl4_3 | ~spl4_8 | ~spl4_9)),
% 1.62/1.39 inference(superposition,[status(thm)],[f113,f335])).
% 1.62/1.39 thf(f335,plain,(
% 1.62/1.39 ((sK1 @ (sK7 @ sK11)) = $false) | (~spl4_2 | ~spl4_3 | ~spl4_8 | ~spl4_9)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f331])).
% 1.62/1.39 thf(f331,plain,(
% 1.62/1.39 ($false = $true) | ((sK1 @ (sK7 @ sK11)) = $false) | (~spl4_2 | ~spl4_3 | ~spl4_8 | ~spl4_9)),
% 1.62/1.39 inference(superposition,[status(thm)],[f87,f322])).
% 1.62/1.39 thf(f322,plain,(
% 1.62/1.39 ($false = (sK11 @ (sK7 @ sK11) @ sK6)) | (~spl4_3 | ~spl4_8 | ~spl4_9)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f321])).
% 1.62/1.39 thf(f321,plain,(
% 1.62/1.39 ($false = $true) | ($false = (sK11 @ (sK7 @ sK11) @ sK6)) | (~spl4_3 | ~spl4_8 | ~spl4_9)),
% 1.62/1.39 inference(forward_demodulation,[status(thm)],[f312,f113])).
% 1.62/1.39 thf(f312,plain,(
% 1.62/1.39 ((sK1 @ (sK7 @ sK11)) = $false) | ($false = (sK11 @ (sK7 @ sK11) @ sK6)) | (~spl4_3 | ~spl4_8)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f305])).
% 1.62/1.39 thf(f305,plain,(
% 1.62/1.39 ($false = (sK11 @ (sK7 @ sK11) @ sK6)) | ((sK1 @ (sK7 @ sK11)) = $false) | ($false = $true) | (~spl4_3 | ~spl4_8)),
% 1.62/1.39 inference(superposition,[status(thm)],[f91,f109])).
% 1.62/1.39 thf(f120,plain,(
% 1.62/1.39 spl4_10 | spl4_9),
% 1.62/1.39 inference(avatar_split_clause,[status(thm)],[f52,f112,f116])).
% 1.62/1.39 thf(f52,plain,(
% 1.62/1.39 ( ! [X1 : ((a > $o) > $o) > a > $o] : (($true = (sK1 @ sK8)) | ($true = (sK1 @ (sK7 @ X1)))) )),
% 1.62/1.39 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 1.62/1.39 thf(f50,plain,(
% 1.62/1.39 ( ! [X1 : ((a > $o) > $o) > a > $o] : ((((sK1 @ (sK7 @ X1)) => ((sK7 @ X1 @ (X1 @ (sK7 @ X1))) & (X1 @ (sK7 @ X1) @ sK6))) = $false) | ($true = (sK1 @ sK8))) )),
% 1.62/1.39 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.62/1.39 thf(f48,plain,(
% 1.62/1.39 ( ! [X1 : ((a > $o) > $o) > a > $o] : (($false = ((sK1 @ sK8) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((sK8 @ Y0) & (Y0 @ sK6)))))) | (((sK1 @ (sK7 @ X1)) => ((sK7 @ X1 @ (X1 @ (sK7 @ X1))) & (X1 @ (sK7 @ X1) @ sK6))) = $false)) )),
% 1.62/1.39 inference(beta_eta_normalization,[status(thm)],[f47])).
% 1.62/1.39 thf(f47,plain,(
% 1.62/1.39 ( ! [X1 : ((a > $o) > $o) > a > $o] : (($false = ((^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK6)))))) @ sK8)) | (((sK1 @ (sK7 @ X1)) => ((sK7 @ X1 @ (X1 @ (sK7 @ X1))) & (X1 @ (sK7 @ X1) @ sK6))) = $false)) )),
% 1.62/1.39 inference(sigma_clausification,[status(thm)],[f46])).
