%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV506^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 1.64s 1.33s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 6
% Syntax : Number of formulae : 81 ( 38 unt; 0 typ; 2 def)
% Number of atoms : 572 ( 203 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 1033 ( 35 ~; 50 |; 32 &; 799 @)
% ( 2 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 9 con; 0-3 aty)
% ( 66 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 173 ( 80 ^; 93 !; 0 ?; 173 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
'type/nums/num': $tType ).
thf(func_def_0,type,
'type/nums/num': $tType ).
thf(func_def_1,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf(func_def_4,type,
'const/nums/_0': 'type/nums/num' ).
thf(func_def_5,type,
'const/iterate/nsum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/nums/num' ) > 'type/nums/num' ) ).
thf(func_def_6,type,
'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_7,type,
'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
thf(func_def_22,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
sK2: 'type/nums/num' ).
thf(func_def_24,type,
sK3: 'type/nums/num' ).
thf(func_def_25,type,
sK4: 'type/nums/num' > 'type/nums/num' ).
thf(func_def_26,type,
sK5:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/nums/num' ) > X0 ) ).
thf(func_def_27,type,
sK6: 'type/nums/num' ).
thf(f520,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f77,f442,f518]) ).
thf(f518,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[status(thm)],[f517]) ).
thf(f517,plain,
( $false
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f512]) ).
thf(f512,plain,
( ( $true = $false )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f506,f23]) ).
thf(f23,plain,
! [X2: 'type/nums/num',X1: 'type/nums/num'] :
( $true
= ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ X2 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
! [X2: 'type/nums/num',X1: 'type/nums/num'] :
( ( ^ [Y0: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: 'type/nums/num'] :
( $true
= ( !! @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ Y0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: 'type/nums/num'] :
( ( ^ [Y0: 'type/nums/num'] :
( !! @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ Y1 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( !! @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( !! @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ Y1 @ Y0 ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( !! @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( !! @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ Y1 @ Y0 ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: 'type/nums/num',X1: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ X0 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.6dAD0J2TVR/DTF2THF_32467.p','thm/iterate/FINITE_NUMSEG_') ).
thf(f506,plain,
( ( $false
= ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f505]) ).
thf(f505,plain,
( ( $true = $false )
| ( $false
= ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) ) )
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f504]) ).
thf(f504,plain,
( ( ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= $false )
| ( $false
= ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) ) )
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f501,f450]) ).
thf(f450,plain,
( ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) @ sK4 ) )
| ~ spl0_4 ),
inference(equality_proxy_clausification,[status(thm)],[f446]) ).
thf(f446,plain,
( ( $false
!= ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) @ sK4 ) ) )
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f61,f76]) ).
thf(f76,plain,
( ( $false
= ( !! @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ Y0 @ sK2 )
& ( 'const/arith/<=' @ sK3 @ Y0 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( sK4 @ Y0 ) ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f75]) ).
thf(f75,definition,
( spl0_4
<=> ( $false
= ( !! @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ Y0 @ sK2 )
& ( 'const/arith/<=' @ sK3 @ Y0 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( sK4 @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f61,plain,
( ( !! @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ Y0 @ sK2 )
& ( 'const/arith/<=' @ sK3 @ Y0 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( sK4 @ Y0 ) ) ) )
!= ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) @ sK4 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
( $false
= ( ( !! @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ Y0 @ sK2 )
& ( 'const/arith/<=' @ sK3 @ Y0 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( sK4 @ Y0 ) ) ) )
= ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) @ sK4 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f59]) ).
thf(f59,plain,
( $false
= ( ^ [Y0: 'type/nums/num' > 'type/nums/num'] :
( ( !! @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ Y1 @ sK2 )
& ( 'const/arith/<=' @ sK3 @ Y1 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( Y0 @ Y1 ) ) ) )
= ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) @ Y0 ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f58]) ).
thf(f58,plain,
( $false
= ( !! @ ( 'type/nums/num' > 'type/nums/num' )
@ ^ [Y0: 'type/nums/num' > 'type/nums/num'] :
( ( !! @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ Y1 @ sK2 )
& ( 'const/arith/<=' @ sK3 @ Y1 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( Y0 @ Y1 ) ) ) )
= ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ^ [Y0: 'type/nums/num'] :
( !! @ ( 'type/nums/num' > 'type/nums/num' )
@ ^ [Y1: 'type/nums/num' > 'type/nums/num'] :
( ( !! @ 'type/nums/num'
@ ^ [Y2: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ Y2 @ sK2 )
& ( 'const/arith/<=' @ Y0 @ Y2 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( Y1 @ Y2 ) ) ) )
= ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ Y0 @ sK2 ) @ Y1 ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
( $false
= ( !! @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( !! @ ( 'type/nums/num' > 'type/nums/num' )
@ ^ [Y1: 'type/nums/num' > 'type/nums/num'] :
( ( !! @ 'type/nums/num'
@ ^ [Y2: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ Y2 @ sK2 )
& ( 'const/arith/<=' @ Y0 @ Y2 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( Y1 @ Y2 ) ) ) )
= ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ Y0 @ sK2 ) @ Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ^ [Y0: 'type/nums/num'] :
( !! @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] :
( !! @ ( 'type/nums/num' > 'type/nums/num' )
@ ^ [Y2: 'type/nums/num' > 'type/nums/num'] :
( ( !! @ 'type/nums/num'
@ ^ [Y3: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ Y3 @ Y0 )
& ( 'const/arith/<=' @ Y1 @ Y3 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( Y2 @ Y3 ) ) ) )
= ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ Y1 @ Y0 ) @ Y2 ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
( $false
= ( !! @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( !! @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] :
( !! @ ( 'type/nums/num' > 'type/nums/num' )
@ ^ [Y2: 'type/nums/num' > 'type/nums/num'] :
( ( !! @ 'type/nums/num'
@ ^ [Y3: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ Y3 @ Y0 )
& ( 'const/arith/<=' @ Y1 @ Y3 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( Y2 @ Y3 ) ) ) )
= ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ~ ( !! @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( !! @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] :
( !! @ ( 'type/nums/num' > 'type/nums/num' )
@ ^ [Y2: 'type/nums/num' > 'type/nums/num'] :
( ( !! @ 'type/nums/num'
@ ^ [Y3: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ Y3 @ Y0 )
& ( 'const/arith/<=' @ Y1 @ Y3 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( Y2 @ Y3 ) ) ) )
= ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ~ ( !! @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( !! @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] :
( !! @ ( 'type/nums/num' > 'type/nums/num' )
@ ^ [Y2: 'type/nums/num' > 'type/nums/num'] :
( ( !! @ 'type/nums/num'
@ ^ [Y3: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ Y3 @ Y0 )
& ( 'const/arith/<=' @ Y1 @ Y3 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( Y2 @ Y3 ) ) ) )
= ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ Y1 @ Y0 ) @ Y2 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num',X3: 'type/nums/num'] :
( ( ( ( 'const/arith/<=' @ X1 @ X3 )
& ( 'const/arith/<=' @ X3 @ X2 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( X0 @ X3 ) ) )
= ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num',X3: 'type/nums/num'] :
( ( ( ( 'const/arith/<=' @ X1 @ X3 )
& ( 'const/arith/<=' @ X3 @ X2 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( X0 @ X3 ) ) )
= ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
! [X0: 'type/nums/num' > 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num',X3: 'type/nums/num'] :
( ( ( ( 'const/arith/<=' @ X1 @ X3 )
& ( 'const/arith/<=' @ X3 @ X2 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( X0 @ X3 ) ) )
= ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ X1 @ X2 ) @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6dAD0J2TVR/DTF2THF_32467.p','thm/iterate/NSUM_EQ_0_IFF_NUMSEG_') ).
thf(f501,plain,
( ( $false
= ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) @ sK4 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
| ( $false
= ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f493]) ).
thf(f493,plain,
( ( $false
= ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) ) )
| ( $false
= ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) @ sK4 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
| ( $true = $false )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f487,f156]) ).
thf(f156,plain,
! [X0: $tType,X2: X0 > 'type/nums/num',X3: X0,X1: X0 > $o] :
( ( $true
= ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( X2 @ X3 ) ) ) )
| ( $false
= ( ( 'const/iterate/nsum' @ X0 @ X1 @ X2 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f147]) ).
thf(f147,plain,
! [X0: $tType,X2: X0 > 'type/nums/num',X3: X0,X1: X0 > $o] :
( ( $true
= ( ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( X2 @ Y0 ) ) )
@ X3 ) )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $false )
| ( $false
= ( ( 'const/iterate/nsum' @ X0 @ X1 @ X2 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ),
inference(pi_clausification,[status(thm)],[f98]) ).
thf(f98,plain,
! [X0: $tType,X2: X0 > 'type/nums/num',X1: X0 > $o] :
( ( ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( X2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( ( 'const/iterate/nsum' @ X0 @ X1 @ X2 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f91]) ).
thf(f91,plain,
! [X0: $tType,X2: X0 > 'type/nums/num',X1: X0 > $o] :
( ( ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( X2 @ Y0 ) ) ) )
= ( ( 'const/iterate/nsum' @ X0 @ X1 @ X2 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
! [X0: $tType,X2: X0 > 'type/nums/num',X1: X0 > $o] :
( ( $true
= ( ( ( 'const/iterate/nsum' @ X0 @ X1 @ X2 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( X2 @ Y0 ) ) ) ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f38]) ).
thf(f38,plain,
! [X0: $tType,X2: X0 > 'type/nums/num',X1: X0 > $o] :
( $true
= ( ( 'const/sets/FINITE' @ X0 @ X1 )
=> ( ( ( 'const/iterate/nsum' @ X0 @ X1 @ X2 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( X2 @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: $tType,X2: X0 > 'type/nums/num',X1: X0 > $o] :
( $true
= ( ^ [Y0: X0 > 'type/nums/num'] :
( ( 'const/sets/FINITE' @ X0 @ X1 )
=> ( ( ( 'const/iterate/nsum' @ X0 @ X1 @ Y0 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( !! @ X0
@ ^ [Y1: X0] :
( ( 'const/sets/IN' @ X0 @ Y1 @ X1 )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( Y0 @ Y1 ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: $tType,X1: X0 > $o] :
( $true
= ( !! @ ( X0 > 'type/nums/num' )
@ ^ [Y0: X0 > 'type/nums/num'] :
( ( 'const/sets/FINITE' @ X0 @ X1 )
=> ( ( ( 'const/iterate/nsum' @ X0 @ X1 @ Y0 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( !! @ X0
@ ^ [Y1: X0] :
( ( 'const/sets/IN' @ X0 @ Y1 @ X1 )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f35]) ).
