Proof step 325 from proof inv-rename-overwrite-keep-parent (previous step)

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

• Proof step 326:

  ¬ boolvar1 ↔ ¬ boolvar0, fs0[ri0[dentrykey(ino, str1)]] = dentrynode(key, m7), fs0[ri0[inodekey(m2)]] = inodenode(key1, md0, boolvar0, m5, m9, m10), fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m2), fs0[ri0[dentrykey(m, str0)]] = dentrynode(key4, m1), fs0[ri0[inodekey(m1)]] = inodenode(key3, md3, boolvar1, m8 + 1, m11, m12), fs0[ri0[inodekey(ino)]].directory, 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[dentrykey(ino, str1)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, ri0[inodekey(m1)] ∈ fs0, ri0[dentrykey(m, str0)] ∈ fs0, inodekey(m) ∈ ri0, ri0[inodekey(m2)] ∈ fs0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m1) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m2) ∈ ri0, dentrykey(m, str) ∈ ri0, dentrykey(ino, str1) ∈ ri0, inodekey(m7) ∈ ri0, inodekey(ino) ∈ ri0, boolvar1 → dentrykeys(inodekey(m1), ri0) = ∅, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar1 ∧ boolvar2 ∧ m6 = m12, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, m4 ≠ 0 ∨ m = ROOT_INO, dentrykey(m, str) = dentrykey(m, str0) ∨ dentrykey(ino, str1) ≠ dentrykey(m, str) ⊦ adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, m = 0, m1 = 0, m1 = ROOT_INO, m8 = 0, mkdentry(str, m2) = mkdentry(str0, m1), ( adr4 = (dentrykey(m, str0) = dentrykey(ino, str1) ⊃ adr2;(dentrykey(m, str) = dentrykey(ino, str1) ⊃ (∅)[dentrykey(m, str)];ri0[dentrykey(ino, str1)])) ⊃ inodenode(inodekey(m1), md1, boolvar2, m8, m11, m6) ;( adr3 = (dentrykey(m, str0) = dentrykey(ino, str1) ⊃ adr2;(dentrykey(m, str) = dentrykey(ino, str1) ⊃ (∅)[dentrykey(m, str)];ri0[dentrykey(ino, str1)])) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;( adr2 = (dentrykey(m, str0) = dentrykey(ino, str1) ⊃ adr2 ;(dentrykey(m, str) = dentrykey(ino, str1) ⊃ (∅)[dentrykey(m, str)];ri0[dentrykey(ino, str1)]) ) ⊃ dentrynode(dentrykey(m, str0), m2) ;( adr1 = (dentrykey(m, str0) = dentrykey(ino, str1) ⊃ adr2 ;(dentrykey(m, str) = dentrykey(ino, str1) ⊃ (∅)[dentrykey(m, str)];ri0[dentrykey(ino, str1)]) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(dentrykey(m, str0) = dentrykey(ino, str1) ⊃ adr2 ;(dentrykey(m, str) = dentrykey(ino, str1) ⊃ (∅)[dentrykey(m, str)];ri0[dentrykey(ino, str1)]) ) ] ) ) ) ) .dentry?, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2], inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3], inodekey(m7) ∈ ro, inodekey(ino) ∈ ro

• Proof step 329:

