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Proof step 335 from proof inv-rename-overwrite-reparent (previous step)

m11 + 1 = fs0[ri0[inodekey(m8)]].nlink, ¬ fs0[ri0[inodekey(m8)]].directory ↔ ¬ fs0[ri0[inodekey(m5)]].directory, fs0[ri0[dentrykey(m, str)]] = dentrynode(key1, m5), fs0[ri0[inodekey(m0)]] = inodenode(key0, md1, true, m9, m12, m13), fs0[ri0[dentrykey(m0, str0)]] = dentrynode(key3, m8), 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), ri0[inodekey(m)] ∈ fs0, ri0[dentrykey(m0, str0)] ∈ fs0, inodekey(m0) ∈ ri0, inodekey(m) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m8) ∈ ri0, dentrykey(m0, str0) ∈ ri0, inodekey(m5) ∈ ri0, dentrykey(m, str) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, key2 ∈ ri0, fs0[ri0[inodekey(m8)]].directory → dentrykeys(inodekey(m8), ri0) = ∅, key2 ∈ ri0 → ri0[key2] ∈ fs0 ∧ (key2.inode? → fs0[ri0[key2]].inode? ∧ key2.ino ≠ 0) ∧ ( key2.dentry? → fs0[ri0[key2]].dentry? ∧ inodekey(key2.ino) ∈ ri0 ∧ inodekey(fs0[ri0[key2]].ino) ∈ ri0 ∧ ¬ inodekey(key2.ino) ∈ ro ∧ ¬ inodekey(fs0[ri0[key2]].ino) ∈ ro ∧ fs0[ri0[inodekey(key2.ino)]].directory) ∧ ( key2.data? → fs0[ri0[key2]].data? ∧ inodekey(key2.ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(key2.ino)]].directory ∧ # fs0[ri0[key2]].data = VFS_PAGE_SIZE), ¬ fs0[ri0[inodekey(m5)]].directory ∧ ¬ boolvar1 ∨ fs0[ri0[inodekey(m8)]].directory ∧ boolvar1 ∧ m7 = fs0[ri0[inodekey(m8)]].size, ¬ fs0[ri0[inodekey(m5)]].directory ∧ ¬ boolvar3 ∨ fs0[ri0[inodekey(m5)]].directory ∧ boolvar3 ∧ m4 = fs0[ri0[inodekey(m5)]].size, m9 ≠ 0 ∨ m0 = ROOT_INO, m10 ≠ 0 ∨ m = ROOT_INO, key2 = inodekey(m8) ∨ key2 = inodekey(m0) ∨ key2 = inodekey(m) ∨ key2 = dentrykey(m0, str0) ∨ key2 ≠ dentrykey(m, str) ∧ key2 ∈ ri0 ⊦ adr1 = adr5, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr5, adr2 = adr4, adr2 = adr3, adr3 = adr5, adr3 = adr4, adr4 = adr5, m = 0, m0 = 0, m0 = m, m11 = 0, m8 = 0, m8 = ROOT_INO, adr5 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3][inodekey(m0), adr4], adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2], inodekey(m0) ∈ ro, inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr5 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3], ( (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) = adr5 ∨ (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) = adr4 ∨ (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) = adr3 ∨ (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) = adr2 ∨ (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) = adr1 ∨ (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ∈ fs0) ∧ ( adr5 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;( adr4 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;( adr3 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;( adr2 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ dentrynode(dentrykey(m0, str0), m5) ;( adr1 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ] ) ) ) ) ) .key = key2 ∧ ( key2.inode? → ( adr5 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;( adr4 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;( adr3 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;( adr2 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ dentrynode(dentrykey(m0, str0), m5) ;( adr1 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ] ) ) ) ) ) .inode? ∧ key2.ino ≠ 0) ∧ ( key2.dentry? → ( adr5 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;( adr4 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;( adr3 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;( adr2 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ dentrynode(dentrykey(m0, str0), m5) ;( adr1 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ] ) ) ) ) ) .dentry? ∧ inodekey(key2.ino) ∈ ri0 ∧ ( ( adr5 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;( adr4 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;( adr3 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;( adr2 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ dentrynode(dentrykey(m0, str0), m5) ;( adr1 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ] ) ) ) ) ) .ino = m8 ∨ ( adr5 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;( adr4 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;( adr3 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;( adr2 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ dentrynode(dentrykey(m0, str0), m5) ;( adr1 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ] ) ) ) ) ) .ino = m0 ∨ ( adr5 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;( adr4 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;( adr3 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;( adr2 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ dentrynode(dentrykey(m0, str0), m5) ;( adr1 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ] ) ) ) ) ) .ino = m ∨ inodekey (( adr5 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;( adr4 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;( adr3 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;( adr2 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ dentrynode(dentrykey(m0, str0), m5) ;( adr1 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ] ) ) ) ) ) .ino) ∈ ri0) ∧ ¬ inodekey(key2.ino) ∈ ro ∧ ¬ inodekey (( adr5 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;( adr4 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;( adr3 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;( adr2 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ dentrynode(dentrykey(m0, str0), m5) ;( adr1 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ] ) ) ) ) ) .ino) ∈ ro ∧ (adr5 = (m8 = key2.ino ⊃ adr5;(m0 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]))) ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = (m8 = key2.ino ⊃ adr5;(m0 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]))) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = (m8 = key2.ino ⊃ adr5;(m0 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]))) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;(adr2 = (m8 = key2.ino ⊃ adr5;(m0 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]))) ⊃ dentrynode(dentrykey(m0, str0), m5) ;(adr1 = (m8 = key2.ino ⊃ adr5;(m0 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(m8 = key2.ino ⊃ adr5;(m0 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)])))] ) ) ) ) ) .directory) ∧ ( key2.data? → ( adr5 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;( adr4 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;( adr3 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;( adr2 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ dentrynode(dentrykey(m0, str0), m5) ;( adr1 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ] ) ) ) ) ) .data? ∧ inodekey(key2.ino) ∈ ri0 ∧ ¬ (adr5 = (m8 = key2.ino ⊃ adr5;(m0 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]))) ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = (m8 = key2.ino ⊃ adr5;(m0 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]))) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = (m8 = key2.ino ⊃ adr5;(m0 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]))) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;(adr2 = (m8 = key2.ino ⊃ adr5;(m0 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]))) ⊃ dentrynode(dentrykey(m0, str0), m5) ;(adr1 = (m8 = key2.ino ⊃ adr5;(m0 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(m8 = key2.ino ⊃ adr5;(m0 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)])))] ) ) ) ) ) .directory ∧ # ( adr5 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;( adr4 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;( adr3 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;( adr2 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ dentrynode(dentrykey(m0, str0), m5) ;( adr1 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ) ] ) ) ) ) ) .data = VFS_PAGE_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 336:
m11 + 1 = fs0[ri0[inodekey(m8)]].nlink, ¬ fs0[ri0[inodekey(m8)]].directory ↔ ¬ fs0[ri0[inodekey(m5)]].directory, fs0[ri0[dentrykey(m, str)]] = dentrynode(key1, m5), fs0[ri0[inodekey(m0)]] = inodenode(key0, md1, true, m9, m12, m13), fs0[ri0[dentrykey(m0, str0)]] = dentrynode(key3, m8), 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), ri0[key2] ∈ fs0, ri0[inodekey(m)] ∈ fs0, ri0[dentrykey(m0, str0)] ∈ fs0, inodekey(m0) ∈ ri0, inodekey(m) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m8) ∈ ri0, dentrykey(m0, str0) ∈ ri0, inodekey(m5) ∈ ri0, dentrykey(m, str) ∈ ri0, ri0[inodekey(m0)] ∈ fs0, key2 ∈ ri0, fs0[ri0[inodekey(m8)]].directory → dentrykeys(inodekey(m8), ri0) = ∅, key2.data? → fs0[ri0[key2]].data? ∧ inodekey(key2.ino) ∈ ri0 ∧ ¬ fs0[ri0[inodekey(key2.ino)]].directory ∧ # fs0[ri0[key2]].data = VFS_PAGE_SIZE, key2.dentry? → fs0[ri0[key2]].dentry? ∧ inodekey(key2.ino) ∈ ri0 ∧ inodekey(fs0[ri0[key2]].ino) ∈ ri0 ∧ ¬ inodekey(key2.ino) ∈ ro ∧ ¬ inodekey(fs0[ri0[key2]].ino) ∈ ro ∧ fs0[ri0[inodekey(key2.ino)]].directory, key2.inode? → fs0[ri0[key2]].inode? ∧ key2.ino ≠ 0, ¬ fs0[ri0[inodekey(m5)]].directory ∧ ¬ boolvar1 ∨ fs0[ri0[inodekey(m8)]].directory ∧ boolvar1 ∧ m7 = fs0[ri0[inodekey(m8)]].size, ¬ fs0[ri0[inodekey(m5)]].directory ∧ ¬ boolvar3 ∨ fs0[ri0[inodekey(m5)]].directory ∧ boolvar3 ∧ m4 = fs0[ri0[inodekey(m5)]].size, m9 ≠ 0 ∨ m0 = ROOT_INO, m10 ≠ 0 ∨ m = ROOT_INO ⊦ adr1 = adr5, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr5, adr2 = adr4, adr2 = adr3, adr3 = adr5, adr3 = adr4, adr4 = adr5, dentrykey(m, str) = dentrykey(m0, str0), key2 = dentrykey(m, str), m = 0, m0 = 0, m0 = m, m11 = 0, m8 = 0, m8 = ROOT_INO, adr5 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3][inodekey(m0), adr4], adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2], inodekey(m0) ∈ ro, inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr5 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3], ( (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) = adr5 ∨ (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) = adr4 ∨ (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) = adr3 ∨ (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) = adr2 ∨ (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) = adr1 ∨ (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ∈ fs0) ∧ (adr5 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;(adr2 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ dentrynode(dentrykey(m0, str0), m5) ;(adr1 