%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV229^5 : 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 : n029.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 09:40:36 AM UTC 2026
% Result : Theorem 1.60s 1.33s
% Output : Refutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 118 ( 9 unt; 0 typ; 12 def)
% Number of atoms : 871 ( 191 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 900 ( 97 ~; 202 |; 53 &; 413 @)
% ( 12 <=>; 83 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 21 usr; 19 con; 0-2 aty)
% ( 40 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 99 ( 62 ^; 37 !; 0 ?; 99 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cE: a > $o ).
thf(func_def_2,type,
cD: a > $o ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_14,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sK2: a > $o ).
thf(func_def_16,type,
sK3: a ).
thf(func_def_17,type,
sK4: a ).
thf(func_def_18,type,
sK5: a ).
thf(func_def_19,type,
sK6: a ).
thf(f180,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f64,f65,f83,f88,f93,f94,f107,f112,f113,f114,f124,f142,f158,f162,f176,f179]) ).
thf(f179,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f178]) ).
thf(f178,plain,
( $false
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f177]) ).
thf(f177,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_7 ),
inference(backward_demodulation,[status(thm)],[f134,f78]) ).
thf(f78,plain,
( ( $false
= ( cE @ sK6 ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f76]) ).
thf(f76,definition,
( spl0_5
<=> ( $false
= ( cE @ sK6 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f134,plain,
( ( ( cE @ sK6 )
= $true )
| ~ spl0_1
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f132]) ).
thf(f132,plain,
( ( $false = $true )
| ( ( cE @ sK6 )
= $true )
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f59,f87]) ).
thf(f87,plain,
( ( ( sK2 @ sK6 )
= $true )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f85]) ).
thf(f85,definition,
( spl0_7
<=> ( ( sK2 @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f59,plain,
( ! [X1: a] :
( ( $false
= ( sK2 @ X1 ) )
| ( ( cE @ X1 )
= $true ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f58]) ).
thf(f58,definition,
( spl0_1
<=> ! [X1: a] :
( ( $false
= ( sK2 @ X1 ) )
| ( ( cE @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f176,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f175]) ).
thf(f175,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f174]) ).
thf(f174,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f167,f70]) ).
thf(f70,plain,
( ( $false
= ( cD @ sK4 ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f68]) ).
thf(f68,definition,
( spl0_3
<=> ( $false
= ( cD @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f167,plain,
( ( ( cD @ sK4 )
= $true )
| ~ spl0_2
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f165]) ).
thf(f165,plain,
( ( $false = $true )
| ( ( cD @ sK4 )
= $true )
| ~ spl0_2
| ~ spl0_8 ),
inference(superposition,[status(thm)],[f62,f92]) ).
thf(f92,plain,
( ( ( sK2 @ sK4 )
= $true )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f90]) ).
thf(f90,definition,
( spl0_8
<=> ( ( sK2 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f62,plain,
( ! [X2: a] :
( ( ( sK2 @ X2 )
= $false )
| ( ( cD @ X2 )
= $true ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f61]) ).
thf(f61,definition,
( spl0_2
<=> ! [X2: a] :
( ( ( sK2 @ X2 )
= $false )
| ( ( cD @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f162,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f161]) ).
thf(f161,plain,
( $false
| ~ spl0_1
| ~ spl0_10
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f160]) ).
thf(f160,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_12 ),
inference(forward_demodulation,[status(thm)],[f149,f102]) ).
thf(f102,plain,
( ( ( cE @ sK5 )
= $false )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f100]) ).
thf(f100,definition,
( spl0_10
<=> ( ( cE @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f149,plain,
( ( ( cE @ sK5 )
= $true )
| ~ spl0_1
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f148]) ).
thf(f148,plain,
( ( ( cE @ sK5 )
= $true )
| ( $false = $true )
| ~ spl0_1
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f59,f111]) ).
thf(f111,plain,
( ( ( sK2 @ sK5 )
= $true )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f109]) ).
thf(f109,definition,
( spl0_12
<=> ( ( sK2 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f158,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f157]) ).
thf(f157,plain,
( $false
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f156]) ).
thf(f156,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[status(thm)],[f150,f106]) ).
thf(f106,plain,
( ( ( cD @ sK5 )
= $false )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f104]) ).
thf(f104,definition,
( spl0_11
<=> ( ( cD @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f150,plain,
( ( ( cD @ sK5 )
= $true )
| ~ spl0_2
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f147]) ).
thf(f147,plain,
( ( $false = $true )
| ( ( cD @ sK5 )
= $true )
| ~ spl0_2
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f62,f111]) ).
thf(f142,plain,
( ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f141]) ).
thf(f141,plain,
( $false
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f140]) ).
thf(f140,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_demodulation,[status(thm)],[f133,f82]) ).
thf(f82,plain,
( ( ( cD @ sK6 )
= $false )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f80]) ).
thf(f80,definition,
( spl0_6
<=> ( ( cD @ sK6 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f133,plain,
( ( ( cD @ sK6 )
= $true )
| ~ spl0_2
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f129]) ).
thf(f129,plain,
( ( ( cD @ sK6 )
= $true )
| ( $false = $true )
| ~ spl0_2
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f87,f62]) ).
thf(f124,plain,
( ~ spl0_1
| ~ spl0_4
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f123]) ).
thf(f123,plain,
( $false
| ~ spl0_1
| ~ spl0_4
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f122]) ).
thf(f122,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f117,f74]) ).
thf(f74,plain,
( ( $false
= ( cE @ sK3 ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f72]) ).
thf(f72,definition,
( spl0_4
<=> ( $false
= ( cE @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f117,plain,
( ( ( cE @ sK3 )
= $true )
| ~ spl0_1
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f115]) ).
thf(f115,plain,
( ( ( cE @ sK3 )
= $true )
| ( $false = $true )
| ~ spl0_1
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f98,f59]) ).
thf(f98,plain,
( ( ( sK2 @ sK3 )
= $true )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f96]) ).
thf(f96,definition,
( spl0_9
<=> ( ( sK2 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f114,plain,
( spl0_8
| spl0_12
| spl0_9 ),
inference(avatar_split_clause,[status(thm)],[f24,f96,f109,f90]) ).
