Proof step 1 from proof step-absstep-W4-W5-tau-other (conclusion) (back to tree)

System applied rule normalize

And obtained the following new goals

• Proof step 2:

  ls.l = als.il, ags.pm = gs.mem, ags.pm = ∅ ⊕ (ags.h | true), lsf(t0).t = alsf(t0).t, ls.t = als.t, lsf(t0).t = t0, lsf(t).t = t, alsf(t).t = t, ls.v = als.iv, ags.vm = gs.mem ⊕ gs.p, ags.vm = ∅ ⊕ ags.h, W5 = pcstepf(gs, ls, W4, pwbPSC(t, l)), alsf(t) = als, apc = resWrite, apcf(t) = apc, gs0 = gstepf(gs, ls, W4, pwbPSC(t, l)), ls0 = lstepf(gs, ls, W4, pwbPSC(t, l)), lsf(t) = ls, lsf0(t) = ls0, pcf(t) = W4, pcf0(t) = W5, t ≠ t0, FLITPSCLInv(gs0, lsf(t0), pcf(t0)), FLITPSCLInv(gs, lsf(t0), pcf(t0)), FOFollowsW(t, gs0.p(ls0.l)), PLIBLInv(ags, alsf(t0), apcf(t0)), PLIBLInv(ags, als, apc), abs(ags.h, gs.readers, gs.p), allReadsOK(ags.h), allWritesOK(ags.h), ctrok(gs0.ctr, gs0.writers), ctrok(gs.ctr, gs.writers), notMember(t, gs0.readers), notMember(t, gs.readers), oneMember(t, ls0.l, gs0.writers), oneMember(t, ls.l, gs.writers), onePendingW(t, ls0.l, gs0.p), onePendingW(t, ls.l, gs.p), pendingOk(gs0.p), pendingOk(gs.p), pre(gs, ls, W4, pwbPSC(t, l)), writersOk(gs0.p, gs0.writers), writersOk(gs.p, gs.writers), pcf(t0) = idle → apcf(t0) = idle, pcf(t0) = ready → apcf(t0) = ready, pcf(t0) = crashed → apcf(t0) = crashed, pcf(t0) = R1 → apcf(t0) = invRead, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → apcf(t0) = resRead, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 → apcf(t0) = invWrite, pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → apcf(t0) = resWrite, pcf(t0) = R1 → lsf(t0).l = alsf(t0).il, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → lsf(t0).v = alsf(t0).ov, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → lsf(t0).l = alsf(t0).il ∧ lsf(t0).v = alsf(t0).iv, pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → (∀ l. ¬ FO(lsf(t0).t) ∈ gs.p(l) → ((ags.h | l) | lsf(t0).t) | false = []), pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → (∀ l. ((ags.h | l) | lsf(t0).t) | false = []), pcf(t0) = R2 ∨ pcf(t0) = R3 → (∀ l0. l0 ≠ lsf(t0).l ∧ ¬ FO(lsf(t0).t) ∈ gs.p(l0) → ((ags.h | l0) | lsf(t0).t) | false = []), pcf(t0) = R2 → gs.ctr(lsf(t0).l) = 0 → ((ags.h | lsf(t0).l) | lsf(t0).t) | false = [], pcf(t0) = W4 → ((ags.h | lsf(t0).l) | lsf(t0).t) | false = (W(lsf(t0).t, lsf(t0).l, lsf(t0).v), false) ' ∨ ((ags.h | lsf(t0).l) | lsf(t0).t) | false = [], ∀ t1. t1 ≠ t ∧ t1 ≠ t0 → FLITPSCLInv(gs, lsf(t1), pcf(t1)) ∧ PLIBLInv(ags, alsf(t1), apcf(t1)) ∧ labs(gs, lsf(t1), pcf(t1), ags, alsf(t1), apcf(t1)), ∀ t0. t0 ≠ t → alsf(t0).t = t0, ∀ t0. t0 ≠ t → lsf(t0).t = t0, ((ags.h | ls.l) | ls.t) | false = (W(ls.t, ls.l, ls.v), false) ' ∨ ((ags.h | ls.l) | ls.t) | false = [] ⊦ lsf(t0).t = alsf(t0).t ∧ (pcf(t0) = idle → apcf(t0) = idle) ∧ (pcf(t0) = ready → apcf(t0) = ready) ∧ (pcf(t0) = crashed → apcf(t0) = crashed) ∧ (pcf(t0) = R1 → apcf(t0) = invRead) ∧ (pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → apcf(t0) = resRead) ∧ (pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 → apcf(t0) = invWrite) ∧ (pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → apcf(t0) = resWrite) ∧ (pcf(t0) = R1 → lsf(t0).l = alsf(t0).il) ∧ (pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → lsf(t0).v = alsf(t0).ov) ∧ ( pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → lsf(t0).l = alsf(t0).il ∧ lsf(t0).v = alsf(t0).iv) ∧ ( pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → (∀ l. ¬ FO(lsf(t0).t) ∈ gs0.p(l) → ((ags.h | l) | lsf(t0).t) | false = [])) ∧ (pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → (∀ l. ((ags.h | l) | lsf(t0).t) | false = [])) ∧ (pcf(t0) = R2 ∨ pcf(t0) = R3 → (∀ l0. l0 ≠ lsf(t0).l ∧ ¬ FO(lsf(t0).t) ∈ gs0.p(l0) → ((ags.h | l0) | lsf(t0).t) | false = [])) ∧ (pcf(t0) = R2 → gs0.ctr(lsf(t0).l) = 0 → ((ags.h | lsf(t0).l) | lsf(t0).t) | false = []) ∧ ( pcf(t0) = W4 → ((ags.h | lsf(t0).l) | lsf(t0).t) | false = (W(lsf(t0).t, lsf(t0).l, lsf(t0).v), false) ' ∨ ((ags.h | lsf(t0).l) | lsf(t0).t) | false = [])

Rule argument

Additional information

Proof step 2 from proof step-absstep-W4-W5-tau-other (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 3:

  lsf(t).l = alsf(t).il, gs.mem = ∅ ⊕ (ags.h | true), ags.pm = gs.mem, lsf(t0).t = t0, lsf(t).t = t, alsf(t0).t = t0, alsf(t).t = t, lsf(t).v = alsf(t).iv, ags.vm = gs.mem ⊕ gs.p, ags.vm = ∅ ⊕ ags.h, apcf(t) = resWrite, lsf0(t) = lsf(t), pcf(t) = W4, pcf0(t) = W5, t ≠ t0, FLITPSCLInv(gs.p:= gs.p(alsf(t).il := gs.p(alsf(t).il) + FO(t) '), lsf(t0), pcf(t0)), FLITPSCLInv(gs, lsf(t0), pcf(t0)), FOFollowsW(t, gs.p(alsf(t).il) + FO(t) '), PLIBLInv(ags, alsf(t0), apcf(t0)), PLIBLInv(ags, alsf(t), resWrite), abs(ags.h, gs.readers, gs.p), allReadsOK(ags.h), allWritesOK(ags.h), ctrok(gs.ctr, gs.writers), notMember(t, gs.readers), oneMember(t, alsf(t).il, gs.writers), onePendingW(t, alsf(t).il, gs.p(alsf(t).il := gs.p(alsf(t).il) + FO(t) ')), onePendingW(t, alsf(t).il, gs.p), pendingOk(gs.p(alsf(t).il := gs.p(alsf(t).il) + FO(t) ')), pendingOk(gs.p), writersOk(gs.p(alsf(t).il := gs.p(alsf(t).il) + FO(t) '), gs.writers), writersOk(gs.p, gs.writers), pcf(t0) = idle → apcf(t0) = idle, pcf(t0) = ready → apcf(t0) = ready, pcf(t0) = crashed → apcf(t0) = crashed, pcf(t0) = R1 → apcf(t0) = invRead, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → apcf(t0) = resRead, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 → apcf(t0) = invWrite, pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → apcf(t0) = resWrite, pcf(t0) = R1 → lsf(t0).l = alsf(t0).il, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → lsf(t0).v = alsf(t0).ov, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → lsf(t0).l = alsf(t0).il ∧ lsf(t0).v = alsf(t0).iv, pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → (∀ l. ¬ FO(t0) ∈ gs.p(l) → ((ags.h | l) | t0) | false = []), pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → (∀ l. ((ags.h | l) | t0) | false = []), pcf(t0) = R2 ∨ pcf(t0) = R3 → (∀ l0. l0 ≠ lsf(t0).l ∧ ¬ FO(t0) ∈ gs.p(l0) → ((ags.h | l0) | t0) | false = []), pcf(t0) = R2 → gs.ctr(lsf(t0).l) = 0 → ((ags.h | lsf(t0).l) | t0) | false = [], pcf(t0) = W4 → ((ags.h | lsf(t0).l) | t0) | false = (W(t0, lsf(t0).l, lsf(t0).v), false) ' ∨ ((ags.h | lsf(t0).l) | t0) | false = [], ∀ t1. alsf(t1).t = t1, ∀ t1. lsf(t1).t = t1, ∀ t1. t1 ≠ t ∧ t1 ≠ t0 → FLITPSCLInv(gs, lsf(t1), pcf(t1)) ∧ PLIBLInv(ags, alsf(t1), apcf(t1)) ∧ labs(gs, lsf(t1), pcf(t1), ags, alsf(t1), apcf(t1)), ((ags.h | alsf(t).il) | t) | false = (W(t, alsf(t).il, alsf(t).iv), false) ' ∨ ((ags.h | alsf(t).il) | t) | false = [] ⊦ ( pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → ¬ FO(t0) ∈ (alsf(t).il = l0 ⊃ gs.p(alsf(t).il) + FO(t) ';gs.p(l0)) → ((ags.h | l0) | t0) | false = []) ∧ ( pcf(t0) = R2 ∨ pcf(t0) = R3 → l1 ≠ lsf(t0).l ∧ ¬ FO(t0) ∈ (alsf(t).il = l1 ⊃ gs.p(alsf(t).il) + FO(t) ';gs.p(l1)) → ((ags.h | l1) | t0) | false = [])

Rule argument

Additional information

Used simplifier rules: ⊦ (gs.p:= p).ctr = gs.ctr; (s) ⊦ x + a = x + a '; (s) ⊦ gstepf(gs, ls, W4, a) = gs.p:= gs.p(ls.l := gs.p(ls.l) + FO(ls.t)); (s) ⊦ (gs.p:= p).p = p; (s) ⊦ (gs.p:= p).writers = gs.writers; (s) ⊦ (gs.p:= p).readers = gs.readers; (s) ⊦ pwbPSC(t, l) = pwbPSC(t0, l0) ↔ t = t0 ∧ l = l0; (ws) ⊦ pre(gs, ls, W4, a) ↔ a = pwbPSC(ls.t, ls.l); (s) ⊦ pcstepf(gs, ls, W4, a) = W5; (s) ⊦ lstepf(gs, ls, W4, a) = ls; (s)

