%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV444^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 09:41:15 AM UTC 2026
% Result : Theorem 1.41s 1.20s
% Output : Refutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 80 ( 6 unt; 0 typ; 11 def)
% Number of atoms : 454 ( 115 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 441 ( 87 ~; 110 |; 5 &; 224 @)
% ( 12 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 15 con; 0-3 aty)
% Number of variables : 56 ( 0 ^; 39 !; 17 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
sK1: sK0 > $o ).
thf(func_def_5,type,
sK2: sK0 > $o ).
thf(func_def_6,type,
sK3: sK0 ).
thf(func_def_9,type,
ph5:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
sK6: sK0 ).
thf(f199,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f28,f33,f43,f53,f67,f73,f87,f96,f99,f128,f144,f158,f198]) ).
thf(f198,plain,
( ~ spl4_2
| ~ spl4_4
| ~ spl4_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f197]) ).
thf(f197,plain,
( $false
| ~ spl4_2
| ~ spl4_4
| ~ spl4_7 ),
inference(trivial_inequality_removal,[status(thm)],[f196]) ).
thf(f196,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_4
| ~ spl4_7 ),
inference(forward_demodulation,[status(thm)],[f191,f52]) ).
thf(f52,plain,
( ( ( sK1 @ sK3 )
= $false )
| ~ spl4_7 ),
inference(avatar_component_clause,[status(thm)],[f50]) ).
thf(f50,definition,
( spl4_7
<=> ( ( sK1 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl4_7])],[avatar_definition]) ).
thf(f191,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_2
| ~ spl4_4 ),
inference(superposition,[status(thm)],[f166,f13]) ).
thf(f13,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/sandbox/tmp/tmp.vCeZtj0KwW/DTF2THF_31042.p','thm/sets/IN_') ).
thf(f166,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK1 ) )
| ~ spl4_2
| ~ spl4_4 ),
inference(superposition,[status(thm)],[f38,f27]) ).
thf(f27,plain,
( ( sK1 = sK2 )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f25]) ).
thf(f25,definition,
( spl4_2
<=> ( sK1 = sK2 ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f38,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f36,definition,
( spl4_4
<=> ( $true
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition]) ).
thf(f158,plain,
( spl4_10
| ~ spl4_1
| ~ spl4_11 ),
inference(avatar_split_clause,[status(thm)],[f141,f93,f22,f89]) ).
thf(f89,definition,
( spl4_10
<=> ( ( sK2 @ sK6 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl4_10])],[avatar_definition]) ).
thf(f22,definition,
( spl4_1
<=> ! [X4: sK0] :
( ( $false
= ( 'const/sets/IN' @ sK0 @ X4 @ sK2 ) )
| ( $true
= ( sK1 @ X4 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f93,definition,
( spl4_11
<=> ( $false
= ( sK1 @ sK6 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_11])],[avatar_definition]) ).
thf(f141,plain,
( ( ( sK2 @ sK6 )
= $false )
| ~ spl4_1
| ~ spl4_11 ),
inference(trivial_inequality_removal,[status(thm)],[f138]) ).
thf(f138,plain,
( ( ( sK2 @ sK6 )
= $false )
| ( $true = $false )
| ~ spl4_1
| ~ spl4_11 ),
inference(superposition,[status(thm)],[f103,f95]) ).
thf(f95,plain,
( ( $false
= ( sK1 @ sK6 ) )
| ~ spl4_11 ),
inference(avatar_component_clause,[status(thm)],[f93]) ).
thf(f103,plain,
( ! [X0: sK0] :
( ( $true
= ( sK1 @ X0 ) )
| ( ( sK2 @ X0 )
= $false ) )
| ~ spl4_1 ),
inference(superposition,[status(thm)],[f23,f13]) ).
thf(f23,plain,
( ! [X4: sK0] :
( ( $false
= ( 'const/sets/IN' @ sK0 @ X4 @ sK2 ) )
| ( $true
= ( sK1 @ X4 ) ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f22]) ).
thf(f144,plain,
( ~ spl4_8
| ~ spl4_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f143]) ).
thf(f143,plain,
( $false
| ~ spl4_8
| ~ spl4_11 ),
inference(trivial_inequality_removal,[status(thm)],[f136]) ).
thf(f136,plain,
( ( $true = $false )
| ~ spl4_8
| ~ spl4_11 ),
inference(superposition,[status(thm)],[f82,f95]) ).
thf(f82,plain,
( ( $true
= ( sK1 @ sK6 ) )
| ~ spl4_8 ),
inference(avatar_component_clause,[status(thm)],[f80]) ).
thf(f80,definition,
( spl4_8
<=> ( $true
= ( sK1 @ sK6 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_8])],[avatar_definition]) ).
thf(f128,plain,
( spl4_11
| ~ spl4_3
| ~ spl4_10 ),
inference(avatar_split_clause,[status(thm)],[f124,f89,f31,f93]) ).
thf(f31,definition,
( spl4_3
<=> ! [X4: sK0] :
( ( $false
= ( sK1 @ X4 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ X4 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition]) ).
thf(f124,plain,
( ( $false
= ( sK1 @ sK6 ) )
| ~ spl4_3
| ~ spl4_10 ),
inference(trivial_inequality_removal,[status(thm)],[f122]) ).
thf(f122,plain,
( ( $false
= ( sK1 @ sK6 ) )
| ( $true = $false )
| ~ spl4_3
| ~ spl4_10 ),
inference(superposition,[status(thm)],[f91,f105]) ).
