%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV504^1 : 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 09:41:24 AM UTC 2026
% Result : Theorem 1.89s 1.65s
% Output : Refutation 1.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 9
% Syntax : Number of formulae : 92 ( 13 unt; 0 typ; 2 def)
% Number of atoms : 793 ( 191 equ; 0 cnn)
% Maximal formula atoms : 7 ( 8 avg)
% Number of connectives : 1231 ( 91 ~; 122 |; 33 &; 954 @)
% ( 2 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 141 ( 141 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 16 usr; 6 con; 0-4 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 215 ( 6 ^; 194 !; 15 ?; 215 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/nums/num': $tType ).
thf(type_def_7,type,
sK0: $tType ).
thf(func_def_0,type,
'type/nums/num': $tType ).
thf(func_def_1,type,
'const/sets/SUBSET':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
'const/sets/DIFF':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_5,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_6,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_7,type,
'const/iterate/nsum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/nums/num' ) > 'type/nums/num' ) ).
thf(func_def_8,type,
'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_18,type,
sK1: sK0 > $o ).
thf(func_def_19,type,
sK2: sK0 > $o ).
thf(func_def_20,type,
sK3: sK0 > 'type/nums/num' ).
thf(func_def_21,type,
sK4:
!>[X0: $tType] : ( ( X0 > 'type/nums/num' ) > ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_23,type,
sK6:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_24,type,
ph7:
!>[X0: $tType] : X0 ).
thf(f429,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f66,f75,f428]) ).
thf(f428,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f427]) ).
thf(f427,plain,
( $false
| ~ spl5_1
| ~ spl5_2 ),
inference(trivial_inequality_removal,[status(thm)],[f423]) ).
thf(f423,plain,
( ( $true = $false )
| ~ spl5_1
| ~ spl5_2 ),
inference(superposition,[status(thm)],[f421,f87]) ).
thf(f87,plain,
( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ sK0 @ sK1 @ sK3 ) @ ( 'const/iterate/nsum' @ sK0 @ sK2 @ sK3 ) )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f86]) ).
thf(f86,plain,
( ( $true != $true )
| ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ sK0 @ sK1 @ sK3 ) @ ( 'const/iterate/nsum' @ sK0 @ sK2 @ sK3 ) )
= $false ) ),
inference(fool_paramodulation,[status(thm)],[f32]) ).
thf(f32,plain,
( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ sK0 @ sK1 @ sK3 ) @ ( 'const/iterate/nsum' @ sK0 @ sK2 @ sK3 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ sK0 @ sK1 @ sK3 ) @ ( 'const/iterate/nsum' @ sK0 @ sK2 @ sK3 ) )
!= $true )
& ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
= $true )
& ( ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f21,f24]) ).
thf(f24,plain,
( ? [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > 'type/nums/num'] :
( ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ X0 @ X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ X2 @ X3 ) )
!= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
& ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true ) )
=> ( ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ sK0 @ sK1 @ sK3 ) @ ( 'const/iterate/nsum' @ sK0 @ sK2 @ sK3 ) )
!= $true )
& ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
= $true )
& ( ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > 'type/nums/num'] :
( ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ X0 @ X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ X2 @ X3 ) )
!= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
& ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true ) ),
inference(flattening,[status(thm)],[f20]) ).
thf(f20,plain,
? [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > 'type/nums/num'] :
( ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ X0 @ X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ X2 @ X3 ) )
!= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
& ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > 'type/nums/num'] :
( ( ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
& ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true ) )
=> ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ X0 @ X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ X2 @ X3 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > 'type/nums/num'] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X2 ) )
=> ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ X0 @ X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ X2 @ X3 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > 'type/nums/num'] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X2 ) )
=> ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ X0 @ X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ X2 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > 'type/nums/num'] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X2 ) )
=> ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ X0 @ X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0D0tWxMeC6/DTF2THF_1241.p','thm/iterate/NSUM_SUBSET_SIMPLE_') ).
thf(f421,plain,
( ! [X0: sK0 > 'type/nums/num'] :
( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ sK0 @ sK1 @ X0 ) @ ( 'const/iterate/nsum' @ sK0 @ sK2 @ X0 ) )
= $true )
| ~ spl5_1
| ~ spl5_2 ),
inference(trivial_inequality_removal,[status(thm)],[f420]) ).
thf(f420,plain,
( ! [X0: sK0 > 'type/nums/num'] :
( ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ sK0 @ sK1 @ X0 ) @ ( 'const/iterate/nsum' @ sK0 @ sK2 @ X0 ) )
= $true )
| ( $true != $true ) )
| ~ spl5_1
| ~ spl5_2 ),
inference(forward_demodulation,[status(thm)],[f419,f60]) ).
thf(f60,plain,
( ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
= $true )
| ~ spl5_1 ),
inference(avatar_component_clause,[status(thm)],[f59]) ).
thf(f59,definition,
( spl5_1
<=> ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition]) ).
thf(f419,plain,
( ! [X0: sK0 > 'type/nums/num'] :
( ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
!= $true )
| ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ sK0 @ sK1 @ X0 ) @ ( 'const/iterate/nsum' @ sK0 @ sK2 @ X0 ) )
= $true ) )
| ~ spl5_1
| ~ spl5_2 ),
inference(trivial_inequality_removal,[status(thm)],[f418]) ).
thf(f418,plain,
( ! [X0: sK0 > 'type/nums/num'] :
( ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
!= $true )
| ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ sK0 @ sK1 @ X0 ) @ ( 'const/iterate/nsum' @ sK0 @ sK2 @ X0 ) )
= $true )
| ( $true != $true ) )
| ~ spl5_1
| ~ spl5_2 ),
inference(forward_demodulation,[status(thm)],[f415,f65]) ).
thf(f65,plain,
( ( $true
= ( 'const/sets/FINITE' @ sK0 @ sK1 ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[status(thm)],[f63]) ).
thf(f63,definition,
( spl5_2
<=> ( $true
= ( 'const/sets/FINITE' @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition]) ).
thf(f415,plain,
( ! [X0: sK0 > 'type/nums/num'] :
( ( $true
!= ( 'const/sets/FINITE' @ sK0 @ sK1 ) )
| ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ sK0 @ sK1 @ X0 ) @ ( 'const/iterate/nsum' @ sK0 @ sK2 @ X0 ) )
= $true )
| ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
!= $true ) )
| ~ spl5_1
| ~ spl5_2 ),
inference(trivial_inequality_removal,[status(thm)],[f414]) ).
thf(f414,plain,
( ! [X0: sK0 > 'type/nums/num'] :
( ( $true = $false )
| ( $true
!= ( 'const/sets/FINITE' @ sK0 @ sK1 ) )
| ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
!= $true )
| ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ sK0 @ sK1 @ X0 ) @ ( 'const/iterate/nsum' @ sK0 @ sK2 @ X0 ) )
= $true ) )
| ~ spl5_1
| ~ spl5_2 ),
inference(duplicate_literal_removal,[status(thm)],[f398]) ).
thf(f398,plain,
( ! [X0: sK0 > 'type/nums/num'] :
( ( $true
!= ( 'const/sets/FINITE' @ sK0 @ sK1 ) )
| ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ sK0 @ sK1 @ X0 ) @ ( 'const/iterate/nsum' @ sK0 @ sK2 @ X0 ) )
= $true )
| ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
!= $true )
| ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ sK0 @ sK1 @ X0 ) @ ( 'const/iterate/nsum' @ sK0 @ sK2 @ X0 ) )
= $true )
| ( $true = $false ) )
| ~ spl5_1
| ~ spl5_2 ),
inference(superposition,[status(thm)],[f390,f35]) ).
thf(f35,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > 'type/nums/num',X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ ( sK4 @ X0 @ X3 @ X2 @ X1 ) @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true )
| ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ X0 @ X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ X2 @ X3 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > 'type/nums/num'] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true )
| ( ( ( 'const/sets/IN' @ X0 @ ( sK4 @ X0 @ X3 @ X2 @ X1 ) @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
= $true )
& ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
!= ( X3 @ ( sK4 @ X0 @ X3 @ X2 @ X1 ) ) ) )
| ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ X0 @ X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ X2 @ X3 ) )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f19,f26]) ).
thf(f26,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > 'type/nums/num'] :
( ? [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
= $true )
& ( ( X3 @ X4 )
!= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
=> ( ( ( 'const/sets/IN' @ X0 @ ( sK4 @ X0 @ X3 @ X2 @ X1 ) @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
= $true )
& ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
!= ( X3 @ ( sK4 @ X0 @ X3 @ X2 @ X1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > 'type/nums/num'] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true )
| ? [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
= $true )
& ( ( X3 @ X4 )
!= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
| ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ X0 @ X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ X2 @ X3 ) )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > 'type/nums/num'] :
( ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ X0 @ X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ X2 @ X3 ) )
= $true )
| ? [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
= $true )
& ( ( X3 @ X4 )
!= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > 'type/nums/num'] :
( ( ! [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
= $true )
=> ( ( X3 @ X4 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
& ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
& ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) )
=> ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ X0 @ X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ X2 @ X3 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > 'type/nums/num'] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X1 )
& ! [X4: X0] :
( ( 'const/sets/IN' @ X0 @ X4 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
=> ( ( X3 @ X4 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) )
=> ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ X0 @ X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ X2 @ X3 ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0 > 'type/nums/num'] :
( ( ( 'const/sets/FINITE' @ X0 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X1 )
& ! [X4: X0] :
( ( 'const/sets/IN' @ X0 @ X4 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
=> ( ( X3 @ X4 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) )
=> ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ X0 @ X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0D0tWxMeC6/DTF2THF_1241.p','thm/iterate/NSUM_SUBSET_') ).
thf(f390,plain,
( ! [X2: sK0 > $o,X0: sK0 > 'type/nums/num'] :
( ( ( 'const/sets/IN' @ sK0 @ ( sK4 @ sK0 @ X0 @ sK2 @ sK1 ) @ X2 )
= $false )
| ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ sK0 @ sK1 @ X0 ) @ ( 'const/iterate/nsum' @ sK0 @ sK2 @ X0 ) )
= $true ) )
| ~ spl5_1
| ~ spl5_2 ),
inference(trivial_inequality_removal,[status(thm)],[f376]) ).
thf(f376,plain,
( ! [X2: sK0 > $o,X0: sK0 > 'type/nums/num'] :
( ( $true = $false )
| ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ sK0 @ sK1 @ X0 ) @ ( 'const/iterate/nsum' @ sK0 @ sK2 @ X0 ) )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK4 @ sK0 @ X0 @ sK2 @ sK1 ) @ X2 )
= $false ) )
| ~ spl5_1
| ~ spl5_2 ),
inference(superposition,[status(thm)],[f369,f40]) ).
thf(f40,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
= $false )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
= $false )
| ( ( ~ ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( ~ ( 'const/sets/IN' @ X0 @ X3 @ X2 )
& ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
= ( ~ ( 'const/sets/IN' @ X0 @ X3 @ X2 )
& ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
= ( ~ ( 'const/sets/IN' @ X0 @ X3 @ X2 )
& ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
& ~ ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
& ~ ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.0D0tWxMeC6/DTF2THF_1241.p','thm/sets/IN_DIFF_') ).
