ืื ื’ืœื™ืชืฆืจืคืชื™ืชืกืคืจื“ื™

ืกืžืœ OnWorks

FLOTTER - ืžืงื•ื•ืŸ ื‘ืขื ืŸ

ื”ืคืขืœ ืืช FLOTTER ื‘ืกืคืง ืื™ืจื•ื— ื—ื™ื ืžื™ ืฉืœ OnWorks ืขืœ ืื•ื‘ื•ื ื˜ื• ืื•ื ืœื™ื™ืŸ, ืคื“ื•ืจื” ืื•ื ืœื™ื™ืŸ, ืืžื•ืœื˜ื•ืจ ืžืงื•ื•ืŸ ืฉืœ Windows ืื• ืืžื•ืœื˜ื•ืจ ืžืงื•ื•ืŸ ืฉืœ MAC OS

ื–ื•ื”ื™ ื”ืคืงื•ื“ื” FLOTTER ืฉื ื™ืชืŸ ืœื”ืคืขื™ืœ ื‘ืกืคืง ื”ืื™ืจื•ื— ื”ื—ื™ื ืžื™ ืฉืœ OnWorks ื‘ืืžืฆืขื•ืช ืื—ืช ืžืชื—ื ื•ืช ื”ืขื‘ื•ื“ื” ื”ืžืงื•ื•ื ื•ืช ื”ืžืจื•ื‘ื•ืช ืฉืœื ื•, ื›ื’ื•ืŸ Ubuntu Online, Fedora Online, ืืžื•ืœื˜ื•ืจ ืžืงื•ื•ืŸ ืฉืœ Windows ืื• ืืžื•ืœื˜ื•ืจ ืžืงื•ื•ืŸ ืฉืœ MAC OS

ืชึธื›ึฐื ึดื™ืช:

ืฉืึตื


SPASS - ืžื•ื›ื™ื— ืžืฉืคื˜ ืื•ื˜ื•ืžื˜ื™ ืœืœื•ื’ื™ืงื” ืžืœืื” ืžืกื“ืจ ืจืืฉื•ืŸ ืขื ืฉื•ื•ื™ื•ืŸ

ืชึทืงืฆึดื™ืจ


SPASS [ืืคืฉืจื•ื™ื•ืช] [ืงื•ื‘ืฅ ืงืœื˜]

ืชื™ืื•ืจ


SPASS ื”ื•ื ืžื•ื›ื™ื— ืžืฉืคื˜ ืื•ื˜ื•ืžื˜ื™ ืœืœื•ื’ื™ืงื” ืžืžื•ื™ื ืช ืžืœืื” ืžืกื“ืจ ืจืืฉื•ืŸ ืขื ืฉื•ื•ื™ื•ืŸ ื–ื”
ืžืจื—ื™ื‘ ืืช ื”ืกื•ืคืจืคื•ื–ื™ืฆื™ื” ืœืคื™ ืžื™ื•ืŸ ื•ื›ืœืœ ืคื™ืฆื•ืœ ืœื ื™ืชื•ื— ืžืงืจื™ื. SPASS ื™ื›ื•ืœ ืœื”ื™ื•ืช ื’ื
ืžืฉืžืฉ ื›ืžื•ื›ื™ื— ืœื•ื’ื™ืงื” ืžื•ื“ืืœื™ืช ื•ืžืฉืคื˜ ืชื™ืื•ืจ.

ืืคืฉืจื•ื™ื•ืช


ืืคืฉืจื•ื™ื•ืช ืฉื•ืจืช ื”ืคืงื•ื“ื” ื‘-SPASS ืžื™ื•ืฉืžื•ืช ื‘ืืžืฆืขื•ืช ืฉื™ื ื•ื™ื™ื ื‘ืฉื•ืจืช ื”ืคืงื•ื“ื” ืฉืœ GNU
ื—ื‘ื™ืœืช ืื•ืคืฆื™ื•ืช ืขื‘ื•ืจ C. ืจืง ืžืชืŸ ื”ืื•ืคืฆื™ื” ืงื•ื‘ืข ืืช ื”ืขืจืš ืฉืœื” ืœ-1 ื•ืคื™ืจื•ืฉื• ื”ืคืขืœืช ื”
ืื•ึนืคึผึฐืฆึดื™ึธื”. ืขืœ ืžื ืช ืœื‘ื˜ืœ ืืคืฉืจื•ืช ื™ืฉ ืœื”ื’ื“ื™ืจ ืืช ื”ืขืจืš ืœ-0 ืขืœ ื™ื“ื™ ื”ืฆื”ืจืช -ืืคืฉืจื•ืช= 0.
ื”ืืคืฉืจื•ื™ื•ืช ื”ื‘ืื•ืช ื ืชืžื›ื•ืช ื›ืขืช ืขืœ ื™ื“ื™ SPASS:

-ืื•ื˜ื•ืžื˜ื™
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื”ืžืฆื‘ ื”ืื•ื˜ื•ืžื˜ื™ ืฉื‘ื• SPASS ืžื’ื“ื™ืจ ืืช ืขืฆืžื• ื‘ืื•ืคืŸ ืื•ื˜ื•ืžื˜ื™. ื”
ื›ืœืœื™ ืžืกืงื ื•ืช/ืฆืžืฆื•ื, ื˜ื›ื ื•ืœื•ื’ื™ื™ืช ื”ืžื™ื•ืŸ, ื”ืกื“ืจ ื•ื”ืงื“ื™ืžื•ืช ื•ื›ืŸ
ืืกื˜ืจื˜ื’ื™ื™ืช ื”ืคื™ืฆื•ืœ ื•ื”ื‘ื—ื™ืจื” ื ืงื‘ืขื•ืช. ื‘ืžืฆื‘ ืื•ื˜ื•ืžื˜ื™ SPASS ื”ื•ืฉืœื. ืขึดืจื‘ึผื•ึผื‘
ื”ืžืฆื‘ ื”ืื•ื˜ื•ืžื˜ื™ ืขื ืืคืฉืจื•ื™ื•ืช ืžื•ื’ื“ืจื•ืช ืขืœ ื™ื“ื™ ื”ืžืฉืชืžืฉ ืขืœื•ืœ ืœื”ืจื•ืก ืืช ื”ืฉืœืžื•ืช. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 1.

-Stdin
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืงืœื˜ ื‘-SPASS ื‘ืืžืฆืขื•ืช stdin. ืžืชืขืœืžื™ื ืžืืจื’ื•ืžื ื˜ ื”ืงื•ื‘ืฅ. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-ืื™ื ื˜ืจืืงื˜ื™ื‘ื™
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื”ืžืฆื‘ ื”ืื™ื ื˜ืจืืงื˜ื™ื‘ื™. ืจืืฉื™ืช, ืœ-SPASS ื ื™ืชืŸ ืงื‘ื•ืฆื” ืฉืœ ืืงืกื™ื•ืžื•ืช ื•ืœืื—ืจ ืžื›ืŸ
ื”ืžื•ื›ื™ื— ืžืงื‘ืœ ืžืฉื™ืžื•ืช ื”ื•ื›ื—ื” ืขื•ืงื‘ื•ืช. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-ืคืœื˜ืจ
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ืžืฆื‘ ื”ืชืจื’ื•ื CNF ืฉืœ SPASS. ืื ื”ืืคืฉืจื•ืช ืžื•ื’ื“ืจืช, SPASS ื‘ืœื‘ื“
ืžื‘ืฆืข ืชืจื’ื•ื ืฆื•ืจื” ืจื’ื™ืœื” ืฉืœ ืกืขื™ืฃ. ืื ืœื ื ื™ืชืŸ ืืจื’ื•ืžื ื˜ ืงื•ื‘ืฅ ืคืœื˜ SPASS
ืžื“ืคื™ืก ืืช ื”-CNF ืœ-stdout. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-ื”ึทืฆึดื™ืœื•ึผ
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ืžืขืจืš ืืกื˜ืจื˜ื’ื™ื™ืช ื”ืชืžื™ื›ื”. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-ืคื™ืฆื•ืœื™ื=n
ืžื’ื“ื™ืจ ืืช ืžืกืคืจ ื™ื™ืฉื•ืžื™ ื”ืคื™ืฆื•ืœ ื”ืืคืฉืจื™ื™ื ืœ n. ืื n=-1 ื•ืื– ื”ืžืกืคืจ ืฉืœ
ืคื™ืฆื•ืœื™ื ืื™ื ื ืžื•ื’ื‘ืœื™ื. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-ื–ื™ื›ืจื•ืŸ=n
ืžื’ื“ื™ืจ ืืช ื›ืžื•ืช ื”ื–ื™ื›ืจื•ืŸ ื”ื–ืžื™ื ื” ืœ-SPASS ืขื‘ื•ืจ ื—ื™ืคื•ืฉ ื”ื”ื’ื”ื” n ื‘ื™ื™ื˜ื™ื. ื”
ืœื ื ื™ืชืŸ ืœื”ื’ื‘ื™ืœ ืืช ื”ื–ื™ื›ืจื•ืŸ ื”ื“ืจื•ืฉ ืœื”ืคืขืœืช SPASS. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื -1 ื›ืœื•ืžืจ
ื”ืงืฆืื•ืช ื–ื™ื›ืจื•ืŸ ืžื•ื’ื‘ืœื•ืช ืจืง ืขืœ ื™ื“ื™ ื–ื™ื›ืจื•ืŸ ืคื ื•ื™.