thf(f105,plain,
( ! [X0: sK0] :
( ( $true
= ( sK2 @ X0 ) )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl4_3 ),
inference(superposition,[status(thm)],[f32,f13]) ).
thf(f32,plain,
( ! [X4: sK0] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ X4 @ sK2 ) )
| ( $false
= ( sK1 @ X4 ) ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f91,plain,
( ( ( sK2 @ sK6 )
= $false )
| ~ spl4_10 ),
inference(avatar_component_clause,[status(thm)],[f89]) ).
thf(f99,plain,
( ~ spl4_9
| ~ spl4_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f98]) ).
thf(f98,plain,
( $false
| ~ spl4_9
| ~ spl4_10 ),
inference(trivial_inequality_removal,[status(thm)],[f97]) ).
thf(f97,plain,
( ( $true = $false )
| ~ spl4_9
| ~ spl4_10 ),
inference(forward_demodulation,[status(thm)],[f86,f91]) ).
thf(f86,plain,
( ( $true
= ( sK2 @ sK6 ) )
| ~ spl4_9 ),
inference(avatar_component_clause,[status(thm)],[f84]) ).
thf(f84,definition,
( spl4_9
<=> ( $true
= ( sK2 @ sK6 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_9])],[avatar_definition]) ).
thf(f96,plain,
( spl4_10
| spl4_11
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f78,f25,f93,f89]) ).
thf(f78,plain,
( ( $false
= ( sK1 @ sK6 ) )
| ( ( sK2 @ sK6 )
= $false )
| spl4_2 ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
( ( ( sK2 @ sK6 )
!= ( sK1 @ sK6 ) )
| spl4_2 ),
inference(negative_extensionality,[status(thm)],[f26]) ).
thf(f26,plain,
( ( sK1 != sK2 )
| spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f25]) ).
thf(f87,plain,
( spl4_8
| spl4_9
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f77,f25,f84,f80]) ).
thf(f77,plain,
( ( $true
= ( sK1 @ sK6 ) )
| ( $true
= ( sK2 @ sK6 ) )
| spl4_2 ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f73,plain,
( ~ spl4_5
| ~ spl4_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f72]) ).
thf(f72,plain,
( $false
| ~ spl4_5
| ~ spl4_7 ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ( $true = $false )
| ~ spl4_5
| ~ spl4_7 ),
inference(superposition,[status(thm)],[f42,f52]) ).
thf(f42,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl4_5
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition]) ).
thf(f67,plain,
( spl4_7
| ~ spl4_2
| ~ spl4_6 ),
inference(avatar_split_clause,[status(thm)],[f64,f46,f25,f50]) ).
thf(f46,definition,
( spl4_6
<=> ( ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition]) ).
thf(f64,plain,
( ( ( sK1 @ sK3 )
= $false )
| ~ spl4_2
| ~ spl4_6 ),
inference(superposition,[status(thm)],[f54,f13]) ).
thf(f54,plain,
( ( ( 'const/sets/IN' @ sK0 @ sK3 @ sK1 )
= $false )
| ~ spl4_2
| ~ spl4_6 ),
inference(forward_demodulation,[status(thm)],[f48,f27]) ).
thf(f48,plain,
( ( ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 )
= $false )
| ~ spl4_6 ),
inference(avatar_component_clause,[status(thm)],[f46]) ).
thf(f53,plain,
( spl4_6
| ~ spl4_2
| spl4_7 ),
inference(avatar_split_clause,[status(thm)],[f44,f50,f25,f46]) ).
thf(f44,plain,
( ( ( sK1 @ sK3 )
= $false )
| ( sK1 != sK2 )
| ( ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 )
= $false ) ),
inference(forward_demodulation,[status(thm)],[f17,f13]) ).
thf(f17,plain,
( ( ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 )
= $false )
| ( ( 'const/sets/IN' @ sK0 @ sK3 @ sK1 )
= $false )
| ( sK1 != sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( ( sK1 != sK2 )
| ( ( 'const/sets/IN' @ sK0 @ sK3 @ sK1 )
!= ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( ( 'const/sets/IN' @ sK0 @ sK3 @ sK1 )
!= ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 ) )
| ( sK1 != sK2 ) )
& ( ! [X4: sK0] :
( ( 'const/sets/IN' @ sK0 @ X4 @ sK1 )
= ( 'const/sets/IN' @ sK0 @ X4 @ sK2 ) )
| ( sK1 = sK2 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f9,f11,f10]) ).
thf(f10,plain,
( ? [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ? [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
!= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
| ( X1 != X2 ) )
& ( ! [X4: X0] :
( ( 'const/sets/IN' @ X0 @ X4 @ X2 )
= ( 'const/sets/IN' @ X0 @ X4 @ X1 ) )
| ( X1 = X2 ) ) )
=> ( ( ? [X3: sK0] :
( ( 'const/sets/IN' @ sK0 @ X3 @ sK2 )
!= ( 'const/sets/IN' @ sK0 @ X3 @ sK1 ) )
| ( sK1 != sK2 ) )
& ( ! [X4: sK0] :
( ( 'const/sets/IN' @ sK0 @ X4 @ sK1 )
= ( 'const/sets/IN' @ sK0 @ X4 @ sK2 ) )
| ( sK1 = sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X3: sK0] :
( ( 'const/sets/IN' @ sK0 @ X3 @ sK2 )
!= ( 'const/sets/IN' @ sK0 @ X3 @ sK1 ) )
=> ( ( 'const/sets/IN' @ sK0 @ sK3 @ sK1 )
!= ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ? [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
!= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
| ( X1 != X2 ) )
& ( ! [X4: X0] :
( ( 'const/sets/IN' @ X0 @ X4 @ X2 )
= ( 'const/sets/IN' @ X0 @ X4 @ X1 ) )
| ( X1 = X2 ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ? [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
!= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
| ( X1 != X2 ) )
& ( ! [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
| ( X1 = X2 ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( X1 = X2 )
<~> ! [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( X1 = X2 )
<=> ! [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
= ( X1 = X2 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X2 )
= ( 'const/sets/IN' @ X0 @ X4 @ X3 ) )
= ( X2 = X3 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X2 )
= ( 'const/sets/IN' @ X0 @ X4 @ X3 ) )
= ( X2 = X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.vCeZtj0KwW/DTF2THF_31042.p','thm/sets/EXTENSION_') ).
