TPTP Problem File: DAT296^1.p
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% File : DAT296^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Analysis
% Problem : ALL2_AND_RIGHT
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : ALL2_AND_RIGHT_.p [Kal16]
% Status : Theorem
% Rating : 1.00 v7.1.0
% Syntax : Number of formulae : 13 ( 7 unt; 5 typ; 0 def)
% Number of atoms : 22 ( 7 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 104 ( 0 ~; 0 |; 5 &; 97 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 2 con; 0-5 aty)
% Number of variables : 44 ( 2 ^; 37 !; 0 ?; 44 :)
% ( 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/ALL2',type,
'const/lists/ALL2':
!>[A: $tType,A0: $tType] : ( ( A > A0 > $o ) > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A0 ) > $o ) ).
thf('thf_const_const/lists/ALL',type,
'const/lists/ALL':
!>[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/lists/ALL2_3',axiom,
! [A: $tType,A0: $tType,A1: A,A2: A0,P: A > A0 > $o,A3: 'type/ind_types/list' @ A,A4: 'type/ind_types/list' @ A0] :
( ( 'const/lists/ALL2' @ A @ A0 @ P @ ( 'const/ind_types/CONS' @ A @ A1 @ A3 ) @ ( 'const/ind_types/CONS' @ A0 @ A2 @ A4 ) )
= ( ( P @ A1 @ A2 )
& ( 'const/lists/ALL2' @ A @ A0 @ P @ A3 @ A4 ) ) ) ).
thf('thm/lists/ALL2_1',axiom,
! [A: $tType,A0: $tType,P: A > A0 > $o,A1: A,A2: 'type/ind_types/list' @ A] :
( ( 'const/lists/ALL2' @ A @ A0 @ P @ ( 'const/ind_types/CONS' @ A @ A1 @ A2 ) @ ( 'const/ind_types/NIL' @ A0 ) )
= $false ) ).
thf('thm/lists/ALL_1',axiom,
! [A: $tType,A0: A,P: A > $o,A1: 'type/ind_types/list' @ A] :
( ( 'const/lists/ALL' @ A @ P @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) )
= ( ( P @ A0 )
& ( 'const/lists/ALL' @ A @ P @ A1 ) ) ) ).
thf('thm/lists/ALL2_2',axiom,
! [A: $tType,A0: $tType,P: A > A0 > $o,A1: A0,A2: 'type/ind_types/list' @ A0] :
( ( 'const/lists/ALL2' @ A @ A0 @ P @ ( 'const/ind_types/NIL' @ A ) @ ( 'const/ind_types/CONS' @ A0 @ A1 @ A2 ) )
= $false ) ).
thf('thm/lists/ALL2_0',axiom,
! [A: $tType,A0: $tType,P: A > A0 > $o] :
( ( 'const/lists/ALL2' @ A @ A0 @ P @ ( 'const/ind_types/NIL' @ A ) @ ( 'const/ind_types/NIL' @ A0 ) )
= $true ) ).
thf('thm/lists/ALL_0',axiom,
! [A: $tType,P: A > $o] :
( ( 'const/lists/ALL' @ A @ P @ ( 'const/ind_types/NIL' @ A ) )
= $true ) ).
thf('thm/lists/ALL2_AND_RIGHT_',conjecture,
! [A: $tType,A0: $tType,A1: 'type/ind_types/list' @ A,A2: 'type/ind_types/list' @ A0,P: A > $o,Q: A > A0 > $o] :
( ( 'const/lists/ALL2' @ A @ A0
@ ^ [A3: A,A4: A0] :
( ( P @ A3 )
& ( Q @ A3 @ A4 ) )
@ A1
@ A2 )
= ( ( 'const/lists/ALL' @ A @ P @ A1 )
& ( 'const/lists/ALL2' @ A @ A0 @ Q @ A1 @ A2 ) ) ) ).
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