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Proof step 36 from proof rename-precond-abs (previous step)

inodekey(fs[ri[dentrykey(m3, str0)]].ino) ∈ ri ∧ ¬ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory ↔ ¬ fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory, fs[ri[inodekey(m4)]].directory, fs[ri[inodekey(m3)]].directory, orphans(fs, ri).inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(fi), ri-inj(ri), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), inodekey(fs[ri[dentrykey(m4, str)]].ino) ∈ ri, dentrykey(m4, str) ∈ ri, inodekey(m3) ∈ ri, inodekey(m4) ∈ ri, dentrykey(m3, str0) ∈ ri, m3 = m4 → md = md0, inodekey(fs[ri[dentrykey(m3, str0)]].ino) ∈ ri ∧ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory → fs[ri[dentrykey(m3, str0)]].ino ≠ ROOT_INO ∧ abs-children(fs[ri[dentrykey(m3, str0)]].ino, fs, ri) = ∅, links(m4, abs-dirs(fs, ri)) ≠ ∅ ∨ m4 = ROOT_INO, links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO, inodekey(fs[ri[dentrykey(m3, str0)]].ino) ∈ ri ∧ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory ∨ ¬ fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory, inodekey(fs[ri[dentrykey(m3, str0)]].ino) ∈ ri ∧ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nlink ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].size ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nsubdirs ∧ boolvar ∨ inodekey(fs[ri[dentrykey(m3, str0)]].ino) ∈ ri ∧ ¬ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nlink ∧ m1 = 0 ∧ ¬ boolvar, fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory ∧ m8 = fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].size ∧ m7 = fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].nsubdirs ∧ boolvar0 ∨ inodekey(fs[ri[dentrykey(m3, str0)]].ino) ∈ ri ∧ ¬ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory ∧ m7 = 0 ∧ ¬ boolvar0 ⊦ (fs[ri[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO) ∧ inodekey(fs[ri[dentrykey(m3, str0)]].ino) ∈ ri ∧ ( ¬ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory ∧ ¬ boolvar ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nlink ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory ∧ boolvar ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nlink ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nsubdirs ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].size) ∧ (fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory → dentrykeys(inodekey(fs[ri[dentrykey(m3, str0)]].ino), ri) = ∅) ∧ fs[ri[dentrykey(m3, str0)]].ino ≠ ROOT_INO ∧ m0 ≠ 0 ∧ (m0 = 1 → links(fs[ri[dentrykey(m3, str0)]].ino, fs, ri) = ∅ ++ dentrykey(m3, str0))

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 37:
inodekey(fs[ri[dentrykey(m3, str0)]].ino) ∈ ri ∧ ¬ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory ↔ ¬ fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory, fs[ri[inodekey(m3)]].directory, fs[ri[inodekey(m4)]].directory, orphans(fs, ri).inodes?, afs-cons(abs-dirs(fs, ri), abs-files(fs, ri)), file-node-cons(fs, ri), log-cons(log, fs), replay-cons-strong(fs, ri, orphans(fs, ri), fi, fo, log), ri-inj(ri), ri-inj(fi), ubifs-cons(fs, ri, orphans(fs, ri), fi, fo, log), dentrykey(m3, str0) ∈ ri, inodekey(m4) ∈ ri, inodekey(m3) ∈ ri, dentrykey(m4, str) ∈ ri, inodekey(fs[ri[dentrykey(m4, str)]].ino) ∈ ri, inodekey(fs[ri[dentrykey(m3, str0)]].ino) ∈ ri, inodekey(fs[ri[dentrykey(m3, str0)]].ino) ∈ ri ∧ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory → fs[ri[dentrykey(m3, str0)]].ino ≠ ROOT_INO ∧ abs-children(fs[ri[dentrykey(m3, str0)]].ino, fs, ri) = ∅, m3 = m4 → md = md0, fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory ∧ m8 = fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].size ∧ m7 = fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].nsubdirs ∧ boolvar0 ∨ inodekey(fs[ri[dentrykey(m3, str0)]].ino) ∈ ri ∧ ¬ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory ∧ m7 = 0 ∧ ¬ boolvar0, inodekey(fs[ri[dentrykey(m3, str0)]].ino) ∈ ri ∧ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nlink ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].size ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nsubdirs ∧ boolvar ∨ inodekey(fs[ri[dentrykey(m3, str0)]].ino) ∈ ri ∧ ¬ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nlink ∧ m1 = 0 ∧ ¬ boolvar, inodekey(fs[ri[dentrykey(m3, str0)]].ino) ∈ ri ∧ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory ∨ ¬ fs[ri[inodekey(fs[ri[dentrykey(m4, str)]].ino)]].directory, links(m3, abs-dirs(fs, ri)) ≠ ∅ ∨ m3 = ROOT_INO, links(m4, abs-dirs(fs, ri)) ≠ ∅ ∨ m4 = ROOT_INO ⊦ (fs[ri[inodekey(m3)]].nlink ≠ 0 ∨ m3 = ROOT_INO) ∧ inodekey(fs[ri[dentrykey(m3, str0)]].ino) ∈ ri ∧ ( ¬ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory ∧ ¬ boolvar ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nlink ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nsubdirs ∨ fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory ∧ boolvar ∧ m0 = fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nlink ∧ m1 = fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].nsubdirs ∧ m2 = fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].size) ∧ (fs[ri[inodekey(fs[ri[dentrykey(m3, str0)]].ino)]].directory → dentrykeys(inodekey(fs[ri[dentrykey(m3, str0)]].ino), ri) = ∅) ∧ fs[ri[dentrykey(m3, str0)]].ino ≠ ROOT_INO ∧ m0 ≠ 0 ∧ (m0 = 1 → links(fs[ri[dentrykey(m3, str0)]].ino, fs, ri) = ∅ ++ dentrykey(m3, str0))

Rule argument

fma: inodekey(fs[ri[dentrykey(m3, str0)]].ino) ∈ ri

Additional information

Used formulas: inodekey(fs[ri[dentrykey(m3, str0)]].ino) ∈ ri