thf(f24,plain,
( ( ( sK2 @ sK4 )
= $true )
| ( ( sK2 @ sK3 )
= $true )
| ( ( sK2 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( ( sK2 @ sK5 )
=> ( ( cE @ sK5 )
& ( cD @ sK5 ) ) )
= $false )
| ( ( sK2 @ sK4 )
= $true )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( sK2 @ sK3 )
= $true )
| ( ( ( sK2 @ sK4 )
=> ( cD @ sK4 ) )
= $false )
| ( ( ( sK2 @ sK5 )
=> ( ( cE @ sK5 )
& ( cD @ sK5 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ( cE @ Y0 )
& ( cD @ Y0 ) ) )
@ sK5 )
= $false )
| ( ( ( sK2 @ sK4 )
=> ( cD @ sK4 ) )
= $false )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ( cE @ Y0 )
& ( cD @ Y0 ) ) ) )
= $false )
| ( ( sK2 @ sK3 )
= $true )
| ( ( ( sK2 @ sK4 )
=> ( cD @ sK4 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( ( sK2 @ sK3 )
=> ( cE @ sK3 ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ( cE @ Y0 )
& ( cD @ Y0 ) ) ) )
= $false )
| ( ( ( sK2 @ sK4 )
=> ( cD @ sK4 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ( ( sK2 @ sK3 )
=> ( cE @ sK3 ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ( cE @ Y0 )
& ( cD @ Y0 ) ) ) )
= $false )
| ( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( cD @ Y0 ) )
@ sK4 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( cD @ Y0 ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ( cE @ Y0 )
& ( cD @ Y0 ) ) ) )
= $false )
| ( ( ( sK2 @ sK3 )
=> ( cE @ sK3 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( cD @ Y0 ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ( cE @ Y0 )
& ( cD @ Y0 ) ) ) )
= $false )
| ( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( cE @ Y0 ) )
@ sK3 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( cE @ Y0 ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ( cE @ Y0 )
& ( cD @ Y0 ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( cD @ Y0 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( cD @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( cE @ Y0 ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ( cE @ Y0 )
& ( cD @ Y0 ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( cD @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( cE @ Y0 ) ) ) )
!= ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ( cE @ Y0 )
& ( cD @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cD @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cE @ Y1 ) ) ) )
@ sK2 )
!= ( ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( ( cE @ Y1 )
& ( cD @ Y1 ) ) ) )
@ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cD @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cE @ Y1 ) ) ) ) )
!= ( ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( ( cE @ Y1 )
& ( cD @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cD @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cE @ Y1 ) ) ) ) )
!= ( ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( ( cE @ Y1 )
& ( cD @ Y1 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ^ [Y0: a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cD @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( cE @ Y1 ) ) ) ) )
!= ( ^ [Y0: a > $o] :
( !! @ a
@ ^ [Y1: a] :
( ( Y0 @ Y1 )
=> ( ( cE @ Y1 )
& ( cD @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
( ( ^ [X0: a > $o] :
( ! [X1: a] :
( ( X0 @ X1 )
=> ( cE @ X1 ) )
& ! [X2: a] :
( ( X0 @ X2 )
=> ( cD @ X2 ) ) ) )
!= ( ^ [X3: a > $o] :
! [X4: a] :
( ( X3 @ X4 )
=> ( ( cD @ X4 )
& ( cE @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
( ( ^ [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cE @ X2 ) )
& ! [X2: a] :
( ( X1 @ X2 )
=> ( cD @ X2 ) ) ) )
!= ( ^ [X0: a > $o] :
! [X1: a] :
( ( X0 @ X1 )
=> ( ( cD @ X1 )
& ( cE @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ^ [X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( cE @ X2 ) )
& ! [X2: a] :
( ( X1 @ X2 )
=> ( cD @ X2 ) ) ) )
= ( ^ [X0: a > $o] :
! [X1: a] :
( ( X0 @ X1 )
=> ( ( cD @ X1 )
& ( cE @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.TiRQ90Rd6R/DTF2THF_20538.p',cX5209_pme) ).
thf(f113,plain,
( spl0_10
| spl0_9
| spl0_11
| spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f25,f90,f104,f96,f100]) ).
thf(f25,plain,
( ( ( sK2 @ sK4 )
= $true )
| ( ( cD @ sK5 )
= $false )
| ( ( sK2 @ sK3 )
= $true )
| ( ( cE @ sK5 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( ( sK2 @ sK4 )
= $true )
| ( ( ( cE @ sK5 )
& ( cD @ sK5 ) )
= $false )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f112,plain,
( spl0_9
| spl0_12
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f27,f68,f109,f96]) ).
thf(f27,plain,
( ( $false
= ( cD @ sK4 ) )
| ( ( sK2 @ sK5 )
= $true )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( ( sK2 @ sK5 )
=> ( ( cE @ sK5 )
& ( cD @ sK5 ) ) )
= $false )
| ( $false
= ( cD @ sK4 ) )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f107,plain,
( spl0_9
| spl0_10
| spl0_3
| spl0_11 ),
inference(avatar_split_clause,[status(thm)],[f28,f104,f68,f100,f96]) ).
thf(f28,plain,
( ( ( cE @ sK5 )
= $false )
| ( ( sK2 @ sK3 )
= $true )
| ( ( cD @ sK5 )
= $false )
| ( $false
= ( cD @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( ( cE @ sK5 )
& ( cD @ sK5 ) )
= $false )
| ( $false
= ( cD @ sK4 ) )
| ( ( sK2 @ sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f94,plain,
( spl0_4
| spl0_7
| spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f34,f90,f85,f72]) ).
thf(f34,plain,
( ( ( sK2 @ sK6 )
= $true )
| ( $false
= ( cE @ sK3 ) )
| ( ( sK2 @ sK4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ( ( sK2 @ sK6 )
=> ( ( cE @ sK6 )
& ( cD @ sK6 ) ) )
= $false )
| ( ( sK2 @ sK4 )
= $true )
| ( $false
= ( cE @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ( ( sK2 @ sK4 )
=> ( cD @ sK4 ) )
= $false )
| ( $false
= ( cE @ sK3 ) )
| ( ( ( sK2 @ sK6 )
=> ( ( cE @ sK6 )
& ( cD @ sK6 ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( ( sK2 @ sK4 )
=> ( cD @ sK4 ) )
= $false )
| ( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ( cE @ Y0 )
& ( cD @ Y0 ) ) )
@ sK6 )
= $false )
| ( $false
= ( cE @ sK3 ) ) ),
inference(sigma_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ( cE @ Y0 )
& ( cD @ Y0 ) ) ) )
= $false )
| ( ( ( sK2 @ sK4 )
=> ( cD @ sK4 ) )
= $false )
| ( $false
= ( cE @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f93,plain,
( spl0_8
| spl0_4
| spl0_6
| spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f35,f76,f80,f72,f90]) ).
thf(f35,plain,
( ( $false
= ( cE @ sK6 ) )
| ( ( sK2 @ sK4 )
= $true )
| ( ( cD @ sK6 )
= $false )
| ( $false
= ( cE @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( sK2 @ sK4 )
= $true )
| ( ( ( cE @ sK6 )
& ( cD @ sK6 ) )
= $false )
| ( $false
= ( cE @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f88,plain,
( spl0_3
| spl0_7
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f37,f72,f85,f68]) ).
thf(f37,plain,
( ( ( sK2 @ sK6 )
= $true )
| ( $false
= ( cD @ sK4 ) )
| ( $false
= ( cE @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ( ( sK2 @ sK6 )
=> ( ( cE @ sK6 )
& ( cD @ sK6 ) ) )
= $false )
| ( $false
= ( cE @ sK3 ) )
| ( $false
= ( cD @ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f83,plain,
( spl0_3
| spl0_4
| spl0_5
| spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f38,f80,f76,f72,f68]) ).
thf(f38,plain,
( ( $false
= ( cD @ sK4 ) )
| ( $false
= ( cE @ sK3 ) )
| ( $false
= ( cE @ sK6 ) )
| ( ( cD @ sK6 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( ( cE @ sK6 )
& ( cD @ sK6 ) )
= $false )
| ( $false
= ( cD @ sK4 ) )
| ( $false
= ( cE @ sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f65,plain,
( spl0_2
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f47,f61,f61]) ).
