Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  report on a project to use a theorem prover to find proofs of the theorems in Tarskian geometry. These theorems start with fundamental properties of betenness, proceed through the derivations of several famous theorems due to Gupta and end with the derivation from Tarski’s axioms of Hilbert’s 1899 axioms for geometry. They include the four challenge problems left unsolved by Quaife, who two decades ago found some OTTER proofs in Tarskian geometry (solving challenges issued in Wos’s 1998 book). There are 212 theorems in this collection.  re able to find OTTER proofs of all these theorems.  developed a methodology for the automated preparation and checking of the input files for those theorems, to ensure that no human error has corrupted the formal development of an entire theory as embodied in two hundred input files and proofs.  distinguish beten proofs that re found completely mechanically (without reference to the steps of a book proof) and proofs that re constructed by some technique that involved a human knowing the steps of a book proof. Proofs of length 40–100, roughly speaking, are difficult exercises for a human, and proofs of 100–250 steps belong in a Ph.D. thesis or publication. 29 of the proofs in our collection are longer than 40 steps, and ten are longer than 90 steps.  re able to derive completely mechanically all but 26 of the 183 theorems that have “short” proofs (40 or fer deduction steps).  found proofs of the rest, as ll as the 29 “hard” theorems, using a method that requires consulting the book proof at the outset. Our “subformula strategy” enabled us to prove four of the 29 hard theorems completely mechanically. These are Ph.D. level proofs, of length up to 108.
['Michael J. Beeson', 'Larry Wos']
I am writing a research paper on a idea Finding Proofs in Tarskian Geometry
[{"from": "human", "value": "I am writing a research paper on a idea Finding Proofs in Tarskian Geometry"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  report on a project to use a theorem prover to find proofs of the theorems in Tarskian geometry. These theorems start with fundamental properties of betenness, proceed through the derivations of several famous theorems due to Gupta and end with the derivation from Tarski\u2019s axioms of Hilbert\u2019s 1899 axioms for geometry. They include the four challenge problems left unsolved by Quaife, who two decades ago found some OTTER proofs in Tarskian geometry (solving challenges issued in Wos\u2019s 1998 book). There are 212 theorems in this collection.  re able to find OTTER proofs of all these theorems.  developed a methodology for the automated preparation and checking of the input files for those theorems, to ensure that no human error has corrupted the formal development of an entire theory as embodied in two hundred input files and proofs.  distinguish beten proofs that re found completely mechanically (without reference to the steps of a book proof) and proofs that re constructed by some technique that involved a human knowing the steps of a book proof. Proofs of length 40\u2013100, roughly speaking, are difficult exercises for a human, and proofs of 100\u2013250 steps belong in a Ph.D. thesis or publication. 29 of the proofs in our collection are longer than 40 steps, and ten are longer than 90 steps.  re able to derive completely mechanically all but 26 of the 183 theorems that have \u201cshort\u201d proofs (40 or fer deduction steps).  found proofs of the rest, as ll as the 29 \u201chard\u201d theorems, using a method that requires consulting the book proof at the outset. Our \u201csubformula strategy\u201d enabled us to prove four of the 29 hard theorems completely mechanically. These are Ph.D. level proofs, of length up to 108."}]