-ืžื’ื‘ืœืช ื–ืžืŸ=n
ืžื’ื“ื™ืจ ืžื’ื‘ืœืช ื–ืžืŸ ืœื—ื™ืคื•ืฉ ื”ื”ื•ื›ื—ื” ืœ n ืฉื ื™ื•ืช. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื -1 ื›ืœื•ืžืจ SPASS
ืขืฉื•ื™ ืœืจื•ืฅ ืœื ืฆื—. ืžื’ื‘ืœืช ื”ื–ืžืŸ ื ื‘ื“ืงืช ื›ืืฉืจ SPASS ื‘ื•ื—ืจ ืกืขื™ืฃ ื—ื“ืฉ ืขื‘ื•ืจ
ืžืกืงื ื•ืช. ืื ืฉืœื‘ ืžืกืงื ื•ืช ื‘ื•ื“ื“ ื’ื•ืจื ืœืคื™ืฆื•ืฅ ืœืžืกืคืจ ืฉื ื•ืฆืจ
ืœืคื™ ืกืขื™ืคื™ื, ืขืœื•ืœ ืœืงืจื•ืช ืฉื—ืจื’ื” ืžืฉืžืขื•ืชื™ืช ืžืžื’ื‘ืœืช ื–ืžืŸ ื ืชื•ื ื”.

-DocSST
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืคืœื˜ ืชื™ืขื•ื“ ืขื‘ื•ืจ ื”ืงืœื“ื” ืจื›ื” ืกื˜ื˜ื™ืช. ืชื•ืจืช ื”ืžื™ื•ืŸ ื”ืžืฉื•ืžืฉืช ื›
ื›ืžื• ื›ืŸ ืžื•ื“ืคืก ื ื™ืกื™ื•ืŸ ื”ื”ื•ื›ื—ื” (ื”ื›ื•ืฉืœ) ืขื‘ื•ืจ ืื™ืœื•ืฅ ื”ืžื™ื•ืŸ. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-DocProof
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืชื™ืขื•ื“ ื”ื•ื›ื—ื”. ืื SPASS ืžื•ืฆื ื”ื•ื›ื—ื” ื”ื™ื ืžื•ื“ืคืกืช ื‘ืกื•ืคื• ืฉืœ ื“ื‘ืจ.
ืื SPASS ืžื•ืฆื ืจื•ื•ื™ื”, ื‘ืกื•ืคื• ืฉืœ ื“ื‘ืจ ืžื•ื“ืคืก ืงื‘ื•ืฆืช ื”ืกืขื™ืคื™ื ื”ืจื•ื•ื™ื”.
ื”ืคืขืœืช ืชื™ืขื•ื“ ื”ื•ื›ื—ื” ืขืฉื•ื™ื” ืœื”ืคื—ื™ืช ืžืฉืžืขื•ืชื™ืช ืืช ื”ื‘ื™ืฆื•ืขื™ื ืฉืœ SPASS, ืžื›ื™ื•ื•ืŸ
ื”ืžื•ื›ื™ื— ื—ื™ื™ื‘ ืœืื—ืกืŸ ืกืขื™ืคื™ื ืฉื ื™ืชืŸ ืœื–ืจื•ืง ืื—ืจืช. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-DocSplit
ืžื’ื“ื™ืจ ืืช ื”ืชื™ืขื•ื“ ืฉืœ ืฉืœื‘ื™ ืžืขืงื‘ ืœืื—ื•ืจ ืžืคื•ืฆืœื™ื. ืื ืžื•ื’ื“ืจ ืœ-1, ื”ื ื•ื›ื—ื™
ืจืžืช ื”ื—ื–ืจื” ืœืื—ื•ืจ ืžื•ื“ืคืกืช. ืื ืžื•ื’ื“ืจ ืœ-2, ื”ื•ื ืžื•ื“ืคืก ื’ื ื‘ืžืงืจื” ืฉืœ ืคื™ืฆื•ืœ
ื—ื–ื•ืจ ืœืื—ื•ืจ ื‘ืกืขื™ืฃ ืฉื—ื–ืจ ื‘ื•. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-ืœื•ืœืื•ืช
ืžื’ื“ื™ืจ ืืช ื”ืžืกืคืจ ื”ืžืจื‘ื™ ืฉืœ ืื™ื˜ืจืฆื™ื•ืช mainloop ืขื‘ื•ืจ SPASS. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื -1.

-PSub
ืžืืคืฉืจ/ืžืฉื‘ื™ืช ื”ื“ืคืกื” ืฉืœ ืกืขื™ืคื™ื ืžืฆื•ืžืฆืžื™ื. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-PRew
ืžืืคืฉืจ/ืžืฉื‘ื™ืช ื”ื“ืคืกื” ืฉืœ ื™ื™ืฉื•ืžื™ ืฉื›ืชื•ื‘ ืคืฉื•ื˜ื™ื. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-PCon
ืžืืคืฉืจ/ืžืฉื‘ื™ืช ื”ื“ืคืกื” ืฉืœ ื™ื™ืฉื•ืžื™ ืขื™ื‘ื•ื™. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-PTaut
ืžืืคืฉืจ/ืžืฉื‘ื™ืช ื”ื“ืคืกื” ืฉืœ ื™ื™ืฉื•ืžื™ ืžื—ื™ืงืช ื˜ืื•ื˜ื•ืœื•ื’ื™ื”. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-PObv
ืžืืคืฉืจ/ืžืฉื‘ื™ืช ื”ื“ืคืกื” ืฉืœ ื™ื™ืฉื•ืžื™ ืฆืžืฆื•ื ื‘ืจื•ืจื™ื. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-PSSi
ืžืืคืฉืจ/ืžืฉื‘ื™ืช ื”ื“ืคืกื” ืฉืœ ื™ื™ืฉื•ืžื™ ืคื™ืฉื•ื˜ ืžื™ื•ืŸ. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-PSST
ืžืืคืฉืจ/ืžืฉื‘ื™ืช ื”ื“ืคืกื” ืฉืœ ื™ื™ืฉื•ืžื™ ื”ืงืœื“ื” ืจื›ื” ืกื˜ื˜ื™ืช. ื›ืœ ื”ืกืขื™ืคื™ื ืฉื ืžื—ืงื• ื”ื
ืžื•ื“ืคืก. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-PMRR
ืžืืคืฉืจ/ืžืฉื‘ื™ืช ื”ื“ืคืกื” ืฉืœ ื™ื™ืฉื•ืžื™ ืจื–ื•ืœื•ืฆื™ื” ื—ืœื•ืคื™ืช ืชื•ืืžืช. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื
0.

-PUnC
ืžืืคืฉืจ/ืžืฉื‘ื™ืช ื”ื“ืคืกื” ืฉืœ ื™ื™ืฉื•ืžื™ื ืžืชื ื’ืฉื™ื ื‘ื™ื—ื™ื“ื”. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-PAED
ืžืืคืฉืจ/ืžืฉื‘ื™ืช ื”ื“ืคืกื” ืฉืœ ืกืขื™ืคื™ื ืฉื‘ื”ื ื”ื•ืกืจื• ืžืฉื•ื•ืื•ืช ืžื™ื•ืชืจื•ืช
(ืžื—ื™ืงืช ืžืฉื•ื•ืืช ื”ืงืฆืื”).

-PDer
ืžืืคืฉืจ/ืžืฉื‘ื™ืช ื”ื“ืคืกื” ืฉืœ ืกืขื™ืคื™ื ืฉื ื’ื–ืจื• ืขืœ ื™ื“ื™ ืžืกืงื ื•ืช. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-PGiven
ืžืืคืฉืจ/ืžืฉื‘ื™ืช ื”ื“ืคืกื” ืฉืœ ื”ืกืขื™ืฃ ื”ื ืชื•ืŸ, ืฉื ื‘ื—ืจ ืœื‘ื™ืฆื•ืข ื”ืกืงื•ืช.
ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-ืชื•ื•ื™ื•ืช PL
ืžืืคืฉืจ/ืžืฉื‘ื™ืช ื”ื“ืคืกื” ืฉืœ ืชื•ื•ื™ื•ืช. ืื -DocProof ืžื•ื’ื“ืจ ื•ืื™ืŸ ืชื•ื•ื™ื•ืช ืขื‘ื•ืจ
ื ื•ืกื—ืื•ืช ืžืกื•ืคืงื•ืช ืขืœ ื™ื“ื™ ื”ืงืœื˜, SPASS ืžื™ื™ืฆืจ ืชื•ื•ื™ื•ืช ื’ื ืจื™ื•ืช ืฉื”ืŸ ืื–
ืžื•ื“ืคืก ืขืœ ื™ื“ื™ ื”ืคืขืœืช ืืคืฉืจื•ืช ื–ื•. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-PKept
ืžืืคืฉืจ/ืžืฉื‘ื™ืช ื”ื“ืคืกื” ืฉืœ ืกืขื™ืคื™ื ืฉืžื•ืจื™ื. ืืœื” ื”ื ืกืขื™ืคื™ื ืฉื ื•ืฆืจื• ืขืœ ื™ื“ื™ ืžืกืงื ื•ืช
(ื—ื–ืจื” ืœืื—ื•ืจ) ืฉืื™ื ื ืžื™ื•ืชืจื™ื. ืกืขื™ืคื™ื ืฉื ื’ื–ืจื• ื‘ืžื”ืœืš ื”ืงืœื˜
ื”ืคื—ืชื”/ืจื•ื•ื™ื” ืื™ื ื ืžื•ื“ืคืกื™ื. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-P ื‘ืขื™ื”
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ื”ื“ืคืกื” ืฉืœ ืขืจื›ืช ืกืขื™ืคื™ ื”ืงืœื˜. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 1.

