
    \h\                     l    S r SSKJr  SSKJr  SSKJr  \S 5       r\S 5       r\S 5       r	\S 5       r
g	)
zC
Do NOT manually edit this file.
Instead, run ./bin/ask_update.py.
    )Q)Literal)cacheitc            
      %   1 [        [        [        R                  S5      [        [        R                  S5      [        [        R
                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      [        [        R
                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      [        [        R
                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R
                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R
                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R                   S5      45      i[        [        [        R"                  S5      [        [        R$                  S5      [        [        R                  S5      [        [        R&                  S5      45      i[        [        [        R"                  S5      [        [        R$                  S5      [        [        R(                  S5      45      i[        [        [        R"                  S5      [        [        R                  S5      45      i[        [        [        R"                  S5      [        [        R&                  S5      45      i[        [        [        R*                  S5      [        [        R,                  S5      [        [        R.                  S5      45      i[        [        [        R*                  S5      [        [        R,                  S5      45      i[        [        [        R*                  S5      [        [        R0                  S5      45      i[        [        [        R*                  S5      [        [        R2                  S5      45      i[        [        [        R*                  S5      [        [        R.                  S5      45      i[        [        [        R$                  S5      [        [        R(                  S5      [        [        R&                  S5      45      i[        [        [        R$                  S5      [        [        R                  S5      45      i[        [        [        R$                  S5      [        [        R(                  S5      45      i[        [        [        R$                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R
                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R4                  S5      [        [        R6                  S5      45      i[        [        [        R4                  S5      [        [        R6                  S5      [        [        R8                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R:                  S5      45      i[        [        [        R                  S5      [        [        R<                  S5      45      i[        [        [        R>                  S5      [        [        R                   S5      45      i[        [        [        R6                  S5      [        [        R@                  S5      45      i[        [        [        R6                  S5      [        [        RB                  S5      45      i[        [        [        R6                  S5      [        [        RD                  S5      45      i[        [        [        R6                  S5      [        [        RB                  S5      45      i[        [        [        R6                  S5      [        [        R8                  S5      45      i[        [        [        RF                  S5      [        [        R                  S5      [        [        R                  S5      45      i[        [        [        RF                  S5      [        [        R                  S5      [        [        R                  S5      45      i[        [        [        RF                  S5      [        [        R                  S5      [        [        R                  S5      45      i[        [        [        RF                  S5      [        [        R                  S5      [        [        R                  S5      [        [        R                  S5      45      i[        [        [        RF                  S5      [        [        R                  S5      45      i[        [        [        R,                  S5      [        [        RH                  S5      [        [        R.                  S5      45      i[        [        [        R,                  S5      [        [        RH                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R:                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R<                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R:                  S5      [        [        R                  S5      45      i[        [        [        R:                  S5      [        [        R<                  S5      45      i[        [        [        R:                  S5      [        [        R                  S5      45      i[        [        [        R0                  S5      [        [        RD                  S5      45      i[        [        [        R0                  S5      [        [        R8                  S5      45      i[        [        [        R(                  S5      [        [        R                  S5      45      i[        [        [        RJ                  S5      [        [        R                   S5      [        [        RD                  S5      45      i[        [        [        RJ                  S5      [        [        R@                  S5      45      i[        [        [        RJ                  S5      [        [        RD                  S5      45      i[        [        [        R                  S5      [        [        R&                  S5      45      i[        [        [        R                  S5      [        [        R<                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R<                  S5      [        [        R                  S5      45      i[        [        [        R8                  S5      [        [        R2                  S5      45      i[        [        [        RH                  S5      [        [        RL                  S5      45      i[        [        [        RH                  S5      [        [        R.                  S5      45      i$ )z6
Known facts between unary predicates as CNF clauses.
FT)'	frozensetr   r   	algebraic	imaginarytranscendentalnegativepositiverationalzerofiniteantihermitian	hermitiancommutativeinfinitecomplex_elementsreal_elements	compositeevenprimeodddiagonallower_triangularupper_triangularnormal	symmetricfullrank
invertiblesquarenegative_infinitepositive_infiniteinteger_elementspositive_definitesingularunitary
irrational
triangular
orthogonalunit_triangular     W/var/www/auris/envauris/lib/python3.13/site-packages/sympy/assumptions/ask_generated.pyget_all_known_factsr/   
   s   
H71;;.T0JGTUTdTdfkLlmnH71;;.

