%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV447^1 : 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 : n001.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 1.61s 1.30s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 78 ( 6 unt; 0 typ; 9 def)
% Number of atoms : 575 ( 153 equ; 0 cnn)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 600 ( 137 ~; 138 |; 17 &; 291 @)
% ( 14 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 15 con; 0-3 aty)
% Number of variables : 60 ( 0 ^; 37 !; 23 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
sK1: $tType ).
thf(func_def_0,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
sK0:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_5,type,
sK2: sK1 > $o ).
thf(func_def_6,type,
sK3: sK1 > $o ).
thf(func_def_7,type,
sK4: sK1 ).
thf(func_def_9,type,
ph6:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
sK7: sK1 ).
thf(func_def_12,type,
sK8: sK1 ).
thf(func_def_13,type,
sK9: sK1 ).
thf(f182,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f42,f44,f49,f54,f66,f75,f122,f136,f138,f148,f169,f181]) ).
thf(f181,plain,
( ~ spl5_1
| spl5_2
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f180]) ).
thf(f180,plain,
( $false
| ~ spl5_1
| spl5_2
| ~ spl5_3 ),
inference(subsumption_resolution,[status(thm)],[f177,f36]) ).
thf(f36,plain,
( ( $true
!= ( sK2 @ sK4 ) )
| spl5_2 ),
inference(avatar_component_clause,[status(thm)],[f35]) ).
thf(f35,definition,
( spl5_2
<=> ( $true
= ( sK2 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition]) ).
thf(f177,plain,
( ( $true
= ( sK2 @ sK4 ) )
| ~ spl5_1
| ~ spl5_3 ),
inference(superposition,[status(thm)],[f23,f173]) ).
thf(f173,plain,
( ( ( 'const/sets/IN' @ sK1 @ sK4 @ sK2 )
= $true )
| ~ spl5_1
| ~ spl5_3 ),
inference(superposition,[status(thm)],[f41,f32]) ).
thf(f32,plain,
( ( sK3 = sK2 )
| ~ spl5_1 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f31,definition,
( spl5_1
<=> ( sK3 = sK2 ) ),
introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition]) ).
thf(f41,plain,
( ( $true
= ( 'const/sets/IN' @ sK1 @ sK4 @ sK3 ) )
| ~ spl5_3 ),
inference(avatar_component_clause,[status(thm)],[f39]) ).
thf(f39,definition,
( spl5_3
<=> ( $true
= ( 'const/sets/IN' @ sK1 @ sK4 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition]) ).
thf(f23,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.WLHhUiEQ5c/DTF2THF_28338.p','thm/sets/IN_') ).
thf(f169,plain,
( ~ spl5_4
| spl5_6
| ~ spl5_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f168]) ).
thf(f168,plain,
( $false
| ~ spl5_4
| spl5_6
| ~ spl5_7 ),
inference(subsumption_resolution,[status(thm)],[f166,f65]) ).
thf(f65,plain,
( ( ( sK2 @ sK7 )
= $true )
| ~ spl5_7 ),
inference(avatar_component_clause,[status(thm)],[f63]) ).
thf(f63,definition,
( spl5_7
<=> ( ( sK2 @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_7])],[avatar_definition]) ).
thf(f166,plain,
( ( ( sK2 @ sK7 )
!= $true )
| ~ spl5_4
| spl5_6 ),
inference(trivial_inequality_removal,[status(thm)],[f165]) ).
thf(f165,plain,
( ( $true != $true )
| ( ( sK2 @ sK7 )
!= $true )
| ~ spl5_4
| spl5_6 ),
inference(superposition,[status(thm)],[f60,f157]) ).
thf(f157,plain,
( ! [X0: sK1] :
( ( ( sK3 @ X0 )
= $true )
| ( $true
!= ( sK2 @ X0 ) ) )
| ~ spl5_4 ),
inference(superposition,[status(thm)],[f48,f23]) ).
thf(f48,plain,
( ! [X3: sK1] :
( ( $true
= ( 'const/sets/IN' @ sK1 @ X3 @ sK3 ) )
| ( ( sK2 @ X3 )
!= $true ) )
| ~ spl5_4 ),
inference(avatar_component_clause,[status(thm)],[f47]) ).
thf(f47,definition,
( spl5_4
<=> ! [X3: sK1] :
( ( $true
= ( 'const/sets/IN' @ sK1 @ X3 @ sK3 ) )
| ( ( sK2 @ X3 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition]) ).
thf(f60,plain,
( ( $true
!= ( sK3 @ sK7 ) )
| spl5_6 ),
inference(avatar_component_clause,[status(thm)],[f59]) ).
thf(f59,definition,
( spl5_6
<=> ( $true
= ( sK3 @ sK7 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_6])],[avatar_definition]) ).
thf(f148,plain,
( ~ spl5_1
| ~ spl5_2
| spl5_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f147]) ).
thf(f147,plain,
( $false
| ~ spl5_1
| ~ spl5_2
| spl5_3 ),
inference(subsumption_resolution,[status(thm)],[f146,f37]) ).
thf(f37,plain,
( ( $true
= ( sK2 @ sK4 ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[status(thm)],[f35]) ).
thf(f146,plain,
( ( $true
!= ( sK2 @ sK4 ) )
| ~ spl5_1
| spl5_3 ),
inference(superposition,[status(thm)],[f142,f23]) ).
thf(f142,plain,
( ( ( 'const/sets/IN' @ sK1 @ sK4 @ sK2 )
!= $true )
| ~ spl5_1
| spl5_3 ),
inference(superposition,[status(thm)],[f40,f32]) ).
thf(f40,plain,
( ( $true
!= ( 'const/sets/IN' @ sK1 @ sK4 @ sK3 ) )
| spl5_3 ),
inference(avatar_component_clause,[status(thm)],[f39]) ).
thf(f138,plain,
( ~ spl5_7
| ~ spl5_4
| ~ spl5_9 ),
inference(avatar_split_clause,[status(thm)],[f133,f72,f47,f63]) ).
thf(f72,definition,
( spl5_9
<=> ( $false
= ( sK3 @ sK7 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_9])],[avatar_definition]) ).
thf(f133,plain,
( ( ( sK2 @ sK7 )
!= $true )
| ~ spl5_4
| ~ spl5_9 ),
inference(trivial_inequality_removal,[status(thm)],[f130]) ).