-PEmptyClause
ืžืืคืฉืจ/ืžืฉื‘ื™ืช ื”ื“ืคืกื” ืฉืœ ืกืขื™ืคื™ื ืจื™ืงื™ื ื ื’ื–ืจื™ื. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-PSื˜ื˜ื™ืกื˜ื™ืงื”
ืžืืคืฉืจ/ืžืฉื‘ื™ืช ื”ื“ืคืกื” ืฉืœ ืกื˜ื˜ื™ืกื˜ื™ืงื” ืกื•ืคื™ืช ืขืœ ืกืขื™ืคื™ื ื ื’ื–ืจื™ื/ื ืขื–ืจื™ื/ืฉืžื•ืจื™ื,
ื‘ื™ืฆืขื• ืคื™ืฆื•ืœื™ื, ื”ืฉืชืžืฉื• ื‘ื–ืžืŸ ื•ื”ืฉืชืžืฉื• ื‘ื—ืœืœ. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 1.

-FPModel
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื”ืคืœื˜ ืฉืœ ืžื•ื“ืœ ืฉื ืžืฆื ื‘ืกื•ืคื• ืฉืœ ื“ื‘ืจ ืœืงื•ื‘ืฅ. ืื ืžื•ื’ื“ืจ ืœ-1, ื”ื›ืœ
ืกืขื™ืคื™ื ื‘ืกื˜ ื”ืกื•ืคื™ ืžื•ื“ืคืกื™ื. ืื ืžื•ื’ื“ืจ ืœ-2, ืจืง ืกืขื™ืคื™ื ื‘ืขืœื™ ืคื•ื˜ื ืฆื™ืืœ ืคืจื•ื“ื•ืงื˜ื™ื‘ื™
ืžื•ื“ืคืกื™ื, ื›ืœื•ืžืจ ืกืขื™ืคื™ื ืœืœื ืžื™ืœื•ืœื™ืช ืฉืœื™ืœื™ืช ื ื‘ื—ืจื” ื•ื—ื™ื•ื‘ ืžืงืกื™ืžืœื™
ืื—ื“. ืื ื”ื•ื ื”ืฉื ืฉืœ ื‘ืขื™ื™ืช ื”ืงืœื˜ ื•ื”ืฉื ืฉื ื•ืฆืจ ื‘ืกื•ืคื• ืฉืœ ื“ื‘ืจ
ื”ืกื˜ ืจื•ื•ื™, ื”ืจื•ื•ื™ื” ืžื•ื“ืคืกืช ืœืงื•ื‘ืฅ .ืžื•ื“ืœ, ืขื‘ื•ืจ
ืื—ืจืช ืœ .ืกืขื™ืคื™ื. ื”ืžืงืจื” ื”ืื—ืจื•ืŸ ืขืฉื•ื™, ืœืžืฉืœ, ืœื”ื™ื’ืจื ืขืœ ื™ื“ื™ ื–ืžืŸ
ืœึฐื”ึทื’ื‘ึผึดื™ืœ. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-FPDFGProof
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื”ืคืœื˜ ืฉืœ ื”ื•ื›ื—ื” ืฉื ืžืฆืื” ื‘ืกื•ืคื• ืฉืœ ื“ื‘ืจ ืœืงื•ื‘ืฅ. ืฉื™ืžื•ืฉ ื‘ืืคืฉืจื•ืช ื–ื•
ื“ื•ืจืฉ ืœื”ื’ื“ื™ืจ ืืช ื”ืืคืฉืจื•ืช -DocProof. ืื ื”ื•ื ืฉื ื”ืงืœื˜
ื‘ืขื™ื” ืฉื‘ื” ื”ื”ื’ื”ื” ืžื•ื“ืคืกืช .prf. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

- PFlags
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื”ืคืœื˜ ืฉืœ ื›ืœ ืขืจื›ื™ ื”ื“ื’ืœ. ื”ื’ื“ืจื•ืช ื”ื“ื’ืœ ืžื•ื“ืคืกื•ืช ื‘-
ืกื•ืฃ ืจื™ืฆืช SPASS ื‘ืฆื•ืจื” ืฉืœ ืงื˜ืข ืงืœื˜ DFG-Syntax. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-POptSkolem
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื”ืคืœื˜ ืฉืœ ื™ื™ืฉื•ืžื™ Skolemization ืื•ืคื˜ื™ืžืœื™ื™ื. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-PSrSkolem
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื”ืคืœื˜ ืฉืœ ื™ื™ืฉื•ืžื™ Skolemization ื—ื–ืงื™ื. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-PBDC
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื”ืคืœื˜ ืฉืœ ืกืขื™ืคื™ื ืฉื ืžื—ืงื• ื‘ื’ืœืœ ื”ื’ื‘ืœื•ืช ืงืฉื•ืจื•ืช. ื‘ึผึฐืจึดื™ืจึทืช ืžึถื—ื“ึธืœ
ื”ื•ื 0.

-PBInc
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื”ืคืœื˜ ืฉืœ ืฉื™ื ื•ื™ื™ื ื‘ื”ื’ื‘ืœื” ืงืฉื•ืจื”. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-PAplyDefs
ืžืืคืฉืจ/ืžืฉื‘ื™ืช ื”ื“ืคืกื” ืฉืœ ื”ืจื—ื‘ื•ืช ืฉืœ ื”ื’ื“ืจื•ืช ืื˜ื•ืžื™ื. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-ื‘ื—ืจ
ืžื’ื“ื™ืจ ืืช ืืกื˜ืจื˜ื’ื™ื™ืช ื”ื‘ื—ื™ืจื” ืขื‘ื•ืจ SPASS. ืื ืžื•ื’ื“ืจ ืœ-0, ืื™ืŸ ื‘ื—ื™ืจื” ืฉืœ ืžื™ืœื™ื ืฉืœื™ืœื™ื•ืช
ื ืขืฉื”. ืื ืžื•ื’ื“ืจ ืœืขืจืš ืื—ืจ, ืœื›ืœ ื”ื™ื•ืชืจ ืžื™ืœื•ืœื™ืช ืฉืœื™ืœื™ืช ืื—ืช ื‘ืคืกืงื” ื”ื™ื
ื ื‘ื—ืจ. ืื ืžื•ื’ื“ืจ ืœ-1 ืžื™ืœื•ืœื™ ืฉืœื™ืœื™ ื‘ืกืขื™ืคื™ื ืขื ื™ื•ืชืจ ืžืžื™ืœื•ืœื™ ืžืงืกื™ืžืœื™ ืื—ื“
ื ื‘ื—ืจื™ื. ืื• ืžื™ืœื•ืœื™ืช ืฉืœื™ืœื™ืช ืขื ืคืจื“ื™ืงื˜ ืžืจืฉื™ืžืช ื”ื‘ื—ื™ืจื” (ืจืื”
ืœื”ืœืŸ) ื ื‘ื—ืจ ืื• ืื ืื™ืŸ ืžื™ืœื•ืœื™ืช ืฉืœื™ืœื™ืช ื›ื–ื• ื–ืžื™ื ื”, ืžื™ืœื•ืœื™ืช ืฉืœื™ืœื™ืช ืขื
ื ื‘ื—ืจ ืžืฉืงืœ ืžืงืกื™ืžืœื™. ืื ืžื•ื’ื“ืจ ืœ-2 ืžื™ืœื™ื ืฉืœื™ืœื™ื•ืช ืชืžื™ื“ ื ื‘ื—ืจื™ื. ืฉื•ื‘,
ืื• ืžื™ืœื•ืœื™ืช ืฉืœื™ืœื™ืช ืขื ืคืจื“ื™ืงื˜ ืžืจืฉื™ืžืช ื”ื‘ื—ื™ืจื” (ืจืื” ืœื”ืœืŸ).
ื ื‘ื—ืจ ืื• ืื ืื™ืŸ ืžื™ืœื•ืœื™ืช ืฉืœื™ืœื™ืช ื›ื–ื• ื–ืžื™ื ื”, ืžื™ืœื•ืœื™ืช ืฉืœื™ืœื™ืช ืขื ืžืงืกื™ืžื•ื
ื ื‘ื—ืจ ืžืฉืงืœ. ื”ืžืงืจื” ื”ืื—ืจื•ืŸ ืžื‘ื™ื ืœืจื–ื•ืœื•ืฆื™ื™ืช ื™ืชืจ ืžืกื•ื“ืจืช ื›ืžื• ื”ืชื ื”ื’ื•ืช
ืฉืœ ืจื–ื•ืœื•ืฆื™ื” ืžืกื•ื“ืจืช. ืื ืžื•ื’ื“ืจ ืœ-3 ื›ืœ ืžื™ืœื•ืœื™ืช ืฉืœื™ืœื™ืช ืขื ืคืจื“ื™ืงื˜ ืฉืฆื•ื™ืŸ ืขืœ ื™ื“ื™
ืจืฉื™ืžืช ื”ื‘ื—ื™ืจื” (ืจืื” ืœื”ืœืŸ) ื ื‘ื—ืจืช. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 1.

-RIinput
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื”ื”ืคื—ืชื” ืฉืœ ืขืจื›ืช ื”ืกืขื™ืคื™ื ื”ืจืืฉื•ื ื™ืช. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 1.