thf(f47,plain,
! [X2: a,X1: a] :
( ( $false
= ( sK2 @ X1 ) )
| ( ( cD @ X1 )
= $true )
| ( ( sK2 @ X2 )
= $false )
| ( ( cD @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,plain,
! [X2: a,X1: a] :
( ( ( ( cE @ X2 )
& ( cD @ X2 ) )
= $true )
| ( ( cD @ X1 )
= $true )
| ( ( sK2 @ X2 )
= $false )
| ( $false
= ( sK2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f45]) ).
thf(f45,plain,
! [X2: a,X1: a] :
( ( ( cD @ X1 )
= $true )
| ( ( ( sK2 @ X2 )
=> ( ( cE @ X2 )
& ( cD @ X2 ) ) )
= $true )
| ( $false
= ( sK2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
! [X2: a,X1: a] :
( ( ( ( sK2 @ X1 )
=> ( cD @ X1 ) )
= $true )
| ( ( ( sK2 @ X2 )
=> ( ( cE @ X2 )
& ( cD @ X2 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: a,X1: a] :
( ( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ( cE @ Y0 )
& ( cD @ Y0 ) ) )
@ X2 )
= $true )
| ( ( ( sK2 @ X1 )
=> ( cD @ X1 ) )
= $true ) ),
inference(pi_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X1: a] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ( cE @ Y0 )
& ( cD @ Y0 ) ) ) )
= $true )
| ( ( ( sK2 @ X1 )
=> ( cD @ X1 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f41]) ).
thf(f41,plain,
! [X1: a] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ( cE @ Y0 )
& ( cD @ Y0 ) ) ) )
= $true )
| ( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( cD @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( cD @ Y0 ) ) )
= $true )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ( cE @ Y0 )
& ( cD @ Y0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( cD @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( cE @ Y0 ) ) ) )
= $true )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ( cE @ Y0 )
& ( cD @ Y0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f64,plain,
( spl0_1
| spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f56,f58,f58]) ).
thf(f56,plain,
! [X2: a,X1: a] :
( ( ( cE @ X1 )
= $true )
| ( $false
= ( sK2 @ X1 ) )
| ( ( sK2 @ X2 )
= $false )
| ( ( cE @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f54]) ).
thf(f54,plain,
! [X2: a,X1: a] :
( ( ( cE @ X1 )
= $true )
| ( ( ( cE @ X2 )
& ( cD @ X2 ) )
= $true )
| ( ( sK2 @ X2 )
= $false )
| ( $false
= ( sK2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
! [X2: a,X1: a] :
( ( $false
= ( sK2 @ X1 ) )
| ( ( ( sK2 @ X2 )
=> ( ( cE @ X2 )
& ( cD @ X2 ) ) )
= $true )
| ( ( cE @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
! [X2: a,X1: a] :
( ( ( ( sK2 @ X1 )
=> ( cE @ X1 ) )
= $true )
| ( ( ( sK2 @ X2 )
=> ( ( cE @ X2 )
& ( cD @ X2 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f51]) ).
thf(f51,plain,
! [X2: a,X1: a] :
( ( ( ( sK2 @ X1 )
=> ( cE @ X1 ) )
= $true )
| ( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ( cE @ Y0 )
& ( cD @ Y0 ) ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f50]) ).
thf(f50,plain,
! [X1: a] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ( cE @ Y0 )
& ( cD @ Y0 ) ) ) )
= $true )
| ( ( ( sK2 @ X1 )
=> ( cE @ X1 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f49]) ).
thf(f49,plain,
! [X1: a] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ( cE @ Y0 )
& ( cD @ Y0 ) ) ) )
= $true )
| ( ( ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( cE @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( cE @ Y0 ) ) )
= $true )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK2 @ Y0 )
=> ( ( cE @ Y0 )
& ( cD @ Y0 ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV229^5 : 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 : n029.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:42:29 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
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : SEV229^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.47 % Domain : Set Theory (Sets of sets)
% 0.28/0.47 % Problem : TPS problem X5209
% 0.28/0.47 % Version : Especial.
% 0.28/0.47 % English :
% 0.28/0.47
% 0.28/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.47 % Source : [Bro09]
% 0.28/0.47 % Names : tps_0304 [Bro09]
% 0.28/0.47 % : X5209 [TPS]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 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 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.28/0.47 % Syntax : Number of formulae : 4 ( 1 unt; 3 typ; 0 def)
% 0.28/0.47 % Number of atoms : 5 ( 1 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 1 ( 5 avg)
% 0.28/0.47 % Number of connectives : 12 ( 0 ~; 0 |; 2 &; 7 @)
% 0.28/0.47 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 1 ( 1 avg)
% 0.28/0.47 % Number of types : 2 ( 1 usr)
% 0.28/0.47 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.28/0.47 % Number of variables : 5 ( 2 ^; 3 !; 0 ?; 5 :)
% 0.28/0.47 % SPC : TH0_THM_EQU_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.47 % : Polymorphic definitions expanded.
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 thf(a_type,type,
% 0.28/0.47 a: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(cE,type,
% 0.28/0.47 cE: a > $o ).
% 0.28/0.47
% 0.28/0.47 thf(cD,type,
% 0.28/0.47 cD: a > $o ).
% 0.28/0.47
% 0.28/0.47 thf(cX5209_pme,conjecture,
% 0.28/0.47 ( ( ^ [R: a > $o] :
% 0.28/0.47 ! [Xx: a] :
% 0.28/0.47 ( ( R @ Xx )
% 0.28/0.47 => ( ( cD @ Xx )
% 0.28/0.47 & ( cE @ Xx ) ) ) )
% 0.28/0.47 = ( ^ [Xx: a > $o] :
% 0.28/0.47 ( ! [Xx0: a] :
% 0.28/0.47 ( ( Xx @ Xx0 )
% 0.28/0.47 => ( cD @ Xx0 ) )
% 0.28/0.47 & ! [Xx0: a] :
% 0.28/0.47 ( ( Xx @ Xx0 )
% 0.28/0.47 => ( cE @ Xx0 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 1.45/1.28 ---- Embedded in THF ---
% 1.45/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.29 %%% Generated on Tue Feb 24 12:42:30 EST 2026
% 1.45/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.29 %%% Logic specification used:
% 1.45/1.29 %%% thf(spec, logic, $$dhol).
% 1.45/1.29
% 1.45/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.TiRQ90Rd6R/DTF2DTF20538.p
% See solution above
% 1.45/1.29 ------------------------
% 1.45/1.30 ---- Cleaned THF ---
% 1.60/1.30 thf(a_type,type,
% 1.60/1.30 a: $tType ).
% 1.60/1.30
% 1.60/1.30 thf(cE,type,
% 1.60/1.30 cE: a > $o ).
% 1.60/1.30
% 1.60/1.30 thf(cD,type,
% 1.60/1.30 cD: a > $o ).
% 1.60/1.30
% 1.60/1.30 thf(cX5209_pme,conjecture,
% 1.60/1.30 ( ( ^ [R: a > $o] :
% 1.60/1.30 ! [Xx: a] :
% 1.60/1.30 ( ( R @ Xx )
% 1.60/1.30 => ( ( cD @ Xx )
% 1.60/1.30 & ( cE @ Xx ) ) ) )
% 1.60/1.30 = ( ^ [Xx: a > $o] :
% 1.60/1.30 ( ! [Xx0: a] :
% 1.60/1.30 ( ( Xx @ Xx0 )
% 1.60/1.30 => ( cD @ Xx0 ) )
% 1.60/1.30 & ! [Xx0: a] :
% 1.60/1.30 ( ( Xx @ Xx0 )
% 1.60/1.30 => ( cE @ Xx0 ) ) ) ) ) ).