D0I7STScScejKklmH 	71;;.

D0I7STScScejKklmH 	71;;.

D0IJK	H
 	71;;.8H8H%0PRYZ[Z`Z`bfRghiH 	71;;-wqxx/GHIH 	71;;-wq7G7G/NOPH 	71??E2GAKK4OQXYZY_Y_aeQfghH 	71??E2GAKK4NOPH 	71==%0'!((D2IJKH 	71==%0'!**d2KLMH 	71--u5wqPT7UVWH 	71;;.0Ewqzz[_G`bijkjqjqsxbyz{H 	71;;-wqvvu/EwquuV[G\]^H 	71;;-wqzz5/IJKH  	71;;-wqww/EFG!H" 	71::u-wq7I7I4/PRYZ[ZlZlnrRstu#H$ 	71::t,ga6H6H%.PQR%H& 	71::t,gahh.FGH'H( 	71::t,gakk5.IJK)H* 	71::t,ga6H6H%.PQR+H, 	71665)7155%+@'!''SWBXYZ-H. 	71665)71664+@AB/H0 	71664('!%%*>?@1H2 	71664('!**e*DEF3H4 	7188U+WQ5E5Et-LMN5H6 	7188T*GAJJ,EFG7H8 	71::u-wq||T/JKL9H: 	71::t,gallE.JGTUT\T\^bLcde;H< 	71;;.

D0IJK=H> 	71;;.

D0IJK?H@ 	71;;.0EFGAHB 	71;;-wqzz4/HIJCHD 	71;;-wqzz4/HIJEHF 	71;;-wqvvt/DEFGHH 	71::u-wq7J7JD/QRSIHJ 	71::u-wq7J7JD/QRSKHL 	71--t4gaoou6UVWMHN 	71<</9L9Ld1STUOHP 	71<</U1KLMQHR 	71<</D1IJKSHT 	71<<.

D0IJKUHV 	71<<.%0HIJWHX 	71<</T1JGTUT^T^`eLfghYHZ 	71<</T1JGTUT^T^`eLfgh[H\ 	71<</U1KWUVU[U[]aMbcd]H^ 	71<<.

E0JGTUT^T^`eLfhopqpvpvx}h~  	A_H` 	71<<.

D0IJKaHb 	71--u5wq||T7RT[\]\n\npuTvwxcHd 	71--t4gallE6RSTeHf 	71::u-wqzz5/I7STS]S]_cKdfmnontntv{f|}~gHh 	71::t,ga6I6I4.PQRiHj 	71::t,gajj$.GHIkHl 	71::t,ga6I6I4.PQRmHn 	71::t,gaffd.CDEoHp 	71..5wqzz47PQRqHr 	71..5wq?R?RTX7YZ[sHt 	71..5wqvvt7LMNuHv 	7188U+WQYY-EFGwHx 	7188T*GAHHe,DEFyHz 	7155$'U)CDE{H| 	71<</$1OQXYZYbYbdhQijk}H~ 	71<<.8K8KU0STUH@ 	71<<.		50IJKAHB 	71::u-wqww/EFGCHD 	71::t,ga6I6I4.PQREHF 	71::t,gaffd.CDEGHH 	71..5wqvvt7LMNIHJ 	7188U+WQ[[$-GHIKHL 	71<</9J9JD1QRSMHN 	71<</9K9KT1RSTOH Hr-   c                     [        [        [        R                  S5      [        [        R                  S5      45      [        [        [        R
                  S5      [        [        R                  S5      [        [        R                  S5      45      [        [        [        R
                  S5      [        [        R                  S5      45      [        [        [        R
                  S5      [        [        R                  S5      45      [        [        [        R
                  S5      [        [        R                  S5      45      [        [        [        R
                  S5      [        [        R                  S5      45      [        [        [        R                  S5      [        [        R                  S5      45      [        [        [        R                  S5      [        [        R                  S5      [        [        R                  S5      45      [        [        [        R                  S5      [        [        R                  S5      45      [        [        [        R                  S5      [        [        R                  S5      45      [        [        [        R                  S5      [        [        R                  S5      45      [        [        [        R                  S5      [        [        R                   S5      45      [        [        [        R                  S5      [        [        R                  S5      45      [        [        [        R                  S5      [        [        R                  S5      45      [        [        [        R                  S5      [        [        R"                  S5      [        [        R                  S5      45      [        [        [        R                  S5      [        [        R"                  S5      45      [        [        [        R                  S5      [        [        R                   S5      45      [        [        [        R                  S5      [        [        R                  S5      45      [        [        [        R$                  S5      [        [        R                  S5      [        [        R                   S5      45      [        [        [        R$                  S5      [        [        R                  S5      45      [        [        [        R$                  S5      [        [        R                   S5      45      [        [        [        R                  S5      [        [        R                  S5      45      [        [        [        R"                  S5      [        [        R&                  S5      45      [        [        [        R"                  S5      [        [        R                  S5      45      1$ )zC
Known facts between unary predicates for matrices as CNF clauses.
FT)r   r   r   r   r   r   r   r   r   r   r   r    r!   r$   r%   r&   r'   r)   r*   r+   r,   r-   r.   get_all_known_matrix_factsr1   Y   s    	71--u5wqPT7UVW71::u-wq7I7I4/PRYZ[ZlZlnrRstu71::t,ga6H6H%.PQR71::t,gahh.FGH71::t,gakk5.IJK71::t,ga6H6H%.PQR71::u-wq||T/JKL71::t,gallE.JGTUT\T\^bLcde71--t4gaoou6UVW71<</9L9Ld1STU71<</U1KLM71<</D1IJK71<<.