thf(f43,plain,
( spl4_4
| ~ spl4_2
| spl4_5 ),
inference(avatar_split_clause,[status(thm)],[f34,f40,f25,f36]) ).
thf(f34,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 ) )
| ( sK1 != sK2 )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(forward_demodulation,[status(thm)],[f16,f13]) ).
thf(f16,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK1 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ sK3 @ sK2 ) )
| ( sK1 != sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f33,plain,
( spl4_2
| spl4_3 ),
inference(avatar_split_clause,[status(thm)],[f29,f31,f25]) ).
thf(f29,plain,
! [X4: sK0] :
( ( sK1 = sK2 )
| ( $false
= ( sK1 @ X4 ) )
| ( $true
= ( 'const/sets/IN' @ sK0 @ X4 @ sK2 ) ) ),
inference(forward_demodulation,[status(thm)],[f19,f13]) ).
thf(f19,plain,
! [X4: sK0] :
( ( sK1 = sK2 )
| ( ( 'const/sets/IN' @ sK0 @ X4 @ sK1 )
= $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ X4 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
! [X4: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X4 @ sK1 )
= ( 'const/sets/IN' @ sK0 @ X4 @ sK2 ) )
| ( sK1 = sK2 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f28,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[status(thm)],[f20,f25,f22]) ).
thf(f20,plain,
! [X4: sK0] :
( ( sK1 = sK2 )
| ( $false
= ( 'const/sets/IN' @ sK0 @ X4 @ sK2 ) )
| ( $true
= ( sK1 @ X4 ) ) ),
inference(forward_demodulation,[status(thm)],[f18,f13]) ).
thf(f18,plain,
! [X4: sK0] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ X4 @ sK1 ) )
| ( sK1 = sK2 )
| ( $false
= ( 'const/sets/IN' @ sK0 @ X4 @ sK2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV444^1 : TPTP v9.2.1. Released v7.0.0.
% 0.11/0.14 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n020.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 12:46:57 EST 2026
% 0.15/0.35 % CPUTime :
% 0.15/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.26/0.45 ---- Original DTF file ---
% 0.26/0.45 thf(spec,logic,$$dhol).
% 0.26/0.45 %------------------------------------------------------------------------------
% 0.26/0.45 % File : SEV444^1 : TPTP v9.2.1. Released v7.0.0.
% 0.26/0.45 % Domain : Analysis
% 0.26/0.45 % Problem : EXTENSION
% 0.26/0.45 % Version : Especial.
% 0.26/0.45 % English :
% 0.26/0.45
% 0.26/0.45 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.26/0.45 % Source : [Kal16]
% 0.26/0.45 % Names : EXTENSION_.p [Kal16]
% 0.26/0.45
% 0.26/0.45 % Status : Theorem
% 0.26/0.45 % Rating : 0.00 v7.5.0, 0.33 v7.2.0, 0.25 v7.1.0
% 0.26/0.45 % Syntax : Number of formulae : 3 ( 2 unt; 1 typ; 0 def)
% 0.26/0.45 % Number of atoms : 7 ( 4 equ; 0 cnn)
% 0.26/0.45 % Maximal formula atoms : 1 ( 3 avg)
% 0.26/0.45 % Number of connectives : 10 ( 0 ~; 0 |; 0 &; 10 @)
% 0.26/0.45 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.26/0.45 % Maximal formula depth : 4 ( 4 avg)
% 0.26/0.45 % Number of types : 1 ( 0 usr)
% 0.26/0.45 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.26/0.45 % Number of symbols : 2 ( 1 usr; 0 con; 2-3 aty)
% 0.26/0.45 % Number of variables : 8 ( 0 ^; 7 !; 0 ?; 8 :)
% 0.26/0.45 % ( 1 !>; 0 ?*; 0 @-; 0 @+)
% 0.26/0.45 % SPC : TH1_THM_EQU_NAR
% 0.26/0.45
% 0.26/0.45 % Comments : Exported from core HOL Light.
% 0.26/0.45 %------------------------------------------------------------------------------
% 0.26/0.45 thf('thf_const_const/sets/IN',type,
% 0.26/0.45 'const/sets/IN':
% 0.26/0.45 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.26/0.45
% 0.26/0.45 thf('thm/sets/IN_',axiom,
% 0.26/0.45 ! [A: $tType,P: A > $o,A0: A] :
% 0.26/0.45 ( ( 'const/sets/IN' @ A @ A0 @ P )
% 0.26/0.45 = ( P @ A0 ) ) ).
