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Proof step 54 from proof long-automatic (previous step)

¬ 0 ≤ i ∨ ¬ i % 18446744073709551616 ≤ 9223372036854775807, j % 18446744073709551616 = (0 ≤ i ∧ 9223372036854775807 < i % 18446744073709551616 ⊃ i % 18446744073709551616 - 18446744073709551616 ;(i < 0 ∧ i % 18446744073709551616 < ~9223372036854775808 ⊃ 18446744073709551616 + i % 18446744073709551616 ;(i < 0 ∧ ~9223372036854775808 ≤ i % 18446744073709551616 ⊃ i % 18446744073709551616;i) ) ) + 18446744073709551616, 0 ≤ j, 0 < j % 18446744073709551616, 9223372036854775807 < j % 18446744073709551616, i < 0 ∨ 9223372036854775807 < i % 18446744073709551616, i < 0 ∨ i % 18446744073709551616 ≤ 9223372036854775807, 0 ≤ i ∨ ~9223372036854775808 ≤ i % 18446744073709551616, 0 ≤ i ∨ i % 18446744073709551616 < ~9223372036854775808 ⊦ j % 18446744073709551616 = i + 18446744073709551616

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 55:
j % 18446744073709551616 = (0 ≤ i ∧ 9223372036854775807 < i % 18446744073709551616 ⊃ i % 18446744073709551616 - 18446744073709551616 ;(i < 0 ∧ i % 18446744073709551616 < ~9223372036854775808 ⊃ 18446744073709551616 + i % 18446744073709551616 ;(i < 0 ∧ ~9223372036854775808 ≤ i % 18446744073709551616 ⊃ i % 18446744073709551616;i) ) ) + 18446744073709551616, 0 ≤ j, 0 < j % 18446744073709551616, 9223372036854775807 < j % 18446744073709551616, i < 0 ∨ i % 18446744073709551616 ≤ 9223372036854775807, 0 ≤ i ∨ ~9223372036854775808 ≤ i % 18446744073709551616, 0 ≤ i ∨ i % 18446744073709551616 < ~9223372036854775808, i < 0 ∨ 9223372036854775807 < i % 18446744073709551616 ⊦ j % 18446744073709551616 = i + 18446744073709551616

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;