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    {þdÆ¾  ã                	   @   sJ  d dl mZ d dlmZ d dlmZ d dlmZmZm	Z	 d dl
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lmZ d dlmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;m<Z<m=Z=m>Z>m?Z?m@Z@mAZAmBZBmCZCmDZDmEZEmFZFmGZGmHZH d dlImJZJ d dlKmLZLmMZMmNZN d dlOmPZPmQZQmRZR edƒ\ZSZTZUZVedƒ\	ZWZXZYZZZ[Z\Z]Z^Z_dd„ Z`dd„ Zadd„ Zbdd„ Zcdd„ Zddd„ Zedd„ Zfdd „ Zgd!d"„ Zhd#d$„ Zid%d&„ Zjd'd(„ Zkd)d*„ Zld+d,„ Zmd-d.„ Znd/d0„ Zod1d2„ Zpd3d4„ Zqd5d6„ Zrd7d8„ Zsd9d:„ Ztd;d<„ Zud=d>„ Zvd?d@„ ZwdAdB„ ZxdCdD„ ZydEdF„ ZzdGdH„ Z{dIdJ„ Z|dKdL„ Z}dMdN„ Z~dOdP„ ZdQdR„ Z€dSdT„ ZdUdV„ Z‚dWdX„ ZƒdYdZ„ Z„d[d\„ Z…d]d^„ Z†d_d`„ Z‡dadb„ Zˆdcdd„ Z‰dedf„ ZŠdgdh„ Z‹didj„ ZŒdkdl„ ZeMdmdn„ ƒZŽdodp„ Zdqdr„ Zdsdt„ Z‘dudv„ Z’dwdx„ Z“dydz„ Z”d{d|„ Z•d}d~„ Z–dd€„ Z—dd‚„ Z˜dƒd„„ Z™d…d†„ Zšd‡dˆ„ Z›d‰dŠ„ Zœd‹dŒ„ ZddŽ„ Zždd„ ZŸd‘d’„ Z eNd“d”„ ƒZ¡d•d–„ Z¢d—d˜„ Z£d™dš„ Z¤d›dœ„ Z¥ddž„ Z¦dŸd „ Z§d¡d¢„ Z¨d£d¤„ Z©d¥d¦„ Zªd§d¨„ Z«d©dª„ Z¬d«d¬„ Z­d­d®„ Z®d¯d°„ Z¯d±d²„ Z°d³d´„ Z±dµS )¶é    )ÚQ)Úrefine)Úoo)ÚEqualityÚEqÚNe)ÚS)ÚDummyÚsymbols)Ú	Piecewise)ÚcosÚsin)ÚIntervalÚUnion©Úsimplify)/ÚAndÚBooleanÚ
EquivalentÚITEÚImpliesÚNandÚNorÚNotÚOrÚPOSformÚSOPformÚXorÚXnorÚ	conjunctsÚ	disjunctsÚdistribute_or_over_andÚdistribute_and_over_orÚeliminate_implicationsÚis_nnfÚis_cnfÚis_dnfÚsimplify_logicÚto_nnfÚto_cnfÚto_dnfÚto_int_reprÚbool_mapÚtrueÚfalseÚBooleanAtomÚ
is_literalÚterm_to_integerÚtruth_tableÚ
as_BooleanÚto_anfÚis_anfÚdistribute_xor_over_andÚ
anf_coeffsÚANFformÚbool_mintermÚbool_maxtermÚbool_monomialÚ_check_pairÚ_convert_to_varsSOPÚ_convert_to_varsPOSÚ	ExclusiveÚgateinputcount)ÚCNF)ÚraisesÚXFAILÚslow)ÚcombinationsÚpermutationsÚproductzA:Dza:e w:zc                   C   s¤   t t@ tt tƒksJ ‚t tB tt tƒks,J ‚t t@ tB ttt tƒtƒksLJ ‚t t? tt tƒksbJ ‚t t> ttt ƒksxJ ‚t  tt ƒksŠJ ‚t tA tt tƒks J ‚dS )z)Test that |, & are overloaded as expectedN)ÚAÚBr   r   ÚCr   r   r   © rK   rK   úg/var/www/html/stable-diffusion-webui/venv/lib/python3.9/site-packages/sympy/logic/tests/test_boolalg.pyÚtest_overloading    s     rM   c                  C   sè  t ƒ tu sJ ‚t tƒtksJ ‚t dƒtu s.J ‚t dƒtu s>J ‚t ddƒtu sPJ ‚t ddƒtu sbJ ‚t ddƒtu stJ ‚t dtƒtks†J ‚t dtƒtu s˜J ‚t dddƒtu s¬J ‚t ddtƒtksÀJ ‚t ddtƒtu sÔJ ‚t dtƒtksæJ ‚ttdd„ ƒ ttdd„ ƒ t tdk tdkƒtu sJ ‚tdk} t | | jƒ| jks>J ‚ttkttk ttkttkf\}}}}t ||||ƒt ||ƒks€J ‚dd„ t||||fƒD ƒt ||ƒhks¬J ‚t t t	t
d	ƒt	td	ƒƒt tt
d	ƒt	td	ƒƒƒtu säJ ‚d S )
NTFé   c                   S   s
   t dtƒS ©Né   ©r   rH   rK   rK   rK   rL   Ú<lambda>:   ó    ztest_And.<locals>.<lambda>c                   S   s   t tdk tƒS rO   rQ   rK   rK   rK   rL   rR   ;   rS   c                 S   s   h | ]}t |Ž ’qS rK   )r   ©Ú.0ÚirK   rK   rL   Ú	<setcomp>A   rS   ztest_And.<locals>.<setcomp>r   )r   r-   rH   r.   rB   Ú	TypeErrorÚ	canonicalrI   rF   r   ÚaÚbr   Úc©ÚeÚgÚlÚgeÚlerK   rK   rL   Útest_And,   s,    $,rc   c                  C   s‚  t ƒ tu sJ ‚t tƒtksJ ‚t dƒtu s.J ‚t dƒtu s>J ‚t ddƒtu sPJ ‚t ddƒtu sbJ ‚t ddƒtu stJ ‚t dtƒtu s†J ‚t dtƒtks˜J ‚t dddƒtu s¬J ‚t ddtƒtu sÀJ ‚t ddtƒtksÔJ ‚t dtƒtu sæJ ‚ttdd„ ƒ ttdd„ ƒ t tdk tdkƒtu sJ ‚tdk} t | | jƒ| ks<J ‚ttkttk ttkttkf\}}}}t ||||ƒt ||ƒks~J ‚d S )NTFrN   c                   S   s
   t dtƒS rO   ©r   rH   rK   rK   rK   rL   rR   S   rS   ztest_Or.<locals>.<lambda>c                   S   s   t tdk tƒS rO   rd   rK   rK   rK   rL   rR   T   rS   )r   r.   rH   r-   rB   rX   rY   rI   r]   rK   rK   rL   Útest_OrE   s(    $re   c                  C   s  t ƒ tu sJ ‚t tƒtksJ ‚t ttƒtu s0J ‚t dttƒtu sDJ ‚t tttttƒtks\J ‚t dddttƒt ttƒ ks|J ‚t dƒtu sŒJ ‚t dƒtu sœJ ‚t ddƒtu s®J ‚t ddƒtu sÀJ ‚t ddƒtu sÒJ ‚t dtƒt ksæJ ‚t dtƒtksøJ ‚t dddƒtu sJ ‚t ddtƒt ks&J ‚t ddtƒtks<J ‚tt ttƒt ƒsRJ ‚t ttt ttƒƒt ttttƒksxJ ‚t ttt ttƒƒt ttƒksšJ ‚t tdk tdktƒt ddtƒ  krÒt ddtƒksØn J ‚tdk} t | | jƒt ddƒ  krt ddƒksn J ‚d S ©NTFrN   r   )	r   r.   rH   r-   rI   Ú
isinstancerJ   ÚDrY   )r^   rK   rK   rL   Útest_Xor\   s,     &">ri   c                  C   s.   t tA } |  t¡t tB t  t B @ ks*J ‚d S ©N)ÚxÚyÚrewriter   ©ÚexprrK   rK   rL   Útest_rewrite_as_Andu   s    rp   c                  C   s.   t tA } |  t¡t t @ tt  @ B ks*J ‚d S rj   )rk   rl   rm   r   rn   rK   rK   rL   Útest_rewrite_as_Orz   s    rq   c                  C   s<   t t@ tt @ B } |  t¡t t@  tt @  @  ks8J ‚d S rj   )rl   ÚzÚwrm   r   rn   rK   rK   rL   Útest_rewrite_as_Nand   s    rt   c                  C   s4   t tt B @ } |  t¡t  tt B  B  ks0J ‚d S rj   )rr   rl   rs   rm   r   rn   rK   rK   rL   Útest_rewrite_as_Nor„   s    ru   c                   C   sb   t tdd„ ƒ tdƒtu sJ ‚tdƒtu s.J ‚tdƒtu s>J ‚tdƒtu sNJ ‚tdƒtu s^J ‚d S )Nc                   S   s
