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Proof step 398 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), replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, 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), replay-safe(log0, fs0, fi ⊖ fo), 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, adr4 ∈ log0, adr5 ∈ log0, 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], replay-safe (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)], fi ⊖ fo) ∧ ¬ adr1 ∈ replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)], fi ⊖ fo) ∧ ¬ adr2 ∈ replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)], fi ⊖ fo) -- dentrykey(m, str) ∧ ¬ adr3 ∈ (m5 ≠ 0 ⊃ ( replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)] [adr3, inodenode(inodekey(m), md, true, m10, n0, m1) ], fi ⊖ fo) -- dentrykey(m, str) )[dentrykey(m0, str0), adr2 ] ; replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), 0)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)], fi ⊖ fo) -- dentrykey(m, str) -- dentrykey(m0, str0) ) ∧ ¬ adr4 ∈ (m5 ≠ 0 ⊃ ( replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)] [adr3, inodenode(inodekey(m), md, true, m10, n0, m1) ], fi ⊖ fo) -- dentrykey(m, str) )[dentrykey(m0, str0), adr2 ] ; replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), 0)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)], fi ⊖ fo) -- dentrykey(m, str) -- dentrykey(m0, str0) ) [inodekey(m), adr3 ] ∧ ¬ adr5 ∈ (m5 ≠ 0 ⊃ ( replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)] [adr3, inodenode(inodekey(m), md, true, m10, n0, m1) ], fi ⊖ fo) -- dentrykey(m, str) )[dentrykey(m0, str0), adr2 ] ; replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), 0)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)], fi ⊖ fo) -- dentrykey(m, str) -- dentrykey(m0, str0) ) [inodekey(m), adr3 ] [inodekey(m0), adr4 ] ∧ (m5 ≠ 0 ⊃ ( replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)] [adr3, inodenode(inodekey(m), md, true, m10, n0, m1) ], fi ⊖ fo) -- dentrykey(m, str) )[dentrykey(m0, str0), adr2 ] ; replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), 0)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)], fi ⊖ fo) -- dentrykey(m, str) -- dentrykey(m0, str0) ) [inodekey(m), adr3 ] [inodekey(m0), adr4 ] [inodekey(m8), adr5 ] = (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3][inodekey(m0), adr4][inodekey(m8), adr5] ⊖ ro

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 399:
m11 + 1 = fs0[ri0[inodekey(m8)]].nlink, ¬ fs0[ri0[inodekey(m8)]].directory ↔ ¬ fs0[ri0[inodekey(m5)]].directory, fs0[ri0[dentrykey(m0, str0)]] = dentrynode(key3, m8), fs0[ri0[inodekey(m0)]] = inodenode(key0, md1, true, m9, m12, m13), fs0[ri0[dentrykey(m, str)]] = dentrynode(key1, m5), replay-log(log0, fs0, fi ⊖ fo) = ri0 ⊖ ro, 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), replay-safe(log0, fs0, fi ⊖ fo), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(m0)] ∈ fs0, dentrykey(m, str) ∈ ri0, inodekey(m5) ∈ ri0, dentrykey(m0, str0) ∈ ri0, inodekey(m8) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m) ∈ ri0, inodekey(m0) ∈ ri0, ri0[dentrykey(m0, str0)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, fs0[ri0[inodekey(m8)]].directory → dentrykeys(inodekey(m8), ri0) = ∅, m10 ≠ 0 ∨ m = ROOT_INO, m9 ≠ 0 ∨ m0 = ROOT_INO, ¬ fs0[ri0[inodekey(m5)]].directory ∧ ¬ boolvar3 ∨ fs0[ri0[inodekey(m5)]].directory ∧ boolvar3 ∧ m4 = fs0[ri0[inodekey(m5)]].size, ¬ fs0[ri0[inodekey(m5)]].directory ∧ ¬ boolvar1 ∨ fs0[ri0[inodekey(m8)]].directory ∧ boolvar1 ∧ m7 = fs0[ri0[inodekey(m8)]].size ⊦ adr1 = adr2, adr1 = adr3, adr1 = adr4, adr1 = adr5, adr2 = adr3, adr2 = adr4, adr2 = adr5, adr3 = adr4, adr3 = adr5, adr4 = adr5, m = 0, m0 = m, m0 = 0, m11 = 0, m8 = ROOT_INO, m8 = 0, adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3], adr2 ∈ ri0 -- dentrykey(m, str), adr5 ∈ fs0, adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m) ∈ ro, inodekey(m0) ∈ ro, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2], adr5 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3][inodekey(m0), adr4], adr5 ∈ log0, adr4 ∈ log0, adr3 ∈ log0, replay-safe (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)], fi ⊖ fo) ∧ ¬ adr1 ∈ replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)], fi ⊖ fo) ∧ ¬ adr2 ∈ replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)], fi ⊖ fo) -- dentrykey(m, str) ∧ ¬ adr3 ∈ (m5 ≠ 0 ⊃ ( replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)] [adr3, inodenode(inodekey(m), md, true, m10, n0, m1) ], fi ⊖ fo) -- dentrykey(m, str) )[dentrykey(m0, str0), adr2 ] ; replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), 0)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)], fi ⊖ fo) -- dentrykey(m, str) -- dentrykey(m0, str0) ) ∧ ¬ adr4 ∈ (m5 ≠ 0 ⊃ ( replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)] [adr3, inodenode(inodekey(m), md, true, m10, n0, m1) ], fi ⊖ fo) -- dentrykey(m, str) )[dentrykey(m0, str0), adr2 ] ; replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), 0)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)], fi ⊖ fo) -- dentrykey(m, str) -- dentrykey(m0, str0) ) [inodekey(m), adr3 ] ∧ ¬ adr5 ∈ (m5 ≠ 0 ⊃ ( replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)] [adr3, inodenode(inodekey(m), md, true, m10, n0, m1) ], fi ⊖ fo) -- dentrykey(m, str) )[dentrykey(m0, str0), adr2 ] ; replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), 0)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)], fi ⊖ fo) -- dentrykey(m, str) -- dentrykey(m0, str0) ) [inodekey(m), adr3 ] [inodekey(m0), adr4 ] ∧ (m5 ≠ 0 ⊃ ( replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), m5)] [adr3, inodenode(inodekey(m), md, true, m10, n0, m1) ], fi ⊖ fo) -- dentrykey(m, str) )[dentrykey(m0, str0), adr2 ] ; replay-log (log0, fs0[adr1, dentrynode(dentrykey(m, str), 0)][adr2, dentrynode(dentrykey(m0, str0), 0)][adr3, inodenode(inodekey(m), md, true, m10, n0, m1)], fi ⊖ fo) -- dentrykey(m, str) -- dentrykey(m0, str0) ) [inodekey(m), adr3 ] [inodekey(m0), adr4 ] [inodekey(m8), adr5 ] = (ri0 -- dentrykey(m, str))[dentrykey(m0, str0), adr2][inodekey(m), adr3][inodekey(m0), adr4][inodekey(m8), adr5] ⊖ ro

Rule argument

fma: adr3 ∈ log0

Additional information

Used simplifier rules: ⊦ log-cons(log, fs) ∧ adr ∈ log → adr ∈ fs; (ss) Used formulas: adr3 ∈ log0