% 1.60/1.30 ------------------------
% 1.60/1.31 % (20812)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20538 for (2999ds/2Mi)
% 1.60/1.31 % (20812)Instruction limit reached!
% 1.60/1.31 % (20812)------------------------------
% 1.60/1.31 % (20812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.31 % (20812)Termination reason: Unknown
% 1.60/1.31 % (20812)Termination phase: Saturation
% 1.60/1.31
% 1.60/1.31 % (20812)Memory used [KB]: 5373
% 1.60/1.31 % (20812)Time elapsed: 0.002 s
% 1.60/1.31 % (20812)Instructions burned: 2 (million)
% 1.60/1.31 % (20812)------------------------------
% 1.60/1.31 % (20812)------------------------------
% 1.60/1.32 % (20809)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20538 for (2999ds/183Mi)
% 1.60/1.32 % (20810)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_20538 for (2999ds/4Mi)
% 1.60/1.32 % (20811)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_20538 for (2999ds/27Mi)
% 1.60/1.32 % (20813)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_20538 for (2999ds/2Mi)
% 1.60/1.32 % (20814)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_20538 for (2999ds/275Mi)
% 1.60/1.32 % (20815)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20538 for (2999ds/18Mi)
% 1.60/1.32 % (20813)Instruction limit reached!
% 1.60/1.32 % (20813)------------------------------
% 1.60/1.32 % (20813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.32 % (20813)Termination reason: Unknown
% 1.60/1.32 % (20813)Termination phase: Saturation
% 1.60/1.32
% 1.60/1.32 % (20813)Memory used [KB]: 895
% 1.60/1.32 % (20813)Time elapsed: 0.003 s
% 1.60/1.32 % (20813)Instructions burned: 2 (million)
% 1.60/1.32 % (20813)------------------------------
% 1.60/1.32 % (20813)------------------------------
% 1.60/1.32 % (20816)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20538 for (2999ds/3Mi)
% 1.60/1.32 % (20810)Instruction limit reached!
% 1.60/1.32 % (20810)------------------------------
% 1.60/1.32 % (20810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.32 % (20810)Termination reason: Unknown
% 1.60/1.32 % (20810)Termination phase: Saturation
% 1.60/1.32
% 1.60/1.32 % (20810)Memory used [KB]: 5500
% 1.60/1.32 % (20810)Time elapsed: 0.005 s
% 1.60/1.32 % (20810)Instructions burned: 4 (million)
% 1.60/1.32 % (20810)------------------------------
% 1.60/1.32 % (20810)------------------------------
% 1.60/1.32 % (20816)Refutation not found, incomplete strategy
% 1.60/1.32 % (20816)------------------------------
% 1.60/1.32 % (20816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.32 % (20816)Termination reason: Refutation not found, incomplete strategy
% 1.60/1.32
% 1.60/1.32
% 1.60/1.32 % (20816)Memory used [KB]: 5500
% 1.60/1.32 % (20816)Time elapsed: 0.001 s
% 1.60/1.32 % (20816)Instructions burned: 1 (million)
% 1.60/1.32 % (20816)------------------------------
% 1.60/1.32 % (20816)------------------------------
% 1.60/1.33 % (20811)First to succeed.
% 1.60/1.33 % (20814)Also succeeded, but the first one will report.
% 1.60/1.33 % (20815)Also succeeded, but the first one will report.
% 1.60/1.33 % (20811)Refutation found. Thanks to Tanya!
% 1.60/1.33 % SZS status Theorem for DTF2THF_20538
% 1.60/1.33 % SZS output start Proof for DTF2THF_20538
% 1.60/1.33 thf(type_def_5, type, a: $tType).
% 1.60/1.33 thf(func_def_0, type, a: $tType).
% 1.60/1.33 thf(func_def_1, type, cE: a > $o).
% 1.60/1.33 thf(func_def_2, type, cD: a > $o).
% 1.60/1.33 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.60/1.33 thf(func_def_14, type, ph1: !>[X0: $tType]:(X0)).
% 1.60/1.33 thf(func_def_15, type, sK2: a > $o).
% 1.60/1.33 thf(func_def_16, type, sK3: a).
% 1.60/1.33 thf(func_def_17, type, sK4: a).
% 1.60/1.33 thf(func_def_18, type, sK5: a).
% 1.60/1.33 thf(func_def_19, type, sK6: a).
% 1.60/1.33 thf(f180,plain,(
% 1.60/1.33 $false),
% 1.60/1.33 inference(avatar_sat_refutation,[status(thm)],[f64,f65,f83,f88,f93,f94,f107,f112,f113,f114,f124,f142,f158,f162,f176,f179])).
% 1.60/1.33 thf(f179,plain,(
% 1.60/1.33 ~spl0_1 | ~spl0_5 | ~spl0_7),
% 1.60/1.33 inference(avatar_contradiction_clause,[status(thm)],[f178])).
% 1.60/1.33 thf(f178,plain,(
% 1.60/1.33 $false | (~spl0_1 | ~spl0_5 | ~spl0_7)),
% 1.60/1.33 inference(trivial_inequality_removal,[status(thm)],[f177])).
% 1.60/1.33 thf(f177,plain,(
% 1.60/1.33 ($false = $true) | (~spl0_1 | ~spl0_5 | ~spl0_7)),
% 1.60/1.33 inference(backward_demodulation,[status(thm)],[f134,f78])).
% 1.60/1.33 thf(f78,plain,(
% 1.60/1.33 ($false = (cE @ sK6)) | ~spl0_5),
% 1.60/1.33 inference(avatar_component_clause,[status(thm)],[f76])).
% 1.60/1.33 thf(f76,definition,(
% 1.60/1.33 spl0_5 <=> ($false = (cE @ sK6))),
% 1.60/1.33 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.60/1.33 thf(f134,plain,(
% 1.60/1.33 ((cE @ sK6) = $true) | (~spl0_1 | ~spl0_7)),
% 1.60/1.33 inference(trivial_inequality_removal,[status(thm)],[f132])).
% 1.60/1.33 thf(f132,plain,(
% 1.60/1.33 ($false = $true) | ((cE @ sK6) = $true) | (~spl0_1 | ~spl0_7)),
% 1.60/1.33 inference(superposition,[status(thm)],[f59,f87])).
% 1.60/1.33 thf(f87,plain,(
% 1.60/1.33 ((sK2 @ sK6) = $true) | ~spl0_7),
% 1.60/1.33 inference(avatar_component_clause,[status(thm)],[f85])).
% 1.60/1.33 thf(f85,definition,(
% 1.60/1.33 spl0_7 <=> ((sK2 @ sK6) = $true)),
% 1.60/1.33 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.60/1.33 thf(f59,plain,(
% 1.60/1.33 ( ! [X1 : a] : (($false = (sK2 @ X1)) | ((cE @ X1) = $true)) ) | ~spl0_1),
% 1.60/1.33 inference(avatar_component_clause,[status(thm)],[f58])).