% 1.62/1.39 thf(f46,plain,(
% 1.62/1.39 ( ! [X1 : ((a > $o) > $o) > a > $o] : (((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK6))))))) = $false) | (((sK1 @ (sK7 @ X1)) => ((sK7 @ X1 @ (X1 @ (sK7 @ X1))) & (X1 @ (sK7 @ X1) @ sK6))) = $false)) )),
% 1.62/1.39 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.62/1.39 thf(f45,plain,(
% 1.62/1.39 ( ! [X1 : ((a > $o) > $o) > a > $o] : (($false = ((^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => ((Y0 @ (X1 @ Y0)) & (X1 @ Y0 @ sK6)))) @ (sK7 @ X1))) | ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK6))))))) = $false)) )),
% 1.62/1.39 inference(sigma_clausification,[status(thm)],[f44])).
% 1.62/1.39 thf(f44,plain,(
% 1.62/1.39 ( ! [X1 : ((a > $o) > $o) > a > $o] : (($false = (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => ((Y0 @ (X1 @ Y0)) & (X1 @ Y0 @ sK6)))))) | ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK6))))))) = $false)) )),
% 1.62/1.39 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.62/1.39 thf(f43,plain,(
% 1.62/1.39 ( ! [X1 : ((a > $o) > $o) > a > $o] : (((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK6))))))) = $false) | ($false = ((^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK1 @ Y1) => ((Y1 @ (Y0 @ Y1)) & (Y0 @ Y1 @ sK6)))))) @ X1))) )),
% 1.62/1.39 inference(pi_clausification,[status(thm)],[f42])).
% 1.62/1.39 thf(f42,plain,(
% 1.62/1.39 ((?? @ (((a > $o) > $o) > a > $o) @ (^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK1 @ Y1) => ((Y1 @ (Y0 @ Y1)) & (Y0 @ Y1 @ sK6))))))) = $false) | ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK6))))))) = $false)),
% 1.62/1.39 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.62/1.39 thf(f40,plain,(
% 1.62/1.39 ((?? @ (((a > $o) > $o) > a > $o) @ (^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK1 @ Y1) => ((Y1 @ (Y0 @ Y1)) & (Y0 @ Y1 @ sK6))))))) != (!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK6))))))))),
% 1.62/1.39 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.62/1.39 thf(f39,plain,(
% 1.62/1.39 (((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK1 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0)))))))) @ sK6) != ((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((sK1 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))) @ sK6))),
% 1.62/1.39 inference(negative_extensionality,[status(thm)],[f15])).
% 1.62/1.39 thf(f15,plain,(
% 1.62/1.39 ((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK1 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0)))))))) != (^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((sK1 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))))),
% 1.62/1.39 inference(cnf_transformation,[status(thm)],[f12])).
% 1.62/1.39 thf(f12,plain,(
% 1.62/1.39 ! [X1 : (a > $o) > $o] : (($true = (X1 @ (sK0 @ X1))) | ! [X2 : a > $o] : ((X1 @ X2) != $true)) & (((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK1 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0)))))))) != (^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((sK1 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0))))))))) & ! [X4 : (a > $o) > $o] : (((X4 @ (sK2 @ X4)) = $true) | ($true != (sK1 @ X4))) & ((sK1 @ sK3) = $true))),
% 1.62/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f7,f11,f10,f9,f8])).
% 1.62/1.39 thf(f8,plain,(
% 1.62/1.39 ? [X0 : ((a > $o) > $o) > a > $o] : ! [X1 : (a > $o) > $o] : (((X1 @ (X0 @ X1)) = $true) | ! [X2 : a > $o] : ((X1 @ X2) != $true)) => ! [X1 : (a > $o) > $o] : (($true = (X1 @ (sK0 @ X1))) | ! [X2 : a > $o] : ((X1 @ X2) != $true))),
% 1.62/1.39 introduced(definition,[],[choice_axiom])).