   t ddƒS ©NTF)r   rK   rK   rK   rL   rR   Š   rS   ztest_Not.<locals>.<lambda>TFr   rN   rP   )rB   rX   r   r.   r-   rK   rK   rK   rL   Útest_Not‰   s    rw   c                   C   sÞ   t ƒ tu sJ ‚t tƒt ks J ‚t dƒtu s0J ‚t dƒtu s@J ‚t ddƒtu sRJ ‚t ddƒtu sdJ ‚t ddƒtu svJ ‚t dtƒt ksŠJ ‚t dtƒtu sœJ ‚t dddƒtu s°J ‚t ddtƒt ksÆJ ‚t ddtƒtu sÚJ ‚d S rv   )r   r.   rH   r-   rK   rK   rK   rL   Ú	test_Nand’   s    rx   c                   C   sÜ   t ƒ tu sJ ‚t tƒt ks J ‚t dƒtu s0J ‚t dƒtu s@J ‚t ddƒtu sRJ ‚t ddƒtu sdJ ‚t ddƒtu svJ ‚t dtƒtu sˆJ ‚t dtƒt ksœJ ‚t dddƒtu s°J ‚t ddtƒtu sÄJ ‚t ddtƒtu sØJ ‚d S rv   )r   r-   rH   r.   rK   rK   rK   rL   Útest_Nor¡   s    ry   c                   C   s"  t ƒ tu sJ ‚t tƒt ks J ‚t ttƒtu s2J ‚t dttƒtu sFJ ‚t tttttƒt ks`J ‚t dƒtu spJ ‚t dƒtu s€J ‚t ddƒtu s’J ‚t ddƒtu s¤J ‚t ddƒtu s¶J ‚t dtƒtksÈJ ‚t dtƒt ksÜJ ‚t dddƒtu sðJ ‚t ddtƒtksJ ‚t ddtƒt ksJ ‚d S rv   )r   r-   rH   r.   rK   rK   rK   rL   Ú	test_Xnor°   s    rz   c                   C   sê   t tdd„ ƒ tddƒtu s J ‚tddƒtu s2J ‚tddƒtu sDJ ‚tddƒtu sVJ ‚tdtƒtu shJ ‚tddƒtu szJ ‚tddƒtu sŒJ ‚tt? tt> ks J ‚tdk tdk? tdkks¼J ‚tdk tjtk? tu sÖJ ‚tt? tu sæJ ‚d S )Nc                   S   s   t tttƒS rj   )r   rH   rI   rJ   rK   rK   rK   rL   rR   Ã   rS   ztest_Implies.<locals>.<lambda>TFr   rN   )	rB   Ú
ValueErrorr   r-   r.   rH   rI   r   ÚOnerK   rK   rK   rL   Útest_ImpliesÂ   s    r}   c                   C   s  t ttƒt ttƒ  kr(t tttƒks.n J ‚t ƒ tu s<J ‚t ttƒt tƒ  krZtu s`n J ‚t ddƒt ddƒ  kr€tu s†n J ‚t ddƒt ddƒ  kr¦tu s¬n J ‚t tdƒtks¾J ‚t tdƒttƒksÔJ ‚t ttdƒtt@ ksìJ ‚t ttdƒt t @ ks
J ‚t dtƒtksJ ‚t dtƒttƒks6J ‚t tt ttƒƒt t ttƒtƒks\J ‚t tdk tdkƒtu sxJ ‚t tdk tdkdƒtu s–J ‚t tdk tdkdƒtu s´J ‚t tdk tjtkƒt ddƒ  krèt ddƒksîn J ‚t t	ttƒt	ttƒƒtu sJ ‚d S rf   )
r   rH   rI   r-   r.   r   rJ   r   r|   r   rK   rK   rK   rL   Útest_EquivalentÑ   s"    .$&&&:r~   c                   C   sT   t dddƒtu sJ ‚t dddƒtu s(J ‚t dddƒtu s<J ‚t dddƒtu sPJ ‚d S )NFT)r?   r-   r.   rK   rK   rK   rL   Útest_Exclusiveå   s    r   c                   C   sÒ   t tttƒƒ tt tƒt tƒƒ¡du s*J ‚tttƒ tt? tt? @ ¡du sNJ ‚tt B t tB @  t t @ tt@ B ¡du s€J ‚tt?  t t ? ¡du sžJ ‚ttt? ?  ttt? ? ¡du sÀJ ‚tt	dd„ ƒ d S )NTFc                   S   s   t t@  t tk¡S rj   )rH   rI   ÚequalsrK   rK   rK   rL   rR   ò   rS   ztest_equals.<locals>.<lambda>)
r   r   rH   rI   r€   r   r   rJ   rB   ÚNotImplementedErrorrK   rK   rK   rL   Útest_equalsì   s    *$2"r‚   c               	      sò	  g d¢g d¢g d¢g d¢g} g d¢g d¢g d¢g d¢g}t tttg| ƒttttƒtƒtttƒtƒƒksjJ ‚tt tttg|ƒƒtttttƒttƒƒtttƒƒƒks¤J ‚ttttg| | ƒtu sÀJ ‚t tttg| | ƒtu sÜJ ‚t t	ƒ t	ƒ t	ƒ g| | ƒtu sþJ ‚g d	¢g d
¢g d¢g d¢g d¢g‰ g d¢g d¢g d¢g}t t
tttgˆ |ƒttttƒttt
ƒttƒƒƒksnJ ‚tt
tttgˆ |ƒtttt
ƒtƒtƒksœJ ‚g d¢‰ g d¢}t t
tttgˆ |ƒttttƒttt
ƒttƒƒƒksäJ ‚tt
tttgˆ |ƒtttt
ƒtƒtƒksJ ‚dg d
¢dg d¢g d¢g‰ dg d¢dg}t t
tttgˆ |ƒttttƒttt
ƒttƒƒƒksrJ ‚tt
tttgˆ |ƒtttt
ƒtƒtƒks J ‚dtdtdig‰ dg d¢dg}t t
tttgˆ |ƒttttƒttt
ƒttƒƒƒksöJ ‚tt
tttgˆ |ƒtttt
ƒtƒtƒks$J ‚tdtdidg‰ g d¢g}g d¢g‰ tt‡ fdd„ƒ tt‡ fdd„ƒ ttdd„ ƒ tttttƒƒ}ttttB @ ƒ|ks¤J ‚ttt@ tt@ B ƒ|ksÂJ ‚ttttƒƒtttƒtƒksäJ ‚ttttƒƒttttƒtttƒttƒƒƒksJ ‚ttttdƒtƒƒtttdƒtƒks@J ‚ttttdƒtƒƒtju s`J ‚ttttdƒtƒƒtttdƒtƒksŠJ ‚tttttƒtƒƒttttƒtƒks´J ‚tttttdƒtƒtttdƒtƒƒƒtttdƒtttƒƒksöJ ‚t t @ t @ t t @ t@ B }tt|ƒ}t|ƒtt @ t @ ks@J ‚ttdd„ ƒ ttttktttk tƒƒƒttkksxJ ‚ttttktttktƒƒƒttkks¢J ‚ttttktttk tƒƒƒttkksÌJ ‚tdƒ\	}}}}}}	}
}}||@ |@ |@ |@ |	@ |
@ |@ |@ ||@ |@ |@ |@ |	@ |
@ |@ | @ B }t|ƒ|ksBJ ‚t||@ |B |B ||@ d||B kslJ ‚t ttgddggƒ}t ttgddggƒ|ksžJ ‚tttgddggƒ|ks¼J ‚ttd d„ ƒ t tgdggdggƒtu sêJ ‚t tgdggdggƒtu s
J ‚t tgg g ƒtu s"J ‚ttd!d„ ƒ ttgdggdggƒtu sPJ ‚ttgdggdggƒtu spJ ‚ttgg g ƒtu sˆJ ‚ttt@ tt@ B ƒtttttƒƒks²J ‚tttttƒƒƒd"ksÎJ ‚tttttƒƒƒd#ksêJ ‚ttttdƒtttƒƒƒtttdƒttdƒƒks J ‚tttd dƒtttƒƒ ¡ tttdƒttdƒƒksZJ ‚tttd dƒtttƒƒ ¡ tttdƒtttƒƒks”J ‚tttd dƒtttƒƒ ¡ tttdƒttdƒƒksÎJ ‚tttd dƒtttt ƒttt dƒƒ ¡ tttdƒttd$ƒttdƒƒk	s J ‚tttd dƒttd dƒƒ ¡ ttdƒk	sRJ ‚tttd dƒttd dƒƒ ¡ ttdƒk	s„J ‚tttd dƒttd dƒƒ ¡ d"k	s°J ‚tttd dƒttd dƒƒ ¡ tttdƒttdƒƒk	sîJ ‚d%S )&z1
    Test working of simplification methods.
