Proof step 332 from proof inv-rename-overwrite-reparent (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 333:

  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, fs0[ri0[inodekey(m8)]].directory → dentrykeys(inodekey(m8), ri0) = ∅, ¬ 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, 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], ( ( 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)) → key2 = inodekey(m8) ∨ key2 = inodekey(m0) ∨ key2 = inodekey(m) ∨ key2 = dentrykey(m0, str0) ∨ key2 ≠ dentrykey(m, str) ∧ key2 ∈ ri0 → ( (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)) ∧ ( ( adr ∈ log0 → adr ∈ fs0 ∧ (fs0[adr].inode? → fs0[adr].key.inode? ∧ fs0[adr].key.ino ≠ 0) ∧ (fs0[adr].dentry? → fs0[adr].key.dentry?) ∧ (fs0[adr].data? → fs0[adr].key.data?) ∧ (fs0[adr].trunc? → fs0[adr].key.inode?)) → adr ∈ log0 ∨ adr = adr1 ∨ adr = adr2 ∨ adr = adr3 ∨ adr = adr4 ∨ adr = adr5 → (adr = adr5 ∨ adr = adr4 ∨ adr = adr3 ∨ adr = adr2 ∨ adr = adr1 ∨ adr ∈ fs0) ∧ ( (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) ) ) .inode? → (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) ) ) .key .inode? ∧ (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) ) ) .key .ino ≠ 0) ∧ ( (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) ) ) .dentry? → (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) ) ) .key .dentry?) ∧ ( (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) ) ) .data? → (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) ) ) .key .data?) ∧ ( (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) ) ) .trunc? → (adr5 = adr ⊃ inodenode(inodekey(m8), md2, boolvar1, m11, fs0[ri0[inodekey(m8)]].nsubdirs, m7) ;(adr4 = adr ⊃ inodenode(inodekey(m0), md0, true, m9, m12, m13) ;(adr3 = adr ⊃ inodenode(inodekey(m), md, true, m10, n0, m1) ;(adr2 = adr ⊃ dentrynode(dentrykey(m0, str0), m5);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) ) ) .key .inode?))

Rule argument

Additional information

Used simplifier rules: ubifs-cons-reduce: ⊦ ubifs-cons(fs0, ri0, ro0, fi0, fo0, log0) → ( ubifs-cons(fs1, ri1, ro1, fi1, fo1, log1) ↔ ¬ inodekey(0) ∈ ri1 ∧ (ro0.inodes? → ro1.inodes?) ∧ (fo0.inodes? → fo1.inodes?) ∧ (ro0 ⊆ dom ri0 → (∀ key. key ∈ ro1 → key ∈ ri1)) ∧ (fo0 ⊆ dom fi0 → (∀ key. key ∈ fo1 → key ∈ fi1)) ∧ (¬ dups(log0) → ¬ dups(log1)) ∧ (∀ key. ( key ∈ ri0 → ri0[key] ∈ fs0 ∧ fs0[ri0[key]].key = key ∧ (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) ∈ ro0 ∧ ¬ inodekey(fs0[ri0[key]].ino) ∈ ro0 ∧ 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)) → key ∈ ri1 → ri1[key] ∈ fs1 ∧ fs1[ri1[key]].key = key ∧ (key.inode? → fs1[ri1[key]].inode? ∧ key.ino ≠ 0) ∧ ( key.dentry? → fs1[ri1[key]].dentry? ∧ inodekey(key.ino) ∈ ri1 ∧ inodekey(fs1[ri1[key]].ino) ∈ ri1 ∧ ¬ inodekey(key.ino) ∈ ro1 ∧ ¬ inodekey(fs1[ri1[key]].ino) ∈ ro1 ∧ fs1[ri1[inodekey(key.ino)]].directory) ∧ ( key.data? → fs1[ri1[key]].data? ∧ inodekey(key.ino) ∈ ri1 ∧ ¬ fs1[ri1[inodekey(key.ino)]].directory ∧ # fs1[ri1[key]].data = VFS_PAGE_SIZE)) ∧ (∀ adr. ( adr ∈ log0 → adr ∈ fs0 ∧ ( fs0[adr].inode? → fs0[adr].key.inode? ∧ fs0[adr].key.ino ≠ 0) ∧ (fs0[adr].dentry? → fs0[adr].key.dentry?) ∧ (fs0[adr].data? → fs0[adr].key.data?) ∧ (fs0[adr].trunc? → fs0[adr].key.inode?)) → adr ∈ log1 → adr ∈ fs1 ∧ ( fs1[adr].inode? → fs1[adr].key.inode? ∧ fs1[adr].key.ino ≠ 0) ∧ (fs1[adr].dentry? → fs1[adr].key.dentry?) ∧ (fs1[adr].data? → fs1[adr].key.data?) ∧ (fs1[adr].trunc? → fs1[adr].key.inode?)));%in-ri: ⊦ key0 ∈ ri[key1, adr] ↔ key0 = key1 ∨ key0 ∈ ri;%at-ri: ⊦ ri[key0, adr][key1] = (key0 = key1 ⊃ adr;ri[key1]);%at-del-ri: ⊦ (ri -- key0)[key1] = (key0 = key1 ⊃ (∅)[key0];ri[key1]);%at-fs: ⊦ fs[adr0, nd][adr1] = (adr0 = adr1 ⊃ nd;fs[adr1]);% ⊦ ks.inodes? → ¬ dentrykey(ino, str) ∈ ks; (s)% ⊦ adr ∈ adr0 ' ↔ adr = adr0; (s)% ⊦ adr ∈ adr0 ' + ax ↔ adr = adr0 ∨ adr ∈ ax; (s)% ⊦ adr ∈ ax + ax0 ↔ adr ∈ ax ∨ adr ∈ ax0; (s)% ⊦ adr ∈ fs[adr1, nd] ↔ adr = adr1 ∨ adr ∈ fs; (s)% ⊦ ri-cons(ri, fs) ∧ key ∈ ri → fs[ri[key]].key = key; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]%⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ ¬ adr0 ∈ fs ∧ ¬ adr1 ∈ fs ∧ ¬ adr2 ∈ fs ∧ ¬ adr3 ∈ fs ∧ ¬ adr4 ∈ fs ∧ adr0 ≠ adr1 ∧ adr0 ≠ adr2 ∧ adr1 ≠ adr2 ∧ adr0 ≠ adr3 ∧ adr1 ≠ adr3 ∧ adr2 ≠ adr3 ∧ adr0 ≠ adr4 ∧ adr1 ≠ adr4 ∧ adr2 ≠ adr4 ∧ adr3 ≠ adr4 → ¬ dups(log + adr0 ' + adr1 ' + adr2 ' + adr3 ' + adr4 '); (s)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → ¬ dups(log); (s)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ key ∈ fo → key ∈ fi; (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ key ∈ ro → key ∈ ri; (ss)% ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → ¬ inodekey(0) ∈ ri; (s)% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)% ⊦ inodekey(m) ≠ dentrykey(m0, str); (s)% ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)