% 1.62/1.39 thf(f9,plain,(
% 1.62/1.39 ? [X3 : ((a > $o) > $o) > $o] : (((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((X3 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))) != (^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((X3 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0))))))))) & ! [X4 : (a > $o) > $o] : (? [X5 : a > $o] : ($true = (X4 @ X5)) | ($true != (X3 @ X4))) & ? [X6 : (a > $o) > $o] : ((X3 @ X6) = $true)) => (((^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK1 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0)))))))) != (^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((sK1 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0))))))))) & ! [X4 : (a > $o) > $o] : (? [X5 : a > $o] : ($true = (X4 @ X5)) | ($true != (sK1 @ X4))) & ? [X6 : (a > $o) > $o] : ((sK1 @ X6) = $true))),
% 1.62/1.39 introduced(definition,[],[choice_axiom])).
% 1.62/1.39 thf(f10,plain,(
% 1.62/1.39 ! [X4 : (a > $o) > $o] : (? [X5 : a > $o] : ($true = (X4 @ X5)) => ((X4 @ (sK2 @ X4)) = $true))),
% 1.62/1.39 introduced(definition,[],[choice_axiom])).
% 1.62/1.39 thf(f11,plain,(
% 1.62/1.39 ? [X6 : (a > $o) > $o] : ((sK1 @ X6) = $true) => ((sK1 @ sK3) = $true)),
% 1.62/1.39 introduced(definition,[],[choice_axiom])).
% 1.62/1.39 thf(f7,plain,(
% 1.62/1.39 ? [X0 : ((a > $o) > $o) > a > $o] : ! [X1 : (a > $o) > $o] : (((X1 @ (X0 @ X1)) = $true) | ! [X2 : a > $o] : ((X1 @ X2) != $true)) & ? [X3 : ((a > $o) > $o) > $o] : (((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((X3 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))) != (^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((X3 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0))))))))) & ! [X4 : (a > $o) > $o] : (? [X5 : a > $o] : ($true = (X4 @ X5)) | ($true != (X3 @ X4))) & ? [X6 : (a > $o) > $o] : ((X3 @ X6) = $true))),
% 1.62/1.39 inference(flattening,[status(thm)],[f6])).
% 1.62/1.39 thf(f6,plain,(
% 1.62/1.39 ? [X3 : ((a > $o) > $o) > $o] : (((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((X3 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))) != (^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((X3 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0))))))))) & (! [X4 : (a > $o) > $o] : (? [X5 : a > $o] : ($true = (X4 @ X5)) | ($true != (X3 @ X4))) & ? [X6 : (a > $o) > $o] : ((X3 @ X6) = $true))) & ? [X0 : ((a > $o) > $o) > a > $o] : ! [X1 : (a > $o) > $o] : (((X1 @ (X0 @ X1)) = $true) | ! [X2 : a > $o] : ((X1 @ X2) != $true))),
% 1.62/1.39 inference(ennf_transformation,[status(thm)],[f5])).
% 1.62/1.39 thf(f5,plain,(
% 1.62/1.39 ~(? [X0 : ((a > $o) > $o) > a > $o] : ! [X1 : (a > $o) > $o] : (? [X2 : a > $o] : ((X1 @ X2) = $true) => ((X1 @ (X0 @ X1)) = $true)) => ! [X3 : ((a > $o) > $o) > $o] : ((! [X4 : (a > $o) > $o] : (($true = (X3 @ X4)) => ? [X5 : a > $o] : ($true = (X4 @ X5))) & ? [X6 : (a > $o) > $o] : ((X3 @ X6) = $true)) => ((^[Y0 : a]: (?? @ (((a > $o) > $o) > a > $o) @ (^[Y1 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y2 : (a > $o) > $o]: ((X3 @ Y2) => ((Y2 @ (Y1 @ Y2)) & (Y1 @ Y2 @ Y0)))))))) = (^[Y0 : a]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((X3 @ Y1) => (?? @ (a > $o) @ (^[Y2 : a > $o]: ((Y1 @ Y2) & (Y2 @ Y0)))))))))))),
% 1.62/1.39 inference(fool_elimination,[status(thm)],[f4])).
