TPTP Problem File: DAT270^1.p
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% File : DAT270^1 : TPTP v9.0.0. Released v7.0.0.
% Domain : Analysis
% Problem : ITLIST_
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : ITLIST_1.p [Kal16]
% Status : Theorem
% Rating : 1.00 v7.1.0
% Syntax : Number of formulae : 6 ( 1 unt; 4 typ; 0 def)
% Number of atoms : 3 ( 3 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 34 ( 0 ~; 0 |; 1 &; 33 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 8 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 4 usr; 0 con; 1-5 aty)
% Number of variables : 17 ( 0 ^; 12 !; 1 ?; 17 :)
% ( 4 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments : Exported from core HOL Light.
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thf('thf_type_type/ind_types/list',type,
'type/ind_types/list': $tType > $tType ).
thf('thf_const_const/lists/ITLIST',type,
'const/lists/ITLIST':
!>[A: $tType,A0: $tType] : ( ( A > A0 > A0 ) > ( 'type/ind_types/list' @ A ) > A0 > A0 ) ).
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_RECURSION_',axiom,
! [Z: $tType,A: $tType,A0: Z,A1: A > ( 'type/ind_types/list' @ A ) > Z > Z] :
? [A2: ( 'type/ind_types/list' @ A ) > Z] :
( ( ( A2 @ ( 'const/ind_types/NIL' @ A ) )
= A0 )
& ! [A3: A,A4: 'type/ind_types/list' @ A] :
( ( A2 @ ( 'const/ind_types/CONS' @ A @ A3 @ A4 ) )
= ( A1 @ A3 @ A4 @ ( A2 @ A4 ) ) ) ) ).
thf('thm/lists/ITLIST_1',conjecture,
! [A: $tType,A0: $tType,A1: A,A2: A > A0 > A0,A3: 'type/ind_types/list' @ A,A4: A0] :
( ( 'const/lists/ITLIST' @ A @ A0 @ A2 @ ( 'const/ind_types/CONS' @ A @ A1 @ A3 ) @ A4 )
= ( A2 @ A1 @ ( 'const/lists/ITLIST' @ A @ A0 @ A2 @ A3 @ A4 ) ) ) ).
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