%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV448^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 09:41:16 AM UTC 2026
% Result : Theorem 1.69s 1.62s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 105 ( 12 unt; 0 typ; 9 def)
% Number of atoms : 616 ( 141 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 607 ( 77 ~; 134 |; 13 &; 359 @)
% ( 9 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 45 ( 45 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 17 usr; 13 con; 0-3 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 98 ( 6 ^; 86 !; 6 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/SUBSET':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_1,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_11,type,
sK1: sK0 > $o ).
thf(func_def_12,type,
sK2: sK0 > $o ).
thf(func_def_14,type,
sK4:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_15,type,
sK5:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_16,type,
ph6:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
sK7: sK0 ).
thf(f393,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f60,f65,f74,f162,f166,f169,f184,f193,f261,f264,f268,f388,f391]) ).
thf(f391,plain,
( ~ spl3_1
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f390]) ).
thf(f390,plain,
( $false
| ~ spl3_1
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f389]) ).
thf(f389,plain,
( ( $false = $true )
| ~ spl3_1
| ~ spl3_4 ),
inference(backward_demodulation,[status(thm)],[f55,f69]) ).
thf(f69,plain,
( ( ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 )
= $false )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f67]) ).
thf(f67,definition,
( spl3_4
<=> ( ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f55,plain,
( ( ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 )
= $true )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f53]) ).
thf(f53,definition,
( spl3_1
<=> ( ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f388,plain,
( spl3_5
| ~ spl3_7
| ~ spl3_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f387]) ).
thf(f387,plain,
( $false
| spl3_5
| ~ spl3_7
| ~ spl3_9 ),
inference(trivial_inequality_removal,[status(thm)],[f386]) ).
thf(f386,plain,
( ( $false = $true )
| spl3_5
| ~ spl3_7
| ~ spl3_9 ),
inference(forward_demodulation,[status(thm)],[f373,f192]) ).
thf(f192,plain,
( ( ( sK1 @ sK7 )
= $false )
| ~ spl3_9 ),
inference(avatar_component_clause,[status(thm)],[f190]) ).
thf(f190,definition,
( spl3_9
<=> ( ( sK1 @ sK7 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_9])],[avatar_definition]) ).
thf(f373,plain,
( ( ( sK1 @ sK7 )
= $true )
| spl3_5
| ~ spl3_7 ),
inference(trivial_inequality_removal,[status(thm)],[f367]) ).
thf(f367,plain,
( ( $false = $true )
| ( ( sK1 @ sK7 )
= $true )
| spl3_5
| ~ spl3_7 ),
inference(superposition,[status(thm)],[f331,f183]) ).
thf(f183,plain,
( ( ( sK2 @ sK7 )
= $true )
| ~ spl3_7 ),
inference(avatar_component_clause,[status(thm)],[f181]) ).
thf(f181,definition,
( spl3_7
<=> ( ( sK2 @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_7])],[avatar_definition]) ).
thf(f331,plain,
( ! [X0: sK0] :
( ( $false
= ( sK2 @ X0 ) )
| ( ( sK1 @ X0 )
= $true ) )
| spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f317]) ).
thf(f317,plain,
( ! [X0: sK0] :
( ( $false
= ( sK2 @ X0 ) )
| ( ( sK1 @ X0 )
= $true )
| ( $false = $true ) )
| spl3_5 ),
inference(superposition,[status(thm)],[f251,f20]) ).
thf(f20,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
| ( ( X1 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( X1 @ X2 ) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( X1 @ X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.MLbOgFZgl2/DTF2THF_11229.p','thm/sets/IN_') ).
thf(f251,plain,
( ! [X0: sK0] :
( ( $false
= ( 'const/sets/IN' @ sK0 @ X0 @ sK2 ) )
| ( ( sK1 @ X0 )
= $true ) )
| spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f246]) ).
thf(f246,plain,
( ! [X0: sK0] :
( ( $false
= ( 'const/sets/IN' @ sK0 @ X0 @ sK2 ) )
| ( $false = $true )
| ( ( sK1 @ X0 )
= $true ) )
| spl3_5 ),
inference(superposition,[status(thm)],[f21,f196]) ).
thf(f196,plain,
( ! [X0: sK0] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ X0 @ sK1 ) )
| ( $false
= ( 'const/sets/IN' @ sK0 @ X0 @ sK2 ) ) )
| spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f194]) ).
thf(f194,plain,
( ! [X0: sK0] :
( ( $false != $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ X0 @ sK1 ) )
| ( $false
= ( 'const/sets/IN' @ sK0 @ X0 @ sK2 ) ) )
| spl3_5 ),
inference(superposition,[status(thm)],[f72,f37]) ).
thf(f37,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $false )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $false )
| ( ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
=> ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
=> ( 'const/sets/IN' @ X0 @ Y0 @ X2 ) )
@ X3 ) ) ),
inference(pi_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $false )
| ( ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
=> ( 'const/sets/IN' @ X0 @ Y0 @ X2 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
=> ( 'const/sets/IN' @ X0 @ Y0 @ X2 ) ) )
= ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
=> ( 'const/sets/IN' @ X0 @ Y0 @ X2 ) ) )
= ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
=> ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
= ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X2 )
=> ( 'const/sets/IN' @ X0 @ X4 @ X3 ) )
= ( 'const/sets/SUBSET' @ X0 @ X2 @ X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.MLbOgFZgl2/DTF2THF_11229.p','thm/sets/SUBSET_') ).
thf(f72,plain,
( ( $false
!= ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 ) )
| spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f71]) ).
thf(f71,definition,
( spl3_5
<=> ( $false
= ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f21,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $false )
| ( ( X1 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f18]) ).
thf(f268,plain,
( ~ spl3_7
| ~ spl3_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f267]) ).
thf(f267,plain,
( $false
| ~ spl3_7
| ~ spl3_8 ),
inference(trivial_inequality_removal,[status(thm)],[f266]) ).
thf(f266,plain,
( ( $false = $true )
| ~ spl3_7
| ~ spl3_8 ),
inference(forward_demodulation,[status(thm)],[f183,f188]) ).
thf(f188,plain,
( ( ( sK2 @ sK7 )
= $false )
| ~ spl3_8 ),
inference(avatar_component_clause,[status(thm)],[f186]) ).
thf(f186,definition,
( spl3_8
<=> ( ( sK2 @ sK7 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition]) ).
thf(f264,plain,
( ~ spl3_6
| ~ spl3_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f263]) ).
thf(f263,plain,
( $false
| ~ spl3_6
| ~ spl3_9 ),
inference(trivial_inequality_removal,[status(thm)],[f262]) ).
thf(f262,plain,
( ( $false = $true )
| ~ spl3_6
| ~ spl3_9 ),
inference(backward_demodulation,[status(thm)],[f179,f192]) ).
thf(f179,plain,
( ( ( sK1 @ sK7 )
= $true )
| ~ spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f177]) ).
thf(f177,definition,
( spl3_6
<=> ( ( sK1 @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f261,plain,
( spl3_9
| spl3_4
| ~ spl3_8 ),
inference(avatar_split_clause,[status(thm)],[f258,f186,f67,f190]) ).
thf(f258,plain,
( ( ( sK1 @ sK7 )
= $false )
| spl3_4
| ~ spl3_8 ),
inference(trivial_inequality_removal,[status(thm)],[f256]) ).
thf(f256,plain,
( ( ( sK1 @ sK7 )
= $false )
| ( $false = $true )
| spl3_4
| ~ spl3_8 ),
inference(superposition,[status(thm)],[f238,f188]) ).
thf(f238,plain,
( ! [X0: sK0] :
( ( ( sK2 @ X0 )
= $true )
| ( ( sK1 @ X0 )
= $false ) )
| spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f233]) ).
thf(f233,plain,
( ! [X0: sK0] :
( ( ( sK2 @ X0 )
= $true )
| ( ( sK1 @ X0 )
= $false )
| ( $false = $true ) )
| spl3_4 ),
inference(superposition,[status(thm)],[f21,f226]) ).
thf(f226,plain,
( ! [X0: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X0 @ sK2 )
= $true )
| ( ( sK1 @ X0 )
= $false ) )
| spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f218]) ).
thf(f218,plain,
( ! [X0: sK0] :
( ( ( sK1 @ X0 )
= $false )
| ( ( 'const/sets/IN' @ sK0 @ X0 @ sK2 )
= $true )
| ( $false = $true ) )
| spl3_4 ),
inference(superposition,[status(thm)],[f20,f172]) ).
thf(f172,plain,
( ! [X0: sK0] :
( ( $false
= ( 'const/sets/IN' @ sK0 @ X0 @ sK1 ) )
| ( ( 'const/sets/IN' @ sK0 @ X0 @ sK2 )
= $true ) )
| spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f170]) ).
thf(f170,plain,
( ! [X0: sK0] :
( ( $false != $false )
| ( $false
= ( 'const/sets/IN' @ sK0 @ X0 @ sK1 ) )
| ( ( 'const/sets/IN' @ sK0 @ X0 @ sK2 )
= $true ) )
| spl3_4 ),
inference(superposition,[status(thm)],[f68,f37]) ).