D0IJK71<<.%0HIJ71--u5wq||T7RT[\]\n\npuTvwx71--t4gallE6RST7188U+WQYY-EFG7188T*GAHHe,DEF71<</$1OQXYZYbYbdhQijk71<<.8K8KU0STU71<<.		50IJK7188U+WQ[[$-GHI71<</9J9JD1QRS71<</9K9KT1RST1 r-   c            
         1 [        [        [        R                  S5      [        [        R                  S5      [        [        R
                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      [        [        R
                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      [        [        R
                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R
                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R
                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R                   S5      [        [        R                  S5      [        [        R"                  S5      45      i[        [        [        R                  S5      [        [        R                   S5      [        [        R$                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R"                  S5      45      i[        [        [        R                   S5      [        [        R$                  S5      [        [        R"                  S5      45      i[        [        [        R                   S5      [        [        R                  S5      45      i[        [        [        R                   S5      [        [        R$                  S5      45      i[        [        [        R                   S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R
                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R&                  S5      45      i[        [        [        R                  S5      [        [        R(                  S5      45      i[        [        [        R*                  S5      [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R*                  S5      [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R*                  S5      [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R*                  S5      [        [        R                  S5      [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R*                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R&                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R(                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R&                  S5      [        [        R                  S5      45      i[        [        [        R&                  S5      [        [        R(                  S5      45      i[        [        [        R&                  S5      [        [        R                  S5      45      i[        [        [        R$                  S5      [        [        R                  S5      45      i[        [        [        R                  S5      [        [        R"                  S5      45      i[        [        [        R                  S5      [        [        R(                  S5      45      i[        [        [        R                  S5      [        [        R                  S5      45      i[        [        [        R(                  S5      [        [        R                  S5      45      i$ )zB
Known facts between unary predicates for numbers as CNF clauses.
FT)r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r"   r#   r(   r,   r-   r.   get_all_known_number_factsr3   y   s	   
071;;.T0JGTUTdTdfkLlmn071;;.

D0I7STScScejKklm0 	71;;.

D0I7STScScejKklm0 	71;;.

