Is there any class of software that can help me with the following problem in first order logic: given $\phi$ a formula with a "hole" in it (a subformula which is undetermined) and a particular set of assumptions $\Gamma$, find a formula $\psi$ such that $\phi$ with the hole replaced with $\psi$ can be proved under assumptions in $\Gamma$?
I don't expect to find a solution that works for any formula... I just wonder if there is a class of programs that try to solve this problem.