-ืžื™ื™ื ื™ื
ืงื•ื‘ืข ืืช ื”ืžื™ืœื•ืœื™ื ื”ืžื•ื ื“ื™ื™ื ืฉื‘ื ื• ืืช ืื™ืœื•ืฅ ื”ืžื™ื•ืŸ ืขื‘ื•ืจ ื”ืกืขื™ืฃ ื”ืจืืฉื•ื ื™
ืžึทืขึฒืจึถื›ึถืช. ืื ืžื•ื’ื“ืจ ืœ-0, ืœื ื ื‘ื ื” ืื™ืœื•ืฅ ืžื™ื•ืŸ. ืื ืžื•ื’ื“ืจ ืœ-1, ื”ื›ืœ ืžื•ื ื“ื™ ืฉืœื™ืœื™
ืžื™ืœื•ืœื™ื™ื ืขื ืžืฉืชื ื” ื›ืืจื’ื•ืžื ื˜ ื™ื•ืฆืจื™ื ืืช ืื™ืœื•ืฅ ื”ืžื™ื•ืŸ. ืื ืžื•ื’ื“ืจ ืœ-2, ื”ื›ืœ
ืžื™ืœื™ื ืžื•ื ื“ื™ื•ืช ืฉืœื™ืœื™ื•ืช ื™ื•ืฆืจื•ืช ืืช ืื™ืœื•ืฅ ื”ืžื™ื•ืŸ. ื”ื’ื“ืจื” -ืžื™ื™ื ืช ืขื“ 2 ืขืœื•ืœื” ืœื”ื–ื™ืง
ืฉืœืžื•ืช, ืฉื›ืŸ ืื™ืœื•ืฆื™ ืžื™ื•ืŸ ื›ืคื•ืคื™ื ืœืืกื˜ืจื˜ื’ื™ื” ื”ื‘ืกื™ืกื™ืช ื•ืœืกื˜ื˜ื™
ื”ืงืœื“ื” ืจื›ื”. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 1.

-SatInput
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ืจื•ื•ื™ืช ื”ืงืœื˜. ื”ืจื•ื•ื™ื” ืื™ื ื” ืฉืœืžื” ืืš ืžื•ื‘ื˜ื—ืช
ืœื‘ื˜ืœ, ืœืกื™ื™ื. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-WDRatio
ืžื’ื“ื™ืจ ืืช ื”ื™ื—ืก ื‘ื™ืŸ ืกืขื™ืคื™ื ื ืชื•ื ื™ื ืฉื ื‘ื—ืจื• ืœืคื™ ืžืฉืงืœ ืื• ื”ืขื•ืžืง ื‘ื—ื™ืคื•ืฉ
ืžึถืจื—ึธื‘. ื”ืžืฉืงืœ ื”ื•ื ื”ืกื›ื•ื ืฉืœ ื›ืœ ืžืฉืงืœื™ ื”ืกืžืœื™ื ืฉื ืงื‘ืขื• ืขืœ ื™ื“ื™ -FuncWeight ื•
-ืืคืฉืจื•ื™ื•ืช VarWeight. ื”ืขื•ืžืง ืฉืœ ื›ืœ ื”ืกืขื™ืคื™ื ื”ืจืืฉื•ื ื™ื™ื ื”ื•ื 0 ื•ื”ืกืขื™ืคื™ื ืฉื ื•ืฆืจื• ืขืœ ื™ื“ื™
ืžืกืงื ื•ืช ืžืงื‘ืœื™ื ืืช ื”ืขื•ืžืง ื”ืžืงืกื™ืžืœื™ ืฉืœ ืกืขื™ืฃ ืื‘ ืคืœื•ืก 1. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 5, ื›ืœื•ืžืจ
ืฉ-4 ืกืขื™ืคื™ื ื ื‘ื—ืจื™ื ืœืคื™ ืžืฉืงืœ ื•ื”ืกืขื™ืฃ ื”ื—ืžื™ืฉื™ ื ื‘ื—ืจ ืœืคื™ ืขื•ืžืง.

-PrefCon
ืžื’ื“ื™ืจ ืืช ื”ื™ื—ืก ืœื—ื™ืฉื•ื‘ ื”ืžืฉืงืœ ืขื‘ื•ืจ ืกืขื™ืคื™ ื”ืฉืขืจื” ื•ืœื›ืŸ ืžืืคืฉืจ
ืžืขื“ื™ืคื™ื ื›ืืœื”. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0 ื›ืœื•ืžืจ ื—ื™ืฉื•ื‘ ื”ืžืฉืงืœ ืขื‘ื•ืจ ืกืขื™ืคื™ ื”ืฉืขืจื”
ืื™ื ื• ืžืฉืชื ื”.

-ืื“ื•ื ืžืœื
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ื”ืคื—ืชื” ืžืœืื”. ืื ืžื•ื’ื“ืจ ืœ-0, ืจืง ืงื‘ื•ืฆืช ื”ืกืขื™ืคื™ื ืฉื”ื•ืคืขืœื• ื”ื™ื
ืžื•ืคื—ืช ืœื—ืœื•ื˜ื™ืŸ. ืื ืžื•ื’ื“ืจ ืœ-1, ื›ื•ืœื ืžื—ื–ื™ืงื™ื ื›ืจื’ืข ื‘ืกืขื™ืคื™ื (ืขื•ื‘ื“ื™ื ืขืœ ื•
ืฉืžื™ืฉ) ืžื•ืคื—ืชื™ื ืœื—ืœื•ื˜ื™ืŸ. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 1.

- ืžืฉืงืœ Func
ืžื’ื“ื™ืจ ืืช ื”ืžืฉืงืœ ืฉืœ ืกืžืœื™ ืคื•ื ืงืฆื™ื”/ืคืจื“ื™ืงื˜ื™ื. ืžืฉืงืœ ื”ืกืขื™ืคื™ื ื”ื•ื ืกื›ื•ื ื”ื›ืœ
ืžืฉืงืœื™ ืกืžืœื™ื. ืžืฉืงืœ ื–ื” ื ื—ืฉื‘ ืœื‘ื—ื™ืจืช ื”ืกืขื™ืฃ ื”ื ืชื•ืŸ.
ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 1.

-VarWeight
ืžื’ื“ื™ืจ ืืช ื”ืžืฉืงืœ ืฉืœ ืกืžืœื™ื ืžืฉืชื ื™ื (ืจืื” -FuncWeight). ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 1.

-PrefVar
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื”ื”ืขื“ืคื” ืœืกืขื™ืคื™ื ืขื ืžืฉืชื ื™ื ืจื‘ื™ื. ื‘ืขื•ื“ ืฉืกืขื™ืคื™ื ื›ืŸ
ื ื‘ื—ืจ ืœืคื™ ืžืฉืงืœ, ืื ืืคืฉืจื•ืช ื–ื• ืžื•ื’ื“ืจืช ื•ืœืฉื ื™ ืกืขื™ืคื™ื ื™ืฉ ืžืฉืงืœ ื–ื”ื”, ื”
ืžื•ืขื“ืฃ ืกืขื™ืฃ ืขื ื™ื•ืชืจ ืžื•ืคืขื™ื ืžืฉืชื ื™ื. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-BoundMode
ื‘ื•ื—ืจ ืืช ื”ืžืฆื‘ ืขื‘ื•ืจ ื”ื’ื‘ืœื•ืช ืงืฉื•ืจื•ืช. ืžืฆื‘ 0 ืคื™ืจื•ืฉื• ืฉืื™ืŸ ื”ื’ื‘ืœื”, ืื ืžื•ื’ื“ืจ ืœ-1 ื”ื›ืœ
ืกืขื™ืคื™ื ื—ื“ืฉื™ื ืฉื ื•ืฆืจื• ืžื•ื’ื‘ืœื™ื ืœืคื™ ืžืฉืงืœ (ืจืื” -BoundStart) ื•ืื ืžื•ื’ื“ืจื™ื ืœ-2
ืกืขื™ืคื™ื ืžื•ื’ื‘ืœื™ื ืขืœ ื™ื“ื™ ืขื•ืžืง. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-BoundStart
ื”ื’ื‘ืœืช ื”ื”ืชื—ืœื” ืฉืœ ืžืฆื‘ ื”ื›ืจื™ื›ื” ืฉื ื‘ื—ืจ. ืœื“ื•ื’ืžื”, ืื ืžืฆื‘ bound ื”ื•ื 1 ื•
ื”ืชื—ืœื” ืงืฉื•ืจื” ืžื•ื’ื“ืจืช ืœ-5, ื›ืœ ื”ืกืขื™ืคื™ื ืขื ืžืฉืงืœ ื’ื“ื•ืœ ืž-5 ื ืžื—ืงื™ื ืขื“ ืœ-
ื”ืกื˜ ืจื•ื•ื™. ื–ื” ื’ื•ืจื ืœืขืœื™ื™ื” ืฉืœ ื”ืขืจืš ื”ื’ื‘ื•ืœ ื”ืžืฉืžืฉ ืฉื ืงื‘ืข
ืขืœ ื™ื“ื™ ื”ื’ื™ื“ื•ืœ ื”ืžื™ื ื™ืžืœื™ ืฉืžื™ืจืช ืกืขื™ืฃ ืœืคื ื™ ืฉื ืžื—ืง. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื -1 ื›ืœื•ืžืจ ืœืœื bound
ื”ึทื’ื‘ึผึธืœึธื”.

-BoundLoops
ืžืกืคืจ ืœื•ืœืื•ืช ื”ืžื—ื™ืœื•ืช ืืช ื”ื’ื‘ืœื•ืช ื”ืคืขื•ืœื•ืช / ื”ื’ื“ืœืช ื”ื’ื‘ื•ืœ. ืื ื”ืžืกืคืจ
ื—ืจื™ื’ื” ืฉืœ ืœื•ืœืื•ืช ื›ืœ ื”ื”ื’ื‘ืœื•ืช ื”ืžื—ื•ื‘ืจื•ืช ืžื‘ื•ื˜ืœื•ืช. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 1.

-ApplyDefs
ืžื’ื“ื™ืจ ืืช ื”ืžืกืคืจ ื”ืžืจื‘ื™ ืฉืœ ื™ื™ืฉื•ืžื™ื ืฉืœ ื”ื’ื“ืจื•ืช ืื˜ื•ื ืœื ื•ืกื—ืื•ืช ืงืœื˜.
ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0, ื›ืœื•ืžืจ ืื™ืŸ ืืคืœื™ืงืฆื™ื•ืช ื›ืœืœ.

