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Proof step 84 from proof afs-cons-rename-dir-negdentry (previous step)

(m0 = m ⊃ mkdir(m1, md, # links(m, dirs0), m2, entries2 -- str);mkdir(m8, md5, # links(m0, dirs0), m10, entries3)) = mkdir(m4, md3, m6, m7, entries0), dirs0[entries2[str]] = mkdir(m3, md4, # links(entries2[str], dirs0), m5, entries1), dirs0[m0] = mkdir(m8, md5, # links(m0, dirs0), m10, entries3), dirs0[m] = mkdir(m1 + 1, md, # links(m, dirs0), m2 + 1, entries2), files[ino] = mkfile(m9, md2, m11, content), dirs0[ino] = mkdir(m12, md6, m13, m14, entries), afs-cons(dirs0, files), ROOT_INO ∈ dirs0, m0 ∈ dirs0, entries2[str] ∈ dirs0, str ∈ entries2, m ∈ dirs0, ino ∈ dirs0 ∧ name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs0 ∧ m11 = # links(ino, dirs0), ino ∈ dirs0 → m13 = # links(ino, dirs0) ∧ m13 ≤ 1 ∧ m12 = # entries ∧ m14 = # subdirs(ino, dirs0), ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅, m0 = m → md1 = md0, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ str0 ∈ entries3, ( ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links (ino, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries2 -- str) ) .meta:= md0 ] [m0, (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ]) = ∅ → (ino = m0 ⊃ (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ;(ino = m ⊃ mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str);dirs0[ino]) ) .entries = ∅) ∧ ( ino ∈ dirs0 → (ino = m0 ⊃ (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ;(ino = m ⊃ mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str);dirs0[ino]) ) .nlink = # links (ino, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries2 -- str) ) .meta:= md0 ] [m0, (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ]) ∧ (ino = m0 ⊃ (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ;(ino = m ⊃ mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str);dirs0[ino]) ) .nlink ≤ 1 ∧ (ino = m0 ⊃ (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ;(ino = m ⊃ mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str);dirs0[ino]) ) .size = # (ino = m0 ⊃ (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ;(ino = m ⊃ mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str);dirs0[ino]) ) .entries ∧ (ino = m0 ⊃ (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ;(ino = m ⊃ mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str);dirs0[ino]) ) .nsubdirs = # subdirs (ino, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries2 -- str) ) .meta:= md0 ] [m0, (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ])) ∧ ( ino ∈ files → ¬ ino ∈ dirs0 ∧ m11 = # links (ino, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries2 -- str) ) .meta:= md0 ] [m0, (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ])) ∧ ( ino ∈ dirs0 ∧ name ∈ (ino = m0 ⊃ (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ;(ino = m ⊃ mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str);dirs0[ino]) ) .entries → (ino = m0 ⊃ (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ;(ino = m ⊃ mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str);dirs0[ino]) ) .entries [name ] ∈ dirs0 ∨ (ino = m0 ⊃ (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ;(ino = m ⊃ mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str);dirs0[ino]) ) .entries [name ] ∈ files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 85:
(m0 = m ⊃ mkdir(m1, md, # links(m, dirs0), m2, entries2 -- str);mkdir(m8, md5, # links(m0, dirs0), m10, entries3)) = mkdir(m4, md3, m6, m7, entries0), dirs0[ino] = mkdir(m12, md6, m13, m14, entries), files[ino] = mkfile(m9, md2, m11, content), dirs0[m] = mkdir(m1 + 1, md, # links(m, dirs0), m2 + 1, entries2), dirs0[m0] = mkdir(m8, md5, # links(m0, dirs0), m10, entries3), dirs0[entries2[str]] = mkdir(m3, md4, # links(entries2[str], dirs0), m5, entries1), afs-cons(dirs0, files), m ∈ dirs0, str ∈ entries2, entries2[str] ∈ dirs0, m0 ∈ dirs0, ROOT_INO ∈ dirs0, m0 = m → md1 = md0, ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅, ino ∈ files → ¬ ino ∈ dirs0 ∧ m11 = # links(ino, dirs0), ino ∈ dirs0 ∧ name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files, ino ∈ dirs0 → m13 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m12 = # entries ∧ m14 = # subdirs(ino, dirs0), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ str0 ∈ entries3, ( ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links (ino, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries2 -- str) ) .meta:= md0 ] [m0, (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ]) = ∅ → (ino = m0 ⊃ (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ;(ino = m ⊃ mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str);mkdir(m12, md6, m13, m14, entries)) ) .entries = ∅) ∧ ( ino ∈ dirs0 → (ino = m0 ⊃ (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ;(ino = m ⊃ mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str);mkdir(m12, md6, m13, m14, entries)) ) .nlink = # links (ino, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries2 -- str) ) .meta:= md0 ] [m0, (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ]) ∧ (ino = m0 ⊃ (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ;(ino = m ⊃ mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str);mkdir(m12, md6, m13, m14, entries)) ) .nlink ≤ 1 ∧ (ino = m0 ⊃ (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ;(ino = m ⊃ mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str);mkdir(m12, md6, m13, m14, entries)) ) .size = # (ino = m0 ⊃ (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ;(ino = m ⊃ mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str);mkdir(m12, md6, m13, m14, entries)) ) .entries ∧ (ino = m0 ⊃ (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ;(ino = m ⊃ mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str);mkdir(m12, md6, m13, m14, entries)) ) .nsubdirs = # subdirs (ino, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries2 -- str) ) .meta:= md0 ] [m0, (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ])) ∧ ( ino ∈ files → ¬ ino ∈ dirs0 ∧ m11 = # links (ino, dirs0 [m, (m = m0 ⊃ mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m1, md, # links(m, dirs0), m2, entries2 -- str) ) .meta:= md0 ] [m0, (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ])) ∧ ( ino ∈ dirs0 ∧ name ∈ (ino = m0 ⊃ (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ;(ino = m ⊃ mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str);mkdir(m12, md6, m13, m14, entries)) ) .entries → (ino = m0 ⊃ (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ;(ino = m ⊃ mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str);mkdir(m12, md6, m13, m14, entries)) ) .entries [name ] ∈ dirs0 ∨ (ino = m0 ⊃ (m0 = m ⊃ mkdir(m4 + 1, md0, m6, m7 + 1, entries0[str0, entries2[str]]) ;mkdir(m4 + 1, md3, m6, m7 + 1, entries0[str0, entries2[str]]) ) .meta:= md1 ;(ino = m ⊃ mkdir(m1, md0, # links(m, dirs0), m2, entries2 -- str);mkdir(m12, md6, m13, m14, entries)) ) .entries [name ] ∈ files)

Proof step 84 from proof afs-cons-rename-dir-negdentry (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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