thf(f35,plain,
! [X0: $tType,X1: X0 > $o] :
( $true
= ( ^ [Y0: X0 > $o] :
( !! @ ( X0 > 'type/nums/num' )
@ ^ [Y1: X0 > 'type/nums/num'] :
( ( 'const/sets/FINITE' @ X0 @ Y0 )
=> ( ( ( 'const/iterate/nsum' @ X0 @ Y0 @ Y1 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( !! @ X0
@ ^ [Y2: X0] :
( ( 'const/sets/IN' @ X0 @ Y2 @ Y0 )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( Y1 @ Y2 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $tType] :
( $true
= ( !! @ ( X0 > $o )
@ ^ [Y0: X0 > $o] :
( !! @ ( X0 > 'type/nums/num' )
@ ^ [Y1: X0 > 'type/nums/num'] :
( ( 'const/sets/FINITE' @ X0 @ Y0 )
=> ( ( ( 'const/iterate/nsum' @ X0 @ Y0 @ Y1 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( !! @ X0
@ ^ [Y2: X0] :
( ( 'const/sets/IN' @ X0 @ Y2 @ Y0 )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $tType] :
( $true
= ( !! @ ( X0 > $o )
@ ^ [Y0: X0 > $o] :
( !! @ ( X0 > 'type/nums/num' )
@ ^ [Y1: X0 > 'type/nums/num'] :
( ( 'const/sets/FINITE' @ X0 @ Y0 )
=> ( ( ( 'const/iterate/nsum' @ X0 @ Y0 @ Y1 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( !! @ X0
@ ^ [Y2: X0] :
( ( 'const/sets/IN' @ X0 @ Y2 @ Y0 )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(closure,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $tType] :
( $true
= ( !! @ ( X0 > $o )
@ ^ [Y0: X0 > $o] :
( !! @ ( X0 > 'type/nums/num' )
@ ^ [Y1: X0 > 'type/nums/num'] :
( ( 'const/sets/FINITE' @ X0 @ Y0 )
=> ( ( ( 'const/iterate/nsum' @ X0 @ Y0 @ Y1 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( !! @ X0
@ ^ [Y2: X0] :
( ( 'const/sets/IN' @ X0 @ Y2 @ Y0 )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $tType,X1: X0 > 'type/nums/num',X2: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X2 )
=> ( ( ( 'const/iterate/nsum' @ X0 @ X2 @ X1 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( ! [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( X1 @ X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: X0 > 'type/nums/num',X2: X0 > $o] :
( ( 'const/sets/FINITE' @ X0 @ X2 )
=> ( ( ( 'const/iterate/nsum' @ X0 @ X2 @ X1 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
= ( ! [X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6dAD0J2TVR/DTF2THF_32467.p','thm/iterate/NSUM_EQ_0_IFF_') ).
thf(f487,plain,
( ( $false
= ( ( 'const/sets/IN' @ 'type/nums/num' @ sK6 @ ( 'const/iterate/..' @ sK3 @ sK2 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( sK4 @ sK6 ) ) ) )
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f486,f30]) ).
thf(f30,plain,
! [X2: 'type/nums/num',X3: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ X1 @ X2 )
& ( 'const/arith/<=' @ X3 @ X1 ) )
= ( 'const/sets/IN' @ 'type/nums/num' @ X1 @ ( 'const/iterate/..' @ X3 @ X2 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: 'type/nums/num',X3: 'type/nums/num',X1: 'type/nums/num'] :
( ( ( 'const/sets/IN' @ 'type/nums/num' @ X1 @ ( 'const/iterate/..' @ X3 @ X2 ) )
= ( ( 'const/arith/<=' @ X1 @ X2 )
& ( 'const/arith/<=' @ X3 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f28]) ).
thf(f28,plain,
! [X2: 'type/nums/num',X3: 'type/nums/num',X1: 'type/nums/num'] :
( $true
= ( ^ [Y0: 'type/nums/num'] :
( ( 'const/sets/IN' @ 'type/nums/num' @ X1 @ ( 'const/iterate/..' @ Y0 @ X2 ) )
= ( ( 'const/arith/<=' @ X1 @ X2 )
& ( 'const/arith/<=' @ Y0 @ X1 ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X2: 'type/nums/num',X1: 'type/nums/num'] :
( ( !! @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ( 'const/sets/IN' @ 'type/nums/num' @ X1 @ ( 'const/iterate/..' @ Y0 @ X2 ) )
= ( ( 'const/arith/<=' @ X1 @ X2 )
& ( 'const/arith/<=' @ Y0 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X2: 'type/nums/num',X1: 'type/nums/num'] :
( $true
= ( ^ [Y0: 'type/nums/num'] :
( !! @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] :
( ( 'const/sets/IN' @ 'type/nums/num' @ X1 @ ( 'const/iterate/..' @ Y1 @ Y0 ) )
= ( ( 'const/arith/<=' @ X1 @ Y0 )
& ( 'const/arith/<=' @ Y1 @ X1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: 'type/nums/num'] :
( $true
= ( !! @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( !! @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] :
( ( 'const/sets/IN' @ 'type/nums/num' @ X1 @ ( 'const/iterate/..' @ Y1 @ Y0 ) )
= ( ( 'const/arith/<=' @ X1 @ Y0 )
& ( 'const/arith/<=' @ Y1 @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: 'type/nums/num'] :
( $true
= ( ^ [Y0: 'type/nums/num'] :
( !! @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] :
( !! @ 'type/nums/num'
@ ^ [Y2: 'type/nums/num'] :
( ( 'const/sets/IN' @ 'type/nums/num' @ Y0 @ ( 'const/iterate/..' @ Y2 @ Y1 ) )
= ( ( 'const/arith/<=' @ Y0 @ Y1 )
& ( 'const/arith/<=' @ Y2 @ Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( $true
= ( !! @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( !! @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] :
( !! @ 'type/nums/num'
@ ^ [Y2: 'type/nums/num'] :
( ( 'const/sets/IN' @ 'type/nums/num' @ Y0 @ ( 'const/iterate/..' @ Y2 @ Y1 ) )
= ( ( 'const/arith/<=' @ Y0 @ Y1 )
& ( 'const/arith/<=' @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( $true
= ( !! @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( !! @ 'type/nums/num'
@ ^ [Y1: 'type/nums/num'] :
( !! @ 'type/nums/num'
@ ^ [Y2: 'type/nums/num'] :
( ( 'const/sets/IN' @ 'type/nums/num' @ Y0 @ ( 'const/iterate/..' @ Y2 @ Y1 ) )
= ( ( 'const/arith/<=' @ Y0 @ Y1 )
& ( 'const/arith/<=' @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( ( 'const/sets/IN' @ 'type/nums/num' @ X2 @ ( 'const/iterate/..' @ X0 @ X1 ) )
= ( 'const/arith/<=' @ X0 @ X2 ) )
& ( 'const/arith/<=' @ X2 @ X1 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: 'type/nums/num',X1: 'type/nums/num',X2: 'type/nums/num'] :
( ( ( 'const/sets/IN' @ 'type/nums/num' @ X2 @ ( 'const/iterate/..' @ X0 @ X1 ) )
= ( 'const/arith/<=' @ X0 @ X2 ) )
& ( 'const/arith/<=' @ X2 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.6dAD0J2TVR/DTF2THF_32467.p','thm/iterate/IN_NUMSEG_') ).
thf(f486,plain,
( ( ( ( ( 'const/arith/<=' @ sK6 @ sK2 )
& ( 'const/arith/<=' @ sK3 @ sK6 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( sK4 @ sK6 ) ) )
= $false )
| ~ spl0_4 ),
inference(beta_eta_normalization,[status(thm)],[f485]) ).
thf(f485,plain,
( ( $false
= ( ^ [Y0: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ Y0 @ sK2 )
& ( 'const/arith/<=' @ sK3 @ Y0 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( sK4 @ Y0 ) ) )
@ sK6 ) )
| ~ spl0_4 ),
inference(sigma_clausification,[status(thm)],[f76]) ).
thf(f442,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[status(thm)],[f441]) ).
thf(f441,plain,
( $false
| ~ spl0_3 ),
inference(subsumption_resolution,[status(thm)],[f424,f83]) ).
thf(f83,plain,
( ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
!= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) @ sK4 ) )
| ~ spl0_3 ),
inference(equality_proxy_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
( ( $false
= ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) @ sK4 ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f72]) ).
thf(f72,definition,
( spl0_3
<=> ( $false
= ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) @ sK4 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f424,plain,
( ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) @ sK4 ) )
| ~ spl0_3 ),
inference(equality_proxy_clausification,[status(thm)],[f419]) ).
thf(f419,plain,
( ( $true
= ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) @ sK4 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f418]) ).
thf(f418,plain,
( ( $true = $false )
| ( $true
= ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) @ sK4 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f402,f23]) ).
thf(f402,plain,
( ( $true
= ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) @ sK4 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
| ( $false
= ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) ) )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f393]) ).
thf(f393,plain,
( ( $false
= ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) ) )
| ( $true
= ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) @ sK4 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
| ( $true = $false )
| ~ spl0_3 ),
inference(superposition,[status(thm)],[f255,f315]) ).
thf(f315,plain,
( ! [X1: 'type/nums/num'] :
( $true
= ( ( 'const/sets/IN' @ 'type/nums/num' @ X1 @ ( 'const/iterate/..' @ sK3 @ sK2 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( sK4 @ X1 ) ) ) )
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f314,f30]) ).
thf(f314,plain,
( ! [X1: 'type/nums/num'] :
( $true
= ( ( ( 'const/arith/<=' @ X1 @ sK2 )
& ( 'const/arith/<=' @ sK3 @ X1 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( sK4 @ X1 ) ) ) )
| ~ spl0_3 ),
inference(beta_eta_normalization,[status(thm)],[f313]) ).
thf(f313,plain,
( ! [X1: 'type/nums/num'] :
( ( ^ [Y0: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ Y0 @ sK2 )
& ( 'const/arith/<=' @ sK3 @ Y0 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( sK4 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_clausification,[status(thm)],[f292]) ).