D0IJK	0
 	71;;.8H8H%0PRYZ[Z`Z`bfRghi0 	71;;-wqxx/GHI0 	71;;-wq7G7G/NOP0 	71??E2GAKK4OQXYZY_Y_aeQfgh0 	71??E2GAKK4NOP0 	71==%0'!((D2IJK0 	71==%0'!**d2KLM0 	71;;.0Ewqzz[_G`bijkjqjqsxbyz{0 	71;;-wqvvu/EwquuV[G\]^0 	71;;-wqzz5/IJK0 	71;;-wqww/EFG0  	71665)7155%+@'!''SWBXYZ!0" 	71665)71664+@AB#0$ 	71664('!%%*>?@%0& 	71664('!**e*DEF'0( 	7188U+WQ5E5Et-LMN)0* 	7188T*GAJJ,EFG+0, 	71;;.

D0IJK-0. 	71;;.

D0IJK/00 	71;;.0EFG102 	71;;-wqzz4/HIJ304 	71;;-wqzz4/HIJ506 	71;;-wqvvt/DEF708 	71::u-wq7J7JD/QRS90: 	71::u-wq7J7JD/QRS;0< 	71<</T1JGTUT^T^`eLfgh=0> 	71<</T1JGTUT^T^`eLfgh?0@ 	71<</U1KWUVU[U[]aMbcdA0B 	71<<.

E0JGTUT^T^`eLfhopqpvpvx}h~  	AC0D 	71<<.