% 0.26/0.45
% 0.26/0.45 thf('thm/sets/EXTENSION_',conjecture,
% 0.26/0.45 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 0.26/0.45 ( ( A0 = A1 )
% 0.26/0.45 = ( ! [A2: A] :
% 0.26/0.45 ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 0.26/0.45 = ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
% 0.26/0.45
% 0.26/0.45 %------------------------------------------------------------------------------
% 0.26/0.45 ------------------------
% 1.29/1.16 ---- Embedded in THF ---
% 1.29/1.16 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.29/1.16 %%% Generated on Tue Feb 24 12:46:58 EST 2026
% 1.29/1.16 %%% using '$$dhol' embedding, version 1.3.0.
% 1.29/1.16 %%% Logic specification used:
% 1.29/1.16 %%% thf(spec, logic, $$dhol).
% 1.29/1.16
% 1.29/1.16 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.vCeZtj0KwW/DTF2DTF31042.p
% See solution above
% 1.29/1.16 ------------------------
% 1.29/1.17 ---- Cleaned THF ---
% 1.29/1.17 thf('thf_const_const/sets/IN',type,
% 1.29/1.17 'const/sets/IN':
% 1.29/1.17 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.29/1.17
% 1.29/1.17 thf('thm/sets/IN_',axiom,
% 1.29/1.17 ! [A: $tType,P: A > $o,A0: A] :
% 1.29/1.17 ( ( 'const/sets/IN' @ A @ A0 @ P )
% 1.29/1.17 = ( P @ A0 ) ) ).
% 1.29/1.17
% 1.29/1.17 thf('thm/sets/EXTENSION_',conjecture,
% 1.29/1.17 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 1.29/1.17 ( ( A0 = A1 )
% 1.29/1.17 = ( ! [A2: A] :
% 1.29/1.17 ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 1.29/1.17 = ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
% 1.29/1.17 ------------------------
% 1.29/1.18 % (31140)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_31042 for (2999ds/4Mi)
% 1.29/1.18 % (31142)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_31042 for (2999ds/2Mi)
% 1.29/1.19 % (31142)Instruction limit reached!
% 1.29/1.19 % (31142)------------------------------
% 1.29/1.19 % (31142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.29/1.19 % (31142)Termination reason: Unknown
% 1.29/1.19 % (31142)Termination phase: Saturation
% 1.29/1.19
% 1.29/1.19 % (31142)Memory used [KB]: 5500
% 1.29/1.19 % (31142)Time elapsed: 0.003 s
% 1.29/1.19 % (31142)Instructions burned: 2 (million)
% 1.29/1.19 % (31142)------------------------------
% 1.29/1.19 % (31142)------------------------------
% 1.29/1.19 % (31144)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_31042 for (2999ds/275Mi)
% 1.29/1.19 % (31145)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_31042 for (2999ds/18Mi)
% 1.29/1.19 % (31143)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_31042 for (2999ds/2Mi)
% 1.29/1.19 % Exception at run slice level
% 1.29/1.19 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
% 1.29/1.19 % (31141)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_31042 for (2999ds/27Mi)
% 1.29/1.20 % (31139)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_31042 for (2999ds/183Mi)
% 1.41/1.20 % (31146)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_31042 for (2999ds/3Mi)
% 1.41/1.20 % (31140)Instruction limit reached!
% 1.41/1.20 % (31140)------------------------------
% 1.41/1.20 % (31140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.41/1.20 % (31140)Termination reason: Unknown
% 1.41/1.20 % (31140)Termination phase: Saturation
% 1.41/1.20
% 1.41/1.20 % (31140)Memory used [KB]: 5500
% 1.41/1.20 % (31140)Time elapsed: 0.004 s
% 1.41/1.20 % (31140)Instructions burned: 4 (million)
% 1.41/1.20 % (31140)------------------------------
% 1.41/1.20 % (31140)------------------------------
% 1.41/1.20 % (31146)Instruction limit reached!
% 1.41/1.20 % (31146)------------------------------
% 1.41/1.20 % (31146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.41/1.20 % (31144)First to succeed.
% 1.41/1.20 % (31146)Termination reason: Unknown
% 1.41/1.20 % (31146)Termination phase: Saturation
% 1.41/1.20
% 1.41/1.20 % (31146)Memory used [KB]: 5500
% 1.41/1.20 % (31146)Time elapsed: 0.003 s
% 1.41/1.20 % (31146)Instructions burned: 3 (million)
% 1.41/1.20 % (31146)------------------------------
% 1.41/1.20 % (31146)------------------------------
% 1.41/1.20 % (31144)Refutation found. Thanks to Tanya!
% 1.41/1.20 % SZS status Theorem for DTF2THF_31042
% 1.41/1.20 % SZS output start Proof for DTF2THF_31042
% 1.41/1.20 thf(type_def_6, type, sK0: $tType).
% 1.41/1.20 thf(func_def_0, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.41/1.20 thf(func_def_4, type, sK1: sK0 > $o).
% 1.41/1.20 thf(func_def_5, type, sK2: sK0 > $o).
% 1.41/1.20 thf(func_def_6, type, sK3: sK0).
% 1.41/1.20 thf(func_def_9, type, ph5: !>[X0: $tType]:(X0)).
% 1.41/1.20 thf(func_def_10, type, sK6: sK0).
% 1.41/1.20 thf(f199,plain,(
% 1.41/1.20 $false),
% 1.41/1.20 inference(avatar_sat_refutation,[status(thm)],[f28,f33,f43,f53,f67,f73,f87,f96,f99,f128,f144,f158,f198])).
% 1.41/1.20 thf(f198,plain,(
% 1.41/1.20 ~spl4_2 | ~spl4_4 | ~spl4_7),
% 1.41/1.20 inference(avatar_contradiction_clause,[status(thm)],[f197])).