thf(f68,plain,
( ( ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 )
!= $false )
| spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f67]) ).
thf(f193,plain,
( spl3_8
| spl3_9
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f175,f57,f190,f186]) ).
thf(f57,definition,
( spl3_2
<=> ( sK1 = sK2 ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f175,plain,
( ( ( sK1 @ sK7 )
= $false )
| ( ( sK2 @ sK7 )
= $false )
| spl3_2 ),
inference(binary_proxy_clausification,[status(thm)],[f173]) ).
thf(f173,plain,
( ( ( sK1 @ sK7 )
!= ( sK2 @ sK7 ) )
| spl3_2 ),
inference(negative_extensionality,[status(thm)],[f58]) ).
thf(f58,plain,
( ( sK1 != sK2 )
| spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f57]) ).
thf(f184,plain,
( spl3_6
| spl3_7
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f174,f57,f181,f177]) ).
thf(f174,plain,
( ( ( sK1 @ sK7 )
= $true )
| ( ( sK2 @ sK7 )
= $true )
| spl3_2 ),
inference(binary_proxy_clausification,[status(thm)],[f173]) ).
thf(f169,plain,
( ~ spl3_3
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f168]) ).
thf(f168,plain,
( $false
| ~ spl3_3
| ~ spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f167]) ).
thf(f167,plain,
( ( $false = $true )
| ~ spl3_3
| ~ spl3_5 ),
inference(backward_demodulation,[status(thm)],[f64,f73]) ).
thf(f73,plain,
( ( $false
= ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 ) )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f71]) ).
thf(f64,plain,
( ( ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 )
= $true )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f62]) ).
thf(f62,definition,
( spl3_3
<=> ( ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f166,plain,
( ~ spl3_2
| spl3_4
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f165]) ).
thf(f165,plain,
( $false
| ~ spl3_2
| spl3_4
| ~ spl3_5 ),
inference(subsumption_resolution,[status(thm)],[f164,f163]) ).
thf(f163,plain,
( ( $false
= ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK1 ) )
| ~ spl3_2
| ~ spl3_5 ),
inference(forward_demodulation,[status(thm)],[f73,f59]) ).
thf(f59,plain,
( ( sK1 = sK2 )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f57]) ).
thf(f164,plain,
( ( $false
!= ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK1 ) )
| ~ spl3_2
| spl3_4 ),
inference(forward_demodulation,[status(thm)],[f68,f59]) ).
thf(f162,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f161]) ).
thf(f161,plain,
( $false
| ~ spl3_2
| ~ spl3_4 ),
inference(trivial_inequality_removal,[status(thm)],[f155]) ).
thf(f155,plain,
( ( $false = $true )
| ~ spl3_2
| ~ spl3_4 ),
inference(superposition,[status(thm)],[f75,f151]) ).
thf(f151,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X1 @ X1 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f150]) ).
thf(f150,plain,
! [X0: $tType,X1: X0 > $o] :
( ( $false = $true )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X1 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f144]) ).
thf(f144,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X1 )
= $true )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X1 )
= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f33,f34]) ).
thf(f34,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ ( sK4 @ X0 @ X1 @ X2 ) @ X1 )
= $true )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( $false
= ( ( 'const/sets/IN' @ X0 @ ( sK4 @ X0 @ X1 @ X2 ) @ X1 )
=> ( 'const/sets/IN' @ X0 @ ( sK4 @ X0 @ X1 @ X2 ) @ X2 ) ) )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
=> ( 'const/sets/IN' @ X0 @ Y0 @ X2 ) )
@ ( sK4 @ X0 @ X1 @ X2 ) )
= $false )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
=> ( 'const/sets/IN' @ X0 @ Y0 @ X2 ) ) )
= $false )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f33,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ ( sK4 @ X0 @ X1 @ X2 ) @ X2 )
= $false )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f32]) ).
thf(f75,plain,
( ( $false
= ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK1 ) )
| ~ spl3_2
| ~ spl3_4 ),
inference(backward_demodulation,[status(thm)],[f69,f59]) ).
thf(f74,plain,
( spl3_4
| spl3_5
| ~ spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f25,f57,f71,f67]) ).
thf(f25,plain,
( ( ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 )
= $false )
| ( sK1 != sK2 )
| ( $false
= ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
( ( $false
= ( ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 )
& ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 ) ) )
| ( sK1 != sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f23]) ).
thf(f23,plain,
( ( $false
= ( sK1 = sK2 ) )
| ( $false
= ( ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 )
& ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 )
& ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 ) )
!= ( sK1 = sK2 ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 )
& ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 ) )
!= ( sK1 = sK2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f14]) ).
thf(f14,plain,
( ? [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X2 @ X1 )
& ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 ) )
!= ( X1 = X2 ) )
=> ( ( ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 )
& ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 ) )
!= ( sK1 = sK2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X2 @ X1 )
& ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 ) )
!= ( X1 = X2 ) ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X2 @ X1 )
& ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 ) )
= ( X1 = X2 ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
& ( ( 'const/sets/SUBSET' @ X0 @ X2 @ X1 )
= ( X1 = X2 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X0: $tType,X2: X0 > $o,X3: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X2 @ X3 )
& ( ( 'const/sets/SUBSET' @ X0 @ X3 @ X2 )
= ( X2 = X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X2 @ X3 )
& ( ( 'const/sets/SUBSET' @ X0 @ X3 @ X2 )
= ( X2 = X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MLbOgFZgl2/DTF2THF_11229.p','thm/sets/SUBSET_ANTISYM_EQ_') ).
thf(f65,plain,
( spl3_2
| spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f28,f62,f57]) ).
thf(f28,plain,
( ( sK1 = sK2 )
| ( ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 )
& ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 ) )
= $true )
| ( sK1 = sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( $true
= ( sK1 = sK2 ) )
| ( ( ( 'const/sets/SUBSET' @ sK0 @ sK2 @ sK1 )
& ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f60,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f27,f57,f53]) ).
thf(f27,plain,
( ( ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 )
= $true )
| ( sK1 = sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV448^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.31 % Computer : n009.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Tue Feb 24 12:46:55 EST 2026
% 0.11/0.31 % CPUTime :
% 0.11/0.31 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.41 ---- Original DTF file ---
% 0.18/0.41 thf(spec,logic,$$dhol).
% 0.18/0.41 %------------------------------------------------------------------------------
% 0.18/0.41 % File : SEV448^1 : TPTP v9.2.1. Released v7.0.0.
% 0.18/0.41 % Domain : Analysis
% 0.18/0.41 % Problem : SUBSET_ANTISYM_EQ
% 0.18/0.41 % Version : Especial.
% 0.18/0.41 % English :
% 0.18/0.41
% 0.18/0.41 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.18/0.41 % Source : [Kal16]
% 0.18/0.41 % Names : SUBSET_ANTISYM_EQ_.p [Kal16]
% 0.18/0.41
% 0.18/0.41 % Status : Theorem
% 0.18/0.41 % Rating : 0.00 v7.1.0
% 0.18/0.41 % Syntax : Number of formulae : 6 ( 4 unt; 2 typ; 0 def)
% 0.18/0.41 % Number of atoms : 15 ( 7 equ; 0 cnn)
% 0.18/0.41 % Maximal formula atoms : 1 ( 3 avg)
% 0.18/0.41 % Number of connectives : 27 ( 0 ~; 0 |; 1 &; 25 @)
% 0.18/0.41 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.18/0.41 % Maximal formula depth : 4 ( 4 avg)
% 0.18/0.41 % Number of types : 1 ( 0 usr)
% 0.18/0.41 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.18/0.41 % Number of symbols : 3 ( 2 usr; 0 con; 2-3 aty)
% 0.18/0.41 % Number of variables : 16 ( 0 ^; 14 !; 0 ?; 16 :)
% 0.18/0.41 % ( 2 !>; 0 ?*; 0 @-; 0 @+)
% 0.18/0.41 % SPC : TH1_THM_EQU_NAR
% 0.18/0.41
% 0.18/0.41 % Comments : Exported from core HOL Light.
% 0.18/0.41 %------------------------------------------------------------------------------
% 0.18/0.41 thf('thf_const_const/sets/SUBSET',type,
% 0.18/0.41 'const/sets/SUBSET':
% 0.18/0.41 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > $o ) ).
% 0.18/0.41
% 0.18/0.41 thf('thf_const_const/sets/IN',type,
% 0.18/0.41 'const/sets/IN':
% 0.18/0.41 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.18/0.41
% 0.18/0.41 thf('thm/sets/IN_',axiom,
% 0.18/0.41 ! [A: $tType,P: A > $o,A0: A] :
% 0.18/0.41 ( ( 'const/sets/IN' @ A @ A0 @ P )
% 0.18/0.41 = ( P @ A0 ) ) ).