  ¬ boolvar1 ↔ ¬ boolvar0, fs0[ri0[dentrykey(ino, str1)]] = dentrynode(key, m7), fs0[ri0[inodekey(m2)]] = inodenode(key1, md0, boolvar0, m5, m9, m10), fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m2), fs0[ri0[dentrykey(m, str0)]] = dentrynode(key4, m1), fs0[ri0[inodekey(m1)]] = inodenode(key3, md3, boolvar1, m8 + 1, m11, m12), fs0[ri0[inodekey(ino)]].directory, 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[dentrykey(ino, str1)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, ri0[inodekey(m1)] ∈ fs0, ri0[dentrykey(m, str0)] ∈ fs0, inodekey(m) ∈ ri0, ri0[inodekey(m2)] ∈ fs0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m1) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m2) ∈ ri0, dentrykey(m, str) ∈ ri0, dentrykey(ino, str1) ∈ ri0, inodekey(m7) ∈ ri0, inodekey(ino) ∈ ri0, boolvar1 → dentrykeys(inodekey(m1), ri0) = ∅, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar1 ∧ boolvar2 ∧ m6 = m12, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, m4 ≠ 0 ∨ m = ROOT_INO, dentrykey(m, str) = dentrykey(m, str0) ∨ dentrykey(ino, str1) ≠ dentrykey(m, str) ⊦ ( adr4 = (dentrykey(m, str0) = dentrykey(ino, str1) ⊃ adr2 ;(dentrykey(m, str) = dentrykey(ino, str1) ⊃ (∅)[dentrykey(m, str)];ri0[dentrykey(ino, str1)]) ) ⊃ inodenode(inodekey(m1), md1, boolvar2, m8, m11, m6) ;( adr3 = (dentrykey(m, str0) = dentrykey(ino, str1) ⊃ adr2 ;(dentrykey(m, str) = dentrykey(ino, str1) ⊃ (∅)[dentrykey(m, str)];ri0[dentrykey(ino, str1)]) ) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;( adr2 = (dentrykey(m, str0) = dentrykey(ino, str1) ⊃ adr2 ;(dentrykey(m, str) = dentrykey(ino, str1) ⊃ (∅)[dentrykey(m, str)];ri0[dentrykey(ino, str1)]) ) ⊃ dentrynode(dentrykey(m, str0), m2) ;( adr1 = (dentrykey(m, str0) = dentrykey(ino, str1) ⊃ adr2 ;(dentrykey(m, str) = dentrykey(ino, str1) ⊃ (∅)[dentrykey(m, str)];ri0[dentrykey(ino, str1)]) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(dentrykey(m, str0) = dentrykey(ino, str1) ⊃ adr2 ;(dentrykey(m, str) = dentrykey(ino, str1) ⊃ (∅)[dentrykey(m, str)];ri0[dentrykey(ino, str1)]) ) ] ) ) ) ) .ino = m1, ( adr4 = (dentrykey(m, str0) = dentrykey(ino, str1) ⊃ adr2 ;(dentrykey(m, str) = dentrykey(ino, str1) ⊃ (∅)[dentrykey(m, str)];ri0[dentrykey(ino, str1)]) ) ⊃ inodenode(inodekey(m1), md1, boolvar2, m8, m11, m6) ;( adr3 = (dentrykey(m, str0) = dentrykey(ino, str1) ⊃ adr2 ;(dentrykey(m, str) = dentrykey(ino, str1) ⊃ (∅)[dentrykey(m, str)];ri0[dentrykey(ino, str1)]) ) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;( adr2 = (dentrykey(m, str0) = dentrykey(ino, str1) ⊃ adr2 ;(dentrykey(m, str) = dentrykey(ino, str1) ⊃ (∅)[dentrykey(m, str)];ri0[dentrykey(ino, str1)]) ) ⊃ dentrynode(dentrykey(m, str0), m2) ;( adr1 = (dentrykey(m, str0) = dentrykey(ino, str1) ⊃ adr2 ;(dentrykey(m, str) = dentrykey(ino, str1) ⊃ (∅)[dentrykey(m, str)];ri0[dentrykey(ino, str1)]) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(dentrykey(m, str0) = dentrykey(ino, str1) ⊃ adr2 ;(dentrykey(m, str) = dentrykey(ino, str1) ⊃ (∅)[dentrykey(m, str)];ri0[dentrykey(ino, str1)]) ) ] ) ) ) ) .ino = m, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, m = 0, m1 = 0, m1 = ROOT_INO, m8 = 0, mkdentry(str, m2) = mkdentry(str0, m1), adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2], inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3], inodekey(m7) ∈ ro, inodekey(ino) ∈ ro, inodekey (( adr4 = (dentrykey(m, str0) = dentrykey(ino, str1) ⊃ adr2 ;(dentrykey(m, str) = dentrykey(ino, str1) ⊃ (∅)[dentrykey(m, str)];ri0[dentrykey(ino, str1)]) ) ⊃ inodenode(inodekey(m1), md1, boolvar2, m8, m11, m6) ;( adr3 = (dentrykey(m, str0) = dentrykey(ino, str1) ⊃ adr2 ;(dentrykey(m, str) = dentrykey(ino, str1) ⊃ (∅)[dentrykey(m, str)];ri0[dentrykey(ino, str1)]) ) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;( adr2 = (dentrykey(m, str0) = dentrykey(ino, str1) ⊃ adr2 ;(dentrykey(m, str) = dentrykey(ino, str1) ⊃ (∅)[dentrykey(m, str)];ri0[dentrykey(ino, str1)]) ) ⊃ dentrynode(dentrykey(m, str0), m2) ;( adr1 = (dentrykey(m, str0) = dentrykey(ino, str1) ⊃ adr2 ;(dentrykey(m, str) = dentrykey(ino, str1) ⊃ (∅)[dentrykey(m, str)];ri0[dentrykey(ino, str1)]) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(dentrykey(m, str0) = dentrykey(ino, str1) ⊃ adr2 ;(dentrykey(m, str) = dentrykey(ino, str1) ⊃ (∅)[dentrykey(m, str)];ri0[dentrykey(ino, str1)]) ) ] ) ) ) ) .ino) ∈ ri0

• Proof step 332:

  ¬ boolvar1 ↔ ¬ boolvar0, fs0[ri0[dentrykey(ino, str1)]] = dentrynode(key, m7), fs0[ri0[inodekey(m2)]] = inodenode(key1, md0, boolvar0, m5, m9, m10), fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m2), fs0[ri0[dentrykey(m, str0)]] = dentrynode(key4, m1), fs0[ri0[inodekey(m1)]] = inodenode(key3, md3, boolvar1, m8 + 1, m11, m12), fs0[ri0[inodekey(ino)]].directory, 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), inodekey (( adr4 = (dentrykey(m, str0) = dentrykey(ino, str1) ⊃ adr2;(dentrykey(m, str) = dentrykey(ino, str1) ⊃ (∅)[dentrykey(m, str)];ri0[dentrykey(ino, str1)])) ⊃ inodenode(inodekey(m1), md1, boolvar2, m8, m11, m6) ;( adr3 = (dentrykey(m, str0) = dentrykey(ino, str1) ⊃ adr2 ;(dentrykey(m, str) = dentrykey(ino, str1) ⊃ (∅)[dentrykey(m, str)];ri0[dentrykey(ino, str1)]) ) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;( adr2 = (dentrykey(m, str0) = dentrykey(ino, str1) ⊃ adr2 ;(dentrykey(m, str) = dentrykey(ino, str1) ⊃ (∅)[dentrykey(m, str)];ri0[dentrykey(ino, str1)]) ) ⊃ dentrynode(dentrykey(m, str0), m2) ;( adr1 = (dentrykey(m, str0) = dentrykey(ino, str1) ⊃ adr2 ;(dentrykey(m, str) = dentrykey(ino, str1) ⊃ (∅)[dentrykey(m, str)];ri0[dentrykey(ino, str1)]) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(dentrykey(m, str0) = dentrykey(ino, str1) ⊃ adr2 ;(dentrykey(m, str) = dentrykey(ino, str1) ⊃ (∅)[dentrykey(m, str)];ri0[dentrykey(ino, str1)]) ) ] ) ) ) ) .ino) ∈ ro, ri0[dentrykey(ino, str1)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, ri0[inodekey(m1)] ∈ fs0, ri0[dentrykey(m, str0)] ∈ fs0, inodekey(m) ∈ ri0, ri0[inodekey(m2)] ∈ fs0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m1) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m2) ∈ ri0, dentrykey(m, str) ∈ ri0, dentrykey(ino, str1) ∈ ri0, inodekey(m7) ∈ ri0, inodekey(ino) ∈ ri0, boolvar1 → dentrykeys(inodekey(m1), ri0) = ∅, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar1 ∧ boolvar2 ∧ m6 = m12, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, m4 ≠ 0 ∨ m = ROOT_INO, dentrykey(m, str) = dentrykey(m, str0) ∨ dentrykey(ino, str1) ≠ dentrykey(m, str) ⊦ adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, m = 0, m1 = 0, m1 = ROOT_INO, m8 = 0, mkdentry(str, m2) = mkdentry(str0, m1), adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2], inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3], inodekey(m7) ∈ ro, inodekey(ino) ∈ ro

• Proof step 347:

  ¬ boolvar1 ↔ ¬ boolvar0, fs0[ri0[dentrykey(ino, str1)]] = dentrynode(key, m7), fs0[ri0[inodekey(m2)]] = inodenode(key1, md0, boolvar0, m5, m9, m10), fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m2), fs0[ri0[dentrykey(m, str0)]] = dentrynode(key4, m1), fs0[ri0[inodekey(m1)]] = inodenode(key3, md3, boolvar1, m8 + 1, m11, m12), fs0[ri0[inodekey(ino)]].directory, 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[dentrykey(ino, str1)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, ri0[inodekey(m1)] ∈ fs0, ri0[dentrykey(m, str0)] ∈ fs0, inodekey(m) ∈ ri0, ri0[inodekey(m2)] ∈ fs0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m1) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m2) ∈ ri0, dentrykey(m, str) ∈ ri0, dentrykey(ino, str1) ∈ ri0, inodekey(m7) ∈ ri0, inodekey(ino) ∈ ri0, boolvar1 → dentrykeys(inodekey(m1), ri0) = ∅, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar1 ∧ boolvar2 ∧ m6 = m12, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, m4 ≠ 0 ∨ m = ROOT_INO, dentrykey(m, str) = dentrykey(m, str0) ∨ dentrykey(ino, str1) ≠ dentrykey(m, str) ⊦ adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, m = 0, m1 = 0, m1 = ROOT_INO, m8 = 0, mkdentry(str, m2) = mkdentry(str0, m1), (adr4 = (m1 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ inodenode(inodekey(m1), md1, boolvar2, m8, m11, m6) ;(adr3 = (m1 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;(adr2 = (m1 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ dentrynode(dentrykey(m, str0), m2) ;(adr1 = (m1 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)])) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(m1 = ino ⊃ adr4;(m = ino ⊃ adr3;ri0[inodekey(ino)]))] ) ) ) ) .directory, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2], inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3], inodekey(m7) ∈ ro, inodekey(ino) ∈ ro

Rule argument

Additional information