TPTP Problem File: DAT305^1.p
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% File : DAT305^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Analysis
% Problem : MAP_SND_ZIP
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : MAP_SND_ZIP_.p [Kal16]
% Status : Theorem
% Rating : 1.00 v7.1.0
% Syntax : Number of formulae : 24 ( 9 unt; 13 typ; 0 def)
% Number of atoms : 13 ( 13 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 129 ( 1 ~; 0 |; 1 &; 124 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 12 usr; 1 con; 0-4 aty)
% Number of variables : 47 ( 0 ^; 36 !; 0 ?; 47 :)
% ( 11 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments : Exported from core HOL Light.
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thf('thf_type_type/pair/prod',type,
'type/pair/prod': $tType > $tType > $tType ).
thf('thf_type_type/nums/num',type,
'type/nums/num': $tType ).
thf('thf_type_type/ind_types/list',type,
'type/ind_types/list': $tType > $tType ).
thf('thf_const_const/pair/SND',type,
'const/pair/SND':
!>[A: $tType,B: $tType] : ( ( 'type/pair/prod' @ A @ B ) > B ) ).
thf('thf_const_const/pair/,',type,
'const/pair/,':
!>[A: $tType,B: $tType] : ( A > B > ( 'type/pair/prod' @ A @ B ) ) ).
thf('thf_const_const/nums/SUC',type,
'const/nums/SUC': 'type/nums/num' > 'type/nums/num' ).
thf('thf_const_const/nums/NUMERAL',type,
'const/nums/NUMERAL': 'type/nums/num' > 'type/nums/num' ).
thf('thf_const_const/nums/_0',type,
'const/nums/_0': 'type/nums/num' ).
thf('thf_const_const/lists/ZIP',type,
'const/lists/ZIP':
!>[A: $tType,A0: $tType] : ( ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A0 ) > ( 'type/ind_types/list' @ ( 'type/pair/prod' @ A @ A0 ) ) ) ).
thf('thf_const_const/lists/MAP',type,
'const/lists/MAP':
!>[A: $tType,B: $tType] : ( ( A > B ) > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ B ) ) ).
thf('thf_const_const/lists/LENGTH',type,
'const/lists/LENGTH':
!>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > 'type/nums/num' ) ).
thf('thf_const_const/ind_types/NIL',type,
'const/ind_types/NIL':
!>[A: $tType] : ( 'type/ind_types/list' @ A ) ).
thf('thf_const_const/ind_types/CONS',type,
'const/ind_types/CONS':
!>[A: $tType] : ( A > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
thf('thm/ind_types/list_INDUCT_',axiom,
! [A: $tType,P: ( 'type/ind_types/list' @ A ) > $o] :
( ( ( P @ ( 'const/ind_types/NIL' @ A ) )
& ! [A0: A,A1: 'type/ind_types/list' @ A] :
( ( P @ A1 )
=> ( P @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) ) ) )
=> ! [A0: 'type/ind_types/list' @ A] : ( P @ A0 ) ) ).
thf('thm/nums/SUC_INJ_',axiom,
! [A: 'type/nums/num',A0: 'type/nums/num'] :
( ( ( 'const/nums/SUC' @ A )
= ( 'const/nums/SUC' @ A0 ) )
= ( A = A0 ) ) ).
thf('thm/lists/LENGTH_1',axiom,
! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
( ( 'const/lists/LENGTH' @ A @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) )
= ( 'const/nums/SUC' @ ( 'const/lists/LENGTH' @ A @ A1 ) ) ) ).
thf('thm/pair/SND_',axiom,
! [A: $tType,B: $tType,A0: A,A1: B] :
( ( 'const/pair/SND' @ A @ B @ ( 'const/pair/,' @ A @ B @ A0 @ A1 ) )
= A1 ) ).
thf('thm/lists/MAP_1',axiom,
! [B: $tType,A: $tType,A0: A > B,A1: A,A2: 'type/ind_types/list' @ A] :
( ( 'const/lists/MAP' @ A @ B @ A0 @ ( 'const/ind_types/CONS' @ A @ A1 @ A2 ) )
= ( 'const/ind_types/CONS' @ B @ ( A0 @ A1 ) @ ( 'const/lists/MAP' @ A @ B @ A0 @ A2 ) ) ) ).
thf('thm/lists/ZIP_1',axiom,
! [A: $tType,A0: $tType,A1: A,A2: A0,A3: 'type/ind_types/list' @ A,A4: 'type/ind_types/list' @ A0] :
( ( 'const/lists/ZIP' @ A @ A0 @ ( 'const/ind_types/CONS' @ A @ A1 @ A3 ) @ ( 'const/ind_types/CONS' @ A0 @ A2 @ A4 ) )
= ( 'const/ind_types/CONS' @ ( 'type/pair/prod' @ A @ A0 ) @ ( 'const/pair/,' @ A @ A0 @ A1 @ A2 ) @ ( 'const/lists/ZIP' @ A @ A0 @ A3 @ A4 ) ) ) ).
thf('thm/nums/NOT_SUC_',axiom,
! [A: 'type/nums/num'] :
( ( 'const/nums/SUC' @ A )
!= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ).
thf('thm/lists/LENGTH_0',axiom,
! [A: $tType] :
( ( 'const/lists/LENGTH' @ A @ ( 'const/ind_types/NIL' @ A ) )
= ( 'const/nums/NUMERAL' @ 'const/nums/_0' ) ) ).
thf('thm/lists/MAP_0',axiom,
! [A: $tType,B: $tType,A0: A > B] :
( ( 'const/lists/MAP' @ A @ B @ A0 @ ( 'const/ind_types/NIL' @ A ) )
= ( 'const/ind_types/NIL' @ B ) ) ).
thf('thm/lists/ZIP_0',axiom,
! [A: $tType,A0: $tType] :
( ( 'const/lists/ZIP' @ A @ A0 @ ( 'const/ind_types/NIL' @ A ) @ ( 'const/ind_types/NIL' @ A0 ) )
= ( 'const/ind_types/NIL' @ ( 'type/pair/prod' @ A @ A0 ) ) ) ).
thf('thm/lists/MAP_SND_ZIP_',conjecture,
! [A: $tType,A0: $tType,A1: 'type/ind_types/list' @ A,A2: 'type/ind_types/list' @ A0] :
( ( ( 'const/lists/LENGTH' @ A @ A1 )
= ( 'const/lists/LENGTH' @ A0 @ A2 ) )
=> ( ( 'const/lists/MAP' @ ( 'type/pair/prod' @ A @ A0 ) @ A0 @ ( 'const/pair/SND' @ A @ A0 ) @ ( 'const/lists/ZIP' @ A @ A0 @ A1 @ A2 ) )
= A2 ) ) ).
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