thf(f130,plain,
( ( $false = $true )
| ( ( sK2 @ sK7 )
!= $true )
| ~ spl5_4
| ~ spl5_9 ),
inference(superposition,[status(thm)],[f83,f74]) ).
thf(f74,plain,
( ( $false
= ( sK3 @ sK7 ) )
| ~ spl5_9 ),
inference(avatar_component_clause,[status(thm)],[f72]) ).
thf(f83,plain,
( ! [X0: sK1] :
( ( ( sK3 @ X0 )
= $true )
| ( $true
!= ( sK2 @ X0 ) ) )
| ~ spl5_4 ),
inference(superposition,[status(thm)],[f48,f23]) ).
thf(f136,plain,
( ~ spl5_6
| ~ spl5_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f135]) ).
thf(f135,plain,
( $false
| ~ spl5_6
| ~ spl5_9 ),
inference(trivial_inequality_removal,[status(thm)],[f129]) ).
thf(f129,plain,
( ( $false = $true )
| ~ spl5_6
| ~ spl5_9 ),
inference(superposition,[status(thm)],[f61,f74]) ).
thf(f61,plain,
( ( $true
= ( sK3 @ sK7 ) )
| ~ spl5_6 ),
inference(avatar_component_clause,[status(thm)],[f59]) ).
thf(f122,plain,
( ~ spl5_5
| ~ spl5_6
| ~ spl5_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f121]) ).
thf(f121,plain,
( $false
| ~ spl5_5
| ~ spl5_6
| ~ spl5_8 ),
inference(subsumption_resolution,[status(thm)],[f117,f61]) ).
thf(f117,plain,
( ( $true
!= ( sK3 @ sK7 ) )
| ~ spl5_5
| ~ spl5_8 ),
inference(trivial_inequality_removal,[status(thm)],[f115]) ).
thf(f115,plain,
( ( $false = $true )
| ( $true
!= ( sK3 @ sK7 ) )
| ~ spl5_5
| ~ spl5_8 ),
inference(superposition,[status(thm)],[f70,f96]) ).
thf(f96,plain,
( ! [X0: sK1] :
( ( $true
= ( sK2 @ X0 ) )
| ( ( sK3 @ X0 )
!= $true ) )
| ~ spl5_5 ),
inference(superposition,[status(thm)],[f53,f23]) ).
thf(f53,plain,
( ! [X3: sK1] :
( ( $true
!= ( 'const/sets/IN' @ sK1 @ X3 @ sK3 ) )
| ( ( sK2 @ X3 )
= $true ) )
| ~ spl5_5 ),
inference(avatar_component_clause,[status(thm)],[f52]) ).
thf(f52,definition,
( spl5_5
<=> ! [X3: sK1] :
( ( $true
!= ( 'const/sets/IN' @ sK1 @ X3 @ sK3 ) )
| ( ( sK2 @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl5_5])],[avatar_definition]) ).
thf(f70,plain,
( ( $false
= ( sK2 @ sK7 ) )
| ~ spl5_8 ),
inference(avatar_component_clause,[status(thm)],[f68]) ).
thf(f68,definition,
( spl5_8
<=> ( $false
= ( sK2 @ sK7 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_8])],[avatar_definition]) ).
thf(f75,plain,
( spl5_8
| spl5_9
| spl5_1 ),
inference(avatar_split_clause,[status(thm)],[f57,f31,f72,f68]) ).
thf(f57,plain,
( ( $false
= ( sK3 @ sK7 ) )
| ( $false
= ( sK2 @ sK7 ) )
| spl5_1 ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ( sK2 @ sK7 )
!= ( sK3 @ sK7 ) )
| spl5_1 ),
inference(negative_extensionality,[status(thm)],[f33]) ).
thf(f33,plain,
( ( sK3 != sK2 )
| spl5_1 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f66,plain,
( spl5_6
| spl5_7
| spl5_1 ),
inference(avatar_split_clause,[status(thm)],[f56,f31,f63,f59]) ).
thf(f56,plain,
( ( $true
= ( sK3 @ sK7 ) )
| ( ( sK2 @ sK7 )
= $true )
| spl5_1 ),
inference(binary_proxy_clausification,[status(thm)],[f55]) ).
thf(f54,plain,
( spl5_5
| spl5_1 ),
inference(avatar_split_clause,[status(thm)],[f50,f31,f52]) ).
thf(f50,plain,
! [X3: sK1] :
( ( sK3 = sK2 )
| ( $true
!= ( 'const/sets/IN' @ sK1 @ X3 @ sK3 ) )
| ( ( sK2 @ X3 )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f27,f23]) ).
thf(f27,plain,
! [X3: sK1] :
( ( $true
!= ( 'const/sets/IN' @ sK1 @ X3 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ X3 @ sK2 )
= $true )
| ( sK3 = sK2 ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( sK3 = sK2 )
| ! [X3: sK1] :
( ( ( ( 'const/sets/IN' @ sK1 @ X3 @ sK2 )
= $true )
| ( $true
!= ( 'const/sets/IN' @ sK1 @ X3 @ sK3 ) ) )
& ( ( ( 'const/sets/IN' @ sK1 @ X3 @ sK2 )
!= $true )
| ( $true
= ( 'const/sets/IN' @ sK1 @ X3 @ sK3 ) ) ) ) )
& ( ( sK3 != sK2 )
| ( ( ( $true
= ( 'const/sets/IN' @ sK1 @ sK4 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ sK4 @ sK2 )
= $true ) )
& ( ( ( 'const/sets/IN' @ sK1 @ sK4 @ sK2 )
!= $true )
| ( $true
!= ( 'const/sets/IN' @ sK1 @ sK4 @ sK3 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f17,f19,f18]) ).