thf(f292,plain,
( ( $false
!= ( !! @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ Y0 @ sK2 )
& ( 'const/arith/<=' @ sK3 @ Y0 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( sK4 @ Y0 ) ) ) ) )
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f61,f73]) ).
thf(f255,plain,
! [X0: $tType,X2: X0 > 'type/nums/num',X1: X0 > $o] :
( ( $false
= ( ( 'const/sets/IN' @ X0 @ ( sK5 @ X0 @ X1 @ X2 ) @ X1 )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( X2 @ ( sK5 @ X0 @ X1 @ X2 ) ) ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $false )
| ( $true
= ( ( 'const/iterate/nsum' @ X0 @ X1 @ X2 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f246]) ).
thf(f246,plain,
! [X0: $tType,X2: X0 > 'type/nums/num',X1: X0 > $o] :
( ( $true
= ( ( 'const/iterate/nsum' @ X0 @ X1 @ X2 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
| ( $false
= ( ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( X2 @ Y0 ) ) )
@ ( sK5 @ X0 @ X1 @ X2 ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f99]) ).
thf(f99,plain,
! [X0: $tType,X2: X0 > 'type/nums/num',X1: X0 > $o] :
( ( ( !! @ X0
@ ^ [Y0: X0] :
( ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( X2 @ Y0 ) ) ) )
= $false )
| ( $true
= ( ( 'const/iterate/nsum' @ X0 @ X1 @ X2 )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) )
| ( ( 'const/sets/FINITE' @ X0 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f91]) ).
thf(f77,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f63,f75,f72]) ).
thf(f63,plain,
( ( $false
= ( !! @ 'type/nums/num'
@ ^ [Y0: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ Y0 @ sK2 )
& ( 'const/arith/<=' @ sK3 @ Y0 ) )
=> ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( sK4 @ Y0 ) ) ) ) )
| ( $false
= ( ( 'const/nums/NUMERAL' @ 'const/nums/_0' )
= ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ sK3 @ sK2 ) @ sK4 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV506^1 : TPTP v9.2.1. Released v7.0.0.
% 0.13/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n008.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 12:48:24 EST 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.45 ---- Original DTF file ---
% 0.20/0.45 thf(spec,logic,$$dhol).
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 % File : SEV506^1 : TPTP v9.2.1. Released v7.0.0.
% 0.20/0.45 % Domain : Analysis
% 0.20/0.45 % Problem : NSUM_EQ_0_IFF_NUMSEG
% 0.20/0.45 % Version : Especial.
% 0.20/0.45 % English :
% 0.20/0.45
% 0.20/0.45 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.20/0.45 % Source : [Kal16]
% 0.20/0.45 % Names : NSUM_EQ_0_IFF_NUMSEG_.p [Kal16]
% 0.20/0.45
% 0.20/0.45 % Status : Theorem
% 0.20/0.45 % Rating : 0.00 v7.1.0
% 0.20/0.45 % Syntax : Number of formulae : 12 ( 2 unt; 8 typ; 0 def)
% 0.20/0.45 % Number of atoms : 18 ( 7 equ; 0 cnn)
% 0.20/0.45 % Maximal formula atoms : 2 ( 4 avg)
% 0.20/0.45 % Number of connectives : 41 ( 0 ~; 0 |; 2 &; 36 @)
% 0.20/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.20/0.45 % Maximal formula depth : 7 ( 5 avg)
% 0.20/0.45 % Number of types : 2 ( 1 usr)
% 0.20/0.45 % Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% 0.20/0.45 % Number of symbols : 8 ( 7 usr; 1 con; 0-3 aty)
% 0.20/0.45 % Number of variables : 16 ( 0 ^; 13 !; 0 ?; 16 :)
% 0.20/0.45 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.20/0.45 % SPC : TH1_THM_EQU_NAR
% 0.20/0.45
% 0.20/0.45 % Comments : Exported from core HOL Light.
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 thf('thf_type_type/nums/num',type,
% 0.20/0.45 'type/nums/num': $tType ).
% 0.20/0.45
% 0.20/0.45 thf('thf_const_const/sets/IN',type,
% 0.20/0.45 'const/sets/IN':
% 0.20/0.45 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.20/0.45
% 0.20/0.45 thf('thf_const_const/sets/FINITE',type,
% 0.20/0.45 'const/sets/FINITE':
% 0.20/0.45 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 0.20/0.45
% 0.20/0.45 thf('thf_const_const/nums/NUMERAL',type,
% 0.20/0.45 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 0.20/0.45
% 0.20/0.45 thf('thf_const_const/nums/_0',type,
% 0.20/0.45 'const/nums/_0': 'type/nums/num' ).
% 0.20/0.45
% 0.20/0.45 thf('thf_const_const/iterate/nsum',type,
% 0.20/0.45 'const/iterate/nsum':
% 0.20/0.45 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/nums/num' ) > 'type/nums/num' ) ).
% 0.20/0.45
% 0.20/0.45 thf('thf_const_const/iterate/..',type,
% 0.20/0.45 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
% 0.20/0.45
% 0.20/0.45 thf('thf_const_const/arith/<=',type,
% 0.20/0.45 'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
% 0.20/0.45
% 0.20/0.45 thf('thm/iterate/IN_NUMSEG_',axiom,
% 0.20/0.45 ! [A: 'type/nums/num',A0: 'type/nums/num',A1: 'type/nums/num'] :
% 0.20/0.45 ( ( 'const/sets/IN' @ 'type/nums/num' @ A1 @ ( 'const/iterate/..' @ A @ A0 ) )
% 0.20/0.45 = ( ( 'const/arith/<=' @ A @ A1 )
% 0.20/0.45 & ( 'const/arith/<=' @ A1 @ A0 ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf('thm/iterate/NSUM_EQ_0_IFF_',axiom,
% 0.20/0.45 ! [A: $tType,A0: A > 'type/nums/num',A1: A > $o] :
% 0.20/0.45 ( ( 'const/sets/FINITE' @ A @ A1 )
% 0.20/0.45 => ( ( ( 'const/iterate/nsum' @ A @ A1 @ A0 )
% 0.20/0.45 = ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
% 0.20/0.45 = ( ! [A2: A] :
% 0.20/0.45 ( ( 'const/sets/IN' @ A @ A2 @ A1 )
% 0.20/0.45 => ( ( A0 @ A2 )
% 0.20/0.45 = ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 thf('thm/iterate/FINITE_NUMSEG_',axiom,
% 0.20/0.45 ! [A: 'type/nums/num',A0: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ A @ A0 ) ) ).
% 0.20/0.45
% 0.20/0.45 thf('thm/iterate/NSUM_EQ_0_IFF_NUMSEG_',conjecture,
% 0.20/0.45 ! [A: 'type/nums/num' > 'type/nums/num',A0: 'type/nums/num',A1: 'type/nums/num'] :
% 0.20/0.45 ( ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A0 @ A1 ) @ A )
% 0.20/0.45 = ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
% 0.20/0.45 = ( ! [A2: 'type/nums/num'] :
% 0.20/0.45 ( ( ( 'const/arith/<=' @ A0 @ A2 )
% 0.20/0.45 & ( 'const/arith/<=' @ A2 @ A1 ) )
% 0.20/0.45 => ( ( A @ A2 )
% 0.20/0.45 = ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ) ) ).
% 0.20/0.45
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 ------------------------
% 1.57/1.23 ---- Embedded in THF ---
% 1.57/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.57/1.23 %%% Generated on Tue Feb 24 12:48:25 EST 2026
% 1.57/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.57/1.23 %%% Logic specification used:
% 1.57/1.23 %%% thf(spec, logic, $$dhol).
% 1.57/1.23
% 1.57/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.6dAD0J2TVR/DTF2DTF32467.p
% See solution above
% 1.57/1.23 ------------------------
% 1.57/1.24 ---- Cleaned THF ---
% 1.57/1.24 thf('thf_type_type/nums/num',type,
% 1.57/1.24 'type/nums/num': $tType ).
% 1.57/1.24
% 1.57/1.24 thf('thf_const_const/sets/IN',type,
% 1.57/1.24 'const/sets/IN':
% 1.57/1.24 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.57/1.24
% 1.57/1.24 thf('thf_const_const/sets/FINITE',type,
% 1.57/1.24 'const/sets/FINITE':
% 1.57/1.24 !>[A: $tType] : ( ( A > $o ) > $o ) ).
% 1.57/1.24
% 1.57/1.24 thf('thf_const_const/nums/NUMERAL',type,
% 1.57/1.24 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
% 1.57/1.24
% 1.57/1.24 thf('thf_const_const/nums/_0',type,
% 1.57/1.24 'const/nums/_0': 'type/nums/num' ).
% 1.57/1.24
% 1.57/1.24 thf('thf_const_const/iterate/nsum',type,
% 1.57/1.24 'const/iterate/nsum':
% 1.57/1.24 !>[A: $tType] : ( ( A > $o ) > ( A > 'type/nums/num' ) > 'type/nums/num' ) ).
% 1.57/1.24
% 1.57/1.24 thf('thf_const_const/iterate/..',type,
% 1.57/1.24 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o ).
% 1.57/1.24
% 1.57/1.24 thf('thf_const_const/arith/<=',type,
% 1.57/1.24 'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
% 1.57/1.24
% 1.57/1.24 thf('thm/iterate/IN_NUMSEG_',axiom,
% 1.57/1.24 ! [A: 'type/nums/num',A0: 'type/nums/num',A1: 'type/nums/num'] :
% 1.57/1.24 ( ( 'const/sets/IN' @ 'type/nums/num' @ A1 @ ( 'const/iterate/..' @ A @ A0 ) )
% 1.57/1.24 = ( ( 'const/arith/<=' @ A @ A1 )
% 1.57/1.24 & ( 'const/arith/<=' @ A1 @ A0 ) ) ) ).
% 1.57/1.24
% 1.57/1.24 thf('thm/iterate/NSUM_EQ_0_IFF_',axiom,
% 1.57/1.24 ! [A: $tType,A0: A > 'type/nums/num',A1: A > $o] :
% 1.57/1.24 ( ( 'const/sets/FINITE' @ A @ A1 )
% 1.57/1.24 => ( ( ( 'const/iterate/nsum' @ A @ A1 @ A0 )
% 1.57/1.24 = ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
% 1.57/1.24 = ( ! [A2: A] :
% 1.57/1.24 ( ( 'const/sets/IN' @ A @ A2 @ A1 )
% 1.57/1.24 => ( ( A0 @ A2 )
% 1.57/1.24 = ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ) ) ) ).
