TPTP Problem File: DAT274^1.p
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% File : DAT274^1 : TPTP v8.2.0. Released v7.0.0.
% Domain : Analysis
% Problem : ALL2_
% Version : Especial.
% English :
% Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% Source : [Kal16]
% Names : ALL2_3.p [Kal16]
% Status : Theorem
% Rating : 1.00 v7.1.0
% Syntax : Number of formulae : 29 ( 13 unt; 15 typ; 0 def)
% Number of atoms : 28 ( 18 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 118 ( 1 ~; 0 |; 4 &; 113 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 2 con; 0-5 aty)
% Number of variables : 47 ( 0 ^; 38 !; 2 ?; 47 :)
% ( 7 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_THM_EQU_NAR
% Comments : Exported from core HOL Light.
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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/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/BIT1',type,
'const/nums/BIT1': 'type/nums/num' > 'type/nums/num' ).
thf('thf_const_const/nums/_0',type,
'const/nums/_0': 'type/nums/num' ).
thf('thf_const_const/lists/TL',type,
'const/lists/TL':
!>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
thf('thf_const_const/lists/HD',type,
'const/lists/HD':
!>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > A ) ).
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/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('thf_const_const/class/COND',type,
'const/class/COND':
!>[A: $tType] : ( $o > A > A > A ) ).
thf('thf_const_const/arith/+',type,
'const/arith/+': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf('thf_const_const/arith/<=',type,
'const/arith/<=': 'type/nums/num' > 'type/nums/num' > $o ).
thf('thf_const_const/arith/<',type,
'const/arith/<': 'type/nums/num' > 'type/nums/num' > $o ).
thf('thm/lists/TL_',axiom,
! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
( ( 'const/lists/TL' @ A @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) )
= A1 ) ).
thf('thm/lists/HD_',axiom,
! [A: $tType,A0: 'type/ind_types/list' @ A,A1: A] :
( ( 'const/lists/HD' @ A @ ( 'const/ind_types/CONS' @ A @ A1 @ A0 ) )
= A1 ) ).
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/calc_num/ARITH_3',axiom,
( ( 'const/nums/SUC' @ 'const/nums/_0' )
= ( 'const/nums/BIT1' @ 'const/nums/_0' ) ) ).
thf('thm/calc_num/ARITH_11',axiom,
( ( 'const/arith/+' @ 'const/nums/_0' @ 'const/nums/_0' )
= 'const/nums/_0' ) ).
thf('thm/arith/ADD_SYM_',axiom,
! [A: 'type/nums/num',A0: 'type/nums/num'] :
( ( 'const/arith/+' @ A @ A0 )
= ( 'const/arith/+' @ A0 @ A ) ) ).
thf('thm/arith/ADD_SUC_',axiom,
! [A: 'type/nums/num',A0: 'type/nums/num'] :
( ( 'const/arith/+' @ A @ ( 'const/nums/SUC' @ A0 ) )
= ( 'const/nums/SUC' @ ( 'const/arith/+' @ A @ A0 ) ) ) ).
thf('thm/arith/LT_EXISTS_',axiom,
! [A: 'type/nums/num',A0: 'type/nums/num'] :
( ( 'const/arith/<' @ A @ A0 )
= ( ? [A1: 'type/nums/num'] :
( A0
= ( 'const/arith/+' @ A @ ( 'const/nums/SUC' @ A1 ) ) ) ) ) ).
thf('thm/arith/NOT_LE_',axiom,
! [A: 'type/nums/num',A0: 'type/nums/num'] :
( ( ~ ( 'const/arith/<=' @ A @ A0 ) )
= ( 'const/arith/<' @ A0 @ A ) ) ).
thf('thm/arith/ADD_CLAUSES_2',axiom,
! [A: 'type/nums/num',A0: 'type/nums/num'] :
( ( 'const/arith/+' @ ( 'const/nums/SUC' @ A ) @ A0 )
= ( 'const/nums/SUC' @ ( 'const/arith/+' @ A @ A0 ) ) ) ).
thf('thm/nums/NUMERAL_',axiom,
! [A: 'type/nums/num'] :
( ( 'const/nums/NUMERAL' @ A )
= A ) ).
thf('thm/arith/LE_ANTISYM_',axiom,
! [A: 'type/nums/num',A0: 'type/nums/num'] :
( ( ( 'const/arith/<=' @ A @ A0 )
& ( 'const/arith/<=' @ A0 @ A ) )
= ( A = A0 ) ) ).
thf('thm/lists/ALL2_DEF_1',axiom,
! [A: $tType,A0: $tType,A1: A,P: A > A0 > $o,A2: 'type/ind_types/list' @ A,A3: 'type/ind_types/list' @ A0] :
( ( 'const/lists/ALL2' @ A @ A0 @ P @ ( 'const/ind_types/CONS' @ A @ A1 @ A2 ) @ A3 )
= ( 'const/class/COND' @ $o
@ ( A3
= ( 'const/ind_types/NIL' @ A0 ) )
@ $false
@ ( ( P @ A1 @ ( 'const/lists/HD' @ A0 @ A3 ) )
& ( 'const/lists/ALL2' @ A @ A0 @ P @ A2 @ ( 'const/lists/TL' @ A0 @ A3 ) ) ) ) ) ).
thf('thm/lists/ALL2_3',conjecture,
! [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 ) ) ) ).
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