thf(f18,plain,
( ? [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( X1 = X2 )
| ! [X3: X0] :
( ( ( $true
= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) )
& ( ( $true
!= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
| ( $true
= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ) ) )
& ( ( X1 != X2 )
| ? [X4: X0] :
( ( ( ( 'const/sets/IN' @ X0 @ X4 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
= $true ) )
& ( ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
!= $true )
| ( ( 'const/sets/IN' @ X0 @ X4 @ X2 )
!= $true ) ) ) ) )
=> ( ( ( sK3 = sK2 )
| ! [X3: sK1] :
( ( ( ( 'const/sets/IN' @ sK1 @ X3 @ sK2 )
= $true )
| ( $true
!= ( 'const/sets/IN' @ sK1 @ X3 @ sK3 ) ) )
& ( ( ( 'const/sets/IN' @ sK1 @ X3 @ sK2 )
!= $true )
| ( $true
= ( 'const/sets/IN' @ sK1 @ X3 @ sK3 ) ) ) ) )
& ( ( sK3 != sK2 )
| ? [X4: sK1] :
( ( ( ( 'const/sets/IN' @ sK1 @ X4 @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ X4 @ sK2 )
= $true ) )
& ( ( ( 'const/sets/IN' @ sK1 @ X4 @ sK2 )
!= $true )
| ( ( 'const/sets/IN' @ sK1 @ X4 @ sK3 )
!= $true ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
( ? [X4: sK1] :
( ( ( ( 'const/sets/IN' @ sK1 @ X4 @ sK3 )
= $true )
| ( ( 'const/sets/IN' @ sK1 @ X4 @ sK2 )
= $true ) )
& ( ( ( 'const/sets/IN' @ sK1 @ X4 @ sK2 )
!= $true )
| ( ( 'const/sets/IN' @ sK1 @ X4 @ sK3 )
!= $true ) ) )
=> ( ( ( $true
= ( 'const/sets/IN' @ sK1 @ sK4 @ sK3 ) )
| ( ( 'const/sets/IN' @ sK1 @ sK4 @ sK2 )
= $true ) )
& ( ( ( 'const/sets/IN' @ sK1 @ sK4 @ sK2 )
!= $true )
| ( $true
!= ( 'const/sets/IN' @ sK1 @ sK4 @ sK3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( X1 = X2 )
| ! [X3: X0] :
( ( ( $true
= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) )
& ( ( $true
!= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
| ( $true
= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ) ) )
& ( ( X1 != X2 )
| ? [X4: X0] :
( ( ( ( 'const/sets/IN' @ X0 @ X4 @ X2 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
= $true ) )
& ( ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
!= $true )
| ( ( 'const/sets/IN' @ X0 @ X4 @ X2 )
!= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( X1 = X2 )
| ! [X3: X0] :
( ( ( $true
= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) )
& ( ( $true
!= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
| ( $true
= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ) ) )
& ( ( X1 != X2 )
| ? [X3: X0] :
( ( ( $true
= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
| ( $true
= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) )
& ( ( $true
!= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
| ( $true
!= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ? [X3: X0] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
<=> ( $true
!= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) )
<~> ( X1 != X2 ) ),
inference(ennf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( X1 != X2 )
<=> ? [X3: X0] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
<=> ( $true
!= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) ) ),
inference(flattening,[status(thm)],[f9]) ).
thf(f9,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ? [X3: X0] :
( ( $true
!= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
<=> ( $true
= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) )
<=> ( X1 != X2 ) ),
inference(fool_elimination,[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 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,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)],[f3]) ).
thf(f3,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.WLHhUiEQ5c/DTF2THF_28338.p','thm/sets/NOT_EQUAL_SETS_') ).
thf(f49,plain,
( spl5_4
| spl5_1 ),
inference(avatar_split_clause,[status(thm)],[f45,f31,f47]) ).
thf(f45,plain,
! [X3: sK1] :
( ( sK3 = sK2 )
| ( $true
= ( 'const/sets/IN' @ sK1 @ X3 @ sK3 ) )
| ( ( sK2 @ X3 )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f26,f23]) ).
thf(f26,plain,
! [X3: sK1] :
( ( ( 'const/sets/IN' @ sK1 @ X3 @ sK2 )
!= $true )
| ( sK3 = sK2 )
| ( $true
= ( 'const/sets/IN' @ sK1 @ X3 @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f44,plain,
( ~ spl5_2
| ~ spl5_1
| ~ spl5_3 ),
inference(avatar_split_clause,[status(thm)],[f43,f39,f31,f35]) ).
thf(f43,plain,
( ( sK3 != sK2 )
| ( $true
!= ( 'const/sets/IN' @ sK1 @ sK4 @ sK3 ) )
| ( $true
!= ( sK2 @ sK4 ) ) ),
inference(forward_demodulation,[status(thm)],[f24,f23]) ).
thf(f24,plain,
( ( ( 'const/sets/IN' @ sK1 @ sK4 @ sK2 )
!= $true )
| ( sK3 != sK2 )
| ( $true
!= ( 'const/sets/IN' @ sK1 @ sK4 @ sK3 ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f42,plain,
( ~ spl5_1
| spl5_2
| spl5_3 ),
inference(avatar_split_clause,[status(thm)],[f29,f39,f35,f31]) ).
thf(f29,plain,
( ( $true
= ( 'const/sets/IN' @ sK1 @ sK4 @ sK3 ) )
| ( $true
= ( sK2 @ sK4 ) )
| ( sK3 != sK2 ) ),
inference(forward_demodulation,[status(thm)],[f25,f23]) ).
thf(f25,plain,
( ( ( 'const/sets/IN' @ sK1 @ sK4 @ sK2 )
= $true )
| ( $true
= ( 'const/sets/IN' @ sK1 @ sK4 @ sK3 ) )
| ( sK3 != sK2 ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV447^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n001.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:47:50 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.44 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SEV447^1 : TPTP v9.2.1. Released v7.0.0.
% 0.19/0.45 % Domain : Analysis
% 0.19/0.45 % Problem : NOT_EQUAL_SETS
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Kal16]
% 0.19/0.45 % Names : NOT_EQUAL_SETS_.p [Kal16]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.00 v7.1.0
% 0.19/0.45 % Syntax : Number of formulae : 4 ( 3 unt; 1 typ; 0 def)
% 0.19/0.45 % Number of atoms : 12 ( 7 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 1 ( 4 avg)
% 0.19/0.45 % Number of connectives : 18 ( 2 ~; 0 |; 0 &; 16 @)
% 0.19/0.45 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 4 ( 4 avg)
% 0.19/0.45 % Number of types : 1 ( 0 usr)
% 0.19/0.45 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 2 ( 1 usr; 0 con; 2-3 aty)
% 0.19/0.45 % Number of variables : 12 ( 0 ^; 10 !; 1 ?; 12 :)
% 0.19/0.45 % ( 1 !>; 0 ?*; 0 @-; 0 @+)
% 0.19/0.45 % SPC : TH1_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : Exported from core HOL Light.