% 0.18/0.41
% 0.18/0.41 thf('thm/sets/EXTENSION_',axiom,
% 0.18/0.41 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 0.18/0.41 ( ( A0 = A1 )
% 0.18/0.41 = ( ! [A2: A] :
% 0.18/0.41 ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 0.18/0.41 = ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
% 0.18/0.41
% 0.18/0.41 thf('thm/sets/SUBSET_',axiom,
% 0.18/0.41 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 0.18/0.41 ( ( 'const/sets/SUBSET' @ A @ A0 @ A1 )
% 0.18/0.41 = ( ! [A2: A] :
% 0.18/0.41 ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 0.18/0.41 => ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
% 0.18/0.41
% 0.18/0.41 thf('thm/sets/SUBSET_ANTISYM_EQ_',conjecture,
% 0.18/0.41 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 0.18/0.41 ( ( ( 'const/sets/SUBSET' @ A @ A0 @ A1 )
% 0.18/0.41 & ( 'const/sets/SUBSET' @ A @ A1 @ A0 ) )
% 0.18/0.41 = ( A0 = A1 ) ) ).
% 0.18/0.41
% 0.18/0.41 %------------------------------------------------------------------------------
% 0.18/0.41 ------------------------
% 1.48/1.40 ---- Embedded in THF ---
% 1.67/1.40 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.67/1.40 %%% Generated on Tue Feb 24 12:46:56 EST 2026
% 1.67/1.40 %%% using '$$dhol' embedding, version 1.3.0.
% 1.67/1.40 %%% Logic specification used:
% 1.67/1.40 %%% thf(spec, logic, $$dhol).
% 1.67/1.40
% 1.67/1.40 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.MLbOgFZgl2/DTF2DTF11229.p
% See solution above
% 1.67/1.40 ------------------------
% 1.67/1.41 ---- Cleaned THF ---
% 1.67/1.41 thf('thf_const_const/sets/SUBSET',type,
% 1.67/1.41 'const/sets/SUBSET':
% 1.67/1.41 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > $o ) ).
% 1.67/1.41
% 1.67/1.41 thf('thf_const_const/sets/IN',type,
% 1.67/1.41 'const/sets/IN':
% 1.67/1.41 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.67/1.41
% 1.67/1.41 thf('thm/sets/IN_',axiom,
% 1.67/1.41 ! [A: $tType,P: A > $o,A0: A] :
% 1.67/1.41 ( ( 'const/sets/IN' @ A @ A0 @ P )
% 1.67/1.41 = ( P @ A0 ) ) ).
% 1.67/1.41
% 1.67/1.41 thf('thm/sets/EXTENSION_',axiom,
% 1.67/1.41 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 1.67/1.41 ( ( A0 = A1 )
% 1.67/1.41 = ( ! [A2: A] :
% 1.67/1.41 ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 1.67/1.41 = ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
% 1.67/1.41
% 1.67/1.41 thf('thm/sets/SUBSET_',axiom,
% 1.67/1.41 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 1.67/1.41 ( ( 'const/sets/SUBSET' @ A @ A0 @ A1 )
% 1.67/1.41 = ( ! [A2: A] :
% 1.67/1.41 ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 1.67/1.41 => ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
% 1.67/1.41
% 1.67/1.41 thf('thm/sets/SUBSET_ANTISYM_EQ_',conjecture,
% 1.67/1.41 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 1.67/1.41 ( ( ( 'const/sets/SUBSET' @ A @ A0 @ A1 )
% 1.67/1.41 & ( 'const/sets/SUBSET' @ A @ A1 @ A0 ) )
% 1.67/1.41 = ( A0 = A1 ) ) ).
% 1.67/1.41 ------------------------
% 1.67/1.43 % (11332)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11229 for (2999ds/18Mi)
% 1.67/1.43 % (11328)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_11229 for (2999ds/27Mi)
% 1.67/1.43 % (11326)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11229 for (2999ds/183Mi)
% 1.67/1.43 % (11327)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_11229 for (2999ds/4Mi)
% 1.67/1.43 % (11330)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_11229 for (2999ds/2Mi)
% 1.67/1.43 % (11331)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_11229 for (2999ds/275Mi)
% 1.67/1.43 % (11329)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11229 for (2999ds/2Mi)
% 1.67/1.43 % Exception at run slice level
% 1.67/1.43 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.67/1.43 % (11329)Instruction limit reached!
% 1.67/1.43 % (11329)------------------------------
% 1.67/1.43 % (11329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.43 % (11329)Termination reason: Unknown
% 1.67/1.43 % (11329)Termination phase: Saturation
% 1.67/1.43
% 1.67/1.43 % (11329)Memory used [KB]: 5500
% 1.67/1.43 % (11329)Time elapsed: 0.003 s
% 1.67/1.43 % (11329)Instructions burned: 3 (million)
% 1.67/1.43 % (11329)------------------------------
% 1.67/1.43 % (11329)------------------------------
% 1.67/1.43 % (11327)Instruction limit reached!
% 1.67/1.43 % (11327)------------------------------
% 1.67/1.43 % (11327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.43 % (11327)Termination reason: Unknown
% 1.67/1.43 % (11327)Termination phase: Saturation
% 1.67/1.43
% 1.67/1.43 % (11327)Memory used [KB]: 5500
% 1.67/1.43 % (11327)Time elapsed: 0.004 s
% 1.67/1.43 % (11327)Instructions burned: 4 (million)
% 1.67/1.43 % (11327)------------------------------
% 1.67/1.43 % (11327)------------------------------
% 1.67/1.43 % (11331)Refutation not found, incomplete strategy
% 1.67/1.43 % (11331)------------------------------
% 1.67/1.43 % (11331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.43 % (11331)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.43
% 1.67/1.43
% 1.67/1.43 % (11331)Memory used [KB]: 5500
% 1.67/1.43 % (11331)Time elapsed: 0.004 s
% 1.67/1.43 % (11331)Instructions burned: 4 (million)
% 1.67/1.43 % (11331)------------------------------
% 1.67/1.43 % (11331)------------------------------
% 1.67/1.44 % (11332)Instruction limit reached!
% 1.67/1.44 % (11332)------------------------------
% 1.67/1.44 % (11332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.44 % (11332)Termination reason: Unknown
% 1.67/1.44 % (11332)Termination phase: Saturation
% 1.67/1.44
% 1.67/1.44 % (11332)Memory used [KB]: 5628
% 1.67/1.44 % (11332)Time elapsed: 0.013 s
% 1.67/1.44 % (11332)Instructions burned: 19 (million)
% 1.67/1.44 % (11332)------------------------------
% 1.67/1.44 % (11332)------------------------------
% 1.67/1.44 % (11328)Instruction limit reached!
% 1.67/1.44 % (11328)------------------------------
% 1.67/1.44 % (11328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.44 % (11328)Termination reason: Unknown
% 1.67/1.44 % (11328)Termination phase: Saturation
% 1.67/1.44
% 1.67/1.44 % (11328)Memory used [KB]: 5628
% 1.67/1.44 % (11328)Time elapsed: 0.016 s
% 1.67/1.44 % (11328)Instructions burned: 28 (million)
% 1.67/1.44 % (11328)------------------------------
% 1.67/1.44 % (11328)------------------------------
% 1.67/1.45 % (11333)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_11229 for (2999ds/3Mi)
% 1.67/1.45 % (11334)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_11229 for (2999ds/37Mi)
% 1.67/1.45 % (11335)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_11229 for (2999ds/15Mi)
% 1.67/1.45 % Exception at run slice level
% 1.67/1.45 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.67/1.45 % (11336)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_11229 for (2999ds/3Mi)
% 1.67/1.45 % (11333)Instruction limit reached!
% 1.67/1.45 % (11333)------------------------------
% 1.67/1.45 % (11333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.45 % (11333)Termination reason: Unknown
% 1.67/1.45 % (11333)Termination phase: Saturation
% 1.67/1.45
% 1.67/1.45 % (11333)Memory used [KB]: 5500
% 1.67/1.45 % (11333)Time elapsed: 0.004 s
% 1.67/1.45 % (11333)Instructions burned: 4 (million)
% 1.67/1.45 % (11333)------------------------------
% 1.67/1.45 % (11333)------------------------------
% 1.67/1.45 % (11336)Instruction limit reached!
% 1.67/1.45 % (11336)------------------------------
% 1.67/1.45 % (11336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.45 % (11336)Termination reason: Unknown
% 1.67/1.45 % (11336)Termination phase: Saturation
% 1.67/1.45
% 1.67/1.45 % (11336)Memory used [KB]: 5500
% 1.67/1.45 % (11336)Time elapsed: 0.003 s
% 1.67/1.45 % (11336)Instructions burned: 3 (million)
% 1.67/1.45 % (11336)------------------------------
% 1.67/1.45 % (11336)------------------------------
% 1.67/1.45 % (11335)Instruction limit reached!