% 1.57/1.24
% 1.57/1.24 thf('thm/iterate/FINITE_NUMSEG_',axiom,
% 1.57/1.24 ! [A: 'type/nums/num',A0: 'type/nums/num'] : ( 'const/sets/FINITE' @ 'type/nums/num' @ ( 'const/iterate/..' @ A @ A0 ) ) ).
% 1.57/1.24
% 1.57/1.24 thf('thm/iterate/NSUM_EQ_0_IFF_NUMSEG_',conjecture,
% 1.57/1.24 ! [A: 'type/nums/num' > 'type/nums/num',A0: 'type/nums/num',A1: 'type/nums/num'] :
% 1.57/1.24 ( ( ( 'const/iterate/nsum' @ 'type/nums/num' @ ( 'const/iterate/..' @ A0 @ A1 ) @ A )
% 1.57/1.24 = ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) )
% 1.57/1.24 = ( ! [A2: 'type/nums/num'] :
% 1.57/1.24 ( ( ( 'const/arith/<=' @ A0 @ A2 )
% 1.57/1.24 & ( 'const/arith/<=' @ A2 @ A1 ) )
% 1.57/1.24 => ( ( A @ A2 )
% 1.57/1.24 = ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ) ) ) ).
% 1.57/1.24 ------------------------
% 1.57/1.25 % (32680)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32467 for (3000ds/18Mi)
% 1.57/1.26 % (32674)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32467 for (3000ds/183Mi)
% 1.57/1.26 % (32679)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_32467 for (3000ds/275Mi)
% 1.57/1.26 % (32678)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_32467 for (3000ds/2Mi)
% 1.57/1.26 % (32678)Instruction limit reached!
% 1.57/1.26 % (32678)------------------------------
% 1.57/1.26 % (32678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.26 % (32678)Termination reason: Unknown
% 1.57/1.26 % (32678)Termination phase: Property scanning
% 1.57/1.26
% 1.57/1.26 % (32678)Memory used [KB]: 895
% 1.57/1.26 % (32678)Time elapsed: 0.002 s
% 1.57/1.26 % (32678)Instructions burned: 2 (million)
% 1.57/1.26 % (32678)------------------------------
% 1.57/1.26 % (32678)------------------------------
% 1.57/1.26 % (32676)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_32467 for (3000ds/27Mi)
% 1.57/1.26 % (32675)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_32467 for (3000ds/4Mi)
% 1.57/1.26 % (32677)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32467 for (3000ds/2Mi)
% 1.57/1.26 % (32680)Instruction limit reached!
% 1.57/1.26 % (32680)------------------------------
% 1.57/1.26 % (32680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.26 % (32680)Termination reason: Unknown
% 1.57/1.26 % (32680)Termination phase: Saturation
% 1.57/1.26
% 1.57/1.26 % (32680)Memory used [KB]: 5628
% 1.57/1.26 % (32680)Time elapsed: 0.009 s
% 1.57/1.26 % (32680)Instructions burned: 20 (million)
% 1.57/1.26 % (32680)------------------------------
% 1.57/1.26 % (32680)------------------------------
% 1.57/1.26 % (32677)Instruction limit reached!
% 1.57/1.26 % (32677)------------------------------
% 1.57/1.26 % (32677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.26 % (32677)Termination reason: Unknown
% 1.57/1.26 % (32677)Termination phase: Property scanning
% 1.57/1.26
% 1.57/1.26 % (32677)Memory used [KB]: 895
% 1.57/1.26 % (32677)Time elapsed: 0.003 s
% 1.57/1.26 % (32677)Instructions burned: 2 (million)
% 1.57/1.26 % (32677)------------------------------
% 1.57/1.26 % (32677)------------------------------
% 1.57/1.26 % (32679)Refutation not found, incomplete strategy
% 1.57/1.26 % (32679)------------------------------
% 1.57/1.26 % (32679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.26 % (32679)Termination reason: Refutation not found, incomplete strategy
% 1.57/1.26
% 1.57/1.26
% 1.57/1.26 % (32679)Memory used [KB]: 5500
% 1.57/1.26 % (32679)Time elapsed: 0.004 s
% 1.57/1.26 % (32679)Instructions burned: 7 (million)
% 1.57/1.26 % (32679)------------------------------
% 1.57/1.26 % (32679)------------------------------
% 1.57/1.26 % (32675)Instruction limit reached!
% 1.57/1.26 % (32675)------------------------------
% 1.57/1.26 % (32675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.26 % (32675)Termination reason: Unknown
% 1.57/1.26 % (32675)Termination phase: Saturation
% 1.57/1.26
% 1.57/1.26 % (32675)Memory used [KB]: 5500
% 1.57/1.26 % (32675)Time elapsed: 0.004 s
% 1.57/1.26 % (32675)Instructions burned: 4 (million)
% 1.57/1.26 % (32675)------------------------------
% 1.57/1.26 % (32675)------------------------------
% 1.57/1.27 % (32691)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_32467 for (2999ds/1041Mi)
% 1.57/1.27 % (32676)Instruction limit reached!
% 1.57/1.27 % (32676)------------------------------
% 1.57/1.27 % (32676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.27 % (32676)Termination reason: Unknown
% 1.57/1.27 % (32676)Termination phase: Saturation
% 1.57/1.27
% 1.57/1.27 % (32676)Memory used [KB]: 5628
% 1.57/1.27 % (32676)Time elapsed: 0.017 s
% 1.57/1.27 % (32676)Instructions burned: 27 (million)
% 1.57/1.27 % (32676)------------------------------
% 1.57/1.27 % (32676)------------------------------
% 1.57/1.28 % (32690)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_32467 for (2999ds/3Mi)
% 1.57/1.28 % (32688)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_32467 for (2999ds/37Mi)
% 1.57/1.28 % (32687)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_32467 for (2999ds/3Mi)
% 1.57/1.28 % (32690)Instruction limit reached!
% 1.57/1.28 % (32690)------------------------------
% 1.57/1.28 % (32690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.28 % (32690)Termination reason: Unknown
% 1.57/1.28 % (32690)Termination phase: Saturation
% 1.57/1.28
% 1.57/1.28 % (32690)Memory used [KB]: 5500
% 1.57/1.28 % (32690)Time elapsed: 0.003 s
% 1.57/1.28 % (32690)Instructions burned: 3 (million)
% 1.57/1.28 % (32690)------------------------------
% 1.57/1.28 % (32690)------------------------------
% 1.57/1.28 % (32687)Instruction limit reached!
% 1.57/1.28 % (32687)------------------------------
% 1.57/1.28 % (32687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.28 % (32687)Termination reason: Unknown
% 1.57/1.28 % (32687)Termination phase: Saturation
% 1.57/1.28
% 1.57/1.28 % (32687)Memory used [KB]: 5500
% 1.57/1.28 % (32687)Time elapsed: 0.004 s
% 1.57/1.28 % (32687)Instructions burned: 4 (million)
% 1.57/1.28 % (32687)------------------------------
% 1.57/1.28 % (32687)------------------------------
% 1.57/1.29 % (32689)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_32467 for (2999ds/15Mi)
% 1.57/1.29 % (32698)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_32467 for (2999ds/16Mi)
% 1.57/1.29 % (32688)Instruction limit reached!
% 1.57/1.29 % (32688)------------------------------
% 1.57/1.29 % (32688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.29 % (32688)Termination reason: Unknown
% 1.57/1.29 % (32688)Termination phase: Saturation
% 1.57/1.29
% 1.57/1.29 % (32688)Memory used [KB]: 5756
% 1.57/1.29 % (32688)Time elapsed: 0.015 s
% 1.57/1.29 % (32688)Instructions burned: 37 (million)
% 1.57/1.29 % (32688)------------------------------
% 1.57/1.29 % (32688)------------------------------
% 1.57/1.29 % (32697)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_32467 for (2999ds/7Mi)
% 1.57/1.29 % (32689)Instruction limit reached!
% 1.57/1.29 % (32689)------------------------------
% 1.57/1.29 % (32689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.29 % (32689)Termination reason: Unknown
% 1.57/1.29 % (32689)Termination phase: Saturation
% 1.57/1.29
% 1.57/1.29 % (32689)Memory used [KB]: 5756
% 1.57/1.29 % (32689)Time elapsed: 0.011 s
% 1.57/1.29 % (32689)Instructions burned: 16 (million)
% 1.57/1.29 % (32689)------------------------------
% 1.57/1.29 % (32689)------------------------------
% 1.57/1.29 % (32698)Instruction limit reached!
% 1.57/1.29 % (32698)------------------------------
% 1.57/1.29 % (32698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.29 % (32698)Termination reason: Unknown
% 1.57/1.29 % (32698)Termination phase: Saturation
% 1.57/1.29
% 1.57/1.29 % (32698)Memory used [KB]: 5756
% 1.57/1.29 % (32698)Time elapsed: 0.007 s
% 1.57/1.29 % (32698)Instructions burned: 16 (million)
% 1.57/1.29 % (32698)------------------------------
% 1.57/1.29 % (32698)------------------------------
% 1.64/1.30 % (32697)Instruction limit reached!
% 1.64/1.30 % (32697)------------------------------
% 1.64/1.30 % (32697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (32697)Termination reason: Unknown
% 1.64/1.30 % (32697)Termination phase: Saturation
% 1.64/1.30
% 1.64/1.30 % (32697)Memory used [KB]: 1023
% 1.64/1.30 % (32697)Time elapsed: 0.006 s
% 1.64/1.30 % (32697)Instructions burned: 8 (million)
% 1.64/1.30 % (32697)------------------------------
% 1.64/1.30 % (32697)------------------------------
% 1.64/1.30 % (32700)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_32467 for (2999ds/3Mi)
% 1.64/1.30 % (32700)Instruction limit reached!
% 1.64/1.30 % (32700)------------------------------
% 1.64/1.30 % (32700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.30 % (32700)Termination reason: Unknown
% 1.64/1.30 % (32700)Termination phase: Property scanning
% 1.64/1.30
% 1.64/1.30 % (32700)Memory used [KB]: 1023
% 1.64/1.30 % (32700)Time elapsed: 0.003 s
% 1.64/1.30 % (32700)Instructions burned: 3 (million)
% 1.64/1.30 % (32700)------------------------------
% 1.64/1.30 % (32700)------------------------------
% 1.64/1.31 % (32707)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_32467 for (2999ds/3Mi)
% 1.64/1.31 % (32707)Instruction limit reached!