% 1.41/1.20 thf(f197,plain,(
% 1.41/1.20 $false | (~spl4_2 | ~spl4_4 | ~spl4_7)),
% 1.41/1.20 inference(trivial_inequality_removal,[status(thm)],[f196])).
% 1.41/1.20 thf(f196,plain,(
% 1.41/1.20 ($true = $false) | (~spl4_2 | ~spl4_4 | ~spl4_7)),
% 1.41/1.20 inference(forward_demodulation,[status(thm)],[f191,f52])).
% 1.41/1.20 thf(f52,plain,(
% 1.41/1.20 ((sK1 @ sK3) = $false) | ~spl4_7),
% 1.41/1.20 inference(avatar_component_clause,[status(thm)],[f50])).
% 1.41/1.20 thf(f50,definition,(
% 1.41/1.20 spl4_7 <=> ((sK1 @ sK3) = $false)),
% 1.41/1.20 introduced(definition,[new_symbols(naming,[spl4_7])],[avatar_definition])).
% 1.41/1.20 thf(f191,plain,(
% 1.41/1.20 ($true = (sK1 @ sK3)) | (~spl4_2 | ~spl4_4)),
% 1.41/1.20 inference(superposition,[status(thm)],[f166,f13])).
% 1.41/1.20 thf(f13,plain,(
% 1.41/1.20 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X2 @ X1) = (X1 @ X2))) )),
% 1.41/1.20 inference(cnf_transformation,[status(thm)],[f1])).
% 1.41/1.20 thf(f1,axiom,(
% 1.41/1.20 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : (('const/sets/IN' @ X0 @ X2 @ X1) = (X1 @ X2))),
% 1.41/1.20 file('/export/starexec/sandbox/tmp/tmp.vCeZtj0KwW/DTF2THF_31042.p','thm/sets/IN_')).
% 1.41/1.20 thf(f166,plain,(
% 1.41/1.20 ($true = ('const/sets/IN' @ sK0 @ sK3 @ sK1)) | (~spl4_2 | ~spl4_4)),
% 1.41/1.20 inference(superposition,[status(thm)],[f38,f27])).
% 1.41/1.20 thf(f27,plain,(
% 1.41/1.20 (sK1 = sK2) | ~spl4_2),
% 1.41/1.20 inference(avatar_component_clause,[status(thm)],[f25])).
% 1.41/1.20 thf(f25,definition,(
% 1.41/1.20 spl4_2 <=> (sK1 = sK2)),
% 1.41/1.20 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.41/1.20 thf(f38,plain,(
% 1.41/1.20 ($true = ('const/sets/IN' @ sK0 @ sK3 @ sK2)) | ~spl4_4),
% 1.41/1.20 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.41/1.20 thf(f36,definition,(
% 1.41/1.20 spl4_4 <=> ($true = ('const/sets/IN' @ sK0 @ sK3 @ sK2))),
% 1.41/1.20 introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition])).
% 1.41/1.20 thf(f158,plain,(
% 1.41/1.20 spl4_10 | ~spl4_1 | ~spl4_11),
% 1.41/1.20 inference(avatar_split_clause,[status(thm)],[f141,f93,f22,f89])).
% 1.41/1.20 thf(f89,definition,(
% 1.41/1.20 spl4_10 <=> ((sK2 @ sK6) = $false)),
% 1.41/1.20 introduced(definition,[new_symbols(naming,[spl4_10])],[avatar_definition])).
% 1.41/1.20 thf(f22,definition,(
% 1.41/1.20 spl4_1 <=> ! [X4 : sK0] : (($false = ('const/sets/IN' @ sK0 @ X4 @ sK2)) | ($true = (sK1 @ X4)))),
% 1.41/1.20 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.41/1.20 thf(f93,definition,(
% 1.41/1.20 spl4_11 <=> ($false = (sK1 @ sK6))),
% 1.41/1.20 introduced(definition,[new_symbols(naming,[spl4_11])],[avatar_definition])).
% 1.41/1.20 thf(f141,plain,(
% 1.41/1.20 ((sK2 @ sK6) = $false) | (~spl4_1 | ~spl4_11)),
% 1.41/1.20 inference(trivial_inequality_removal,[status(thm)],[f138])).
% 1.41/1.20 thf(f138,plain,(
% 1.41/1.20 ((sK2 @ sK6) = $false) | ($true = $false) | (~spl4_1 | ~spl4_11)),
% 1.41/1.20 inference(superposition,[status(thm)],[f103,f95])).
% 1.41/1.20 thf(f95,plain,(
% 1.41/1.20 ($false = (sK1 @ sK6)) | ~spl4_11),
% 1.41/1.20 inference(avatar_component_clause,[status(thm)],[f93])).
% 1.41/1.20 thf(f103,plain,(
% 1.41/1.20 ( ! [X0 : sK0] : (($true = (sK1 @ X0)) | ((sK2 @ X0) = $false)) ) | ~spl4_1),
% 1.41/1.20 inference(superposition,[status(thm)],[f23,f13])).
% 1.41/1.20 thf(f23,plain,(
% 1.41/1.20 ( ! [X4 : sK0] : (($false = ('const/sets/IN' @ sK0 @ X4 @ sK2)) | ($true = (sK1 @ X4))) ) | ~spl4_1),
% 1.41/1.20 inference(avatar_component_clause,[status(thm)],[f22])).
% 1.41/1.20 thf(f144,plain,(
% 1.41/1.20 ~spl4_8 | ~spl4_11),
% 1.41/1.20 inference(avatar_contradiction_clause,[status(thm)],[f143])).
