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Proof step 56 from proof inv-unlink (previous step)

1 = fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nlink, links(fs0[ri0[dentrykey(m1, str)]].ino, fs0, ri0) = ∅ ++ dentrykey(m1, str), fs0[ri0[dentrykey(m1, str)]].dentry?, fs0[ri0[inodekey(m1)]].directory, fs0[ri0[inodekey(m1)]].inode?, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].inode?, ro.inodes?, fo.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons(fs0, ri0, ro), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), key ∈ ri0, ri0[inodekey(m1)] ∈ fs0, inodekey(m1) ∈ ri0, ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)] ∈ fs0, inodekey(fs0[ri0[dentrykey(m1, str)]].ino) ∈ ri0, ri0[dentrykey(m1, str)] ∈ fs0, dentrykey(m1, str) ∈ ri0, ri0[key] ∈ fs0, 1 ≤ fs0[ri0[inodekey(m1)]].size, key.inode? → fs0[ri0[key]].inode? ∧ key.ino ≠ 0, key.dentry? → fs0[ri0[key]].dentry? ∧ inodekey(key.ino) ∈ ri0 ∧ inodekey(fs0[ri0[key]].ino) ∈ ri0 ∧ ¬ inodekey(key.ino) ∈ ro ∧ ¬ inodekey(fs0[ri0[key]].ino) ∈ ro ∧ fs0[ri0[inodekey(key.ino)]].directory, key.data? → fs0[ri0[key]].data? ∧ inodekey(key.ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(key.ino)]].directory ∧ # fs0[ri0[key]].data = VFS_PAGE_SIZE, fs0[ri0[inodekey(m1)]].nlink ≠ 0 ∨ m1 = ROOT_INO ⊦ fs0[ri0[dentrykey(m1, str)]].ino = 0, fs0[ri0[dentrykey(m1, str)]].ino = ROOT_INO, fs0[ri0[inodekey(m1)]].size = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, key = dentrykey(m1, str), m1 = 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].directory, inodekey(m1) ∈ ro, inodekey(fs0[ri0[dentrykey(m1, str)]].ino) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, ( (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) = adr3 ∨ (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) = adr2 ∨ (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) = adr1 ∨ (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ∈ fs0) ∧ (adr3 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;(adr2 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[(inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key]))] ) ) ) .key = key ∧ ( key.inode? → (adr3 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;(adr2 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[(inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key]))] ) ) ) .inode? ∧ key.ino ≠ 0) ∧ ( key.dentry? → (adr3 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;(adr2 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[(inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key]))] ) ) ) .dentry? ∧ inodekey(key.ino) ∈ ri0 ∧ ( (adr3 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;(adr2 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[(inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key]))] ) ) ) .ino = m1 ∨ inodekey ((adr3 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ inodenode (inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;(adr2 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[(inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key]))] ) ) ) .ino) ∈ ri0) ∧ key.ino ≠ fs0[ri0[dentrykey(m1, str)]].ino ∧ ¬ inodekey(key.ino) ∈ ro ∧ (adr3 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;(adr2 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[(inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key]))] ) ) ) .ino ≠ fs0[ri0[dentrykey(m1, str)]].ino ∧ ¬ inodekey ((adr3 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;(adr2 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[(inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key]))] ) ) ) .ino) ∈ ro ∧ (adr3 = (m1 = key.ino ⊃ adr1;ri0[inodekey(key.ino)]) ⊃ inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;(adr2 = (m1 = key.ino ⊃ adr1;ri0[inodekey(key.ino)]) ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = (m1 = key.ino ⊃ adr1;ri0[inodekey(key.ino)]) ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[(m1 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])] ) ) ) .directory) ∧ ( key.data? → (adr3 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;(adr2 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[(inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key]))] ) ) ) .data? ∧ (key.ino = fs0[ri0[dentrykey(m1, str)]].ino ∨ inodekey(key.ino) ∈ ri0) ∧ ¬ (adr3 = (fs0[ri0[dentrykey(m1, str)]].ino = key.ino ⊃ adr3;(m1 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;(adr2 = (fs0[ri0[dentrykey(m1, str)]].ino = key.ino ⊃ adr3;(m1 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = (fs0[ri0[dentrykey(m1, str)]].ino = key.ino ⊃ adr3;(m1 = key.ino ⊃ adr1;ri0[inodekey(key.ino)])) ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[(fs0[ri0[dentrykey(m1, str)]].ino = key.ino ⊃ adr3;(m1 = key.ino ⊃ adr1;ri0[inodekey(key.ino)]))] ) ) ) .directory ∧ # (adr3 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ inodenode(inodekey(fs0[ri0[dentrykey(m1, str)]].ino), md, false, 0, fs0[ri0[inodekey(fs0[ri0[dentrykey(m1, str)]].ino)]].nsubdirs, m2) ;(adr2 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ dentrynode(dentrykey(m1, str), 0) ;(adr1 = (inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key])) ⊃ inodenode(inodekey(m1), md0, true, fs0[ri0[inodekey(m1)]].nlink, fs0[ri0[inodekey(m1)]].nsubdirs, fs0[ri0[inodekey(m1)]].size - 1) ;fs0[(inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key ⊃ adr3;(inodekey(m1) = key ⊃ adr1;ri0[key]))] ) ) ) .data = VFS_PAGE_SIZE)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Rule argument

fma: inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key

Additional information

Used simplifier rules: ⊦ inodekey(m) ≠ dentrykey(m0, str); (s)% ⊦ inodekey(m).inode?; (s)% ⊦ inodekey(m).ino = m; (s)% ⊦ ¬ inodekey(m).dentry?; (s)% ⊦ ¬ inodekey(m).data?; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).key = key; (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).inode?; (s) Used formulas: inodekey(fs0[ri0[dentrykey(m1, str)]].ino) = key