% 1.62/1.39 thf(f4,plain,(
% 1.62/1.39 ~(? [X0 : ((a > $o) > $o) > a > $o] : ! [X1 : (a > $o) > $o] : (? [X2 : a > $o] : (X1 @ X2) => (X1 @ (X0 @ X1))) => ! [X3 : ((a > $o) > $o) > $o] : ((! [X4 : (a > $o) > $o] : ((X3 @ X4) => ? [X5 : a > $o] : (X4 @ X5)) & ? [X6 : (a > $o) > $o] : (X3 @ X6)) => ((^[X7 : a] : (! [X8 : (a > $o) > $o] : ((X3 @ X8) => ? [X9 : a > $o] : ((X9 @ X7) & (X8 @ X9))))) = (^[X10 : a] : (? [X11 : ((a > $o) > $o) > a > $o] : ! [X12 : (a > $o) > $o] : ((X3 @ X12) => ((X11 @ X12 @ X10) & (X12 @ (X11 @ X12)))))))))),
% 1.62/1.39 inference(rectify,[status(thm)],[f2])).
% 1.62/1.39 thf(f2,negated_conjecture,(
% 1.62/1.39 ~(? [X0 : ((a > $o) > $o) > a > $o] : ! [X1 : (a > $o) > $o] : (? [X2 : a > $o] : (X1 @ X2) => (X1 @ (X0 @ X1))) => ! [X3 : ((a > $o) > $o) > $o] : ((! [X1 : (a > $o) > $o] : ((X3 @ X1) => ? [X4 : a > $o] : (X1 @ X4)) & ? [X1 : (a > $o) > $o] : (X3 @ X1)) => ((^[X5 : a] : (! [X6 : (a > $o) > $o] : ((X3 @ X6) => ? [X7 : a > $o] : ((X7 @ X5) & (X6 @ X7))))) = (^[X5 : a] : (? [X0 : ((a > $o) > $o) > a > $o] : ! [X6 : (a > $o) > $o] : ((X3 @ X6) => ((X0 @ X6 @ X5) & (X6 @ (X0 @ X6)))))))))),
% 1.62/1.39 inference(negated_conjecture,[status(cth)],[f1])).
% 1.62/1.39 thf(f1,conjecture,(
% 1.62/1.39 ? [X0 : ((a > $o) > $o) > a > $o] : ! [X1 : (a > $o) > $o] : (? [X2 : a > $o] : (X1 @ X2) => (X1 @ (X0 @ X1))) => ! [X3 : ((a > $o) > $o) > $o] : ((! [X1 : (a > $o) > $o] : ((X3 @ X1) => ? [X4 : a > $o] : (X1 @ X4)) & ? [X1 : (a > $o) > $o] : (X3 @ X1)) => ((^[X5 : a] : (! [X6 : (a > $o) > $o] : ((X3 @ X6) => ? [X7 : a > $o] : ((X7 @ X5) & (X6 @ X7))))) = (^[X5 : a] : (? [X0 : ((a > $o) > $o) > a > $o] : ! [X6 : (a > $o) > $o] : ((X3 @ X6) => ((X0 @ X6 @ X5) & (X6 @ (X0 @ X6))))))))),
% 1.62/1.39 file('/export/starexec/sandbox2/tmp/tmp.9y3h8pOOCz/DTF2THF_9293.p',cTHM535B)).
% 1.62/1.39 thf(f119,plain,(
% 1.62/1.39 spl4_8 | spl4_10),
% 1.62/1.39 inference(avatar_split_clause,[status(thm)],[f53,f116,f108])).
% 1.62/1.39 thf(f53,plain,(
% 1.62/1.39 ( ! [X1 : ((a > $o) > $o) > a > $o] : (($true = (sK1 @ sK8)) | ((X1 @ (sK7 @ X1) @ sK6) = $false) | ($false = (sK7 @ X1 @ (X1 @ (sK7 @ X1))))) )),
% 1.62/1.39 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 1.62/1.39 thf(f51,plain,(
% 1.62/1.39 ( ! [X1 : ((a > $o) > $o) > a > $o] : (($true = (sK1 @ sK8)) | ($false = ((sK7 @ X1 @ (X1 @ (sK7 @ X1))) & (X1 @ (sK7 @ X1) @ sK6)))) )),
% 1.62/1.39 inference(binary_proxy_clausification,[status(thm)],[f50])).
