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Proof step 94 from proof inv-rename-new-keep-parent (previous step)

fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m0), fs0[ri0[inodekey(m)]] = inodenode(key1, md0, true, m4, m5, m6), 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-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m0) ∈ ri0, dentrykey(m, str) ∈ ri0, 1 ≤ m6, 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?), boolvar2 → 1 ≤ m5, adr ∈ log0 ∨ adr = adr1 ∨ adr = adr2 ∨ adr = adr3, ¬ fs0[ri0[inodekey(m0)]].directory ∧ ¬ boolvar2 ∨ fs0[ri0[inodekey(m0)]].directory ∧ boolvar2 ∧ m3 = fs0[ri0[inodekey(m0)]].size, m4 ≠ 0 ∨ m = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr2 = adr3, m = 0, m6 = 0, adr2 ∈ ri0 -- dentrykey(m, str), adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, dentrykey(m, str0) ∈ ri0, inodekey(m) ∈ ro, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2], (adr = adr3 ∨ adr = adr2 ∨ adr = adr1 ∨ adr ∈ fs0) ∧ ( (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .inode? → (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .key .inode? ∧ (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .key .ino ≠ 0) ∧ ( (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .dentry? → (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .key .dentry?) ∧ ( (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .data? → (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .key .data?) ∧ ( (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .trunc? → (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .key .inode?)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 95:
fs0[ri0[inodekey(m)]] = inodenode(key1, md0, true, m4, m5, m6), fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m0), fo.inodes?, ro.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-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), dentrykey(m, str) ∈ ri0, inodekey(m0) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, 1 ≤ m6, boolvar2 → 1 ≤ m5, 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?), m4 ≠ 0 ∨ m = ROOT_INO, ¬ fs0[ri0[inodekey(m0)]].directory ∧ ¬ boolvar2 ∨ fs0[ri0[inodekey(m0)]].directory ∧ boolvar2 ∧ m3 = fs0[ri0[inodekey(m0)]].size, adr ∈ log0 ∨ adr = adr1 ∨ adr = adr2 ∨ adr = adr3 ⊦ adr1 = adr3, adr1 = adr2, adr2 = adr3, m = 0, m6 = 0, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2], inodekey(m) ∈ ro, dentrykey(m, str0) ∈ ri0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), adr ∈ log0, (adr = adr3 ∨ adr = adr2 ∨ adr = adr1 ∨ adr ∈ fs0) ∧ ( (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .inode? → (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .key .inode? ∧ (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .key .ino ≠ 0) ∧ ( (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .dentry? → (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .key .dentry?) ∧ ( (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .data? → (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .key .data?) ∧ ( (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .trunc? → (adr3 = adr ⊃ inodenode(inodekey(m), md, true, m4, m5, m6) ;(adr2 = adr ⊃ dentrynode(dentrykey(m, str0), m0);(adr1 = adr ⊃ dentrynode(dentrykey(m, str), 0);fs0[adr])) ) .key .inode?)

Rule argument

fma: adr ∈ log0

Additional information

Used formulas: adr ∈ log0