CTL-RP: A computation tree logic resolution prover

1 procedure eres(T, C) 2 // T is a set of clauses 3 // C is a sometime clause Q ⇒ A♦¬l or Q ⇒ E♦¬l〈LC(ind)〉 4 begin 5 if C is an A-sometime clause then 6 SOS := {D | D is a global or step clause in T}; 7 else if C is an E-sometime clause then 8 SOS := {D | D is a global, A-step, or E-step clause with the index ind in T}; 9 end if 10 i := 0; 11 H−1(x) := true; 12 do 13 Goals := {ls(x) ∨ ¬Ql(app(s, x)) ∨ ¬Hi−1(x)σ}, where σ = {x ← app(s, x)}; 14 T1 := resolution sos(SOS, Goals); 15 T2 := {G(x) | G(x) ∨ ls(x) ∈ T1 and depth(G(x)) ≤ 1}; 16 Hi(x) := ¬( ∧ T2); 17 if Hi(x) is equivalent to true then 18 return eresolvent(C, true); 19 else if Hi(x) is equivalent to false then 20 return ∅ 21 else if Hi(x) is equivalent to Hi−1(x) then 22 return eresolvent(C, Hi(x)); 23 end if 24 i := i+1; 25 while (T2 6= ∅) 26 end Comparison to TWB (1)