    ©r   r   rN   ©r   rN   rN   ©rN   r   r   )rN   rN   r   )r   r   r   ©r   rN   r   ©rN   r   rN   ©rN   rN   rN   ©r   r   r   rN   ©r   r   rN   rN   ©r   rN   rN   rN   ©rN   r   rN   rN   ©rN   rN   rN   rN   )r   r   r   r   )r   r   rN   r   ©r   rN   r   rN   )rN   é   é   é   é   )r   rP   é   rN   r   r   r“   c                      s   t ttttgˆ ƒS rj   )r   rs   rk   rl   rr   rK   ©ÚmintermsrK   rL   rR   %  rS   z-test_simplification_boolalg.<locals>.<lambda>c                      s   t ttttgˆ ƒS rj   ©r   rs   rk   rl   rr   rK   r”   rK   rL   rR   &  rS   c                   S   s   t ttttgdgƒS )NZabcdefgr–   rK   rK   rK   rL   rR   (  rS   rP   r   c                   S   s   t tttB @ ddS )NZblabla)Úform)r'   rH   rI   rJ   rK   rK   rK   rL   rR   :  rS   za b c d e f g h j)Zdontcarec                   S   s   t tgdggdggƒS ©NrN   )r   rk   rK   rK   rK   rL   rR   O  rS   c                   S   s   t tgdggdggƒS r˜   )r   rk   rK   rK   rK   rL   rR   T  rS   FTéÿÿÿÿN)r   rk   rl   rr   r   r   r   r   r-   r	   rs   rB   r{   rX   rH   rI   rJ   r'   r   r   r   r   r.   r   r
   r   r   )Zset1Zset2Ú	dontcaresZansr[   r^   rZ   r\   ÚdÚfr_   ÚhÚjro   rK   r”   rL   Útest_simplification_boolalgõ   sÊ    2 ÿ"ÿÿÿ.ÿÿ.ÿÿÿ.ÿÿ.

"ÿ
* **$ÿ
"
***"$ÿ*    *6:::,ÿ
22, ÿrŸ   c               
   C   sè  g d¢g d¢g d¢g d¢g d¢g} t tttƒƒtƒtttifksDJ ‚t tttttg| ƒtttttg| ƒƒt	t
ttƒtƒt
ttƒtƒtƒttttttttifks¢J ‚t ttttgg d¢gƒttttgg d¢gƒƒdksØJ ‚ttttgg d¢g d¢gƒ}ttttgg d¢g d	¢gƒ}t ||ƒ|ttttifks0J ‚t tttƒtttƒ ƒdksRJ ‚t t	ttƒt
ttƒƒd
u srJ ‚t t	ttƒt	tttƒƒd
u s”J ‚t ttttƒttttƒ ƒdksºJ ‚t tttttƒtttttƒ ƒdksäJ ‚d
S )z,
    Test working of bool_map function.
    r‰   rŠ   r‹   rŒ   r   r‡   Frƒ   r…   N)r,   r   rZ   r   rs   rk   rl   rr   r   r   r   r[   r\   r   )r•   Z	function1Z	function2rK   rK   rL   Útest_bool_mapj  s0    ÿ"ÿ2þÿÿÿ
" "&r    c                   C   st   t tdƒtksJ ‚t tddƒtks&J ‚t tdƒtu s8J ‚t tddƒtu sLJ ‚ttdƒtu s^J ‚ttdƒtkspJ ‚dS )zBTest that mixing symbols with boolean values
    works as expectedTFN)r   rH   r.   r   r-   rK   rK   rK   rL   Útest_bool_symbolƒ  s    r¡   c                   C   sÞ   t dtƒdu sJ ‚t ttƒdu s$J ‚ddks0J ‚dtks<J ‚dtkdu sLJ ‚ddksXJ ‚dtksdJ ‚dtkdu stJ ‚tjdu s‚J ‚tt@ jsJ ‚ttB jsžJ ‚t jsªJ ‚ttA js¸J ‚tjt ttƒksÌJ ‚t ttƒsÚJ ‚d S rf   )rg   r   r-   r.   Z
is_BooleanrH   rI   rK   rK   rK   rL   Útest_is_boolean  s    r¢   c                   C   s   t t@  t d¡tksJ ‚t t@  t d¡tu s0J ‚t t@  td¡t ksHJ ‚t t@  td¡tu s`J ‚t t@  t dtdi¡tu s~J ‚t tB  t d¡tu s–J ‚t tB  t d¡tks®J ‚t tB  td¡tu sÆJ ‚t tB  td¡t ksÞJ ‚t tB  t dtdi¡tu süJ ‚d S rv   )rH   rI   Úsubsr.   r-   rK   rK   rK   rL   Ú	test_subs¡  s    r¤   c                  C   s>   t ttdƒƒ\} }| |@ || @ ks&J ‚| |B || B ks:J ‚dS )z$Test for commutativity of And and OrzA,BN)Úmapr   r
   )rH   rI   rK   rK   rL   Útest_commutative´  s    r¦   c                   C   s    t t@ t@ t tt@ @ ksJ ‚dS )zTest for associativity of AndN©rH   rI   rJ   rK   rK   rK   rL   Útest_and_associativity¼  s    r¨   c                   C   s    t tB tB t ttB B ksJ ‚d S rj   r§   rK   rK   rK   rL   Útest_or_assicativityÂ  s    r©   c                  C   s   t ƒ } |   | ksJ ‚d S rj   )r   )rZ   rK   rK   rL   Útest_double_negationÆ  s    rª   c                   C   s–   t tttddƒt tB ks J ‚t ttttƒ? ? ƒttttƒttƒƒttƒƒksTJ ‚t tttttƒƒt tB t tB @ t tB @ t tB @ ks’J ‚d S )NF©Úevaluate)	r#   r   rH   rI   rJ   r   r   r   rh   rK   rK   rK   rL   Útest_eliminate_implicationsÍ  s     ÿÿ&ÿr­   c                   C   sx   t tt@ t@ ƒttthksJ ‚t ttB t@ ƒttB thks>J ‚t tƒthksPJ ‚t dƒdhksbJ ‚t dƒdhkstJ ‚d S rv   )r   rH   rI   rJ   rK   rK   rK   rL   Útest_conjunctsÕ  s
     r®   c                   C   sz   t ttB tB ƒttthksJ ‚t ttB t@ ƒttB t@ hks@J ‚t tƒthksRJ ‚t dƒdhksdJ ‚t dƒdhksvJ ‚d S rv   )r    rH   rI   rJ   rK   rK   rK   rL   Útest_disjunctsÝ  s
    "r¯   c                   C   sŽ   t ttttƒtƒƒttttƒtttƒƒks.J ‚ttttttƒƒƒttttƒtttƒƒks\J ‚ttttttƒƒƒttttƒtttƒƒksŠJ ‚d S rj   )	r"   r   r   rH   rI   rJ   r!   r6   r   rK   rK   rK   rL   Útest_distributeå  s    ..r°   c               	   C   sf  t dƒ\} }}tt| |ƒƒt| |ƒks*J ‚tt| |ƒƒt| |t| |ƒƒksNJ ‚ttt| |ƒt| |ƒ|ƒƒt| d| |@ ddks‚J ‚ttt| |ƒt| |ƒt| |ƒt| |ƒƒƒdks´J ‚tt| t	|ƒt| |ƒt| |ƒt||ƒƒƒtdt||ƒt| ||ƒddksJ ‚tt| |ƒƒt| |ƒks J ‚tt	| ƒƒt| dddks@J ‚tt| |ƒƒtdt| |ƒddkshJ ‚tt| |ƒƒt| |dt| |ƒddks”J ‚tt| |ƒƒt| dt| |ƒddks¾J ‚tt
| |ƒƒt| |dddksâJ ‚tt| |B | |? ƒddtdtt| |ƒt| |ƒƒddks"J ‚tt| |A | |@ ƒddtdtt| |ƒt| |ƒƒddksbJ ‚d S )Núx,y,zTF©Zremove_true)Údeep)r
   r4   r   r   r   r   r   r   r   r   r   ©rk   rl   rr   rK   rK   rL   Útest_to_anfë  s,    $ÿ2(ÿ
 (,*$ÿ