% 1.67/1.45 % (11335)------------------------------
% 1.67/1.45 % (11335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.45 % (11335)Termination reason: Unknown
% 1.67/1.45 % (11335)Termination phase: Saturation
% 1.67/1.45
% 1.67/1.45 % (11335)Memory used [KB]: 5628
% 1.67/1.45 % (11335)Time elapsed: 0.010 s
% 1.67/1.45 % (11335)Instructions burned: 15 (million)
% 1.67/1.45 % (11335)------------------------------
% 1.67/1.45 % (11335)------------------------------
% 1.67/1.45 % (11337)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_11229 for (2999ds/1041Mi)
% 1.67/1.45 % Exception at run slice level
% 1.67/1.45 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.67/1.46 % (11338)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_11229 for (2999ds/7Mi)
% 1.67/1.46 % (11338)Instruction limit reached!
% 1.67/1.46 % (11338)------------------------------
% 1.67/1.46 % (11338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.46 % (11338)Termination reason: Unknown
% 1.67/1.46 % (11338)Termination phase: Saturation
% 1.67/1.46
% 1.67/1.46 % (11338)Memory used [KB]: 1023
% 1.67/1.46 % (11338)Time elapsed: 0.006 s
% 1.67/1.46 % (11338)Instructions burned: 7 (million)
% 1.67/1.46 % (11338)------------------------------
% 1.67/1.46 % (11338)------------------------------
% 1.67/1.46 % (11339)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_11229 for (2999ds/16Mi)
% 1.67/1.46 % (11341)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_11229 for (2999ds/3Mi)
% 1.67/1.46 % (11340)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_11229 for (2999ds/3Mi)
% 1.67/1.46 % (11341)Instruction limit reached!
% 1.67/1.46 % (11341)------------------------------
% 1.67/1.46 % (11341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.46 % (11341)Termination reason: Unknown
% 1.67/1.46 % (11341)Termination phase: Saturation
% 1.67/1.46
% 1.67/1.46 % (11341)Memory used [KB]: 1023
% 1.67/1.46 % (11341)Time elapsed: 0.003 s
% 1.67/1.46 % (11341)Instructions burned: 3 (million)
% 1.67/1.46 % (11341)------------------------------
% 1.67/1.46 % (11341)------------------------------
% 1.67/1.47 % (11340)Instruction limit reached!
% 1.67/1.47 % (11340)------------------------------
% 1.67/1.47 % (11340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.47 % (11340)Termination reason: Unknown
% 1.67/1.47 % (11340)Termination phase: Saturation
% 1.67/1.47
% 1.67/1.47 % (11340)Memory used [KB]: 5500
% 1.67/1.47 % (11340)Time elapsed: 0.004 s
% 1.67/1.47 % (11340)Instructions burned: 4 (million)
% 1.67/1.47 % (11340)------------------------------
% 1.67/1.47 % (11340)------------------------------
% 1.67/1.47 % (11342)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_11229 for (2999ds/7Mi)
% 1.67/1.47 % (11343)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_11229 for (2999ds/3Mi)
% 1.67/1.47 % Exception at run slice level
% 1.67/1.47 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.67/1.47 % (11339)Instruction limit reached!
% 1.67/1.47 % (11339)------------------------------
% 1.67/1.47 % (11339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.47 % (11339)Termination reason: Unknown
% 1.67/1.47 % (11339)Termination phase: Saturation
% 1.67/1.47
% 1.67/1.47 % (11339)Memory used [KB]: 5756
% 1.67/1.47 % (11339)Time elapsed: 0.012 s
% 1.67/1.47 % (11339)Instructions burned: 17 (million)
% 1.67/1.47 % (11339)------------------------------
% 1.67/1.47 % (11339)------------------------------
% 1.67/1.47 % (11342)Refutation not found, incomplete strategy
% 1.67/1.47 % (11342)------------------------------
% 1.67/1.47 % (11342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.47 % (11342)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.47
% 1.67/1.47
% 1.67/1.47 % (11342)Memory used [KB]: 5500
% 1.67/1.47 % (11342)Time elapsed: 0.005 s
% 1.67/1.47 % (11342)Instructions burned: 5 (million)
% 1.67/1.47 % (11342)------------------------------
% 1.67/1.47 % (11342)------------------------------
% 1.67/1.48 % (11344)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_11229 for (2999ds/4Mi)
% 1.67/1.48 % (11344)Instruction limit reached!
% 1.67/1.48 % (11344)------------------------------
% 1.67/1.48 % (11344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.48 % (11344)Termination reason: Unknown
% 1.67/1.48 % (11344)Termination phase: Saturation
% 1.67/1.48
% 1.67/1.48 % (11344)Memory used [KB]: 5500
% 1.67/1.48 % (11344)Time elapsed: 0.004 s
% 1.67/1.48 % (11344)Instructions burned: 5 (million)
% 1.67/1.48 % (11344)------------------------------
% 1.67/1.48 % (11344)------------------------------
% 1.67/1.48 % (11345)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_11229 for (2999ds/18Mi)
% 1.67/1.48 % (11346)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_11229 for (2999ds/710Mi)
% 1.67/1.49 % (11347)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_11229 for (2999ds/6Mi)
% 1.67/1.49 % (11348)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_11229 for (2999ds/902Mi)
% 1.67/1.49 % (11349)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_11229 for (2999ds/21Mi)
% 1.67/1.49 % (11347)Instruction limit reached!
% 1.67/1.49 % (11347)------------------------------
% 1.67/1.49 % (11347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.49 % (11347)Termination reason: Unknown
% 1.67/1.49 % (11347)Termination phase: Saturation
% 1.67/1.49
% 1.67/1.49 % (11347)Memory used [KB]: 5500
% 1.67/1.49 % (11347)Time elapsed: 0.006 s
% 1.67/1.49 % (11347)Instructions burned: 6 (million)
% 1.67/1.49 % (11347)------------------------------
% 1.67/1.49 % (11347)------------------------------
% 1.67/1.49 % (11345)Instruction limit reached!
% 1.67/1.49 % (11345)------------------------------
% 1.67/1.49 % (11345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.49 % (11345)Termination reason: Unknown
% 1.67/1.49 % (11345)Termination phase: Saturation
% 1.67/1.49
% 1.67/1.49 % (11345)Memory used [KB]: 5628
% 1.67/1.49 % (11345)Time elapsed: 0.012 s
% 1.67/1.49 % (11345)Instructions burned: 19 (million)
% 1.67/1.49 % (11345)------------------------------
% 1.67/1.49 % (11345)------------------------------
% 1.67/1.49 % (11350)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_11229 for (2999ds/5Mi)
% 1.67/1.49 % Exception at run slice level
% 1.67/1.49 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.67/1.49 % (11348)Refutation not found, incomplete strategy
% 1.67/1.49 % (11348)------------------------------
% 1.67/1.49 % (11348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.49 % (11348)Termination reason: Refutation not found, incomplete strategy
% 1.67/1.49
% 1.67/1.49
% 1.67/1.49 % (11348)Memory used [KB]: 5500
% 1.67/1.49 % (11348)Time elapsed: 0.008 s
% 1.67/1.49 % (11348)Instructions burned: 12 (million)
% 1.67/1.49 % (11348)------------------------------
% 1.67/1.49 % (11348)------------------------------
% 1.69/1.50 % (11349)Instruction limit reached!
% 1.69/1.50 % (11349)------------------------------
% 1.69/1.50 % (11349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.50 % (11349)Termination reason: Unknown
% 1.69/1.50 % (11349)Termination phase: Saturation
% 1.69/1.50
% 1.69/1.50 % (11349)Memory used [KB]: 5628
% 1.69/1.50 % (11349)Time elapsed: 0.015 s
% 1.69/1.50 % (11349)Instructions burned: 22 (million)
% 1.69/1.50 % (11349)------------------------------
% 1.69/1.50 % (11349)------------------------------
% 1.69/1.51 % (11351)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_11229 for (2999ds/6Mi)
% 1.69/1.51 % (11352)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_11229 for (2999ds/377Mi)
% 1.69/1.51 % Exception at run slice level
% 1.69/1.51 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.69/1.51 % (11353)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_11229 for (2999ds/779Mi)
% 1.69/1.51 % Exception at run slice level
% 1.69/1.51 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.69/1.51 % (11354)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_11229 for (2999ds/19Mi)
% 1.69/1.51 % Exception at run slice level
% 1.69/1.51 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.69/1.52 % (11326)Instruction limit reached!
% 1.69/1.52 % (11326)------------------------------
% 1.69/1.52 % (11326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.52 % (11326)Termination reason: Unknown
% 1.69/1.52 % (11326)Termination phase: Saturation
% 1.69/1.52
% 1.69/1.52 % (11326)Memory used [KB]: 6780
% 1.69/1.52 % (11326)Time elapsed: 0.091 s
% 1.69/1.52 % (11326)Instructions burned: 184 (million)
% 1.69/1.52 % (11326)------------------------------
% 1.69/1.52 % (11326)------------------------------
% 1.69/1.52 % (11355)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_11229 for (2999ds/879Mi)
% 1.69/1.52 % (11356)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_11229 for (2999ds/17Mi)
% 1.69/1.52 % (11357)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_11229 for (2999ds/3Mi)
% 1.69/1.53 % (11357)Instruction limit reached!