Proof step 3 from proof step-absstep-W4-W5-tau-other (previous step) (back to tree)

Heuristic elimination applied rule apply elim lemma

And obtained the following new goals

• Proof step 4:

  lsf(t).l = alsf(t).il, gs.mem = ∅ ⊕ (h | true), alsf(t).t = t, alsf(t0).t = t0, lsf(t).t = t, lsf(t0).t = t0, lsf(t).v = alsf(t).iv, ags = mkPLIBgs(mem, mem0, h), apcf(t) = resWrite, lsf0(t) = lsf(t), mem = ∅ ⊕ h, mem = gs.mem ⊕ gs.p, mem0 = gs.mem, pcf(t) = W4, pcf0(t) = W5, t ≠ t0, FLITPSCLInv(gs, lsf(t0), pcf(t0)), FLITPSCLInv(gs.p:= gs.p(alsf(t).il := gs.p(alsf(t).il) + FO(t) '), lsf(t0), pcf(t0)), FOFollowsW(t, gs.p(alsf(t).il) + FO(t) '), PLIBLInv(ags, alsf(t), resWrite), PLIBLInv(ags, alsf(t0), apcf(t0)), abs(h, gs.readers, gs.p), allReadsOK(h), allWritesOK(h), ctrok(gs.ctr, gs.writers), notMember(t, gs.readers), oneMember(t, alsf(t).il, gs.writers), onePendingW(t, alsf(t).il, gs.p), onePendingW(t, alsf(t).il, gs.p(alsf(t).il := gs.p(alsf(t).il) + FO(t) ')), pendingOk(gs.p), pendingOk(gs.p(alsf(t).il := gs.p(alsf(t).il) + FO(t) ')), writersOk(gs.p, gs.writers), writersOk(gs.p(alsf(t).il := gs.p(alsf(t).il) + FO(t) '), gs.writers), pcf(t0) = W4 → ((h | lsf(t0).l) | t0) | false = (W(t0, lsf(t0).l, lsf(t0).v), false) ' ∨ ((h | lsf(t0).l) | t0) | false = [], pcf(t0) = R2 → gs.ctr(lsf(t0).l) = 0 → ((h | lsf(t0).l) | t0) | false = [], pcf(t0) = R2 ∨ pcf(t0) = R3 → (∀ l0. l0 ≠ lsf(t0).l ∧ ¬ FO(t0) ∈ gs.p(l0) → ((h | l0) | t0) | false = []), pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → (∀ l. ((h | l) | t0) | false = []), pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → (∀ l. ¬ FO(t0) ∈ gs.p(l) → ((h | l) | t0) | false = []), pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → lsf(t0).l = alsf(t0).il ∧ lsf(t0).v = alsf(t0).iv, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → lsf(t0).v = alsf(t0).ov, pcf(t0) = R1 → lsf(t0).l = alsf(t0).il, pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → apcf(t0) = resWrite, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 → apcf(t0) = invWrite, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → apcf(t0) = resRead, pcf(t0) = R1 → apcf(t0) = invRead, pcf(t0) = crashed → apcf(t0) = crashed, pcf(t0) = ready → apcf(t0) = ready, pcf(t0) = idle → apcf(t0) = idle, ∀ t1. t1 ≠ t ∧ t1 ≠ t0 → FLITPSCLInv(gs, lsf(t1), pcf(t1)) ∧ PLIBLInv(ags, alsf(t1), apcf(t1)) ∧ labs(gs, lsf(t1), pcf(t1), ags, alsf(t1), apcf(t1)), ∀ t1. lsf(t1).t = t1, ∀ t1. alsf(t1).t = t1, ((h | alsf(t).il) | t) | false = (W(t, alsf(t).il, alsf(t).iv), false) ' ∨ ((h | alsf(t).il) | t) | false = [] ⊦ ( pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → ¬ FO(t0) ∈ (alsf(t).il = l0 ⊃ gs.p(alsf(t).il) + FO(t) ';gs.p(l0)) → ((h | l0) | t0) | false = []) ∧ (pcf(t0) = R2 ∨ pcf(t0) = R3 → l1 ≠ lsf(t0).l ∧ ¬ FO(t0) ∈ (alsf(t).il = l1 ⊃ gs.p(alsf(t).il) + FO(t) ';gs.p(l1)) → ((h | l1) | t0) | false = [])

Rule argument

Additional information

Used simplifier rules: ⊦ (vm = gs.vm ∧ pm = gs.pm) ∧ h = gs.h ↔ gs = mkPLIBgs(vm, pm, h); (elim) Used terms: ags, mem, mem0, h

Proof step 4 from proof step-absstep-W4-W5-tau-other (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 5:

  lsf(t).l = alsf(t).il, gs.mem = ∅ ⊕ (h | true), lsf(t0).t = t0, lsf(t).t = t, alsf(t0).t = t0, alsf(t).t = t, lsf(t).v = alsf(t).iv, apcf(t) = resWrite, lsf0(t) = lsf(t), pcf(t) = W4, pcf0(t) = W5, gs.mem ⊕ gs.p = ∅ ⊕ h, t ≠ t0, FLITPSCLInv(gs.p:= gs.p(alsf(t).il := gs.p(alsf(t).il) + FO(t) '), lsf(t0), pcf(t0)), FLITPSCLInv(gs, lsf(t0), pcf(t0)), FOFollowsW(t, gs.p(alsf(t).il) + FO(t) '), PLIBLInv(mkPLIBgs(∅ ⊕ h, gs.mem, h), alsf(t0), apcf(t0)), PLIBLInv(mkPLIBgs(∅ ⊕ h, gs.mem, h), alsf(t), resWrite), abs(h, gs.readers, gs.p), allReadsOK(h), allWritesOK(h), ctrok(gs.ctr, gs.writers), notMember(t, gs.readers), oneMember(t, alsf(t).il, gs.writers), onePendingW(t, alsf(t).il, gs.p(alsf(t).il := gs.p(alsf(t).il) + FO(t) ')), onePendingW(t, alsf(t).il, gs.p), pendingOk(gs.p(alsf(t).il := gs.p(alsf(t).il) + FO(t) ')), pendingOk(gs.p), writersOk(gs.p(alsf(t).il := gs.p(alsf(t).il) + FO(t) '), gs.writers), writersOk(gs.p, gs.writers), pcf(t0) = idle → apcf(t0) = idle, pcf(t0) = ready → apcf(t0) = ready, pcf(t0) = crashed → apcf(t0) = crashed, pcf(t0) = R1 → apcf(t0) = invRead, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → apcf(t0) = resRead, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 → apcf(t0) = invWrite, pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → apcf(t0) = resWrite, pcf(t0) = R1 → lsf(t0).l = alsf(t0).il, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → lsf(t0).v = alsf(t0).ov, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → lsf(t0).l = alsf(t0).il ∧ lsf(t0).v = alsf(t0).iv, pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → (∀ l. ¬ FO(t0) ∈ gs.p(l) → ((h | l) | t0) | false = []), pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → (∀ l. ((h | l) | t0) | false = []), pcf(t0) = R2 ∨ pcf(t0) = R3 → (∀ l0. l0 ≠ lsf(t0).l ∧ ¬ FO(t0) ∈ gs.p(l0) → ((h | l0) | t0) | false = []), pcf(t0) = R2 → gs.ctr(lsf(t0).l) = 0 → ((h | lsf(t0).l) | t0) | false = [], pcf(t0) = W4 → ((h | lsf(t0).l) | t0) | false = (W(t0, lsf(t0).l, lsf(t0).v), false) ' ∨ ((h | lsf(t0).l) | t0) | false = [], ∀ t1. alsf(t1).t = t1, ∀ t1. lsf(t1).t = t1, ∀ t1. t1 ≠ t ∧ t1 ≠ t0 → FLITPSCLInv(gs, lsf(t1), pcf(t1)) ∧ PLIBLInv(mkPLIBgs(∅ ⊕ h, gs.mem, h), alsf(t1), apcf(t1)) ∧ labs(gs, lsf(t1), pcf(t1), mkPLIBgs(∅ ⊕ h, gs.mem, h), alsf(t1), apcf(t1)), ((h | alsf(t).il) | t) | false = (W(t, alsf(t).il, alsf(t).iv), false) ' ∨ ((h | alsf(t).il) | t) | false = [] ⊦ ( pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → ¬ FO(t0) ∈ (alsf(t).il = l0 ⊃ gs.p(alsf(t).il) + FO(t) ';gs.p(l0)) → ((h | l0) | t0) | false = []) ∧ (pcf(t0) = R2 ∨ pcf(t0) = R3 → l1 ≠ lsf(t0).l ∧ ¬ FO(t0) ∈ (alsf(t).il = l1 ⊃ gs.p(alsf(t).il) + FO(t) ';gs.p(l1)) → ((h | l1) | t0) | false = [])

Rule argument

Additional information

Proof step 5 from proof step-absstep-W4-W5-tau-other (previous step) (back to tree)

Heuristic elimination applied rule apply elim lemma

And obtained the following new goals

• Proof step 6:

  lsf(t).l = alsf(t).il, alsf(t).t = t, alsf(t0).t = t0, lsf(t).t = t, lsf(t0).t = t0, lsf(t).v = alsf(t).iv, apcf(t) = resWrite, gs = mkFLITPSCgs(mem, p, ctr, writers, writers0), lsf0(t) = lsf(t), mem = ∅ ⊕ (h | true), pcf(t) = W4, pcf0(t) = W5, mem ⊕ p = ∅ ⊕ h, t ≠ t0, FLITPSCLInv(gs, lsf(t0), pcf(t0)), FLITPSCLInv(gs.p:= p(alsf(t).il := p(alsf(t).il) + FO(t) '), lsf(t0), pcf(t0)), FOFollowsW(t, p(alsf(t).il) + FO(t) '), PLIBLInv(mkPLIBgs(∅ ⊕ h, mem, h), alsf(t), resWrite), PLIBLInv(mkPLIBgs(∅ ⊕ h, mem, h), alsf(t0), apcf(t0)), abs(h, writers0, p), allReadsOK(h), allWritesOK(h), ctrok(ctr, writers), notMember(t, writers0), oneMember(t, alsf(t).il, writers), onePendingW(t, alsf(t).il, p), onePendingW(t, alsf(t).il, p(alsf(t).il := p(alsf(t).il) + FO(t) ')), pendingOk(p), pendingOk(p(alsf(t).il := p(alsf(t).il) + FO(t) ')), writersOk(p, writers), writersOk(p(alsf(t).il := p(alsf(t).il) + FO(t) '), writers), pcf(t0) = W4 → ((h | lsf(t0).l) | t0) | false = (W(t0, lsf(t0).l, lsf(t0).v), false) ' ∨ ((h | lsf(t0).l) | t0) | false = [], pcf(t0) = R2 → ctr(lsf(t0).l) = 0 → ((h | lsf(t0).l) | t0) | false = [], pcf(t0) = R2 ∨ pcf(t0) = R3 → (∀ l0. l0 ≠ lsf(t0).l ∧ ¬ FO(t0) ∈ p(l0) → ((h | l0) | t0) | false = []), pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → (∀ l. ((h | l) | t0) | false = []), pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → (∀ l. ¬ FO(t0) ∈ p(l) → ((h | l) | t0) | false = []), pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → lsf(t0).l = alsf(t0).il ∧ lsf(t0).v = alsf(t0).iv, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → lsf(t0).v = alsf(t0).ov, pcf(t0) = R1 → lsf(t0).l = alsf(t0).il, pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → apcf(t0) = resWrite, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 → apcf(t0) = invWrite, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → apcf(t0) = resRead, pcf(t0) = R1 → apcf(t0) = invRead, pcf(t0) = crashed → apcf(t0) = crashed, pcf(t0) = ready → apcf(t0) = ready, pcf(t0) = idle → apcf(t0) = idle, ∀ t1. t1 ≠ t ∧ t1 ≠ t0 → FLITPSCLInv(gs, lsf(t1), pcf(t1)) ∧ PLIBLInv(mkPLIBgs(∅ ⊕ h, mem, h), alsf(t1), apcf(t1)) ∧ labs(gs, lsf(t1), pcf(t1), mkPLIBgs(∅ ⊕ h, mem, h), alsf(t1), apcf(t1)), ∀ t1. lsf(t1).t = t1, ∀ t1. alsf(t1).t = t1, ((h | alsf(t).il) | t) | false = (W(t, alsf(t).il, alsf(t).iv), false) ' ∨ ((h | alsf(t).il) | t) | false = [] ⊦ ( pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → ¬ FO(t0) ∈ (alsf(t).il = l0 ⊃ p(alsf(t).il) + FO(t) ';p(l0)) → ((h | l0) | t0) | false = []) ∧ (pcf(t0) = R2 ∨ pcf(t0) = R3 → l1 ≠ lsf(t0).l ∧ ¬ FO(t0) ∈ (alsf(t).il = l1 ⊃ p(alsf(t).il) + FO(t) ';p(l1)) → ((h | l1) | t0) | false = [])

Rule argument

Additional information

Used simplifier rules: ⊦ (((mem = gs.mem ∧ p = gs.p) ∧ ctr = gs.ctr) ∧ writers = gs.writers) ∧ readers = gs.readers ↔ gs = mkFLITPSCgs(mem, p, ctr, writers, readers); (elim) Used terms: gs, mem, ctr, writers, writers0, p

Proof step 6 from proof step-absstep-W4-W5-tau-other (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 7:

  lsf(t).l = alsf(t).il, lsf(t0).t = t0, lsf(t).t = t, alsf(t0).t = t0, alsf(t).t = t, lsf(t).v = alsf(t).iv, apcf(t) = resWrite, lsf0(t) = lsf(t), pcf(t) = W4, pcf0(t) = W5, (∅ ⊕ (h | true)) ⊕ p = ∅ ⊕ h, t ≠ t0, FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t0), pcf(t0)), FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p(alsf(t).il := p(alsf(t).il) + FO(t) '), ctr, writers, writers0), lsf(t0), pcf(t0)), FOFollowsW(t, p(alsf(t).il) + FO(t) '), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t0), apcf(t0)), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t), resWrite), abs(h, writers0, p), allReadsOK(h), allWritesOK(h), ctrok(ctr, writers), notMember(t, writers0), oneMember(t, alsf(t).il, writers), onePendingW(t, alsf(t).il, p(alsf(t).il := p(alsf(t).il) + FO(t) ')), onePendingW(t, alsf(t).il, p), pendingOk(p(alsf(t).il := p(alsf(t).il) + FO(t) ')), pendingOk(p), writersOk(p(alsf(t).il := p(alsf(t).il) + FO(t) '), writers), writersOk(p, writers), pcf(t0) = idle → apcf(t0) = idle, pcf(t0) = ready → apcf(t0) = ready, pcf(t0) = crashed → apcf(t0) = crashed, pcf(t0) = R1 → apcf(t0) = invRead, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → apcf(t0) = resRead, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 → apcf(t0) = invWrite, pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → apcf(t0) = resWrite, pcf(t0) = R1 → lsf(t0).l = alsf(t0).il, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → lsf(t0).v = alsf(t0).ov, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → lsf(t0).l = alsf(t0).il ∧ lsf(t0).v = alsf(t0).iv, pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → (∀ l. ¬ FO(t0) ∈ p(l) → ((h | l) | t0) | false = []), pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → (∀ l. ((h | l) | t0) | false = []), pcf(t0) = R2 ∨ pcf(t0) = R3 → (∀ l0. l0 ≠ lsf(t0).l ∧ ¬ FO(t0) ∈ p(l0) → ((h | l0) | t0) | false = []), pcf(t0) = R2 → ctr(lsf(t0).l) = 0 → ((h | lsf(t0).l) | t0) | false = [], pcf(t0) = W4 → ((h | lsf(t0).l) | t0) | false = (W(t0, lsf(t0).l, lsf(t0).v), false) ' ∨ ((h | lsf(t0).l) | t0) | false = [], ∀ t1. alsf(t1).t = t1, ∀ t1. lsf(t1).t = t1, ∀ t1. t1 ≠ t ∧ t1 ≠ t0 → FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1)) ∧ PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)) ∧ labs(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1), mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)), ((h | alsf(t).il) | t) | false = (W(t, alsf(t).il, alsf(t).iv), false) ' ∨ ((h | alsf(t).il) | t) | false = [] ⊦ ( pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → ¬ FO(t0) ∈ (alsf(t).il = l0 ⊃ p(alsf(t).il) + FO(t) ';p(l0)) → ((h | l0) | t0) | false = []) ∧ (pcf(t0) = R2 ∨ pcf(t0) = R3 → l1 ≠ lsf(t0).l ∧ ¬ FO(t0) ∈ (alsf(t).il = l1 ⊃ p(alsf(t).il) + FO(t) ';p(l1)) → ((h | l1) | t0) | false = [])

Rule argument

Additional information

Used simplifier rules: ⊦ mkFLITPSCgs(mem, p, ctr, writers, writers0).p:= p0 = mkFLITPSCgs(mem, p0, ctr, writers, writers0); (s)

Proof step 7 from proof step-absstep-W4-W5-tau-other (previous step) (back to tree)

Heuristic elimination applied rule apply elim lemma

And obtained the following new goals

• Proof step 8:

  lsf(t).l = alsf(t).il, alsf(t).t = t, lsf(t).t = t, lsf(t0).t = t0, lsf(t).v = alsf(t).iv, alsf(t0) = mkPLIBls(t2, il, iv, ov), apcf(t) = resWrite, lsf0(t) = lsf(t), pcf(t) = W4, pcf0(t) = W5, t2 = t0, (∅ ⊕ (h | true)) ⊕ p = ∅ ⊕ h, t ≠ t0, FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p(alsf(t).il := p(alsf(t).il) + FO(t) '), ctr, writers, writers0), lsf(t0), pcf(t0)), FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t0), pcf(t0)), FOFollowsW(t, p(alsf(t).il) + FO(t) '), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t), resWrite), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t0), apcf(t0)), abs(h, writers0, p), allReadsOK(h), allWritesOK(h), ctrok(ctr, writers), notMember(t, writers0), oneMember(t, alsf(t).il, writers), onePendingW(t, alsf(t).il, p), onePendingW(t, alsf(t).il, p(alsf(t).il := p(alsf(t).il) + FO(t) ')), pendingOk(p), pendingOk(p(alsf(t).il := p(alsf(t).il) + FO(t) ')), writersOk(p, writers), writersOk(p(alsf(t).il := p(alsf(t).il) + FO(t) '), writers), pcf(t0) = W4 → ((h | lsf(t0).l) | t0) | false = (W(t0, lsf(t0).l, lsf(t0).v), false) ' ∨ ((h | lsf(t0).l) | t0) | false = [], pcf(t0) = R2 → ctr(lsf(t0).l) = 0 → ((h | lsf(t0).l) | t0) | false = [], pcf(t0) = R2 ∨ pcf(t0) = R3 → (∀ l0. l0 ≠ lsf(t0).l ∧ ¬ FO(t0) ∈ p(l0) → ((h | l0) | t0) | false = []), pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → (∀ l. ((h | l) | t0) | false = []), pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → (∀ l. ¬ FO(t0) ∈ p(l) → ((h | l) | t0) | false = []), pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → lsf(t0).l = il ∧ lsf(t0).v = iv, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → lsf(t0).v = ov, pcf(t0) = R1 → lsf(t0).l = il, pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → apcf(t0) = resWrite, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 → apcf(t0) = invWrite, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → apcf(t0) = resRead, pcf(t0) = R1 → apcf(t0) = invRead, pcf(t0) = crashed → apcf(t0) = crashed, pcf(t0) = ready → apcf(t0) = ready, pcf(t0) = idle → apcf(t0) = idle, ∀ t1. t1 ≠ t ∧ t1 ≠ t0 → FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1)) ∧ PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)) ∧ labs(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1), mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)), ∀ t1. lsf(t1).t = t1, ∀ t1. alsf(t1).t = t1, ((h | alsf(t).il) | t) | false = (W(t, alsf(t).il, alsf(t).iv), false) ' ∨ ((h | alsf(t).il) | t) | false = [] ⊦ ( pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → ¬ FO(t0) ∈ (alsf(t).il = l0 ⊃ p(alsf(t).il) + FO(t) ';p(l0)) → ((h | l0) | t0) | false = []) ∧ (pcf(t0) = R2 ∨ pcf(t0) = R3 → l1 ≠ lsf(t0).l ∧ ¬ FO(t0) ∈ (alsf(t).il = l1 ⊃ p(alsf(t).il) + FO(t) ';p(l1)) → ((h | l1) | t0) | false = [])

Rule argument

Additional information

Used simplifier rules: ⊦ ((t = ls.t ∧ il = ls.il) ∧ iv = ls.iv) ∧ ov = ls.ov ↔ ls = mkPLIBls(t, il, iv, ov); (elim) Used terms: alsf(t0), iv, t2, il, ov