% 1.60/1.33 thf(f58,definition,(
% 1.60/1.33 spl0_1 <=> ! [X1 : a] : (($false = (sK2 @ X1)) | ((cE @ X1) = $true))),
% 1.60/1.33 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.60/1.33 thf(f176,plain,(
% 1.60/1.33 ~spl0_2 | ~spl0_3 | ~spl0_8),
% 1.60/1.33 inference(avatar_contradiction_clause,[status(thm)],[f175])).
% 1.60/1.33 thf(f175,plain,(
% 1.60/1.33 $false | (~spl0_2 | ~spl0_3 | ~spl0_8)),
% 1.60/1.33 inference(trivial_inequality_removal,[status(thm)],[f174])).
% 1.60/1.33 thf(f174,plain,(
% 1.60/1.33 ($false = $true) | (~spl0_2 | ~spl0_3 | ~spl0_8)),
% 1.60/1.33 inference(forward_demodulation,[status(thm)],[f167,f70])).
% 1.60/1.33 thf(f70,plain,(
% 1.60/1.33 ($false = (cD @ sK4)) | ~spl0_3),
% 1.60/1.33 inference(avatar_component_clause,[status(thm)],[f68])).
% 1.60/1.33 thf(f68,definition,(
% 1.60/1.33 spl0_3 <=> ($false = (cD @ sK4))),
% 1.60/1.33 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.60/1.33 thf(f167,plain,(
% 1.60/1.33 ((cD @ sK4) = $true) | (~spl0_2 | ~spl0_8)),
% 1.60/1.33 inference(trivial_inequality_removal,[status(thm)],[f165])).
% 1.60/1.33 thf(f165,plain,(
% 1.60/1.33 ($false = $true) | ((cD @ sK4) = $true) | (~spl0_2 | ~spl0_8)),
% 1.60/1.33 inference(superposition,[status(thm)],[f62,f92])).
% 1.60/1.33 thf(f92,plain,(
% 1.60/1.33 ((sK2 @ sK4) = $true) | ~spl0_8),
% 1.60/1.33 inference(avatar_component_clause,[status(thm)],[f90])).
% 1.60/1.33 thf(f90,definition,(
% 1.60/1.33 spl0_8 <=> ((sK2 @ sK4) = $true)),
% 1.60/1.33 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.60/1.33 thf(f62,plain,(
% 1.60/1.33 ( ! [X2 : a] : (((sK2 @ X2) = $false) | ((cD @ X2) = $true)) ) | ~spl0_2),
% 1.60/1.33 inference(avatar_component_clause,[status(thm)],[f61])).
% 1.60/1.33 thf(f61,definition,(
% 1.60/1.33 spl0_2 <=> ! [X2 : a] : (((sK2 @ X2) = $false) | ((cD @ X2) = $true))),
% 1.60/1.33 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.60/1.33 thf(f162,plain,(
% 1.60/1.33 ~spl0_1 | ~spl0_10 | ~spl0_12),
% 1.60/1.33 inference(avatar_contradiction_clause,[status(thm)],[f161])).
% 1.60/1.33 thf(f161,plain,(
% 1.60/1.33 $false | (~spl0_1 | ~spl0_10 | ~spl0_12)),
% 1.60/1.33 inference(trivial_inequality_removal,[status(thm)],[f160])).
% 1.60/1.33 thf(f160,plain,(
% 1.60/1.33 ($false = $true) | (~spl0_1 | ~spl0_10 | ~spl0_12)),
% 1.60/1.33 inference(forward_demodulation,[status(thm)],[f149,f102])).
% 1.60/1.33 thf(f102,plain,(
% 1.60/1.33 ((cE @ sK5) = $false) | ~spl0_10),
% 1.60/1.33 inference(avatar_component_clause,[status(thm)],[f100])).
% 1.60/1.33 thf(f100,definition,(
% 1.60/1.33 spl0_10 <=> ((cE @ sK5) = $false)),
% 1.60/1.33 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.60/1.33 thf(f149,plain,(
% 1.60/1.33 ((cE @ sK5) = $true) | (~spl0_1 | ~spl0_12)),
% 1.60/1.33 inference(trivial_inequality_removal,[status(thm)],[f148])).
% 1.60/1.33 thf(f148,plain,(
% 1.60/1.33 ((cE @ sK5) = $true) | ($false = $true) | (~spl0_1 | ~spl0_12)),
% 1.60/1.33 inference(superposition,[status(thm)],[f59,f111])).
% 1.60/1.33 thf(f111,plain,(
% 1.60/1.33 ((sK2 @ sK5) = $true) | ~spl0_12),
% 1.60/1.33 inference(avatar_component_clause,[status(thm)],[f109])).
% 1.60/1.33 thf(f109,definition,(
% 1.60/1.33 spl0_12 <=> ((sK2 @ sK5) = $true)),
% 1.60/1.33 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.60/1.33 thf(f158,plain,(
% 1.60/1.33 ~spl0_2 | ~spl0_11 | ~spl0_12),
% 1.60/1.33 inference(avatar_contradiction_clause,[status(thm)],[f157])).
% 1.60/1.33 thf(f157,plain,(
% 1.60/1.33 $false | (~spl0_2 | ~spl0_11 | ~spl0_12)),
% 1.60/1.33 inference(trivial_inequality_removal,[status(thm)],[f156])).
% 1.60/1.33 thf(f156,plain,(
% 1.60/1.33 ($false = $true) | (~spl0_2 | ~spl0_11 | ~spl0_12)),
% 1.60/1.33 inference(forward_demodulation,[status(thm)],[f150,f106])).
% 1.60/1.33 thf(f106,plain,(
% 1.60/1.33 ((cD @ sK5) = $false) | ~spl0_11),
% 1.60/1.33 inference(avatar_component_clause,[status(thm)],[f104])).
% 1.60/1.33 thf(f104,definition,(
% 1.60/1.33 spl0_11 <=> ((cD @ sK5) = $false)),
% 1.60/1.33 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 1.60/1.33 thf(f150,plain,(
% 1.60/1.33 ((cD @ sK5) = $true) | (~spl0_2 | ~spl0_12)),
% 1.60/1.33 inference(trivial_inequality_removal,[status(thm)],[f147])).
% 1.60/1.33 thf(f147,plain,(
% 1.60/1.33 ($false = $true) | ((cD @ sK5) = $true) | (~spl0_2 | ~spl0_12)),
% 1.60/1.33 inference(superposition,[status(thm)],[f62,f111])).
% 1.60/1.33 thf(f142,plain,(
% 1.60/1.33 ~spl0_2 | ~spl0_6 | ~spl0_7),
% 1.60/1.33 inference(avatar_contradiction_clause,[status(thm)],[f141])).
% 1.60/1.33 thf(f141,plain,(
% 1.60/1.33 $false | (~spl0_2 | ~spl0_6 | ~spl0_7)),
% 1.60/1.33 inference(trivial_inequality_removal,[status(thm)],[f140])).
% 1.60/1.33 thf(f140,plain,(
% 1.60/1.33 ($false = $true) | (~spl0_2 | ~spl0_6 | ~spl0_7)),
% 1.60/1.33 inference(forward_demodulation,[status(thm)],[f133,f82])).
% 1.60/1.33 thf(f82,plain,(
% 1.60/1.33 ((cD @ sK6) = $false) | ~spl0_6),
% 1.60/1.33 inference(avatar_component_clause,[status(thm)],[f80])).
