### Table 4. Theorem prover results: Percentage of solved proof tasks and total ATP-times.

"... In PAGE 14: ...2. Running the Theorem Provers Table4 summarizes the results obtained from running the theorem provers on all proof obligations (except for the two invalid obligations from the inuse-policy). For the prover families E-Setheo and Vampire, however, the table only contains entries for the best vari- ants, E-Setheo-03n and Vampire 6.... In PAGE 16: ...3. Comparing Prover Variants The results in Table4 indicate there is no single best theorem prover. Even variants of the same prover can differ widely in their results.... ..."

### Table 4. Comparing Combinations of Provers on the uHOL Problem Set.

in NASA/CP-2003-212448 Design and Application of Strategies/Tactics in Higher Order Logics Edited by

2003

"... In PAGE 58: ... All descriptor lists are then concatenated to build a single list before substitutions are performed. Table4 lists the strategies provided; several are discussed below. I invoke command amp;rest expr-specs This strategy is used to invoke command after applying substitutions extracted by evaluating the expression specifications expr-specs.... In PAGE 59: ...52 Ben L. Di Vito Table4 . Summary of higher-order strategies Syntax Function (invoke command amp;rest expr-specs) Invoke command by instantiating (for-each command amp;rest expr-specs) Instantiate and invoke separately (f or-each-rev command amp;rest expr-specs) Invoke in reverse order (show-subst command amp;rest expr-specs) Show but don apos;t invoke the (claim cond amp;opt (try-just nil) Claims condition on terms (name-extract name amp;rest expr-specs) from expressions and patterns for each expression instantiated command amp;rest expr-specs) Extract amp; name expr, then replace (invoke (case It%, lt;= %2 quot;) (? 3 quot;f(%l) lt;= f(%2) quot;)) would apply pattern matching to formula 3 to create bindings %I= quot;x! 1 + y ! 1 quot; and %2 = quot;a! 1 * (z! 1 + 1) It, which would result in the prover command (case quot;x!l + y!l lt;= a!l * (z!l + 1) quot;) being invoked.... ..."

### Table 4: Prover performmme

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### Table 6: A Larch Prover Sample Proof

2001

"... In PAGE 11: ...able 5: Formal Specification for Composite System................................................. 71 Table6 : A Larch Prover Sample Proof .... ..."

### Table 3: Summary of Propositional Logic Theorem Provers

1996

"... In PAGE 30: ....1.1.5 Summary of Propositional logic theorem proving The following Table3 is a summary of the theorem provers just described. The information is based on readings from [17, 19, 16, 5, 12]... ..."

### Table 4. Experiments with cooperating theorem provers

"... In PAGE 7: ...s in Section 3.2. All in all, we tackled 81 provable problems. Results can be found in Table4 . Results of SPASS, SETHEO using the weighted depth bound (SETHEO wd), and SETHEO using the depth bound (SETHEO d) are displayed in columns 2{4.... In PAGE 7: ...Table 4. Experiments with cooperating theorem provers Table4 reveals the high potential of cooperation. The number of solved problems could be increased, additionally the runtimes could be decreased.... ..."

### Table 3. An exercise using an external theorem prover

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### Table 3. An exercise using an external theorem prover

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### Table 5: Experiments with cooperating theorem provers

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### Table 1. Prover commands for strategy-based proofs. Class No. of formulas Prover command

"... In PAGE 7: ...2. Table1 shows the PVS prover commands used Table 1. Prover commands for strategy-based proofs.... ..."