thf(f369,plain,
( ! [X0: sK0 > 'type/nums/num',X1: sK0 > $o] :
( ( ( 'const/sets/IN' @ sK0 @ ( sK4 @ sK0 @ X0 @ sK2 @ sK1 ) @ X1 )
= $true )
| ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ sK0 @ sK1 @ X0 ) @ ( 'const/iterate/nsum' @ sK0 @ sK2 @ X0 ) )
= $true ) )
| ~ spl5_1
| ~ spl5_2 ),
inference(trivial_inequality_removal,[status(thm)],[f368]) ).
thf(f368,plain,
( ! [X0: sK0 > 'type/nums/num',X1: sK0 > $o] :
( ( ( 'const/sets/IN' @ sK0 @ ( sK4 @ sK0 @ X0 @ sK2 @ sK1 ) @ X1 )
= $true )
| ( $true != $true )
| ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ sK0 @ sK1 @ X0 ) @ ( 'const/iterate/nsum' @ sK0 @ sK2 @ X0 ) )
= $true ) )
| ~ spl5_1
| ~ spl5_2 ),
inference(forward_demodulation,[status(thm)],[f367,f65]) ).
thf(f367,plain,
( ! [X0: sK0 > 'type/nums/num',X1: sK0 > $o] :
( ( $true
!= ( 'const/sets/FINITE' @ sK0 @ sK1 ) )
| ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ sK0 @ sK1 @ X0 ) @ ( 'const/iterate/nsum' @ sK0 @ sK2 @ X0 ) )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK4 @ sK0 @ X0 @ sK2 @ sK1 ) @ X1 )
= $true ) )
| ~ spl5_1 ),
inference(trivial_inequality_removal,[status(thm)],[f366]) ).
thf(f366,plain,
( ! [X0: sK0 > 'type/nums/num',X1: sK0 > $o] :
( ( $true
!= ( 'const/sets/FINITE' @ sK0 @ sK1 ) )
| ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ sK0 @ sK1 @ X0 ) @ ( 'const/iterate/nsum' @ sK0 @ sK2 @ X0 ) )
= $true )
| ( $true != $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK4 @ sK0 @ X0 @ sK2 @ sK1 ) @ X1 )
= $true ) )
| ~ spl5_1 ),
inference(forward_demodulation,[status(thm)],[f364,f60]) ).
thf(f364,plain,
! [X0: sK0 > 'type/nums/num',X1: sK0 > $o] :
( ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ sK0 @ sK1 @ X0 ) @ ( 'const/iterate/nsum' @ sK0 @ sK2 @ X0 ) )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ ( sK4 @ sK0 @ X0 @ sK2 @ sK1 ) @ X1 )
= $true )
| ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
!= $true )
| ( $true
!= ( 'const/sets/FINITE' @ sK0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f349]) ).
thf(f349,plain,
! [X0: sK0 > 'type/nums/num',X1: sK0 > $o] :
( ( $true = $false )
| ( ( 'const/sets/IN' @ sK0 @ ( sK4 @ sK0 @ X0 @ sK2 @ sK1 ) @ X1 )
= $true )
| ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
!= $true )
| ( $true
!= ( 'const/sets/FINITE' @ sK0 @ sK1 ) )
| ( ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ sK0 @ sK1 @ X0 ) @ ( 'const/iterate/nsum' @ sK0 @ sK2 @ X0 ) )
= $true ) ),
inference(superposition,[status(thm)],[f302,f35]) ).
thf(f302,plain,
! [X0: sK0 > $o,X1: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X1 @ ( 'const/sets/DIFF' @ sK0 @ sK1 @ sK2 ) )
= $false )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f293]) ).
thf(f293,plain,
! [X0: sK0 > $o,X1: sK0] :
( ( ( 'const/sets/IN' @ sK0 @ X1 @ X0 )
= $true )
| ( ( 'const/sets/IN' @ sK0 @ X1 @ ( 'const/sets/DIFF' @ sK0 @ sK1 @ sK2 ) )
= $false )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f291,f47]) ).
thf(f47,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $false )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= $false )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f46]) ).
thf(f46,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)],[f45]) ).
thf(f45,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( $true
= ( ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
=> ( 'const/sets/IN' @ X0 @ Y0 @ X2 ) )
@ X3 ) )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f44]) ).
thf(f44,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)],[f33]) ).
thf(f33,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
=> ( 'const/sets/IN' @ X0 @ Y0 @ X2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
=> ( 'const/sets/IN' @ X0 @ Y0 @ X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= ( ! [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
=> ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= ( ! [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
=> ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0D0tWxMeC6/DTF2THF_1241.p','thm/sets/SUBSET_') ).
thf(f291,plain,
! [X0: sK0 > $o] :
( $true
= ( 'const/sets/SUBSET' @ sK0 @ ( 'const/sets/DIFF' @ sK0 @ sK1 @ sK2 ) @ X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f290]) ).
thf(f290,plain,
! [X0: sK0 > $o] :
( ( $true = $false )
| ( $true
= ( 'const/sets/SUBSET' @ sK0 @ ( 'const/sets/DIFF' @ sK0 @ sK1 @ sK2 ) @ X0 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f285]) ).
thf(f285,plain,
! [X0: sK0 > $o] :
( ( $true
= ( 'const/sets/SUBSET' @ sK0 @ ( 'const/sets/DIFF' @ sK0 @ sK1 @ sK2 ) @ X0 ) )
| ( $true
= ( 'const/sets/SUBSET' @ sK0 @ ( 'const/sets/DIFF' @ sK0 @ sK1 @ sK2 ) @ X0 ) )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f143,f243]) ).
thf(f243,plain,
! [X0: sK0 > $o,X1: sK0 > $o] :
( ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ ( 'const/sets/DIFF' @ sK0 @ X0 @ sK2 ) @ X1 ) @ sK1 )
= $false )
| ( $true
= ( 'const/sets/SUBSET' @ sK0 @ ( 'const/sets/DIFF' @ sK0 @ X0 @ sK2 ) @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f233]) ).
thf(f233,plain,
! [X0: sK0 > $o,X1: sK0 > $o] :
( ( $true = $false )
| ( $true
= ( 'const/sets/SUBSET' @ sK0 @ ( 'const/sets/DIFF' @ sK0 @ X0 @ sK2 ) @ X1 ) )
| ( ( 'const/sets/IN' @ sK0 @ ( sK6 @ sK0 @ ( 'const/sets/DIFF' @ sK0 @ X0 @ sK2 ) @ X1 ) @ sK1 )
= $false ) ),
inference(superposition,[status(thm)],[f153,f113]) ).
thf(f113,plain,
! [X0: sK0] :
( ( $true
= ( 'const/sets/IN' @ sK0 @ X0 @ sK2 ) )
| ( ( 'const/sets/IN' @ sK0 @ X0 @ sK1 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f105]) ).
thf(f105,plain,
! [X0: sK0] :
( ( $true = $false )
| ( ( 'const/sets/IN' @ sK0 @ X0 @ sK1 )
= $false )
| ( $true
= ( 'const/sets/IN' @ sK0 @ X0 @ sK2 ) ) ),
inference(superposition,[status(thm)],[f47,f30]) ).
thf(f30,plain,
( ( 'const/sets/SUBSET' @ sK0 @ sK1 @ sK2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f153,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ ( sK6 @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) @ X3 ) @ X2 )
= $false )
| ( ( 'const/sets/SUBSET' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f148]) ).
thf(f148,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) @ X3 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ ( sK6 @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) @ X3 ) @ X2 )
= $false )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f40,f51]) ).
thf(f51,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ ( sK6 @ X0 @ X1 @ X2 ) @ X1 )
= $true )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f49]) ).
thf(f49,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true )
| ( $false
= ( ( 'const/sets/IN' @ X0 @ ( sK6 @ X0 @ X1 @ X2 ) @ X1 )
=> ( 'const/sets/IN' @ X0 @ ( sK6 @ X0 @ X1 @ X2 ) @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f48]) ).
thf(f48,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true )
| ( ( ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
=> ( 'const/sets/IN' @ X0 @ Y0 @ X2 ) )
@ ( sK6 @ X0 @ X1 @ X2 ) )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true )
| ( ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
=> ( 'const/sets/IN' @ X0 @ Y0 @ X2 ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f33]) ).
thf(f143,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ ( sK6 @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) @ X3 ) @ X1 )
= $true )
| ( ( 'const/sets/SUBSET' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f139]) ).
thf(f139,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0 > $o] :
( ( $true = $false )
| ( ( 'const/sets/SUBSET' @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) @ X3 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ ( sK6 @ X0 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) @ X3 ) @ X1 )
= $true ) ),
inference(superposition,[status(thm)],[f38,f51]) ).
thf(f38,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/DIFF' @ X0 @ X1 @ X2 ) )
= $false )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f75,plain,
spl5_1,
inference(avatar_contradiction_clause,[status(thm)],[f74]) ).
thf(f74,plain,
( $false
| spl5_1 ),
inference(trivial_inequality_removal,[status(thm)],[f73]) ).
thf(f73,plain,
( ( $true = $false )
| spl5_1 ),
inference(backward_demodulation,[status(thm)],[f31,f71]) ).
thf(f71,plain,
( ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
= $false )
| spl5_1 ),
inference(trivial_inequality_removal,[status(thm)],[f67]) ).
thf(f67,plain,
( ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
= $false )
| ( $true != $true )
| spl5_1 ),
inference(fool_paramodulation,[status(thm)],[f61]) ).
thf(f61,plain,
( ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
!= $true )
| spl5_1 ),
inference(avatar_component_clause,[status(thm)],[f59]) ).
thf(f31,plain,
( ( 'const/sets/FINITE' @ sK0 @ sK2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f66,plain,
( ~ spl5_1
| spl5_2 ),
inference(avatar_split_clause,[status(thm)],[f57,f63,f59]) ).
thf(f57,plain,
( ( $true
= ( 'const/sets/FINITE' @ sK0 @ sK1 ) )
| ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ( 'const/sets/FINITE' @ sK0 @ sK2 )
!= $true )
| ( $true
= ( 'const/sets/FINITE' @ sK0 @ sK1 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f29,f30]) ).
thf(f29,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true ) ),
inference(flattening,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X2 )
!= $true )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true )
& ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true ) )
=> ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X2 ) )
=> ( 'const/sets/FINITE' @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X2 ) )
=> ( 'const/sets/FINITE' @ X0 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.0D0tWxMeC6/DTF2THF_1241.p','thm/sets/FINITE_SUBSET_') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV504^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.32 % Computer : n001.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue Feb 24 12:49:05 EST 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.43 ---- Original DTF file ---
% 0.18/0.43 thf(spec,logic,$$dhol).
% 0.18/0.43 %------------------------------------------------------------------------------
% 0.18/0.43 % File : SEV504^1 : TPTP v9.2.1. Released v7.0.0.
