| odd(i1) ∧ even(i2) ∨ even(i1) ∧ odd(i2), odd(i) ∧ even(i0) ∨ even(i) ∧ odd(i0) ⊦ ∃ i3, i4, i5, i6. even(i3 + i4) ∧ even(i5 + i6) ∧ i3 ^2 + i4 ^2 + i5 ^2 + i6 ^2 = (i ^2 + i0 ^2) + i1 ^2 + i2 ^2 |
odd(i1) ∧ even(i2), odd(i) ∧ even(i0) ∨ even(i) ∧ odd(i0) ⊦ ∃ i3, i4, i5, i6. even(i3 + i4) ∧ even(i5 + i6) ∧ i3 ^2 + i4 ^2 + i5 ^2 + i6 ^2 = (i ^2 + i0 ^2) + i1 ^2 + i2 ^2
even(i1) ∧ odd(i2), odd(i) ∧ even(i0) ∨ even(i) ∧ odd(i0) ⊦ ∃ i3, i4, i5, i6. even(i3 + i4) ∧ even(i5 + i6) ∧ i3 ^2 + i4 ^2 + i5 ^2 + i6 ^2 = (i ^2 + i0 ^2) + i1 ^2 + i2 ^2