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf('thf_const_const/sets/IN',type,
% 0.19/0.45 'const/sets/IN':
% 0.19/0.45 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf('thm/sets/IN_',axiom,
% 0.19/0.45 ! [A: $tType,P: A > $o,A0: A] :
% 0.19/0.45 ( ( 'const/sets/IN' @ A @ A0 @ P )
% 0.19/0.45 = ( P @ A0 ) ) ).
% 0.19/0.45
% 0.19/0.45 thf('thm/sets/EXTENSION_',axiom,
% 0.19/0.45 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 0.19/0.45 ( ( A0 = A1 )
% 0.19/0.45 = ( ! [A2: A] :
% 0.19/0.45 ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 0.19/0.45 = ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf('thm/sets/NOT_EQUAL_SETS_',conjecture,
% 0.19/0.45 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 0.19/0.45 ( ( A0 != A1 )
% 0.19/0.45 = ( ? [A2: A] :
% 0.19/0.45 ( ( 'const/sets/IN' @ A @ A2 @ A1 )
% 0.19/0.45 = ( ~ ( 'const/sets/IN' @ A @ A2 @ A0 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.45/1.27 ---- Embedded in THF ---
% 1.45/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.27 %%% Generated on Tue Feb 24 12:47:51 EST 2026
% 1.45/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.27 %%% Logic specification used:
% 1.45/1.27 %%% thf(spec, logic, $$dhol).
% 1.45/1.27
% 1.45/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.WLHhUiEQ5c/DTF2DTF28338.p
% See solution above
% 1.45/1.27 ------------------------
% 1.45/1.28 ---- Cleaned THF ---
% 1.45/1.28 thf('thf_const_const/sets/IN',type,
% 1.45/1.28 'const/sets/IN':
% 1.45/1.28 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.45/1.28
% 1.45/1.28 thf('thm/sets/IN_',axiom,
% 1.45/1.28 ! [A: $tType,P: A > $o,A0: A] :
% 1.45/1.28 ( ( 'const/sets/IN' @ A @ A0 @ P )
% 1.45/1.28 = ( P @ A0 ) ) ).
% 1.45/1.28
% 1.45/1.28 thf('thm/sets/EXTENSION_',axiom,
% 1.45/1.28 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 1.45/1.28 ( ( A0 = A1 )
% 1.45/1.28 = ( ! [A2: A] :
% 1.45/1.28 ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 1.45/1.28 = ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
% 1.45/1.28
% 1.45/1.28 thf('thm/sets/NOT_EQUAL_SETS_',conjecture,
% 1.45/1.28 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 1.45/1.28 ( ( A0 != A1 )
% 1.45/1.28 = ( ? [A2: A] :
% 1.45/1.28 ( ( 'const/sets/IN' @ A @ A2 @ A1 )
% 1.45/1.28 = ( ~ ( 'const/sets/IN' @ A @ A2 @ A0 ) ) ) ) ) ).
% 1.45/1.28 ------------------------
% 1.45/1.29 % (28529)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28338 for (3000ds/183Mi)
% 1.45/1.29 % (28531)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_28338 for (3000ds/27Mi)
% 1.45/1.29 % (28534)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_28338 for (3000ds/275Mi)
% 1.61/1.30 % (28533)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_28338 for (3000ds/2Mi)
% 1.61/1.30 % (28532)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28338 for (3000ds/2Mi)
% 1.61/1.30 % Exception at run slice level
% 1.61/1.30 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
% 1.61/1.30 % (28532)Instruction limit reached!
% 1.61/1.30 % (28532)------------------------------
% 1.61/1.30 % (28532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (28532)Termination reason: Unknown
% 1.61/1.30 % (28532)Termination phase: Saturation
% 1.61/1.30
% 1.61/1.30 % (28532)Memory used [KB]: 5500
% 1.61/1.30 % (28532)Time elapsed: 0.003 s
% 1.61/1.30 % (28532)Instructions burned: 2 (million)
% 1.61/1.30 % (28532)------------------------------
% 1.61/1.30 % (28532)------------------------------
% 1.61/1.30 % (28534)First to succeed.
% 1.61/1.30 % (28531)Instruction limit reached!
% 1.61/1.30 % (28531)------------------------------
% 1.61/1.30 % (28531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (28531)Termination reason: Unknown
% 1.61/1.30 % (28531)Termination phase: Saturation
% 1.61/1.30
% 1.61/1.30 % (28531)Memory used [KB]: 5628
% 1.61/1.30 % (28531)Time elapsed: 0.012 s
% 1.61/1.30 % (28531)Instructions burned: 28 (million)
% 1.61/1.30 % (28531)------------------------------
% 1.61/1.30 % (28531)------------------------------
% 1.61/1.30 % (28534)Refutation found. Thanks to Tanya!
% 1.61/1.30 % SZS status Theorem for DTF2THF_28338
% 1.61/1.30 % SZS output start Proof for DTF2THF_28338
% 1.61/1.30 thf(type_def_6, type, sK1: $tType).
% 1.61/1.30 thf(func_def_0, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.61/1.30 thf(func_def_4, type, sK0: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 1.61/1.30 thf(func_def_5, type, sK2: sK1 > $o).
% 1.61/1.30 thf(func_def_6, type, sK3: sK1 > $o).
% 1.61/1.30 thf(func_def_7, type, sK4: sK1).
% 1.61/1.30 thf(func_def_9, type, ph6: !>[X0: $tType]:(X0)).
% 1.61/1.30 thf(func_def_11, type, sK7: sK1).
% 1.61/1.30 thf(func_def_12, type, sK8: sK1).
% 1.61/1.30 thf(func_def_13, type, sK9: sK1).
% 1.61/1.30 thf(f182,plain,(
% 1.61/1.30 $false),
% 1.61/1.30 inference(avatar_sat_refutation,[status(thm)],[f42,f44,f49,f54,f66,f75,f122,f136,f138,f148,f169,f181])).