-ืžื–ืžื™ืŸ
ืžื’ื“ื™ืจ ืืช ืกื“ืจ ื”ืžื•ื ื—ื™ื. ืื 0 ืื–ื™ ื ื‘ื—ืจ KBO, ืื 1 ื ื‘ื—ืจ ื”-RPOS. ื‘ึผึฐืจึดื™ืจึทืช ืžึถื—ื“ึธืœ
ื”ื•ื 0.

-CNFQuantExch
ืื ืžื•ื’ื“ืจื™ื, ืžื•ื—ืœืคื™ื ืžื•ื ื—ื™ Skolem ืฉืื™ื ื ืงื‘ื•ืขื™ื ื‘ืฆื•ืจื” ื”ืกื™ื™ื’ืœื™ืช ืฉืœ ื”ื”ืฉืขืจื”
ืœืคื™ ืงื‘ื•ืขื™ื. ื™ื•ื’ื“ืจ ืื•ื˜ื•ืžื˜ื™ืช ืœืชืจื’ื•ื ืคื•ื ืงืฆื™ื•ื ืœื™ ืื•ืคื˜ื™ืžืœื™ ืฉืœ
ื ื•ืกื—ืื•ืช ืœื•ื’ื™ืงื” ืžื•ื“ืืœื™ืช ืื• ืชื™ืื•ืจื™ืช. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-CNFOptSkolem
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช Skolemization ืื•ืคื˜ื™ืžืœื™. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 1.

-CNFStrSkolem
ืžืืคืฉืจ/ืžืฉื‘ื™ืช Strong Skolemization. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 1.

-CNFProofSteps
ืžื’ื“ื™ืจ ืืช ื”ืžืกืคืจ ื”ืžืจื‘ื™ ืฉืœ ืฉืœื‘ื™ ื”ื•ื›ื—ื” ื‘ื ื™ืกื™ื•ืŸ ื”ื•ื›ื—ื” ืื•ืคื˜ื™ืžืœื™ ืฉืœ Skolemization.
ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 100.

-CNFSub
ืžืืคืฉืจ/ืžืฉื‘ื™ืช ืชืช-ื”ืคืจืฉื” ืขืœ ื”ืกืขื™ืคื™ื ืฉื ื•ืฆืจื• ืขืœ ื™ื“ื™ ื”ืœื™ืš CNF. ื‘ึผึฐืจึดื™ืจึทืช ืžึถื—ื“ึธืœ
ื”ื•ื 1.

-CNFCon
ืžืืคืฉืจ/ืžื‘ื˜ืœ ืขื™ื‘ื•ื™ ืขืœ ื”ืกืขื™ืคื™ื ืฉื ื•ืฆืจื• ืขืœ ื™ื“ื™ ื”ืœื™ืš CNF. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื
1.

-CNFRedTime
ืžื’ื“ื™ืจ ืืช ืžืฉืš ื”ื–ืžืŸ ื”ื›ื•ืœืœ ื‘ืฉื ื™ื•ืช ืฉื™ืฉ ืœื”ืฉืงื™ืข ื‘ื”ืคื—ืชื” ื‘ืžื”ืœืš CNF
ื˜ืจื ืกืคื•ืจืžืฆื™ื”. ื”ื”ืคื—ืชื•ืช ื”ืžื•ืฉืคืขื•ืช ื”ืŸ ืื•ืคื˜ื™ืžื™ื–ืฆื™ื” ืฉืœ Skolemization, ืขื™ื‘ื•ื™ ื•
ื”ื ื—ื”. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื -1 ื›ืœื•ืžืจ ื–ืžืŸ ื”ื”ืคื—ืชื” ืื™ื ื• ืžื•ื’ื‘ืœ ื›ืœืœ.

-CNFRname
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ืฉื™ื ื•ื™ ืฉื ื”ื ื•ืกื—ื”. ืื ืžื•ื’ื“ืจ ืœ-1 ืฉื™ื ื•ื™ ืฉื ืื•ืคื˜ื™ืžืœื™ ืžื•ืคืขืœ
ืžืžื–ืขืจ ืืช ืžืกืคืจ ื”ืกืขื™ืคื™ื ืฉื ื•ืฆืจื• ื‘ืกื•ืคื• ืฉืœ ื“ื‘ืจ. ืื ืžื•ื’ื“ืจ ืœ-2, ืฉื™ื ื•ื™ ืฉื ืžื•ืจื›ื‘ ื”ื•ื
ืžื•ืคืขืœืช ืฉืžืฆื™ื’ื” ืคืจื™ื“ื™ืงื˜ ื—ื“ืฉ ืฉืœ Skolem ืขื‘ื•ืจ ื›ืœ ื ื•ืกื—ื” ืžื•ืจื›ื‘ืช, ื›ืœื•ืžืจ ื›ืœ ื ื•ืกื—ื”
ื ื•ืกื—ื” ืฉืื™ื ื” ืžื™ืœื•ืœื™ืช. ืื ืžื•ื’ื“ืจ ืœ-3, ืฉื™ื ื•ื™ ื”ืฉื ืžื•ืคืขืœ
ืžืฆื™ื’ ืคืจื™ื“ื™ืงื˜ ื—ื“ืฉ ืฉืœ Skolem ืขื‘ื•ืจ ื›ืœ ืชืช-ื ื•ืกื—ื” ืฉืžืชื—ื™ืœื” ื‘ื›ื™ืžื•ืช.
ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 1.

-CNFRenMatch
ืื ืžื•ื’ื“ืจ, ืฉื™ื ื•ื™ ืฉืžื•ืช ื”ืžืฉื ื” ืฉืœ ื•ืจื™ืื ื˜ื™ื ืžื•ื—ืœืคื™ื ื‘ืื•ืชื• ืžื™ืœื•ืœื™ ืฉืœ Skolem. ื‘ึผึฐืจึดื™ืจึทืช ืžึถื—ื“ึธืœ
ื”ื•ื 1.

-ืฉื™ื ื•ื™ ืฉื CNFFP
ืžืืคืฉืจ/ืžืฉื‘ื™ืช ืืช ื”ื”ื“ืคืกื” ืฉืœ ื™ื™ืฉื•ืžื™ ืฉื™ื ื•ื™ ืฉืžื•ืช ืฉืœ ื ื•ืกื—ืื•ืช. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-CNFFEqR
ืžืืคืฉืจ/ืžืฉื‘ื™ืช ื˜ื›ื ื™ืงื•ืช ืžืกื•ื™ืžื•ืช ืœื”ืคื—ืชืช ืฉื•ื•ื™ื•ืŸ ื‘ืจืžืช ื”ื ื•ืกื—ื”. ื‘ึผึฐืจึดื™ืจึทืช ืžึถื—ื“ึธืœ
ื”ื•ื 1.

-IEmS
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืกืงืช ืžื™ื•ืŸ ืจื™ืง. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-ISoR
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืกืงืช ืžื™ื•ืŸ ืžื™ื•ืŸ. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-IEqR
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืกืงืช Equal Resolution. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-IERR
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืกืงื” Reflexivity Resolution. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-IEqF
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืกืงื•ืช Equal Factoring. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-IMPm
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืกืงื” ืžื™ื–ื•ื’ ืคืจืžื•ื“ื•ืœืฆื™ื”. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-ISpR
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืกืงื” Superposition Right. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-IOPm
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืกืงื” Orded Paramodulation. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-ISPm
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืกืงื” Standard Paramodulation. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-ISpL
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืกืงื” Superposition Left. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-IORe
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืกืงื” Orded Resolution. ืื ืžื•ื’ื“ืจ ืœ-1, ื”ื•ื–ืžืŸ
ื”ืจื–ื•ืœื•ืฆื™ื” ืžื•ืคืขืœืช ืืš ืœื ื ื•ืฆืจื•ืช ืžืกืงื ื•ืช ืจื–ื•ืœื•ืฆื™ื” ืขื ืžืฉื•ื•ืื•ืช. ืื
ืžื•ื’ื“ืจ ืœ-2, ืžืฉื•ื•ืื•ืช ื ื—ืฉื‘ื•ืช ื’ื ืขื‘ื•ืจ ืฉืœื‘ื™ ืจื–ื•ืœื•ืฆื™ื” ืžืกื•ื“ืจืช. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื
0.

-ISRe
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืกืงื” ื‘ืจื–ื•ืœื•ืฆื™ื” ืกื˜ื ื“ืจื˜ื™ืช. ืื ืžื•ื’ื“ืจ ืœ-1, ืกื˜ื ื“ืจื˜ื™
ื”ืจื–ื•ืœื•ืฆื™ื” ืžื•ืคืขืœืช ืืš ืœื ื ื•ืฆืจื•ืช ืžืกืงื ื•ืช ืจื–ื•ืœื•ืฆื™ื” ืขื ืžืฉื•ื•ืื•ืช. ืื
ืžื•ื’ื“ืจ ืœ-2, ืžืฉื•ื•ืื•ืช ื ื—ืฉื‘ื•ืช ื’ื ืขื‘ื•ืจ ืฉืœื‘ื™ ื”ืจื–ื•ืœื•ืฆื™ื” ื”ืกื˜ื ื“ืจื˜ื™ืช. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื
0.

