TPTP Problem File: DAT300^1.p
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% File : DAT300^1 : TPTP v9.0.0. Released v7.0.0.
% Domain : Analysis
% Problem : EX_MAP
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : EX_MAP_.p [Kal16]
% Status : Theorem
% Rating : 1.00 v7.1.0
% Syntax : Number of formulae : 13 ( 6 unt; 6 typ; 0 def)
% Number of atoms : 12 ( 6 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 82 ( 0 ~; 1 |; 1 &; 78 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 1 con; 0-6 aty)
% Number of variables : 38 ( 0 ^; 30 !; 0 ?; 38 :)
% ( 8 !>; 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/trivia/o',type,
'const/trivia/o':
!>[B: $tType,A: $tType,C: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
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/EX',type,
'const/lists/EX':
!>[A: $tType] : ( ( A > $o ) > ( 'type/ind_types/list' @ A ) > $o ) ).
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/trivia/o_THM_',axiom,
! [C: $tType,B: $tType,A: $tType,A0: B > C,A1: A > B,A2: A] :
( ( 'const/trivia/o' @ B @ A @ C @ A0 @ A1 @ A2 )
= ( A0 @ ( A1 @ A2 ) ) ) ).
thf('thm/lists/EX_1',axiom,
! [A: $tType,A0: A,P: A > $o,A1: 'type/ind_types/list' @ A] :
( ( 'const/lists/EX' @ A @ P @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) )
= ( ( P @ A0 )
| ( 'const/lists/EX' @ A @ P @ 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/EX_0',axiom,
! [A: $tType,P: A > $o] :
( ( 'const/lists/EX' @ A @ P @ ( 'const/ind_types/NIL' @ A ) )
= $false ) ).
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/EX_MAP_',conjecture,
! [A: $tType,A0: $tType,P: A > $o,A1: A0 > A,A2: 'type/ind_types/list' @ A0] :
( ( 'const/lists/EX' @ A @ P @ ( 'const/lists/MAP' @ A0 @ A @ A1 @ A2 ) )
= ( 'const/lists/EX' @ A0 @ ( 'const/trivia/o' @ A @ A0 @ $o @ P @ A1 ) @ A2 ) ) ).
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