% 1.61/1.30 thf(f181,plain,(
% 1.61/1.30 ~spl5_1 | spl5_2 | ~spl5_3),
% 1.61/1.30 inference(avatar_contradiction_clause,[status(thm)],[f180])).
% 1.61/1.30 thf(f180,plain,(
% 1.61/1.30 $false | (~spl5_1 | spl5_2 | ~spl5_3)),
% 1.61/1.30 inference(subsumption_resolution,[status(thm)],[f177,f36])).
% 1.61/1.30 thf(f36,plain,(
% 1.61/1.30 ($true != (sK2 @ sK4)) | spl5_2),
% 1.61/1.30 inference(avatar_component_clause,[status(thm)],[f35])).
% 1.61/1.30 thf(f35,definition,(
% 1.61/1.30 spl5_2 <=> ($true = (sK2 @ sK4))),
% 1.61/1.30 introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition])).
% 1.61/1.30 thf(f177,plain,(
% 1.61/1.30 ($true = (sK2 @ sK4)) | (~spl5_1 | ~spl5_3)),
% 1.61/1.30 inference(superposition,[status(thm)],[f23,f173])).
% 1.61/1.30 thf(f173,plain,(
% 1.61/1.30 (('const/sets/IN' @ sK1 @ sK4 @ sK2) = $true) | (~spl5_1 | ~spl5_3)),
% 1.61/1.30 inference(superposition,[status(thm)],[f41,f32])).
% 1.61/1.30 thf(f32,plain,(
% 1.61/1.30 (sK3 = sK2) | ~spl5_1),
% 1.61/1.30 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.61/1.30 thf(f31,definition,(
% 1.61/1.30 spl5_1 <=> (sK3 = sK2)),
% 1.61/1.30 introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition])).
% 1.61/1.30 thf(f41,plain,(
% 1.61/1.30 ($true = ('const/sets/IN' @ sK1 @ sK4 @ sK3)) | ~spl5_3),
% 1.61/1.30 inference(avatar_component_clause,[status(thm)],[f39])).
% 1.61/1.30 thf(f39,definition,(
% 1.61/1.30 spl5_3 <=> ($true = ('const/sets/IN' @ sK1 @ sK4 @ sK3))),
% 1.61/1.30 introduced(definition,[new_symbols(naming,[spl5_3])],[avatar_definition])).
% 1.61/1.30 thf(f23,plain,(
% 1.61/1.30 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X2 @ X1) = (X1 @ X2))) )),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f1])).
% 1.61/1.30 thf(f1,axiom,(
% 1.61/1.30 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : (('const/sets/IN' @ X0 @ X2 @ X1) = (X1 @ X2))),
% 1.61/1.30 file('/export/starexec/sandbox/tmp/tmp.WLHhUiEQ5c/DTF2THF_28338.p','thm/sets/IN_')).
% 1.61/1.30 thf(f169,plain,(
% 1.61/1.30 ~spl5_4 | spl5_6 | ~spl5_7),
% 1.61/1.30 inference(avatar_contradiction_clause,[status(thm)],[f168])).
% 1.61/1.30 thf(f168,plain,(
% 1.61/1.30 $false | (~spl5_4 | spl5_6 | ~spl5_7)),
% 1.61/1.30 inference(subsumption_resolution,[status(thm)],[f166,f65])).
% 1.61/1.30 thf(f65,plain,(
% 1.61/1.30 ((sK2 @ sK7) = $true) | ~spl5_7),
% 1.61/1.30 inference(avatar_component_clause,[status(thm)],[f63])).
% 1.61/1.30 thf(f63,definition,(
% 1.61/1.30 spl5_7 <=> ((sK2 @ sK7) = $true)),
% 1.61/1.30 introduced(definition,[new_symbols(naming,[spl5_7])],[avatar_definition])).
% 1.61/1.30 thf(f166,plain,(
% 1.61/1.30 ((sK2 @ sK7) != $true) | (~spl5_4 | spl5_6)),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f165])).
% 1.61/1.30 thf(f165,plain,(
% 1.61/1.30 ($true != $true) | ((sK2 @ sK7) != $true) | (~spl5_4 | spl5_6)),
% 1.61/1.30 inference(superposition,[status(thm)],[f60,f157])).
% 1.61/1.30 thf(f157,plain,(
% 1.61/1.30 ( ! [X0 : sK1] : (((sK3 @ X0) = $true) | ($true != (sK2 @ X0))) ) | ~spl5_4),
% 1.61/1.30 inference(superposition,[status(thm)],[f48,f23])).
% 1.61/1.30 thf(f48,plain,(
% 1.61/1.30 ( ! [X3 : sK1] : (($true = ('const/sets/IN' @ sK1 @ X3 @ sK3)) | ((sK2 @ X3) != $true)) ) | ~spl5_4),
% 1.61/1.30 inference(avatar_component_clause,[status(thm)],[f47])).
% 1.61/1.30 thf(f47,definition,(
% 1.61/1.30 spl5_4 <=> ! [X3 : sK1] : (($true = ('const/sets/IN' @ sK1 @ X3 @ sK3)) | ((sK2 @ X3) != $true))),
% 1.61/1.30 introduced(definition,[new_symbols(naming,[spl5_4])],[avatar_definition])).
% 1.61/1.30 thf(f60,plain,(
% 1.61/1.30 ($true != (sK3 @ sK7)) | spl5_6),
% 1.61/1.30 inference(avatar_component_clause,[status(thm)],[f59])).
% 1.61/1.30 thf(f59,definition,(
% 1.61/1.30 spl5_6 <=> ($true = (sK3 @ sK7))),
% 1.61/1.30 introduced(definition,[new_symbols(naming,[spl5_6])],[avatar_definition])).
% 1.61/1.30 thf(f148,plain,(
% 1.61/1.30 ~spl5_1 | ~spl5_2 | spl5_3),
% 1.61/1.30 inference(avatar_contradiction_clause,[status(thm)],[f147])).
% 1.61/1.30 thf(f147,plain,(
% 1.61/1.30 $false | (~spl5_1 | ~spl5_2 | spl5_3)),
% 1.61/1.30 inference(subsumption_resolution,[status(thm)],[f146,f37])).
% 1.61/1.30 thf(f37,plain,(
% 1.61/1.30 ($true = (sK2 @ sK4)) | ~spl5_2),
% 1.61/1.30 inference(avatar_component_clause,[status(thm)],[f35])).