% 1.60/1.33 thf(f80,definition,(
% 1.60/1.33 spl0_6 <=> ((cD @ sK6) = $false)),
% 1.60/1.33 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.60/1.33 thf(f133,plain,(
% 1.60/1.33 ((cD @ sK6) = $true) | (~spl0_2 | ~spl0_7)),
% 1.60/1.33 inference(trivial_inequality_removal,[status(thm)],[f129])).
% 1.60/1.33 thf(f129,plain,(
% 1.60/1.33 ((cD @ sK6) = $true) | ($false = $true) | (~spl0_2 | ~spl0_7)),
% 1.60/1.33 inference(superposition,[status(thm)],[f87,f62])).
% 1.60/1.33 thf(f124,plain,(
% 1.60/1.33 ~spl0_1 | ~spl0_4 | ~spl0_9),
% 1.60/1.33 inference(avatar_contradiction_clause,[status(thm)],[f123])).
% 1.60/1.33 thf(f123,plain,(
% 1.60/1.33 $false | (~spl0_1 | ~spl0_4 | ~spl0_9)),
% 1.60/1.33 inference(trivial_inequality_removal,[status(thm)],[f122])).
% 1.60/1.33 thf(f122,plain,(
% 1.60/1.33 ($false = $true) | (~spl0_1 | ~spl0_4 | ~spl0_9)),
% 1.60/1.33 inference(forward_demodulation,[status(thm)],[f117,f74])).
% 1.60/1.33 thf(f74,plain,(
% 1.60/1.33 ($false = (cE @ sK3)) | ~spl0_4),
% 1.60/1.33 inference(avatar_component_clause,[status(thm)],[f72])).
% 1.60/1.33 thf(f72,definition,(
% 1.60/1.33 spl0_4 <=> ($false = (cE @ sK3))),
% 1.60/1.33 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.60/1.33 thf(f117,plain,(
% 1.60/1.33 ((cE @ sK3) = $true) | (~spl0_1 | ~spl0_9)),
% 1.60/1.33 inference(trivial_inequality_removal,[status(thm)],[f115])).
% 1.60/1.33 thf(f115,plain,(
% 1.60/1.33 ((cE @ sK3) = $true) | ($false = $true) | (~spl0_1 | ~spl0_9)),
% 1.60/1.33 inference(superposition,[status(thm)],[f98,f59])).
% 1.60/1.33 thf(f98,plain,(
% 1.60/1.33 ((sK2 @ sK3) = $true) | ~spl0_9),
% 1.60/1.33 inference(avatar_component_clause,[status(thm)],[f96])).
% 1.60/1.33 thf(f96,definition,(
% 1.60/1.33 spl0_9 <=> ((sK2 @ sK3) = $true)),
% 1.60/1.33 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.60/1.33 thf(f114,plain,(
% 1.60/1.33 spl0_8 | spl0_12 | spl0_9),
% 1.60/1.33 inference(avatar_split_clause,[status(thm)],[f24,f96,f109,f90])).
% 1.60/1.33 thf(f24,plain,(
% 1.60/1.33 ((sK2 @ sK4) = $true) | ((sK2 @ sK3) = $true) | ((sK2 @ sK5) = $true)),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.60/1.33 thf(f22,plain,(
% 1.60/1.33 (((sK2 @ sK5) => ((cE @ sK5) & (cD @ sK5))) = $false) | ((sK2 @ sK4) = $true) | ((sK2 @ sK3) = $true)),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.60/1.33 thf(f20,plain,(
% 1.60/1.33 ((sK2 @ sK3) = $true) | (((sK2 @ sK4) => (cD @ sK4)) = $false) | (((sK2 @ sK5) => ((cE @ sK5) & (cD @ sK5))) = $false)),
% 1.60/1.33 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.60/1.33 thf(f19,plain,(
% 1.60/1.33 (((^[Y0 : a]: ((sK2 @ Y0) => ((cE @ Y0) & (cD @ Y0)))) @ sK5) = $false) | (((sK2 @ sK4) => (cD @ sK4)) = $false) | ((sK2 @ sK3) = $true)),
% 1.60/1.33 inference(sigma_clausification,[status(thm)],[f18])).
% 1.60/1.33 thf(f18,plain,(
% 1.60/1.33 ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => ((cE @ Y0) & (cD @ Y0))))) = $false) | ((sK2 @ sK3) = $true) | (((sK2 @ sK4) => (cD @ sK4)) = $false)),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.60/1.33 thf(f16,plain,(
% 1.60/1.33 (((sK2 @ sK3) => (cE @ sK3)) = $false) | ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => ((cE @ Y0) & (cD @ Y0))))) = $false) | (((sK2 @ sK4) => (cD @ sK4)) = $false)),
% 1.60/1.33 inference(beta_eta_normalization,[status(thm)],[f15])).
% 1.60/1.33 thf(f15,plain,(
% 1.60/1.33 (((sK2 @ sK3) => (cE @ sK3)) = $false) | ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => ((cE @ Y0) & (cD @ Y0))))) = $false) | (((^[Y0 : a]: ((sK2 @ Y0) => (cD @ Y0))) @ sK4) = $false)),
% 1.60/1.33 inference(sigma_clausification,[status(thm)],[f14])).
% 1.60/1.33 thf(f14,plain,(
% 1.60/1.33 ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (cD @ Y0)))) = $false) | ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => ((cE @ Y0) & (cD @ Y0))))) = $false) | (((sK2 @ sK3) => (cE @ sK3)) = $false)),
% 1.60/1.33 inference(beta_eta_normalization,[status(thm)],[f13])).
% 1.60/1.33 thf(f13,plain,(
% 1.60/1.33 ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (cD @ Y0)))) = $false) | ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => ((cE @ Y0) & (cD @ Y0))))) = $false) | (((^[Y0 : a]: ((sK2 @ Y0) => (cE @ Y0))) @ sK3) = $false)),
% 1.60/1.33 inference(sigma_clausification,[status(thm)],[f12])).
% 1.60/1.33 thf(f12,plain,(
% 1.60/1.33 ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (cE @ Y0)))) = $false) | ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => ((cE @ Y0) & (cD @ Y0))))) = $false) | ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (cD @ Y0)))) = $false)),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.60/1.33 thf(f11,plain,(
% 1.60/1.33 (((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (cD @ Y0)))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (cE @ Y0))))) = $false) | ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => ((cE @ Y0) & (cD @ Y0))))) = $false)),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.60/1.33 thf(f9,plain,(
% 1.60/1.33 (((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (cD @ Y0)))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (cE @ Y0))))) != (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => ((cE @ Y0) & (cD @ Y0))))))),
% 1.60/1.33 inference(beta_eta_normalization,[status(thm)],[f8])).
% 1.60/1.33 thf(f8,plain,(
% 1.60/1.33 (((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cD @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cE @ Y1)))))) @ sK2) != ((^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => ((cE @ Y1) & (cD @ Y1)))))) @ sK2))),
% 1.60/1.33 inference(negative_extensionality,[status(thm)],[f7])).
% 1.60/1.33 thf(f7,plain,(
% 1.60/1.33 ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cD @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cE @ Y1)))))) != (^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => ((cE @ Y1) & (cD @ Y1)))))))),
% 1.60/1.33 inference(cnf_transformation,[status(thm)],[f6])).