% 1.64/1.31 % (32707)------------------------------
% 1.64/1.31 % (32707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (32707)Termination reason: Unknown
% 1.64/1.31 % (32707)Termination phase: Property scanning
% 1.64/1.31
% 1.64/1.31 % (32707)Memory used [KB]: 1023
% 1.64/1.31 % (32707)Time elapsed: 0.002 s
% 1.64/1.31 % (32707)Instructions burned: 3 (million)
% 1.64/1.31 % (32707)------------------------------
% 1.64/1.31 % (32707)------------------------------
% 1.64/1.31 % (32708)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_32467 for (2999ds/7Mi)
% 1.64/1.31 % (32709)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_32467 for (2999ds/3Mi)
% 1.64/1.31 % (32709)Instruction limit reached!
% 1.64/1.31 % (32709)------------------------------
% 1.64/1.31 % (32709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (32709)Termination reason: Unknown
% 1.64/1.31 % (32709)Termination phase: Saturation
% 1.64/1.31
% 1.64/1.31 % (32709)Memory used [KB]: 1023
% 1.64/1.31 % (32709)Time elapsed: 0.003 s
% 1.64/1.31 % (32709)Instructions burned: 3 (million)
% 1.64/1.31 % (32709)------------------------------
% 1.64/1.31 % (32709)------------------------------
% 1.64/1.31 % (32708)Refutation not found, incomplete strategy
% 1.64/1.31 % (32708)------------------------------
% 1.64/1.31 % (32708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.31 % (32708)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.31
% 1.64/1.31
% 1.64/1.31 % (32708)Memory used [KB]: 5500
% 1.64/1.31 % (32708)Time elapsed: 0.004 s
% 1.64/1.31 % (32708)Instructions burned: 4 (million)
% 1.64/1.31 % (32708)------------------------------
% 1.64/1.31 % (32708)------------------------------
% 1.64/1.32 % (32710)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_32467 for (2999ds/4Mi)
% 1.64/1.32 % (32711)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_32467 for (2999ds/18Mi)
% 1.64/1.32 % (32717)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_32467 for (2999ds/710Mi)
% 1.64/1.32 % (32710)Instruction limit reached!
% 1.64/1.32 % (32710)------------------------------
% 1.64/1.32 % (32710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.32 % (32710)Termination reason: Unknown
% 1.64/1.32 % (32710)Termination phase: Saturation
% 1.64/1.32
% 1.64/1.32 % (32710)Memory used [KB]: 5500
% 1.64/1.32 % (32710)Time elapsed: 0.004 s
% 1.64/1.32 % (32710)Instructions burned: 5 (million)
% 1.64/1.32 % (32710)------------------------------
% 1.64/1.32 % (32710)------------------------------
% 1.64/1.32 % (32718)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_32467 for (2999ds/6Mi)
% 1.64/1.33 % (32711)Instruction limit reached!
% 1.64/1.33 % (32711)------------------------------
% 1.64/1.33 % (32711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.33 % (32711)Termination reason: Unknown
% 1.64/1.33 % (32711)Termination phase: Saturation
% 1.64/1.33
% 1.64/1.33 % (32711)Memory used [KB]: 5628
% 1.64/1.33 % (32711)Time elapsed: 0.011 s
% 1.64/1.33 % (32711)Instructions burned: 18 (million)
% 1.64/1.33 % (32711)------------------------------
% 1.64/1.33 % (32711)------------------------------
% 1.64/1.33 % (32718)Instruction limit reached!
% 1.64/1.33 % (32718)------------------------------
% 1.64/1.33 % (32718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.33 % (32718)Termination reason: Unknown
% 1.64/1.33 % (32718)Termination phase: Saturation
% 1.64/1.33
% 1.64/1.33 % (32718)Memory used [KB]: 5500
% 1.64/1.33 % (32718)Time elapsed: 0.005 s
% 1.64/1.33 % (32718)Instructions burned: 7 (million)
% 1.64/1.33 % (32718)------------------------------
% 1.64/1.33 % (32718)------------------------------
% 1.64/1.33 % (32691)First to succeed.
% 1.64/1.33 % (32720)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_32467 for (2999ds/902Mi)
% 1.64/1.33 % (32691)Refutation found. Thanks to Tanya!
% 1.64/1.33 % SZS status Theorem for DTF2THF_32467
% 1.64/1.33 % SZS output start Proof for DTF2THF_32467
% 1.64/1.33 thf(type_def_6, type, 'type/nums/num': $tType).
% 1.64/1.33 thf(func_def_0, type, 'type/nums/num': $tType).
% 1.64/1.33 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.64/1.33 thf(func_def_2, type, 'const/sets/FINITE': !>[X0: $tType]:((X0 > $o) > $o)).
% 1.64/1.33 thf(func_def_3, type, 'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num').
% 1.64/1.33 thf(func_def_4, type, 'const/nums/_0': 'type/nums/num').
% 1.64/1.33 thf(func_def_5, type, 'const/iterate/nsum': !>[X0: $tType]:((X0 > $o) > (X0 > 'type/nums/num') > 'type/nums/num')).
% 1.64/1.33 thf(func_def_6, type, 'const/iterate/..': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' > $o).
% 1.64/1.33 thf(func_def_7, type, 'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o).
% 1.64/1.33 thf(func_def_22, type, ph1: !>[X0: $tType]:(X0)).
% 1.64/1.33 thf(func_def_23, type, sK2: 'type/nums/num').
% 1.64/1.33 thf(func_def_24, type, sK3: 'type/nums/num').
% 1.64/1.33 thf(func_def_25, type, sK4: 'type/nums/num' > 'type/nums/num').
% 1.64/1.33 thf(func_def_26, type, sK5: !>[X0: $tType]:((X0 > $o) > (X0 > 'type/nums/num') > X0)).
% 1.64/1.33 thf(func_def_27, type, sK6: 'type/nums/num').
% 1.64/1.33 thf(f520,plain,(
% 1.64/1.33 $false),
% 1.64/1.33 inference(avatar_sat_refutation,[status(thm)],[f77,f442,f518])).
% 1.64/1.33 thf(f518,plain,(
% 1.64/1.33 ~spl0_4),
% 1.64/1.33 inference(avatar_contradiction_clause,[status(thm)],[f517])).
% 1.64/1.33 thf(f517,plain,(
% 1.64/1.33 $false | ~spl0_4),
% 1.64/1.33 inference(trivial_inequality_removal,[status(thm)],[f512])).
% 1.64/1.33 thf(f512,plain,(
% 1.64/1.33 ($true = $false) | ~spl0_4),
% 1.64/1.33 inference(superposition,[status(thm)],[f506,f23])).
% 1.64/1.33 thf(f23,plain,(
% 1.64/1.33 ( ! [X2 : 'type/nums/num',X1 : 'type/nums/num'] : (($true = ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X2 @ X1)))) )),
% 1.64/1.33 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.64/1.33 thf(f22,plain,(
% 1.64/1.33 ( ! [X2 : 'type/nums/num',X1 : 'type/nums/num'] : ((((^[Y0 : 'type/nums/num']: ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ Y0 @ X1))) @ X2) = $true)) )),
% 1.64/1.33 inference(pi_clausification,[status(thm)],[f21])).
% 1.64/1.33 thf(f21,plain,(
% 1.64/1.33 ( ! [X1 : 'type/nums/num'] : (($true = (!! @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ Y0 @ X1)))))) )),
% 1.64/1.33 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.64/1.33 thf(f20,plain,(
% 1.64/1.33 ( ! [X1 : 'type/nums/num'] : ((((^[Y0 : 'type/nums/num']: (!! @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ Y1 @ Y0))))) @ X1) = $true)) )),
% 1.64/1.33 inference(pi_clausification,[status(thm)],[f17])).
% 1.64/1.33 thf(f17,plain,(
% 1.64/1.33 ((!! @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: (!! @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ Y1 @ Y0)))))) = $true)),
% 1.64/1.33 inference(cnf_transformation,[status(thm)],[f8])).
% 1.64/1.33 thf(f8,plain,(
% 1.64/1.33 ((!! @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: (!! @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ Y1 @ Y0)))))) = $true)),
% 1.64/1.33 inference(fool_elimination,[status(thm)],[f7])).
% 1.64/1.33 thf(f7,plain,(
% 1.64/1.33 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1))),
% 1.64/1.33 inference(rectify,[status(thm)],[f3])).
% 1.64/1.33 thf(f3,axiom,(
% 1.64/1.33 ! [X0 : 'type/nums/num',X1 : 'type/nums/num'] : ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ X0 @ X1))),
% 1.64/1.33 file('/export/starexec/sandbox2/tmp/tmp.6dAD0J2TVR/DTF2THF_32467.p','thm/iterate/FINITE_NUMSEG_')).
% 1.64/1.33 thf(f506,plain,(
% 1.64/1.33 ($false = ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2))) | ~spl0_4),
% 1.64/1.33 inference(trivial_inequality_removal,[status(thm)],[f505])).
% 1.64/1.33 thf(f505,plain,(
% 1.64/1.33 ($true = $false) | ($false = ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2))) | ~spl0_4),
% 1.64/1.33 inference(boolean_simplification,[status(thm)],[f504])).
% 1.64/1.33 thf(f504,plain,(
% 1.64/1.33 ((('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/nums/NUMERAL' @ 'const/nums/_0')) = $false) | ($false = ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2))) | ~spl0_4),
% 1.64/1.33 inference(forward_demodulation,[status(thm)],[f501,f450])).
% 1.64/1.33 thf(f450,plain,(
% 1.64/1.33 (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK4)) | ~spl0_4),
% 1.64/1.33 inference(equality_proxy_clausification,[status(thm)],[f446])).
% 1.64/1.33 thf(f446,plain,(
% 1.64/1.33 ($false != (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK4))) | ~spl0_4),
% 1.64/1.33 inference(forward_demodulation,[status(thm)],[f61,f76])).
% 1.64/1.33 thf(f76,plain,(
% 1.64/1.33 ($false = (!! @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: ((('const/arith/<=' @ Y0 @ sK2) & ('const/arith/<=' @ sK3 @ Y0)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (sK4 @ Y0)))))) | ~spl0_4),
% 1.64/1.33 inference(avatar_component_clause,[status(thm)],[f75])).