% 1.41/1.20 thf(f143,plain,(
% 1.41/1.20 $false | (~spl4_8 | ~spl4_11)),
% 1.41/1.20 inference(trivial_inequality_removal,[status(thm)],[f136])).
% 1.41/1.20 thf(f136,plain,(
% 1.41/1.20 ($true = $false) | (~spl4_8 | ~spl4_11)),
% 1.41/1.20 inference(superposition,[status(thm)],[f82,f95])).
% 1.41/1.20 thf(f82,plain,(
% 1.41/1.20 ($true = (sK1 @ sK6)) | ~spl4_8),
% 1.41/1.20 inference(avatar_component_clause,[status(thm)],[f80])).
% 1.41/1.20 thf(f80,definition,(
% 1.41/1.20 spl4_8 <=> ($true = (sK1 @ sK6))),
% 1.41/1.20 introduced(definition,[new_symbols(naming,[spl4_8])],[avatar_definition])).
% 1.41/1.20 thf(f128,plain,(
% 1.41/1.20 spl4_11 | ~spl4_3 | ~spl4_10),
% 1.41/1.20 inference(avatar_split_clause,[status(thm)],[f124,f89,f31,f93])).
% 1.41/1.20 thf(f31,definition,(
% 1.41/1.20 spl4_3 <=> ! [X4 : sK0] : (($false = (sK1 @ X4)) | ($true = ('const/sets/IN' @ sK0 @ X4 @ sK2)))),
% 1.41/1.20 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 1.41/1.20 thf(f124,plain,(
% 1.41/1.20 ($false = (sK1 @ sK6)) | (~spl4_3 | ~spl4_10)),
% 1.41/1.20 inference(trivial_inequality_removal,[status(thm)],[f122])).
% 1.41/1.20 thf(f122,plain,(
% 1.41/1.20 ($false = (sK1 @ sK6)) | ($true = $false) | (~spl4_3 | ~spl4_10)),
% 1.41/1.20 inference(superposition,[status(thm)],[f91,f105])).
% 1.41/1.20 thf(f105,plain,(
% 1.41/1.20 ( ! [X0 : sK0] : (($true = (sK2 @ X0)) | ($false = (sK1 @ X0))) ) | ~spl4_3),
% 1.41/1.20 inference(superposition,[status(thm)],[f32,f13])).
% 1.41/1.20 thf(f32,plain,(
% 1.41/1.20 ( ! [X4 : sK0] : (($true = ('const/sets/IN' @ sK0 @ X4 @ sK2)) | ($false = (sK1 @ X4))) ) | ~spl4_3),
% 1.41/1.20 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.41/1.20 thf(f91,plain,(
% 1.41/1.20 ((sK2 @ sK6) = $false) | ~spl4_10),
% 1.41/1.20 inference(avatar_component_clause,[status(thm)],[f89])).
% 1.41/1.20 thf(f99,plain,(
% 1.41/1.20 ~spl4_9 | ~spl4_10),
% 1.41/1.20 inference(avatar_contradiction_clause,[status(thm)],[f98])).
% 1.41/1.20 thf(f98,plain,(
% 1.41/1.20 $false | (~spl4_9 | ~spl4_10)),
% 1.41/1.20 inference(trivial_inequality_removal,[status(thm)],[f97])).
% 1.41/1.20 thf(f97,plain,(
% 1.41/1.20 ($true = $false) | (~spl4_9 | ~spl4_10)),
% 1.41/1.20 inference(forward_demodulation,[status(thm)],[f86,f91])).
% 1.41/1.20 thf(f86,plain,(
% 1.41/1.20 ($true = (sK2 @ sK6)) | ~spl4_9),
% 1.41/1.20 inference(avatar_component_clause,[status(thm)],[f84])).
% 1.41/1.20 thf(f84,definition,(
% 1.41/1.20 spl4_9 <=> ($true = (sK2 @ sK6))),
% 1.41/1.20 introduced(definition,[new_symbols(naming,[spl4_9])],[avatar_definition])).
% 1.41/1.20 thf(f96,plain,(
% 1.41/1.20 spl4_10 | spl4_11 | spl4_2),
% 1.41/1.20 inference(avatar_split_clause,[status(thm)],[f78,f25,f93,f89])).
% 1.41/1.20 thf(f78,plain,(
% 1.41/1.20 ($false = (sK1 @ sK6)) | ((sK2 @ sK6) = $false) | spl4_2),
% 1.41/1.20 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.41/1.20 thf(f76,plain,(
% 1.41/1.20 ((sK2 @ sK6) != (sK1 @ sK6)) | spl4_2),
% 1.41/1.20 inference(negative_extensionality,[status(thm)],[f26])).
% 1.41/1.20 thf(f26,plain,(
% 1.41/1.20 (sK1 != sK2) | spl4_2),
% 1.41/1.20 inference(avatar_component_clause,[status(thm)],[f25])).
% 1.41/1.20 thf(f87,plain,(
% 1.41/1.20 spl4_8 | spl4_9 | spl4_2),
% 1.41/1.20 inference(avatar_split_clause,[status(thm)],[f77,f25,f84,f80])).
% 1.41/1.20 thf(f77,plain,(
% 1.41/1.20 ($true = (sK1 @ sK6)) | ($true = (sK2 @ sK6)) | spl4_2),
% 1.41/1.20 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.41/1.20 thf(f73,plain,(
% 1.41/1.20 ~spl4_5 | ~spl4_7),
% 1.41/1.20 inference(avatar_contradiction_clause,[status(thm)],[f72])).