% 1.60/1.33 thf(f6,plain,(
% 1.60/1.33 ((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cD @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cE @ Y1)))))) != (^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => ((cE @ Y1) & (cD @ Y1)))))))),
% 1.60/1.33 inference(flattening,[status(thm)],[f5])).
% 1.60/1.33 thf(f5,plain,(
% 1.60/1.33 ~((^[Y0 : a > $o]: ((!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cD @ Y1)))) & (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => (cE @ Y1)))))) = (^[Y0 : a > $o]: (!! @ a @ (^[Y1 : a]: ((Y0 @ Y1) => ((cE @ Y1) & (cD @ Y1)))))))),
% 1.60/1.33 inference(fool_elimination,[status(thm)],[f4])).
% 1.60/1.33 thf(f4,plain,(
% 1.60/1.33 ~((^[X0 : a > $o] : (! [X1 : a] : ((X0 @ X1) => (cE @ X1)) & ! [X2 : a] : ((X0 @ X2) => (cD @ X2)))) = (^[X3 : a > $o] : (! [X4 : a] : ((X3 @ X4) => ((cD @ X4) & (cE @ X4))))))),
% 1.60/1.33 inference(rectify,[status(thm)],[f2])).
% 1.60/1.33 thf(f2,negated_conjecture,(
% 1.60/1.33 ~((^[X1 : a > $o] : (! [X2 : a] : ((X1 @ X2) => (cE @ X2)) & ! [X2 : a] : ((X1 @ X2) => (cD @ X2)))) = (^[X0 : a > $o] : (! [X1 : a] : ((X0 @ X1) => ((cD @ X1) & (cE @ X1))))))),
% 1.60/1.33 inference(negated_conjecture,[status(cth)],[f1])).
% 1.60/1.33 thf(f1,conjecture,(
% 1.60/1.33 ((^[X1 : a > $o] : (! [X2 : a] : ((X1 @ X2) => (cE @ X2)) & ! [X2 : a] : ((X1 @ X2) => (cD @ X2)))) = (^[X0 : a > $o] : (! [X1 : a] : ((X0 @ X1) => ((cD @ X1) & (cE @ X1))))))),
% 1.60/1.33 file('/export/starexec/sandbox2/tmp/tmp.TiRQ90Rd6R/DTF2THF_20538.p',cX5209_pme)).
% 1.60/1.33 thf(f113,plain,(
% 1.60/1.33 spl0_10 | spl0_9 | spl0_11 | spl0_8),
% 1.60/1.33 inference(avatar_split_clause,[status(thm)],[f25,f90,f104,f96,f100])).
% 1.60/1.33 thf(f25,plain,(
% 1.60/1.33 ((sK2 @ sK4) = $true) | ((cD @ sK5) = $false) | ((sK2 @ sK3) = $true) | ((cE @ sK5) = $false)),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f23])).
% 1.60/1.33 thf(f23,plain,(
% 1.60/1.33 ((sK2 @ sK4) = $true) | (((cE @ sK5) & (cD @ sK5)) = $false) | ((sK2 @ sK3) = $true)),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.60/1.33 thf(f112,plain,(
% 1.60/1.33 spl0_9 | spl0_12 | spl0_3),
% 1.60/1.33 inference(avatar_split_clause,[status(thm)],[f27,f68,f109,f96])).
% 1.60/1.33 thf(f27,plain,(
% 1.60/1.33 ($false = (cD @ sK4)) | ((sK2 @ sK5) = $true) | ((sK2 @ sK3) = $true)),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.60/1.33 thf(f21,plain,(
% 1.60/1.33 (((sK2 @ sK5) => ((cE @ sK5) & (cD @ sK5))) = $false) | ($false = (cD @ sK4)) | ((sK2 @ sK3) = $true)),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.60/1.33 thf(f107,plain,(
% 1.60/1.33 spl0_9 | spl0_10 | spl0_3 | spl0_11),
% 1.60/1.33 inference(avatar_split_clause,[status(thm)],[f28,f104,f68,f100,f96])).
% 1.60/1.33 thf(f28,plain,(
% 1.60/1.33 ((cE @ sK5) = $false) | ((sK2 @ sK3) = $true) | ((cD @ sK5) = $false) | ($false = (cD @ sK4))),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.60/1.33 thf(f26,plain,(
% 1.60/1.33 (((cE @ sK5) & (cD @ sK5)) = $false) | ($false = (cD @ sK4)) | ((sK2 @ sK3) = $true)),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.60/1.33 thf(f94,plain,(
% 1.60/1.33 spl0_4 | spl0_7 | spl0_8),
% 1.60/1.33 inference(avatar_split_clause,[status(thm)],[f34,f90,f85,f72])).
% 1.60/1.33 thf(f34,plain,(
% 1.60/1.33 ((sK2 @ sK6) = $true) | ($false = (cE @ sK3)) | ((sK2 @ sK4) = $true)),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.60/1.33 thf(f32,plain,(
% 1.60/1.33 (((sK2 @ sK6) => ((cE @ sK6) & (cD @ sK6))) = $false) | ((sK2 @ sK4) = $true) | ($false = (cE @ sK3))),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.60/1.33 thf(f30,plain,(
% 1.60/1.33 (((sK2 @ sK4) => (cD @ sK4)) = $false) | ($false = (cE @ sK3)) | (((sK2 @ sK6) => ((cE @ sK6) & (cD @ sK6))) = $false)),
% 1.60/1.33 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.60/1.33 thf(f29,plain,(
% 1.60/1.33 (((sK2 @ sK4) => (cD @ sK4)) = $false) | (((^[Y0 : a]: ((sK2 @ Y0) => ((cE @ Y0) & (cD @ Y0)))) @ sK6) = $false) | ($false = (cE @ sK3))),
% 1.60/1.33 inference(sigma_clausification,[status(thm)],[f17])).
% 1.60/1.33 thf(f17,plain,(
% 1.60/1.33 ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => ((cE @ Y0) & (cD @ Y0))))) = $false) | (((sK2 @ sK4) => (cD @ sK4)) = $false) | ($false = (cE @ sK3))),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.60/1.33 thf(f93,plain,(
% 1.60/1.33 spl0_8 | spl0_4 | spl0_6 | spl0_5),
% 1.60/1.33 inference(avatar_split_clause,[status(thm)],[f35,f76,f80,f72,f90])).
% 1.60/1.33 thf(f35,plain,(
% 1.60/1.33 ($false = (cE @ sK6)) | ((sK2 @ sK4) = $true) | ((cD @ sK6) = $false) | ($false = (cE @ sK3))),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.60/1.33 thf(f33,plain,(
% 1.60/1.33 ((sK2 @ sK4) = $true) | (((cE @ sK6) & (cD @ sK6)) = $false) | ($false = (cE @ sK3))),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.60/1.33 thf(f88,plain,(
% 1.60/1.33 spl0_3 | spl0_7 | spl0_4),
% 1.60/1.33 inference(avatar_split_clause,[status(thm)],[f37,f72,f85,f68])).
% 1.60/1.33 thf(f37,plain,(
% 1.60/1.33 ((sK2 @ sK6) = $true) | ($false = (cD @ sK4)) | ($false = (cE @ sK3))),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.60/1.33 thf(f31,plain,(
% 1.60/1.33 (((sK2 @ sK6) => ((cE @ sK6) & (cD @ sK6))) = $false) | ($false = (cE @ sK3)) | ($false = (cD @ sK4))),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.60/1.33 thf(f83,plain,(
% 1.60/1.33 spl0_3 | spl0_4 | spl0_5 | spl0_6),
% 1.60/1.33 inference(avatar_split_clause,[status(thm)],[f38,f80,f76,f72,f68])).
