
AutoToS prompt:

Logical deduction is performed by applying rules of the form if X then Y to our current knowledge about a world, extending our knowledge with each single rule application. 
A rule if X then Y is applicable if we know X. If a state is defined as our current knowledge of the world, how are successor states defined, given a collection of rules? Please think step by step. Then, provide only the Python implementation for the successor function that receives a state and rules and returns a list of successor states.

Example initial state: {"integer"}
Example rules: [("integer", "real number"), ("integer", "float")]

Model response:
```python
def successor_states(state, rules):
    """
    Generate successor states based on the current state and the provided rules.

    :param state: Set of strings representing the current state.
    :param rules: List of tuples where each tuple represents a rule (X, Y).
    :return: List of sets representing all successor states.
    """
    successors = []

    for X, Y in rules:
        if X in state:
            new_state = set(state)
            new_state.add(Y)
            if new_state != state:
                successors.append(new_state)

    return successors
```

AutoToS prompt:

Provide only the Python function for the goal test function that tests, given a target fact, whether a state is a goal state. 

Model response:
```python
def is_goal_state(state, target_fact):
    """
    Test whether the given state is a goal state containing the target fact.

    :param state: Set of strings representing the current state.
    :param target_fact: String representing the target fact.
    :return: Boolean indicating whether the state is a goal state.
    """
    return target_fact in state
```

System message:
Goal Soundness Test Passed
Soundness test

System message:
Successor States Soundness Test Passed
Completeness test
Successor Completeness Test Passed
Success: 4000, failure: 0, total expansions 85837, total evaluations 169779