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2]))))] ) ) ) ) ) .key = key2 ∧ ( key2.inode? → (adr5 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;( adr2 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ dentrynode(dentrykey(m0, str0), m5) ;( adr1 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2]))))] ) ) ) ) ) .inode? ∧ key2.ino ≠ 0) ∧ ( key2.dentry? → (adr5 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;( adr2 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ dentrynode(dentrykey(m0, str0), m5) ;( adr1 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2]))))] ) ) ) ) ) .dentry? ∧ inodekey(key2.ino) ∈ ri0 ∧ ( ( adr5 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;( adr4 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;( adr3 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;( adr2 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2]))) ) ⊃ dentrynode(dentrykey(m0, str0), m5) ;( adr1 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2]))) ) ] ) ) ) ) ) .ino = m8 ∨ ( adr5 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;( adr4 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;( adr3 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;( adr2 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2]))) ) ⊃ dentrynode(dentrykey(m0, str0), m5) ;( adr1 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2]))) ) ] ) ) ) ) ) .ino = m0 ∨ ( adr5 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;( adr4 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;( adr3 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;( adr2 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2]))) ) ⊃ dentrynode(dentrykey(m0, str0), m5) ;( adr1 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2]))) ) ] ) ) ) ) ) .ino = m ∨ inodekey (( adr5 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;( adr4 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;( adr3 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2]))) ) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;( adr2 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2]))) ) ⊃ dentrynode(dentrykey(m0, str0), m5) ;( adr1 = (inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m8) = key2 ⊃ adr5 ;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2]))) ) ] ) ) ) ) ) .ino) ∈ ri0) ∧ ¬ inodekey(key2.ino) ∈ ro ∧ ¬ inodekey (( adr5 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;( adr4 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;( adr3 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;( adr2 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ dentrynode(dentrykey(m0, str0), m5) ;( adr1 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ] ) ) ) ) ) .ino) ∈ ro ∧ (adr5 = (m8 = key2.ino ⊃ adr5;(m0 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]))) ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = (m8 = key2.ino ⊃ adr5;(m0 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]))) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = (m8 = key2.ino ⊃ adr5;(m0 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]))) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;(adr2 = (m8 = key2.ino ⊃ adr5;(m0 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]))) ⊃ dentrynode(dentrykey(m0, str0), m5) ;(adr1 = (m8 = key2.ino ⊃ adr5;(m0 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(m8 = key2.ino ⊃ adr5;(m0 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)])))] ) ) ) ) ) .directory) ∧ ( key2.data? → (adr5 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;( adr2 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ dentrynode(dentrykey(m0, str0), m5) ;( adr1 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2]))))] ) ) ) ) ) .data? ∧ inodekey(key2.ino) ∈ ri0 ∧ ¬ (adr5 = (m8 = key2.ino ⊃ adr5;(m0 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]))) ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = (m8 = key2.ino ⊃ adr5;(m0 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]))) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = (m8 = key2.ino ⊃ adr5;(m0 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]))) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;(adr2 = (m8 = key2.ino ⊃ adr5;(m0 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]))) ⊃ dentrynode(dentrykey(m0, str0), m5) ;(adr1 = (m8 = key2.ino ⊃ adr5;(m0 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(m8 = key2.ino ⊃ adr5;(m0 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)])))] ) ) ) ) ) .directory ∧ # (adr5 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;( adr4 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;( adr3 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;( adr2 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ dentrynode(dentrykey(m0, str0), m5) ;( adr1 = (inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m8) = key2 ⊃ adr5;(inodekey(m0) = key2 ⊃ adr4;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m0, str0) = key2 ⊃ adr2;ri0[key2])))) ] ) ) ) ) ) .data = VFS_PAGE_SIZE)

Rule argument

Additional information

Used simplifier rules: ⊦ dentrykey(m, str) = dentrykey(m0, str0) ↔ m = m0 ∧ str = str0; (ws)% ⊦ inodekey(m) ≠ dentrykey(m0, str); (s)