1. 1
2. 2
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6. 6
7. 7

!(defq add_zero_eq_zero_add_protocol_loaded !(load-expr "protocol"))

!(def add_zero_eq_zero_add_solution '(1n (2n (1n (2n (2n (2n (2n (18n) (4n (4n (15n) (3n 0)) (4n (2n (0n 0) (4n (15n) (3n 0)) (16n) (15n)) (4n (4n (15n) (4n (2n (0n 2) (4n (15n) (3n 0)) (0n 0) (15n)) (2n (0n 3) (4n (15n) (3n 0)) (2n (17n) (4n (15n) (15n)) (0n 1) (15n)) (15n)))) (4n (15n) (2n (0n 3) (4n (15n) (3n 0)) (0n 0) (15n)))))) (1n (12n (0n 0) (2n (2n (1n (2n (2n (2n (18n) (4n (4n (15n) (3n 0)) (4n (2n (0n 0) (4n (15n) (3n 0)) (16n) (15n)) (4n (4n (15n) (4n (2n (0n 2) (4n (15n) (3n 0)) (0n 0) (15n)) (2n (0n 3) (4n (15n) (3n 0)) (2n (17n) (4n (15n) (15n)) (0n 1) (15n)) (15n)))) (4n (15n) (2n (0n 3) (4n (15n) (3n 0)) (0n 0) (15n)))))) (1n (15n) (3n 0)) (4n (15n) (3n 0))) (4n (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (16n) (15n)) (4n (4n (15n) (4n (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (0n 0) (15n)) (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (2n (17n) (4n (15n) (15n)) (0n 1) (15n)) (15n)))) (4n (15n) (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (0n 0) (15n))))) (0n 0) (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (16n) (15n))) (4n (4n (15n) (4n (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (0n 0) (15n)) (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (2n (17n) (4n (15n) (15n)) (0n 1) (15n)) (15n)))) (4n (15n) (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (0n 0) (15n)))) (1n (1n (2n (17n) (4n (15n) (15n)) (0n 0) (15n)) (15n)) (4n (15n) (15n))) (4n (15n) (4n (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (0n 0) (15n)) (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (2n (17n) (4n (15n) (15n)) (0n 1) (15n)) (15n))))) (4n (15n) (15n))) (4n (15n) (4n (15n) (15n))) (16n) (15n)) (4n (15n) (15n)) (0n 0) (15n)) (15n)) (3n 0)) (4n (15n) (3n 0))) (4n (2n (1n (12n (0n 0) (2n (2n (1n (2n (2n (2n (18n) (4n (4n (15n) (3n 0)) (4n (2n (0n 0) (4n (15n) (3n 0)) (16n) (15n)) (4n (4n (15n) (4n (2n (0n 2) (4n (15n) (3n 0)) (0n 0) (15n)) (2n (0n 3) (4n (15n) (3n 0)) (2n (17n) (4n (15n) (15n)) (0n 1) (15n)) (15n)))) (4n (15n) (2n (0n 3) (4n (15n) (3n 0)) (0n 0) (15n)))))) (1n (15n) (3n 0)) (4n (15n) (3n 0))) (4n (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (16n) (15n)) (4n (4n (15n) (4n (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (0n 0) (15n)) (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (2n (17n) (4n (15n) (15n)) (0n 1) (15n)) (15n)))) (4n (15n) (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (0n 0) (15n))))) (0n 0) (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (16n) (15n))) (4n (4n (15n) (4n (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (0n 0) (15n)) (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (2n (17n) (4n (15n) (15n)) (0n 1) (15n)) (15n)))) (4n (15n) (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (0n 0) (15n)))) (1n (1n (2n (17n) (4n (15n) (15n)) (0n 0) (15n)) (15n)) (4n (15n) (15n))) (4n (15n) (4n (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (0n 0) (15n)) (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (2n (17n) (4n (15n) (15n)) (0n 1) (15n)) (15n))))) (4n (15n) (15n))) (4n (15n) (4n (15n) (15n))) (16n) (15n)) (4n (15n) (15n)) (0n 0) (15n)) (15n)) (3n 0)) (4n (15n) (3n 0)) (16n) (15n)) (4n (4n (15n) (4n (2n (1n (12n (0n 0) (2n (2n (1n (2n (2n (2n (18n) (4n (4n (15n) 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(15n)) (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (2n (17n) (4n (15n) (15n)) (0n 1) (15n)) (15n))))) (4n (15n) (15n))) (4n (15n) (4n (15n) (15n))) (16n) (15n)) (4n (15n) (15n)) (0n 0) (15n)) (15n)) (3n 0)) (4n (15n) (3n 0)) (0n 0) (15n)) (2n (1n (12n (0n 0) (2n (2n (1n (2n (2n (2n (18n) (4n (4n (15n) (3n 0)) (4n (2n (0n 0) (4n (15n) (3n 0)) (16n) (15n)) (4n (4n (15n) (4n (2n (0n 2) (4n (15n) (3n 0)) (0n 0) (15n)) (2n (0n 3) (4n (15n) (3n 0)) (2n (17n) (4n (15n) (15n)) (0n 1) (15n)) (15n)))) (4n (15n) (2n (0n 3) (4n (15n) (3n 0)) (0n 0) (15n)))))) (1n (15n) (3n 0)) (4n (15n) (3n 0))) (4n (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (16n) (15n)) (4n (4n (15n) (4n (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (0n 0) (15n)) (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (2n (17n) (4n (15n) (15n)) (0n 1) (15n)) (15n)))) (4n (15n) (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (0n 0) (15n))))) (0n 0) (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (16n) (15n))) (4n (4n (15n) (4n (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (0n 0) 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(15n) (4n (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (0n 0) (15n)) (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (2n (17n) (4n (15n) (15n)) (0n 1) (15n)) (15n)))) (4n (15n) (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (0n 0) (15n))))) (0n 0) (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (16n) (15n))) (4n (4n (15n) (4n (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (0n 0) (15n)) (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (2n (17n) (4n (15n) (15n)) (0n 1) (15n)) (15n)))) (4n (15n) (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (0n 0) (15n)))) (1n (1n (2n (17n) (4n (15n) (15n)) (0n 0) (15n)) (15n)) (4n (15n) (15n))) (4n (15n) (4n (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (0n 0) (15n)) (2n (1n (15n) (3n 0)) (4n (15n) (3n 0)) (2n (17n) (4n (15n) (15n)) (0n 1) (15n)) (15n))))) (4n (15n) (15n))) (4n (15n) (4n (15n) (15n))) (16n) (15n)) (4n (15n) (15n)) (0n 0) (15n)) (15n)) (3n 0)) (4n (15n) (3n 0)) (0n 0) (15n))))) (2n (2n (13n) (4n (3n 0) (4n (0n 0) (12n (0n 0) (0n 0) (0n 1)))) (15n) (3n 0)) (4n (15n) (12n (0n 0) (0n 0) (15n))) 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!(def comm_term_test (hide #0x2903850943570 add_zero_eq_zero_add_solution))

!(prove-protocol add_zero_eq_zero_add_protocol_loaded "proof" comm_term_test)