Proof step 8 from proof step-absstep-W4-W5-tau-other (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 9:

  lsf(t).l = alsf(t).il, lsf(t0).t = t0, lsf(t).t = t, alsf(t).t = t, lsf(t).v = alsf(t).iv, alsf(t0) = mkPLIBls(t0, il, iv, ov), apcf(t) = resWrite, lsf0(t) = lsf(t), pcf(t) = W4, pcf0(t) = W5, (∅ ⊕ (h | true)) ⊕ p = ∅ ⊕ h, t ≠ t0, FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t0), pcf(t0)), FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p(alsf(t).il := p(alsf(t).il) + FO(t) '), ctr, writers, writers0), lsf(t0), pcf(t0)), FOFollowsW(t, p(alsf(t).il) + FO(t) '), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t0, il, iv, ov), apcf(t0)), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t), resWrite), abs(h, writers0, p), allReadsOK(h), allWritesOK(h), ctrok(ctr, writers), notMember(t, writers0), oneMember(t, alsf(t).il, writers), onePendingW(t, alsf(t).il, p(alsf(t).il := p(alsf(t).il) + FO(t) ')), onePendingW(t, alsf(t).il, p), pendingOk(p(alsf(t).il := p(alsf(t).il) + FO(t) ')), pendingOk(p), writersOk(p(alsf(t).il := p(alsf(t).il) + FO(t) '), writers), writersOk(p, writers), pcf(t0) = idle → apcf(t0) = idle, pcf(t0) = ready → apcf(t0) = ready, pcf(t0) = crashed → apcf(t0) = crashed, pcf(t0) = R1 → apcf(t0) = invRead, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → apcf(t0) = resRead, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 → apcf(t0) = invWrite, pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → apcf(t0) = resWrite, pcf(t0) = R1 → lsf(t0).l = il, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → lsf(t0).v = ov, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → lsf(t0).l = il ∧ lsf(t0).v = iv, pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → (∀ l. ¬ FO(t0) ∈ p(l) → ((h | l) | t0) | false = []), pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → (∀ l. ((h | l) | t0) | false = []), pcf(t0) = R2 ∨ pcf(t0) = R3 → (∀ l0. l0 ≠ lsf(t0).l ∧ ¬ FO(t0) ∈ p(l0) → ((h | l0) | t0) | false = []), pcf(t0) = R2 → ctr(lsf(t0).l) = 0 → ((h | lsf(t0).l) | t0) | false = [], pcf(t0) = W4 → ((h | lsf(t0).l) | t0) | false = (W(t0, lsf(t0).l, lsf(t0).v), false) ' ∨ ((h | lsf(t0).l) | t0) | false = [], ∀ t1. alsf(t1).t = t1, ∀ t1. lsf(t1).t = t1, ∀ t1. t1 ≠ t ∧ t1 ≠ t0 → FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1)) ∧ PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)) ∧ labs(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1), mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)), ((h | alsf(t).il) | t) | false = (W(t, alsf(t).il, alsf(t).iv), false) ' ∨ ((h | alsf(t).il) | t) | false = [] ⊦ ( pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → ¬ FO(t0) ∈ (alsf(t).il = l0 ⊃ p(alsf(t).il) + FO(t) ';p(l0)) → ((h | l0) | t0) | false = []) ∧ (pcf(t0) = R2 ∨ pcf(t0) = R3 → l1 ≠ lsf(t0).l ∧ ¬ FO(t0) ∈ (alsf(t).il = l1 ⊃ p(alsf(t).il) + FO(t) ';p(l1)) → ((h | l1) | t0) | false = [])

Rule argument

Additional information

Proof step 9 from proof step-absstep-W4-W5-tau-other (previous step) (back to tree)

Heuristic elimination applied rule apply elim lemma

And obtained the following new goals

• Proof step 10:

  lsf(t).l = il0, lsf(t).t = t, lsf(t0).t = t0, lsf(t).v = iv0, alsf(t0) = mkPLIBls(t0, il, iv, ov), alsf(t) = mkPLIBls(t2, il0, iv0, ov0), apcf(t) = resWrite, lsf0(t) = lsf(t), pcf(t) = W4, pcf0(t) = W5, t2 = t, (∅ ⊕ (h | true)) ⊕ p = ∅ ⊕ h, t ≠ t0, FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p(il0 := p(il0) + FO(t) '), ctr, writers, writers0), lsf(t0), pcf(t0)), FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t0), pcf(t0)), FOFollowsW(t, p(il0) + FO(t) '), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t), resWrite), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t0, il, iv, ov), apcf(t0)), abs(h, writers0, p), allReadsOK(h), allWritesOK(h), ctrok(ctr, writers), notMember(t, writers0), oneMember(t, il0, writers), onePendingW(t, il0, p), onePendingW(t, il0, p(il0 := p(il0) + FO(t) ')), pendingOk(p), pendingOk(p(il0 := p(il0) + FO(t) ')), writersOk(p, writers), writersOk(p(il0 := p(il0) + FO(t) '), writers), pcf(t0) = W4 → ((h | lsf(t0).l) | t0) | false = (W(t0, lsf(t0).l, lsf(t0).v), false) ' ∨ ((h | lsf(t0).l) | t0) | false = [], pcf(t0) = R2 → ctr(lsf(t0).l) = 0 → ((h | lsf(t0).l) | t0) | false = [], pcf(t0) = R2 ∨ pcf(t0) = R3 → (∀ l0. l0 ≠ lsf(t0).l ∧ ¬ FO(t0) ∈ p(l0) → ((h | l0) | t0) | false = []), pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → (∀ l. ((h | l) | t0) | false = []), pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → (∀ l. ¬ FO(t0) ∈ p(l) → ((h | l) | t0) | false = []), pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → lsf(t0).l = il ∧ lsf(t0).v = iv, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → lsf(t0).v = ov, pcf(t0) = R1 → lsf(t0).l = il, pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → apcf(t0) = resWrite, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 → apcf(t0) = invWrite, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → apcf(t0) = resRead, pcf(t0) = R1 → apcf(t0) = invRead, pcf(t0) = crashed → apcf(t0) = crashed, pcf(t0) = ready → apcf(t0) = ready, pcf(t0) = idle → apcf(t0) = idle, ∀ t1. t1 ≠ t ∧ t1 ≠ t0 → FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1)) ∧ PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)) ∧ labs(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1), mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)), ∀ t1. lsf(t1).t = t1, ∀ t1. alsf(t1).t = t1, ((h | il0) | t) | false = (W(t, il0, iv0), false) ' ∨ ((h | il0) | t) | false = [] ⊦ ( pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → ¬ FO(t0) ∈ (il0 = l0 ⊃ p(il0) + FO(t) ';p(l0)) → ((h | l0) | t0) | false = []) ∧ (pcf(t0) = R2 ∨ pcf(t0) = R3 → l1 ≠ lsf(t0).l ∧ ¬ FO(t0) ∈ (il0 = l1 ⊃ p(il0) + FO(t) ';p(l1)) → ((h | l1) | t0) | false = [])

Rule argument

Additional information

Used simplifier rules: ⊦ ((t = ls.t ∧ il = ls.il) ∧ iv = ls.iv) ∧ ov = ls.ov ↔ ls = mkPLIBls(t, il, iv, ov); (elim) Used terms: alsf(t), iv0, t2, il0, ov0

Proof step 10 from proof step-absstep-W4-W5-tau-other (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 11:

  lsf(t0).t = t0, lsf(t).t = t, alsf(t) = mkPLIBls(t, lsf(t).l, lsf(t).v, ov0), alsf(t0) = mkPLIBls(t0, il, iv, ov), apcf(t) = resWrite, lsf0(t) = lsf(t), pcf(t) = W4, pcf0(t) = W5, (∅ ⊕ (h | true)) ⊕ p = ∅ ⊕ h, t ≠ t0, FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t0), pcf(t0)), FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p(lsf(t).l := p(lsf(t).l) + FO(t) '), ctr, writers, writers0), lsf(t0), pcf(t0)), FOFollowsW(t, p(lsf(t).l) + FO(t) '), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t0, il, iv, ov), apcf(t0)), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t, lsf(t).l, lsf(t).v, ov0), resWrite), abs(h, writers0, p), allReadsOK(h), allWritesOK(h), ctrok(ctr, writers), notMember(t, writers0), oneMember(t, lsf(t).l, writers), onePendingW(t, lsf(t).l, p(lsf(t).l := p(lsf(t).l) + FO(t) ')), onePendingW(t, lsf(t).l, p), pendingOk(p(lsf(t).l := p(lsf(t).l) + FO(t) ')), pendingOk(p), writersOk(p(lsf(t).l := p(lsf(t).l) + FO(t) '), writers), writersOk(p, writers), pcf(t0) = idle → apcf(t0) = idle, pcf(t0) = ready → apcf(t0) = ready, pcf(t0) = crashed → apcf(t0) = crashed, pcf(t0) = R1 → apcf(t0) = invRead, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → apcf(t0) = resRead, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 → apcf(t0) = invWrite, pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → apcf(t0) = resWrite, pcf(t0) = R1 → lsf(t0).l = il, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → lsf(t0).v = ov, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → lsf(t0).l = il ∧ lsf(t0).v = iv, pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → (∀ l. ¬ FO(t0) ∈ p(l) → ((h | l) | t0) | false = []), pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → (∀ l. ((h | l) | t0) | false = []), pcf(t0) = R2 ∨ pcf(t0) = R3 → (∀ l0. l0 ≠ lsf(t0).l ∧ ¬ FO(t0) ∈ p(l0) → ((h | l0) | t0) | false = []), pcf(t0) = R2 → ctr(lsf(t0).l) = 0 → ((h | lsf(t0).l) | t0) | false = [], pcf(t0) = W4 → ((h | lsf(t0).l) | t0) | false = (W(t0, lsf(t0).l, lsf(t0).v), false) ' ∨ ((h | lsf(t0).l) | t0) | false = [], ∀ t1. alsf(t1).t = t1, ∀ t1. lsf(t1).t = t1, ∀ t1. t1 ≠ t ∧ t1 ≠ t0 → FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1)) ∧ PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)) ∧ labs(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1), mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)), ((h | lsf(t).l) | t) | false = (W(t, lsf(t).l, lsf(t).v), false) ' ∨ ((h | lsf(t).l) | t) | false = [] ⊦ ( pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → ¬ FO(t0) ∈ (lsf(t).l = l0 ⊃ p(lsf(t).l) + FO(t) ';p(l0)) → ((h | l0) | t0) | false = []) ∧ (pcf(t0) = R2 ∨ pcf(t0) = R3 → l1 ≠ lsf(t0).l ∧ ¬ FO(t0) ∈ (lsf(t).l = l1 ⊃ p(lsf(t).l) + FO(t) ';p(l1)) → ((h | l1) | t0) | false = [])

Rule argument

Additional information

Proof step 11 from proof step-absstep-W4-W5-tau-other (previous step) (back to tree)