% 1.62/1.39 thf(f114,plain,(
% 1.62/1.39 spl4_7 | spl4_9),
% 1.62/1.39 inference(avatar_split_clause,[status(thm)],[f58,f112,f105])).
% 1.62/1.39 thf(f58,plain,(
% 1.62/1.39 ( ! [X2 : a > $o,X1 : ((a > $o) > $o) > a > $o] : (($true = (sK1 @ (sK7 @ X1))) | ($false = (X2 @ sK6)) | ($false = (sK8 @ X2))) )),
% 1.62/1.39 inference(binary_proxy_clausification,[status(thm)],[f57])).
% 1.62/1.39 thf(f57,plain,(
% 1.62/1.39 ( ! [X2 : a > $o,X1 : ((a > $o) > $o) > a > $o] : (($true = (sK1 @ (sK7 @ X1))) | ($false = ((sK8 @ X2) & (X2 @ sK6)))) )),
% 1.62/1.39 inference(beta_eta_normalization,[status(thm)],[f56])).
% 1.62/1.39 thf(f56,plain,(
% 1.62/1.39 ( ! [X2 : a > $o,X1 : ((a > $o) > $o) > a > $o] : (($false = ((^[Y0 : a > $o]: ((sK8 @ Y0) & (Y0 @ sK6))) @ X2)) | ($true = (sK1 @ (sK7 @ X1)))) )),
% 1.62/1.39 inference(pi_clausification,[status(thm)],[f55])).
% 1.62/1.39 thf(f55,plain,(
% 1.62/1.39 ( ! [X1 : ((a > $o) > $o) > a > $o] : (($true = (sK1 @ (sK7 @ X1))) | ($false = (?? @ (a > $o) @ (^[Y0 : a > $o]: ((sK8 @ Y0) & (Y0 @ sK6)))))) )),
% 1.62/1.39 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.62/1.39 thf(f49,plain,(
% 1.62/1.39 ( ! [X1 : ((a > $o) > $o) > a > $o] : ((((sK1 @ (sK7 @ X1)) => ((sK7 @ X1 @ (X1 @ (sK7 @ X1))) & (X1 @ (sK7 @ X1) @ sK6))) = $false) | ($false = (?? @ (a > $o) @ (^[Y0 : a > $o]: ((sK8 @ Y0) & (Y0 @ sK6)))))) )),
% 1.62/1.39 inference(binary_proxy_clausification,[status(thm)],[f48])).
% 1.62/1.39 thf(f110,plain,(
% 1.62/1.39 spl4_7 | spl4_8),
% 1.62/1.39 inference(avatar_split_clause,[status(thm)],[f62,f108,f105])).
% 1.62/1.39 thf(f62,plain,(
% 1.62/1.39 ( ! [X2 : a > $o,X1 : ((a > $o) > $o) > a > $o] : (($false = (X2 @ sK6)) | ($false = (sK7 @ X1 @ (X1 @ (sK7 @ X1)))) | ($false = (sK8 @ X2)) | ((X1 @ (sK7 @ X1) @ sK6) = $false)) )),
% 1.62/1.39 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.62/1.39 thf(f61,plain,(
% 1.62/1.39 ( ! [X2 : a > $o,X1 : ((a > $o) > $o) > a > $o] : (($false = ((sK8 @ X2) & (X2 @ sK6))) | ((X1 @ (sK7 @ X1) @ sK6) = $false) | ($false = (sK7 @ X1 @ (X1 @ (sK7 @ X1))))) )),
% 1.62/1.39 inference(beta_eta_normalization,[status(thm)],[f60])).
% 1.62/1.39 thf(f60,plain,(
% 1.62/1.39 ( ! [X2 : a > $o,X1 : ((a > $o) > $o) > a > $o] : (($false = ((^[Y0 : a > $o]: ((sK8 @ Y0) & (Y0 @ sK6))) @ X2)) | ((X1 @ (sK7 @ X1) @ sK6) = $false) | ($false = (sK7 @ X1 @ (X1 @ (sK7 @ X1))))) )),
% 1.62/1.39 inference(pi_clausification,[status(thm)],[f59])).