% 1.69/1.53 % (11357)------------------------------
% 1.69/1.53 % (11357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.53 % (11357)Termination reason: Unknown
% 1.69/1.53 % (11357)Termination phase: Saturation
% 1.69/1.53
% 1.69/1.53 % (11357)Memory used [KB]: 1023
% 1.69/1.53 % (11357)Time elapsed: 0.003 s
% 1.69/1.53 % (11357)Instructions burned: 4 (million)
% 1.69/1.53 % (11357)------------------------------
% 1.69/1.53 % (11357)------------------------------
% 1.69/1.53 % (11358)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_11229 for (2999ds/30Mi)
% 1.69/1.53 % (11356)Instruction limit reached!
% 1.69/1.53 % (11356)------------------------------
% 1.69/1.53 % (11356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.53 % (11356)Termination reason: Unknown
% 1.69/1.53 % (11359)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_11229 for (2999ds/127Mi)
% 1.69/1.53 % (11356)Termination phase: Saturation
% 1.69/1.53
% 1.69/1.53 % (11356)Memory used [KB]: 5628
% 1.69/1.53 % (11356)Time elapsed: 0.012 s
% 1.69/1.53 % (11356)Instructions burned: 17 (million)
% 1.69/1.53 % (11356)------------------------------
% 1.69/1.53 % (11356)------------------------------
% 1.69/1.54 % (11360)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_11229 for (2998ds/100Mi)
% 1.69/1.54 % (11358)Instruction limit reached!
% 1.69/1.54 % (11358)------------------------------
% 1.69/1.54 % (11358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.54 % (11358)Termination reason: Unknown
% 1.69/1.54 % (11358)Termination phase: Saturation
% 1.69/1.54
% 1.69/1.54 % (11358)Memory used [KB]: 5628
% 1.69/1.54 % (11358)Time elapsed: 0.017 s
% 1.69/1.54 % (11358)Instructions burned: 31 (million)
% 1.69/1.54 % (11358)------------------------------
% 1.69/1.54 % (11358)------------------------------
% 1.69/1.55 % (11361)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_11229 for (2998ds/3Mi)
% 1.69/1.55 % Exception at run slice level
% 1.69/1.55 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.69/1.56 % (11362)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_11229 for (2998ds/20Mi)
% 1.69/1.57 % (11363)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_11229 for (2998ds/86Mi)
% 1.69/1.57 % (11362)Instruction limit reached!
% 1.69/1.57 % (11362)------------------------------
% 1.69/1.57 % (11362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.57 % (11362)Termination reason: Unknown
% 1.69/1.57 % (11362)Termination phase: Saturation
% 1.69/1.57
% 1.69/1.57 % (11362)Memory used [KB]: 5628
% 1.69/1.57 % (11362)Time elapsed: 0.034 s
% 1.69/1.57 % (11362)Instructions burned: 20 (million)
% 1.69/1.57 % (11362)------------------------------
% 1.69/1.57 % (11362)------------------------------
% 1.69/1.59 % (11364)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_11229 for (2998ds/107Mi)
% 1.69/1.59 % (11360)Instruction limit reached!
% 1.69/1.59 % (11360)------------------------------
% 1.69/1.59 % (11360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.59 % (11360)Termination reason: Unknown
% 1.69/1.59 % (11360)Termination phase: Saturation
% 1.69/1.59
% 1.69/1.59 % (11360)Memory used [KB]: 5884
% 1.69/1.59 % (11360)Time elapsed: 0.054 s
% 1.69/1.59 % (11360)Instructions burned: 101 (million)
% 1.69/1.59 % (11360)------------------------------
% 1.69/1.59 % (11360)------------------------------
% 1.69/1.60 % (11359)Instruction limit reached!
% 1.69/1.60 % (11359)------------------------------
% 1.69/1.60 % (11359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.60 % (11359)Termination reason: Unknown
% 1.69/1.60 % (11359)Termination phase: Saturation
% 1.69/1.60
% 1.69/1.60 % (11359)Memory used [KB]: 5884
% 1.69/1.60 % (11359)Time elapsed: 0.065 s
% 1.69/1.60 % (11359)Instructions burned: 128 (million)
% 1.69/1.60 % (11359)------------------------------
% 1.69/1.60 % (11359)------------------------------
% 1.69/1.61 % (11365)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_11229 for (2998ds/39Mi)
% 1.69/1.61 % Exception at run slice level
% 1.69/1.61 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.69/1.61 % (11366)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_11229 for (2998ds/448Mi)
% 1.69/1.61 % Exception at run slice level
% 1.69/1.61 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.69/1.61 % (11363)Instruction limit reached!
% 1.69/1.61 % (11363)------------------------------
% 1.69/1.61 % (11363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.61 % (11363)Termination reason: Unknown
% 1.69/1.61 % (11363)Termination phase: Saturation
% 1.69/1.61
% 1.69/1.61 % (11363)Memory used [KB]: 6012
% 1.69/1.61 % (11363)Time elapsed: 0.069 s
% 1.69/1.61 % (11363)Instructions burned: 87 (million)
% 1.69/1.61 % (11363)------------------------------
% 1.69/1.61 % (11363)------------------------------
% 1.69/1.62 % (11364)First to succeed.
% 1.69/1.62 % (11364)Refutation found. Thanks to Tanya!
% 1.69/1.62 % SZS status Theorem for DTF2THF_11229
% 1.69/1.62 % SZS output start Proof for DTF2THF_11229
% 1.69/1.62 thf(type_def_6, type, sK0: $tType).
% 1.69/1.62 thf(func_def_0, type, 'const/sets/SUBSET': !>[X0: $tType]:((X0 > $o) > (X0 > $o) > $o)).
% 1.69/1.62 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.69/1.62 thf(func_def_11, type, sK1: sK0 > $o).
% 1.69/1.62 thf(func_def_12, type, sK2: sK0 > $o).
% 1.69/1.62 thf(func_def_14, type, sK4: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 1.69/1.62 thf(func_def_15, type, sK5: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 1.69/1.62 thf(func_def_16, type, ph6: !>[X0: $tType]:(X0)).
% 1.69/1.62 thf(func_def_17, type, sK7: sK0).
% 1.69/1.62 thf(f393,plain,(
% 1.69/1.62 $false),
% 1.69/1.62 inference(avatar_sat_refutation,[status(thm)],[f60,f65,f74,f162,f166,f169,f184,f193,f261,f264,f268,f388,f391])).
% 1.69/1.62 thf(f391,plain,(
% 1.69/1.62 ~spl3_1 | ~spl3_4),
% 1.69/1.62 inference(avatar_contradiction_clause,[status(thm)],[f390])).
% 1.69/1.62 thf(f390,plain,(
% 1.69/1.62 $false | (~spl3_1 | ~spl3_4)),
% 1.69/1.62 inference(trivial_inequality_removal,[status(thm)],[f389])).
% 1.69/1.62 thf(f389,plain,(
% 1.69/1.62 ($false = $true) | (~spl3_1 | ~spl3_4)),
% 1.69/1.62 inference(backward_demodulation,[status(thm)],[f55,f69])).
% 1.69/1.62 thf(f69,plain,(
% 1.69/1.62 (('const/sets/SUBSET' @ sK0 @ sK1 @ sK2) = $false) | ~spl3_4),
% 1.69/1.62 inference(avatar_component_clause,[status(thm)],[f67])).
% 1.69/1.62 thf(f67,definition,(
% 1.69/1.62 spl3_4 <=> (('const/sets/SUBSET' @ sK0 @ sK1 @ sK2) = $false)),
% 1.69/1.62 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.69/1.62 thf(f55,plain,(
% 1.69/1.62 (('const/sets/SUBSET' @ sK0 @ sK1 @ sK2) = $true) | ~spl3_1),
% 1.69/1.62 inference(avatar_component_clause,[status(thm)],[f53])).
% 1.69/1.62 thf(f53,definition,(
% 1.69/1.62 spl3_1 <=> (('const/sets/SUBSET' @ sK0 @ sK1 @ sK2) = $true)),
% 1.69/1.62 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.69/1.62 thf(f388,plain,(
% 1.69/1.62 spl3_5 | ~spl3_7 | ~spl3_9),
% 1.69/1.62 inference(avatar_contradiction_clause,[status(thm)],[f387])).
% 1.69/1.62 thf(f387,plain,(
% 1.69/1.62 $false | (spl3_5 | ~spl3_7 | ~spl3_9)),
% 1.69/1.62 inference(trivial_inequality_removal,[status(thm)],[f386])).
% 1.69/1.62 thf(f386,plain,(
% 1.69/1.62 ($false = $true) | (spl3_5 | ~spl3_7 | ~spl3_9)),
% 1.69/1.62 inference(forward_demodulation,[status(thm)],[f373,f192])).