% 0.18/0.43 % Domain : Analysis
% 0.18/0.43 % Problem : NSUM_SUBSET_SIMPLE
% 0.18/0.43 % Version : Especial.
% 0.18/0.43 % English :
% 0.18/0.43
% 0.18/0.43 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.18/0.43 % Source : [Kal16]
% 0.18/0.43 % Names : NSUM_SUBSET_SIMPLE_.p [Kal16]
% 0.18/0.43
% 0.18/0.43 % Status : Theorem
% 0.18/0.43 % Rating : 0.00 v7.1.0
% 0.18/0.43 % Syntax : Number of formulae : 14 ( 2 unt; 9 typ; 0 def)
% 0.18/0.43 % Number of atoms : 21 ( 3 equ; 0 cnn)
% 0.18/0.43 % Maximal formula atoms : 6 ( 4 avg)
% 0.18/0.43 % Number of connectives : 72 ( 1 ~; 0 |; 5 &; 61 @)
% 0.18/0.43 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.18/0.43 % Maximal formula depth : 14 ( 9 avg)
% 0.18/0.43 % Number of types : 2 ( 1 usr)
% 0.18/0.43 % Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% 0.18/0.43 % Number of symbols : 9 ( 8 usr; 1 con; 0-4 aty)
% 0.18/0.43 % Number of variables : 25 ( 0 ^; 20 !; 0 ?; 25 :)
% 0.18/0.43 % ( 5 !>; 0 ?*; 0 @-; 0 @+)
% 0.18/0.43 % SPC : TH1_THM_EQU_NAR
% 0.18/0.43
% 0.18/0.43 % Comments : Exported from core HOL Light.
% 0.18/0.43 %------------------------------------------------------------------------------
% 0.18/0.43 thf('thf_type_type/nums/num',type,
% 0.18/0.43 'type/nums/num': $tType ).
% 0.18/0.43
% 0.18/0.43 thf('thf_const_const/sets/SUBSET',type,
% 0.18/0.43 'const/sets/SUBSET':
% 0.18/0.43 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > $o ) ).
% 0.18/0.43
% 0.18/0.43 thf('thf_const_const/sets/IN',type,
% 0.18/0.43 'const/sets/IN':
% 0.18/0.43 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.18/0.43
% 0.18/0.43 thf('thf_const_const/sets/FINITE',type,
% 0.18/0.43 'const/sets/FINITE':
% 0.18/0.43 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.18/0.43
% 0.18/0.43 thf('thf_const_const/sets/DIFF',type,
% 0.18/0.43 'const/sets/DIFF':
% 0.18/0.43 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > A > $o ) ).
% 0.18/0.43
% 0.18/0.43 thf('thf_const_const/nums/NUMERAL',type,
% 0.18/0.43 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 0.18/0.43
% 0.18/0.43 thf('thf_const_const/nums/_0',type,
% 0.18/0.43 'const/nums/_0': 'type/nums/num' ).
% 0.18/0.43
% 0.18/0.43 thf('thf_const_const/iterate/nsum',type,
% 0.18/0.43 'const/iterate/nsum':
% 0.18/0.43 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/nums/num' ) > 'type/nums/num' ) ).
% 0.18/0.43
% 0.18/0.43 thf('thf_const_const/arith/<=',type,
% 0.18/0.43 'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
% 0.18/0.43
% 0.18/0.43 thf('thm/iterate/NSUM_SUBSET_',axiom,
% 0.18/0.43 ! [A: $tType,A0: A > $o,A1: A > $o,A2: A > 'type/nums/num'] :
% 0.18/0.43 ( ( ( 'const/sets/FINITE' @ A @ A0 )
% 0.18/0.43 & ( 'const/sets/FINITE' @ A @ A1 )
% 0.18/0.43 & ! [A3: A] :
% 0.18/0.43 ( ( 'const/sets/IN' @ A @ A3 @ ( 'const/sets/DIFF' @ A @ A0 @ A1 ) )
% 0.18/0.43 => ( ( A2 @ A3 )
% 0.18/0.43 = ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) )
% 0.18/0.43 => ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ A @ A0 @ A2 ) @ ( 'const/iterate/nsum' @ A @ A1 @ A2 ) ) ) ).
% 0.18/0.43
% 0.18/0.43 thf('thm/sets/FINITE_SUBSET_',axiom,
% 0.18/0.43 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 0.18/0.43 ( ( ( 'const/sets/FINITE' @ A @ A1 )
% 0.18/0.43 & ( 'const/sets/SUBSET' @ A @ A0 @ A1 ) )
% 0.18/0.43 => ( 'const/sets/FINITE' @ A @ A0 ) ) ).
% 0.18/0.43
% 0.18/0.43 thf('thm/sets/SUBSET_',axiom,
% 0.18/0.43 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 0.18/0.43 ( ( 'const/sets/SUBSET' @ A @ A0 @ A1 )
% 0.18/0.43 = ( ! [A2: A] :
% 0.18/0.43 ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 0.18/0.43 => ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
% 0.18/0.43
% 0.18/0.43 thf('thm/sets/IN_DIFF_',axiom,
% 0.18/0.43 ! [A: $tType,A0: A > $o,A1: A > $o,A2: A] :
% 0.18/0.43 ( ( 'const/sets/IN' @ A @ A2 @ ( 'const/sets/DIFF' @ A @ A0 @ A1 ) )
% 0.18/0.43 = ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 0.18/0.43 & ~ ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ).
% 0.18/0.43
% 0.18/0.43 thf('thm/iterate/NSUM_SUBSET_SIMPLE_',conjecture,
% 0.18/0.43 ! [A: $tType,A0: A > $o,A1: A > $o,A2: A > 'type/nums/num'] :
% 0.18/0.43 ( ( ( 'const/sets/FINITE' @ A @ A1 )
% 0.18/0.43 & ( 'const/sets/SUBSET' @ A @ A0 @ A1 ) )
% 0.18/0.43 => ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ A @ A0 @ A2 ) @ ( 'const/iterate/nsum' @ A @ A1 @ A2 ) ) ) ).
% 0.18/0.43
% 0.18/0.43 %------------------------------------------------------------------------------
% 0.18/0.43 ------------------------
% 1.73/1.46 ---- Embedded in THF ---
% 1.73/1.47 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.73/1.47 %%% Generated on Tue Feb 24 12:49:06 EST 2026
% 1.73/1.47 %%% using '$$dhol' embedding, version 1.3.0.
% 1.73/1.47 %%% Logic specification used:
% 1.73/1.47 %%% thf(spec, logic, $$dhol).
% 1.73/1.47
% 1.73/1.47 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.0D0tWxMeC6/DTF2DTF1241.p
% See solution above
% 1.73/1.47 ------------------------
% 1.73/1.48 ---- Cleaned THF ---
% 1.73/1.48 thf('thf_type_type/nums/num',type,
% 1.73/1.48 'type/nums/num': $tType ).
% 1.73/1.48
% 1.73/1.48 thf('thf_const_const/sets/SUBSET',type,
% 1.73/1.48 'const/sets/SUBSET':
% 1.73/1.48 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > $o ) ).
% 1.73/1.48
% 1.73/1.48 thf('thf_const_const/sets/IN',type,
% 1.73/1.48 'const/sets/IN':
% 1.73/1.48 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.73/1.48
% 1.73/1.48 thf('thf_const_const/sets/FINITE',type,
% 1.73/1.48 'const/sets/FINITE':
% 1.73/1.48 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 1.73/1.48
% 1.73/1.48 thf('thf_const_const/sets/DIFF',type,
% 1.73/1.48 'const/sets/DIFF':
% 1.73/1.48 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > A > $o ) ).
% 1.73/1.48
% 1.73/1.48 thf('thf_const_const/nums/NUMERAL',type,
% 1.73/1.48 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 1.73/1.48
% 1.73/1.48 thf('thf_const_const/nums/_0',type,
% 1.73/1.48 'const/nums/_0': 'type/nums/num' ).
% 1.73/1.48
% 1.73/1.48 thf('thf_const_const/iterate/nsum',type,
% 1.73/1.48 'const/iterate/nsum':
% 1.73/1.48 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/nums/num' ) > 'type/nums/num' ) ).
% 1.73/1.48
% 1.73/1.48 thf('thf_const_const/arith/<=',type,
% 1.73/1.48 'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
% 1.73/1.48
% 1.73/1.48 thf('thm/iterate/NSUM_SUBSET_',axiom,
% 1.73/1.48 ! [A: $tType,A0: A > $o,A1: A > $o,A2: A > 'type/nums/num'] :
% 1.73/1.48 ( ( ( 'const/sets/FINITE' @ A @ A0 )
% 1.73/1.48 & ( 'const/sets/FINITE' @ A @ A1 )
% 1.73/1.48 & ! [A3: A] :
% 1.73/1.48 ( ( 'const/sets/IN' @ A @ A3 @ ( 'const/sets/DIFF' @ A @ A0 @ A1 ) )
% 1.73/1.48 => ( ( A2 @ A3 )
% 1.73/1.48 = ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) )
% 1.73/1.48 => ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ A @ A0 @ A2 ) @ ( 'const/iterate/nsum' @ A @ A1 @ A2 ) ) ) ).
% 1.73/1.48
% 1.73/1.48 thf('thm/sets/FINITE_SUBSET_',axiom,
% 1.73/1.48 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 1.73/1.48 ( ( ( 'const/sets/FINITE' @ A @ A1 )
% 1.73/1.48 & ( 'const/sets/SUBSET' @ A @ A0 @ A1 ) )
% 1.73/1.48 => ( 'const/sets/FINITE' @ A @ A0 ) ) ).
% 1.73/1.48
% 1.73/1.48 thf('thm/sets/SUBSET_',axiom,
% 1.73/1.48 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 1.73/1.48 ( ( 'const/sets/SUBSET' @ A @ A0 @ A1 )
% 1.73/1.48 = ( ! [A2: A] :
% 1.73/1.48 ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 1.73/1.48 => ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
% 1.73/1.48
% 1.73/1.48 thf('thm/sets/IN_DIFF_',axiom,
% 1.73/1.48 ! [A: $tType,A0: A > $o,A1: A > $o,A2: A] :
% 1.73/1.48 ( ( 'const/sets/IN' @ A @ A2 @ ( 'const/sets/DIFF' @ A @ A0 @ A1 ) )
% 1.73/1.48 = ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 1.73/1.48 & ~ ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ).
% 1.73/1.48
% 1.73/1.48 thf('thm/iterate/NSUM_SUBSET_SIMPLE_',conjecture,
% 1.73/1.48 ! [A: $tType,A0: A > $o,A1: A > $o,A2: A > 'type/nums/num'] :
% 1.73/1.48 ( ( ( 'const/sets/FINITE' @ A @ A1 )
% 1.73/1.48 & ( 'const/sets/SUBSET' @ A @ A0 @ A1 ) )
% 1.73/1.48 => ( 'const/arith/<=' @ ( 'const/iterate/nsum' @ A @ A0 @ A2 ) @ ( 'const/iterate/nsum' @ A @ A1 @ A2 ) ) ) ).