% 1.64/1.33 thf(f75,definition,(
% 1.64/1.33 spl0_4 <=> ($false = (!! @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: ((('const/arith/<=' @ Y0 @ sK2) & ('const/arith/<=' @ sK3 @ Y0)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (sK4 @ Y0))))))),
% 1.64/1.33 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.64/1.33 thf(f61,plain,(
% 1.64/1.33 ((!! @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: ((('const/arith/<=' @ Y0 @ sK2) & ('const/arith/<=' @ sK3 @ Y0)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (sK4 @ Y0))))) != (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK4)))),
% 1.64/1.33 inference(equality_proxy_clausification,[status(thm)],[f60])).
% 1.64/1.33 thf(f60,plain,(
% 1.64/1.33 ($false = ((!! @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: ((('const/arith/<=' @ Y0 @ sK2) & ('const/arith/<=' @ sK3 @ Y0)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (sK4 @ Y0))))) = (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK4))))),
% 1.64/1.33 inference(beta_eta_normalization,[status(thm)],[f59])).
% 1.64/1.33 thf(f59,plain,(
% 1.64/1.33 ($false = ((^[Y0 : 'type/nums/num' > 'type/nums/num']: ((!! @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: ((('const/arith/<=' @ Y1 @ sK2) & ('const/arith/<=' @ sK3 @ Y1)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (Y0 @ Y1))))) = (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ Y0)))) @ sK4))),
% 1.64/1.33 inference(sigma_clausification,[status(thm)],[f58])).
% 1.64/1.33 thf(f58,plain,(
% 1.64/1.33 ($false = (!! @ ('type/nums/num' > 'type/nums/num') @ (^[Y0 : 'type/nums/num' > 'type/nums/num']: ((!! @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: ((('const/arith/<=' @ Y1 @ sK2) & ('const/arith/<=' @ sK3 @ Y1)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (Y0 @ Y1))))) = (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ Y0))))))),
% 1.64/1.33 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.64/1.33 thf(f57,plain,(
% 1.64/1.33 (((^[Y0 : 'type/nums/num']: (!! @ ('type/nums/num' > 'type/nums/num') @ (^[Y1 : 'type/nums/num' > 'type/nums/num']: ((!! @ 'type/nums/num' @ (^[Y2 : 'type/nums/num']: ((('const/arith/<=' @ Y2 @ sK2) & ('const/arith/<=' @ Y0 @ Y2)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (Y1 @ Y2))))) = (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ Y0 @ sK2) @ Y1)))))) @ sK3) = $false)),
% 1.64/1.33 inference(sigma_clausification,[status(thm)],[f56])).
% 1.64/1.33 thf(f56,plain,(
% 1.64/1.33 ($false = (!! @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: (!! @ ('type/nums/num' > 'type/nums/num') @ (^[Y1 : 'type/nums/num' > 'type/nums/num']: ((!! @ 'type/nums/num' @ (^[Y2 : 'type/nums/num']: ((('const/arith/<=' @ Y2 @ sK2) & ('const/arith/<=' @ Y0 @ Y2)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (Y1 @ Y2))))) = (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ Y0 @ sK2) @ Y1))))))))),
% 1.64/1.33 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.64/1.33 thf(f55,plain,(
% 1.64/1.33 (((^[Y0 : 'type/nums/num']: (!! @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: (!! @ ('type/nums/num' > 'type/nums/num') @ (^[Y2 : 'type/nums/num' > 'type/nums/num']: ((!! @ 'type/nums/num' @ (^[Y3 : 'type/nums/num']: ((('const/arith/<=' @ Y3 @ Y0) & ('const/arith/<=' @ Y1 @ Y3)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (Y2 @ Y3))))) = (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ Y1 @ Y0) @ Y2)))))))) @ sK2) = $false)),
% 1.64/1.33 inference(sigma_clausification,[status(thm)],[f47])).
% 1.64/1.33 thf(f47,plain,(
% 1.64/1.33 ($false = (!! @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: (!! @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: (!! @ ('type/nums/num' > 'type/nums/num') @ (^[Y2 : 'type/nums/num' > 'type/nums/num']: ((!! @ 'type/nums/num' @ (^[Y3 : 'type/nums/num']: ((('const/arith/<=' @ Y3 @ Y0) & ('const/arith/<=' @ Y1 @ Y3)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (Y2 @ Y3))))) = (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ Y1 @ Y0) @ Y2))))))))))),
% 1.64/1.33 inference(not_proxy_clausification,[status(thm)],[f18])).
% 1.64/1.33 thf(f18,plain,(
% 1.64/1.33 ((~ (!! @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: (!! @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: (!! @ ('type/nums/num' > 'type/nums/num') @ (^[Y2 : 'type/nums/num' > 'type/nums/num']: ((!! @ 'type/nums/num' @ (^[Y3 : 'type/nums/num']: ((('const/arith/<=' @ Y3 @ Y0) & ('const/arith/<=' @ Y1 @ Y3)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (Y2 @ Y3))))) = (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ Y1 @ Y0) @ Y2)))))))))) = $true)),
% 1.64/1.33 inference(cnf_transformation,[status(thm)],[f12])).
% 1.64/1.33 thf(f12,plain,(
% 1.64/1.33 ((~ (!! @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: (!! @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: (!! @ ('type/nums/num' > 'type/nums/num') @ (^[Y2 : 'type/nums/num' > 'type/nums/num']: ((!! @ 'type/nums/num' @ (^[Y3 : 'type/nums/num']: ((('const/arith/<=' @ Y3 @ Y0) & ('const/arith/<=' @ Y1 @ Y3)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (Y2 @ Y3))))) = (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ Y1 @ Y0) @ Y2)))))))))) = $true)),
% 1.64/1.33 inference(fool_elimination,[status(thm)],[f11])).
% 1.64/1.33 thf(f11,plain,(
% 1.64/1.33 ~! [X0 : 'type/nums/num' > 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : (! [X3 : 'type/nums/num'] : ((('const/arith/<=' @ X1 @ X3) & ('const/arith/<=' @ X3 @ X2)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X0 @ X3))) = (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)))),
% 1.64/1.33 inference(rectify,[status(thm)],[f5])).
% 1.64/1.33 thf(f5,negated_conjecture,(
% 1.64/1.33 ~! [X0 : 'type/nums/num' > 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : (! [X3 : 'type/nums/num'] : ((('const/arith/<=' @ X1 @ X3) & ('const/arith/<=' @ X3 @ X2)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X0 @ X3))) = (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)))),
% 1.64/1.33 inference(negated_conjecture,[status(cth)],[f4])).
% 1.64/1.33 thf(f4,conjecture,(
% 1.64/1.33 ! [X0 : 'type/nums/num' > 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : (! [X3 : 'type/nums/num'] : ((('const/arith/<=' @ X1 @ X3) & ('const/arith/<=' @ X3 @ X2)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X0 @ X3))) = (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ X1 @ X2) @ X0)))),
% 1.64/1.33 file('/export/starexec/sandbox2/tmp/tmp.6dAD0J2TVR/DTF2THF_32467.p','thm/iterate/NSUM_EQ_0_IFF_NUMSEG_')).
% 1.64/1.33 thf(f501,plain,(
% 1.64/1.33 ($false = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK4) = ('const/nums/NUMERAL' @ 'const/nums/_0'))) | ($false = ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2))) | ~spl0_4),
% 1.64/1.33 inference(trivial_inequality_removal,[status(thm)],[f493])).
% 1.64/1.33 thf(f493,plain,(
% 1.64/1.33 ($false = ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2))) | ($false = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK4) = ('const/nums/NUMERAL' @ 'const/nums/_0'))) | ($true = $false) | ~spl0_4),
% 1.64/1.33 inference(superposition,[status(thm)],[f487,f156])).
% 1.64/1.33 thf(f156,plain,(
% 1.64/1.33 ( ! [X0 : $tType,X2 : X0 > 'type/nums/num',X3 : X0,X1 : X0 > $o] : (($true = (('const/sets/IN' @ X0 @ X3 @ X1) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X2 @ X3)))) | ($false = (('const/iterate/nsum' @ X0 @ X1 @ X2) = ('const/nums/NUMERAL' @ 'const/nums/_0'))) | (('const/sets/FINITE' @ X0 @ X1) = $false)) )),
% 1.64/1.33 inference(beta_eta_normalization,[status(thm)],[f147])).
% 1.64/1.33 thf(f147,plain,(
% 1.64/1.33 ( ! [X0 : $tType,X2 : X0 > 'type/nums/num',X3 : X0,X1 : X0 > $o] : (($true = ((^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X1) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X2 @ Y0)))) @ X3)) | (('const/sets/FINITE' @ X0 @ X1) = $false) | ($false = (('const/iterate/nsum' @ X0 @ X1 @ X2) = ('const/nums/NUMERAL' @ 'const/nums/_0')))) )),
% 1.64/1.33 inference(pi_clausification,[status(thm)],[f98])).
% 1.64/1.33 thf(f98,plain,(
% 1.64/1.33 ( ! [X0 : $tType,X2 : X0 > 'type/nums/num',X1 : X0 > $o] : (((!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X1) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X2 @ Y0))))) = $true) | ($false = (('const/iterate/nsum' @ X0 @ X1 @ X2) = ('const/nums/NUMERAL' @ 'const/nums/_0'))) | (('const/sets/FINITE' @ X0 @ X1) = $false)) )),
% 1.64/1.33 inference(binary_proxy_clausification,[status(thm)],[f91])).
% 1.64/1.33 thf(f91,plain,(
% 1.64/1.33 ( ! [X0 : $tType,X2 : X0 > 'type/nums/num',X1 : X0 > $o] : (((!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X1) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X2 @ Y0))))) = (('const/iterate/nsum' @ X0 @ X1 @ X2) = ('const/nums/NUMERAL' @ 'const/nums/_0'))) | (('const/sets/FINITE' @ X0 @ X1) = $false)) )),
% 1.64/1.33 inference(equality_proxy_clausification,[status(thm)],[f39])).
% 1.64/1.33 thf(f39,plain,(
% 1.64/1.33 ( ! [X0 : $tType,X2 : X0 > 'type/nums/num',X1 : X0 > $o] : (($true = ((('const/iterate/nsum' @ X0 @ X1 @ X2) = ('const/nums/NUMERAL' @ 'const/nums/_0')) = (!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X1) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X2 @ Y0))))))) | (('const/sets/FINITE' @ X0 @ X1) = $false)) )),
% 1.64/1.33 inference(binary_proxy_clausification,[status(thm)],[f38])).