D0IJKE0F 	71::u-wqzz5/I7STS]S]_cKdfmnontntv{f|}~G0H 	71::t,ga6I6I4.PQRI0J 	71::t,gajj$.GHIK0L 	71::t,ga6I6I4.PQRM0N 	71::t,gaffd.CDEO0P 	71..5wqzz47PQRQ0R 	71..5wq?R?RTX7YZ[S0T 	71..5wqvvt7LMNU0V 	7155$'U)CDEW0X 	71::u-wqww/EFGY0Z 	71::t,ga6I6I4.PQR[0\ 	71::t,gaffd.CDE]0^ 	71..5wqvvt7LMN_0 0r-   c                  TK   0 [         R                  [        [         R                  [         R                  [         R                  [         R
                  /5      [        [         R                  [         R                  [         R                  [         R                  /5      4_[         R                  [        [         R                  /5      [        / 5      4_[         R                  [        [         R                  /5      [        / 5      4_[         R                  [        [         R                  [         R                  [         R
                  /5      [        [         R                  [         R                  [         R                  /5      4_[         R                  [        [         R                  /5      [        / 5      4_[         R                  [        [         R                  [         R                  [         R                  [         R                  [         R                  [         R                  [         R                  [         R                   [         R
                  [         R"                  [         R$                  [         R&                  [         R(                  [         R*                  [         R,                  [         R.                  /5      [        [         R0                  [         R2                  [         R4                  [         R                  [         R6                  [         R8                  [         R                  [         R:                  [         R                  [         R<                  [         R                  [         R>                  /5      4_[         R@                  [        [         R@                  [         RB                  [         RD                  [         RF                  [         RH                  [         RJ                  [         RL                  /5      [        / 5      4_[         RN                  [        [         R                  [         R                  [         R                  [         RN                  [         R                   [         R
                  [         R"                  [         R$                  [         R,                  [         R.                  /
5      [        [         R4                  [         R                  [         R6                  [         R                  [         RP                  [         R                  [         R                  /5      4_[         R0                  [        [         R                  [         R0                  [         R2                  [         R                  [         R                   /5      [        [         R                  [         R                  [         R                  [         R4                  [         R&                  [         R*                  [         R                  [         R<                  [         R>                  /	5      4_[         R                  [        [         R                  [         R                  [         R                   /5      [        [         R0                  [         R4                  [         R8                  [         R                  /5      4_[         R2                  [        [         R                  [         R2                  [         R                   /5      [        [         R                  [         R                  [         R4                  [         R*                  [         R                  [         R<                  /5      4_[         R                  [        [         R                  [         R                  [         R                   /5      [        [         R4                  [         R>                  /5      4_[         R                  [        [         R                  [         R                  [         R                  [         R                  [         R                   /5      [        [         R0                  [         R2                  [         R4                  [         R8                  [         R                  [         R:                  [         R>                  /5      4_[         R                   [        [         R                  [         R                   /5      [        [         R4                  /5      4_[         R
                  [        [         R                  [         R
                  /5      [        [         R                  [         R                  [         R                  /5      4_[         RR                  [        [         RR                  /5      [        / 5      4_[         R"                  [        [         R"                  /5      [        / 5      4_0 [         R4                  [        [         R                  [         R                  [         R                  [         R
                  [         R4                  /5      [        [         R                  [         RN                  [         R0                  [         R                  [         R2                  [         R                  [         R                  [         R                   [         R                  [         R$                  [         R6                  [         R8                  [         R                  [         R&                  [         R:                  [         R(                  [         RP                  [         R*                  [         R                  [         R<                  [         R,                  [         R.                  [         R>                  /5      4_[         R                  [        [         R                  [         R                  /5      [        [         R                  [         R                  [         R                  [         RN                  [         R
                  [         R4                  [         R$                  [         R6                  [         R8                  [         R&                  [         R:                  [         R(                  [         RP                  [         R*                  [         R<                  [         R,                  [         R.                  [         R                  [         R>                  /5      4_[         R$                  [        [         R                  [         R                  [         R                  [         R                   [         R
                  [         R"                  [         R$                  [         R,                  [         R.                  /	5      [        [         R4                  [         R                  [         R6                  [         R                  [         R                  [         R                  /5      4_[         RT                  [        [         R                  [         RT                  [         RV                  /5      [        / 5      4_[         RX                  [        [         RR                  [         RX                  [         RF                  /5      [        [         RZ                  /5      4_[         R6                  [        [         R                  [         R                  [         R                  [         R                   [         R
                  [         R"                  [         R6                  [         R(                  [         R.                  /	5      [        [         R                  [         RN                  [         R4                  [         R                  [         R$                  [         R                  [         RP                  [         R                  [         R<                  [         R,                  [         R>                  /5      4_[         R\                  [        [         R\                  /5      [        / 5      4_[         RB                  [        [         RB                  [         RJ                  /5      [        / 5      4_[         R8                  [        [         R                  [         R                  [         R0                  [         R2                  [         R                  [         R                   [         R
                  [         R"                  [         R8                  [         R:                  [         R(                  [         R.                  /5      [        [         R                  [         R                  [         R                  [         R4                  [         R                  [         R                  [         R&                  [         R*                  [         R                  [         R<                  [         R>                  /5      4_[         R                  [        [         R                  [         R0                  [         R2                  [         R                  [         R                   [         R                  [         R                  /5      [        [         R                  [         R                  [         R                  [         RN                  [         R                  [         R                  [         R