% 1.73/1.48 ------------------------
% 1.89/1.50 % (1342)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1241 for (2999ds/183Mi)
% 1.89/1.50 % (1345)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1241 for (2999ds/2Mi)
% 1.89/1.50 % (1348)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1241 for (2999ds/18Mi)
% 1.89/1.50 % (1343)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_1241 for (2999ds/4Mi)
% 1.89/1.50 % (1345)Instruction limit reached!
% 1.89/1.50 % (1345)------------------------------
% 1.89/1.50 % (1345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.50 % (1345)Termination reason: Unknown
% 1.89/1.50 % (1345)Termination phase: Saturation
% 1.89/1.50
% 1.89/1.50 % (1345)Memory used [KB]: 5500
% 1.89/1.50 % (1345)Time elapsed: 0.003 s
% 1.89/1.50 % (1345)Instructions burned: 3 (million)
% 1.89/1.50 % (1345)------------------------------
% 1.89/1.50 % (1345)------------------------------
% 1.89/1.50 % (1343)Instruction limit reached!
% 1.89/1.50 % (1343)------------------------------
% 1.89/1.50 % (1343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.50 % (1343)Termination reason: Unknown
% 1.89/1.50 % (1343)Termination phase: Saturation
% 1.89/1.50
% 1.89/1.50 % (1343)Memory used [KB]: 5500
% 1.89/1.50 % (1343)Time elapsed: 0.004 s
% 1.89/1.50 % (1343)Instructions burned: 5 (million)
% 1.89/1.50 % (1343)------------------------------
% 1.89/1.50 % (1343)------------------------------
% 1.89/1.50 % (1346)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_1241 for (2999ds/2Mi)
% 1.89/1.50 % (1344)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_1241 for (2999ds/27Mi)
% 1.89/1.50 % (1347)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_1241 for (2999ds/275Mi)
% 1.89/1.50 % (1346)Instruction limit reached!
% 1.89/1.50 % (1346)------------------------------
% 1.89/1.50 % (1346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.50 % (1346)Termination reason: Unknown
% 1.89/1.50 % (1346)Termination phase: shuffling
% 1.89/1.50
% 1.89/1.50 % (1346)Memory used [KB]: 895
% 1.89/1.50 % (1346)Time elapsed: 0.003 s
% 1.89/1.50 % (1346)Instructions burned: 2 (million)
% 1.89/1.50 % (1346)------------------------------
% 1.89/1.50 % (1346)------------------------------
% 1.89/1.50 % (1347)Refutation not found, incomplete strategy
% 1.89/1.50 % (1347)------------------------------
% 1.89/1.50 % (1347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.50 % (1347)Termination reason: Refutation not found, incomplete strategy
% 1.89/1.50
% 1.89/1.50
% 1.89/1.50 % (1347)Memory used [KB]: 5500
% 1.89/1.50 % (1347)Time elapsed: 0.005 s
% 1.89/1.50 % (1347)Instructions burned: 4 (million)
% 1.89/1.50 % (1347)------------------------------
% 1.89/1.50 % (1347)------------------------------
% 1.89/1.51 % (1348)Instruction limit reached!
% 1.89/1.51 % (1348)------------------------------
% 1.89/1.51 % (1348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.51 % (1348)Termination reason: Unknown
% 1.89/1.51 % (1348)Termination phase: Saturation
% 1.89/1.51
% 1.89/1.51 % (1348)Memory used [KB]: 5628
% 1.89/1.51 % (1348)Time elapsed: 0.012 s
% 1.89/1.51 % (1348)Instructions burned: 18 (million)
% 1.89/1.51 % (1348)------------------------------
% 1.89/1.51 % (1348)------------------------------
% 1.89/1.51 % (1350)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_1241 for (2999ds/37Mi)
% 1.89/1.51 % (1349)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1241 for (2999ds/3Mi)
% 1.89/1.52 % Exception at run slice level
% 1.89/1.52 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
% 1.89/1.52 % (1349)Instruction limit reached!
% 1.89/1.52 % (1349)------------------------------
% 1.89/1.52 % (1349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.52 % (1349)Termination reason: Unknown
% 1.89/1.52 % (1349)Termination phase: Saturation
% 1.89/1.52 % (1344)Instruction limit reached!
% 1.89/1.52 % (1344)------------------------------
% 1.89/1.52 % (1344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.52 % (1344)Termination reason: Unknown
% 1.89/1.52 % (1344)Termination phase: Saturation
% 1.89/1.52
% 1.89/1.52 % (1344)Memory used [KB]: 5628
% 1.89/1.52 % (1344)Time elapsed: 0.018 s
% 1.89/1.52 % (1344)Instructions burned: 27 (million)
% 1.89/1.52 % (1344)------------------------------
% 1.89/1.52 % (1344)------------------------------
% 1.89/1.52
% 1.89/1.52 % (1349)Memory used [KB]: 5500
% 1.89/1.52 % (1349)Time elapsed: 0.004 s
% 1.89/1.52 % (1349)Instructions burned: 3 (million)
% 1.89/1.52 % (1349)------------------------------
% 1.89/1.52 % (1349)------------------------------
% 1.89/1.52 % (1351)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_1241 for (2999ds/15Mi)
% 1.89/1.52 % (1353)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_1241 for (2999ds/1041Mi)
% 1.89/1.52 % Exception at run slice level
% 1.89/1.52 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
% 1.89/1.52 % (1352)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_1241 for (2999ds/3Mi)
% 1.89/1.53 % (1352)Instruction limit reached!
% 1.89/1.53 % (1352)------------------------------
% 1.89/1.53 % (1352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.53 % (1352)Termination reason: Unknown
% 1.89/1.53 % (1352)Termination phase: Saturation
% 1.89/1.53
% 1.89/1.53 % (1352)Memory used [KB]: 5500
% 1.89/1.53 % (1352)Time elapsed: 0.004 s
% 1.89/1.53 % (1352)Instructions burned: 3 (million)
% 1.89/1.53 % (1352)------------------------------
% 1.89/1.53 % (1352)------------------------------
% 1.89/1.53 % (1351)Instruction limit reached!
% 1.89/1.53 % (1351)------------------------------
% 1.89/1.53 % (1351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.53 % (1351)Termination reason: Unknown
% 1.89/1.53 % (1351)Termination phase: Saturation
% 1.89/1.53
% 1.89/1.53 % (1351)Memory used [KB]: 5628
% 1.89/1.53 % (1351)Time elapsed: 0.011 s
% 1.89/1.53 % (1351)Instructions burned: 15 (million)
% 1.89/1.53 % (1351)------------------------------
% 1.89/1.53 % (1351)------------------------------
% 1.89/1.53 % (1354)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_1241 for (2999ds/7Mi)
% 1.89/1.53 % (1356)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_1241 for (2999ds/3Mi)
% 1.89/1.53 % (1356)Instruction limit reached!
% 1.89/1.53 % (1356)------------------------------
% 1.89/1.53 % (1356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.53 % (1356)Termination reason: Unknown
% 1.89/1.53 % (1356)Termination phase: Saturation
% 1.89/1.53
% 1.89/1.53 % (1356)Memory used [KB]: 5500
% 1.89/1.53 % (1356)Time elapsed: 0.004 s
% 1.89/1.53 % (1356)Instructions burned: 4 (million)
% 1.89/1.53 % (1356)------------------------------
% 1.89/1.53 % (1356)------------------------------
% 1.89/1.54 % (1354)Instruction limit reached!
% 1.89/1.54 % (1354)------------------------------
% 1.89/1.54 % (1354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.54 % (1354)Termination reason: Unknown
% 1.89/1.54 % (1354)Termination phase: Saturation
% 1.89/1.54
% 1.89/1.54 % (1354)Memory used [KB]: 1023
% 1.89/1.54 % (1354)Time elapsed: 0.006 s
% 1.89/1.54 % (1354)Instructions burned: 8 (million)
% 1.89/1.54 % (1354)------------------------------
% 1.89/1.54 % (1354)------------------------------
% 1.89/1.54 % (1355)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_1241 for (2999ds/16Mi)
% 1.89/1.54 % (1357)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_1241 for (2999ds/3Mi)
% 1.89/1.54 % (1357)Instruction limit reached!
% 1.89/1.54 % (1357)------------------------------
% 1.89/1.54 % (1357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.54 % (1357)Termination reason: Unknown
% 1.89/1.54 % (1357)Termination phase: Property scanning
% 1.89/1.54
% 1.89/1.54 % (1357)Memory used [KB]: 1023
% 1.89/1.54 % (1357)Time elapsed: 0.003 s
% 1.89/1.54 % (1357)Instructions burned: 3 (million)
% 1.89/1.54 % (1357)------------------------------
% 1.89/1.54 % (1357)------------------------------
% 1.89/1.54 % (1358)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_1241 for (2999ds/7Mi)
% 1.89/1.55 % (1355)Instruction limit reached!
% 1.89/1.55 % (1355)------------------------------
% 1.89/1.55 % (1355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.55 % (1355)Termination reason: Unknown
% 1.89/1.55 % (1355)Termination phase: Saturation
% 1.89/1.55
% 1.89/1.55 % (1355)Memory used [KB]: 5756
% 1.89/1.55 % (1355)Time elapsed: 0.013 s
% 1.89/1.55 % (1355)Instructions burned: 16 (million)
% 1.89/1.55 % (1355)------------------------------
% 1.89/1.55 % (1355)------------------------------
% 1.89/1.55 % (1358)Instruction limit reached!
% 1.89/1.55 % (1358)------------------------------
% 1.89/1.55 % (1358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.55 % (1358)Termination reason: Unknown
% 1.89/1.55 % (1358)Termination phase: Saturation
% 1.89/1.55
% 1.89/1.55 % (1358)Memory used [KB]: 5500
% 1.89/1.55 % (1358)Time elapsed: 0.005 s
% 1.89/1.55 % (1358)Instructions burned: 7 (million)
% 1.89/1.55 % (1358)------------------------------
% 1.89/1.55 % (1358)------------------------------
% 1.89/1.55 % (1359)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_1241 for (2999ds/3Mi)
% 1.89/1.55 % Exception at run slice level
% 1.89/1.55 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
% 1.89/1.55 % (1361)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_1241 for (2999ds/18Mi)
% 1.89/1.55 % (1360)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_1241 for (2999ds/4Mi)
% 1.89/1.56 % (1362)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_1241 for (2999ds/710Mi)
% 1.89/1.56 % (1360)Instruction limit reached!
% 1.89/1.56 % (1360)------------------------------
% 1.89/1.56 % (1360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.56 % (1360)Termination reason: Unknown
% 1.89/1.56 % (1360)Termination phase: Saturation
% 1.89/1.56
% 1.89/1.56 % (1360)Memory used [KB]: 5500
% 1.89/1.56 % (1360)Time elapsed: 0.004 s
% 1.89/1.56 % (1360)Instructions burned: 4 (million)
% 1.89/1.56 % (1360)------------------------------
% 1.89/1.56 % (1360)------------------------------
% 1.89/1.56 % (1361)Instruction limit reached!