Heuristic elimination applied rule apply elim lemma

And obtained the following new goals

• Proof step 12:

  lsf(t).t = t, alsf(t0) = mkPLIBls(t0, il, iv, ov), alsf(t) = mkPLIBls(t, lsf(t).l, lsf(t).v, ov0), apcf(t) = resWrite, lsf(t0) = mkFLITPSCls(t2, l2, v), lsf0(t) = lsf(t), pcf(t) = W4, pcf0(t) = W5, t2 = t0, (∅ ⊕ (h | true)) ⊕ p = ∅ ⊕ h, t ≠ t0, FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p(lsf(t).l := p(lsf(t).l) + FO(t) '), ctr, writers, writers0), lsf(t0), pcf(t0)), FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t0), pcf(t0)), FOFollowsW(t, p(lsf(t).l) + FO(t) '), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t, lsf(t).l, lsf(t).v, ov0), resWrite), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t0, il, iv, ov), apcf(t0)), abs(h, writers0, p), allReadsOK(h), allWritesOK(h), ctrok(ctr, writers), notMember(t, writers0), oneMember(t, lsf(t).l, writers), onePendingW(t, lsf(t).l, p), onePendingW(t, lsf(t).l, p(lsf(t).l := p(lsf(t).l) + FO(t) ')), pendingOk(p), pendingOk(p(lsf(t).l := p(lsf(t).l) + FO(t) ')), writersOk(p, writers), writersOk(p(lsf(t).l := p(lsf(t).l) + FO(t) '), writers), pcf(t0) = W4 → ((h | l2) | t0) | false = (W(t0, l2, v), false) ' ∨ ((h | l2) | t0) | false = [], pcf(t0) = R2 → ctr(l2) = 0 → ((h | l2) | t0) | false = [], pcf(t0) = R2 ∨ pcf(t0) = R3 → (∀ l0. l0 ≠ l2 ∧ ¬ FO(t0) ∈ p(l0) → ((h | l0) | t0) | false = []), pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → (∀ l. ((h | l) | t0) | false = []), pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → (∀ l. ¬ FO(t0) ∈ p(l) → ((h | l) | t0) | false = []), pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → l2 = il ∧ v = iv, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → v = ov, pcf(t0) = R1 → l2 = il, pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → apcf(t0) = resWrite, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 → apcf(t0) = invWrite, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → apcf(t0) = resRead, pcf(t0) = R1 → apcf(t0) = invRead, pcf(t0) = crashed → apcf(t0) = crashed, pcf(t0) = ready → apcf(t0) = ready, pcf(t0) = idle → apcf(t0) = idle, ∀ t1. t1 ≠ t ∧ t1 ≠ t0 → FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1)) ∧ PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)) ∧ labs(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1), mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)), ∀ t1. lsf(t1).t = t1, ∀ t1. alsf(t1).t = t1, ((h | lsf(t).l) | t) | false = (W(t, lsf(t).l, lsf(t).v), false) ' ∨ ((h | lsf(t).l) | t) | false = [] ⊦ ( pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → ¬ FO(t0) ∈ (lsf(t).l = l0 ⊃ p(lsf(t).l) + FO(t) ';p(l0)) → ((h | l0) | t0) | false = []) ∧ (pcf(t0) = R2 ∨ pcf(t0) = R3 → l1 ≠ l2 ∧ ¬ FO(t0) ∈ (lsf(t).l = l1 ⊃ p(lsf(t).l) + FO(t) ';p(l1)) → ((h | l1) | t0) | false = [])

Rule argument

Additional information

Used simplifier rules: ⊦ (t = ls.t ∧ l = ls.l) ∧ v = ls.v ↔ ls = mkFLITPSCls(t, l, v); (elim) Used terms: lsf(t0), t2, l2, v

Proof step 12 from proof step-absstep-W4-W5-tau-other (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 13:

  lsf(t).t = t, alsf(t) = mkPLIBls(t, lsf(t).l, lsf(t).v, ov0), alsf(t0) = mkPLIBls(t0, il, iv, ov), apcf(t) = resWrite, lsf(t0) = mkFLITPSCls(t0, l2, v), lsf0(t) = lsf(t), pcf(t) = W4, pcf0(t) = W5, (∅ ⊕ (h | true)) ⊕ p = ∅ ⊕ h, t ≠ t0, FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p(lsf(t).l := p(lsf(t).l) + FO(t) '), ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FOFollowsW(t, p(lsf(t).l) + FO(t) '), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t0, il, iv, ov), apcf(t0)), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t, lsf(t).l, lsf(t).v, ov0), resWrite), abs(h, writers0, p), allReadsOK(h), allWritesOK(h), ctrok(ctr, writers), notMember(t, writers0), oneMember(t, lsf(t).l, writers), onePendingW(t, lsf(t).l, p(lsf(t).l := p(lsf(t).l) + FO(t) ')), onePendingW(t, lsf(t).l, p), pendingOk(p(lsf(t).l := p(lsf(t).l) + FO(t) ')), pendingOk(p), writersOk(p(lsf(t).l := p(lsf(t).l) + FO(t) '), writers), writersOk(p, writers), pcf(t0) = idle → apcf(t0) = idle, pcf(t0) = ready → apcf(t0) = ready, pcf(t0) = crashed → apcf(t0) = crashed, pcf(t0) = R1 → apcf(t0) = invRead, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → apcf(t0) = resRead, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 → apcf(t0) = invWrite, pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → apcf(t0) = resWrite, pcf(t0) = R1 → l2 = il, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → v = ov, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → l2 = il ∧ v = iv, pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → (∀ l. ¬ FO(t0) ∈ p(l) → ((h | l) | t0) | false = []), pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → (∀ l. ((h | l) | t0) | false = []), pcf(t0) = R2 ∨ pcf(t0) = R3 → (∀ l0. l0 ≠ l2 ∧ ¬ FO(t0) ∈ p(l0) → ((h | l0) | t0) | false = []), pcf(t0) = R2 → ctr(l2) = 0 → ((h | l2) | t0) | false = [], pcf(t0) = W4 → ((h | l2) | t0) | false = (W(t0, l2, v), false) ' ∨ ((h | l2) | t0) | false = [], ∀ t1. alsf(t1).t = t1, ∀ t1. lsf(t1).t = t1, ∀ t1. t1 ≠ t ∧ t1 ≠ t0 → FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1)) ∧ PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)) ∧ labs(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1), mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)), ((h | lsf(t).l) | t) | false = (W(t, lsf(t).l, lsf(t).v), false) ' ∨ ((h | lsf(t).l) | t) | false = [] ⊦ ( pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → ¬ FO(t0) ∈ (lsf(t).l = l0 ⊃ p(lsf(t).l) + FO(t) ';p(l0)) → ((h | l0) | t0) | false = []) ∧ (pcf(t0) = R2 ∨ pcf(t0) = R3 → l1 ≠ l2 ∧ ¬ FO(t0) ∈ (lsf(t).l = l1 ⊃ p(lsf(t).l) + FO(t) ';p(l1)) → ((h | l1) | t0) | false = [])

Rule argument

Additional information

Proof step 13 from proof step-absstep-W4-W5-tau-other (previous step) (back to tree)

Heuristic elimination applied rule apply elim lemma

And obtained the following new goals

• Proof step 14:

  alsf(t0) = mkPLIBls(t0, il, iv, ov), alsf(t) = mkPLIBls(t, l3, v0, ov0), apcf(t) = resWrite, lsf(t0) = mkFLITPSCls(t0, l2, v), lsf(t) = mkFLITPSCls(t2, l3, v0), lsf0(t) = lsf(t), pcf(t) = W4, pcf0(t) = W5, t2 = t, (∅ ⊕ (h | true)) ⊕ p = ∅ ⊕ h, t ≠ t0, FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p(l3 := p(l3) + FO(t) '), ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FOFollowsW(t, p(l3) + FO(t) '), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t, l3, v0, ov0), resWrite), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t0, il, iv, ov), apcf(t0)), abs(h, writers0, p), allReadsOK(h), allWritesOK(h), ctrok(ctr, writers), notMember(t, writers0), oneMember(t, l3, writers), onePendingW(t, l3, p), onePendingW(t, l3, p(l3 := p(l3) + FO(t) ')), pendingOk(p), pendingOk(p(l3 := p(l3) + FO(t) ')), writersOk(p, writers), writersOk(p(l3 := p(l3) + FO(t) '), writers), pcf(t0) = W4 → ((h | l2) | t0) | false = (W(t0, l2, v), false) ' ∨ ((h | l2) | t0) | false = [], pcf(t0) = R2 → ctr(l2) = 0 → ((h | l2) | t0) | false = [], pcf(t0) = R2 ∨ pcf(t0) = R3 → (∀ l0. l0 ≠ l2 ∧ ¬ FO(t0) ∈ p(l0) → ((h | l0) | t0) | false = []), pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → (∀ l. ((h | l) | t0) | false = []), pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → (∀ l. ¬ FO(t0) ∈ p(l) → ((h | l) | t0) | false = []), pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → l2 = il ∧ v = iv, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → v = ov, pcf(t0) = R1 → l2 = il, pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → apcf(t0) = resWrite, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 → apcf(t0) = invWrite, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → apcf(t0) = resRead, pcf(t0) = R1 → apcf(t0) = invRead, pcf(t0) = crashed → apcf(t0) = crashed, pcf(t0) = ready → apcf(t0) = ready, pcf(t0) = idle → apcf(t0) = idle, ∀ t1. t1 ≠ t ∧ t1 ≠ t0 → FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1)) ∧ PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)) ∧ labs(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1), mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)), ∀ t1. lsf(t1).t = t1, ∀ t1. alsf(t1).t = t1, ((h | l3) | t) | false = (W(t, l3, v0), false) ' ∨ ((h | l3) | t) | false = [] ⊦ ( pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → ¬ FO(t0) ∈ (l3 = l0 ⊃ p(l3) + FO(t) ';p(l0)) → ((h | l0) | t0) | false = []) ∧ (pcf(t0) = R2 ∨ pcf(t0) = R3 → l1 ≠ l2 ∧ ¬ FO(t0) ∈ (l3 = l1 ⊃ p(l3) + FO(t) ';p(l1)) → ((h | l1) | t0) | false = [])

Rule argument

Additional information

Used simplifier rules: ⊦ (t = ls.t ∧ l = ls.l) ∧ v = ls.v ↔ ls = mkFLITPSCls(t, l, v); (elim) Used terms: lsf(t), t2, l3, v0