% 1.62/1.39 thf(f59,plain,(
% 1.62/1.39 ( ! [X1 : ((a > $o) > $o) > a > $o] : (($false = (sK7 @ X1 @ (X1 @ (sK7 @ X1)))) | ((X1 @ (sK7 @ X1) @ sK6) = $false) | ($false = (?? @ (a > $o) @ (^[Y0 : a > $o]: ((sK8 @ Y0) & (Y0 @ sK6)))))) )),
% 1.62/1.39 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.62/1.39 thf(f54,plain,(
% 1.62/1.39 ( ! [X1 : ((a > $o) > $o) > a > $o] : (($false = ((sK7 @ X1 @ (X1 @ (sK7 @ X1))) & (X1 @ (sK7 @ X1) @ sK6))) | ($false = (?? @ (a > $o) @ (^[Y0 : a > $o]: ((sK8 @ Y0) & (Y0 @ sK6)))))) )),
% 1.62/1.39 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.62/1.39 thf(f103,plain,(
% 1.62/1.39 spl4_5 | spl4_6),
% 1.62/1.39 inference(avatar_split_clause,[status(thm)],[f76,f101,f97])).
% 1.62/1.39 thf(f76,plain,(
% 1.62/1.39 ( ! [X2 : (a > $o) > $o,X1 : (a > $o) > $o] : (((X1 @ (sK9 @ X1)) = $true) | ((X2 @ (sK10 @ X2)) = $true) | ($false = (sK1 @ X2)) | ($false = (sK1 @ X1))) )),
% 1.62/1.39 inference(binary_proxy_clausification,[status(thm)],[f74])).
% 1.62/1.39 thf(f74,plain,(
% 1.62/1.39 ( ! [X2 : (a > $o) > $o,X1 : (a > $o) > $o] : (((X1 @ (sK9 @ X1)) = $true) | ($false = (sK1 @ X1)) | (((X2 @ (sK10 @ X2)) & (sK10 @ X2 @ sK6)) = $true) | ($false = (sK1 @ X2))) )),
% 1.62/1.39 inference(beta_eta_normalization,[status(thm)],[f73])).
% 1.62/1.39 thf(f73,plain,(
% 1.62/1.39 ( ! [X2 : (a > $o) > $o,X1 : (a > $o) > $o] : (((X1 @ (sK9 @ X1)) = $true) | ($false = (sK1 @ X1)) | ($false = (sK1 @ X2)) | (((^[Y0 : a > $o]: ((X2 @ Y0) & (Y0 @ sK6))) @ (sK10 @ X2)) = $true)) )),
% 1.62/1.39 inference(sigma_clausification,[status(thm)],[f72])).
% 1.62/1.39 thf(f72,plain,(
% 1.62/1.39 ( ! [X2 : (a > $o) > $o,X1 : (a > $o) > $o] : (($false = (sK1 @ X2)) | ($false = (sK1 @ X1)) | ($true = (?? @ (a > $o) @ (^[Y0 : a > $o]: ((X2 @ Y0) & (Y0 @ sK6))))) | ((X1 @ (sK9 @ X1)) = $true)) )),
% 1.62/1.39 inference(binary_proxy_clausification,[status(thm)],[f71])).
% 1.62/1.39 thf(f71,plain,(
% 1.62/1.39 ( ! [X2 : (a > $o) > $o,X1 : (a > $o) > $o] : (((X1 @ (sK9 @ X1)) = $true) | ($false = (sK1 @ X1)) | (((sK1 @ X2) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((X2 @ Y0) & (Y0 @ sK6))))) = $true)) )),
% 1.62/1.39 inference(binary_proxy_clausification,[status(thm)],[f69])).