ÿrµ   c                   C   s  t tƒtu sJ ‚t tƒtu s J ‚t tƒtks0J ‚t tt B tB ƒtu sJJ ‚t tt @ t@ ƒtu sdJ ‚t tt? ƒt tB ks~J ‚t ttttƒƒt tB t tB @ t tB @ ks°J ‚t ttA tA ƒttB tB t t B tB @ tt B t B @ t tB t B @ ksJ ‚t ttttƒƒt tB ttB @ ks*J ‚t tttB tB ƒƒt t @ t @ ksVJ ‚t ttt@ t@ ƒƒt t B t B ks‚J ‚t ttt? ƒƒtt @ ks¢J ‚t tttttƒƒƒt	t
tttƒt
t t t ƒƒksÜJ ‚t tttA tA ƒƒt tB tB tt B tB @ ttB t B @ t t B t B @ ks2J ‚t tttttƒƒƒt t B tt B @ ksbJ ‚t tt? tt? A ƒtt @ t t@ B ksJ ‚t tt? tt? A dƒt t B tB tB tt @ t t@ B @ ksÔJ ‚ttddƒ  ¡ tksîJ ‚ttddƒ  ¡ t ks
J ‚ttdd„ ƒ d S )NFrN   r   c                   S   s   t tdk dgtƒ ¡ S r˜   )r   rH   rI   r(   rK   rK   rK   rL   rR     rS   ztest_to_nnf.<locals>.<lambda>)r(   r-   r.   rH   rI   r   rJ   r   r   r   r   rB   rX   rK   rK   rK   rL   Útest_to_nnf   s4    2:ÿ
(,, ::ÿ
0.&ÿ
r¶   c                	   C   s¨  t ttB  ƒtttƒttƒƒks$J ‚t tt@ tB ƒttttƒtttƒƒksNJ ‚t tt? ƒt tB kshJ ‚t ttt@ ? ƒt tB t tB @ ksJ ‚t tttB @ t ttB @ B dƒttB ks¼J ‚t tt@ ƒtttƒksÖJ ‚t tttƒƒtttttƒƒttttƒƒƒksJ ‚t tttt@ ƒƒt tB t tB @ t t B tB @ ksDJ ‚t ttttB ƒdƒttttƒtƒtttƒtƒtttttƒƒƒksŠJ ‚t td ƒtd ks¤J ‚d S ©NTrN   )r)   rI   rJ   r   r   rH   r   r   rK   rK   rK   rL   Útest_to_cnf  s    $*(,2"ÿ
*ÿ
r¸   c                     s  t dƒ\} }}}}}}}}}	}
}}}}| |@ |@ |@ |@ |@ |@ |@ |@ | |@ |@ |@ |@ |@ |@ |	@ |@ B | |
@ |@ |@ |@ |@ |@ |@ |@ B ‰ ttˆ ƒƒs¢J ‚tt‡ fdd„ƒ tttfttfƒD ]H\}}|| ||||||||ƒ	‰ tt‡ fdd„ƒ |ˆ dddˆ ksÆJ ‚qÆd S )Nzx1:16c                      s   t ˆ ddS ©NTr   ©r)   rK   ©ÚeqrK   rL   rR   2  rS   z"test_issue_18904.<locals>.<lambda>c                      s   t ˆ ddS r¹   rº   rK   r»   rK   rL   rR   5  rS   T)r   Úforce)	r
   r%   r)   rB   r{   Úzipr   r   r*   )Úx1Zx2Zx3Zx4Zx5Zx6Zx7Zx8Zx9Zx10Zx11Zx12Zx13Zx14Zx15rœ   ÚtrK   r»   rL   Útest_issue_18904,  s    &""ÿ"þrÁ   c                   C   s(   t ttdktdktdk @ B ƒƒs$J ‚d S )NéûÿÿÿrP   é   )r%   r)   r[   rZ   rK   rK   rK   rL   Útest_issue_99499  s    rÄ   c                   C   s  t  t  ttB  ¡¡tttB  ƒks(J ‚t  t  tt@ tB ¡¡ttt@ tB ƒksTJ ‚t  t  tt? ¡¡ttt? ƒksxJ ‚t  t  ttt@ ? ¡¡tttt@ ? ƒks¤J ‚t  t  tttB @ t ttB @ B ¡¡ttttB @ t ttB @ B ƒksìJ ‚t  t  tt@ ¡¡ttt@ ƒksJ ‚d S rj   )rA   Z
CNF_to_cnfZto_CNFrI   rJ   r)   rH   rK   rK   rK   rL   Útest_to_CNF=  s    (,$,HrÅ   c                   C   s<  t ttB  ƒtttƒttƒƒks$J ‚t tttB @ ƒttttƒtttƒƒksNJ ‚t tt? ƒt tB kshJ ‚t ttt@ ? ƒt tt@ B ksŠJ ‚t ttB ƒttB ks¢J ‚t tttƒdƒttttƒtttƒttƒƒƒksÔJ ‚t tttt@ ƒdƒtttttƒtttƒttƒƒtttƒttƒƒƒksJ ‚t td ƒtd ks8J ‚d S r·   )r*   rI   rJ   r   r   rH   r   r   rK   rK   rK   rL   Útest_to_dnfF  s    $*"ÿ.ÿ
rÆ   c                     s–   t ttdƒƒ\} }}‡ fdd„‰ ˆ t| |B || B g| ||gƒƒˆ ddgddggƒksXJ ‚ˆ t| |B ||  B g| ||gƒƒˆ ddgddggƒks’J ‚d S )Nr±   c                    s4   zt ‡ fdd„| D ƒƒW S  ty.   |  Y S 0 d S )Nc                 3   s   | ]}ˆ |ƒV  qd S rj   rK   )rU   rk   ©Úsorted_recursiverK   rL   Ú	<genexpr>Y  rS   z=test_to_int_repr.<locals>.sorted_recursive.<locals>.<genexpr>)ÚsortedrX   )ÚargrÇ   rK   rL   rÈ   W  s    z*test_to_int_repr.<locals>.sorted_recursiverN   rP   r   r™   )r¥   r   r
   r+   r´   rK   rÇ   rL   Útest_to_int_reprT  s    ÿ ÿrÌ   c                  C   s¬   t dƒ\} }ttƒdu sJ ‚ttƒdu s,J ‚t| ƒdu s<J ‚tt| |ƒƒdu sRJ ‚tt| |t| |ƒƒƒdu spJ ‚tt| |t| |ƒƒƒdu sŽJ ‚ttt| ƒ|ƒƒdu s¨J ‚d S )Núx,yTF)r
   r5   r-   r.   r   r   r   r   ©rk   rl   rK   rK   rL   Útest_is_anfc  s    rÏ   c                   C   s  t tƒdu sJ ‚t tƒdu s J ‚t t ƒdu s2J ‚t tt@ ƒdu sFJ ‚t tt@ t t@ B t t@ B t t @ B dƒdu s|J ‚t ttB t t B @ ƒdu sœJ ‚t ttttƒƒƒdu s¶J ‚t ttA ƒdu sÊJ ‚t tt@ t t@ B t t@ B t t @ B dƒdu sJ ‚d S rv   )r$   r-   rH   rI   r   r   rK   rK   rK   rL   Útest_is_nnfn  s    6 rÐ   c                   C   sŽ   t tƒdu sJ ‚t ttB tB ƒdu s(J ‚t tt@ t@ ƒdu s@J ‚t ttB t@ ƒdu sXJ ‚t tt@ tB ƒdu spJ ‚t tt@  tB ƒdu sŠJ ‚d S rv   )r%   rk   rl   rr   rK   rK   rK   rL   Útest_is_cnfz  s    rÑ   c                   C   sŽ   t tƒdu sJ ‚t ttB tB ƒdu s(J ‚t tt@ t@ ƒdu s@J ‚t tt@ tB ƒdu sXJ ‚t ttB t@ ƒdu spJ ‚t ttB  t@ ƒdu sŠJ ‚d S rv   )r&   rk   rl   rr   rK   rK   rK   rL   Útest_is_dnfƒ  s    rÒ   c                  C   s°  t dƒ\} }}tdddƒtu s"J ‚tdddƒtu s6J ‚tdddƒtu sJJ ‚tdddƒtu s^J ‚tt| ||ƒtƒstJ ‚d} t| ||ƒ|ksŒJ ‚d} t| ||ƒ|ks¤J ‚d}tt| |ƒ||ƒ|ksÂJ ‚tt| dƒt|dƒdƒtu sâJ ‚tt| |ƒttƒksúJ ‚tt|| ƒtksJ ‚tdtt	ƒtks&J ‚tdtt	ƒt	ks<J ‚t
tdd„ ƒ t
tdd„ ƒ t
td	d„ ƒ t
td
d„ ƒ tdddƒtju sŒJ ‚ttdddddtƒs¨J ‚t
tdd„ ƒ tttdƒt	tƒttt	tƒksÚJ ‚tttdƒt	tƒtt t	tƒks J ‚tttdƒt	tƒtt t	tƒks&J ‚tttdƒt	tƒttt	tƒksJJ ‚tttjtƒt	tƒttt	tƒkspJ ‚tttjtƒt	tƒtt t	tƒks˜J ‚tttjtƒt	tƒtt t	tƒksÀJ ‚tttjtƒt	tƒttt	tƒksæJ ‚tttdƒt	tƒtksJ ‚tttdƒt	tƒtksJ ‚tttdƒt	tƒt	ks:J ‚tttdƒt	tƒt	ksVJ ‚tttdƒt	tƒ td¡t	kszJ ‚tttdƒt	tƒ td¡tksžJ ‚t