% 1.64/1.33 thf(f38,plain,(
% 1.64/1.33 ( ! [X0 : $tType,X2 : X0 > 'type/nums/num',X1 : X0 > $o] : (($true = (('const/sets/FINITE' @ X0 @ X1) => ((('const/iterate/nsum' @ X0 @ X1 @ X2) = ('const/nums/NUMERAL' @ 'const/nums/_0')) = (!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X1) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X2 @ Y0))))))))) )),
% 1.64/1.33 inference(beta_eta_normalization,[status(thm)],[f37])).
% 1.64/1.33 thf(f37,plain,(
% 1.64/1.33 ( ! [X0 : $tType,X2 : X0 > 'type/nums/num',X1 : X0 > $o] : (($true = ((^[Y0 : X0 > 'type/nums/num']: (('const/sets/FINITE' @ X0 @ X1) => ((('const/iterate/nsum' @ X0 @ X1 @ Y0) = ('const/nums/NUMERAL' @ 'const/nums/_0')) = (!! @ X0 @ (^[Y1 : X0]: (('const/sets/IN' @ X0 @ Y1 @ X1) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (Y0 @ Y1)))))))) @ X2))) )),
% 1.64/1.33 inference(pi_clausification,[status(thm)],[f36])).
% 1.64/1.33 thf(f36,plain,(
% 1.64/1.33 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = (!! @ (X0 > 'type/nums/num') @ (^[Y0 : X0 > 'type/nums/num']: (('const/sets/FINITE' @ X0 @ X1) => ((('const/iterate/nsum' @ X0 @ X1 @ Y0) = ('const/nums/NUMERAL' @ 'const/nums/_0')) = (!! @ X0 @ (^[Y1 : X0]: (('const/sets/IN' @ X0 @ Y1 @ X1) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (Y0 @ Y1))))))))))) )),
% 1.64/1.33 inference(beta_eta_normalization,[status(thm)],[f35])).
% 1.64/1.33 thf(f35,plain,(
% 1.64/1.33 ( ! [X0 : $tType,X1 : X0 > $o] : (($true = ((^[Y0 : X0 > $o]: (!! @ (X0 > 'type/nums/num') @ (^[Y1 : X0 > 'type/nums/num']: (('const/sets/FINITE' @ X0 @ Y0) => ((('const/iterate/nsum' @ X0 @ Y0 @ Y1) = ('const/nums/NUMERAL' @ 'const/nums/_0')) = (!! @ X0 @ (^[Y2 : X0]: (('const/sets/IN' @ X0 @ Y2 @ Y0) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (Y1 @ Y2)))))))))) @ X1))) )),
% 1.64/1.33 inference(pi_clausification,[status(thm)],[f16])).
% 1.64/1.33 thf(f16,plain,(
% 1.64/1.33 ( ! [X0 : $tType] : (($true = (!! @ (X0 > $o) @ (^[Y0 : X0 > $o]: (!! @ (X0 > 'type/nums/num') @ (^[Y1 : X0 > 'type/nums/num']: (('const/sets/FINITE' @ X0 @ Y0) => ((('const/iterate/nsum' @ X0 @ Y0 @ Y1) = ('const/nums/NUMERAL' @ 'const/nums/_0')) = (!! @ X0 @ (^[Y2 : X0]: (('const/sets/IN' @ X0 @ Y2 @ Y0) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (Y1 @ Y2))))))))))))) )),
% 1.64/1.33 inference(cnf_transformation,[status(thm)],[f15])).
% 1.64/1.33 thf(f15,plain,(
% 1.64/1.33 ! [X0 : $tType] : ($true = (!! @ (X0 > $o) @ (^[Y0 : X0 > $o]: (!! @ (X0 > 'type/nums/num') @ (^[Y1 : X0 > 'type/nums/num']: (('const/sets/FINITE' @ X0 @ Y0) => ((('const/iterate/nsum' @ X0 @ Y0 @ Y1) = ('const/nums/NUMERAL' @ 'const/nums/_0')) = (!! @ X0 @ (^[Y2 : X0]: (('const/sets/IN' @ X0 @ Y2 @ Y0) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (Y1 @ Y2))))))))))))),
% 1.64/1.33 inference(closure,[status(thm)],[f14])).
% 1.64/1.33 thf(f14,plain,(
% 1.64/1.33 ( ! [X0 : $tType] : (($true = (!! @ (X0 > $o) @ (^[Y0 : X0 > $o]: (!! @ (X0 > 'type/nums/num') @ (^[Y1 : X0 > 'type/nums/num']: (('const/sets/FINITE' @ X0 @ Y0) => ((('const/iterate/nsum' @ X0 @ Y0 @ Y1) = ('const/nums/NUMERAL' @ 'const/nums/_0')) = (!! @ X0 @ (^[Y2 : X0]: (('const/sets/IN' @ X0 @ Y2 @ Y0) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (Y1 @ Y2))))))))))))) )),
% 1.64/1.33 inference(fool_elimination,[status(thm)],[f13])).
% 1.64/1.33 thf(f13,plain,(
% 1.64/1.33 ! [X0 : $tType,X1 : X0 > 'type/nums/num',X2 : X0 > $o] : (('const/sets/FINITE' @ X0 @ X2) => ((('const/iterate/nsum' @ X0 @ X2 @ X1) = ('const/nums/NUMERAL' @ 'const/nums/_0')) = ! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X2) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X1 @ X3)))))),
% 1.64/1.33 inference(rectify,[status(thm)],[f2])).
% 1.64/1.33 thf(f2,axiom,(
% 1.64/1.33 ! [X0 : $tType,X1 : X0 > 'type/nums/num',X2 : X0 > $o] : (('const/sets/FINITE' @ X0 @ X2) => ((('const/iterate/nsum' @ X0 @ X2 @ X1) = ('const/nums/NUMERAL' @ 'const/nums/_0')) = ! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X2) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X1 @ X3)))))),
% 1.64/1.33 file('/export/starexec/sandbox2/tmp/tmp.6dAD0J2TVR/DTF2THF_32467.p','thm/iterate/NSUM_EQ_0_IFF_')).
% 1.64/1.33 thf(f487,plain,(
% 1.64/1.33 ($false = (('const/sets/IN' @ 'type/nums/num' @ sK6 @ ('const/iterate/..' @ sK3 @ sK2)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (sK4 @ sK6)))) | ~spl0_4),
% 1.64/1.33 inference(forward_demodulation,[status(thm)],[f486,f30])).
% 1.64/1.33 thf(f30,plain,(
% 1.64/1.33 ( ! [X2 : 'type/nums/num',X3 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/arith/<=' @ X1 @ X2) & ('const/arith/<=' @ X3 @ X1)) = ('const/sets/IN' @ 'type/nums/num' @ X1 @ ('const/iterate/..' @ X3 @ X2)))) )),
% 1.64/1.33 inference(equality_proxy_clausification,[status(thm)],[f29])).
% 1.64/1.33 thf(f29,plain,(
% 1.64/1.33 ( ! [X2 : 'type/nums/num',X3 : 'type/nums/num',X1 : 'type/nums/num'] : (((('const/sets/IN' @ 'type/nums/num' @ X1 @ ('const/iterate/..' @ X3 @ X2)) = (('const/arith/<=' @ X1 @ X2) & ('const/arith/<=' @ X3 @ X1))) = $true)) )),
% 1.64/1.33 inference(beta_eta_normalization,[status(thm)],[f28])).
% 1.64/1.33 thf(f28,plain,(
% 1.64/1.33 ( ! [X2 : 'type/nums/num',X3 : 'type/nums/num',X1 : 'type/nums/num'] : (($true = ((^[Y0 : 'type/nums/num']: (('const/sets/IN' @ 'type/nums/num' @ X1 @ ('const/iterate/..' @ Y0 @ X2)) = (('const/arith/<=' @ X1 @ X2) & ('const/arith/<=' @ Y0 @ X1)))) @ X3))) )),
% 1.64/1.33 inference(pi_clausification,[status(thm)],[f27])).
% 1.64/1.33 thf(f27,plain,(
% 1.64/1.33 ( ! [X2 : 'type/nums/num',X1 : 'type/nums/num'] : (((!! @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: (('const/sets/IN' @ 'type/nums/num' @ X1 @ ('const/iterate/..' @ Y0 @ X2)) = (('const/arith/<=' @ X1 @ X2) & ('const/arith/<=' @ Y0 @ X1))))) = $true)) )),
% 1.64/1.33 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.64/1.33 thf(f26,plain,(
% 1.64/1.33 ( ! [X2 : 'type/nums/num',X1 : 'type/nums/num'] : (($true = ((^[Y0 : 'type/nums/num']: (!! @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: (('const/sets/IN' @ 'type/nums/num' @ X1 @ ('const/iterate/..' @ Y1 @ Y0)) = (('const/arith/<=' @ X1 @ Y0) & ('const/arith/<=' @ Y1 @ X1)))))) @ X2))) )),
% 1.64/1.33 inference(pi_clausification,[status(thm)],[f25])).
% 1.64/1.33 thf(f25,plain,(
% 1.64/1.33 ( ! [X1 : 'type/nums/num'] : (($true = (!! @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: (!! @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: (('const/sets/IN' @ 'type/nums/num' @ X1 @ ('const/iterate/..' @ Y1 @ Y0)) = (('const/arith/<=' @ X1 @ Y0) & ('const/arith/<=' @ Y1 @ X1))))))))) )),
% 1.64/1.33 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.64/1.33 thf(f24,plain,(
% 1.64/1.33 ( ! [X1 : 'type/nums/num'] : (($true = ((^[Y0 : 'type/nums/num']: (!! @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: (!! @ 'type/nums/num' @ (^[Y2 : 'type/nums/num']: (('const/sets/IN' @ 'type/nums/num' @ Y0 @ ('const/iterate/..' @ Y2 @ Y1)) = (('const/arith/<=' @ Y0 @ Y1) & ('const/arith/<=' @ Y2 @ Y0)))))))) @ X1))) )),
% 1.64/1.33 inference(pi_clausification,[status(thm)],[f19])).