% 1.60/1.33 thf(f38,plain,(
% 1.60/1.33 ($false = (cD @ sK4)) | ($false = (cE @ sK3)) | ($false = (cE @ sK6)) | ((cD @ sK6) = $false)),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.60/1.33 thf(f36,plain,(
% 1.60/1.33 (((cE @ sK6) & (cD @ sK6)) = $false) | ($false = (cD @ sK4)) | ($false = (cE @ sK3))),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.60/1.33 thf(f65,plain,(
% 1.60/1.33 spl0_2 | spl0_2),
% 1.60/1.33 inference(avatar_split_clause,[status(thm)],[f47,f61,f61])).
% 1.60/1.33 thf(f47,plain,(
% 1.60/1.33 ( ! [X2 : a,X1 : a] : (($false = (sK2 @ X1)) | ((cD @ X1) = $true) | ((sK2 @ X2) = $false) | ((cD @ X2) = $true)) )),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.60/1.33 thf(f46,plain,(
% 1.60/1.33 ( ! [X2 : a,X1 : a] : ((((cE @ X2) & (cD @ X2)) = $true) | ((cD @ X1) = $true) | ((sK2 @ X2) = $false) | ($false = (sK2 @ X1))) )),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f45])).
% 1.60/1.33 thf(f45,plain,(
% 1.60/1.33 ( ! [X2 : a,X1 : a] : (((cD @ X1) = $true) | (((sK2 @ X2) => ((cE @ X2) & (cD @ X2))) = $true) | ($false = (sK2 @ X1))) )),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f44])).
% 1.60/1.33 thf(f44,plain,(
% 1.60/1.33 ( ! [X2 : a,X1 : a] : ((((sK2 @ X1) => (cD @ X1)) = $true) | (((sK2 @ X2) => ((cE @ X2) & (cD @ X2))) = $true)) )),
% 1.60/1.33 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.60/1.33 thf(f43,plain,(
% 1.60/1.33 ( ! [X2 : a,X1 : a] : ((((^[Y0 : a]: ((sK2 @ Y0) => ((cE @ Y0) & (cD @ Y0)))) @ X2) = $true) | (((sK2 @ X1) => (cD @ X1)) = $true)) )),
% 1.60/1.33 inference(pi_clausification,[status(thm)],[f42])).
% 1.60/1.33 thf(f42,plain,(
% 1.60/1.33 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => ((cE @ Y0) & (cD @ Y0))))) = $true) | (((sK2 @ X1) => (cD @ X1)) = $true)) )),
% 1.60/1.33 inference(beta_eta_normalization,[status(thm)],[f41])).
% 1.60/1.33 thf(f41,plain,(
% 1.60/1.33 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => ((cE @ Y0) & (cD @ Y0))))) = $true) | (((^[Y0 : a]: ((sK2 @ Y0) => (cD @ Y0))) @ X1) = $true)) )),
% 1.60/1.33 inference(pi_clausification,[status(thm)],[f40])).
% 1.60/1.33 thf(f40,plain,(
% 1.60/1.33 ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (cD @ Y0)))) = $true) | ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => ((cE @ Y0) & (cD @ Y0))))) = $true)),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f10])).
% 1.60/1.33 thf(f10,plain,(
% 1.60/1.33 (((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (cD @ Y0)))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (cE @ Y0))))) = $true) | ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => ((cE @ Y0) & (cD @ Y0))))) = $true)),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.60/1.33 thf(f64,plain,(
% 1.60/1.33 spl0_1 | spl0_1),
% 1.60/1.33 inference(avatar_split_clause,[status(thm)],[f56,f58,f58])).
% 1.60/1.33 thf(f56,plain,(
% 1.60/1.33 ( ! [X2 : a,X1 : a] : (((cE @ X1) = $true) | ($false = (sK2 @ X1)) | ((sK2 @ X2) = $false) | ((cE @ X2) = $true)) )),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f54])).
% 1.60/1.33 thf(f54,plain,(
% 1.60/1.33 ( ! [X2 : a,X1 : a] : (((cE @ X1) = $true) | (((cE @ X2) & (cD @ X2)) = $true) | ((sK2 @ X2) = $false) | ($false = (sK2 @ X1))) )),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f53])).
% 1.60/1.33 thf(f53,plain,(
% 1.60/1.33 ( ! [X2 : a,X1 : a] : (($false = (sK2 @ X1)) | (((sK2 @ X2) => ((cE @ X2) & (cD @ X2))) = $true) | ((cE @ X1) = $true)) )),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.60/1.33 thf(f52,plain,(
% 1.60/1.33 ( ! [X2 : a,X1 : a] : ((((sK2 @ X1) => (cE @ X1)) = $true) | (((sK2 @ X2) => ((cE @ X2) & (cD @ X2))) = $true)) )),
% 1.60/1.33 inference(beta_eta_normalization,[status(thm)],[f51])).
% 1.60/1.33 thf(f51,plain,(
% 1.60/1.33 ( ! [X2 : a,X1 : a] : ((((sK2 @ X1) => (cE @ X1)) = $true) | (((^[Y0 : a]: ((sK2 @ Y0) => ((cE @ Y0) & (cD @ Y0)))) @ X2) = $true)) )),
% 1.60/1.33 inference(pi_clausification,[status(thm)],[f50])).
% 1.60/1.33 thf(f50,plain,(
% 1.60/1.33 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => ((cE @ Y0) & (cD @ Y0))))) = $true) | (((sK2 @ X1) => (cE @ X1)) = $true)) )),
% 1.60/1.33 inference(beta_eta_normalization,[status(thm)],[f49])).
% 1.60/1.33 thf(f49,plain,(
% 1.60/1.33 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => ((cE @ Y0) & (cD @ Y0))))) = $true) | (((^[Y0 : a]: ((sK2 @ Y0) => (cE @ Y0))) @ X1) = $true)) )),
% 1.60/1.33 inference(pi_clausification,[status(thm)],[f39])).
% 1.60/1.33 thf(f39,plain,(
% 1.60/1.33 ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => (cE @ Y0)))) = $true) | ((!! @ a @ (^[Y0 : a]: ((sK2 @ Y0) => ((cE @ Y0) & (cD @ Y0))))) = $true)),
% 1.60/1.33 inference(binary_proxy_clausification,[status(thm)],[f10])).
% 1.60/1.33 % SZS output end Proof for DTF2THF_20538
% 1.60/1.33 % (20811)------------------------------
% 1.60/1.33 % (20811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.60/1.33 % (20811)Termination reason: Refutation
% 1.60/1.33
% 1.60/1.33 % (20811)Memory used [KB]: 5628
% 1.60/1.33 % (20811)Time elapsed: 0.012 s
% 1.60/1.33 % (20811)Instructions burned: 10 (million)
% 1.60/1.33 % (20811)------------------------------
% 1.60/1.33 % (20811)------------------------------
% 1.60/1.33 % (20808)Success in time 0.027 s
%------------------------------------------------------------------------------