% 1.89/1.56 % (1361)------------------------------
% 1.89/1.56 % (1361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.56 % (1361)Termination reason: Unknown
% 1.89/1.56 % (1361)Termination phase: Saturation
% 1.89/1.56
% 1.89/1.56 % (1361)Memory used [KB]: 5628
% 1.89/1.56 % (1361)Time elapsed: 0.011 s
% 1.89/1.56 % (1361)Instructions burned: 19 (million)
% 1.89/1.56 % (1361)------------------------------
% 1.89/1.56 % (1361)------------------------------
% 1.89/1.56 % (1364)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_1241 for (2999ds/902Mi)
% 1.89/1.57 % (1363)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_1241 for (2999ds/6Mi)
% 1.89/1.57 % (1365)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_1241 for (2999ds/21Mi)
% 1.89/1.57 % (1363)Instruction limit reached!
% 1.89/1.57 % (1363)------------------------------
% 1.89/1.57 % (1363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.57 % (1363)Termination reason: Unknown
% 1.89/1.57 % (1363)Termination phase: Saturation
% 1.89/1.57
% 1.89/1.57 % (1363)Memory used [KB]: 5500
% 1.89/1.57 % (1363)Time elapsed: 0.006 s
% 1.89/1.57 % (1363)Instructions burned: 7 (million)
% 1.89/1.57 % (1363)------------------------------
% 1.89/1.57 % (1363)------------------------------
% 1.89/1.58 % (1367)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_1241 for (2999ds/6Mi)
% 1.89/1.58 % (1366)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_1241 for (2999ds/5Mi)
% 1.89/1.58 % Exception at run slice level
% 1.89/1.58 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
% 1.89/1.58 % Exception at run slice level
% 1.89/1.58 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
% 1.89/1.58 % (1365)Instruction limit reached!
% 1.89/1.58 % (1365)------------------------------
% 1.89/1.58 % (1365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.58 % (1365)Termination reason: Unknown
% 1.89/1.58 % (1365)Termination phase: Saturation
% 1.89/1.58
% 1.89/1.58 % (1365)Memory used [KB]: 5628
% 1.89/1.58 % (1365)Time elapsed: 0.015 s
% 1.89/1.58 % (1365)Instructions burned: 21 (million)
% 1.89/1.58 % (1365)------------------------------
% 1.89/1.58 % (1365)------------------------------
% 1.89/1.59 % (1342)Instruction limit reached!
% 1.89/1.59 % (1342)------------------------------
% 1.89/1.59 % (1342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.59 % (1342)Termination reason: Unknown
% 1.89/1.59 % (1342)Termination phase: Saturation
% 1.89/1.59
% 1.89/1.59 % (1342)Memory used [KB]: 6268
% 1.89/1.59 % (1342)Time elapsed: 0.093 s
% 1.89/1.59 % (1342)Instructions burned: 184 (million)
% 1.89/1.59 % (1342)------------------------------
% 1.89/1.59 % (1342)------------------------------
% 1.89/1.59 % (1369)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_1241 for (2999ds/377Mi)
% 1.89/1.59 % (1371)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_1241 for (2999ds/19Mi)
% 1.89/1.59 % Exception at run slice level
% 1.89/1.59 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
% 1.89/1.59 % (1370)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_1241 for (2999ds/779Mi)
% 1.89/1.60 % Exception at run slice level
% 1.89/1.60 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
% 1.89/1.60 % (1372)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_1241 for (2999ds/879Mi)
% 1.89/1.60 % (1373)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_1241 for (2999ds/17Mi)
% 1.89/1.61 % (1374)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_1241 for (2998ds/3Mi)
% 1.89/1.61 % (1374)Instruction limit reached!
% 1.89/1.61 % (1374)------------------------------
% 1.89/1.61 % (1374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.61 % (1374)Termination reason: Unknown
% 1.89/1.61 % (1374)Termination phase: Property scanning
% 1.89/1.61
% 1.89/1.61 % (1374)Memory used [KB]: 1023
% 1.89/1.61 % (1374)Time elapsed: 0.004 s
% 1.89/1.61 % (1374)Instructions burned: 4 (million)
% 1.89/1.61 % (1374)------------------------------
% 1.89/1.61 % (1374)------------------------------
% 1.89/1.61 % (1373)Instruction limit reached!
% 1.89/1.61 % (1373)------------------------------
% 1.89/1.61 % (1373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.61 % (1373)Termination reason: Unknown
% 1.89/1.61 % (1373)Termination phase: Saturation
% 1.89/1.61
% 1.89/1.61 % (1373)Memory used [KB]: 5628
% 1.89/1.61 % (1373)Time elapsed: 0.034 s
% 1.89/1.61 % (1373)Instructions burned: 17 (million)
% 1.89/1.61 % (1373)------------------------------
% 1.89/1.61 % (1373)------------------------------
% 1.89/1.62 % (1375)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_1241 for (2998ds/30Mi)
% 1.89/1.63 % (1376)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_1241 for (2998ds/127Mi)
% 1.89/1.63 % (1375)Instruction limit reached!
% 1.89/1.63 % (1375)------------------------------
% 1.89/1.63 % (1375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.63 % (1375)Termination reason: Unknown
% 1.89/1.63 % (1375)Termination phase: Saturation
% 1.89/1.63
% 1.89/1.63 % (1375)Memory used [KB]: 5628
% 1.89/1.63 % (1375)Time elapsed: 0.020 s
% 1.89/1.63 % (1375)Instructions burned: 30 (million)
% 1.89/1.63 % (1375)------------------------------
% 1.89/1.63 % (1375)------------------------------
% 1.89/1.63 % (1377)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_1241 for (2998ds/100Mi)
% 1.89/1.64 % (1369)First to succeed.
% 1.89/1.65 % (1369)Refutation found. Thanks to Tanya!
% 1.89/1.65 % SZS status Theorem for DTF2THF_1241
% 1.89/1.65 % SZS output start Proof for DTF2THF_1241
% 1.89/1.65 thf(type_def_6, type, 'type/nums/num': $tType).
% 1.89/1.65 thf(type_def_7, type, sK0: $tType).
% 1.89/1.65 thf(func_def_0, type, 'type/nums/num': $tType).
% 1.89/1.65 thf(func_def_1, type, 'const/sets/SUBSET': !>[X0: $tType]:((X0 > $o) > (X0 > $o) > $o)).
% 1.89/1.65 thf(func_def_2, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.89/1.65 thf(func_def_3, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 1.89/1.65 thf(func_def_4, type, 'const/sets/DIFF': !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0 > $o)).
% 1.89/1.65 thf(func_def_5, type, 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num').
% 1.89/1.65 thf(func_def_6, type, 'const/nums/_0': 'type/nums/num').
% 1.89/1.65 thf(func_def_7, type, 'const/iterate/nsum': !>[X0: $tType]:((X0 > $o) > (X0 > 'type/nums/num') > 'type/nums/num')).
% 1.89/1.65 thf(func_def_8, type, 'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o).
% 1.89/1.65 thf(func_def_18, type, sK1: sK0 > $o).
% 1.89/1.65 thf(func_def_19, type, sK2: sK0 > $o).
% 1.89/1.65 thf(func_def_20, type, sK3: sK0 > 'type/nums/num').
% 1.89/1.65 thf(func_def_21, type, sK4: !>[X0: $tType]:((X0 > 'type/nums/num') > (X0 > $o) > (X0 > $o) > X0)).
% 1.89/1.65 thf(func_def_23, type, sK6: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 1.89/1.65 thf(func_def_24, type, ph7: !>[X0: $tType]:(X0)).
% 1.89/1.65 thf(f429,plain,(
% 1.89/1.65 $false),
% 1.89/1.65 inference(avatar_sat_refutation,[status(thm)],[f66,f75,f428])).
% 1.89/1.65 thf(f428,plain,(
% 1.89/1.65 ~spl5_1 | ~spl5_2),
% 1.89/1.65 inference(avatar_contradiction_clause,[status(thm)],[f427])).
% 1.89/1.65 thf(f427,plain,(
% 1.89/1.65 $false | (~spl5_1 | ~spl5_2)),
% 1.89/1.65 inference(trivial_inequality_removal,[status(thm)],[f423])).
% 1.89/1.65 thf(f423,plain,(
% 1.89/1.65 ($true = $false) | (~spl5_1 | ~spl5_2)),
% 1.89/1.65 inference(superposition,[status(thm)],[f421,f87])).
% 1.89/1.65 thf(f87,plain,(
% 1.89/1.65 (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK1 @ sK3) @ ('const/iterate/nsum' @ sK0 @ sK2 @ sK3)) = $false)),
% 1.89/1.65 inference(trivial_inequality_removal,[status(thm)],[f86])).
% 1.89/1.65 thf(f86,plain,(
% 1.89/1.65 ($true != $true) | (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK1 @ sK3) @ ('const/iterate/nsum' @ sK0 @ sK2 @ sK3)) = $false)),
% 1.89/1.65 inference(fool_paramodulation,[status(thm)],[f32])).
% 1.89/1.65 thf(f32,plain,(
% 1.89/1.65 (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK1 @ sK3) @ ('const/iterate/nsum' @ sK0 @ sK2 @ sK3)) != $true)),
% 1.89/1.65 inference(cnf_transformation,[status(thm)],[f25])).
% 1.89/1.65 thf(f25,plain,(
% 1.89/1.65 (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK1 @ sK3) @ ('const/iterate/nsum' @ sK0 @ sK2 @ sK3)) != $true) & (('const/sets/FINITE' @ sK0 @ sK2) = $true) & (('const/sets/SUBSET' @ sK0 @ sK1 @ sK2) = $true)),
% 1.89/1.65 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f21,f24])).
% 1.89/1.65 thf(f24,plain,(
% 1.89/1.65 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/nums/num'] : ((('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3)) != $true) & (('const/sets/FINITE' @ X0 @ X2) = $true) & (('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true)) => ((('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK1 @ sK3) @ ('const/iterate/nsum' @ sK0 @ sK2 @ sK3)) != $true) & (('const/sets/FINITE' @ sK0 @ sK2) = $true) & (('const/sets/SUBSET' @ sK0 @ sK1 @ sK2) = $true))),
% 1.89/1.65 introduced(definition,[],[choice_axiom])).
% 1.89/1.65 thf(f21,plain,(
% 1.89/1.65 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/nums/num'] : ((('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3)) != $true) & (('const/sets/FINITE' @ X0 @ X2) = $true) & (('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true))),
% 1.89/1.65 inference(flattening,[status(thm)],[f20])).
% 1.89/1.65 thf(f20,plain,(
% 1.89/1.65 ? [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/nums/num'] : ((('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3)) != $true) & ((('const/sets/FINITE' @ X0 @ X2) = $true) & (('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true)))),
% 1.89/1.65 inference(ennf_transformation,[status(thm)],[f11])).
% 1.89/1.65 thf(f11,plain,(
% 1.89/1.65 ~! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/nums/num'] : (((('const/sets/FINITE' @ X0 @ X2) = $true) & (('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true)) => (('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3)) = $true))),
% 1.89/1.65 inference(fool_elimination,[status(thm)],[f10])).