                  [         R4                  [         R$                  [         R6                  [         R8                  [         R&                  [         R:                  [         R(                  [         RP                  [         R*                  [         R                  [         R<                  [         R,                  [         R.                  [         R                  [         R>                  /5      4_[         R^                  [        [         R^                  /5      [        / 5      4_[         R&                  [        [         R                  [         R                  [         R                  [         R                   [         R
                  [         R"                  [         R&                  [         R.                  /5      [        [         R0                  [         R4                  [         R                  [         R8                  [         R                  [         R                  /5      4_[         R:                  [        [         R                  [         R                  [         R2                  [         R                   [         R
                  [         R"                  [         R:                  [         R.                  /5      [        [         R                  [         R                  [         R4                  [         R                  [         R                  [         R*                  [         R                  [         R<                  /5      4_[         R(                  [        [         R                  [         R                  [         R                  [         R                   [         R
                  [         R"                  [         R(                  [         R.                  /5      [        [         R4                  [         R                  [         R                  [         R                  [         R>                  /5      4_[         RD                  [        [         RD                  [         RF                  /5      [        / 5      4_[         RP                  [        [         R                  [         R                  [         R                  [         R                  [         R                   [         R
                  [         R"                  [         R$                  [         R(                  [         RP                  [         R,                  [         R.                  /5      [        [         RN                  [         R4                  [         R                  [         R6                  [         R                  [         R                  [         R                  [         R>                  /5      4_[         R`                  [        [         RR                  [         RX                  [         RD                  [         R`                  [         Rb                  [         RF                  [         Rd                  /5      [        [         RZ                  /5      4_E0 [         R*                  [        [         R                  [         R                  [         R                  [         R                  [         R                  [         R                   [         R
                  [         R"                  [         R&                  [         R(                  [         R*                  [         R.                  /5      [        [         R0                  [         R2                  [         R4                  [         R                  [         R8                  [         R                  [         R:                  [         R                  [         R>                  /	5      4_[         Rb                  [        [         RR                  [         RX                  [         Rb                  [         RF                  /5      [        [         RZ                  /5      4_[         R                  [        [         R                  [         R                  [         R                  [         R                  [         R                   [         R                  [         R                  /5      [        [         R                  [         R                  [         R                  [         RN                  [         R0                  [         R2                  [         R
                  [         R4                  [         R$                  [         R6                  [         R8                  [         R                  [         R&                  [         R:                  [         R(                  [         RP                  [         R*                  [         R<                  [         R,                  [         R.                  [         R                  [         R>                  /5      4_[         R<                  [        [         R                  [         R                  [         R                  [         R                  [         R                  [         R                  [         R                   [         R
                  [         R"                  [         R$                  [         R&                  [         R(                  [         R*                  [         R<                  [         R,                  [         R.                  /5      [        [         R                  [         R0                  [         R2                  [         R4                  [         R                  [         R6                  [         R8                  [         R                  [         R:                  [         R                  [         R                  [         R>                  /5      4_[         R,                  [        [         R                  [         R                  [         R                  [         R                   [         R
                  [         R"                  [         R,                  [         R.                  /5      [        [         R4                  [         R                  [         R6                  [         R                  [         R                  [         R                  /5      4_[         R.                  [        [         R                  [         R                  [         R                   [         R
                  [         R"                  [         R.                  /5      [        [         R4                  [         R                  [         R                  [         R                  /5      4_[         RV                  [        [         R                  [         RV                  /5      [        / 5      4_[         RZ                  [        [         RZ                  /5      [        [         RX                  [         R`                  [         Rb                  [         Rd                  /5      4_[         RF                  [        [         RF                  /5      [        / 5      4_[         RH                  [        [         RF                  [         RH                  /5      [        / 5      4_[         R                  [        [         R                  [         R                  [         R
                  [         R                  /5      [        [         R                  [         R                  [         RN                  [         R                  [         R$                  [         R                  [         RP                  [         R                  [         R<                  [         R,                  [         R>                  /5      4_[         RJ                  [        [         RJ                  /5      [        / 5      4_[         Rf                  [        [         RJ                  [         Rf                  /5      [        / 5      4_[         Rd                  [        [         RR                  [         RX                  [         RD                  [         RF                  [         Rd                  /5      [        [         RZ                  /5      4_[         RL                  [        [         RJ                  [         RL                  /5      [        / 5      4_[         R>                  [        [         R                  [         R                  [         R                  [         RN                  [         R                  [         R2                  [         R                   [         R
                  [         R"                  [         R$                  [         R&                  [         R:                  [         R,                  [         R.                  [         R>                  /5      [        [         R                  [         R0                  [         R                  [         R                  [         R4                  [         R                  [         R6                  [         R8                  [         R                  [         R(                  [         RP                  [         R*                  [         R                  [         R<                  [         R                  /5      4_E$ )a  
Logical relations between unary predicates as dictionary.

