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Proof step 201 from proof refine-link (previous step)

fs0[ri0[dentrykey(ino3, str)]] = dentrynode(key4, fs0[ri0[dentrykey(ino1, str)]].ino), fs0[ri0[dentrykey(ino0, str)]] = dentrynode(key2, fs0[ri0[dentrykey(ino1, str)]].ino), fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, m0, m1, m2), fs0[ri0[dentrykey(ino4, str)]] = dentrynode(key, fs0[ri0[dentrykey(ino1, str)]].ino), fs0[ri0[inodekey(fs0[ri0[dentrykey(ino1, str)]].ino)]] = inodenode(key1, md2, false, m3, 0, m5), fs0[ri0[dentrykey(ino2, str)]] = dentrynode(key3, fs0[ri0[dentrykey(ino1, str)]].ino), fs0[ri0[inodekey(ino3)]].directory, fs0[ri0[inodekey(ino4)]].directory, fs0[ri0[inodekey(ino1)]].directory, fs0[ri0[inodekey(ino0)]].directory, fs0[ri0[inodekey(ino2)]].directory, orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons (abs-dirs(fs0, ri0)[m, mkdir(m2 + 1, md, m0, m1, abs-children(m, fs0, ri0)[str0, fs0[ri0[dentrykey(ino1, str)]].ino])], abs-files(fs0, ri0)[fs0[ri0[dentrykey(ino1, str)]].ino, mkfile(m6, md0, m3 + 1, abs-content(fs0[ri0[dentrykey(ino1, str)]].ino, fs0, ri0))]), afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino1, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino1, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino1, str)]].ino), adr3]), log-cons(log0, fs0), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino1, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino1, str)]].ino), md0, false, m3 + 1, 0, m6) ]), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino1, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino1, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino1, str)]].ino), adr3], orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino1, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino1, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino1, str)]].ino), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ri-inj(ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino1, str)]].ino), adr3]), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino1, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino1, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino1, str)]].ino), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ri0[dentrykey(ino3, str)] ∈ fs0, ri0[dentrykey(ino2, str)] ∈ fs0, inodekey(ino4) ∈ ri0, dentrykey(ino3, str) ∈ ri0, inodekey(ino3) ∈ ri0, inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(ino1) ∈ ri0, dentrykey(ino1, str) ∈ ri0, ri0[inodekey(fs0[ri0[dentrykey(ino1, str)]].ino)] ∈ fs0, ri0[dentrykey(ino4, str)] ∈ fs0, dentrykey(ino4, str) ∈ ri0, inodekey(ino2) ∈ ri0, dentrykey(ino2, str) ∈ ri0, ri0[dentrykey(ino0, str)] ∈ fs0, dentrykey(ino0, str) ∈ ri0, inodekey(ino0) ∈ ri0, datakey(fs0[ri0[dentrykey(ino1, str)]].ino, n) ∈ ri0, inodekey(fs0[ri0[dentrykey(ino1, str)]].ino) ∈ ri0, asynced0 → boolvar0, links(ino3, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino3 = ROOT_INO, links(fs0[ri0[dentrykey(ino1, str)]].ino, abs-dirs(fs0, ri0)) ≠ ∅ ∨ fs0[ri0[dentrykey(ino1, str)]].ino = ROOT_INO, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO, links(ino4, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino4 = ROOT_INO, m0 ≠ 0 ∨ m = ROOT_INO, fs0[ri0[inodekey(ino1)]].nlink ≠ 0 ∨ ino1 = ROOT_INO, fs0[ri0[inodekey(ino0)]].nlink ≠ 0 ∨ ino0 = ROOT_INO, m3 ≠ 0 ∨ fs0[ri0[dentrykey(ino1, str)]].ino = ROOT_INO, links(ino2, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino2 = ROOT_INO ⊦ (adr3 = ri0[datakey(fs0[ri0[dentrykey(ino1, str)]].ino, n)] ⊃ inodenode(inodekey(fs0[ri0[dentrykey(ino1, str)]].ino), md0, false, m3 + 1, 0, m6) ;(adr2 = ri0[datakey(fs0[ri0[dentrykey(ino1, str)]].ino, n)] ⊃ dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino1, str)]].ino) ;(adr1 = ri0[datakey(fs0[ri0[dentrykey(ino1, str)]].ino, n)] ⊃ inodenode(inodekey(m), md, true, m0, m1, m2 + 1) ;fs0[ri0[datakey(fs0[ri0[dentrykey(ino1, str)]].ino, n)]] ) ) ) .data = fs0[ri0[datakey(fs0[ri0[dentrykey(ino1, str)]].ino, n)]].data, fs0[ri0[dentrykey(ino1, str)]].ino = 0, adr1 = adr3, adr1 = adr2, adr2 = adr3, m = fs0[ri0[dentrykey(ino1, str)]].ino, m = 0, dentrykey(m, str0) ∈ ri0, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, fs0[ri0[inodekey(ino1)]].nlink = 0 ∧ ino1 ≠ ROOT_INO, m0 = 0 ∧ m ≠ ROOT_INO, m3 = 0 ∧ fs0[ri0[dentrykey(ino1, str)]].ino ≠ ROOT_INO