% 1.89/1.65 thf(f10,plain,(
% 1.89/1.65 ~! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/nums/num'] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) & ('const/sets/FINITE' @ X0 @ X2)) => ('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3)))),
% 1.89/1.65 inference(rectify,[status(thm)],[f6])).
% 1.89/1.65 thf(f6,negated_conjecture,(
% 1.89/1.65 ~! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/nums/num'] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) & ('const/sets/FINITE' @ X0 @ X2)) => ('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3)))),
% 1.89/1.65 inference(negated_conjecture,[status(cth)],[f5])).
% 1.89/1.65 thf(f5,conjecture,(
% 1.89/1.65 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/nums/num'] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) & ('const/sets/FINITE' @ X0 @ X2)) => ('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3)))),
% 1.89/1.65 file('/export/starexec/sandbox/tmp/tmp.0D0tWxMeC6/DTF2THF_1241.p','thm/iterate/NSUM_SUBSET_SIMPLE_')).
% 1.89/1.65 thf(f421,plain,(
% 1.89/1.65 ( ! [X0 : sK0 > 'type/nums/num'] : ((('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK1 @ X0) @ ('const/iterate/nsum' @ sK0 @ sK2 @ X0)) = $true)) ) | (~spl5_1 | ~spl5_2)),
% 1.89/1.65 inference(trivial_inequality_removal,[status(thm)],[f420])).
% 1.89/1.65 thf(f420,plain,(
% 1.89/1.65 ( ! [X0 : sK0 > 'type/nums/num'] : ((('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK1 @ X0) @ ('const/iterate/nsum' @ sK0 @ sK2 @ X0)) = $true) | ($true != $true)) ) | (~spl5_1 | ~spl5_2)),
% 1.89/1.65 inference(forward_demodulation,[status(thm)],[f419,f60])).
% 1.89/1.65 thf(f60,plain,(
% 1.89/1.65 (('const/sets/FINITE' @ sK0 @ sK2) = $true) | ~spl5_1),
% 1.89/1.65 inference(avatar_component_clause,[status(thm)],[f59])).
% 1.89/1.65 thf(f59,definition,(
% 1.89/1.65 spl5_1 <=> (('const/sets/FINITE' @ sK0 @ sK2) = $true)),
% 1.89/1.65 introduced(definition,[new_symbols(naming,[spl5_1])],[avatar_definition])).
% 1.89/1.65 thf(f419,plain,(
% 1.89/1.65 ( ! [X0 : sK0 > 'type/nums/num'] : ((('const/sets/FINITE' @ sK0 @ sK2) != $true) | (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK1 @ X0) @ ('const/iterate/nsum' @ sK0 @ sK2 @ X0)) = $true)) ) | (~spl5_1 | ~spl5_2)),
% 1.89/1.65 inference(trivial_inequality_removal,[status(thm)],[f418])).
% 1.89/1.65 thf(f418,plain,(
% 1.89/1.65 ( ! [X0 : sK0 > 'type/nums/num'] : ((('const/sets/FINITE' @ sK0 @ sK2) != $true) | (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK1 @ X0) @ ('const/iterate/nsum' @ sK0 @ sK2 @ X0)) = $true) | ($true != $true)) ) | (~spl5_1 | ~spl5_2)),
% 1.89/1.65 inference(forward_demodulation,[status(thm)],[f415,f65])).
% 1.89/1.65 thf(f65,plain,(
% 1.89/1.65 ($true = ('const/sets/FINITE' @ sK0 @ sK1)) | ~spl5_2),
% 1.89/1.65 inference(avatar_component_clause,[status(thm)],[f63])).
% 1.89/1.65 thf(f63,definition,(
% 1.89/1.65 spl5_2 <=> ($true = ('const/sets/FINITE' @ sK0 @ sK1))),
% 1.89/1.65 introduced(definition,[new_symbols(naming,[spl5_2])],[avatar_definition])).
% 1.89/1.65 thf(f415,plain,(
% 1.89/1.65 ( ! [X0 : sK0 > 'type/nums/num'] : (($true != ('const/sets/FINITE' @ sK0 @ sK1)) | (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK1 @ X0) @ ('const/iterate/nsum' @ sK0 @ sK2 @ X0)) = $true) | (('const/sets/FINITE' @ sK0 @ sK2) != $true)) ) | (~spl5_1 | ~spl5_2)),
% 1.89/1.65 inference(trivial_inequality_removal,[status(thm)],[f414])).
% 1.89/1.65 thf(f414,plain,(
% 1.89/1.65 ( ! [X0 : sK0 > 'type/nums/num'] : (($true = $false) | ($true != ('const/sets/FINITE' @ sK0 @ sK1)) | (('const/sets/FINITE' @ sK0 @ sK2) != $true) | (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK1 @ X0) @ ('const/iterate/nsum' @ sK0 @ sK2 @ X0)) = $true)) ) | (~spl5_1 | ~spl5_2)),
% 1.89/1.65 inference(duplicate_literal_removal,[status(thm)],[f398])).
% 1.89/1.65 thf(f398,plain,(
% 1.89/1.65 ( ! [X0 : sK0 > 'type/nums/num'] : (($true != ('const/sets/FINITE' @ sK0 @ sK1)) | (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK1 @ X0) @ ('const/iterate/nsum' @ sK0 @ sK2 @ X0)) = $true) | (('const/sets/FINITE' @ sK0 @ sK2) != $true) | (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK1 @ X0) @ ('const/iterate/nsum' @ sK0 @ sK2 @ X0)) = $true) | ($true = $false)) ) | (~spl5_1 | ~spl5_2)),
% 1.89/1.65 inference(superposition,[status(thm)],[f390,f35])).
% 1.89/1.65 thf(f35,plain,(
% 1.89/1.65 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0 > 'type/nums/num',X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X3 @ X2 @ X1) @ ('const/sets/DIFF' @ X0 @ X1 @ X2)) = $true) | (('const/sets/FINITE' @ X0 @ X2) != $true) | (('const/sets/FINITE' @ X0 @ X1) != $true) | (('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3)) = $true)) )),
% 1.89/1.65 inference(cnf_transformation,[status(thm)],[f27])).
% 1.89/1.65 thf(f27,plain,(
% 1.89/1.65 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/nums/num'] : ((('const/sets/FINITE' @ X0 @ X1) != $true) | ((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X3 @ X2 @ X1) @ ('const/sets/DIFF' @ X0 @ X1 @ X2)) = $true) & (('const/nums/NUMERAL' @ 'const/nums/_0') != (X3 @ (sK4 @ X0 @ X3 @ X2 @ X1)))) | (('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3)) = $true) | (('const/sets/FINITE' @ X0 @ X2) != $true))),
% 1.89/1.65 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f19,f26])).
% 1.89/1.65 thf(f26,plain,(
% 1.89/1.65 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/nums/num'] : (? [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ ('const/sets/DIFF' @ X0 @ X1 @ X2)) = $true) & ((X3 @ X4) != ('const/nums/NUMERAL' @ 'const/nums/_0'))) => ((('const/sets/IN' @ X0 @ (sK4 @ X0 @ X3 @ X2 @ X1) @ ('const/sets/DIFF' @ X0 @ X1 @ X2)) = $true) & (('const/nums/NUMERAL' @ 'const/nums/_0') != (X3 @ (sK4 @ X0 @ X3 @ X2 @ X1)))))),
% 1.89/1.65 introduced(definition,[],[choice_axiom])).
% 1.89/1.65 thf(f19,plain,(
% 1.89/1.65 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/nums/num'] : ((('const/sets/FINITE' @ X0 @ X1) != $true) | ? [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ ('const/sets/DIFF' @ X0 @ X1 @ X2)) = $true) & ((X3 @ X4) != ('const/nums/NUMERAL' @ 'const/nums/_0'))) | (('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3)) = $true) | (('const/sets/FINITE' @ X0 @ X2) != $true))),
% 1.89/1.65 inference(flattening,[status(thm)],[f18])).
% 1.89/1.65 thf(f18,plain,(
% 1.89/1.65 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/nums/num'] : ((('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3)) = $true) | (? [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ ('const/sets/DIFF' @ X0 @ X1 @ X2)) = $true) & ((X3 @ X4) != ('const/nums/NUMERAL' @ 'const/nums/_0'))) | (('const/sets/FINITE' @ X0 @ X1) != $true) | (('const/sets/FINITE' @ X0 @ X2) != $true)))),
% 1.89/1.65 inference(ennf_transformation,[status(thm)],[f15])).
% 1.89/1.65 thf(f15,plain,(
% 1.89/1.65 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/nums/num'] : ((! [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ ('const/sets/DIFF' @ X0 @ X1 @ X2)) = $true) => ((X3 @ X4) = ('const/nums/NUMERAL' @ 'const/nums/_0'))) & (('const/sets/FINITE' @ X0 @ X1) = $true) & (('const/sets/FINITE' @ X0 @ X2) = $true)) => (('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3)) = $true))),
% 1.89/1.65 inference(fool_elimination,[status(thm)],[f14])).
% 1.89/1.65 thf(f14,plain,(
% 1.89/1.65 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/nums/num'] : ((('const/sets/FINITE' @ X0 @ X2) & ('const/sets/FINITE' @ X0 @ X1) & ! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ ('const/sets/DIFF' @ X0 @ X1 @ X2)) => ((X3 @ X4) = ('const/nums/NUMERAL' @ 'const/nums/_0')))) => ('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3)))),
% 1.89/1.65 inference(rectify,[status(thm)],[f1])).
% 1.89/1.65 thf(f1,axiom,(
% 1.89/1.65 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0 > 'type/nums/num'] : ((('const/sets/FINITE' @ X0 @ X2) & ('const/sets/FINITE' @ X0 @ X1) & ! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ ('const/sets/DIFF' @ X0 @ X1 @ X2)) => ((X3 @ X4) = ('const/nums/NUMERAL' @ 'const/nums/_0')))) => ('const/arith/<=' @ ('const/iterate/nsum' @ X0 @ X1 @ X3) @ ('const/iterate/nsum' @ X0 @ X2 @ X3)))),
% 1.89/1.65 file('/export/starexec/sandbox/tmp/tmp.0D0tWxMeC6/DTF2THF_1241.p','thm/iterate/NSUM_SUBSET_')).
% 1.89/1.65 thf(f390,plain,(
% 1.89/1.65 ( ! [X2 : sK0 > $o,X0 : sK0 > 'type/nums/num'] : ((('const/sets/IN' @ sK0 @ (sK4 @ sK0 @ X0 @ sK2 @ sK1) @ X2) = $false) | (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK1 @ X0) @ ('const/iterate/nsum' @ sK0 @ sK2 @ X0)) = $true)) ) | (~spl5_1 | ~spl5_2)),
% 1.89/1.65 inference(trivial_inequality_removal,[status(thm)],[f376])).