-ืื ื™ ื‘ื™ื™ืฉืŸ
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืกืงื” Standard Hyper-Resolution. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-IOHy
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืกืงื” Ordered Hyper-Resolution. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-IURR
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืกืงื” Unit Resulting Resolution. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-IOFc
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืกืงื” Orded Factoring. ืื ืžื•ื’ื“ืจ ืœ-1, ืกื“ืจ ืคืงื˜ื•ืจื™ื ื’
ืžื•ืคืขืœ, ืืš ื ื•ืฆืจื•ืช ืจืง ืžืกืงื ื•ืช ืœื’ื•ืจืžื™ื ืขื ืžื™ืœื™ื ื—ื™ื•ื‘ื™ื•ืช. ืื ืžื•ื’ื“ืจ
ืขื“ 2, ืžื™ืœื™ื ืฉืœื™ืœื™ื•ืช ื ื—ืฉื‘ื•ืช ื’ื ืœื”ืกืงืช ืžืกืงื ื•ืช. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-ISFc
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืกืงื” Standard Factoring. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-IUnR
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืกืงื” Unit Resolution. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-IBUR
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืกืงื” Bounded Depth Unit Resolution. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-IDEF
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืกืงื” Apply Definitions. ื›ืจื’ืข ืœื ื ืชืžืš.
ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-RFRew
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืคื—ืชื” ื”ืขื‘ืจื” ืžื—ื“ืฉ. ืื ืžื•ื’ื“ืจ ืœื™ื—ื™ื“ื” ืื—ืช ืฉื›ืชื•ื‘ ื•
ืžื•ืคืขืœ ืฉื›ืชื•ื‘ ืœืœื ื™ื—ื™ื“ื•ืช ื”ืžื‘ื•ืกืก ืขืœ ืžื‘ื—ืŸ ืžืฉื ื”. ืื ืžื•ื’ื“ืจ ืœ-2 ื‘ื ื•ืกืฃ
ืฉื›ืชื•ื‘ ืœื™ื—ื™ื“ื” ื•ืœื ืœื™ื—ื™ื“ื” ืžื•ืคืขืœ ืฉื›ืชื•ื‘ ื”ืงืฉืจ ืžืงื•ืžื™ ืžืงื•ืžื™. ืื ืžื•ื’ื“ืจ ืœ-3
ื‘ื ื•ืกืฃ ืœื™ื—ื™ื“ื” ื•ืœื ื™ื—ื™ื“ื” ื›ืชื™ื‘ื” ืžื—ื“ืฉ ืฉืœ ืชืช ืžื•ื ื—ื™ื ืฉื›ืชื•ื‘ ื”ืงืฉืจ ื”ื•ื
ืžื•ืคืขืœ. ืฉื›ืชื•ื‘ ืงื•ื ื˜ืงืกื˜ื•ืืœื™ ืฉืœ ืชืช ืžื•ื ื— ืžืฉื ื” ืฉื›ืชื•ื‘ ื”ืงืฉืจื™ ืžืงื•ืžื™. ืื ืžื•ื’ื“ืจ
ืœ-4 ื‘ื ื•ืกืฃ ืœื›ืœืœื™ ื”ืฉื›ืชื•ื‘ ืฉืœ 3, ืฉื›ืชื•ื‘ ื”ืงืฉืจื™ ืชืช-ืžื•ื ื— ื’ื ื‘ื•ื—ืŸ
ืœื‘ื™ื˜ื•ืœ ืžื™ืœื•ืœื™ ืฉืœื™ืœื™. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-RBRew
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืคื—ืชื” ืฉื›ืชื•ื‘ ืœืื—ื•ืจ. ืื•ืชื ืขืจื›ื™ื ื•ืžืฉืžืขื•ืช ื›ืžื•
ืขื‘ื•ืจ ื“ื’ืœ -RFRew ืืš ืžืฉืžืฉ ื‘ื›ื™ื•ื•ืŸ ืื—ื•ืจื”. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-RFMRR
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืคื—ืชื” Forward Matching Replacement Resolution. ื‘ึผึฐืจึดื™ืจึทืช ืžึถื—ื“ึธืœ
ื”ื•ื 0.

-RBMRR
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืคื—ืชื” ืจื–ื•ืœื•ืฆื™ื™ืช ื”ื—ืœืคืช ื”ืชืืžื” ืœืื—ื•ืจ. ื‘ึผึฐืจึดื™ืจึทืช ืžึถื—ื“ึธืœ
ื”ื•ื 0.

-RObv
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืคื—ืชื” ื‘ืจื•ืจ ืฆืžืฆื•ื. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-RUnC
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืคื—ืชื” Unit Conflict. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-RTer
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื”-terminator ืขืœ ื™ื“ื™ ื”ื’ื“ืจืช ื”ืžืกืคืจ ื”ืžืจื‘ื™ ืฉืœ ืกืขื™ืคื™ื ืฉืื™ื ื ื™ื—ื™ื“ื” ืœ
ืœืฉืžืฉ ื‘ืžื”ืœืš ื”ื—ื™ืคื•ืฉ. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-RTaut
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืคื—ืชื” ืžื—ื™ืงืช ื˜ืื•ื˜ื•ืœื•ื’ื™ื”. ืื ืžื•ื’ื“ืจ ืœ-1, ืจืง ืชื—ื‘ื™ืจื™
ื˜ืื•ื˜ื•ืœื•ื’ื™ื•ืช ืžื–ื•ื”ื•ืช ื•ื ืžื—ืงื•ืช. ืื ืžื•ื’ื“ืจ ืœ-2, ื‘ื ื•ืกืฃ ื˜ืื•ื˜ื•ืœื•ื’ื™ื•ืช ืกืžื ื˜ื™ื•ืช
ืžื•ืกืจื™ื. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-RSST
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืคื—ืชื” ืกื˜ื˜ื™ Soft Typing. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-RSSi
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืคื—ืชื” ืžื™ื•ืŸ ืคื™ืฉื•ื˜. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-RFSub
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืคื—ืชื” Forward Subsumption Deletion. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-RBSub
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืคื—ืชื” ืžื—ื™ืงืช ืกืคื™ื’ื” ืœืื—ื•ืจ. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-RAED
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืคื—ืชื” ืžื—ื™ืงืช ืžืฉื•ื•ืืช ื”ื”ืงืฆืื”. ื›ืœืœ ื–ื” ืžืกื™ืจ
ืžื•ืคืขื™ื ืžืกื•ื™ืžื™ื ืฉืœ ืžืฉื•ื•ืื•ืช ืžืกืขื™ืคื™ื. ืื ืžื•ื’ื“ืจ ืœ-1, ื”ื”ืคื—ืชื” ื”ื™ื
ืžื•ื‘ื˜ื— ืฉื™ื”ื™ื” ืงื•ืœ. ืื ืžื•ื’ื“ืจ ืœ-2, ื”ื”ืคื—ืชื” ื ืฉืžืขืช ืจืง ืื ื™ืฉ ืคื•ื˜ื ืฆื™ืืœ
ืœืžื•ื“ืœ ืฉืœ ื”ื‘ืขื™ื” ื”ื ื—ืฉื‘ืช ื™ืฉ ืชื—ื•ื ืœื ื˜ืจื™ื•ื•ื™ืืœื™. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-RCon
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื›ืœืœ ื”ื”ืคื—ืชื” ืขื™ื‘ื•ื™. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-TDfg2OtterOptions
ืžืคืขื™ืœ/ืžืฉื‘ื™ืช ืืช ื”ื›ืœืœืช ื›ื•ืชืจืช ืฉืœ ืืคืฉืจื•ื™ื•ืช Otter. ืืคืฉืจื•ืช ื–ื• ื—ืœื” ืจืง ืขืœ
dfg2otter. ืื ืžื•ื’ื“ืจ ืœ-1 ื”ื•ื ื›ื•ืœืœ ื”ื’ื“ืจื” ืฉื’ื•ืจืžืช ืœ-Otter ื›ืžืขื˜ ืœื”ืฉืœื™ื. ืื ืžื•ื’ื“ืจ
ืœ-2 ื–ื” ืžืคืขื™ืœ ืžืฆื‘ ืื•ื˜ื•ืžื˜ื™ ื•ืื ื”ื•ื ืžื•ื’ื“ืจ ืœ-3 ื–ื” ืžืคืขื™ืœ ืืช ืžืฆื‘ auto2. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื
0.

-EML
ื“ื’ืœ EML ืžื™ื•ื—ื“ ืœื ื•ืกื—ืื•ืช ืœื•ื’ื™ืงื” ืžื•ื“ืืœื™ืช ืื• ืชื™ืื•ืจ. ืืฃ ืคืขื ืœื ืฆืจื™ืš ืœื”ื™ื•ืช
ืžื•ื’ื“ืจ ื‘ืžืคื•ืจืฉ. ืžื•ื’ื“ืจ ื‘ืžื”ืœืš ื”ื ื™ืชื•ื—.

