[Imprint][Data Privacy Statement][E-Mail]



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Proof step 5 from proof progress-left (previous step)

¬(P(pm, s2) ∨ ◇ P(pm, S)) ∨ n = N + 1 ∧ N = N'' + 1 until ¬ ◇ P(pm, S), ( ( ( (((P(pm, s2) ∧ (true ⊃ Post1(pm, s, s2);G1(pm, s2, s2))) ∧ (false ⊃ Post2(pm, s, s2);G2(pm, s2, s3))) ∧ ¬ R1(pm, s2, s2)) ∧ ¬ R2(pm, s3, S) ∨ (((P(pm, s2) ∧ (true ⊃ Post1(pm, s, s2);G1(pm, s2, s2))) ∧ (false ⊃ Post2(pm, s, s2);G2(pm, s2, s3)) ∧ R2(pm, s3, S)) ∧ ¬ R1(pm, s2, s2)) ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))) ∨ ((P(pm, s2) ∧ (true ⊃ Post1(pm, s, s2);G1(pm, s2, s2)) ∧ R1(pm, s2, s2)) ∧ (false ⊃ Post2(pm, s, s2);G2(pm, s2, s3))) ∧ ¬ R2(pm, s3, S) ∨ ((P(pm, s2) ∧ (true ⊃ Post1(pm, s, s2);G1(pm, s2, s2)) ∧ R1(pm, s2, s2)) ∧ (false ⊃ Post2(pm, s, s2);G2(pm, s2, s3)) ∧ R2(pm, s3, S)) ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))) ∨ ( (∃ s0. (¬ false ∧ (false ⊃ Post1(pm, s, s2);G1(pm, s2, s3)) ∧ ¬ R1(pm, s3, s0)) ∧ ¬ boolvar ∧ [:S | [PL S = s0 ∧ □ ◇ P(pm, S)] ∥ [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))]]) ∨ (∃ s0, s1. ((((false ⊃ Post1(pm, s, s2);G1(pm, s2, s2)) ∧ (false ⊃ Post2(pm, s, s2);G2(pm, s2, s3))) ∧ ¬ R1(pm, s2, s0)) ∧ ¬ R2(pm, s3, s1)) ∧ [:S | [PL S = s0 ∧ □ ◇ P(pm, S)] ∥ [PL S = s1 ∧ true]]) ∨ (∃ s0, s1. (((false ⊃ Post1(pm, s, s2);G1(pm, s2, s2)) ∧ (false ⊃ Post2(pm, s, s2);G2(pm, s2, s3)) ∧ R2(pm, s3, s1)) ∧ ¬ R1(pm, s2, s0)) ∧ [:S | [PL S = s0 ∧ □ ◇ P(pm, S)] ∥ [PL S = s1 ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))]])) ∨ (∃ s0. (¬ false ∧ (false ⊃ Post1(pm, s, s2);G1(pm, s2, s3)) ∧ R1(pm, s3, s0)) ∧ ¬ boolvar ∧ [:S | [PL S = s0 ∧ □ ◇ P(pm, S) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))] ]) ∨ (∃ s0, s1. ((((false ⊃ Post1(pm, s, s2);G1(pm, s2, s2)) ∧ R1(pm, s2, s0)) ∧ (false ⊃ Post2(pm, s, s2);G2(pm, s2, s3))) ∧ ¬ R2(pm, s3, s1)) ∧ [:S | [PL S = s0 ∧ □ ◇ P(pm, S) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ [PL S = s1 ∧ true]]) ∨ (∃ s0, s1. (((false ⊃ Post1(pm, s, s2);G1(pm, s2, s2)) ∧ R1(pm, s2, s0)) ∧ (false ⊃ Post2(pm, s, s2);G2(pm, s2, s3)) ∧ R2(pm, s3, s1)) ∧ [:S | [PL S = s0 ∧ □ ◇ P(pm, S) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ [PL S = s1 ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))] ])) ∨ ( ( (false ∨ false) ∨ ((((true ⊃ Post2(pm, s, s2);G2(pm, s2, s2)) ∧ (false ⊃ Post1(pm, s, s2);G1(pm, s2, s3))) ∧ ¬ R2(pm, s2, s2)) ∧ ¬ R1(pm, s3, S)) ∧ □ ◇ P(pm, S) ∨ (((true ⊃ Post2(pm, s, s2);G2(pm, s2, s2)) ∧ (false ⊃ Post1(pm, s, s2);G1(pm, s2, s3)) ∧ R1(pm, s3, S)) ∧ ¬ R2(pm, s2, s2)) ∧ □ ◇ P(pm, S) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))) ∨ (∃ s0. (¬ false ∧ (false ⊃ Post2(pm, s, s2);G2(pm, s2, s3)) ∧ ¬ R2(pm, s3, s0)) ∧ ¬ boolvar ∧ [:S | [PL □ ◇ P(pm, S) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ [PL S = s0 ∧ true]]) ∨ (∃ s0, s1. ((((false ⊃ Post2(pm, s, s2);G2(pm, s2, s2)) ∧ (false ⊃ Post1(pm, s, s2);G1(pm, s2, s3))) ∧ ¬ R2(pm, s2, s0)) ∧ ¬ R1(pm, s3, s1)) ∧ [:S | [PL S = s1 ∧ □ ◇ P(pm, S)] ∥ [PL S = s0 ∧ true]]) ∨ (∃ s0, s1. (((false ⊃ Post2(pm, s, s2);G2(pm, s2, s2)) ∧ (false ⊃ Post1(pm, s, s2);G1(pm, s2, s3)) ∧ R1(pm, s3, s1)) ∧ ¬ R2(pm, s2, s0)) ∧ [:S | [PL S = s1 ∧ □ ◇ P(pm, S) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ [PL S = s0 ∧ true]])) ∨ ( (false ∨ false) ∨ ((((true ⊃ Post2(pm, s, s2);G2(pm, s2, s2)) ∧ R2(pm, s2, s2)) ∧ (false ⊃ Post1(pm, s, s2);G1(pm, s2, s3))) ∧ ¬ R1(pm, s3, S)) ∧ □ ◇ P(pm, S) ∨ (((true ⊃ Post2(pm, s, s2);G2(pm, s2, s2)) ∧ R2(pm, s2, s2)) ∧ (false ⊃ Post1(pm, s, s2);G1(pm, s2, s3)) ∧ R1(pm, s3, S)) ∧ □ ◇ P(pm, S) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))) ∨ (∃ s0. (¬ false ∧ (false ⊃ Post2(pm, s, s2);G2(pm, s2, s3)) ∧ R2(pm, s3, s0)) ∧ ¬ boolvar ∧ [:S | [PL □ ◇ P(pm, S) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ [PL S = s0 ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))] ]) ∨ (∃ s0, s1. ((((false ⊃ Post2(pm, s, s2);G2(pm, s2, s2)) ∧ R2(pm, s2, s0)) ∧ (false ⊃ Post1(pm, s, s2);G1(pm, s2, s3))) ∧ ¬ R1(pm, s3, s1)) ∧ [:S | [PL S = s1 ∧ □ ◇ P(pm, S)] ∥ [PL S = s0 ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))]]) ∨ (∃ s0, s1. (((false ⊃ Post2(pm, s, s2);G2(pm, s2, s2)) ∧ R2(pm, s2, s0)) ∧ (false ⊃ Post1(pm, s, s2);G1(pm, s2, s3)) ∧ R1(pm, s3, s1)) ∧ [:S | [PL S = s1 ∧ □ ◇ P(pm, S) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ [PL S = s0 ∧ R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))] ]), □ (R1(pm, S', S'') ∧ R2(pm, S', S'')), \A ∀ N, P, pm, S, Post1, s, G1, R1, Post2, G2, R2, Pre1, I, Pre2. N < m → [:S | [PL □ ◇ P(pm, S) ∧ R1(pm, S', S'') -+-> (last ⊃ Post1(pm, s, S);G1(pm, S, S'))] ∥ [PL R2(pm, S', S'') -+-> (last ⊃ Post2(pm, s, S);G2(pm, S, S'))] ] ∧ □ (R1(pm, S', S'') ∧ R2(pm, S', S'')) ∧ RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2) ∧ stable(pm, I, R1) ∧ stable(pm, I, R2) ∧ I(pm, S) ∧ Pre1(pm, s) ∧ Pre2(pm, s) ∧ P-restr(pm, P, I, R1) → ¬ N = N'' +1 until ¬ ◇ P(pm, S), m = n, RG-restr(pm, R1, G1, Pre1, Post1, I, R2, G2, Pre2, Post2), stable(pm, I, R1), stable(pm, I, R2), I(pm, s2), Pre1(pm, s), Pre2(pm, s), P-restr(pm, P, I, R1), ¬ false, boolvar → s2 = s3 ∧ n = n0, R1(pm, s3, S), R2(pm, s3, S) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information