% 1.61/1.30 thf(f146,plain,(
% 1.61/1.30 ($true != (sK2 @ sK4)) | (~spl5_1 | spl5_3)),
% 1.61/1.30 inference(superposition,[status(thm)],[f142,f23])).
% 1.61/1.30 thf(f142,plain,(
% 1.61/1.30 (('const/sets/IN' @ sK1 @ sK4 @ sK2) != $true) | (~spl5_1 | spl5_3)),
% 1.61/1.30 inference(superposition,[status(thm)],[f40,f32])).
% 1.61/1.30 thf(f40,plain,(
% 1.61/1.30 ($true != ('const/sets/IN' @ sK1 @ sK4 @ sK3)) | spl5_3),
% 1.61/1.30 inference(avatar_component_clause,[status(thm)],[f39])).
% 1.61/1.30 thf(f138,plain,(
% 1.61/1.30 ~spl5_7 | ~spl5_4 | ~spl5_9),
% 1.61/1.30 inference(avatar_split_clause,[status(thm)],[f133,f72,f47,f63])).
% 1.61/1.30 thf(f72,definition,(
% 1.61/1.30 spl5_9 <=> ($false = (sK3 @ sK7))),
% 1.61/1.30 introduced(definition,[new_symbols(naming,[spl5_9])],[avatar_definition])).
% 1.61/1.30 thf(f133,plain,(
% 1.61/1.30 ((sK2 @ sK7) != $true) | (~spl5_4 | ~spl5_9)),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f130])).
% 1.61/1.30 thf(f130,plain,(
% 1.61/1.30 ($false = $true) | ((sK2 @ sK7) != $true) | (~spl5_4 | ~spl5_9)),
% 1.61/1.30 inference(superposition,[status(thm)],[f83,f74])).
% 1.61/1.30 thf(f74,plain,(
% 1.61/1.30 ($false = (sK3 @ sK7)) | ~spl5_9),
% 1.61/1.30 inference(avatar_component_clause,[status(thm)],[f72])).
% 1.61/1.30 thf(f83,plain,(
% 1.61/1.30 ( ! [X0 : sK1] : (((sK3 @ X0) = $true) | ($true != (sK2 @ X0))) ) | ~spl5_4),
% 1.61/1.30 inference(superposition,[status(thm)],[f48,f23])).
% 1.61/1.30 thf(f136,plain,(
% 1.61/1.30 ~spl5_6 | ~spl5_9),
% 1.61/1.30 inference(avatar_contradiction_clause,[status(thm)],[f135])).
% 1.61/1.30 thf(f135,plain,(
% 1.61/1.30 $false | (~spl5_6 | ~spl5_9)),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f129])).
% 1.61/1.30 thf(f129,plain,(
% 1.61/1.30 ($false = $true) | (~spl5_6 | ~spl5_9)),
% 1.61/1.30 inference(superposition,[status(thm)],[f61,f74])).
% 1.61/1.30 thf(f61,plain,(
% 1.61/1.30 ($true = (sK3 @ sK7)) | ~spl5_6),
% 1.61/1.30 inference(avatar_component_clause,[status(thm)],[f59])).
% 1.61/1.30 thf(f122,plain,(
% 1.61/1.30 ~spl5_5 | ~spl5_6 | ~spl5_8),
% 1.61/1.30 inference(avatar_contradiction_clause,[status(thm)],[f121])).
% 1.61/1.30 thf(f121,plain,(
% 1.61/1.30 $false | (~spl5_5 | ~spl5_6 | ~spl5_8)),
% 1.61/1.30 inference(subsumption_resolution,[status(thm)],[f117,f61])).
% 1.61/1.30 thf(f117,plain,(
% 1.61/1.30 ($true != (sK3 @ sK7)) | (~spl5_5 | ~spl5_8)),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f115])).
% 1.61/1.30 thf(f115,plain,(
% 1.61/1.30 ($false = $true) | ($true != (sK3 @ sK7)) | (~spl5_5 | ~spl5_8)),
% 1.61/1.30 inference(superposition,[status(thm)],[f70,f96])).
% 1.61/1.30 thf(f96,plain,(
% 1.61/1.30 ( ! [X0 : sK1] : (($true = (sK2 @ X0)) | ((sK3 @ X0) != $true)) ) | ~spl5_5),
% 1.61/1.30 inference(superposition,[status(thm)],[f53,f23])).
% 1.61/1.30 thf(f53,plain,(
% 1.61/1.30 ( ! [X3 : sK1] : (($true != ('const/sets/IN' @ sK1 @ X3 @ sK3)) | ((sK2 @ X3) = $true)) ) | ~spl5_5),
% 1.61/1.30 inference(avatar_component_clause,[status(thm)],[f52])).
% 1.61/1.30 thf(f52,definition,(
% 1.61/1.30 spl5_5 <=> ! [X3 : sK1] : (($true != ('const/sets/IN' @ sK1 @ X3 @ sK3)) | ((sK2 @ X3) = $true))),
% 1.61/1.30 introduced(definition,[new_symbols(naming,[spl5_5])],[avatar_definition])).
% 1.61/1.30 thf(f70,plain,(
% 1.61/1.30 ($false = (sK2 @ sK7)) | ~spl5_8),
% 1.61/1.30 inference(avatar_component_clause,[status(thm)],[f68])).
% 1.61/1.30 thf(f68,definition,(
% 1.61/1.30 spl5_8 <=> ($false = (sK2 @ sK7))),
% 1.61/1.30 introduced(definition,[new_symbols(naming,[spl5_8])],[avatar_definition])).
% 1.61/1.30 thf(f75,plain,(
% 1.61/1.30 spl5_8 | spl5_9 | spl5_1),
% 1.61/1.30 inference(avatar_split_clause,[status(thm)],[f57,f31,f72,f68])).
% 1.61/1.30 thf(f57,plain,(
% 1.61/1.30 ($false = (sK3 @ sK7)) | ($false = (sK2 @ sK7)) | spl5_1),
% 1.61/1.30 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.61/1.30 thf(f55,plain,(
% 1.61/1.30 ((sK2 @ sK7) != (sK3 @ sK7)) | spl5_1),
% 1.61/1.30 inference(negative_extensionality,[status(thm)],[f33])).
