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Proof step 9 from proof INVR-step (previous step)

reach(source, c1, m0), c1 ∈ succ(v), reach(c1, dest, m), dest ∈ succ(c0), reach(source, c0, m + n), reachS(source, C, n), reachS(source, N, n + 1), dest ∈ succ(c), reach(v, c, m), v ∈ C, m0 ≤ n, ∀ a. a = v ∨ ¬ a ∈ C ∨ (∀ c1. ¬ reach(a, c1, m) ∨ ¬ dest ∈ succ(c1)) ∨ reach<(a, dest, m + 1), ∀ b. ¬ b ∈ N ∪ (succ(v) \ V) ∨ ¬ reach(b, dest, m) ∨ reach<(b, dest, m) ⊦ # succ(v) = 0, succ(c0) = ∅, succ(c) = ∅, # C = 0, v = dest, C = ∅, # succ(c0) = 0, # succ(c) = 0, succ(v) = ∅, ∃ m0. m0 < (m + 1) + n ∧ reach(source, dest, m0), reach<(v, dest, m + 1), ∃ b0. ¬ (b0 ∈ V ↔ reach<(source, b0, n + 1) ∨ (∃ a0. b0 ∈ succ(a0) ∧ reach(source, a0, n) ∧ ¬ reach<(source, a0, n) ∧ ¬ a0 ∈ C)), ∃ b0. ¬ ((∃ c. reach(source, c, n) ∧ b0 ∈ succ(c)) ∧ ¬ reach<(source, b0, n + 1) → b0 ∈ N ∨ (∃ a. a ∈ C ∧ b0 ∈ succ(a) ∧ ¬ b0 ∈ V))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
reach(source, c1, m0), c1 ∈ succ(v), reach(c1, dest, m), dest ∈ succ(c0), reach(source, c0, m + n), reachS(source, C, n), reachS(source, N, n + 1), dest ∈ succ(c), reach(v, c, m), v ∈ C, m0 ≤ n, ∀ a. a = v ∨ ¬ a ∈ C ∨ (∀ c1. ¬ reach(a, c1, m) ∨ ¬ dest ∈ succ(c1)) ∨ reach<(a, dest, m + 1), ∀ b. ¬ b ∈ N ∪ (succ(v) \ V) ∨ ¬ reach(b, dest, m) ∨ reach<(b, dest, m) ⊦ # succ(v) = 0, succ(c0) = ∅, succ(c) = ∅, # C = 0, v = dest, C = ∅, # succ(c0) = 0, # succ(c) = 0, succ(v) = ∅, reach<(v, dest, m + 1), ∃ b0. ¬ (b0 ∈ V ↔ reach<(source, b0, n + 1) ∨ (∃ a0. b0 ∈ succ(a0) ∧ reach(source, a0, n) ∧ ¬ reach<(source, a0, n) ∧ ¬ a0 ∈ C)), ∃ b0. ¬ ((∃ c. reach(source, c, n) ∧ b0 ∈ succ(c)) ∧ ¬ reach<(source, b0, n + 1) → b0 ∈ N ∨ (∃ a. a ∈ C ∧ b0 ∈ succ(a) ∧ ¬ b0 ∈ V)), ∃ m1. ¬ m + n < m1 ∧ reach(source, dest, m1)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m < n + 1 ↔ ¬ n < m])]]