-EMLAuto
ืžื™ื•ืขื“ ืœืžืฆื‘ EML ืื•ื˜ื•ื ื•ืžื™, ืขื“ื™ื™ืŸ ืœื ืคื•ื ืงืฆื™ื•ื ืœื™. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-EML ืชืจื’ื•ื
ืงื•ื‘ืข ืืช ืฉื™ื˜ืช ื”ืชืจื’ื•ื ื”ืžืฉืžืฉืช ืœื ื•ืกื—ืื•ืช ืœื•ื’ื™ืงื” ืžื•ื“ืืœื™ืช ืื• ืชื™ืื•ืจ.
ืื ืžื•ื’ื“ืจ ืœ-0, ืฉื™ื˜ืช ื”ืชืจื’ื•ื ื”ื”ืชื™ื™ื—ืกื•ืชื™ืช ื”ืกื˜ื ื“ืจื˜ื™ืช (ืืฉืจ ื ืงื‘ืขืช ืขืœ ื™ื“ื™
ืกืžื ื˜ื™ืงื” ืจื’ื™ืœื” ืฉืœ Kripke) ืžืฉืžืฉืช. ืื ืžื•ื’ื“ืจ ืœ-1, ืฉื™ื˜ืช ื”ืชืจื’ื•ื ื”ืคื•ื ืงืฆื™ื•ื ืœื™ืช ื”ื™ื
ื‘ืฉื™ืžื•ืฉ. ืื ืžื•ื’ื“ืจ ืœ-2, ื ืขืฉื” ืฉื™ืžื•ืฉ ื‘ืฉื™ื˜ืช ื”ืชืจื’ื•ื ื”ืคื•ื ืงืฆื™ื•ื ืœื™ืช ื”ืžืื•ืคื˜ื™ืžืœื™ืช. ืื ืžื•ื’ื“ืจ ืœ-3,
ื ืขืฉื” ืฉื™ืžื•ืฉ ื‘ืฉื™ื˜ืช ื”ืชืจื’ื•ื ื”ื—ืฆื™-ืคื•ื ืงืฆื™ื•ื ืœื™. ื•ืจื™ืืฆื™ื” ืฉืœ ื”ืื•ืคื˜ื™ืžื™ื–ืฆื™ื”
ื ืขืฉื” ืฉื™ืžื•ืฉ ื‘ืฉื™ื˜ืช ืชืจื’ื•ื ืคื•ื ืงืฆื™ื•ื ืœื™ืช, ื›ืืฉืจ ื”ื”ื’ื“ืจื•ืช ื”ื‘ืื•ืช ืžืฆื•ื™ื ื•ืช:
-EMLTranslation=2 -EMLFuncNary=1. ื”ืชืจื’ื•ื ื™ื”ื™ื” ื‘ืžื•ื ื—ื™ื ืฉืœ n-ary
ืคืจื“ื™ืงื˜ื™ื ื‘ืžืงื•ื ืคืจื“ื™ืงื˜ื™ื ื•ืฉื‘ื™ืœื™ื ืœื ื ืจืื™ื. ื‘ื™ื™ืฉื•ื ื”ื ื•ื›ื—ื™ ื”
ืฉื™ื˜ืช ื”ืชืจื’ื•ื ื”ื”ืชื™ื™ื—ืกื•ืชื™ืช ื”ืกื˜ื ื“ืจื˜ื™ืช ื”ื™ื ื›ืœืœื™ืช ื‘ื™ื•ืชืจ. ื›ืžื” ื”ื’ื‘ืœื•ืช ื—ืœื•ืช ืขืœ
ืฉื™ื˜ื•ืช ืื—ืจื•ืช. ืฉื™ื˜ืช ื”ืชืจื’ื•ื ื”ืคื•ื ืงืฆื™ื•ื ืœื™ ื•ืชืจื’ื•ื ื—ืฆื™ ืคื•ื ืงืฆื™ื•ื ืœื™
ืฉื™ื˜ื•ืช ื–ืžื™ื ื•ืช ืจืง ืขื‘ื•ืจ ื”ื”ื™ื’ื™ื•ืŸ ื”ืจื‘-ืžื•ื“ืืœื™ ื”ื‘ืกื™ืกื™ K(ืž) ืื•ืœื™ ืขื ืกื“ืจืชื™
(ืกื”"ื›) ืื•ืคื ื™ื (-EMLTheory=1), ื‘ืชื•ืกืคืช ื ื•ืžื™ื ืœื™ื (ื”ืฆื”ืจื•ืช ABox), ื˜ืจืžื™ื ื•ืœื•ื’ื™ื•ืช
ืืงืกื™ื•ืžื•ืช ื•ืืงืกื™ื•ืžื•ืช ื›ืœืœื™ื•ืช ืฉืœ ื”ื›ืœืœื” ื•ืฉืงื™ืœื•ืช. ื”ืคื•ื ืงืฆื™ื•ื ืœื™ ื”ืื•ืคื˜ื™ืžืœื™
ืฉื™ื˜ื•ืช ืชืจื’ื•ื ืžื™ื•ืฉืžื•ืช ืจืง ืขื‘ื•ืจ K(ืž), ืื•ืœื™ ืขื ืื•ืคื ื™ื ืกื“ืจืชื™ื™ื.
ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-EML2Rel
ืื ืžื•ื’ื“ืจื™ื, ื ื•ืกื—ืื•ืช ื”ืฆืขื”/ื‘ื•ืœื™ืื ื™ื•ืช ืžื•ืžืจื•ืช ืœื ื•ืกื—ืื•ืช ื™ื—ืกื™ื•ืช
ืœืคื ื™ ืฉื”ื ืžืชื•ืจื’ืžื™ื ืœืœื•ื’ื™ืงื” ืžืกื“ืจ ืจืืฉื•ืŸ. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-EML Theory
ืงื•ื‘ืข ืื™ื–ื• ืชื•ืจืช ืจืงืข ืžื ื™ื—ื”. ืื ืžื•ื’ื“ืจ ืœ-0, ืชื•ืจืช ื”ืจืงืข ื”ื™ื
ืจื™ืง. ืื ืžื•ื’ื“ืจ ืœ-1, ืื–ื™ ื”ืกื“ืจื•ืช (ืชื•ืจืช ื”ืจืงืข ืฉืœ KD) ืžืชื•ื•ืกืคืช ืœื›ื•ืœื
ืื•ืคื ื™ื. ืื ืžื•ื’ื“ืจ ืœ-2, ืื–ื™ ืžืชื•ื•ืกืคืช ืจืคืœืงืกื™ื‘ื™ื•ืช (ืชื•ืจืช ื”ืจืงืข ืขื‘ื•ืจ KT).
ื›ืœ ื”ืฉื™ื˜ื•ืช. ืื ืžื•ื’ื“ืจ ืœ-3, ืื–ื™ ืกื™ืžื˜ืจื™ื” (ืชื•ืจืช ื”ืจืงืข ืฉืœ KB) ืžืชื•ื•ืกืคืช
ืœื›ืœ ื”ืฉื™ื˜ื•ืช. ืื ืžื•ื’ื“ืจ ืœ-4, ืื– ื˜ืจื ื–ื™ื˜ื™ื‘ื™ื•ืช (ืชื™ืื•ืจื™ื™ืช ื”ืจืงืข ืฉืœ K4) ื”ื™ื
ื ื•ืกืฃ ืขื‘ื•ืจ ื›ืœ ื”ืฉื™ื˜ื•ืช. ืื ืžื•ื’ื“ืจ ืœ-5, ืื– ืื•ืงืœื™ื“ื™ื•ืช (ืชื™ืื•ืจื™ื™ืช ื”ืจืงืข ืขื‘ื•ืจ
K5) ื ื•ืกืฃ ืขื‘ื•ืจ ื›ืœ ื”ืฉื™ื˜ื•ืช. ืื ืžื•ื’ื“ืจ ืœ-6, ืื– ื˜ืจื ื–ื™ื˜ื™ื‘ื™ื•ืช ื•ืื•ืงืœื™ื“ื™ื•ืช
(ืชื™ืื•ืจื™ื™ืช ื”ืจืงืข ืขื‘ื•ืจ S4) ืžืชื•ื•ืกืคืช ืขื‘ื•ืจ ื›ืœ ื”ืฉื™ื˜ื•ืช. ืื ืžื•ื’ื“ืจ ืœ-7, ืื–
ืžืชื•ื•ืกืคืช ืจืคืœืงืกื™ื‘ื™ื•ืช, ื˜ืจื ื–ื™ื˜ื™ื‘ื™ื•ืช ื•ืื•ืงืœื™ื“ื™ื•ืช (ืชื™ืื•ืจื™ื™ืช ื”ืจืงืข ืœ-S5).
ืœื›ืœ ื”ืฉื™ื˜ื•ืช. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-EMLFuncNdeQ
ืื ื ืงื‘ืข, ื ื•ืกื—ืื•ืช ื™ื”ืœื•ื ืžืชื•ืจื’ืžื•ืช ืœืคื™ tr(dia(phi),s) = nde(s) /\ ืงื™ื™ื
x tr(phi,[sx]) (ื ื•ืกื—ืช nde / ื›ื™ืžืช), ืื—ืจืช ื”ืชืจื’ื•ื ื ืžืฆื ื‘-
ื‘ื”ืชืื ืœ-tr(dia(phi),s) = ืงื™ื™ื x nde(s) /\ tr(phi,[sx]) (ื›ืžืช / nde
ื ื•ึผืกื—ึธื”). ื”ืชืจื’ื•ื ืขื‘ื•ืจ ื ื•ืกื—ืื•ืช ืชื™ื‘ื” ืžื•ื’ื“ืจ ื›ืคื•ืœ. ื”ื’ื“ืจืช ื”ื“ื’ืœ ื”ื–ื” ื”ื™ื
ืžืฉืžืขื•ืชื™ ืจืง ื›ืืฉืจ ื”ื“ื’ืœ ืขื‘ื•ืจ ืฉื™ื˜ืช ื”ืชืจื’ื•ื ื”ืคื•ื ืงืฆื™ื•ื ืœื™ ืื• ืคื•ื ืงืฆื™ื•ื ืœื™ ืœืžื—ืฆื”
ืžื•ื’ื“ืจ. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 1.