tdd„ ƒ d S )NzA:CTFrN   r   c                   S   s   t dttƒS rO   ©r   rk   rl   rK   rK   rK   rL   rR   Ÿ  rS   ztest_ITE.<locals>.<lambda>c                   S   s   t dg tƒS r˜   ©r   rl   rK   rK   rK   rL   rR      rS   c                   S   s   t ddtƒS )NrN   rK   rÔ   rK   rK   rK   rL   rR   ¡  rS   c                   S   s   t dtg ƒS r˜   rÔ   rK   rK   rK   rL   rR   ¢  rS   r«   c                   S   s   t tdkttƒS r˜   rÓ   rK   rK   rK   rL   rR   ¦  rS   c                   S   s   t tdktttƒS r˜   )r   rk   rl   rr   rK   rK   rK   rL   rR   ¸  rS   )r
   r   r.   r-   rg   r   r   rk   r   rl   rB   rX   r   r   r   rr   r£   r{   r§   rK   rK   rL   Útest_ITEŒ  sN     $&&$&((&$$rÕ   c                   C   sè   t dƒdu sJ ‚t dƒdu s J ‚t tƒdu s0J ‚t t ƒdu sBJ ‚t tttƒƒdu sXJ ‚t t t¡ƒdu snJ ‚t tt t¡ƒƒdu sˆJ ‚t tttƒƒdu sžJ ‚t tt t¡t t¡ƒƒdu sÀJ ‚t tdk ƒsÐJ ‚t tt	 dk ƒräJ ‚d S )NTFr   )
r0   rH   r   rI   r   Úzeror   r   rk   rl   rK   rK   rK   rL   Útest_is_literal»  s    "r×   c                   C   sò  dt @ t d@   krt ks"n J ‚dt @ t d@   kr>dksDn J ‚t t@ tt tƒksZJ ‚dt B t dB   krvdks|n J ‚dt B t dB   kr˜t ksžn J ‚t tB tt tƒks´J ‚t  tt ƒksÆJ ‚dt ? t d>   krât ksèn J ‚dt ? t d>   krdksn J ‚t d? dt >   kr.dks4n J ‚t d? dt >   krVt  ks\n J ‚t t? tt >   kr‚tt tƒksˆn J ‚dt A t dA   krªt  ks°n J ‚dt A t dA   krÐt ksÖn J ‚t tA tt tƒksîJ ‚d S rv   )rH   rI   r   r   r   r   r   rK   rK   rK   rL   Útest_operatorsÉ  s    """""&&(,(&rØ   c                  C   s  t tj u sJ ‚ttju sJ ‚t dus(J ‚tdus4J ‚t s<J ‚trDJ ‚t dksPJ ‚tdks\J ‚t dkrhJ ‚tdkrtJ ‚t tkr€J ‚tt ƒtdƒks”J ‚ttƒtdƒks¨J ‚tt dhƒttdhƒ  krÌdksÒn J ‚tt tƒsàJ ‚tttƒsîJ ‚tt tƒrüJ ‚tttƒrJ ‚tt ƒtu sJ ‚tdƒtu s0J ‚ttƒt u sBJ ‚tdƒt u sTJ ‚t  tu sdJ ‚t t u stJ ‚t	dt fdtfƒD ]f\} }t
| |ƒtu s¤J ‚t
|| ƒtu s¸J ‚t
||ƒtu sÌJ ‚t
| | ƒt u sàJ ‚t
| tƒtksôJ ‚t
|tƒtu sJ ‚| du r|du s@| |@ tu s.J ‚|| @ tu s@J ‚|dur\||@ tu s\J ‚| durx| | @ t u sxJ ‚t| |ƒt u sŒJ ‚t|| ƒt u s J ‚t||ƒtu s´J ‚t| | ƒt u sÈJ ‚t| tƒt u sÜJ ‚t|tƒtksðJ ‚| du r|du s(| |B t u sJ ‚|| B t u s(J ‚|durD||B tu sDJ ‚| dur`| | B t u s`J ‚t| |ƒt u stJ ‚t|| ƒt u sˆJ ‚t||ƒtu sœJ ‚t| | ƒtu s°J ‚t| tƒt ksÆJ ‚t|tƒtksÚJ ‚| du rî|du s| |A t u s J ‚|| A t u sJ ‚|dur.||A tu s.J ‚| durJ| | A tu sJJ ‚t| |ƒt u s^J ‚t|| ƒt u srJ ‚t||ƒt u s†J ‚t| | ƒtu sšJ ‚t| tƒt ks°J ‚t|tƒt u sÄJ ‚t| |ƒtu sØJ ‚t|| ƒtu sìJ ‚t||ƒt u s J ‚t| | ƒtu sJ ‚t| tƒtu s(J ‚t|tƒt ks>J ‚t| |ƒtu sRJ ‚t|| ƒt u sfJ ‚t||ƒt u szJ ‚t| | ƒt u sŽJ ‚t| tƒtks¢J ‚t|tƒt u s¶J ‚tt| ƒt u sÊJ ‚tt|ƒt ksàJ ‚| du rô|du s<| |? tu sJ ‚|| > tu sJ ‚|| ? t u s*J ‚| |> t u s<J ‚|durj||? t u sXJ ‚||> t u sjJ ‚| dur˜| | ? t u s†J ‚| | > t u s˜J ‚t| |ƒtu s¬J ‚t|| ƒtu sÀJ ‚t||ƒt u sÔJ ‚t| | ƒt u sèJ ‚t| tƒtksüJ ‚t|tƒt ksJ ‚tt| ƒtks&J ‚tt|ƒt ks<J ‚t| | | ƒt u sRJ ‚t| | |ƒt u shJ ‚t| || ƒtu s~J ‚t| ||ƒtu s”J ‚t|| | ƒt u sªJ ‚t|| |ƒtu sÀJ ‚t||| ƒt u sÖJ ‚t|||ƒtu s†J ‚q†tdd„ tj tjfD ƒƒsJ ‚d S )NTFrN   c                 s   s   | ]}|  d d¡|u V  qdS )rN   rP   Nr   rT   rK   rK   rL   rÉ   _  rS   z"test_true_false.<locals>.<genexpr>)r-   r   r.   ÚhashÚlenrg   r/   Úboolr   rG   r   rk   r   r   r   r   r   r   r   Úall)ÚTÚFrK   rK   rL   Útest_true_falseÜ  sà    *







rß   c                   C   s°  t tdkdtdkƒ ¡ tdtƒks&J ‚ttdktdkƒ ¡ tddƒksJJ ‚ttdktdkƒ ¡ tt dƒtdtƒ kszJ ‚ttdkƒ ¡ tt dƒksšJ ‚tttdktdk ƒƒ ¡ t	tt dƒtdtƒƒksÐJ ‚t
 ¡ tjksâJ ‚t ¡ tju sôJ ‚t ¡ tjksJ ‚tttdk tdkƒtdk ƒ ¡ t t d¡ks<J ‚ttdk ttƒdk ƒ ¡ tdk  ¡ kshJ ‚ttdd„ ƒ td	tdt ƒd tdt ƒd  ƒ ¡ tju s¬J ‚d S )
Nr   FrN   rP   éþÿÿÿr   c                   S   s   t tƒdk  ¡ S r˜   )r   rk   Úas_setrK   rK   rK   rL   rR   o  rS   z"test_bool_as_set.<locals>.<lambda>r™   )r   rl   rá   r   r   r   rk   r   r   r   r-   r   ZUniversalSetr.   ZEmptySetÚopenr   rB   r   r   r   rK   rK   rK   rL   Útest_bool_as_setb  s    &$0 ÿ4,rã   c                  C   s„   t dƒ\} }t| dk|dkƒ ¡ tdtƒtdtƒ ks:J ‚t| dk|dkƒ ¡ tjtj tt dddƒtt dddƒ  ks€J ‚d S )NrÍ   r   T)r
   r   rá   r   r   r   r   ZRealsrÎ   rK   rK   rL   Útest_multivariate_bool_as_sett  s
    .ÿrä   c                  C   s–   t ddd} | t k| tkf}t|Ž }|jtu rTt|jƒt|ƒ| tj¡ ks`J ‚n|dks`J ‚t	|Ž }|jt	u r†t|jƒdks’J ‚n|dks’J ‚d S )Nrk   T)Zextended_realrP   )
r
   r   r   ÚfuncrÚ   ÚargsÚcountr   r-   r   )rk   ræ   ÚvrK   rK   rL   Útest_all_or_nothing}  s    
$