% 1.41/1.20 thf(f72,plain,(
% 1.41/1.20 $false | (~spl4_5 | ~spl4_7)),
% 1.41/1.20 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.41/1.20 thf(f69,plain,(
% 1.41/1.20 ($true = $false) | (~spl4_5 | ~spl4_7)),
% 1.41/1.20 inference(superposition,[status(thm)],[f42,f52])).
% 1.41/1.20 thf(f42,plain,(
% 1.41/1.20 ($true = (sK1 @ sK3)) | ~spl4_5),
% 1.41/1.20 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.41/1.20 thf(f40,definition,(
% 1.41/1.20 spl4_5 <=> ($true = (sK1 @ sK3))),
% 1.41/1.20 introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition])).
% 1.41/1.20 thf(f67,plain,(
% 1.41/1.20 spl4_7 | ~spl4_2 | ~spl4_6),
% 1.41/1.20 inference(avatar_split_clause,[status(thm)],[f64,f46,f25,f50])).
% 1.41/1.20 thf(f46,definition,(
% 1.41/1.20 spl4_6 <=> (('const/sets/IN' @ sK0 @ sK3 @ sK2) = $false)),
% 1.41/1.20 introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition])).
% 1.41/1.20 thf(f64,plain,(
% 1.41/1.20 ((sK1 @ sK3) = $false) | (~spl4_2 | ~spl4_6)),
% 1.41/1.20 inference(superposition,[status(thm)],[f54,f13])).
% 1.41/1.20 thf(f54,plain,(
% 1.41/1.20 (('const/sets/IN' @ sK0 @ sK3 @ sK1) = $false) | (~spl4_2 | ~spl4_6)),
% 1.41/1.20 inference(forward_demodulation,[status(thm)],[f48,f27])).
% 1.41/1.20 thf(f48,plain,(
% 1.41/1.20 (('const/sets/IN' @ sK0 @ sK3 @ sK2) = $false) | ~spl4_6),
% 1.41/1.20 inference(avatar_component_clause,[status(thm)],[f46])).
% 1.41/1.20 thf(f53,plain,(
% 1.41/1.20 spl4_6 | ~spl4_2 | spl4_7),
% 1.41/1.20 inference(avatar_split_clause,[status(thm)],[f44,f50,f25,f46])).
% 1.41/1.20 thf(f44,plain,(
% 1.41/1.20 ((sK1 @ sK3) = $false) | (sK1 != sK2) | (('const/sets/IN' @ sK0 @ sK3 @ sK2) = $false)),
% 1.41/1.20 inference(forward_demodulation,[status(thm)],[f17,f13])).
% 1.41/1.20 thf(f17,plain,(
% 1.41/1.20 (('const/sets/IN' @ sK0 @ sK3 @ sK2) = $false) | (('const/sets/IN' @ sK0 @ sK3 @ sK1) = $false) | (sK1 != sK2)),
% 1.41/1.20 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.41/1.20 thf(f15,plain,(
% 1.41/1.20 (sK1 != sK2) | (('const/sets/IN' @ sK0 @ sK3 @ sK1) != ('const/sets/IN' @ sK0 @ sK3 @ sK2))),
% 1.41/1.20 inference(cnf_transformation,[status(thm)],[f12])).
% 1.41/1.20 thf(f12,plain,(
% 1.41/1.20 ((('const/sets/IN' @ sK0 @ sK3 @ sK1) != ('const/sets/IN' @ sK0 @ sK3 @ sK2)) | (sK1 != sK2)) & (! [X4 : sK0] : (('const/sets/IN' @ sK0 @ X4 @ sK1) = ('const/sets/IN' @ sK0 @ X4 @ sK2)) | (sK1 = sK2))),
% 1.41/1.20 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f9,f11,f10])).
% 1.41/1.20 thf(f10,plain,(
% 1.41/1.20 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((? [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) != ('const/sets/IN' @ X0 @ X3 @ X2)) | (X1 != X2)) & (! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X2) = ('const/sets/IN' @ X0 @ X4 @ X1)) | (X1 = X2))) => ((? [X3 : sK0] : (('const/sets/IN' @ sK0 @ X3 @ sK2) != ('const/sets/IN' @ sK0 @ X3 @ sK1)) | (sK1 != sK2)) & (! [X4 : sK0] : (('const/sets/IN' @ sK0 @ X4 @ sK1) = ('const/sets/IN' @ sK0 @ X4 @ sK2)) | (sK1 = sK2)))),
% 1.41/1.20 introduced(definition,[],[choice_axiom])).
% 1.41/1.20 thf(f11,plain,(
% 1.41/1.20 ? [X3 : sK0] : (('const/sets/IN' @ sK0 @ X3 @ sK2) != ('const/sets/IN' @ sK0 @ X3 @ sK1)) => (('const/sets/IN' @ sK0 @ sK3 @ sK1) != ('const/sets/IN' @ sK0 @ sK3 @ sK2))),
% 1.41/1.20 introduced(definition,[],[choice_axiom])).
% 1.41/1.20 thf(f9,plain,(
% 1.41/1.20 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((? [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) != ('const/sets/IN' @ X0 @ X3 @ X2)) | (X1 != X2)) & (! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X2) = ('const/sets/IN' @ X0 @ X4 @ X1)) | (X1 = X2)))),
% 1.41/1.20 inference(rectify,[status(thm)],[f8])).
% 1.41/1.20 thf(f8,plain,(
% 1.41/1.20 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((? [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) != ('const/sets/IN' @ X0 @ X3 @ X2)) | (X1 != X2)) & (! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) = ('const/sets/IN' @ X0 @ X3 @ X2)) | (X1 = X2)))),
% 1.41/1.20 inference(nnf_transformation,[status(thm)],[f7])).