% 1.89/1.65 thf(f376,plain,(
% 1.89/1.65 ( ! [X2 : sK0 > $o,X0 : sK0 > 'type/nums/num'] : (($true = $false) | (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK1 @ X0) @ ('const/iterate/nsum' @ sK0 @ sK2 @ X0)) = $true) | (('const/sets/IN' @ sK0 @ (sK4 @ sK0 @ X0 @ sK2 @ sK1) @ X2) = $false)) ) | (~spl5_1 | ~spl5_2)),
% 1.89/1.65 inference(superposition,[status(thm)],[f369,f40])).
% 1.89/1.65 thf(f40,plain,(
% 1.89/1.65 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X3 @ ('const/sets/DIFF' @ X0 @ X1 @ X2)) = $false) | (('const/sets/IN' @ X0 @ X3 @ X2) = $false)) )),
% 1.89/1.65 inference(not_proxy_clausification,[status(thm)],[f39])).
% 1.89/1.65 thf(f39,plain,(
% 1.89/1.65 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X3 @ ('const/sets/DIFF' @ X0 @ X1 @ X2)) = $false) | ((~ ('const/sets/IN' @ X0 @ X3 @ X2)) = $true)) )),
% 1.89/1.65 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.89/1.65 thf(f37,plain,(
% 1.89/1.65 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : ((((~ ('const/sets/IN' @ X0 @ X3 @ X2)) & ('const/sets/IN' @ X0 @ X3 @ X1)) = $true) | (('const/sets/IN' @ X0 @ X3 @ ('const/sets/DIFF' @ X0 @ X1 @ X2)) = $false)) )),
% 1.89/1.65 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.89/1.65 thf(f28,plain,(
% 1.89/1.65 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X3 @ ('const/sets/DIFF' @ X0 @ X1 @ X2)) = ((~ ('const/sets/IN' @ X0 @ X3 @ X2)) & ('const/sets/IN' @ X0 @ X3 @ X1)))) )),
% 1.89/1.65 inference(cnf_transformation,[status(thm)],[f17])).
% 1.89/1.65 thf(f17,plain,(
% 1.89/1.65 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ ('const/sets/DIFF' @ X0 @ X1 @ X2)) = ((~ ('const/sets/IN' @ X0 @ X3 @ X2)) & ('const/sets/IN' @ X0 @ X3 @ X1)))),
% 1.89/1.65 inference(fool_elimination,[status(thm)],[f16])).
% 1.89/1.65 thf(f16,plain,(
% 1.89/1.65 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ ('const/sets/DIFF' @ X0 @ X1 @ X2)) = ('const/sets/IN' @ X0 @ X3 @ X1) & ~('const/sets/IN' @ X0 @ X3 @ X2))),
% 1.89/1.65 inference(rectify,[status(thm)],[f4])).
% 1.89/1.65 thf(f4,axiom,(
% 1.89/1.65 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ ('const/sets/DIFF' @ X0 @ X1 @ X2)) = ('const/sets/IN' @ X0 @ X3 @ X1) & ~('const/sets/IN' @ X0 @ X3 @ X2))),
% 1.89/1.65 file('/export/starexec/sandbox/tmp/tmp.0D0tWxMeC6/DTF2THF_1241.p','thm/sets/IN_DIFF_')).
% 1.89/1.65 thf(f369,plain,(
% 1.89/1.65 ( ! [X0 : sK0 > 'type/nums/num',X1 : sK0 > $o] : ((('const/sets/IN' @ sK0 @ (sK4 @ sK0 @ X0 @ sK2 @ sK1) @ X1) = $true) | (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK1 @ X0) @ ('const/iterate/nsum' @ sK0 @ sK2 @ X0)) = $true)) ) | (~spl5_1 | ~spl5_2)),
% 1.89/1.65 inference(trivial_inequality_removal,[status(thm)],[f368])).
% 1.89/1.65 thf(f368,plain,(
% 1.89/1.65 ( ! [X0 : sK0 > 'type/nums/num',X1 : sK0 > $o] : ((('const/sets/IN' @ sK0 @ (sK4 @ sK0 @ X0 @ sK2 @ sK1) @ X1) = $true) | ($true != $true) | (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK1 @ X0) @ ('const/iterate/nsum' @ sK0 @ sK2 @ X0)) = $true)) ) | (~spl5_1 | ~spl5_2)),
% 1.89/1.65 inference(forward_demodulation,[status(thm)],[f367,f65])).
% 1.89/1.65 thf(f367,plain,(
% 1.89/1.65 ( ! [X0 : sK0 > 'type/nums/num',X1 : sK0 > $o] : (($true != ('const/sets/FINITE' @ sK0 @ sK1)) | (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK1 @ X0) @ ('const/iterate/nsum' @ sK0 @ sK2 @ X0)) = $true) | (('const/sets/IN' @ sK0 @ (sK4 @ sK0 @ X0 @ sK2 @ sK1) @ X1) = $true)) ) | ~spl5_1),
% 1.89/1.65 inference(trivial_inequality_removal,[status(thm)],[f366])).
% 1.89/1.65 thf(f366,plain,(
% 1.89/1.65 ( ! [X0 : sK0 > 'type/nums/num',X1 : sK0 > $o] : (($true != ('const/sets/FINITE' @ sK0 @ sK1)) | (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK1 @ X0) @ ('const/iterate/nsum' @ sK0 @ sK2 @ X0)) = $true) | ($true != $true) | (('const/sets/IN' @ sK0 @ (sK4 @ sK0 @ X0 @ sK2 @ sK1) @ X1) = $true)) ) | ~spl5_1),
% 1.89/1.65 inference(forward_demodulation,[status(thm)],[f364,f60])).
% 1.89/1.65 thf(f364,plain,(
% 1.89/1.65 ( ! [X0 : sK0 > 'type/nums/num',X1 : sK0 > $o] : ((('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK1 @ X0) @ ('const/iterate/nsum' @ sK0 @ sK2 @ X0)) = $true) | (('const/sets/IN' @ sK0 @ (sK4 @ sK0 @ X0 @ sK2 @ sK1) @ X1) = $true) | (('const/sets/FINITE' @ sK0 @ sK2) != $true) | ($true != ('const/sets/FINITE' @ sK0 @ sK1))) )),
% 1.89/1.65 inference(trivial_inequality_removal,[status(thm)],[f349])).
% 1.89/1.65 thf(f349,plain,(
% 1.89/1.65 ( ! [X0 : sK0 > 'type/nums/num',X1 : sK0 > $o] : (($true = $false) | (('const/sets/IN' @ sK0 @ (sK4 @ sK0 @ X0 @ sK2 @ sK1) @ X1) = $true) | (('const/sets/FINITE' @ sK0 @ sK2) != $true) | ($true != ('const/sets/FINITE' @ sK0 @ sK1)) | (('const/arith/<=' @ ('const/iterate/nsum' @ sK0 @ sK1 @ X0) @ ('const/iterate/nsum' @ sK0 @ sK2 @ X0)) = $true)) )),
% 1.89/1.65 inference(superposition,[status(thm)],[f302,f35])).
% 1.89/1.65 thf(f302,plain,(
% 1.89/1.65 ( ! [X0 : sK0 > $o,X1 : sK0] : ((('const/sets/IN' @ sK0 @ X1 @ ('const/sets/DIFF' @ sK0 @ sK1 @ sK2)) = $false) | (('const/sets/IN' @ sK0 @ X1 @ X0) = $true)) )),
% 1.89/1.65 inference(trivial_inequality_removal,[status(thm)],[f293])).
% 1.89/1.65 thf(f293,plain,(
% 1.89/1.65 ( ! [X0 : sK0 > $o,X1 : sK0] : ((('const/sets/IN' @ sK0 @ X1 @ X0) = $true) | (('const/sets/IN' @ sK0 @ X1 @ ('const/sets/DIFF' @ sK0 @ sK1 @ sK2)) = $false) | ($true = $false)) )),
% 1.89/1.65 inference(superposition,[status(thm)],[f291,f47])).
% 1.89/1.65 thf(f47,plain,(
% 1.89/1.65 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) = $false) | (('const/sets/IN' @ X0 @ X3 @ X1) = $false) | (('const/sets/IN' @ X0 @ X3 @ X2) = $true)) )),
% 1.89/1.65 inference(binary_proxy_clausification,[status(thm)],[f46])).
% 1.89/1.65 thf(f46,plain,(
% 1.89/1.65 ( ! [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)) )),
% 1.89/1.65 inference(beta_eta_normalization,[status(thm)],[f45])).
% 1.89/1.65 thf(f45,plain,(
% 1.89/1.65 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : (($true = ((^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X1) => ('const/sets/IN' @ X0 @ Y0 @ X2))) @ X3)) | (('const/sets/SUBSET' @ X0 @ X1 @ X2) = $false)) )),
% 1.89/1.65 inference(pi_clausification,[status(thm)],[f44])).
% 1.89/1.65 thf(f44,plain,(
% 1.89/1.65 ( ! [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)) )),
% 1.89/1.65 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.89/1.65 thf(f33,plain,(
% 1.89/1.65 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) = (!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X1) => ('const/sets/IN' @ X0 @ Y0 @ X2)))))) )),
% 1.89/1.65 inference(cnf_transformation,[status(thm)],[f9])).
% 1.89/1.65 thf(f9,plain,(
% 1.89/1.65 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (('const/sets/SUBSET' @ X0 @ X1 @ X2) = (!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X1) => ('const/sets/IN' @ X0 @ Y0 @ X2)))))),
% 1.89/1.65 inference(fool_elimination,[status(thm)],[f8])).
% 1.89/1.65 thf(f8,plain,(
% 1.89/1.65 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (('const/sets/SUBSET' @ X0 @ X1 @ X2) = ! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) => ('const/sets/IN' @ X0 @ X3 @ X2)))),
% 1.89/1.65 inference(rectify,[status(thm)],[f3])).
% 1.89/1.65 thf(f3,axiom,(
% 1.89/1.65 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (('const/sets/SUBSET' @ X0 @ X1 @ X2) = ! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) => ('const/sets/IN' @ X0 @ X3 @ X2)))),
% 1.89/1.65 file('/export/starexec/sandbox/tmp/tmp.0D0tWxMeC6/DTF2THF_1241.p','thm/sets/SUBSET_')).
% 1.89/1.65 thf(f291,plain,(
% 1.89/1.65 ( ! [X0 : sK0 > $o] : (($true = ('const/sets/SUBSET' @ sK0 @ ('const/sets/DIFF' @ sK0 @ sK1 @ sK2) @ X0))) )),
% 1.89/1.65 inference(trivial_inequality_removal,[status(thm)],[f290])).
% 1.89/1.65 thf(f290,plain,(
% 1.89/1.65 ( ! [X0 : sK0 > $o] : (($true = $false) | ($true = ('const/sets/SUBSET' @ sK0 @ ('const/sets/DIFF' @ sK0 @ sK1 @ sK2) @ X0))) )),
% 1.89/1.65 inference(duplicate_literal_removal,[status(thm)],[f285])).
