DeepSeek: Turns the proposition into a script in first-order format (fof) for use by the Vampire theorem prover.
To represent the argument in First-Order Form (FOF) for the Vampire theorem prover, we formalize the premises and conclusion using TPTP syntax. The key steps include:
- Declaring constants for "god" and "jesus"
- Defining predicates: `created` (created the universe) and `man` (is a man)
- Using equality (`=`) to represent identity
- Negating the conclusion (as required for theorem proving)
**FOF Script for Vampire:**
Code: Select all
```tptp
fof(premise1, axiom, created(god)). % God created the universe
fof(premise2, axiom, jesus = god). % Jesus is God
fof(premise3, axiom, man(jesus)). % Jesus is a man
fof(negated_conclusion, conjecture, % Negate: "a man created the universe"
~? [X] : (man(X) & created(X))). % (No man created the universe)
```
**Explanation:**
1. **Premise 1:** `created(god)`
- `god` is a constant; `created` is a unary predicate.
2. **Premise 2:** `jesus = god`
- Uses equality to state Jesus and God are identical.
3. **Premise 3:** `man(jesus)`
- Applies the `man` predicate to Jesus.
4. **Negated Conclusion:** `~? [X] : (man(X) & created(X))`
- Asserts there exists **no** `X` who is both a man and created the universe.
**Validity Verification:**
- Vampire will derive a **contradiction** from these axioms:
1. Substitute `jesus` for `god` in `created(god)` (using `jesus = god`), yielding `created(jesus)`.
2. Combine `created(jesus)` and `man(jesus)` to prove `? [X] : (man(X) & created(X))`.
3. This contradicts the negated conclusion, confirming the original argument is **valid**.
**Output Expectation:**
Vampire will return `THM` (theorem proven), verifying that the conclusion follows logically from the premises.