# Different Theorem Proving System (TPS)

**Theorem Proving System (TPS)** is also known as an automated proving system. Theorem proving that is applied to real-time systems design and verification generally uses several definitions and different theorems to basically help to design, implement, validate, and also verify requirements. These proving methodologies can also provide a greater level specification of software requirements along with detailed description of the implementation. These implementations then might be checked against specification simply to ensure that either it is correct or not. Automated theorem proving generally focuses and aims upon ‘identifying’ or ‘finding’ aspect.

**Different Theorem Prover Systems :**

There are number of theorem prover systems that are good and are related to our work. Some of them are given below :

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**Interactive Mathematical Proof System (IMPS) :**

Main aim of IMPS is simply to provide mechanized support just for traditional techniques of mathematical reasoning. It also provides large primitive inference steps simply to facilitate human control of deductive process and human comprehension of resulting proofs. It is also very strong alternative to PVS and also might have been required for software inspection. Logic of IMPS also allows partial functions and usually undefined terms.**Isabelle :**

Isabelle is basically generic proof assistant or generic theorem-proof system. It usually provides framework in which various logics can be added by simply specifying their syntax and rules of inference. It was initially developed at University of Cambridge and Technische Universitat Munchen. It also provides meta-logic also known as weak type theory that can be required to encode object logics such as First-Order Logic (FOL), Higher-Order Logic (HOL), etc. It is also being considered as tool for implementing various logics and also defining and examining exotic proof systems.**Higher Order Logic (HOL) Theorem Proving System :**

HOL Theorem Prover is basically general and most widely used computer program for construction od specifications and formal proofs in higher-order logic. It is also used as an open platform for general theorem-proving research, and simply as a platform for just formalized mathematics. It also supports reasoning in various areas, along with hardware design and verification, proofs regarding real-time systems, compiler verification, program correctness, and also program refinement. There are basically four different HOL Systems that are handled, maintained, and developed nowadays i.e. HOL4 stems from HOL88 system, HOL Light, ProofPower, and HOL Zero. It is also used as a platform for theorem proving research.**Prototype Verification System (PVS) :**

PVS generally provides mechanized support for formal specification and verification. It is usually prototype system for simply writing specifications and also constructing proofs. PVS is totally implemented and available freely. It also includes a number of predefined theories, theorem prover, different utilities, and documentation. Its specifications are generally organized into parameterized theory. It also provides extremely expressive and natural specifications.**Theorem Prover System (TPS) :**

It is basically developed as a part of program of research on methods of proving theorems of higher-order logic and first-order logic. Rather than PVS, TPS can be required for our work but PVS is more accessible. It also contains formula editor that simply facilitates the construction of new formulas from other formulas that are already known to TPS.