ré   c                   C   s    t jt ksJ ‚tjtksJ ‚d S rj   )r-   rY   r.   rK   rK   rK   rL   Útest_canonical_atomsŒ  s    rê   c                   C   s    t jtksJ ‚tjt ksJ ‚d S rj   )r-   Znegatedr.   rK   rK   rK   rL   Útest_negated_atoms‘  s    rë   c                   C   sŠ   t tdkttk ƒ ¡ tdtddks(J ‚t tdkttk ƒ ¡ tdtƒksLJ ‚ttk  ¡ tt tƒkshJ ‚tt k ¡ tt tƒks†J ‚d S )NrP   T)Z	left_openrN   )r   rk   r   rá   r   rK   rK   rK   rL   Útest_issue_8777–  s    ($rì   c                   C   sJ   t tt tk tdkƒtdtkttk ƒƒ ¡ tt dƒtdtƒ ksFJ ‚d S )Nrà   rP   )r   r   r   rk   rá   r   rK   rK   rK   rL   Útest_issue_8975  s    *ÿrí   c                   C   s(   t g d¢ƒdksJ ‚t dƒdks$J ‚d S )N)rN   r   rN   r   r   rN   r   éR   Z0010101000111001i9*  )r1   rK   rK   rK   rL   Útest_term_to_integer¢  s    rï   c                  C   s  t dƒ\} }}}| |@ |@ | |@ B }| | |@ |¡||@ |B ksDJ ‚| | |@ |@ |¡| |@ |B kshJ ‚| |B |B | |B @ }| | |B |¡||B |@ ksœJ ‚| | |B |B |¡| |B |@ ksÀJ ‚| |A |A | |A @ }| | |A |¡||A |@ ksôJ ‚| | |A |A |¡| |A |@ ksJ ‚d S )Nza b c d)r
   r£   )rZ   r[   r\   r›   rœ   rK   rK   rL   Útest_issue_21971§  s     $ $ rð   c                   C   sÀ   t ttttƒttgddƒg d¢ks(J ‚t tttB ttgddƒg d¢ksNJ ‚t ttt? ttgddƒg d¢kstJ ‚t ttttƒttgƒƒddgdfddgdfddgdfddgdfgks¼J ‚d S )	NF)Úinput)FFFT)FTTT)TTFTr   rN   T)Úlistr2   r   rk   rl   rK   rK   rK   rL   Útest_truth_table¶  s    ÿÿÿ*ÿró   c                     s  t jt jfD ]ð‰tt‡fdd„ƒ tt‡fdd„ƒ tt‡fdd„ƒ tt‡fdd„ƒ t jt jtfD ]”‰ tdƒD ]†} tt‡ ‡fdd„ƒ tt‡ ‡fdd„ƒ tt‡ ‡fd	d„ƒ tt‡ ‡fd
d„ƒ tt‡ ‡fdd„ƒ tt‡ ‡fdd„ƒ ˆˆ  ‰ ‰qrqfqd S )Nc                      s   ˆ 
 S rj   rK   rK   ©rÀ   rK   rL   rR   Ã  rS   z!test_issue_8571.<locals>.<lambda>c                      s   ˆ  S rj   rK   rK   rô   rK   rL   rR   Ä  rS   c                      s   t ˆ ƒS rj   )ÚabsrK   rô   rK   rL   rR   Å  rS   c                      s   t ˆ ƒS rj   )ÚintrK   rô   rK   rL   rR   Ç  rS   rP   c                      s   ˆ ˆ S rj   rK   rK   ©ÚorÀ   rK   rL   rR   Ë  rS   c                      s   ˆ ˆ S rj   rK   rK   r÷   rK   rL   rR   Ì  rS   c                      s   ˆ ˆ S rj   rK   rK   r÷   rK   rL   rR   Í  rS   c                      s   ˆ ˆ S rj   rK   rK   r÷   rK   rL   rR   Î  rS   c                      s   ˆ ˆ S rj   rK   rK   r÷   rK   rL   rR   Ï  rS   c                      s   ˆ ˆ S rj   rK   rK   r÷   rK   rL   rR   Ð  rS   )	r   r-   r.   rB   rX   ZZeror|   rk   Úrange)Ú_rK   r÷   rL   Útest_issue_8571Á  s    rû   c                  C   s‚   t ddd} t ddd\}}| ||  | d   ||  | d   dk }|tjusVJ ‚| ¡ tju shJ ‚|dk ¡ tju s~J ‚d S )NÚnT)Únegativezp q)ÚpositiverN   r   )r
   r   r.   Úexpandr-   )rü   ÚpÚqÚrrK   rK   rL   Útest_expand_relationalÔ  s    ,r  c                   C   s$   t jjdksJ ‚t jjdks J ‚d S )NT)r   r-   Zis_Atomr.   rK   rK   rK   rL   Útest_issue_12717Ý  s    r  c                     s¦   t ddd} tdd„ dtjd| fD ƒƒs,J ‚t ddd}td	d„ d
tjd|fD ƒƒsXJ ‚tdd„ ttdk fD ƒƒsvJ ‚dtdƒtd g fD ]‰ tt‡ fdd„ƒ qŠd S )NÚnzT)Znonzeroc                 s   s   | ]}t |ƒtju V  qd S rj   )r3   r   r-   rT   rK   rK   rL   rÉ   ä  rS   z"test_as_Boolean.<locals>.<genexpr>rN   rr   )rÖ   c                 s   s   | ]}t |ƒtju V  qd S rj   )r3   r   r.   rT   rK   rK   rL   rÉ   æ  rS   Fr   c                 s   s   | ]}t |ƒ|kV  qd S rj   ©r3   rT   rK   rK   rL   rÉ   ç  rS   rP   c                      s   t ˆ ƒS rj   r  rK   ©rV   rK   rL   rR   é  rS   z!test_as_Boolean.<locals>.<lambda>)r
   rÜ   r   r-   r.   rk   rB   rX   )r  rr   rK   r  rL   Útest_as_Booleanâ  s      r  c                  C   sD  t tdk ttƒjtthksJ ‚ttfD ]F} | tdƒjtƒ ks@J ‚| tdƒjthksVJ ‚| tdƒjthks&J ‚q&tj	jtƒ ks€J ‚tj
jtƒ ks’J ‚tjthks¢J ‚ttttdƒttdƒƒjtthksÈJ ‚t t¡jtƒ ksÞJ ‚t td¡jtƒ ksöJ ‚t t¡jthksJ ‚t td¡jthks(J ‚t t¡jtƒ ks@J ‚d S )NrN   TF)r   rk   rl   rr   Zbinary_symbolsr   r   Úsetr   r-   r.   r   r   ÚprimeÚltZis_truer¼   )rœ   rK   rK   rL   Útest_binary_symbolsì  s    &r  c                   C   s,   t ttƒ t¡tdttdƒfdƒks(J ‚d S )Nr   F)rN   T)r   rk   rl   Údiffr   r   rK   rK   rK   rL   Útest_BooleanFunction_diffý  s    r  c                  C   s  t dƒ\} }}}}}}}||@ |@ | @ ||@ | @ | @ B ||@ | @ | @ B ||@ | @ | @ B ||@ | @ | @ B ||@ | @ | @ B ||@ | @ | @ B ||@ | @ | @ B ||@ |@ | @ B ||@ | @ | @ B ||@ |@ | @ | @ B ||@ |@ | @ | @ B ||@ |  @ | @ | @ B ||@ |  @ | @ | @ B | |@ |@ |@ | @ | @ B }||@ |@ | @ ||@ |@ | @ B ||@ | @ | @ B ||@ | @ | @ B ||@ | @ | @ B ||@ | @ | @ B ||@ | @ | @ B ||@ | @ | @ B ||@ |@ | @ | @ B ||@ |  @ | @ | @ B | |@ |@ |@ | @ | @ B }	||B |B ||B |B @ ||B |B @ ||B |B @ ||B |B @ ||B |B @ ||B | B | B @ | | B | B | B @ || B | B | B | B @ | |B | B | B | B | B @ || B | B | B | B | B @ ||B |B |  B | B | B | B @ }
t|dƒ|	ksPJ ‚t|dƒ|
ksdJ ‚g d¢g d¢g d¢g d¢g d¢g d	¢g}g d
¢g d¢g d¢g d¢g}tttttg|ƒtt @ tt@ t @ B ksØJ ‚tttttg||ƒtt @ tt@ t @ B ks
J ‚d S )NzA B C D E F G HZdnfZcnf)r   rN   r   r   rŽ   )r   rN   rN   r   r‹   rŠ   rŒ   ©rN   r   r   r   ©rN   r   r   rN   )rN   rN   r   r   ©rN   rN   r   rN   )r
   r'   r   rs   rk   rl   rr   )rH   rI   rJ   rh   ÚErÞ   ÚGÚHr  ZsoldnfZsolcnfr•   rš   rK   rK   rL   Útest_issue_14700  sŒ    8ÿÿÿþþþýýýüüû6ÿÿÿþþþýý.