% 1.69/1.62 thf(f192,plain,(
% 1.69/1.62 ((sK1 @ sK7) = $false) | ~spl3_9),
% 1.69/1.62 inference(avatar_component_clause,[status(thm)],[f190])).
% 1.69/1.62 thf(f190,definition,(
% 1.69/1.62 spl3_9 <=> ((sK1 @ sK7) = $false)),
% 1.69/1.62 introduced(definition,[new_symbols(naming,[spl3_9])],[avatar_definition])).
% 1.69/1.62 thf(f373,plain,(
% 1.69/1.62 ((sK1 @ sK7) = $true) | (spl3_5 | ~spl3_7)),
% 1.69/1.62 inference(trivial_inequality_removal,[status(thm)],[f367])).
% 1.69/1.62 thf(f367,plain,(
% 1.69/1.62 ($false = $true) | ((sK1 @ sK7) = $true) | (spl3_5 | ~spl3_7)),
% 1.69/1.62 inference(superposition,[status(thm)],[f331,f183])).
% 1.69/1.62 thf(f183,plain,(
% 1.69/1.62 ((sK2 @ sK7) = $true) | ~spl3_7),
% 1.69/1.62 inference(avatar_component_clause,[status(thm)],[f181])).
% 1.69/1.62 thf(f181,definition,(
% 1.69/1.62 spl3_7 <=> ((sK2 @ sK7) = $true)),
% 1.69/1.62 introduced(definition,[new_symbols(naming,[spl3_7])],[avatar_definition])).
% 1.69/1.62 thf(f331,plain,(
% 1.69/1.62 ( ! [X0 : sK0] : (($false = (sK2 @ X0)) | ((sK1 @ X0) = $true)) ) | spl3_5),
% 1.69/1.62 inference(trivial_inequality_removal,[status(thm)],[f317])).
% 1.69/1.62 thf(f317,plain,(
% 1.69/1.62 ( ! [X0 : sK0] : (($false = (sK2 @ X0)) | ((sK1 @ X0) = $true) | ($false = $true)) ) | spl3_5),
% 1.69/1.62 inference(superposition,[status(thm)],[f251,f20])).
% 1.69/1.62 thf(f20,plain,(
% 1.69/1.62 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X2 @ X1) = $true) | ((X1 @ X2) = $false)) )),
% 1.69/1.62 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.69/1.62 thf(f18,plain,(
% 1.69/1.62 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X2 @ X1) = (X1 @ X2))) )),
% 1.69/1.62 inference(cnf_transformation,[status(thm)],[f1])).
% 1.69/1.62 thf(f1,axiom,(
% 1.69/1.62 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : (('const/sets/IN' @ X0 @ X2 @ X1) = (X1 @ X2))),
% 1.69/1.62 file('/export/starexec/sandbox2/tmp/tmp.MLbOgFZgl2/DTF2THF_11229.p','thm/sets/IN_')).
% 1.69/1.62 thf(f251,plain,(
% 1.69/1.62 ( ! [X0 : sK0] : (($false = ('const/sets/IN' @ sK0 @ X0 @ sK2)) | ((sK1 @ X0) = $true)) ) | spl3_5),
% 1.69/1.62 inference(trivial_inequality_removal,[status(thm)],[f246])).
% 1.69/1.62 thf(f246,plain,(
% 1.69/1.62 ( ! [X0 : sK0] : (($false = ('const/sets/IN' @ sK0 @ X0 @ sK2)) | ($false = $true) | ((sK1 @ X0) = $true)) ) | spl3_5),
% 1.69/1.62 inference(superposition,[status(thm)],[f21,f196])).
% 1.69/1.62 thf(f196,plain,(
% 1.69/1.62 ( ! [X0 : sK0] : (($true = ('const/sets/IN' @ sK0 @ X0 @ sK1)) | ($false = ('const/sets/IN' @ sK0 @ X0 @ sK2))) ) | spl3_5),
% 1.69/1.62 inference(trivial_inequality_removal,[status(thm)],[f194])).
% 1.69/1.62 thf(f194,plain,(
% 1.69/1.62 ( ! [X0 : sK0] : (($false != $false) | ($true = ('const/sets/IN' @ sK0 @ X0 @ sK1)) | ($false = ('const/sets/IN' @ sK0 @ X0 @ sK2))) ) | spl3_5),
% 1.69/1.62 inference(superposition,[status(thm)],[f72,f37])).
% 1.69/1.62 thf(f37,plain,(
% 1.69/1.62 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) = $false) | (('const/sets/IN' @ X0 @ X3 @ X2) = $true) | (('const/sets/IN' @ X0 @ X3 @ X1) = $false)) )),
% 1.69/1.62 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.69/1.62 thf(f36,plain,(
% 1.69/1.62 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) = $false) | ((('const/sets/IN' @ X0 @ X3 @ X1) => ('const/sets/IN' @ X0 @ X3 @ X2)) = $true)) )),
% 1.69/1.62 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.69/1.62 thf(f35,plain,(
% 1.69/1.62 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) = $false) | ($true = ((^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X1) => ('const/sets/IN' @ X0 @ Y0 @ X2))) @ X3))) )),
% 1.69/1.62 inference(pi_clausification,[status(thm)],[f29])).
% 1.69/1.62 thf(f29,plain,(
% 1.69/1.62 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) = $false) | ((!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X1) => ('const/sets/IN' @ X0 @ Y0 @ X2)))) = $true)) )),
% 1.69/1.62 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.69/1.62 thf(f19,plain,(
% 1.69/1.62 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (((!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X1) => ('const/sets/IN' @ X0 @ Y0 @ X2)))) = ('const/sets/SUBSET' @ X0 @ X1 @ X2))) )),
% 1.69/1.62 inference(cnf_transformation,[status(thm)],[f8])).
% 1.69/1.62 thf(f8,plain,(
% 1.69/1.62 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X1) => ('const/sets/IN' @ X0 @ Y0 @ X2)))) = ('const/sets/SUBSET' @ X0 @ X1 @ X2))),
% 1.69/1.62 inference(fool_elimination,[status(thm)],[f7])).
% 1.69/1.62 thf(f7,plain,(
% 1.69/1.62 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) => ('const/sets/IN' @ X0 @ X3 @ X2)) = ('const/sets/SUBSET' @ X0 @ X1 @ X2))),
% 1.69/1.62 inference(rectify,[status(thm)],[f3])).
% 1.69/1.62 thf(f3,axiom,(
% 1.69/1.62 ! [X0 : $tType,X2 : X0 > $o,X3 : X0 > $o] : (! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X2) => ('const/sets/IN' @ X0 @ X4 @ X3)) = ('const/sets/SUBSET' @ X0 @ X2 @ X3))),
% 1.69/1.62 file('/export/starexec/sandbox2/tmp/tmp.MLbOgFZgl2/DTF2THF_11229.p','thm/sets/SUBSET_')).
% 1.69/1.62 thf(f72,plain,(
% 1.69/1.62 ($false != ('const/sets/SUBSET' @ sK0 @ sK2 @ sK1)) | spl3_5),
% 1.69/1.62 inference(avatar_component_clause,[status(thm)],[f71])).
% 1.69/1.62 thf(f71,definition,(
% 1.69/1.62 spl3_5 <=> ($false = ('const/sets/SUBSET' @ sK0 @ sK2 @ sK1))),
% 1.69/1.62 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.69/1.62 thf(f21,plain,(
% 1.69/1.62 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X2 @ X1) = $false) | ((X1 @ X2) = $true)) )),
% 1.69/1.62 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.69/1.62 thf(f268,plain,(
% 1.69/1.62 ~spl3_7 | ~spl3_8),
% 1.69/1.62 inference(avatar_contradiction_clause,[status(thm)],[f267])).
% 1.69/1.62 thf(f267,plain,(
% 1.69/1.62 $false | (~spl3_7 | ~spl3_8)),
% 1.69/1.62 inference(trivial_inequality_removal,[status(thm)],[f266])).
% 1.69/1.62 thf(f266,plain,(
% 1.69/1.62 ($false = $true) | (~spl3_7 | ~spl3_8)),
% 1.69/1.62 inference(forward_demodulation,[status(thm)],[f183,f188])).
% 1.69/1.62 thf(f188,plain,(
% 1.69/1.62 ((sK2 @ sK7) = $false) | ~spl3_8),
% 1.69/1.62 inference(avatar_component_clause,[status(thm)],[f186])).
% 1.69/1.62 thf(f186,definition,(
% 1.69/1.62 spl3_8 <=> ((sK2 @ sK7) = $false)),
% 1.69/1.62 introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition])).
% 1.69/1.62 thf(f264,plain,(
% 1.69/1.62 ~spl3_6 | ~spl3_9),
% 1.69/1.62 inference(avatar_contradiction_clause,[status(thm)],[f263])).
% 1.69/1.62 thf(f263,plain,(
% 1.69/1.62 $false | (~spl3_6 | ~spl3_9)),
% 1.69/1.62 inference(trivial_inequality_removal,[status(thm)],[f262])).
