TPTP Problem File: DAT297^1.p
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% File : DAT297^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Analysis
% Problem : ITLIST_EXTRA
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : ITLIST_EXTRA_.p [Kal16]
% Status : Theorem
% Rating : 0.00 v7.1.0
% Syntax : Number of formulae : 9 ( 4 unt; 5 typ; 0 def)
% Number of atoms : 4 ( 4 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 69 ( 0 ~; 0 |; 0 &; 69 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 7 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 5 usr; 0 con; 1-5 aty)
% Number of variables : 27 ( 0 ^; 22 !; 0 ?; 27 :)
% ( 5 !>; 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/lists/APPEND',type,
'const/lists/APPEND':
!>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
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/lists/ITLIST_0',axiom,
! [A: $tType,A0: $tType,A1: A > A0 > A0,A2: A0] :
( ( 'const/lists/ITLIST' @ A @ A0 @ A1 @ ( 'const/ind_types/NIL' @ A ) @ A2 )
= A2 ) ).
thf('thm/lists/ITLIST_1',axiom,
! [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 ) ) ) ).
thf('thm/lists/ITLIST_APPEND_',axiom,
! [A: $tType,A0: $tType,A1: A > A0 > A0,A2: A0,A3: 'type/ind_types/list' @ A,A4: 'type/ind_types/list' @ A] :
( ( 'const/lists/ITLIST' @ A @ A0 @ A1 @ ( 'const/lists/APPEND' @ A @ A3 @ A4 ) @ A2 )
= ( 'const/lists/ITLIST' @ A @ A0 @ A1 @ A3 @ ( 'const/lists/ITLIST' @ A @ A0 @ A1 @ A4 @ A2 ) ) ) ).
thf('thm/lists/ITLIST_EXTRA_',conjecture,
! [A: $tType,A0: $tType,A1: A > A0 > A0,A2: A,A3: A0,A4: 'type/ind_types/list' @ A] :
( ( 'const/lists/ITLIST' @ A @ A0 @ A1 @ ( 'const/lists/APPEND' @ A @ A4 @ ( 'const/ind_types/CONS' @ A @ A2 @ ( 'const/ind_types/NIL' @ A ) ) ) @ A3 )
= ( 'const/lists/ITLIST' @ A @ A0 @ A1 @ A4 @ ( A1 @ A2 @ A3 ) ) ) ).
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