[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 96 from proof inv-rename-overwrite-keep-parent (previous step)

¬ boolvar1 ↔ ¬ boolvar0, fs0[ri0[dentrykey(m, str0)]] = dentrynode(key4, m1), fs0[ri0[dentrykey(m, str)]] = dentrynode(key0, m2), fs0[ri0[inodekey(m2)]] = inodenode(key1, md0, boolvar0, m5, m9, m10), fs0[ri0[inodekey(m1)]] = inodenode(key3, md3, boolvar1, 1, m11, m12), links(m1, fs0, ri0) = ∅ ++ dentrykey(m, str0), 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-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), dentrykey(m, str) ∈ ri0, inodekey(m2) ∈ ri0, dentrykey(m, str0) ∈ ri0, inodekey(m1) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, ri0[inodekey(m2)] ∈ fs0, inodekey(m) ∈ ri0, ri0[dentrykey(m, str0)] ∈ fs0, ri0[inodekey(m1)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, key2 ∈ ri0, boolvar1 → dentrykeys(inodekey(m1), ri0) = ∅, 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), m4 ≠ 0 ∨ m = ROOT_INO, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar1 ∧ boolvar2 ∧ m6 = m12, key2 = inodekey(m1) ∨ key2 = inodekey(m) ∨ key2 = dentrykey(m, str0) ∨ key2 ≠ dentrykey(m, str) ∧ key2 ∈ ri0 ⊦ adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr4, adr2 = adr3, adr3 = adr4, m = 0, m1 = 0, m1 = ROOT_INO, 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(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) = adr4 ∨ (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) = adr3 ∨ (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) = adr2 ∨ (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) = adr1 ∨ (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ∈ fs0) ∧ ( adr4 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m1), md1, boolvar2, 0, m11, m6) ;( adr3 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;( adr2 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str0), m2) ;( adr1 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ] ) ) ) ) .key = key2 ∧ ( key2.inode? → ( adr4 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m1), md1, boolvar2, 0, m11, m6) ;( adr3 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;( adr2 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str0), m2) ;( adr1 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ] ) ) ) ) .inode? ∧ key2.ino ≠ 0) ∧ ( key2.dentry? → ( adr4 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m1), md1, boolvar2, 0, m11, m6) ;( adr3 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;( adr2 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str0), m2) ;( adr1 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ] ) ) ) ) .dentry? ∧ inodekey(key2.ino) ∈ ri0 ∧ ( ( adr4 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m1), md1, boolvar2, 0, m11, m6) ;( adr3 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;( adr2 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str0), m2) ;( adr1 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ] ) ) ) ) .ino = m ∨ inodekey (( adr4 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m1), md1, boolvar2, 0, m11, m6) ;( adr3 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;( adr2 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str0), m2) ;( adr1 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ] ) ) ) ) .ino) ∈ ri0) ∧ key2.ino ≠ m1 ∧ ¬ inodekey(key2.ino) ∈ ro ∧ ( adr4 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m1), md1, boolvar2, 0, m11, m6) ;( adr3 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;( adr2 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str0), m2) ;( adr1 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ] ) ) ) ) .ino ≠ m1 ∧ ¬ inodekey (( adr4 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m1), md1, boolvar2, 0, m11, m6) ;( adr3 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;( adr2 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str0), m2) ;( adr1 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ] ) ) ) ) .ino) ∈ ro ∧ (adr4 = (m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]) ⊃ inodenode(inodekey(m1), md1, boolvar2, 0, m11, m6) ;(adr3 = (m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;(adr2 = (m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]) ⊃ dentrynode(dentrykey(m, str0), m2) ;(adr1 = (m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)])] ) ) ) ) .directory) ∧ ( key2.data? → ( adr4 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m1), md1, boolvar2, 0, m11, m6) ;( adr3 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;( adr2 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str0), m2) ;( adr1 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ] ) ) ) ) .data? ∧ inodekey(key2.ino) ∈ ri0 ∧ ¬ (adr4 = (m1 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)])) ⊃ inodenode(inodekey(m1), md1, boolvar2, 0, m11, m6) ;(adr3 = (m1 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)])) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;(adr2 = (m1 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)])) ⊃ dentrynode(dentrykey(m, str0), m2) ;(adr1 = (m1 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)])) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(m1 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]))] ) ) ) ) .directory ∧ # ( adr4 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m1), md1, boolvar2, 0, m11, m6) ;( adr3 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;( adr2 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str0), m2) ;( adr1 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ] ) ) ) ) .data = VFS_PAGE_SIZE)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 97:
¬ boolvar1 ↔ ¬ boolvar0, fs0[ri0[inodekey(m1)]] = inodenode(key3, md3, boolvar1, 1, m11, m12), 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), links(m1, fs0, ri0) = ∅ ++ dentrykey(m, str0), 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), key2 ∈ ri0, 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, ri0[key2] ∈ fs0, boolvar1 → dentrykeys(inodekey(m1), ri0) = ∅, 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, dentrykey(m, str) = dentrykey(m, str0) ∨ key2 ≠ dentrykey(m, str), ¬ boolvar0 ∧ ¬ boolvar2 ∨ boolvar1 ∧ boolvar2 ∧ m6 = m12, ¬ boolvar0 ∧ ¬ boolvar3 ∨ boolvar0 ∧ boolvar3 ∧ m3 = m10, m4 ≠ 0 ∨ m = ROOT_INO ⊦ adr1 = adr2, adr1 = adr3, adr1 = adr4, adr2 = adr3, adr2 = adr4, adr3 = adr4, m = 0, m1 = ROOT_INO, m1 = 0, mkdentry(str, m2) = mkdentry(str0, m1), adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2][inodekey(m), adr3], adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m) ∈ ro, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(m, str0), adr2], ( (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) = adr4 ∨ (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) = adr3 ∨ (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) = adr2 ∨ (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) = adr1 ∨ (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ∈ fs0) ∧ ( adr4 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m1), md1, boolvar2, 0, m11, m6) ;( adr3 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;( adr2 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str0), m2) ;( adr1 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ] ) ) ) ) .key = key2 ∧ ( key2.inode? → ( adr4 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m1), md1, boolvar2, 0, m11, m6) ;( adr3 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;( adr2 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str0), m2) ;( adr1 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ] ) ) ) ) .inode? ∧ key2.ino ≠ 0) ∧ ( key2.dentry? → ( adr4 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m1), md1, boolvar2, 0, m11, m6) ;( adr3 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;( adr2 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str0), m2) ;( adr1 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ] ) ) ) ) .dentry? ∧ inodekey(key2.ino) ∈ ri0 ∧ ( ( adr4 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m1), md1, boolvar2, 0, m11, m6) ;( adr3 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;( adr2 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str0), m2) ;( adr1 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ] ) ) ) ) .ino = m ∨ inodekey (( adr4 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m1), md1, boolvar2, 0, m11, m6) ;( adr3 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;( adr2 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str0), m2) ;( adr1 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ] ) ) ) ) .ino) ∈ ri0) ∧ key2.ino ≠ m1 ∧ ¬ inodekey(key2.ino) ∈ ro ∧ ( adr4 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m1), md1, boolvar2, 0, m11, m6) ;( adr3 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;( adr2 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str0), m2) ;( adr1 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ] ) ) ) ) .ino ≠ m1 ∧ ¬ inodekey (( adr4 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m1), md1, boolvar2, 0, m11, m6) ;( adr3 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;( adr2 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str0), m2) ;( adr1 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ] ) ) ) ) .ino) ∈ ro ∧ (adr4 = (m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]) ⊃ inodenode(inodekey(m1), md1, boolvar2, 0, m11, m6) ;(adr3 = (m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;(adr2 = (m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]) ⊃ dentrynode(dentrykey(m, str0), m2) ;(adr1 = (m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)])] ) ) ) ) .directory) ∧ ( key2.data? → ( adr4 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m1), md1, boolvar2, 0, m11, m6) ;( adr3 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;( adr2 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str0), m2) ;( adr1 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ] ) ) ) ) .data? ∧ inodekey(key2.ino) ∈ ri0 ∧ ¬ (adr4 = (m1 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)])) ⊃ inodenode(inodekey(m1), md1, boolvar2, 0, m11, m6) ;(adr3 = (m1 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)])) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;(adr2 = (m1 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)])) ⊃ dentrynode(dentrykey(m, str0), m2) ;(adr1 = (m1 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)])) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0[(m1 = key2.ino ⊃ adr4;(m = key2.ino ⊃ adr3;ri0[inodekey(key2.ino)]))] ) ) ) ) .directory ∧ # ( adr4 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m1), md1, boolvar2, 0, m11, m6) ;( adr3 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ inodenode(inodekey(m), md, true, m4, n0, m0) ;( adr2 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str0), m2) ;( adr1 = (inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ⊃ dentrynode(dentrykey(m, str), 0) ;fs0 [(inodekey(m1) = key2 ⊃ adr4 ;(inodekey(m) = key2 ⊃ adr3;(dentrykey(m, str0) = key2 ⊃ adr2;(dentrykey(m, str) = key2 ⊃ (∅)[dentrykey(m, str)];ri0[key2]))) ) ] ) ) ) ) .data = VFS_PAGE_SIZE)

Rule argument

Additional information

Used simplifier rules: ⊦ inodekey(m) ≠ dentrykey(m0, str); (s)