% 1.69/1.62 thf(f262,plain,(
% 1.69/1.62 ($false = $true) | (~spl3_6 | ~spl3_9)),
% 1.69/1.62 inference(backward_demodulation,[status(thm)],[f179,f192])).
% 1.69/1.62 thf(f179,plain,(
% 1.69/1.62 ((sK1 @ sK7) = $true) | ~spl3_6),
% 1.69/1.62 inference(avatar_component_clause,[status(thm)],[f177])).
% 1.69/1.62 thf(f177,definition,(
% 1.69/1.62 spl3_6 <=> ((sK1 @ sK7) = $true)),
% 1.69/1.62 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 1.69/1.62 thf(f261,plain,(
% 1.69/1.62 spl3_9 | spl3_4 | ~spl3_8),
% 1.69/1.62 inference(avatar_split_clause,[status(thm)],[f258,f186,f67,f190])).
% 1.69/1.62 thf(f258,plain,(
% 1.69/1.62 ((sK1 @ sK7) = $false) | (spl3_4 | ~spl3_8)),
% 1.69/1.62 inference(trivial_inequality_removal,[status(thm)],[f256])).
% 1.69/1.62 thf(f256,plain,(
% 1.69/1.62 ((sK1 @ sK7) = $false) | ($false = $true) | (spl3_4 | ~spl3_8)),
% 1.69/1.62 inference(superposition,[status(thm)],[f238,f188])).
% 1.69/1.62 thf(f238,plain,(
% 1.69/1.62 ( ! [X0 : sK0] : (((sK2 @ X0) = $true) | ((sK1 @ X0) = $false)) ) | spl3_4),
% 1.69/1.62 inference(trivial_inequality_removal,[status(thm)],[f233])).
% 1.69/1.62 thf(f233,plain,(
% 1.69/1.62 ( ! [X0 : sK0] : (((sK2 @ X0) = $true) | ((sK1 @ X0) = $false) | ($false = $true)) ) | spl3_4),
% 1.69/1.62 inference(superposition,[status(thm)],[f21,f226])).
% 1.69/1.62 thf(f226,plain,(
% 1.69/1.62 ( ! [X0 : sK0] : ((('const/sets/IN' @ sK0 @ X0 @ sK2) = $true) | ((sK1 @ X0) = $false)) ) | spl3_4),
% 1.69/1.62 inference(trivial_inequality_removal,[status(thm)],[f218])).
% 1.69/1.62 thf(f218,plain,(
% 1.69/1.62 ( ! [X0 : sK0] : (((sK1 @ X0) = $false) | (('const/sets/IN' @ sK0 @ X0 @ sK2) = $true) | ($false = $true)) ) | spl3_4),
% 1.69/1.62 inference(superposition,[status(thm)],[f20,f172])).
% 1.69/1.62 thf(f172,plain,(
% 1.69/1.62 ( ! [X0 : sK0] : (($false = ('const/sets/IN' @ sK0 @ X0 @ sK1)) | (('const/sets/IN' @ sK0 @ X0 @ sK2) = $true)) ) | spl3_4),
% 1.69/1.62 inference(trivial_inequality_removal,[status(thm)],[f170])).
% 1.69/1.62 thf(f170,plain,(
% 1.69/1.62 ( ! [X0 : sK0] : (($false != $false) | ($false = ('const/sets/IN' @ sK0 @ X0 @ sK1)) | (('const/sets/IN' @ sK0 @ X0 @ sK2) = $true)) ) | spl3_4),
% 1.69/1.62 inference(superposition,[status(thm)],[f68,f37])).
% 1.69/1.62 thf(f68,plain,(
% 1.69/1.62 (('const/sets/SUBSET' @ sK0 @ sK1 @ sK2) != $false) | spl3_4),
% 1.69/1.62 inference(avatar_component_clause,[status(thm)],[f67])).
% 1.69/1.62 thf(f193,plain,(
% 1.69/1.62 spl3_8 | spl3_9 | spl3_2),
% 1.69/1.62 inference(avatar_split_clause,[status(thm)],[f175,f57,f190,f186])).
% 1.69/1.62 thf(f57,definition,(
% 1.69/1.62 spl3_2 <=> (sK1 = sK2)),
% 1.69/1.62 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.69/1.62 thf(f175,plain,(
% 1.69/1.62 ((sK1 @ sK7) = $false) | ((sK2 @ sK7) = $false) | spl3_2),
% 1.69/1.62 inference(binary_proxy_clausification,[status(thm)],[f173])).
% 1.69/1.62 thf(f173,plain,(
% 1.69/1.62 ((sK1 @ sK7) != (sK2 @ sK7)) | spl3_2),
% 1.69/1.62 inference(negative_extensionality,[status(thm)],[f58])).
% 1.69/1.62 thf(f58,plain,(
% 1.69/1.62 (sK1 != sK2) | spl3_2),
% 1.69/1.62 inference(avatar_component_clause,[status(thm)],[f57])).
% 1.69/1.62 thf(f184,plain,(
% 1.69/1.62 spl3_6 | spl3_7 | spl3_2),
% 1.69/1.62 inference(avatar_split_clause,[status(thm)],[f174,f57,f181,f177])).
% 1.69/1.62 thf(f174,plain,(
% 1.69/1.62 ((sK1 @ sK7) = $true) | ((sK2 @ sK7) = $true) | spl3_2),
% 1.69/1.62 inference(binary_proxy_clausification,[status(thm)],[f173])).
% 1.69/1.62 thf(f169,plain,(
% 1.69/1.62 ~spl3_3 | ~spl3_5),
% 1.69/1.62 inference(avatar_contradiction_clause,[status(thm)],[f168])).
% 1.69/1.62 thf(f168,plain,(
% 1.69/1.62 $false | (~spl3_3 | ~spl3_5)),
% 1.69/1.62 inference(trivial_inequality_removal,[status(thm)],[f167])).
% 1.69/1.62 thf(f167,plain,(
% 1.69/1.62 ($false = $true) | (~spl3_3 | ~spl3_5)),
% 1.69/1.62 inference(backward_demodulation,[status(thm)],[f64,f73])).
% 1.69/1.62 thf(f73,plain,(
% 1.69/1.62 ($false = ('const/sets/SUBSET' @ sK0 @ sK2 @ sK1)) | ~spl3_5),
% 1.69/1.62 inference(avatar_component_clause,[status(thm)],[f71])).
% 1.69/1.62 thf(f64,plain,(
% 1.69/1.62 (('const/sets/SUBSET' @ sK0 @ sK2 @ sK1) = $true) | ~spl3_3),
% 1.69/1.62 inference(avatar_component_clause,[status(thm)],[f62])).
% 1.69/1.62 thf(f62,definition,(
% 1.69/1.62 spl3_3 <=> (('const/sets/SUBSET' @ sK0 @ sK2 @ sK1) = $true)),
% 1.69/1.62 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.69/1.62 thf(f166,plain,(
% 1.69/1.62 ~spl3_2 | spl3_4 | ~spl3_5),
% 1.69/1.62 inference(avatar_contradiction_clause,[status(thm)],[f165])).
% 1.69/1.62 thf(f165,plain,(
% 1.69/1.62 $false | (~spl3_2 | spl3_4 | ~spl3_5)),
% 1.69/1.62 inference(subsumption_resolution,[status(thm)],[f164,f163])).
% 1.69/1.62 thf(f163,plain,(
% 1.69/1.62 ($false = ('const/sets/SUBSET' @ sK0 @ sK1 @ sK1)) | (~spl3_2 | ~spl3_5)),
% 1.69/1.62 inference(forward_demodulation,[status(thm)],[f73,f59])).
% 1.69/1.62 thf(f59,plain,(
% 1.69/1.62 (sK1 = sK2) | ~spl3_2),
% 1.69/1.62 inference(avatar_component_clause,[status(thm)],[f57])).
% 1.69/1.62 thf(f164,plain,(
% 1.69/1.62 ($false != ('const/sets/SUBSET' @ sK0 @ sK1 @ sK1)) | (~spl3_2 | spl3_4)),
% 1.69/1.62 inference(forward_demodulation,[status(thm)],[f68,f59])).
% 1.69/1.62 thf(f162,plain,(
% 1.69/1.62 ~spl3_2 | ~spl3_4),
% 1.69/1.62 inference(avatar_contradiction_clause,[status(thm)],[f161])).
% 1.69/1.62 thf(f161,plain,(
% 1.69/1.62 $false | (~spl3_2 | ~spl3_4)),
% 1.69/1.62 inference(trivial_inequality_removal,[status(thm)],[f155])).
% 1.69/1.62 thf(f155,plain,(
% 1.69/1.62 ($false = $true) | (~spl3_2 | ~spl3_4)),
% 1.69/1.62 inference(superposition,[status(thm)],[f75,f151])).