Proof step 14 from proof step-absstep-W4-W5-tau-other (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 15:

  alsf(t) = mkPLIBls(t, l3, v0, ov0), alsf(t0) = mkPLIBls(t0, il, iv, ov), apcf(t) = resWrite, lsf(t) = mkFLITPSCls(t, l3, v0), lsf(t0) = mkFLITPSCls(t0, l2, v), lsf0(t) = mkFLITPSCls(t, l3, v0), pcf(t) = W4, pcf0(t) = W5, (∅ ⊕ (h | true)) ⊕ p = ∅ ⊕ h, t ≠ t0, FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p(l3 := p(l3) + FO(t) '), ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FOFollowsW(t, p(l3) + FO(t) '), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t0, il, iv, ov), apcf(t0)), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t, l3, v0, ov0), resWrite), abs(h, writers0, p), allReadsOK(h), allWritesOK(h), ctrok(ctr, writers), notMember(t, writers0), oneMember(t, l3, writers), onePendingW(t, l3, p(l3 := p(l3) + FO(t) ')), onePendingW(t, l3, p), pendingOk(p(l3 := p(l3) + FO(t) ')), pendingOk(p), writersOk(p(l3 := p(l3) + FO(t) '), writers), writersOk(p, writers), pcf(t0) = idle → apcf(t0) = idle, pcf(t0) = ready → apcf(t0) = ready, pcf(t0) = crashed → apcf(t0) = crashed, pcf(t0) = R1 → apcf(t0) = invRead, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → apcf(t0) = resRead, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 → apcf(t0) = invWrite, pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → apcf(t0) = resWrite, pcf(t0) = R1 → l2 = il, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → v = ov, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → l2 = il ∧ v = iv, pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → (∀ l. ¬ FO(t0) ∈ p(l) → ((h | l) | t0) | false = []), pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → (∀ l. ((h | l) | t0) | false = []), pcf(t0) = R2 ∨ pcf(t0) = R3 → (∀ l0. l0 ≠ l2 ∧ ¬ FO(t0) ∈ p(l0) → ((h | l0) | t0) | false = []), pcf(t0) = R2 → ctr(l2) = 0 → ((h | l2) | t0) | false = [], pcf(t0) = W4 → ((h | l2) | t0) | false = (W(t0, l2, v), false) ' ∨ ((h | l2) | t0) | false = [], ∀ t1. alsf(t1).t = t1, ∀ t1. lsf(t1).t = t1, ∀ t1. t1 ≠ t ∧ t1 ≠ t0 → FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1)) ∧ PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)) ∧ labs(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1), mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)), ((h | l3) | t) | false = (W(t, l3, v0), false) ' ∨ ((h | l3) | t) | false = [] ⊦ ( pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → ¬ FO(t0) ∈ (l3 = l0 ⊃ p(l0) + FO(t) ';p(l0)) → ((h | l0) | t0) | false = []) ∧ (pcf(t0) = R2 ∨ pcf(t0) = R3 → l1 ≠ l2 ∧ ¬ FO(t0) ∈ (l3 = l1 ⊃ p(l1) + FO(t) ';p(l1)) → ((h | l1) | t0) | false = [])

Rule argument

Additional information

Proof step 15 from proof step-absstep-W4-W5-tau-other (previous step) (back to tree)

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

• Proof step 16:

  alsf(t0) = mkPLIBls(t0, il, iv, ov), alsf(t) = mkPLIBls(t, l3, v0, ov0), apcf(t) = resWrite, lsf(t0) = mkFLITPSCls(t0, l2, v), lsf(t) = mkFLITPSCls(t, l3, v0), lsf0(t) = mkFLITPSCls(t, l3, v0), pcf(t) = W4, pcf0(t) = W5, (∅ ⊕ (h | true)) ⊕ p = ∅ ⊕ h, t ≠ t0, ((h | l0) | t0) | false ≠ [], FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p(l3 := p(l3) + FO(t) '), ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FOFollowsW(t, p(l3) + FO(t) '), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t, l3, v0, ov0), resWrite), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t0, il, iv, ov), apcf(t0)), abs(h, writers0, p), allReadsOK(h), allWritesOK(h), ctrok(ctr, writers), notMember(t, writers0), oneMember(t, l3, writers), onePendingW(t, l3, p), onePendingW(t, l3, p(l3 := p(l3) + FO(t) ')), pendingOk(p), pendingOk(p(l3 := p(l3) + FO(t) ')), writersOk(p, writers), writersOk(p(l3 := p(l3) + FO(t) '), writers), ¬ FO(t0) ∈ (l3 = l0 ⊃ p(l0) + FO(t) ';p(l0)), pcf(t0) = W4 → ((h | l2) | t0) | false = (W(t0, l2, v), false) ' ∨ ((h | l2) | t0) | false = [], pcf(t0) = R2 → ctr(l2) = 0 → ((h | l2) | t0) | false = [], pcf(t0) = R2 ∨ pcf(t0) = R3 → (∀ l0. l0 ≠ l2 ∧ ¬ FO(t0) ∈ p(l0) → ((h | l0) | t0) | false = []), pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → (∀ l. ((h | l) | t0) | false = []), pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → (∀ l. ¬ FO(t0) ∈ p(l) → ((h | l) | t0) | false = []), pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → l2 = il ∧ v = iv, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → v = ov, pcf(t0) = R1 → l2 = il, pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → apcf(t0) = resWrite, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 → apcf(t0) = invWrite, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → apcf(t0) = resRead, pcf(t0) = R1 → apcf(t0) = invRead, pcf(t0) = crashed → apcf(t0) = crashed, pcf(t0) = ready → apcf(t0) = ready, pcf(t0) = idle → apcf(t0) = idle, ∀ t1. t1 ≠ t ∧ t1 ≠ t0 → FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1)) ∧ PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)) ∧ labs(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1), mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)), ∀ t1. lsf(t1).t = t1, ∀ t1. alsf(t1).t = t1, pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5, ((h | l3) | t) | false = (W(t, l3, v0), false) ' ∨ ((h | l3) | t) | false = [] ⊦

• Proof step 21:

  alsf(t0) = mkPLIBls(t0, il, iv, ov), alsf(t) = mkPLIBls(t, l3, v0, ov0), apcf(t) = resWrite, lsf(t0) = mkFLITPSCls(t0, l2, v), lsf(t) = mkFLITPSCls(t, l3, v0), lsf0(t) = mkFLITPSCls(t, l3, v0), pcf(t) = W4, pcf0(t) = W5, (∅ ⊕ (h | true)) ⊕ p = ∅ ⊕ h, l1 ≠ l2, t ≠ t0, ((h | l1) | t0) | false ≠ [], FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p(l3 := p(l3) + FO(t) '), ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FOFollowsW(t, p(l3) + FO(t) '), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t, l3, v0, ov0), resWrite), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t0, il, iv, ov), apcf(t0)), abs(h, writers0, p), allReadsOK(h), allWritesOK(h), ctrok(ctr, writers), notMember(t, writers0), oneMember(t, l3, writers), onePendingW(t, l3, p), onePendingW(t, l3, p(l3 := p(l3) + FO(t) ')), pendingOk(p), pendingOk(p(l3 := p(l3) + FO(t) ')), writersOk(p, writers), writersOk(p(l3 := p(l3) + FO(t) '), writers), ¬ FO(t0) ∈ (l3 = l1 ⊃ p(l1) + FO(t) ';p(l1)), pcf(t0) = W4 → ((h | l2) | t0) | false = (W(t0, l2, v), false) ' ∨ ((h | l2) | t0) | false = [], pcf(t0) = R2 → ctr(l2) = 0 → ((h | l2) | t0) | false = [], pcf(t0) = R2 ∨ pcf(t0) = R3 → (∀ l0. l0 ≠ l2 ∧ ¬ FO(t0) ∈ p(l0) → ((h | l0) | t0) | false = []), pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → (∀ l. ((h | l) | t0) | false = []), pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → (∀ l. ¬ FO(t0) ∈ p(l) → ((h | l) | t0) | false = []), pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → l2 = il ∧ v = iv, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → v = ov, pcf(t0) = R1 → l2 = il, pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → apcf(t0) = resWrite, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 → apcf(t0) = invWrite, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → apcf(t0) = resRead, pcf(t0) = R1 → apcf(t0) = invRead, pcf(t0) = crashed → apcf(t0) = crashed, pcf(t0) = ready → apcf(t0) = ready, pcf(t0) = idle → apcf(t0) = idle, ∀ t1. t1 ≠ t ∧ t1 ≠ t0 → FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1)) ∧ PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)) ∧ labs(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1), mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)), ∀ t1. lsf(t1).t = t1, ∀ t1. alsf(t1).t = t1, pcf(t0) = R2 ∨ pcf(t0) = R3, ((h | l3) | t) | false = (W(t, l3, v0), false) ' ∨ ((h | l3) | t) | false = [] ⊦

Rule argument

Additional information

Proof step 16 from proof step-absstep-W4-W5-tau-other (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 17:

  alsf(t) = mkPLIBls(t, l3, v0, ov0), alsf(t0) = mkPLIBls(t0, il, iv, ov), apcf(t) = resWrite, lsf(t) = mkFLITPSCls(t, l3, v0), lsf(t0) = mkFLITPSCls(t0, l2, v), lsf0(t) = mkFLITPSCls(t, l3, v0), pcf(t) = W4, pcf0(t) = W5, (∅ ⊕ (h | true)) ⊕ p = ∅ ⊕ h, t ≠ t0, ((h | l0) | t0) | false ≠ [], FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p(l3 := p(l3) + FO(t) '), ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FOFollowsW(t, p(l3) + FO(t) '), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t0, il, iv, ov), apcf(t0)), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t, l3, v0, ov0), resWrite), abs(h, writers0, p), allReadsOK(h), allWritesOK(h), ctrok(ctr, writers), notMember(t, writers0), oneMember(t, l3, writers), onePendingW(t, l3, p(l3 := p(l3) + FO(t) ')), onePendingW(t, l3, p), pendingOk(p(l3 := p(l3) + FO(t) ')), pendingOk(p), writersOk(p(l3 := p(l3) + FO(t) '), writers), writersOk(p, writers), ¬ FO(t0) ∈ (l3 = l0 ⊃ p(l0) + FO(t) ';p(l0)), pcf(t0) = idle → apcf(t0) = idle, pcf(t0) = ready → apcf(t0) = ready, pcf(t0) = crashed → apcf(t0) = crashed, pcf(t0) = R1 → apcf(t0) = invRead, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → apcf(t0) = resRead, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 → apcf(t0) = invWrite, pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → apcf(t0) = resWrite, pcf(t0) = R1 → l2 = il, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → v = ov, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → l2 = il ∧ v = iv, pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → (∀ l. ((h | l) | t0) | false = []), pcf(t0) = R2 ∨ pcf(t0) = R3 → (∀ l0. l0 ≠ l2 ∧ ¬ FO(t0) ∈ p(l0) → ((h | l0) | t0) | false = []), pcf(t0) = R2 → ctr(l2) = 0 → ((h | l2) | t0) | false = [], pcf(t0) = W4 → ((h | l2) | t0) | false = (W(t0, l2, v), false) ' ∨ ((h | l2) | t0) | false = [], ∀ t1. alsf(t1).t = t1, ∀ t1. lsf(t1).t = t1, ∀ t1. t1 ≠ t ∧ t1 ≠ t0 → FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1)) ∧ PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)) ∧ labs(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1), mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)), ∀ l. ¬ FO(t0) ∈ p(l) → ((h | l) | t0) | false = [], ((h | l3) | t) | false = (W(t, l3, v0), false) ' ∨ ((h | l3) | t) | false = [], pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 ⊦