% 1.64/1.33 thf(f19,plain,(
% 1.64/1.33 ($true = (!! @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: (!! @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: (!! @ 'type/nums/num' @ (^[Y2 : 'type/nums/num']: (('const/sets/IN' @ 'type/nums/num' @ Y0 @ ('const/iterate/..' @ Y2 @ Y1)) = (('const/arith/<=' @ Y0 @ Y1) & ('const/arith/<=' @ Y2 @ Y0))))))))))),
% 1.64/1.33 inference(cnf_transformation,[status(thm)],[f10])).
% 1.64/1.33 thf(f10,plain,(
% 1.64/1.33 ($true = (!! @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: (!! @ 'type/nums/num' @ (^[Y1 : 'type/nums/num']: (!! @ 'type/nums/num' @ (^[Y2 : 'type/nums/num']: (('const/sets/IN' @ 'type/nums/num' @ Y0 @ ('const/iterate/..' @ Y2 @ Y1)) = (('const/arith/<=' @ Y0 @ Y1) & ('const/arith/<=' @ Y2 @ Y0))))))))))),
% 1.64/1.33 inference(fool_elimination,[status(thm)],[f9])).
% 1.64/1.33 thf(f9,plain,(
% 1.64/1.33 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : (('const/sets/IN' @ 'type/nums/num' @ X2 @ ('const/iterate/..' @ X0 @ X1)) = ('const/arith/<=' @ X0 @ X2) & ('const/arith/<=' @ X2 @ X1))),
% 1.64/1.33 inference(rectify,[status(thm)],[f1])).
% 1.64/1.33 thf(f1,axiom,(
% 1.64/1.33 ! [X0 : 'type/nums/num',X1 : 'type/nums/num',X2 : 'type/nums/num'] : (('const/sets/IN' @ 'type/nums/num' @ X2 @ ('const/iterate/..' @ X0 @ X1)) = ('const/arith/<=' @ X0 @ X2) & ('const/arith/<=' @ X2 @ X1))),
% 1.64/1.33 file('/export/starexec/sandbox2/tmp/tmp.6dAD0J2TVR/DTF2THF_32467.p','thm/iterate/IN_NUMSEG_')).
% 1.64/1.33 thf(f486,plain,(
% 1.64/1.33 (((('const/arith/<=' @ sK6 @ sK2) & ('const/arith/<=' @ sK3 @ sK6)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (sK4 @ sK6))) = $false) | ~spl0_4),
% 1.64/1.33 inference(beta_eta_normalization,[status(thm)],[f485])).
% 1.64/1.33 thf(f485,plain,(
% 1.64/1.33 ($false = ((^[Y0 : 'type/nums/num']: ((('const/arith/<=' @ Y0 @ sK2) & ('const/arith/<=' @ sK3 @ Y0)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (sK4 @ Y0)))) @ sK6)) | ~spl0_4),
% 1.64/1.33 inference(sigma_clausification,[status(thm)],[f76])).
% 1.64/1.33 thf(f442,plain,(
% 1.64/1.33 ~spl0_3),
% 1.64/1.33 inference(avatar_contradiction_clause,[status(thm)],[f441])).
% 1.64/1.33 thf(f441,plain,(
% 1.64/1.33 $false | ~spl0_3),
% 1.64/1.33 inference(subsumption_resolution,[status(thm)],[f424,f83])).
% 1.64/1.33 thf(f83,plain,(
% 1.64/1.33 (('const/nums/NUMERAL' @ 'const/nums/_0') != ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK4)) | ~spl0_3),
% 1.64/1.33 inference(equality_proxy_clausification,[status(thm)],[f73])).
% 1.64/1.33 thf(f73,plain,(
% 1.64/1.33 ($false = (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK4))) | ~spl0_3),
% 1.64/1.33 inference(avatar_component_clause,[status(thm)],[f72])).
% 1.64/1.33 thf(f72,definition,(
% 1.64/1.33 spl0_3 <=> ($false = (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK4)))),
% 1.64/1.33 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.64/1.33 thf(f424,plain,(
% 1.64/1.33 (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK4)) | ~spl0_3),
% 1.64/1.33 inference(equality_proxy_clausification,[status(thm)],[f419])).
% 1.64/1.33 thf(f419,plain,(
% 1.64/1.33 ($true = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK4) = ('const/nums/NUMERAL' @ 'const/nums/_0'))) | ~spl0_3),
% 1.64/1.33 inference(trivial_inequality_removal,[status(thm)],[f418])).
% 1.64/1.33 thf(f418,plain,(
% 1.64/1.33 ($true = $false) | ($true = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK4) = ('const/nums/NUMERAL' @ 'const/nums/_0'))) | ~spl0_3),
% 1.64/1.33 inference(forward_demodulation,[status(thm)],[f402,f23])).
% 1.64/1.33 thf(f402,plain,(
% 1.64/1.33 ($true = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK4) = ('const/nums/NUMERAL' @ 'const/nums/_0'))) | ($false = ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2))) | ~spl0_3),
% 1.64/1.33 inference(trivial_inequality_removal,[status(thm)],[f393])).
% 1.64/1.33 thf(f393,plain,(
% 1.64/1.33 ($false = ('const/sets/FINITE' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2))) | ($true = (('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK4) = ('const/nums/NUMERAL' @ 'const/nums/_0'))) | ($true = $false) | ~spl0_3),
% 1.64/1.33 inference(superposition,[status(thm)],[f255,f315])).
% 1.64/1.33 thf(f315,plain,(
% 1.64/1.33 ( ! [X1 : 'type/nums/num'] : (($true = (('const/sets/IN' @ 'type/nums/num' @ X1 @ ('const/iterate/..' @ sK3 @ sK2)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (sK4 @ X1))))) ) | ~spl0_3),
% 1.64/1.33 inference(forward_demodulation,[status(thm)],[f314,f30])).
% 1.64/1.33 thf(f314,plain,(
% 1.64/1.33 ( ! [X1 : 'type/nums/num'] : (($true = ((('const/arith/<=' @ X1 @ sK2) & ('const/arith/<=' @ sK3 @ X1)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (sK4 @ X1))))) ) | ~spl0_3),
% 1.64/1.33 inference(beta_eta_normalization,[status(thm)],[f313])).
% 1.64/1.33 thf(f313,plain,(
% 1.64/1.33 ( ! [X1 : 'type/nums/num'] : ((((^[Y0 : 'type/nums/num']: ((('const/arith/<=' @ Y0 @ sK2) & ('const/arith/<=' @ sK3 @ Y0)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (sK4 @ Y0)))) @ X1) = $true)) ) | ~spl0_3),
% 1.64/1.33 inference(pi_clausification,[status(thm)],[f292])).
% 1.64/1.33 thf(f292,plain,(
% 1.64/1.33 ($false != (!! @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: ((('const/arith/<=' @ Y0 @ sK2) & ('const/arith/<=' @ sK3 @ Y0)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (sK4 @ Y0)))))) | ~spl0_3),
% 1.64/1.33 inference(forward_demodulation,[status(thm)],[f61,f73])).
% 1.64/1.33 thf(f255,plain,(
% 1.64/1.33 ( ! [X0 : $tType,X2 : X0 > 'type/nums/num',X1 : X0 > $o] : (($false = (('const/sets/IN' @ X0 @ (sK5 @ X0 @ X1 @ X2) @ X1) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X2 @ (sK5 @ X0 @ X1 @ X2))))) | (('const/sets/FINITE' @ X0 @ X1) = $false) | ($true = (('const/iterate/nsum' @ X0 @ X1 @ X2) = ('const/nums/NUMERAL' @ 'const/nums/_0')))) )),
% 1.64/1.33 inference(beta_eta_normalization,[status(thm)],[f246])).
% 1.64/1.33 thf(f246,plain,(
% 1.64/1.33 ( ! [X0 : $tType,X2 : X0 > 'type/nums/num',X1 : X0 > $o] : (($true = (('const/iterate/nsum' @ X0 @ X1 @ X2) = ('const/nums/NUMERAL' @ 'const/nums/_0'))) | ($false = ((^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X1) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X2 @ Y0)))) @ (sK5 @ X0 @ X1 @ X2))) | (('const/sets/FINITE' @ X0 @ X1) = $false)) )),
% 1.64/1.33 inference(sigma_clausification,[status(thm)],[f99])).
% 1.64/1.33 thf(f99,plain,(
% 1.64/1.33 ( ! [X0 : $tType,X2 : X0 > 'type/nums/num',X1 : X0 > $o] : (((!! @ X0 @ (^[Y0 : X0]: (('const/sets/IN' @ X0 @ Y0 @ X1) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (X2 @ Y0))))) = $false) | ($true = (('const/iterate/nsum' @ X0 @ X1 @ X2) = ('const/nums/NUMERAL' @ 'const/nums/_0'))) | (('const/sets/FINITE' @ X0 @ X1) = $false)) )),
% 1.64/1.33 inference(binary_proxy_clausification,[status(thm)],[f91])).
% 1.64/1.33 thf(f77,plain,(
% 1.64/1.33 spl0_3 | spl0_4),
% 1.64/1.33 inference(avatar_split_clause,[status(thm)],[f63,f75,f72])).
% 1.64/1.33 thf(f63,plain,(
% 1.64/1.33 ($false = (!! @ 'type/nums/num' @ (^[Y0 : 'type/nums/num']: ((('const/arith/<=' @ Y0 @ sK2) & ('const/arith/<=' @ sK3 @ Y0)) => (('const/nums/NUMERAL' @ 'const/nums/_0') = (sK4 @ Y0)))))) | ($false = (('const/nums/NUMERAL' @ 'const/nums/_0') = ('const/iterate/nsum' @ 'type/nums/num' @ ('const/iterate/..' @ sK3 @ sK2) @ sK4)))),
% 1.64/1.33 inference(binary_proxy_clausification,[status(thm)],[f61])).
% 1.64/1.33 % SZS output end Proof for DTF2THF_32467
% 1.64/1.33 % (32691)------------------------------
% 1.64/1.33 % (32691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.33 % (32691)Termination reason: Refutation
% 1.64/1.33
% 1.64/1.33 % (32691)Memory used [KB]: 5884
% 1.64/1.33 % (32691)Time elapsed: 0.062 s
% 1.64/1.33 % (32691)Instructions burned: 118 (million)
% 1.64/1.33 % (32691)------------------------------
% 1.64/1.33 % (32691)------------------------------
% 1.64/1.33 % (32672)Success in time 0.08 s
%------------------------------------------------------------------------------