ÿ
ÿÿþþý ý"üÿ0ÿr  c                  C   s"  t ddd\} }}}t ddd\}}t||k||k ƒ ¡ tjksDJ ‚t||k||kƒ ¡ tjksdJ ‚t||k| | kƒ ¡ tjksˆJ ‚t||k| | k ƒ ¡ tjks¬J ‚t| | k||k ƒ ¡ tjksÐJ ‚t| | k| | kƒ ¡ tjksøJ ‚t| | k||kƒ ¡ tjksJ ‚t| | k| | k ƒ ¡ tjksHJ ‚t||k||k ƒ ¡ tjksjJ ‚t||k||kƒ ¡ tjksŒJ ‚t||k| | kƒ ¡ tjks²J ‚t||k| | k ƒ ¡ tjksØJ ‚t| | k||k ƒ ¡ tjksþJ ‚t| | k||kƒ ¡ tjks$J ‚t| | k| | kƒ ¡ tjksNJ ‚t| | k| | k ƒ ¡ tjksxJ ‚t||k ||kƒ ¡ tjksšJ ‚t||k||kƒ ¡ tjks¼J ‚t| | k||kƒ ¡ tjksâJ ‚t| | k ||kƒ ¡ tjksJ ‚t||k | | kƒ ¡ tjks.J ‚t| | k| | kƒ ¡ tjksXJ ‚t||k| | kƒ ¡ tjks~J ‚t| | k | | kƒ ¡ tjks¨J ‚t||k ||kƒ ¡ tjksÊJ ‚t||k||kƒ ¡ tjksìJ ‚t| | k||kƒ ¡ tjksJ ‚t| | k ||kƒ ¡ tjks8J ‚t||k | | kƒ ¡ tjks^J ‚t||k| | kƒ ¡ tjks„J ‚t| | k| | kƒ ¡ tjks®J ‚t| | k | | kƒ ¡ tjksØJ ‚t||k| |k ||kƒ ¡ tjks J ‚t||k||k ƒ ¡ tjks"J ‚t||kt||ƒƒ ¡ ||kksHJ ‚t||kt||ƒƒ ¡ t||ƒkspJ ‚tt||ƒ|dkd|k |dk||k ƒ ¡ t||ƒ|dk@ |dk@ ||k@ ksÂJ ‚tt||ƒ||k| |k ||k ƒ ¡ ||k||kB | |k B ksJ ‚tt||ƒ||k| |k ||k||k ƒ ¡ t||ƒ||k@ | |k @ ksNJ ‚tt||ƒ|dkd|k |dk||k ƒ ¡ t||ƒ|dk@ |dk@ ||k@ ks J ‚t||ƒt||ƒ@ ||k@ ||k@  ¡ t||ƒt||ƒ@ ||k@ ksêJ ‚tt||ƒt|| ƒƒ ¡ tt|d	ƒt|d	ƒƒks"J ‚t||k||kƒ ¡ t	||ƒksHJ ‚t|dk|d
k t||ƒƒ ¡ tjksrJ ‚t||kt|d	ƒƒ ¡ t|d	kt|d	ƒƒks¤J ‚tt	|dƒt	|dƒƒ ¡ tjksÊJ ‚tt|dƒt	d|ƒƒ ¡ t|dƒksôJ ‚tt|dƒt	d|ƒƒ ¡ t	|dƒksJ ‚d S )Núw x y zT©Úrealúd eFrN   rP   r“   r   r™   )
r
   r   r   r   r-   r   r.   r   r   r   )rs   rk   rl   rr   r›   r^   rK   rK   rL   Útest_relational_simplification  sx      $$$(&*""&&&&**""&&&*&*""&&&&**("&(( ÿ
"ÿ
(ÿ
( ÿ
&ÿ
8&*2&*r  c                  C   s   t ddd} t| dk | dkƒ ¡ tjks,J ‚t| dk | dkƒ ¡ tjksLJ ‚t| dk | dkƒ ¡ tjkslJ ‚t| dk| dkƒ ¡ tjksŒJ ‚d S )Nrk   Tr  rN   r™   )r
   r   r   r   r-   r   r.   ©rk   rK   rK   rL   Útest_issue_8373`  s
       r  c                  C   s4   t ddd} tt| dƒt| dƒƒ ¡ tjks0J ‚d S )Nrk   Tr  rN   rP   )r
   r   r   r   r   r.   r  rK   rK   rL   Útest_issue_7950h  s    r  c            	      C   s>  dd„ } t ddd\}}}}t ddd\}}tt||ƒ||k||k ||k||k ƒtt||ƒ|dkd	|k |d
k||k ƒtt||ƒ|dkd	|k |d
k||k ƒt||kt||ƒƒttt||ƒ||k||k t||k||k ƒƒtt||ƒ|dkd	|k |dk||k ƒƒt||ƒt||ƒ@ ||k@ ||k@ f}|D ]}| || ¡ ƒ q$d S )Nc           	      S   s~   | j }t|ƒ}ttttt|d  |ƒƒ| |ƒƒƒ}|D ]@}tt||ƒƒ}|  |¡}| |¡}||ks8J d 	| ||¡ƒ‚q8d S )NrN   zHOriginal: {}
and simplified: {}
do not evaluate to the same value for {})
Zfree_symbolsrÚ   rò   r	  rE   rù   Údictr¾   r£   Úformat)	ÚoriginalÚ
simplifiedÚsymbrü   Ú	valuelistÚvaluesÚsublistÚoriginalvalueÚsimplifiedvaluerK   rK   rL   Ú(test_simplification_numerically_functiono  s    &

þz\test_relational_simplification_numerically.<locals>.test_simplification_numerically_functionr  Tr  r  FrN   rP   r“   r™   )r
   r   r   r   r   )	r(  rs   rk   rl   rr   r›   r^   ZexpressionsZ
expressionrK   rK   rL   Ú*test_relational_simplification_numericallym  s     $$$*$ÿ"ú	ÿr)  c               	   C   s  ddl m}  ddlm}m}m} | dƒ}| dƒ}| dƒ}|||g}t|ƒ gt|ƒ gt|ƒ gg}t	t
tt	tddƒƒd dƒƒƒ}	d	d
„ |	D ƒ}	|D ]r\}
}|D ]d}|
|d jŽ }|d }|	D ]D}tt||ƒƒ}| |¡}| |¡}||ksºJ d |d ||¡ƒ‚qºqœqd S )Nr   ©ÚWild)Ú_simplify_patterns_andÚ_simplify_patterns_orÚ_simplify_patterns_xorrZ   r[   r\   rà   r   c                 S   s*   g | ]"}t d d„ |D ƒƒs"t |ƒs|‘qS )c                 S   s   g | ]}|d  ‘qS ©rP   rK   ©rU   rs   rK   rK   rL   Ú
<listcomp>™  rS   zRtest_relational_simplification_patterns_numerically.<locals>.<listcomp>.<listcomp>©Úany©rU   rè   rK   rK   rL   r1  ™  rS   zGtest_relational_simplification_patterns_numerically.<locals>.<listcomp>rN   úGOriginal: {}
and simplified: {}
do not evaluate to the same value for{})Ú
sympy.corer+  Úsympy.logic.boolalgr,  r-  r.  r   r   r   rò   r	  rE   rù   ræ   r  r¾   Úxreplacer  )r+  r,  r-  r.  rZ   r[   r\   r"  Úpatternlistsr#  rå   ÚpatternlistÚpatternr   r!  r$  r%  r&  r'  rK   rK   rL   Ú3test_relational_simplification_patterns_numericallyŒ  s.    