% 1.62/1.39 thf(f69,plain,(
% 1.62/1.39 ( ! [X2 : (a > $o) > $o,X1 : (a > $o) > $o] : (($true = ((X1 @ (sK9 @ X1)) & (sK9 @ X1 @ sK6))) | (((sK1 @ X2) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((X2 @ Y0) & (Y0 @ sK6))))) = $true) | ($false = (sK1 @ X1))) )),
% 1.62/1.39 inference(beta_eta_normalization,[status(thm)],[f68])).
% 1.62/1.39 thf(f68,plain,(
% 1.62/1.39 ( ! [X2 : (a > $o) > $o,X1 : (a > $o) > $o] : ((((^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK6)))))) @ X2) = $true) | ($true = ((X1 @ (sK9 @ X1)) & (sK9 @ X1 @ sK6))) | ($false = (sK1 @ X1))) )),
% 1.62/1.39 inference(pi_clausification,[status(thm)],[f67])).
% 1.62/1.39 thf(f67,plain,(
% 1.62/1.39 ( ! [X1 : (a > $o) > $o] : (($false = (sK1 @ X1)) | ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK6))))))) = $true) | ($true = ((X1 @ (sK9 @ X1)) & (sK9 @ X1 @ sK6)))) )),
% 1.62/1.39 inference(binary_proxy_clausification,[status(thm)],[f66])).
% 1.62/1.39 thf(f66,plain,(
% 1.62/1.39 ( ! [X1 : (a > $o) > $o] : ((((sK1 @ X1) => ((X1 @ (sK9 @ X1)) & (sK9 @ X1 @ sK6))) = $true) | ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK6))))))) = $true)) )),
% 1.62/1.39 inference(beta_eta_normalization,[status(thm)],[f65])).
% 1.62/1.39 thf(f65,plain,(
% 1.62/1.39 ( ! [X1 : (a > $o) > $o] : ((((^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => ((Y0 @ (sK9 @ Y0)) & (sK9 @ Y0 @ sK6)))) @ X1) = $true) | ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK6))))))) = $true)) )),
% 1.62/1.39 inference(pi_clausification,[status(thm)],[f64])).
% 1.62/1.39 thf(f64,plain,(
% 1.62/1.39 ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => ((Y0 @ (sK9 @ Y0)) & (sK9 @ Y0 @ sK6))))) = $true) | ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK6))))))) = $true)),
% 1.62/1.39 inference(beta_eta_normalization,[status(thm)],[f63])).
% 1.62/1.39 thf(f63,plain,(
% 1.62/1.39 (((^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK1 @ Y1) => ((Y1 @ (Y0 @ Y1)) & (Y0 @ Y1 @ sK6)))))) @ sK9) = $true) | ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK6))))))) = $true)),
% 1.62/1.39 inference(sigma_clausification,[status(thm)],[f41])).
% 1.62/1.39 thf(f41,plain,(
% 1.62/1.39 ((?? @ (((a > $o) > $o) > a > $o) @ (^[Y0 : ((a > $o) > $o) > a > $o]: (!! @ ((a > $o) > $o) @ (^[Y1 : (a > $o) > $o]: ((sK1 @ Y1) => ((Y1 @ (Y0 @ Y1)) & (Y0 @ Y1 @ sK6))))))) = $true) | ((!! @ ((a > $o) > $o) @ (^[Y0 : (a > $o) > $o]: ((sK1 @ Y0) => (?? @ (a > $o) @ (^[Y1 : a > $o]: ((Y0 @ Y1) & (Y1 @ sK6))))))) = $true)),
% 1.62/1.39 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.62/1.39 thf(f99,plain,(
% 1.62/1.39 spl4_4 | spl4_5),
% 1.62/1.39 inference(avatar_split_clause,[status(thm)],[f75,f97,f94])).
% 1.62/1.39 thf(f75,plain,(
% 1.62/1.39 ( ! [X2 : (a > $o) > $o,X1 : (a > $o) > $o] : (($false = (sK1 @ X1)) | ($true = (sK10 @ X2 @ sK6)) | ($false = (sK1 @ X2)) | ((X1 @ (sK9 @ X1)) = $true)) )),
% 1.62/1.39 inference(binary_proxy_clausification,[status(thm)],[f74])).