% 1.69/1.62 thf(f151,plain,(
% 1.69/1.62 ( ! [X0 : $tType,X1 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X1) = $true)) )),
% 1.69/1.62 inference(trivial_inequality_removal,[status(thm)],[f150])).
% 1.69/1.62 thf(f150,plain,(
% 1.69/1.62 ( ! [X0 : $tType,X1 : X0 > $o] : (($false = $true) | (('const/sets/SUBSET' @ X0 @ X1 @ X1) = $true)) )),
% 1.69/1.62 inference(duplicate_literal_removal,[status(thm)],[f144])).
% 1.69/1.62 thf(f144,plain,(
% 1.69/1.62 ( ! [X0 : $tType,X1 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X1) = $true) | (('const/sets/SUBSET' @ X0 @ X1 @ X1) = $true) | ($false = $true)) )),
% 1.69/1.62 inference(superposition,[status(thm)],[f33,f34])).
% 1.69/1.62 thf(f34,plain,(
% 1.69/1.62 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X1 @ X2) @ X1) = $true) | (('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true)) )),
% 1.69/1.62 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.69/1.62 thf(f32,plain,(
% 1.69/1.62 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($false = (('const/sets/IN' @ X0 @ (sK4 @ X0 @ X1 @ X2) @ X1) => ('const/sets/IN' @ X0 @ (sK4 @ X0 @ X1 @ X2) @ X2))) | (('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true)) )),
% 1.69/1.62 inference(beta_eta_normalization,[status(thm)],[f31])).
% 1.69/1.62 thf(f31,plain,(
% 1.69/1.62 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((((^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X1) => ('const/sets/IN' @ X0 @ Y0 @ X2))) @ (sK4 @ X0 @ X1 @ X2)) = $false) | (('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true)) )),
% 1.69/1.62 inference(sigma_clausification,[status(thm)],[f30])).
% 1.69/1.62 thf(f30,plain,(
% 1.69/1.62 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (((!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X1) => ('const/sets/IN' @ X0 @ Y0 @ X2)))) = $false) | (('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true)) )),
% 1.69/1.62 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.69/1.62 thf(f33,plain,(
% 1.69/1.62 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X1 @ X2) @ X2) = $false) | (('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true)) )),
% 1.69/1.62 inference(binary_proxy_clausification,[status(thm)],[f32])).
% 1.69/1.62 thf(f75,plain,(
% 1.69/1.62 ($false = ('const/sets/SUBSET' @ sK0 @ sK1 @ sK1)) | (~spl3_2 | ~spl3_4)),
% 1.69/1.62 inference(backward_demodulation,[status(thm)],[f69,f59])).
% 1.69/1.62 thf(f74,plain,(
% 1.69/1.62 spl3_4 | spl3_5 | ~spl3_2),
% 1.69/1.62 inference(avatar_split_clause,[status(thm)],[f25,f57,f71,f67])).
% 1.69/1.62 thf(f25,plain,(
% 1.69/1.62 (('const/sets/SUBSET' @ sK0 @ sK1 @ sK2) = $false) | (sK1 != sK2) | ($false = ('const/sets/SUBSET' @ sK0 @ sK2 @ sK1))),
% 1.69/1.62 inference(binary_proxy_clausification,[status(thm)],[f24])).
% 1.69/1.62 thf(f24,plain,(
% 1.69/1.62 ($false = (('const/sets/SUBSET' @ sK0 @ sK2 @ sK1) & ('const/sets/SUBSET' @ sK0 @ sK1 @ sK2))) | (sK1 != sK2)),
% 1.69/1.62 inference(equality_proxy_clausification,[status(thm)],[f23])).
% 1.69/1.62 thf(f23,plain,(
% 1.69/1.62 ($false = (sK1 = sK2)) | ($false = (('const/sets/SUBSET' @ sK0 @ sK2 @ sK1) & ('const/sets/SUBSET' @ sK0 @ sK1 @ sK2)))),
% 1.69/1.62 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.69/1.62 thf(f16,plain,(
% 1.69/1.62 ((('const/sets/SUBSET' @ sK0 @ sK2 @ sK1) & ('const/sets/SUBSET' @ sK0 @ sK1 @ sK2)) != (sK1 = sK2))),
% 1.69/1.62 inference(cnf_transformation,[status(thm)],[f15])).
% 1.69/1.62 thf(f15,plain,(
% 1.69/1.62 ((('const/sets/SUBSET' @ sK0 @ sK2 @ sK1) & ('const/sets/SUBSET' @ sK0 @ sK1 @ sK2)) != (sK1 = sK2))),
% 1.69/1.62 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f13,f14])).
% 1.69/1.62 thf(f14,plain,(
% 1.69/1.62 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X2 @ X1) & ('const/sets/SUBSET' @ X0 @ X1 @ X2)) != (X1 = X2)) => ((('const/sets/SUBSET' @ sK0 @ sK2 @ sK1) & ('const/sets/SUBSET' @ sK0 @ sK1 @ sK2)) != (sK1 = sK2))),
% 1.69/1.62 introduced(definition,[],[choice_axiom])).
% 1.69/1.62 thf(f13,plain,(
% 1.69/1.62 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X2 @ X1) & ('const/sets/SUBSET' @ X0 @ X1 @ X2)) != (X1 = X2))),
% 1.69/1.62 inference(ennf_transformation,[status(thm)],[f12])).
% 1.69/1.62 thf(f12,plain,(
% 1.69/1.62 ~! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X2 @ X1) & ('const/sets/SUBSET' @ X0 @ X1 @ X2)) = (X1 = X2))),
% 1.69/1.62 inference(fool_elimination,[status(thm)],[f11])).
% 1.69/1.62 thf(f11,plain,(
% 1.69/1.62 ~! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (('const/sets/SUBSET' @ X0 @ X1 @ X2) & ('const/sets/SUBSET' @ X0 @ X2 @ X1) = (X1 = X2))),
% 1.69/1.62 inference(rectify,[status(thm)],[f5])).
% 1.69/1.62 thf(f5,negated_conjecture,(
% 1.69/1.62 ~! [X0 : $tType,X2 : X0 > $o,X3 : X0 > $o] : (('const/sets/SUBSET' @ X0 @ X2 @ X3) & ('const/sets/SUBSET' @ X0 @ X3 @ X2) = (X2 = X3))),
% 1.69/1.62 inference(negated_conjecture,[status(cth)],[f4])).
% 1.69/1.62 thf(f4,conjecture,(
% 1.69/1.62 ! [X0 : $tType,X2 : X0 > $o,X3 : X0 > $o] : (('const/sets/SUBSET' @ X0 @ X2 @ X3) & ('const/sets/SUBSET' @ X0 @ X3 @ X2) = (X2 = X3))),
% 1.69/1.62 file('/export/starexec/sandbox2/tmp/tmp.MLbOgFZgl2/DTF2THF_11229.p','thm/sets/SUBSET_ANTISYM_EQ_')).
% 1.69/1.62 thf(f65,plain,(
% 1.69/1.62 spl3_2 | spl3_3),
% 1.69/1.62 inference(avatar_split_clause,[status(thm)],[f28,f62,f57])).
% 1.69/1.62 thf(f28,plain,(
% 1.69/1.62 (sK1 = sK2) | (('const/sets/SUBSET' @ sK0 @ sK2 @ sK1) = $true)),
% 1.69/1.62 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.69/1.62 thf(f26,plain,(
% 1.69/1.62 ((('const/sets/SUBSET' @ sK0 @ sK2 @ sK1) & ('const/sets/SUBSET' @ sK0 @ sK1 @ sK2)) = $true) | (sK1 = sK2)),
% 1.69/1.62 inference(equality_proxy_clausification,[status(thm)],[f22])).
% 1.69/1.62 thf(f22,plain,(
% 1.69/1.62 ($true = (sK1 = sK2)) | ((('const/sets/SUBSET' @ sK0 @ sK2 @ sK1) & ('const/sets/SUBSET' @ sK0 @ sK1 @ sK2)) = $true)),
% 1.69/1.62 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.69/1.62 thf(f60,plain,(
% 1.69/1.62 spl3_1 | spl3_2),
% 1.69/1.62 inference(avatar_split_clause,[status(thm)],[f27,f57,f53])).
% 1.69/1.62 thf(f27,plain,(
% 1.69/1.62 (('const/sets/SUBSET' @ sK0 @ sK1 @ sK2) = $true) | (sK1 = sK2)),
% 1.69/1.62 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.69/1.62 % SZS output end Proof for DTF2THF_11229
% 1.69/1.62 % (11364)------------------------------
% 1.69/1.62 % (11364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.62 % (11364)Termination reason: Refutation
% 1.69/1.62
% 1.69/1.62 % (11364)Memory used [KB]: 5756
% 1.69/1.62 % (11364)Time elapsed: 0.036 s
% 1.69/1.62 % (11364)Instructions burned: 63 (million)
% 1.69/1.62 % (11364)------------------------------
% 1.69/1.62 % (11364)------------------------------
% 1.69/1.62 % (11325)Success in time 0.209 s
%------------------------------------------------------------------------------