þ 


þr<  c                  C   sT   t dƒ} | dk| dk B | dk| dk @ B  ¡ | dk| dk B | dk| dk @ B ksPJ ‚d S )Nrü   r   r   )r
   r   )rü   rK   rK   rL   Útest_issue_16803§  s    "ÿr=  c                      sŽ   t ttti‰ tt t dkt t dk ƒ ˆ ¡s0J ‚tt t dk t t dk ƒ ˆ ¡rTJ ‚tt‡ fdd„ƒ tt‡ fdd„ƒ tt‡ fdd„ƒ d S )Nr   c                      s    t tt dk tt dk ƒ ˆ ¡S ©Nr   )r   rk   rl   r£   rK   ©r  rK   rL   rR   ²  rS   z"test_issue_17530.<locals>.<lambda>c                      s    t tt dktt dk ƒ ˆ ¡S r>  ©r   rk   rl   r£   rK   r?  rK   rL   rR   ³  rS   c                      s    t tt dktt dk ƒ ˆ ¡S r>  r@  rK   r?  rK   rL   rR   ´  rS   )rk   r   rl   r   r£   r   rB   rX   rK   rK   r?  rL   Útest_issue_17530®  s    $$rA  c                   C   s¬   t ddgƒddgksJ ‚t g d¢ƒg d¢ks0J ‚t g d¢ƒg d¢ksHJ ‚t g d¢ƒg d¢ks`J ‚t g d¢ƒg d¢ksxJ ‚t g d¢ƒg d¢ksJ ‚t g d	¢ƒg d
¢ks¨J ‚d S )NrN   r   r‰   r‹   ©rN   rN   rN   r   r  r  r   r  rŒ   )r7   rK   rK   rK   rL   Útest_anf_coeffs·  s    rC  c                  C   sŒ   t dƒ\} }t| gddgƒdks$J ‚t| gddgƒdks<J ‚t| gddgƒt| dddks^J ‚t| |gg d¢ƒtdt| |ƒddksˆJ ‚d S )NrÍ   rN   Tr   Fr²   rB  )r
   r8   r   r   rÎ   rK   rK   rL   Útest_ANFformÁ  s    "ÿrD  c                  C   sP   t dƒ\} }td| |gƒt| |ƒks(J ‚tddg| |gƒtt|ƒ| ƒksLJ ‚d S )NrÍ   r   rN   r   )r
   r9   r   r   rÎ   rK   rK   rL   Útest_bool_mintermÊ  s    rE  c                  C   sT   t dƒ\} }td| |gƒtt| ƒ|ƒks,J ‚tddg| |gƒtt|ƒ| ƒksPJ ‚d S )NrÍ   rP   r   rN   )r
   r:   r   r   rÎ   rK   rK   rL   Útest_bool_maxtermÐ  s     rF  c                  C   sF   t dƒ\} }td| |gƒ|ks"J ‚tddg| |gƒt| |ƒksBJ ‚d S )NrÍ   rN   )r
   r;   r   rÎ   rK   rK   rL   Útest_bool_monomialÖ  s    rG  c                   C   s8   t g d¢g d¢ƒdksJ ‚t g d¢g d¢ƒdks4J ‚d S )Nr†   r„   rP   rˆ   r™   )r<   rK   rK   rK   rL   Útest_check_pairÜ  s    rH  c                  C   s\   t t@ tt @ B t t  @ B } tt @ tt @ B t  t @ B }t| dd}|| |fv sXJ ‚d S r¹   )rI   rJ   rH   r*   )ro   Zres1ÚresultrK   rK   rL   Útest_issue_19114á  s    rJ  c                  C   sl   t ttttgg d¢ƒ} tt @ tt@ t@ B tt @ t @ B tt @ t @ B tt @ t @ B }| |kshJ ‚d S )N)rN   rP   r   rÃ   r“   é   é   é	   r‘   é   é   r’   )r   rZ   r[   r\   r›   )rI  ÚexpectedrK   rK   rL   Útest_issue_20870é  s    $ÿÿrQ  c                   C   sV   t g d¢tttgƒtttƒtttƒƒks,J ‚t g d¢tttgƒttttƒƒksRJ ‚d S ©Nr†   )r   rN   r   )r=   rk   rl   rr   r   r   rK   rK   rK   rL   Útest_convert_to_varsSOPð  s    ,rS  c                   C   sR   t g d¢tttgƒttttƒtƒks(J ‚t g d¢tttgƒtttƒtƒksNJ ‚d S rR  )r>   rk   rl   rr   r   r   rK   rK   rK   rL   Útest_convert_to_varsPOSõ  s    (rT  c                     sz   t dƒ\‰ ‰} }}ttˆ ˆƒƒdks(J ‚tˆ ˆ| @ |@ |ˆ B A B ƒdksLJ ‚ttˆ dƒƒdksbJ ‚tt‡ ‡fdd„ƒ d S )Nza:erP   rM  Tr   c                      s   t ˆ ˆ ƒS rj   )r@   rK   ©rZ   r[   rK   rL   rR   ÿ  rS   z%test_gateinputcount.<locals>.<lambda>)r
   r@   r   rB   rX   )r\   r›   r^   rK   rU  rL   Útest_gateinputcountú  s
    $rV  c                   C   sx  t tdk tdk  ƒrJ ‚t tdk tdk ƒs.J ‚t tdk dtkƒtju sJJ ‚t tdk tdk ƒtdk kshJ ‚t tdktdk ƒr€J ‚t tdktdkƒs–J ‚t tdkdtkƒtju s²J ‚t tdktdkƒtdkksÐJ ‚t tdktdk ƒrèJ ‚t tdktdkƒsþJ ‚t tdkdtk ƒtju sJ ‚t tdktdkƒtdkks<J ‚t tdktdk ƒrVJ ‚t tdktdkƒsnJ ‚t tdkdtkƒtju sŒJ ‚t tdktdkƒtdkks¬J ‚t ttdƒttdƒ ƒrÊJ ‚t ttdƒttdƒƒsæJ ‚t ttdƒtdtƒƒtju sJ ‚t ttdƒttdƒƒttdƒks.J ‚t ttdƒttdƒ ƒrLJ ‚t ttdƒtdtƒƒtju snJ ‚t ttdƒttdƒƒsŠJ ‚t ttdƒttdƒƒttdƒks°J ‚t ttdktdkƒtdkƒtdkksÚJ ‚t ttdktdkƒtdktdk@ ƒtju s
J ‚t t 	t¡t 	t¡ƒtju s,J ‚t t 	t¡t 
t¡ƒtju sNJ ‚t t 	t¡t t¡ƒt 	t¡kstJ ‚d S r>  )r   rk   r   r-   rl   r   r   r   r   rþ   rý   r.   r  rK   rK   rK   rL   Útest_refine  s:      "&"&*0""rW  c               	   C   sð   ddl m}  ddlm} | dƒ}| dƒ}| dƒ}|||g}t|ƒ gg}tttttddƒƒd dƒƒƒ}d	d
„ |D ƒ}|D ]r\}}	|	D ]d}
||
d j	Ž }|
d }|D ]D}t
t||ƒƒ}| |¡}| |¡}||ks¢J d |
d ||¡ƒ‚q¢q„qxd S )Nr   r*  )Ú_simplify_patterns_and3rZ   r[   r\   rà   r   c                 S   s*   g | ]"}t d d„ |D ƒƒs"t |ƒs|‘qS )c                 S   s   g | ]}|d  ‘qS r/  rK   r0  rK   rK   rL   r1  1  rS   z\test_relational_threeterm_simplification_patterns_numerically.<locals>.<listcomp>.<listcomp>r2  r4  rK   rK   rL   r1  1  rS   zQtest_relational_threeterm_simplification_patterns_numerically.<locals>.<listcomp>rN   r5  )r6  r+  r7  rX  r   rò   r	  rE   rù   ræ   r  r¾   r8  r  )r+  rX  rZ   r[   r\   r"  r9  r#  rå   r:  r;  r   r!  r$  r%  r&  r'  rK   rK   rL   Ú=test_relational_threeterm_simplification_patterns_numerically'  s(    
 


þrY  N)²Zsympy.assumptions.askr   Zsympy.assumptions.refiner   Zsympy.core.numbersr   Zsympy.core.relationalr   r   r   Zsympy.core.singletonr   Zsympy.core.symbolr	   r
   Zsympy.functionsr   Z(sympy.functions.elementary.trigonometricr   r   Zsympy.sets.setsr   r   Zsympy.simplify.simplifyr   r7  r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   Zsympy.assumptions.cnfrA   Zsympy.testing.pytestrB   rC   rD   Ú	itertoolsrE   rF   rG   rH   rI   rJ   rh   rZ   r[   r\   r›   r^   rs   rk   rl   rr   rM   rc   re   ri   rp   rq   rt   ru   rw   rx   ry   rz   r}   r~   r   r‚   rŸ   r    r¡   r¢   r¤   r¦   r¨   r©   rª   r­   r®   r¯   r°   rµ   r¶   r¸   rÁ   rÄ   rÅ   rÆ   rÌ   rÏ   rÐ   rÑ   rÒ   rÕ   r×   rØ   rß   rã   rä   ré   rê   rë   rì   rí   rï   rð   ró   rû   r  r  r  r  r  r  r  r  r  r)  r<  r=  rA  rC  rD  rE  rF  rG  rH  rJ  rQ  rS  rT  rV  rW  rY  rK   rK   rK   rL   Ú<module>   sÈ   Ä		u			/ 
	
B
	
	%