% 1.62/1.39 thf(f92,plain,(
% 1.62/1.39 spl4_3 | spl4_1),
% 1.62/1.39 inference(avatar_split_clause,[status(thm)],[f81,f83,f90])).
% 1.62/1.39 thf(f81,plain,(
% 1.62/1.39 ( ! [X2 : (a > $o) > $o,X1 : (a > $o) > $o] : (((X2 @ (sK11 @ X2)) = $true) | ($false = (sK1 @ X1)) | ((sK9 @ X1 @ sK6) = $true) | ($false = (sK1 @ X2))) )),
% 1.62/1.39 inference(binary_proxy_clausification,[status(thm)],[f79])).
% 1.62/1.39 thf(f79,plain,(
% 1.62/1.39 ( ! [X2 : (a > $o) > $o,X1 : (a > $o) > $o] : (($false = (sK1 @ X1)) | ($false = (sK1 @ X2)) | (((X2 @ (sK11 @ X2)) & (sK11 @ X2 @ sK6)) = $true) | ((sK9 @ X1 @ sK6) = $true)) )),
% 1.62/1.39 inference(beta_eta_normalization,[status(thm)],[f78])).
% 1.62/1.39 thf(f78,plain,(
% 1.62/1.39 ( ! [X2 : (a > $o) > $o,X1 : (a > $o) > $o] : (((sK9 @ X1 @ sK6) = $true) | ($false = (sK1 @ X2)) | ($false = (sK1 @ X1)) | (((^[Y0 : a > $o]: ((X2 @ Y0) & (Y0 @ sK6))) @ (sK11 @ X2)) = $true)) )),
% 1.62/1.39 inference(sigma_clausification,[status(thm)],[f77])).
% 1.62/1.39 thf(f77,plain,(
% 1.62/1.39 ( ! [X2 : (a > $o) > $o,X1 : (a > $o) > $o] : (($false = (sK1 @ X2)) | ((sK9 @ X1 @ sK6) = $true) | ($false = (sK1 @ X1)) | ($true = (?? @ (a > $o) @ (^[Y0 : a > $o]: ((X2 @ Y0) & (Y0 @ sK6)))))) )),
% 1.62/1.39 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.62/1.39 thf(f70,plain,(
% 1.62/1.39 ( ! [X2 : (a > $o) > $o,X1 : (a > $o) > $o] : (($false = (sK1 @ X1)) | ((sK9 @ X1 @ sK6) = $true) | (((sK1 @ X2) => (?? @ (a > $o) @ (^[Y0 : a > $o]: ((X2 @ Y0) & (Y0 @ sK6))))) = $true)) )),
% 1.62/1.39 inference(binary_proxy_clausification,[status(thm)],[f69])).
% 1.62/1.39 thf(f88,plain,(
% 1.62/1.39 spl4_1 | spl4_2),
% 1.62/1.39 inference(avatar_split_clause,[status(thm)],[f80,f86,f83])).
% 1.62/1.39 thf(f80,plain,(
% 1.62/1.39 ( ! [X2 : (a > $o) > $o,X1 : (a > $o) > $o] : (((sK9 @ X1 @ sK6) = $true) | ($false = (sK1 @ X2)) | ($true = (sK11 @ X2 @ sK6)) | ($false = (sK1 @ X1))) )),
% 1.62/1.39 inference(binary_proxy_clausification,[status(thm)],[f79])).
% 1.62/1.39 % SZS output end Proof for DTF2THF_9293
% 1.62/1.39 % (9458)------------------------------
% 1.62/1.39 % (9458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.39 % (9458)Termination reason: Refutation
% 1.62/1.39
% 1.62/1.39 % (9458)Memory used [KB]: 5756
% 1.62/1.39 % (9458)Time elapsed: 0.035 s
% 1.62/1.39 % (9458)Instructions burned: 44 (million)
% 1.62/1.39 % (9458)------------------------------
% 1.62/1.39 % (9458)------------------------------
% 1.62/1.39 % (9452)Success in time 0.047 s
%------------------------------------------------------------------------------