Rule argument

Additional information

Proof step 17 from proof step-absstep-W4-W5-tau-other (previous step) (back to tree)

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

• Proof step 18:

  alsf(t0) = mkPLIBls(t0, il, iv, ov), alsf(t) = mkPLIBls(t, l3, v0, ov0), apcf(t) = resWrite, l3 = l0, lsf(t0) = mkFLITPSCls(t0, l2, v), lsf(t) = mkFLITPSCls(t, l3, v0), lsf0(t) = mkFLITPSCls(t, l3, v0), pcf(t) = W4, pcf0(t) = W5, (∅ ⊕ (h | true)) ⊕ p = ∅ ⊕ h, t ≠ t0, ((h | l0) | t0) | false ≠ [], FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p(l3 := p(l3) + FO(t) '), ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FOFollowsW(t, p(l3) + FO(t) '), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t, l3, v0, ov0), resWrite), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t0, il, iv, ov), apcf(t0)), abs(h, writers0, p), allReadsOK(h), allWritesOK(h), ctrok(ctr, writers), notMember(t, writers0), oneMember(t, l3, writers), onePendingW(t, l3, p), onePendingW(t, l3, p(l3 := p(l3) + FO(t) ')), pendingOk(p), pendingOk(p(l3 := p(l3) + FO(t) ')), writersOk(p, writers), writersOk(p(l3 := p(l3) + FO(t) '), writers), ¬ FO(t0) ∈ p(l0) + FO(t) ', pcf(t0) = W4 → ((h | l2) | t0) | false = (W(t0, l2, v), false) ' ∨ ((h | l2) | t0) | false = [], pcf(t0) = R2 → ctr(l2) = 0 → ((h | l2) | t0) | false = [], pcf(t0) = R2 ∨ pcf(t0) = R3 → (∀ l0. l0 ≠ l2 ∧ ¬ FO(t0) ∈ p(l0) → ((h | l0) | t0) | false = []), pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → (∀ l. ((h | l) | t0) | false = []), pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → l2 = il ∧ v = iv, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → v = ov, pcf(t0) = R1 → l2 = il, pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → apcf(t0) = resWrite, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 → apcf(t0) = invWrite, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → apcf(t0) = resRead, pcf(t0) = R1 → apcf(t0) = invRead, pcf(t0) = crashed → apcf(t0) = crashed, pcf(t0) = ready → apcf(t0) = ready, pcf(t0) = idle → apcf(t0) = idle, ∀ l. ¬ FO(t0) ∈ p(l) → ((h | l) | t0) | false = [], ∀ t1. t1 ≠ t ∧ t1 ≠ t0 → FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1)) ∧ PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)) ∧ labs(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1), mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)), ∀ t1. lsf(t1).t = t1, ∀ t1. alsf(t1).t = t1, pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5, ((h | l3) | t) | false = (W(t, l3, v0), false) ' ∨ ((h | l3) | t) | false = [] ⊦

• Proof step 20:

  alsf(t0) = mkPLIBls(t0, il, iv, ov), alsf(t) = mkPLIBls(t, l3, v0, ov0), apcf(t) = resWrite, lsf(t0) = mkFLITPSCls(t0, l2, v), lsf(t) = mkFLITPSCls(t, l3, v0), lsf0(t) = mkFLITPSCls(t, l3, v0), pcf(t) = W4, pcf0(t) = W5, (∅ ⊕ (h | true)) ⊕ p = ∅ ⊕ h, l3 ≠ l0, t ≠ t0, ((h | l0) | t0) | false ≠ [], FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p(l3 := p(l3) + FO(t) '), ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FOFollowsW(t, p(l3) + FO(t) '), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t, l3, v0, ov0), resWrite), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t0, il, iv, ov), apcf(t0)), abs(h, writers0, p), allReadsOK(h), allWritesOK(h), ctrok(ctr, writers), notMember(t, writers0), oneMember(t, l3, writers), onePendingW(t, l3, p), onePendingW(t, l3, p(l3 := p(l3) + FO(t) ')), pendingOk(p), pendingOk(p(l3 := p(l3) + FO(t) ')), writersOk(p, writers), writersOk(p(l3 := p(l3) + FO(t) '), writers), ¬ FO(t0) ∈ p(l0), pcf(t0) = W4 → ((h | l2) | t0) | false = (W(t0, l2, v), false) ' ∨ ((h | l2) | t0) | false = [], pcf(t0) = R2 → ctr(l2) = 0 → ((h | l2) | t0) | false = [], pcf(t0) = R2 ∨ pcf(t0) = R3 → (∀ l0. l0 ≠ l2 ∧ ¬ FO(t0) ∈ p(l0) → ((h | l0) | t0) | false = []), pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → (∀ l. ((h | l) | t0) | false = []), pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → l2 = il ∧ v = iv, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → v = ov, pcf(t0) = R1 → l2 = il, pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → apcf(t0) = resWrite, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 → apcf(t0) = invWrite, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → apcf(t0) = resRead, pcf(t0) = R1 → apcf(t0) = invRead, pcf(t0) = crashed → apcf(t0) = crashed, pcf(t0) = ready → apcf(t0) = ready, pcf(t0) = idle → apcf(t0) = idle, ∀ l. ¬ FO(t0) ∈ p(l) → ((h | l) | t0) | false = [], ∀ t1. t1 ≠ t ∧ t1 ≠ t0 → FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1)) ∧ PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)) ∧ labs(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1), mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)), ∀ t1. lsf(t1).t = t1, ∀ t1. alsf(t1).t = t1, pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5, ((h | l3) | t) | false = (W(t, l3, v0), false) ' ∨ ((h | l3) | t) | false = [] ⊦

Rule argument

Additional information

Proof step 18 from proof step-absstep-W4-W5-tau-other (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 19:

  alsf(t) = mkPLIBls(t, l0, v0, ov0), alsf(t0) = mkPLIBls(t0, il, iv, ov), apcf(t) = resWrite, lsf(t) = mkFLITPSCls(t, l0, v0), lsf(t0) = mkFLITPSCls(t0, l2, v), lsf0(t) = mkFLITPSCls(t, l0, v0), pcf(t) = W4, pcf0(t) = W5, (∅ ⊕ (h | true)) ⊕ p = ∅ ⊕ h, t ≠ t0, ((h | l0) | t0) | false ≠ [], FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p(l0 := p(l0) + FO(t) '), ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FOFollowsW(t, p(l0) + FO(t) '), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t0, il, iv, ov), apcf(t0)), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t, l0, v0, ov0), resWrite), abs(h, writers0, p), allReadsOK(h), allWritesOK(h), ctrok(ctr, writers), notMember(t, writers0), oneMember(t, l0, writers), onePendingW(t, l0, p(l0 := p(l0) + FO(t) ')), onePendingW(t, l0, p), pendingOk(p(l0 := p(l0) + FO(t) ')), pendingOk(p), writersOk(p(l0 := p(l0) + FO(t) '), writers), writersOk(p, writers), ¬ FO(t0) ∈ p(l0), pcf(t0) = idle → apcf(t0) = idle, pcf(t0) = ready → apcf(t0) = ready, pcf(t0) = crashed → apcf(t0) = crashed, pcf(t0) = R1 → apcf(t0) = invRead, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → apcf(t0) = resRead, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 → apcf(t0) = invWrite, pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → apcf(t0) = resWrite, pcf(t0) = R1 → l2 = il, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → v = ov, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → l2 = il ∧ v = iv, pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → (∀ l. ((h | l) | t0) | false = []), pcf(t0) = R2 ∨ pcf(t0) = R3 → (∀ l0. l0 ≠ l2 ∧ ¬ FO(t0) ∈ p(l0) → ((h | l0) | t0) | false = []), pcf(t0) = R2 → ctr(l2) = 0 → ((h | l2) | t0) | false = [], pcf(t0) = W4 → ((h | l2) | t0) | false = (W(t0, l2, v), false) ' ∨ ((h | l2) | t0) | false = [], ∀ t1. alsf(t1).t = t1, ∀ t1. lsf(t1).t = t1, ∀ t1. t1 ≠ t ∧ t1 ≠ t0 → FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1)) ∧ PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)) ∧ labs(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1), mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)), ∀ l. ¬ FO(t0) ∈ p(l) → ((h | l) | t0) | false = [], ((h | l0) | t) | false = (W(t, l0, v0), false) ' ∨ ((h | l0) | t) | false = [], pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 ⊦

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list ⊦ FO(tid) = FO(tid0) ↔ tid = tid0; (s) ⊦ a ∈ a0 ' ↔ a = a0; (s) ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y; (s)

Proof step 19 from proof step-absstep-W4-W5-tau-other (previous step) (back to tree)

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

Additional information

Used terms: l0

Proof step 20 from proof step-absstep-W4-W5-tau-other (previous step) (back to tree)

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

Additional information

Used terms: l0

Proof step 21 from proof step-absstep-W4-W5-tau-other (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 22:

  alsf(t) = mkPLIBls(t, l3, v0, ov0), alsf(t0) = mkPLIBls(t0, il, iv, ov), apcf(t) = resWrite, lsf(t) = mkFLITPSCls(t, l3, v0), lsf(t0) = mkFLITPSCls(t0, l2, v), lsf0(t) = mkFLITPSCls(t, l3, v0), pcf(t) = W4, pcf0(t) = W5, (∅ ⊕ (h | true)) ⊕ p = ∅ ⊕ h, l1 ≠ l2, t ≠ t0, ((h | l1) | t0) | false ≠ [], FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p(l3 := p(l3) + FO(t) '), ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FOFollowsW(t, p(l3) + FO(t) '), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t0, il, iv, ov), apcf(t0)), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t, l3, v0, ov0), resWrite), abs(h, writers0, p), allReadsOK(h), allWritesOK(h), ctrok(ctr, writers), notMember(t, writers0), oneMember(t, l3, writers), onePendingW(t, l3, p(l3 := p(l3) + FO(t) ')), onePendingW(t, l3, p), pendingOk(p(l3 := p(l3) + FO(t) ')), pendingOk(p), writersOk(p(l3 := p(l3) + FO(t) '), writers), writersOk(p, writers), ¬ FO(t0) ∈ (l3 = l1 ⊃ p(l1) + FO(t) ';p(l1)), pcf(t0) = idle → apcf(t0) = idle, pcf(t0) = ready → apcf(t0) = ready, pcf(t0) = crashed → apcf(t0) = crashed, pcf(t0) = R1 → apcf(t0) = invRead, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → apcf(t0) = resRead, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 → apcf(t0) = invWrite, pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → apcf(t0) = resWrite, pcf(t0) = R1 → l2 = il, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → v = ov, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → l2 = il ∧ v = iv, pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → (∀ l. ¬ FO(t0) ∈ p(l) → ((h | l) | t0) | false = []), pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → (∀ l. ((h | l) | t0) | false = []), pcf(t0) = R2 → ctr(l2) = 0 → ((h | l2) | t0) | false = [], pcf(t0) = W4 → ((h | l2) | t0) | false = (W(t0, l2, v), false) ' ∨ ((h | l2) | t0) | false = [], ∀ t1. alsf(t1).t = t1, ∀ t1. lsf(t1).t = t1, ∀ t1. t1 ≠ t ∧ t1 ≠ t0 → FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1)) ∧ PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)) ∧ labs(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1), mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)), ∀ l0. l0 ≠ l2 ∧ ¬ FO(t0) ∈ p(l0) → ((h | l0) | t0) | false = [], ((h | l3) | t) | false = (W(t, l3, v0), false) ' ∨ ((h | l3) | t) | false = [], pcf(t0) = R2 ∨ pcf(t0) = R3 ⊦

