### Table II. Search complexity for proofs with single construction to the top-level goal Problem First Proof All Proofs

Cited by 4

### Table 1. Some examples run by ABALONE schemes and thereby replaces another search intensive task in theorem proving by induction. In addition, CLAM has a special mechanism for revising incorrect choices of induction schemes. This mechanism is also search intensive and can be applied multiple times in some proofs. We have used analogy to reduce the number of applications and hence reduce the overall search space [9]. We use analogy to override the default planner con guration. Theorem provers generally have a set library of methods to apply. Some methods, however, may be used only rarely and it could be disadvantageous to have these methods available as default. In ABALONE, unusual methods will only be applied when suggested by analogy. This can avoid divergence in the proof planner in certain cases. As an example, consider the normal8 method. The presence of this method 8 normal removes the implication from an implicational goal and appends the ante-

"... In PAGE 6: ... This precondition can be dropped in some cases. zerotimes1-zerotimes3 in Table1 is an example.6 In the planning of zerotimes1 x is replaced by 0 in times(x; y) via the equal method.... In PAGE 7: ... It has been tested on a wide range of examples. We include a selection in Table1 . In addition to these, [10] gives another 30 examples.... In PAGE 9: ...We use normal only when suggested by analogy. For instance, cnc half in Table1 is such that CLAM can only prove it when normal is present. By using analogy with cnc plus, the normal method can be incorporated without fear of divergence.... ..."

### Table 2. Proof System

2004

"... In PAGE 8: ... We now see that it also forms the basis of a sound and complete proof theory, and a decision procedure based on proof-search. The rules of the proof system are shown in Table2 . Since there is no Cut rule, the rules have a rather odd form.... ..."

Cited by 34

### Table 2. Proof System

2004

"... In PAGE 8: ... We now see that it also forms the basis of a sound and complete proof theory, and a decision procedure based on proof-search. The rules of the proof system are shown in Table2 . Since there is no Cut rule, the rules have a rather odd form.... ..."

Cited by 34

### Table 2. Proof System

2004

"... In PAGE 8: ... We now see that it also forms the basis of a sound and complete proof theory, and a decision procedure based on proof-search. The rules of the proof system are shown in Table2 . Since there is no Cut rule, the rules have a rather odd form.... ..."

Cited by 34

### Table 2. Proof System

2004

Cited by 34

### Table 2. Proof System

2004

Cited by 34

### Table 2. Proof System

2004

Cited by 34

### Table 3. Full proof with induction: conflicts, globally true, and simultaneous faslification data

"... In PAGE 17: ... Tables 3 and 4 both originate from the same model-checking runs (simultaneous induction). In Table3 we report the data showing the impact of several advanced features of the SSAT algorithm that do not exist in PISAT and FISAT. The POs in SSAT represent the base and step formulas at different depths.... ..."

### Table 3. Full proof with induction: conflicts, globally true, and simultaneous faslification data.

"... In PAGE 13: ... Tables 3 and 4 both originate from the same model-checking runs (simultaneous induction). In Table3 we report the data showing the impact of several advanced features of the SSAT algorithm that do not exist in PISAT and FISAT. The POs in SSAT represent the base and step formulas at different depths.... ..."