The TPTP language supports a hierarchy of logics from propositional up to dependently types higher-order logic, and non-classical logics. Each logic uses a variant of the TPTP language, to express features of formulae in the logic, thus leading to a family of TPTP languages. All the languages are expressed in a Prolog-based syntax, with each logical formula wrapped in an "annotated formula" record, with one of four principle symbols. From the TFF level upwards, all the languages use the TPTP type system, with increasingly more powerful constructs, with monomorphic (ending in '0') and polymorphic (ending in '1') variants. All the typed languages include arithmetic constructs.
TLA
PRP
CNF
FOF
TFF
TXF
THF
DHF
NXF
NHF
NTF
Logic
Propositional
Clause Normal Form
First-Order Form
Typed FOF
Typed eXtended FOF
Typed HIgher-order Form
Dependently THF
Non-classical TXF
Non-Classical THF
Non-classical Typed Form
AFS
fof
cnf
fof
tff
tff
thf
thf
tff
thf
-
Mono/Poly
-
-
-
TF0/TF1
TX0/TX1
TH0/TH1
DH0/DH1
NX0/NX1
NH0/NH1
NXF & NHF