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 202:
fs0[ri0[dentrykey(ino2, str)]] = dentrynode(key3, fs0[ri0[dentrykey(ino1, str)]].ino), fs0[ri0[inodekey(fs0[ri0[dentrykey(ino1, str)]].ino)]] = inodenode(key1, md2, false, m3, 0, m5), fs0[ri0[dentrykey(ino4, str)]] = dentrynode(key, fs0[ri0[dentrykey(ino1, str)]].ino), fs0[ri0[inodekey(m)]] = inodenode(key0, md1, true, m0, m1, m2), fs0[ri0[dentrykey(ino0, str)]] = dentrynode(key2, fs0[ri0[dentrykey(ino1, str)]].ino), fs0[ri0[dentrykey(ino3, str)]] = dentrynode(key4, fs0[ri0[dentrykey(ino1, str)]].ino), fs0[ri0[inodekey(ino2)]].directory, fs0[ri0[inodekey(ino0)]].directory, fs0[ri0[inodekey(ino1)]].directory, fs0[ri0[inodekey(ino4)]].directory, fs0[ri0[inodekey(ino3)]].directory, fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), afs-cons (abs-dirs(fs0, ri0)[m, mkdir(m2 + 1, md, m0, m1, abs-children(m, fs0, ri0)[str0, fs0[ri0[dentrykey(ino1, str)]].ino])], abs-files(fs0, ri0)[fs0[ri0[dentrykey(ino1, str)]].ino, mkfile(m6, md0, m3 + 1, abs-content(fs0[ri0[dentrykey(ino1, str)]].ino, fs0, ri0))]), file-node-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino1, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino1, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino1, str)]].ino), adr3]), file-node-cons(fs0, ri0), log-cons (log0, fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino1, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino1, str)]].ino), md0, false, m3 + 1, 0, m6) ]), log-cons(log0, fs0), orphans-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino1, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino1, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino1, str)]].ino), adr3], orphans(fs0, ri0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino1, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino1, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino1, str)]].ino), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-cons(ri0, fs0), ri-inj(ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino1, str)]].ino), adr3]), ri-inj(fi), ri-inj(ri0), ubifs-cons (fs0[adr1, inodenode(inodekey(m), md, true, m0, m1, m2 + 1)][adr2, dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino1, str)]].ino)] [adr3, inodenode(inodekey(fs0[ri0[dentrykey(ino1, str)]].ino), md0, false, m3 + 1, 0, m6) ], ri0[inodekey(m), adr1][dentrykey(m, str0), adr2][inodekey(fs0[ri0[dentrykey(ino1, str)]].ino), adr3], orphans(fs0, ri0), fi, fo, ((log0 + adr1 ') + adr2 ') + adr3 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), inodekey(fs0[ri0[dentrykey(ino1, str)]].ino) ∈ ri0, datakey(fs0[ri0[dentrykey(ino1, str)]].ino, n) ∈ ri0, inodekey(ino0) ∈ ri0, dentrykey(ino0, str) ∈ ri0, ri0[dentrykey(ino0, str)] ∈ fs0, dentrykey(ino2, str) ∈ ri0, inodekey(ino2) ∈ ri0, dentrykey(ino4, str) ∈ ri0, ri0[dentrykey(ino4, str)] ∈ fs0, ri0[inodekey(fs0[ri0[dentrykey(ino1, str)]].ino)] ∈ fs0, dentrykey(ino1, str) ∈ ri0, inodekey(ino1) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, inodekey(ino3) ∈ ri0, dentrykey(ino3, str) ∈ ri0, inodekey(ino4) ∈ ri0, ri0[dentrykey(ino2, str)] ∈ fs0, ri0[dentrykey(ino3, str)] ∈ fs0, asynced0 → boolvar0, links(ino2, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino2 = ROOT_INO, m3 ≠ 0 ∨ fs0[ri0[dentrykey(ino1, str)]].ino = ROOT_INO, fs0[ri0[inodekey(ino0)]].nlink ≠ 0 ∨ ino0 = ROOT_INO, fs0[ri0[inodekey(ino1)]].nlink ≠ 0 ∨ ino1 = ROOT_INO, m0 ≠ 0 ∨ m = ROOT_INO, links(ino4, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino4 = ROOT_INO, links(m, abs-dirs(fs0, ri0)) ≠ ∅ ∨ m = ROOT_INO, links(fs0[ri0[dentrykey(ino1, str)]].ino, abs-dirs(fs0, ri0)) ≠ ∅ ∨ fs0[ri0[dentrykey(ino1, str)]].ino = ROOT_INO, links(ino3, abs-dirs(fs0, ri0)) ≠ ∅ ∨ ino3 = ROOT_INO ⊦ (adr3 = ri0[datakey(fs0[ri0[dentrykey(ino1, str)]].ino, n)] ⊃ inodenode(inodekey(fs0[ri0[dentrykey(ino1, str)]].ino), md0, false, m3 + 1, 0, m6) ;(adr2 = ri0[datakey(fs0[ri0[dentrykey(ino1, str)]].ino, n)] ⊃ dentrynode(dentrykey(m, str0), fs0[ri0[dentrykey(ino1, str)]].ino) ;(adr1 = ri0[datakey(fs0[ri0[dentrykey(ino1, str)]].ino, n)] ⊃ inodenode(inodekey(m), md, true, m0, m1, m2 + 1) ;fs0[ri0[datakey(fs0[ri0[dentrykey(ino1, str)]].ino, n)]] ) ) ) .data = fs0[ri0[datakey(fs0[ri0[dentrykey(ino1, str)]].ino, n)]].data, fs0[ri0[dentrykey(ino1, str)]].ino = 0, adr1 = adr2, adr1 = adr3, adr2 = adr3, adr3 = ri0[datakey(fs0[ri0[dentrykey(ino1, str)]].ino, n)], m = 0, m = fs0[ri0[dentrykey(ino1, str)]].ino, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, dentrykey(m, str0) ∈ ri0, m3 = 0 ∧ fs0[ri0[dentrykey(ino1, str)]].ino ≠ ROOT_INO, m0 = 0 ∧ m ≠ ROOT_INO, fs0[ri0[inodekey(ino1)]].nlink = 0 ∧ ino1 ≠ ROOT_INO

Rule argument

fma: adr3 = ri0[datakey(fs0[ri0[dentrykey(ino1, str)]].ino, n)]

Additional information

Used simplifier rules: ⊦ ¬ adr ∈ fs → fs[adr] = (∅)[adr]; (s)% ⊦ key ∈ ri ∧ ri-cons(ri, fs) → ri[key] ∈ fs; (ss) Used formulas: adr3 = ri0[datakey(fs0[ri0[dentrykey(ino1, str)]].ino, n)]