% 1.61/1.30 thf(f33,plain,(
% 1.61/1.30 (sK3 != sK2) | spl5_1),
% 1.61/1.30 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.61/1.30 thf(f66,plain,(
% 1.61/1.30 spl5_6 | spl5_7 | spl5_1),
% 1.61/1.30 inference(avatar_split_clause,[status(thm)],[f56,f31,f63,f59])).
% 1.61/1.30 thf(f56,plain,(
% 1.61/1.30 ($true = (sK3 @ sK7)) | ((sK2 @ sK7) = $true) | spl5_1),
% 1.61/1.30 inference(binary_proxy_clausification,[status(thm)],[f55])).
% 1.61/1.30 thf(f54,plain,(
% 1.61/1.30 spl5_5 | spl5_1),
% 1.61/1.30 inference(avatar_split_clause,[status(thm)],[f50,f31,f52])).
% 1.61/1.30 thf(f50,plain,(
% 1.61/1.30 ( ! [X3 : sK1] : ((sK3 = sK2) | ($true != ('const/sets/IN' @ sK1 @ X3 @ sK3)) | ((sK2 @ X3) = $true)) )),
% 1.61/1.30 inference(forward_demodulation,[status(thm)],[f27,f23])).
% 1.61/1.30 thf(f27,plain,(
% 1.61/1.30 ( ! [X3 : sK1] : (($true != ('const/sets/IN' @ sK1 @ X3 @ sK3)) | (('const/sets/IN' @ sK1 @ X3 @ sK2) = $true) | (sK3 = sK2)) )),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f20])).
% 1.61/1.30 thf(f20,plain,(
% 1.61/1.30 ((sK3 = sK2) | ! [X3 : sK1] : (((('const/sets/IN' @ sK1 @ X3 @ sK2) = $true) | ($true != ('const/sets/IN' @ sK1 @ X3 @ sK3))) & ((('const/sets/IN' @ sK1 @ X3 @ sK2) != $true) | ($true = ('const/sets/IN' @ sK1 @ X3 @ sK3))))) & ((sK3 != sK2) | ((($true = ('const/sets/IN' @ sK1 @ sK4 @ sK3)) | (('const/sets/IN' @ sK1 @ sK4 @ sK2) = $true)) & ((('const/sets/IN' @ sK1 @ sK4 @ sK2) != $true) | ($true != ('const/sets/IN' @ sK1 @ sK4 @ sK3)))))),
% 1.61/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f17,f19,f18])).
% 1.61/1.30 thf(f18,plain,(
% 1.61/1.30 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (((X1 = X2) | ! [X3 : X0] : ((($true = ('const/sets/IN' @ X0 @ X3 @ X1)) | ($true != ('const/sets/IN' @ X0 @ X3 @ X2))) & (($true != ('const/sets/IN' @ X0 @ X3 @ X1)) | ($true = ('const/sets/IN' @ X0 @ X3 @ X2))))) & ((X1 != X2) | ? [X4 : X0] : (((('const/sets/IN' @ X0 @ X4 @ X2) = $true) | (('const/sets/IN' @ X0 @ X4 @ X1) = $true)) & ((('const/sets/IN' @ X0 @ X4 @ X1) != $true) | (('const/sets/IN' @ X0 @ X4 @ X2) != $true))))) => (((sK3 = sK2) | ! [X3 : sK1] : (((('const/sets/IN' @ sK1 @ X3 @ sK2) = $true) | ($true != ('const/sets/IN' @ sK1 @ X3 @ sK3))) & ((('const/sets/IN' @ sK1 @ X3 @ sK2) != $true) | ($true = ('const/sets/IN' @ sK1 @ X3 @ sK3))))) & ((sK3 != sK2) | ? [X4 : sK1] : (((('const/sets/IN' @ sK1 @ X4 @ sK3) = $true) | (('const/sets/IN' @ sK1 @ X4 @ sK2) = $true)) & ((('const/sets/IN' @ sK1 @ X4 @ sK2) != $true) | (('const/sets/IN' @ sK1 @ X4 @ sK3) != $true)))))),
% 1.61/1.30 introduced(definition,[],[choice_axiom])).
% 1.61/1.30 thf(f19,plain,(
% 1.61/1.30 ? [X4 : sK1] : (((('const/sets/IN' @ sK1 @ X4 @ sK3) = $true) | (('const/sets/IN' @ sK1 @ X4 @ sK2) = $true)) & ((('const/sets/IN' @ sK1 @ X4 @ sK2) != $true) | (('const/sets/IN' @ sK1 @ X4 @ sK3) != $true))) => ((($true = ('const/sets/IN' @ sK1 @ sK4 @ sK3)) | (('const/sets/IN' @ sK1 @ sK4 @ sK2) = $true)) & ((('const/sets/IN' @ sK1 @ sK4 @ sK2) != $true) | ($true != ('const/sets/IN' @ sK1 @ sK4 @ sK3))))),
% 1.61/1.30 introduced(definition,[],[choice_axiom])).
% 1.61/1.30 thf(f17,plain,(
% 1.61/1.30 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (((X1 = X2) | ! [X3 : X0] : ((($true = ('const/sets/IN' @ X0 @ X3 @ X1)) | ($true != ('const/sets/IN' @ X0 @ X3 @ X2))) & (($true != ('const/sets/IN' @ X0 @ X3 @ X1)) | ($true = ('const/sets/IN' @ X0 @ X3 @ X2))))) & ((X1 != X2) | ? [X4 : X0] : (((('const/sets/IN' @ X0 @ X4 @ X2) = $true) | (('const/sets/IN' @ X0 @ X4 @ X1) = $true)) & ((('const/sets/IN' @ X0 @ X4 @ X1) != $true) | (('const/sets/IN' @ X0 @ X4 @ X2) != $true)))))),
% 1.61/1.30 inference(rectify,[status(thm)],[f16])).
