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Proof step 57 from proof long-automatic (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 58:
(0 ≤ i ∧ i % 18446744073709551616 ≤ 9223372036854775807 ⊃ i % 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 + j % 18446744073709551616, j % 18446744073709551616 < ~9223372036854775808, j < 0, i < 0 ∨ 9223372036854775807 < i % 18446744073709551616, i < 0 ∨ i % 18446744073709551616 ≤ 9223372036854775807, 0 ≤ i ∨ ~9223372036854775808 ≤ i % 18446744073709551616, 0 ≤ i ∨ i % 18446744073709551616 < ~9223372036854775808 ⊦ i = j % 18446744073709551616 + 18446744073709551616, j % 18446744073709551616 = 0

Rule argument

Additional information

Used simplifier rules: 0 < j ⊦ i % (* j) < 0 ↔ i < 0 ∧ i % j ≠ 0;% ⊦ i < (* j) ∧ j < 0 → i < 0; (forward)% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i < 0 ∧ 0 ≤ j → i < j;%j0 ≠ 0, j ≤ j0 ⊦ i < (* j) → i < (* j0);% ⊦ ¬ i ≤ j ↔ j < i;