Indirect Proof Negated Goal Assumption Validator
Check an atomic classical indirect-proof initial assumption against negated goal; does not establish contradiction or validate proof completion.
Description
Indirect Proof Negated Goal Assumption Validator: return matches negated goal assumption, contradiction or proof established.
An indirect proof may begin by assuming the negation of its intended goal. That opening assumption alone is not a contradiction or a completed proof.
This tool returns matches negated goal assumption, contradiction or proof established. Use the stated units and model convention when interpreting these fields.
When to use this tool
Use this tool when the supplied inputs match the specific operation described above and you need a repeatable result under its stated convention.
- Check the supported input and output contract against an existing calculation or observation.
- Use the complete example to confirm units, selector spelling and result interpretation.
How to use the tool and how it works
- Enter every field in the input table using the stated units and the exact supported selector spelling where applicable.
- Run the tool. Correct input errors before interpreting an output.
- Read the result fields below; use accompanying flags and the stated sign, boundary or model convention when interpreting a number.
Validate an uppercase goal atom and a literal. Compare the literal exactly with ! followed by the goal atom.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| goalAtom | Goal atom. | Text |
| assumedLiteral | Assumed literal. | Text |
| Output field | Interpretation |
|---|---|
| result | Object containing the following named result fields. |
| result.matchesNegatedGoalAssumption | Matches negated goal assumption flag under the exact conditions described above. |
| result.contradictionOrProofEstablished | Always false; the check concerns one proposed assumption. |
{
"input": {
"goalAtom": "P",
"assumedLiteral": "!P"
},
"output": {
"result": {
"matchesNegatedGoalAssumption": true,
"contradictionOrProofEstablished": false
}
}
}Limitations and assumptions
- contradictionOrProofEstablished remains false; the rest of the argument is outside this check.
- Every declared field is required and unexpected fields are rejected. Numeric inputs must be finite; input errors are distinct from a valid false result or an explicitly qualified output.
- Extremely large inputs and nonfinite or excessively large outputs are rejected. List positions reported by the tool use zero-based indices unless stated otherwise.
Alternative or Complementary methods
Check the underlying observations, units and conventions independently before using the result in a larger workflow. The tools listed below address nearby tasks; compare their inputs and scope before substituting one for this operation.
References
Similar or alternative tools
- addition rule step validator
Disjunction introduction adds another possible disjunct to an affirmed premise.
- Conditional Proof Assumption Discharge Depth Tracker
Track nested begin(+1), neutral(0), discharge(-1) assumption events; not a validation of formulas or implication-introduction proof.