% 1.61/1.30 thf(f16,plain,(
% 1.61/1.30 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (((X1 = X2) | ! [X3 : X0] : ((($true = ('const/sets/IN' @ X0 @ X3 @ X1)) | ($true != ('const/sets/IN' @ X0 @ X3 @ X2))) & (($true != ('const/sets/IN' @ X0 @ X3 @ X1)) | ($true = ('const/sets/IN' @ X0 @ X3 @ X2))))) & ((X1 != X2) | ? [X3 : X0] : ((($true = ('const/sets/IN' @ X0 @ X3 @ X2)) | ($true = ('const/sets/IN' @ X0 @ X3 @ X1))) & (($true != ('const/sets/IN' @ X0 @ X3 @ X1)) | ($true != ('const/sets/IN' @ X0 @ X3 @ X2))))))),
% 1.61/1.30 inference(nnf_transformation,[status(thm)],[f11])).
% 1.61/1.30 thf(f11,plain,(
% 1.61/1.30 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (? [X3 : X0] : (($true = ('const/sets/IN' @ X0 @ X3 @ X2)) <=> ($true != ('const/sets/IN' @ X0 @ X3 @ X1))) <~> (X1 != X2))),
% 1.61/1.30 inference(ennf_transformation,[status(thm)],[f10])).
% 1.61/1.30 thf(f10,plain,(
% 1.61/1.30 ~! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((X1 != X2) <=> ? [X3 : X0] : (($true = ('const/sets/IN' @ X0 @ X3 @ X2)) <=> ($true != ('const/sets/IN' @ X0 @ X3 @ X1))))),
% 1.61/1.30 inference(flattening,[status(thm)],[f9])).
% 1.61/1.30 thf(f9,plain,(
% 1.61/1.30 ~! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (? [X3 : X0] : (~($true = ('const/sets/IN' @ X0 @ X3 @ X1)) <=> ($true = ('const/sets/IN' @ X0 @ X3 @ X2))) <=> (X1 != X2))),
% 1.61/1.30 inference(fool_elimination,[status(thm)],[f8])).
% 1.61/1.30 thf(f8,plain,(
% 1.61/1.30 ~! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (? [X3 : X0] : (~('const/sets/IN' @ X0 @ X3 @ X1) = ('const/sets/IN' @ X0 @ X3 @ X2)) = (X1 != X2))),
% 1.61/1.30 inference(rectify,[status(thm)],[f4])).
% 1.61/1.30 thf(f4,negated_conjecture,(
% 1.61/1.30 ~! [X0 : $tType,X2 : X0 > $o,X3 : X0 > $o] : (? [X4 : X0] : (~('const/sets/IN' @ X0 @ X4 @ X2) = ('const/sets/IN' @ X0 @ X4 @ X3)) = (X2 != X3))),
% 1.61/1.30 inference(negated_conjecture,[status(cth)],[f3])).
% 1.61/1.30 thf(f3,conjecture,(
% 1.61/1.30 ! [X0 : $tType,X2 : X0 > $o,X3 : X0 > $o] : (? [X4 : X0] : (~('const/sets/IN' @ X0 @ X4 @ X2) = ('const/sets/IN' @ X0 @ X4 @ X3)) = (X2 != X3))),
% 1.61/1.30 file('/export/starexec/sandbox/tmp/tmp.WLHhUiEQ5c/DTF2THF_28338.p','thm/sets/NOT_EQUAL_SETS_')).
% 1.61/1.30 thf(f49,plain,(
% 1.61/1.30 spl5_4 | spl5_1),
% 1.61/1.30 inference(avatar_split_clause,[status(thm)],[f45,f31,f47])).
% 1.61/1.30 thf(f45,plain,(
% 1.61/1.30 ( ! [X3 : sK1] : ((sK3 = sK2) | ($true = ('const/sets/IN' @ sK1 @ X3 @ sK3)) | ((sK2 @ X3) != $true)) )),
% 1.61/1.30 inference(forward_demodulation,[status(thm)],[f26,f23])).
% 1.61/1.30 thf(f26,plain,(
% 1.61/1.30 ( ! [X3 : sK1] : ((('const/sets/IN' @ sK1 @ X3 @ sK2) != $true) | (sK3 = sK2) | ($true = ('const/sets/IN' @ sK1 @ X3 @ sK3))) )),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f20])).
% 1.61/1.30 thf(f44,plain,(
% 1.61/1.30 ~spl5_2 | ~spl5_1 | ~spl5_3),
% 1.61/1.30 inference(avatar_split_clause,[status(thm)],[f43,f39,f31,f35])).
% 1.61/1.30 thf(f43,plain,(
% 1.61/1.30 (sK3 != sK2) | ($true != ('const/sets/IN' @ sK1 @ sK4 @ sK3)) | ($true != (sK2 @ sK4))),
% 1.61/1.30 inference(forward_demodulation,[status(thm)],[f24,f23])).
% 1.61/1.30 thf(f24,plain,(
% 1.61/1.30 (('const/sets/IN' @ sK1 @ sK4 @ sK2) != $true) | (sK3 != sK2) | ($true != ('const/sets/IN' @ sK1 @ sK4 @ sK3))),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f20])).
% 1.61/1.30 thf(f42,plain,(
% 1.61/1.30 ~spl5_1 | spl5_2 | spl5_3),
% 1.61/1.30 inference(avatar_split_clause,[status(thm)],[f29,f39,f35,f31])).
% 1.61/1.30 thf(f29,plain,(
% 1.61/1.30 ($true = ('const/sets/IN' @ sK1 @ sK4 @ sK3)) | ($true = (sK2 @ sK4)) | (sK3 != sK2)),
% 1.61/1.30 inference(forward_demodulation,[status(thm)],[f25,f23])).
% 1.61/1.30 thf(f25,plain,(
% 1.61/1.30 (('const/sets/IN' @ sK1 @ sK4 @ sK2) = $true) | ($true = ('const/sets/IN' @ sK1 @ sK4 @ sK3)) | (sK3 != sK2)),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f20])).
% 1.61/1.30 % SZS output end Proof for DTF2THF_28338
% 1.61/1.30 % (28534)------------------------------
% 1.61/1.30 % (28534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (28534)Termination reason: Refutation
% 1.61/1.30
% 1.61/1.30 % (28534)Memory used [KB]: 5628
% 1.61/1.30 % (28534)Time elapsed: 0.011 s
% 1.61/1.30 % (28534)Instructions burned: 21 (million)
% 1.61/1.30 % (28534)------------------------------
% 1.61/1.30 % (28534)------------------------------
% 1.61/1.30 % (28528)Success in time 0.008 s
%------------------------------------------------------------------------------