% 1.89/1.65 thf(f285,plain,(
% 1.89/1.65 ( ! [X0 : sK0 > $o] : (($true = ('const/sets/SUBSET' @ sK0 @ ('const/sets/DIFF' @ sK0 @ sK1 @ sK2) @ X0)) | ($true = ('const/sets/SUBSET' @ sK0 @ ('const/sets/DIFF' @ sK0 @ sK1 @ sK2) @ X0)) | ($true = $false)) )),
% 1.89/1.65 inference(superposition,[status(thm)],[f143,f243])).
% 1.89/1.65 thf(f243,plain,(
% 1.89/1.65 ( ! [X0 : sK0 > $o,X1 : sK0 > $o] : ((('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ ('const/sets/DIFF' @ sK0 @ X0 @ sK2) @ X1) @ sK1) = $false) | ($true = ('const/sets/SUBSET' @ sK0 @ ('const/sets/DIFF' @ sK0 @ X0 @ sK2) @ X1))) )),
% 1.89/1.65 inference(trivial_inequality_removal,[status(thm)],[f233])).
% 1.89/1.65 thf(f233,plain,(
% 1.89/1.65 ( ! [X0 : sK0 > $o,X1 : sK0 > $o] : (($true = $false) | ($true = ('const/sets/SUBSET' @ sK0 @ ('const/sets/DIFF' @ sK0 @ X0 @ sK2) @ X1)) | (('const/sets/IN' @ sK0 @ (sK6 @ sK0 @ ('const/sets/DIFF' @ sK0 @ X0 @ sK2) @ X1) @ sK1) = $false)) )),
% 1.89/1.65 inference(superposition,[status(thm)],[f153,f113])).
% 1.89/1.65 thf(f113,plain,(
% 1.89/1.65 ( ! [X0 : sK0] : (($true = ('const/sets/IN' @ sK0 @ X0 @ sK2)) | (('const/sets/IN' @ sK0 @ X0 @ sK1) = $false)) )),
% 1.89/1.65 inference(trivial_inequality_removal,[status(thm)],[f105])).
% 1.89/1.65 thf(f105,plain,(
% 1.89/1.65 ( ! [X0 : sK0] : (($true = $false) | (('const/sets/IN' @ sK0 @ X0 @ sK1) = $false) | ($true = ('const/sets/IN' @ sK0 @ X0 @ sK2))) )),
% 1.89/1.65 inference(superposition,[status(thm)],[f47,f30])).
% 1.89/1.65 thf(f30,plain,(
% 1.89/1.65 (('const/sets/SUBSET' @ sK0 @ sK1 @ sK2) = $true)),
% 1.89/1.65 inference(cnf_transformation,[status(thm)],[f25])).
% 1.89/1.65 thf(f153,plain,(
% 1.89/1.65 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0 > $o,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ (sK6 @ X0 @ ('const/sets/DIFF' @ X0 @ X1 @ X2) @ X3) @ X2) = $false) | (('const/sets/SUBSET' @ X0 @ ('const/sets/DIFF' @ X0 @ X1 @ X2) @ X3) = $true)) )),
% 1.89/1.65 inference(trivial_inequality_removal,[status(thm)],[f148])).
% 1.89/1.65 thf(f148,plain,(
% 1.89/1.65 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0 > $o,X1 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ ('const/sets/DIFF' @ X0 @ X1 @ X2) @ X3) = $true) | (('const/sets/IN' @ X0 @ (sK6 @ X0 @ ('const/sets/DIFF' @ X0 @ X1 @ X2) @ X3) @ X2) = $false) | ($true = $false)) )),
% 1.89/1.65 inference(superposition,[status(thm)],[f40,f51])).
% 1.89/1.65 thf(f51,plain,(
% 1.89/1.65 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ (sK6 @ X0 @ X1 @ X2) @ X1) = $true) | (('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true)) )),
% 1.89/1.65 inference(binary_proxy_clausification,[status(thm)],[f49])).
% 1.89/1.65 thf(f49,plain,(
% 1.89/1.65 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true) | ($false = (('const/sets/IN' @ X0 @ (sK6 @ X0 @ X1 @ X2) @ X1) => ('const/sets/IN' @ X0 @ (sK6 @ X0 @ X1 @ X2) @ X2)))) )),
% 1.89/1.65 inference(beta_eta_normalization,[status(thm)],[f48])).
% 1.89/1.65 thf(f48,plain,(
% 1.89/1.65 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true) | (((^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X1) => ('const/sets/IN' @ X0 @ Y0 @ X2))) @ (sK6 @ X0 @ X1 @ X2)) = $false)) )),
% 1.89/1.65 inference(sigma_clausification,[status(thm)],[f43])).
% 1.89/1.65 thf(f43,plain,(
% 1.89/1.65 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true) | ((!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X1) => ('const/sets/IN' @ X0 @ Y0 @ X2)))) = $false)) )),
% 1.89/1.65 inference(binary_proxy_clausification,[status(thm)],[f33])).
% 1.89/1.65 thf(f143,plain,(
% 1.89/1.65 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0 > $o,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ (sK6 @ X0 @ ('const/sets/DIFF' @ X0 @ X1 @ X2) @ X3) @ X1) = $true) | (('const/sets/SUBSET' @ X0 @ ('const/sets/DIFF' @ X0 @ X1 @ X2) @ X3) = $true)) )),
% 1.89/1.65 inference(trivial_inequality_removal,[status(thm)],[f139])).
% 1.89/1.65 thf(f139,plain,(
% 1.89/1.65 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0 > $o,X1 : X0 > $o] : (($true = $false) | (('const/sets/SUBSET' @ X0 @ ('const/sets/DIFF' @ X0 @ X1 @ X2) @ X3) = $true) | (('const/sets/IN' @ X0 @ (sK6 @ X0 @ ('const/sets/DIFF' @ X0 @ X1 @ X2) @ X3) @ X1) = $true)) )),
% 1.89/1.65 inference(superposition,[status(thm)],[f38,f51])).
% 1.89/1.65 thf(f38,plain,(
% 1.89/1.65 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X3 @ ('const/sets/DIFF' @ X0 @ X1 @ X2)) = $false) | (('const/sets/IN' @ X0 @ X3 @ X1) = $true)) )),
% 1.89/1.65 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.89/1.65 thf(f75,plain,(
% 1.89/1.65 spl5_1),
% 1.89/1.65 inference(avatar_contradiction_clause,[status(thm)],[f74])).
% 1.89/1.65 thf(f74,plain,(
% 1.89/1.65 $false | spl5_1),
% 1.89/1.65 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.89/1.65 thf(f73,plain,(
% 1.89/1.65 ($true = $false) | spl5_1),
% 1.89/1.65 inference(backward_demodulation,[status(thm)],[f31,f71])).
% 1.89/1.65 thf(f71,plain,(
% 1.89/1.65 (('const/sets/FINITE' @ sK0 @ sK2) = $false) | spl5_1),
% 1.89/1.65 inference(trivial_inequality_removal,[status(thm)],[f67])).
% 1.89/1.65 thf(f67,plain,(
% 1.89/1.65 (('const/sets/FINITE' @ sK0 @ sK2) = $false) | ($true != $true) | spl5_1),
% 1.89/1.65 inference(fool_paramodulation,[status(thm)],[f61])).
% 1.89/1.65 thf(f61,plain,(
% 1.89/1.65 (('const/sets/FINITE' @ sK0 @ sK2) != $true) | spl5_1),
% 1.89/1.65 inference(avatar_component_clause,[status(thm)],[f59])).
% 1.89/1.65 thf(f31,plain,(
% 1.89/1.65 (('const/sets/FINITE' @ sK0 @ sK2) = $true)),
% 1.89/1.65 inference(cnf_transformation,[status(thm)],[f25])).
% 1.89/1.65 thf(f66,plain,(
% 1.89/1.65 ~spl5_1 | spl5_2),
% 1.89/1.65 inference(avatar_split_clause,[status(thm)],[f57,f63,f59])).
% 1.89/1.65 thf(f57,plain,(
% 1.89/1.65 ($true = ('const/sets/FINITE' @ sK0 @ sK1)) | (('const/sets/FINITE' @ sK0 @ sK2) != $true)),
% 1.89/1.65 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.89/1.65 thf(f55,plain,(
% 1.89/1.65 (('const/sets/FINITE' @ sK0 @ sK2) != $true) | ($true = ('const/sets/FINITE' @ sK0 @ sK1)) | ($true != $true)),
% 1.89/1.65 inference(superposition,[status(thm)],[f29,f30])).
% 1.89/1.65 thf(f29,plain,(
% 1.89/1.65 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) != $true) | (('const/sets/FINITE' @ X0 @ X2) != $true) | (('const/sets/FINITE' @ X0 @ X1) = $true)) )),
% 1.89/1.65 inference(cnf_transformation,[status(thm)],[f23])).
% 1.89/1.65 thf(f23,plain,(
% 1.89/1.65 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X1) = $true) | (('const/sets/FINITE' @ X0 @ X2) != $true) | (('const/sets/SUBSET' @ X0 @ X1 @ X2) != $true))),
% 1.89/1.65 inference(flattening,[status(thm)],[f22])).
% 1.89/1.65 thf(f22,plain,(
% 1.89/1.65 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((('const/sets/FINITE' @ X0 @ X1) = $true) | ((('const/sets/FINITE' @ X0 @ X2) != $true) | (('const/sets/SUBSET' @ X0 @ X1 @ X2) != $true)))),
% 1.89/1.65 inference(ennf_transformation,[status(thm)],[f13])).
% 1.89/1.65 thf(f13,plain,(
% 1.89/1.65 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (((('const/sets/FINITE' @ X0 @ X2) = $true) & (('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true)) => (('const/sets/FINITE' @ X0 @ X1) = $true))),
% 1.89/1.65 inference(fool_elimination,[status(thm)],[f12])).
% 1.89/1.65 thf(f12,plain,(
% 1.89/1.65 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) & ('const/sets/FINITE' @ X0 @ X2)) => ('const/sets/FINITE' @ X0 @ X1))),
% 1.89/1.65 inference(rectify,[status(thm)],[f2])).
% 1.89/1.65 thf(f2,axiom,(
% 1.89/1.65 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) & ('const/sets/FINITE' @ X0 @ X2)) => ('const/sets/FINITE' @ X0 @ X1))),
% 1.89/1.65 file('/export/starexec/sandbox/tmp/tmp.0D0tWxMeC6/DTF2THF_1241.p','thm/sets/FINITE_SUBSET_')).
% 1.89/1.65 % SZS output end Proof for DTF2THF_1241
% 1.89/1.65 % (1369)------------------------------
% 1.89/1.65 % (1369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.65 % (1369)Termination reason: Refutation
% 1.89/1.65
% 1.89/1.65 % (1369)Memory used [KB]: 5884
% 1.89/1.65 % (1369)Time elapsed: 0.080 s
% 1.89/1.65 % (1369)Instructions burned: 90 (million)
% 1.89/1.65 % (1369)------------------------------
% 1.89/1.65 % (1369)------------------------------
% 1.89/1.65 % (1341)Success in time 0.173 s
%------------------------------------------------------------------------------