TPTP Documents File: AxiomList


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Axioms 1209 sets (152 abstract, 131 CNF, 1039 FOF, 8 TFF, 39 THF)
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AGT001 ( -0 +3 _0 ^0) CPlanT system
ALG001 ( -1 +0 _0 ^0) Abstract algebra axioms, based on Godel set theory
ALG002 ( -0 +1 _0 ^0) Median algebra axioms
ALG003 ( -0 +0 _0 ^1) Untyped lambda sigma calculus
ANA001 ( -1 +0 _0 ^0) Analysis (limits) axioms for continuous functions
ANA002 ( -1 +0 _0 ^0) Analysis (limits) axioms for continuous functions
ANA003 ( -1 +0 _0 ^0) A theory of Big-O notation
BIO001 ( -0 +1 _0 ^0) Textbook biology
BOO001 ( -1 +0 _0 ^0) Ternary Boolean algebra (equality) axioms
BOO002 ( -1 +0 _0 ^0) Boolean algebra axioms
BOO003 ( -1 +0 _0 ^0) Boolean algebra (equality) axioms
BOO004 ( -1 +0 _0 ^0) Boolean algebra (equality) axioms
CAT001 ( -1 +0 _0 ^0) Category theory axioms
CAT002 ( -1 +0 _0 ^0) Category theory (equality) axioms
CAT003 ( -1 +0 _0 ^0) Category theory axioms
CAT004 ( -1 +0 _0 ^0) Category theory axioms
COL001 ( -1 +0 _0 ^0) Type-respecting combinators
COL002 ( -2 +0 _0 ^0) Combinators
COM001 ( -0 +2 _0 ^0) Common axioms for progress/preservation proof
CSR001 ( -0 +4 _0 ^0) Standard discrete event calculus axioms
CSR002 ( -0 +6 _0 ^0) 0 axioms from Cyc
CSR003 ( -0 +6 _0 ^0) SUMO
CSR004 ( -0 +1 _0 ^0) LogAnswer
CSR005 ( -0 +0 _0 ^1) SUMO
DAT001 ( -0 +0 _1 ^0) Integer arrays
DAT002 ( -0 +0 _2 ^0) Integer collections
DAT003 ( -0 +0 _1 ^0) Pointer data types
DAT004 ( -0 +0 _1 ^0) Array data types
DAT005 ( -0 +0 _1 ^0) Heap data types
DAT006 ( -0 +0 _1 ^0) Tree-heap data types
FLD001 ( -1 +0 _0 ^0) Ordered field axioms (axiom formulation glxx)
FLD002 ( -1 +0 _0 ^0) Ordered field axioms (axiom formulation re)
GEO001 ( -2 +0 _0 ^0) Tarski geometry axioms
GEO002 ( -4 +0 _0 ^0) Tarski geometry axioms
GEO003 ( -1 +0 _0 ^0) Hilbert geometry axioms
GEO004 ( -4 +4 _0 ^0) Simple curve axioms
GEO005 ( -1 +0 _0 ^0) Hilbert geometry axioms, adapted to respect multi-sortedness
GEO006 ( -0 +7 _0 ^0) Apartness geometry
GEO007 ( -0 +2 _0 ^0) Ordered affine geometry
GEO008 ( -0 +1 _0 ^0) Apartness geometry
GEO009 ( -0 +1 _0 ^0) Ordered affine geometry with definitions
GEO010 ( -0 +2 _0 ^0) Flyspeck project
GEO011 ( -0 +1 _0 ^0) Tarskian geometry
GRA001 ( -0 +1 _0 ^0) Directed graphs and paths
GRP001 ( -1 +0 _0 ^0) Monoid axioms
GRP002 ( -1 +0 _0 ^0) Semigroup axioms
GRP003 ( -3 +1 _0 ^0) Group theory axioms
GRP004 ( -3 +1 _0 ^0) Group theory (equality) axioms
GRP005 ( -1 +0 _0 ^0) Group theory axioms
GRP006 ( -1 +0 _0 ^0) Group theory (Named groups) axioms
GRP007 ( -0 +1 _0 ^0) Group theory (Named Semigroups) axioms
GRP008 ( -2 +0 _0 ^0) Semigroups axioms
HAL001 ( -0 +1 _0 ^0) Standard homological algebra axioms
HEN001 ( -1 +0 _0 ^0) Henkin model axioms
HEN002 ( -1 +0 _0 ^0) Henkin model axioms
HEN003 ( -1 +0 _0 ^0) Henkin model (equality) axioms
HWC001 ( -1 +0 _0 ^0) Definitions of AND, OR and NOT
HWC002 ( -1 +0 _0 ^0) Definitions of AND, OR and NOT
HWV001 ( -3 +0 _0 ^0) Connections, faults, and gates.