Rule argument

Additional information

Proof step 22 from proof step-absstep-W4-W5-tau-other (previous step) (back to tree)

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

• Proof step 23:

  alsf(t0) = mkPLIBls(t0, il, iv, ov), alsf(t) = mkPLIBls(t, l3, v0, ov0), apcf(t) = resWrite, l3 = l1, lsf(t0) = mkFLITPSCls(t0, l2, v), lsf(t) = mkFLITPSCls(t, l3, v0), lsf0(t) = mkFLITPSCls(t, l3, v0), pcf(t) = W4, pcf0(t) = W5, (∅ ⊕ (h | true)) ⊕ p = ∅ ⊕ h, l1 ≠ l2, t ≠ t0, ((h | l1) | t0) | false ≠ [], FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p(l3 := p(l3) + FO(t) '), ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FOFollowsW(t, p(l3) + FO(t) '), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t, l3, v0, ov0), resWrite), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t0, il, iv, ov), apcf(t0)), abs(h, writers0, p), allReadsOK(h), allWritesOK(h), ctrok(ctr, writers), notMember(t, writers0), oneMember(t, l3, writers), onePendingW(t, l3, p), onePendingW(t, l3, p(l3 := p(l3) + FO(t) ')), pendingOk(p), pendingOk(p(l3 := p(l3) + FO(t) ')), writersOk(p, writers), writersOk(p(l3 := p(l3) + FO(t) '), writers), ¬ FO(t0) ∈ p(l1) + FO(t) ', pcf(t0) = W4 → ((h | l2) | t0) | false = (W(t0, l2, v), false) ' ∨ ((h | l2) | t0) | false = [], pcf(t0) = R2 → ctr(l2) = 0 → ((h | l2) | t0) | false = [], pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → (∀ l. ((h | l) | t0) | false = []), pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → (∀ l. ¬ FO(t0) ∈ p(l) → ((h | l) | t0) | false = []), pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → l2 = il ∧ v = iv, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → v = ov, pcf(t0) = R1 → l2 = il, pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → apcf(t0) = resWrite, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 → apcf(t0) = invWrite, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → apcf(t0) = resRead, pcf(t0) = R1 → apcf(t0) = invRead, pcf(t0) = crashed → apcf(t0) = crashed, pcf(t0) = ready → apcf(t0) = ready, pcf(t0) = idle → apcf(t0) = idle, ∀ l0. l0 ≠ l2 ∧ ¬ FO(t0) ∈ p(l0) → ((h | l0) | t0) | false = [], ∀ t1. t1 ≠ t ∧ t1 ≠ t0 → FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1)) ∧ PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)) ∧ labs(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1), mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)), ∀ t1. lsf(t1).t = t1, ∀ t1. alsf(t1).t = t1, pcf(t0) = R2 ∨ pcf(t0) = R3, ((h | l3) | t) | false = (W(t, l3, v0), false) ' ∨ ((h | l3) | t) | false = [] ⊦

• Proof step 25:

  alsf(t0) = mkPLIBls(t0, il, iv, ov), alsf(t) = mkPLIBls(t, l3, v0, ov0), apcf(t) = resWrite, lsf(t0) = mkFLITPSCls(t0, l2, v), lsf(t) = mkFLITPSCls(t, l3, v0), lsf0(t) = mkFLITPSCls(t, l3, v0), pcf(t) = W4, pcf0(t) = W5, (∅ ⊕ (h | true)) ⊕ p = ∅ ⊕ h, l1 ≠ l2, l3 ≠ l1, t ≠ t0, ((h | l1) | t0) | false ≠ [], FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p(l3 := p(l3) + FO(t) '), ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FOFollowsW(t, p(l3) + FO(t) '), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t, l3, v0, ov0), resWrite), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t0, il, iv, ov), apcf(t0)), abs(h, writers0, p), allReadsOK(h), allWritesOK(h), ctrok(ctr, writers), notMember(t, writers0), oneMember(t, l3, writers), onePendingW(t, l3, p), onePendingW(t, l3, p(l3 := p(l3) + FO(t) ')), pendingOk(p), pendingOk(p(l3 := p(l3) + FO(t) ')), writersOk(p, writers), writersOk(p(l3 := p(l3) + FO(t) '), writers), ¬ FO(t0) ∈ p(l1), pcf(t0) = W4 → ((h | l2) | t0) | false = (W(t0, l2, v), false) ' ∨ ((h | l2) | t0) | false = [], pcf(t0) = R2 → ctr(l2) = 0 → ((h | l2) | t0) | false = [], pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → (∀ l. ((h | l) | t0) | false = []), pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → (∀ l. ¬ FO(t0) ∈ p(l) → ((h | l) | t0) | false = []), pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → l2 = il ∧ v = iv, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → v = ov, pcf(t0) = R1 → l2 = il, pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → apcf(t0) = resWrite, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 → apcf(t0) = invWrite, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → apcf(t0) = resRead, pcf(t0) = R1 → apcf(t0) = invRead, pcf(t0) = crashed → apcf(t0) = crashed, pcf(t0) = ready → apcf(t0) = ready, pcf(t0) = idle → apcf(t0) = idle, ∀ l0. l0 ≠ l2 ∧ ¬ FO(t0) ∈ p(l0) → ((h | l0) | t0) | false = [], ∀ t1. t1 ≠ t ∧ t1 ≠ t0 → FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1)) ∧ PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)) ∧ labs(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1), mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)), ∀ t1. lsf(t1).t = t1, ∀ t1. alsf(t1).t = t1, pcf(t0) = R2 ∨ pcf(t0) = R3, ((h | l3) | t) | false = (W(t, l3, v0), false) ' ∨ ((h | l3) | t) | false = [] ⊦

Rule argument

Additional information

Proof step 23 from proof step-absstep-W4-W5-tau-other (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 24:

  alsf(t) = mkPLIBls(t, l1, v0, ov0), alsf(t0) = mkPLIBls(t0, il, iv, ov), apcf(t) = resWrite, lsf(t) = mkFLITPSCls(t, l1, v0), lsf(t0) = mkFLITPSCls(t0, l2, v), lsf0(t) = mkFLITPSCls(t, l1, v0), pcf(t) = W4, pcf0(t) = W5, (∅ ⊕ (h | true)) ⊕ p = ∅ ⊕ h, l1 ≠ l2, t ≠ t0, ((h | l1) | t0) | false ≠ [], FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p(l1 := p(l1) + FO(t) '), ctr, writers, writers0), mkFLITPSCls(t0, l2, v), pcf(t0)), FOFollowsW(t, p(l1) + FO(t) '), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t0, il, iv, ov), apcf(t0)), PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), mkPLIBls(t, l1, v0, ov0), resWrite), abs(h, writers0, p), allReadsOK(h), allWritesOK(h), ctrok(ctr, writers), notMember(t, writers0), oneMember(t, l1, writers), onePendingW(t, l1, p(l1 := p(l1) + FO(t) ')), onePendingW(t, l1, p), pendingOk(p(l1 := p(l1) + FO(t) ')), pendingOk(p), writersOk(p(l1 := p(l1) + FO(t) '), writers), writersOk(p, writers), ¬ FO(t0) ∈ p(l1), pcf(t0) = idle → apcf(t0) = idle, pcf(t0) = ready → apcf(t0) = ready, pcf(t0) = crashed → apcf(t0) = crashed, pcf(t0) = R1 → apcf(t0) = invRead, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → apcf(t0) = resRead, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 → apcf(t0) = invWrite, pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → apcf(t0) = resWrite, pcf(t0) = R1 → l2 = il, pcf(t0) = R2 ∨ pcf(t0) = R3 ∨ pcf(t0) = R4 → v = ov, pcf(t0) = W1 ∨ pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W4 ∨ pcf(t0) = W5 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → l2 = il ∧ v = iv, pcf(t0) = idle ∨ pcf(t0) = ready ∨ pcf(t0) = R1 ∨ pcf(t0) = R4 ∨ pcf(t0) = W1 ∨ pcf(t0) = W5 → (∀ l. ¬ FO(t0) ∈ p(l) → ((h | l) | t0) | false = []), pcf(t0) = W2 ∨ pcf(t0) = W3 ∨ pcf(t0) = W6 ∨ pcf(t0) = W7 → (∀ l. ((h | l) | t0) | false = []), pcf(t0) = R2 → ctr(l2) = 0 → ((h | l2) | t0) | false = [], pcf(t0) = W4 → ((h | l2) | t0) | false = (W(t0, l2, v), false) ' ∨ ((h | l2) | t0) | false = [], ∀ t1. alsf(t1).t = t1, ∀ t1. lsf(t1).t = t1, ∀ t1. t1 ≠ t ∧ t1 ≠ t0 → FLITPSCLInv(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1)) ∧ PLIBLInv(mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)) ∧ labs(mkFLITPSCgs(∅ ⊕ (h | true), p, ctr, writers, writers0), lsf(t1), pcf(t1), mkPLIBgs(∅ ⊕ h, ∅ ⊕ (h | true), h), alsf(t1), apcf(t1)), ∀ l0. l0 ≠ l2 ∧ ¬ FO(t0) ∈ p(l0) → ((h | l0) | t0) | false = [], ((h | l1) | t) | false = (W(t, l1, v0), false) ' ∨ ((h | l1) | t) | false = [], pcf(t0) = R2 ∨ pcf(t0) = R3 ⊦

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list ⊦ FO(tid) = FO(tid0) ↔ tid = tid0; (s) ⊦ a ∈ a0 ' ↔ a = a0; (s) ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y; (s)

Proof step 24 from proof step-absstep-W4-W5-tau-other (previous step) (back to tree)

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

Additional information

Used terms: l1

Proof step 25 from proof step-absstep-W4-W5-tau-other (previous step) (back to tree)

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

Additional information

Used terms: l1