We also describe the proofs of two examples coming from the TPTP library and produced by this tool, and which are quite comprehensible as well.
As the Super Zenon tool is able to deal with any first order theory, it can be used in many contexts, and in particular, it can be applied to all the first order problems of the TPTP library  (about 6,600 problems), which is a library of test problems for automated theorem proving systems.
Figure 3: Proof of Puzzle #132 of TPTP fof(washington_conjecture, conjecture, (beautiful (washington) & has_crime (washington))).
As a second example of proof, we consider a problem coming from the geometry category of the TPTP library.
The proof of this example uses the following axioms of this theory (we use the names given in the TPTP files):
Figure 4: Proof of Geometry Problem #170+3 of TPTP (Part 1) fof(geometry_conjecture, conjecture, (!
We have also provided some examples of problems, which can be handled by these tools and which come from different theories, such as the B set theory or theories of the TPTP library (in the puzzle and geometry categories, in particular).
For example, Vampire is founded on the theoretical principles of superposition, has a highly efficient implementation in C++ using code trees and advanced structures for representing logical data, is repeatedly tested and tuned on the TPTP problem library, and has special modes for the various divisions of CASC.
Decisions made for CASC (alongside the TPTP) have had an influence on the directions of development in ATP.
CASC-20, 2005, required systems to develop built-in equality reasoning, by removing the equality axioms from all TPTP problems.
Over the years TPTP and CASC have increasingly been used as a conduit for ATP users to provide samples of their problems to ATP system developers.
His most prominent achievements are the first ever development of a heterogeneous parallel deduction system, leading to the development of the SSCPA automated reasoning system; the development and ongoing maintenance of the TPTP problem library, which is now the de facto standard for testing classical logic automated reasoning systems; the development and ongoing organization of the CADE ATP System Competition--the world championship for classical logic automated reasoning systems; and the specification of the TPTP language standards for automated reasoning tools.