HWV002 ( -3 +0 _0 ^0) Connections, faults, and gates.
HWV003 ( -1 +0 _0 ^0) Axioms from a VHDL design description
HWV004 ( -1 +0 _0 ^0) Axioms from a VHDL design description
KLE001 ( -0 +8 _0 ^0) Idempotent semirings
KLE002 ( -0 +1 _0 ^0) Kleene algebra
KLE003 ( -0 +1 _0 ^0) Omega algebra
KLE004 ( -0 +1 _0 ^0) Demonic Refinement Algebra
KRS001 ( -0 +2 _0 ^0) SZS success ontology nodes
LAT001 ( -5 +0 _0 ^0) Lattice theory (equality) axioms
LAT002 ( -1 +0 _0 ^0) Lattice theory axioms
LAT003 ( -1 +0 _0 ^0) Ortholattice theory (equality) axioms
LAT004 ( -1 +0 _0 ^0) Quasilattice theory (equality) axioms
LAT005 ( -1 +0 _0 ^0) Weakly Associative Lattices theory (equality) axioms
LAT006 ( -3 +0 _0 ^0) Tarski's fixed point theorem (equality) axioms
LCL001 ( -3 +0 _0 ^0) Wajsberg algebra
LCL002 ( -2 +0 _0 ^0) Alternative Wajsberg algebra
LCL003 ( -1 +0 _0 ^0) Propositional logic deduction
LCL004 ( -3 +0 _0 ^0) Propositional logic deduction
LCL005 ( -1 +0 _0 ^0) Propositional logic
LCL006 ( -0 +6 _0 ^0) Propositional logic rules and axioms
LCL007 ( -0 +7 _0 ^0) Propositional modal logic rules and axioms
LCL008 ( -0 +0 _0 ^1) Multi-Modal Logic
LCL009 ( -0 +0 _0 ^1) Translating constructive S4 (CS4) to bimodal classical S4 (BS4)
LCL010 ( -0 +0 _0 ^1) Propositional intuitionistic logic in HOL
LCL011 ( -0 +0 _0 ^1) Propositional intuitionistic logic in HOL
LCL012 ( -0 +0 _0 ^1) Propositional intuitionistic logic in HOL
LCL013 ( -0 +0 _0 ^7) Embedding of quantified multimodal logic in simple type theory
LCL014 ( -0 +0 _0 ^1) Region Connection Calculus
LCL015 ( -0 +0 _0 ^2) Embedding of quantified multimodal logic in simple type theory
LCL016 ( -0 +0 _0 ^2) Embedding of second order modal logic in simple type theory
LCL017 ( -0 +0 _0 ^1) Embedding of second order modal logic S5 with universal access
LDA001 ( -1 +0 _0 ^0) Embedding algebra
MAT001 ( -0 +0 _0 ^1) Untyped lambda sigma calculus
MED001 ( -0 +2 _0 ^0) Physiology Diabetes Mellitus type 2
MED002 ( -0 +1 _0 ^0) Medical subject headings
MGT001 ( -1 +1 _0 ^0) Inequalities.