-EMLFuncNary
ืื ืžื•ื’ื“ืจ, ื ืขืฉื” ืฉื™ืžื•ืฉ ื‘ืชืจื’ื•ื ื”ืคื•ื ืงืฆื™ื•ื ืœื™ ืœืœื•ื’ื™ืงื” ืžื—ื•ืจืจืช. ื–ื” ืื•ืžืจ n-ary
ื ืขืฉื” ืฉื™ืžื•ืฉ ื‘ืกืžืœื™ื ืฉืœ ืคืจื“ื™ืงื˜ื™ื ื‘ืžืงื•ื ื‘ืกืžืœื™ื ื•ื‘ื ืชื™ื‘ื™ื ืฉืœ ืคืจื“ื™ืงื˜ื™ื. ืžื’ื“ื™ืจ ืืช ื–ื”
ื”ื“ื’ืœ ื”ื•ื ื‘ืขืœ ืžืฉืžืขื•ืช ืจืง ืœื‘ื“ื™ืงืช ืฉื‘ื™ืขื•ืช ืจืฆื•ืŸ/ืชืงืคื•ืช ืžืงื•ืžื™ืช ื‘-K multi-modal.
ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-EMLFFSorts
ืื ืžื•ื’ื“ืจ, ื ืขืฉื” ืฉื™ืžื•ืฉ ื‘ืžื™ื•ืŸ ืœืžื•ื ื—ื™ื. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-EMLElimComp
ืื ืžื•ื’ื“ืจ, ื ืกื” ืœื‘ื˜ืœ ืืช ื”ื”ืจื›ื‘ ื”ื™ื—ืกื™ ื‘ืคืจืžื˜ืจื™ื ืžื•ื“ืืœื™ื™ื. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-EMLPTrans
ืื ืžื•ื’ื“ืจ, ื”ืชืจื’ื•ื ื”ืœื•ื’ื™ ืฉืœ EML ืœืกื“ืจ ืจืืฉื•ืŸ ืžืชื•ืขื“. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-TPTP
ืื ืžื•ื’ื“ืจ, SPASS ืžืฆืคื” ืœืงื•ื‘ืฅ ืงืœื˜ ื‘ืชื—ื‘ื™ืจ TPTP. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

-rf ืื ืžื•ื’ื“ืจ, SPASS ืžื•ื—ืง ืืช ืงื•ื‘ืฅ ื”ืงืœื˜ ืœืคื ื™ ืกื™ื•ื. ื‘ืจื™ืจืช ื”ืžื—ื“ืœ ื”ื™ื 0.

ื“ื•ื’ืžืื•ืช


ื›ื“ื™ ืœื”ืคืขื™ืœ SPASS ืขืœ ืงื•ื‘ืฅ ื‘ื•ื“ื“ ืœืœื ืืคืฉืจื•ื™ื•ืช:

SPASS I

ื›ื“ื™ ืœื”ืฉื‘ื™ืช ืืช ื›ืœ ืคืœื˜ SPASS ืžืœื‘ื“ ื”ืชื•ืฆืื” ื”ืกื•ืคื™ืช:

SPASS -PGiven=0 -Pื‘ืขื™ื”=0 I

ืื•ืจื™ื


ื ื™ืชืŸ ื’ื ืœืฆื™ื™ืŸ ืืคืฉืจื•ื™ื•ืช ืขื‘ื•ืจ SPASS ื‘ื‘ืขื™ื™ืช ื”ืงืœื˜. ื‘ืชื—ื‘ื™ืจ DFG, ื”ื™ื™ืช ืขื•ืฉื” ื–ืืช
ืœื”ืฉืชืžืฉ

list_of_settings(SPASS).
{*
set_flag(DocProof,1).
*}
ืกื•ืฃ_ื”ืจืฉื™ืžื”.

ื›ื“ื™ ืœื”ื’ื“ื™ืจ ืืช ื“ื’ืœ DocProof.

ื™ืฉื ื ืฉืœื•ืฉื” ืกื•ื’ื™ ืืคืฉืจื•ื™ื•ืช ืฉืืชื” ื™ื›ื•ืœ ืœื”ื’ื“ื™ืจ ื‘ืงืœื˜:

set_flag( , ).
ืžื’ื“ื™ืจ ื“ื’ืœ ืœืขืจืš. ื“ื’ืœื™ื ื•ืขืจื›ื™ื ื—ื•ืงื™ื™ื ืžืชื•ืืจื™ื ื‘ืกืขื™ืฃ ืืคืฉืจื•ื™ื•ืช.

set_precedence( ).
ืงื•ื‘ืข ืืช ื”ืขื“ื™ืคื•ืช ืœืกืžืœื™ื ื”ืจืฉื•ืžื™ื. ื”ืขื“ื™ืคื•ืช ื”ื•ืœื›ืช ื•ืคื•ื—ืชืช ืžืฉืžืืœ ืœ
ื™ืžื™ืŸ, ื›ืœื•ืžืจ ืœืกืžืœ ื”ืฉืžืืœื™ ื‘ื™ื•ืชืจ ื™ืฉ ืืช ื”ืขื“ื™ืคื•ืช ื”ื’ื‘ื•ื”ื” ื‘ื™ื•ืชืจ.

ืœื›ืœ ืขืจืš ื‘ืจืฉื™ืžื” ื™ืฉ ืืช ื”ื˜ื•ืคืก

ืกืžืœ | (ืกืžืœ, ืžืฉืงืœ [, {l, r, m}])

ืืชื” ื™ื›ื•ืœ ืœื”ืฉืชืžืฉ ื‘ื˜ื•ืคืก ื”ืฉื ื™ ื›ื“ื™ ืœื”ืงืฆื•ืช ืžืฉืงืœื™ื ืœืกืžืœื™ื (ืขื‘ื•ืจ KBO) ืื• ืกื˜ื˜ื•ืก (ืขื‘ื•ืจ
RPOS). ื”ืžืฆื‘ ื”ื•ื @t{l} ืขื‘ื•ืจ ืžืฉืžืืœ ืœื™ืžื™ืŸ, @t{m} ืขื‘ื•ืจ multiset, ืื• @t{r} ืขื‘ื•ืจ
ืžื™ืžื™ืŸ ืœืฉืžืืœ. ื”ืžืฉืงืœ ื ื™ืชืŸ ื›ืžืกืคืจ ืฉืœื.

set_DomPred( ).
ืคืจื™ื“ื™ืงื˜ ืจืฉื•ื (DomPred ืขื‘ื•ืจ ืคืจื™ื“ื™ืงื˜ ื“ื•ืžื™ื ื ื˜ื™) ืกืžืœื™ื ืžืกื•ื“ืจื™ื ืชื—ื™ืœื” ืœืคื™
ืขื“ื™ืคื•ืชื, ืœื ืœืคื™ ืจืฉื™ืžื•ืช ื”ื˜ื™ืขื•ื ื™ื ืฉืœื”ื. ืจืง ื‘ืžืงืจื” ืฉืœ ืฉื•ื•ื”
ืคืจื“ื™ืงื˜ื™ื, ื”ื˜ื™ืขื•ื ื™ื ื ื‘ื“ืงื™ื. ืœืžืฉืœ, ืื ื ื•ืกื™ืฃ ืืช ื”ืืคืฉืจื•ืช

set_DomPred(P).

ื•ืื– ื‘ืกืขื™ืฃ

-> R(f(x,y),a), P(x,a).

ื”ืื˜ื•ื P(x,a) ื”ื™ื ืžืงืกื™ืžืœื™ืช ื‘ื”ื—ืœื˜. ืคืจื“ื™ืงื˜ื™ื ื”ืžืคื•ืจื˜ื™ื ืขืœ ื™ื“ื™ set_DomPred ืืคืฉืจื•ืช ื”ื
ื‘ื”ืฉื•ื•ืื” ืœืคื™ ื”ืขื“ื™ืคื•ืช.

set_selection( ).
ืžื’ื“ื™ืจ ืืช ืจืฉื™ืžืช ื”ื‘ื—ื™ืจื” ืฉื ื™ืชืŸ ืœื”ืคืขื™ืœ ืขืœ ื™ื“ื™ ื“ื’ืœ ื”ื‘ื—ื™ืจื” (ืจืื” ืœืžืขืœื”).

set_ClauseFormulaRelation( , ืจืฆืฃ ืฉืœ
ืžื—ืจื•ื–ื•ืช ืฉื ืืงืกื™ื•ืžื”)).
ืจืฉื™ืžื” ื–ื• ืžื•ื’ื“ืจืช ื‘ืžื™ื•ื—ื“ ืขืœ ื™ื“ื™ FLOTTER ื•ืžืืคืฉืจืช SPASS ืœืžืฉื”ื• ืฉื ืžืฆื ื‘ืกื•ืคื• ืฉืœ ื“ื‘ืจ
ื”ื•ื›ื—ื” ื›ื“ื™ ืœื”ืจืื•ืช ืืช ื”ืงืฉืจ ื‘ื™ืŸ ื”ืกืขื™ืคื™ื ื”ืžืฉืžืฉื™ื ื‘ื”ื•ื›ื—ื” ืœื‘ื™ืŸ ื”ืงืœื˜
ื ื•ืกื—ืื•ืช. ืื ืžืฉื•ืœื‘ื™ื ืขื ืืคืฉืจื•ืช DocProof, ืื– ืฆืจื™ืš ืœื”ื™ื•ืช ืขืจืš ืขื‘ื•ืจ ื›ืœ ืื—ื“
ืžืกืคืจ ืกืขื™ืฃ. ืื—ืจืช ืžื“ื•ื•ื—ืช ืขืœ ืฉื’ื™ืื”.

set_ClauseFormulaRelation((1,ax2),(2,ax1),(3,ax3,ax1)).

ื”ืฉืชืžืฉ ื‘-FLOTTER ื‘ืื™ื ื˜ืจื ื˜ ื‘ืืžืฆืขื•ืช ืฉื™ืจื•ืชื™ onworks.net


ืฉืจืชื™ื ื•ืชื—ื ื•ืช ืขื‘ื•ื“ื” ื‘ื—ื™ื ื

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ืคืงื•ื“ื•ืช ืœื™ื ื•ืงืก

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