% 1.41/1.20 thf(f7,plain,(
% 1.41/1.20 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((X1 = X2) <~> ! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) = ('const/sets/IN' @ X0 @ X3 @ X2)))),
% 1.41/1.20 inference(ennf_transformation,[status(thm)],[f6])).
% 1.41/1.20 thf(f6,plain,(
% 1.41/1.20 ~! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((X1 = X2) <=> ! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) = ('const/sets/IN' @ X0 @ X3 @ X2)))),
% 1.41/1.20 inference(fool_elimination,[status(thm)],[f5])).
% 1.41/1.20 thf(f5,plain,(
% 1.41/1.20 ~! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) = ('const/sets/IN' @ X0 @ X3 @ X2)) = (X1 = X2))),
% 1.41/1.20 inference(rectify,[status(thm)],[f3])).
% 1.41/1.20 thf(f3,negated_conjecture,(
% 1.41/1.20 ~! [X0 : $tType,X2 : X0 > $o,X3 : X0 > $o] : (! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X2) = ('const/sets/IN' @ X0 @ X4 @ X3)) = (X2 = X3))),
% 1.41/1.20 inference(negated_conjecture,[status(cth)],[f2])).
% 1.41/1.20 thf(f2,conjecture,(
% 1.41/1.20 ! [X0 : $tType,X2 : X0 > $o,X3 : X0 > $o] : (! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X2) = ('const/sets/IN' @ X0 @ X4 @ X3)) = (X2 = X3))),
% 1.41/1.20 file('/export/starexec/sandbox/tmp/tmp.vCeZtj0KwW/DTF2THF_31042.p','thm/sets/EXTENSION_')).
% 1.41/1.20 thf(f43,plain,(
% 1.41/1.20 spl4_4 | ~spl4_2 | spl4_5),
% 1.41/1.20 inference(avatar_split_clause,[status(thm)],[f34,f40,f25,f36])).
% 1.41/1.20 thf(f34,plain,(
% 1.41/1.20 ($true = ('const/sets/IN' @ sK0 @ sK3 @ sK2)) | (sK1 != sK2) | ($true = (sK1 @ sK3))),
% 1.41/1.20 inference(forward_demodulation,[status(thm)],[f16,f13])).
% 1.41/1.20 thf(f16,plain,(
% 1.41/1.20 ($true = ('const/sets/IN' @ sK0 @ sK3 @ sK1)) | ($true = ('const/sets/IN' @ sK0 @ sK3 @ sK2)) | (sK1 != sK2)),
% 1.41/1.20 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.41/1.20 thf(f33,plain,(
% 1.41/1.20 spl4_2 | spl4_3),
% 1.41/1.20 inference(avatar_split_clause,[status(thm)],[f29,f31,f25])).
% 1.41/1.20 thf(f29,plain,(
% 1.41/1.20 ( ! [X4 : sK0] : ((sK1 = sK2) | ($false = (sK1 @ X4)) | ($true = ('const/sets/IN' @ sK0 @ X4 @ sK2))) )),
% 1.41/1.20 inference(forward_demodulation,[status(thm)],[f19,f13])).
% 1.41/1.20 thf(f19,plain,(
% 1.41/1.20 ( ! [X4 : sK0] : ((sK1 = sK2) | (('const/sets/IN' @ sK0 @ X4 @ sK1) = $false) | ($true = ('const/sets/IN' @ sK0 @ X4 @ sK2))) )),
% 1.41/1.20 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.41/1.20 thf(f14,plain,(
% 1.41/1.20 ( ! [X4 : sK0] : ((('const/sets/IN' @ sK0 @ X4 @ sK1) = ('const/sets/IN' @ sK0 @ X4 @ sK2)) | (sK1 = sK2)) )),
% 1.41/1.20 inference(cnf_transformation,[status(thm)],[f12])).
% 1.41/1.20 thf(f28,plain,(
% 1.41/1.20 spl4_1 | spl4_2),
% 1.41/1.20 inference(avatar_split_clause,[status(thm)],[f20,f25,f22])).
% 1.41/1.20 thf(f20,plain,(
% 1.41/1.20 ( ! [X4 : sK0] : ((sK1 = sK2) | ($false = ('const/sets/IN' @ sK0 @ X4 @ sK2)) | ($true = (sK1 @ X4))) )),
% 1.41/1.20 inference(forward_demodulation,[status(thm)],[f18,f13])).
% 1.41/1.20 thf(f18,plain,(
% 1.41/1.20 ( ! [X4 : sK0] : (($true = ('const/sets/IN' @ sK0 @ X4 @ sK1)) | (sK1 = sK2) | ($false = ('const/sets/IN' @ sK0 @ X4 @ sK2))) )),
% 1.41/1.20 inference(binary_proxy_clausification,[status(thm)],[f14])).
% 1.41/1.20 % SZS output end Proof for DTF2THF_31042
% 1.41/1.20 % (31144)------------------------------
% 1.41/1.20 % (31144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.41/1.20 % (31144)Termination reason: Refutation
% 1.41/1.20
% 1.41/1.20 % (31144)Memory used [KB]: 5628
% 1.41/1.20 % (31144)Time elapsed: 0.011 s
% 1.41/1.20 % (31144)Instructions burned: 13 (million)
% 1.41/1.20 % (31144)------------------------------
% 1.41/1.20 % (31144)------------------------------
% 1.41/1.20 % (31138)Success in time 0.024 s
%------------------------------------------------------------------------------