Selectively instantiating definitions

The CADE ATP System Competition — CASC

“…• Dual instantiation of definitions, and generating substitutions for higher-order variables which contain abbreviations already present in the theorem to be proved [BA98].…”

Definitional Expansions in Mizar

“…when ¬α is a premise, then it is expanded to α ∨α, wherê α is the definitional expansion of the α. Expanding a formula conjunctively or disjunctively depending on its sign (dual instantiation, [5]) creates more premises accessible to VERI-FIER. Still, the satisfiability of the original formula is preserved, since α is satisfiable if and only if α ∧ α is satisfiable, and α is satisfiable if and only if α ∨ α is satisfiable.…”

“…However, they should be used carefully. Too deep expanding can lead to producing a huge number of premises, make the search space unmanageable and systems useless in practice [5,18].…”

TPS: A hybrid automatic-interactive system for developing proofs

“…Using the command PIY2 ("Prove It Yourself, version 2"), DIY2, or DIY2-L, one can direct TPS to apply its proof procedures with each of these 68 modes in turn for a specified time, then increment the time limit and repeat the process, and continue in this way until a proof is found or space or patience is exhausted. Since TPS can prove many theorems of moderate difficulty within a few seconds (see [3,[8][9][10][11][12] for some examples), this makes TPS extremely convenient to use for filling in gaps of moderate difficulty while one is constructing a major proof semi-interactively.…”