MSC001 ( -3 +0 _0 ^0) Sets, numbers, lists, etc, that make up the Isabelle/HOL library
NLP001 ( -0 +1 _0 ^0) Wordnet
NUM001 ( -3 +0 _0 ^0) Number theory axioms
NUM002 ( -1 +0 _0 ^0) Number theory (equality) axioms
NUM003 ( -1 +0 _0 ^0) Number theory axioms, based on Godel set theory
NUM004 ( -1 +0 _0 ^0) Number theory (ordinals) axioms, based on NBG set theory
NUM005 ( -0 +3 _0 ^0) Translating from nXXX to rdn notation
NUM006 ( -0 +0 _0 ^1) Church Numerals in Simple Type Theory
NUM007 ( -0 +0 _0 ^5) Grundlagen preliminaries
PHI001 ( -0 +0 _0 ^1) Axioms for Goedel's Ontological Proof of the Existence of God
PLA001 ( -2 +0 _0 ^0) Blocks world axioms
PLA002 ( -0 +1 _0 ^0) Blocks world axioms
PRD001 ( -0 +1 _0 ^0) Wine facts
PUZ001 ( -1 +0 _0 ^0) Mars and Venus axioms
PUZ002 ( -1 +0 _0 ^0) Truthtellers and Liars axioms for two types of people
PUZ003 ( -1 +0 _0 ^0) Truthtellers and Liars axioms for three types of people
PUZ004 ( -1 +0 _0 ^0) Quo vadis axioms
PUZ005 ( -1 +1 _0 ^0) Sudoku axioms
PUZ006 ( -0 +1 _0 ^0) Sudoku axioms
QUA001 ( -0 +0 _0 ^2) Quantales
REL001 ( -2 +2 _0 ^0) Relation Algebra
RNG001 ( -1 +0 _0 ^0) Ring theory axioms
RNG002 ( -1 +0 _0 ^0) Ring theory (equality) axioms
RNG003 ( -1 +0 _0 ^0) Alternative ring theory (equality) axioms
RNG004 ( -1 +0 _0 ^0) Alternative ring theory (equality) axioms
RNG005 ( -1 +0 _0 ^0) Ring theory (equality) axioms
ROB001 ( -2 +0 _0 ^0) Robbins algebra axioms
SET001 ( -4 +0 _0 ^0) Membership and subsets
SET002 ( -1 +0 _0 ^0) Set theory axioms
SET003 ( -1 +0 _0 ^0) Set theory axioms based on Godel set theory
SET004 ( -2 +0 _0 ^0) Set theory axioms based on NBG set theory
SET005 ( -0 +1 _0 ^0) Set theory axioms based on NBG set theory
SET006 ( -0 +5 _0 ^0) Naive set theory based on Goedel's set theory
SET007 ( -0+930 _0 ^0) Mizar Built-in Notions
SET008 ( -0 +0 _0 ^3) Basic set theory definitions
SET009 ( -0 +0 _0 ^1) Binary relations
SWB001 ( -0 +1 _0 ^0) OWL 2 Full
SWB002 ( -0 +1 _0 ^0) ALCO Full Extensional
SWB003 ( -0 +2 _0 ^0) RDFS
SWC001 ( -1 +1 _0 ^0) List specification
SWV001 ( -1 +0 _0 ^0) Program verification axioms
SWV002 ( -1 +0 _0 ^0) Program verification axioms
SWV003 ( -0 +1 _0 ^0) NASA software certification axioms
SWV004 ( -1 +0 _0 ^0) Cryptographic protocol axioms for messages
SWV005 ( -8 +0 _0 ^0) Cryptographic protocol axioms for messages
SWV006 ( -4 +0 _0 ^0) Cryptographic protocol axioms for public
SWV007 ( -0 +5 _0 ^0) Priority queue checker: quasi-order set with bottom element
SWV008 ( -0 +0 _0 ^3) ICL logic based upon modal logic based upon simple type theory
SWV009 ( -0 +1 _0 ^0) General axioms for access to classified information
SWV010 ( -0 +0 _0 ^1) Translation from Binder Logic (BL) to CS4
SWV011 ( -0 +1 _0 ^0) Axioms for verification of Stoller's leader election algorithm
SWV012 ( -0 +1 _0 ^0) Syntactic definitions of the logical operators 
SWV013 ( -1 +0 _0 ^0) Lists in Separation Logic
SYN000 ( -1 +1 _1 ^1) A simple include file for FOF
SYN001 ( -1 +0 _0 ^0) Synthetic domain theory for EBL
SYN002 ( -0 +1 _0 ^0) Orevkov formula
TOP001 ( -1 +0 _0 ^0) Point-set topology