Each key is a predicate, and item is two groups of predicates.
First group contains the predicates which are implied by the key, and
second group contains the predicates which are rejected by the key.

)4r   r   setr   complexr   r   r"   r#   r
   r   r   r   extended_nonnegativeextended_nonzeroextended_positiveextended_realr   integernonnegativenonzeror   r   realextended_negativeextended_nonpositiver	   r(   r   nonpositiver   r   r   r   r   r!   r   r)   r   r   r   r   r$   r   r    r&   is_true
nonintegerr*   r%   r'   r+   r,   r-   r.   get_known_facts_dictrD      s   f	c1;;qyy!((KLQZZ,,a.A.A	 	f 	
#q/0#b':	f
 	
Q]]O,c"g6f 	
		C		188<=QZZ,,a.A.ABCEf 	
S!"4"4!56B@f 	
c1;;qyy!++	 2 2	Q__ahh			1==!))QZZ		  q**A,B,B	QZZqzz	Q]]A,?,?	!!166+ ,	-f" 	


S!**a&8&8!((AHH	Q\\1#5#57 89<RB#f& 	
akk1==!))QVV	1;;		1::	 q{{AJJ	QUUA$7$7	 'f0 	
c1==!2E2E	 2 2AOO#E FQ[[!00!2E2E	Q]]AJJ0C0C	 	1f: 	
ammQ5K5K	& " 3 3Q[[	

A'' ) *!+;f@ 	
ammQ5K5K	& "Q-@-@	QZZ!4!4agg ? @!AAfF 	
S!--1C1C	" QVV457GfJ 	
c1==!2H2H	A//#B CQ  !"8"8!++	

A''@ 	ABKfR 	
#q}}aoo>?Q[[MSfV 	
3qxx013

	Q0082 43 4WfZ 	


S!**&B0[f\ 	
c1;;-(#b'2]f^ 	
c1??AMM199	!++  !$akk166	Q33	 2 2	Q__ajj!))	ajj!"5"5q}}	qyy!%%	QWWajj!&&!&&&B "CD_fn 	


S!--45sAKK			1;;!++			1<<Q]]	qyy!%%QWW	

AFFA,,aff	<6 87 8ofx 	
		CammQYY	1;;		1::	 q{{AJJ	Q00!2B2BD EFyf@ 	
S!"4"4a6H6H	" r7$AfD 	
sAJJahh?@QZZLEfH 	
sAMM199a6H6H	1;;			166  !++qvvq{{	

AIIq22AEE	QWWajj!&&": ;<IfR 	
		C$c"g.SfT 	
S!"4"4all!CDc"gNUfV 	


S!--A4G4G	 2 2AOO	!++qzz1==!))	  q{{A$:$:	Q[[!**	Q]]AJJ	QWWaff. /0Wfd 	
c1==!2E2E	 2 2AOO	

A''#) *+.			1;;(>(>	QXXq{{AII	ajj!--			155!**a&9&9177	

AFFA,,aff06 ,78eft 	
sALL>*CG4ufv 	
Q]]AIIq7M7M	1;;	 q**AKK	

A'')<)<> ?@wf~ 	
Q]]AIIq7M7M	1;;	 q{{A$7$7	

A''	QWW& '(fH 	
		C		13E3E	1;;		166C DQ[[!**a&9&9	QVV% 	&'IfP 	
3!((+,c"g6QfR 	
Q[[!--	AOOQXXq{{			199aeeQZZ9 : 	QVVQ[[!**all	Q00!2B2B	 	Sf^ 	
sAJJahh	QXXqyy2 3474EG_fb 	


S!--A4J4J	A//	!++q}}aii	  q**A,B,B	QZZQ-@-@	q**AFF4 56cfn 	
c1::q||	QXX#' (),ajj\):<ofr 	
c1==!2H2H	A//	

A''#) *+.			1;;(;(;	!++qyy	ajj!"5"5q}}	qyy!%%QWW	

AFFA,,aff06 ,78sfB 	
#q{{AMM199	 2 2	Q__ahh			1==!))QZZ	

AFF	  "1;;0C0C	QZZ	

A''	Q--qvv#7 8	9CfR 	


S!++q}}aii	1;;

AFFD EQ[[!**all	Q00!2B2BD 	EFSfZ 	
ammQYY	QVV "AKK	Q00$2  34[f` 	
#q111??CDc"gNafb 	


S!**&Q\\1<<	QYY-( )) *cff 	
3z?CG,gfh 	
c188Q[[12CG<ifj 	
3qyy!((	  akk166	

AIIq22AEE	QWWajj!&&!: ;<kfr 	
sALL>*CG4sft 	
Cq/@/@ ABCGLufv 	
		CQ\\188QXX			 !**&(wfz 	
S!,,0B0B!CDc"gN{f| 	
akk1==!))QVV	 6 6	1;;			q}}ajj!&&!&&B C 	Q[[!--q/A/A	Q[[!**all	

A''AEE1::	QWWa&6&68 	9	:}f fr-   N)__doc__sympy.assumptions.askr   sympy.assumptions.cnfr   sympy.core.cacher   r/   r1   r3   rD   r,   r-   r.   <module>rI      si   
 $ ) $L 	L\ 	 	> 	4 	4l 	o 	or-   