TSTP Solution File: NUM017-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM017-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 11:55:00 EDT 2023
% Result : Unsatisfiable 279.84s 35.98s
% Output : Proof 280.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM017-1 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Aug 25 16:12:55 EDT 2023
% 0.12/0.33 % CPUTime :
% 279.84/35.98 Command-line arguments: --flatten
% 279.84/35.98
% 279.84/35.98 % SZS status Unsatisfiable
% 279.84/35.98
% 280.32/36.05 % SZS output start Proof
% 280.32/36.05 Take the following subset of the input axioms:
% 280.32/36.05 fof(a_is_prime, hypothesis, prime(a)).
% 280.32/36.05 fof(b_squared, hypothesis, product(b, b, d)).
% 280.32/36.05 fof(closure_of_product, axiom, ![B, A]: product(A, B, multiply(A, B))).
% 280.32/36.05 fof(divides_implies_product, axiom, ![A2, B2]: (~divides(A2, B2) | product(A2, second_divided_by_1st(A2, B2), B2))).
% 280.32/36.05 fof(divides_substitution1, axiom, ![C, B2, A2_2]: (~equalish(B2, A2_2) | (~divides(C, B2) | divides(C, A2_2)))).
% 280.32/36.05 fof(primes_lemma1, axiom, ![B2, C2, A2_2]: (~divides(A2_2, B2) | (~product(C2, C2, B2) | (~prime(A2_2) | divides(A2_2, C2))))).
% 280.32/36.05 fof(product_associativity2, axiom, ![D, E, F, B2, C2, A2_2]: (~product(A2_2, B2, C2) | (~product(D, B2, E) | (~product(F, D, A2_2) | product(F, E, C2))))).
% 280.32/36.05 fof(product_divisible_by_operand, axiom, ![B2, C2, A2_2]: (~product(A2_2, B2, C2) | divides(A2_2, C2))).
% 280.32/36.05 fof(product_left_cancellation, axiom, ![D2, B2, C2, A2_2]: (~product(A2_2, B2, C2) | (~product(A2_2, D2, C2) | equalish(B2, D2)))).
% 280.32/36.05 fof(product_substitution3, axiom, ![D2, B2, C2, A2_2]: (~equalish(C2, B2) | (~product(C2, D2, A2_2) | product(B2, D2, A2_2)))).
% 280.32/36.05 fof(prove_there_is_no_common_divisor, negated_conjecture, ![A3]: (~divides(A3, c) | ~divides(A3, b))).
% 280.32/36.05 fof(symmetry, axiom, ![X, Y]: (~equalish(X, Y) | equalish(Y, X))).
% 280.32/36.05 fof(well_defined_product, axiom, ![D2, B2, C2, A2_2]: (~product(A2_2, B2, C2) | (~product(A2_2, B2, D2) | equalish(D2, C2)))).
% 280.32/36.05
% 280.32/36.05 Now clausify the problem and encode Horn clauses using encoding 3 of
% 280.32/36.05 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 280.32/36.05 We repeatedly replace C & s=t => u=v by the two clauses:
% 280.32/36.05 fresh(y, y, x1...xn) = u
% 280.32/36.05 C => fresh(s, t, x1...xn) = v
% 280.32/36.05 where fresh is a fresh function symbol and x1..xn are the free
% 280.32/36.05 variables of u and v.
% 280.32/36.05 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 280.32/36.05 input problem has no model of domain size 1).
% 280.32/36.05
% 280.32/36.05 The encoding turns the above axioms into the following unit equations and goals:
% 280.32/36.05
% 280.32/36.05 Axiom 1 (a_is_prime): prime(a) = true2.
% 280.32/36.05 Axiom 2 (b_squared): product(b, b, d) = true2.
% 280.32/36.05 Axiom 3 (well_defined_product): fresh(X, X, Y, Z) = true2.
% 280.32/36.05 Axiom 4 (primes_lemma1): fresh29(X, X, Y, Z) = true2.
% 280.32/36.05 Axiom 5 (divides_implies_product): fresh26(X, X, Y, Z) = true2.
% 280.32/36.05 Axiom 6 (divides_substitution1): fresh25(X, X, Y, Z) = true2.
% 280.32/36.05 Axiom 7 (product_divisible_by_operand): fresh16(X, X, Y, Z) = true2.
% 280.32/36.05 Axiom 8 (product_left_cancellation): fresh14(X, X, Y, Z) = true2.
% 280.32/36.05 Axiom 9 (symmetry): fresh7(X, X, Y, Z) = true2.
% 280.32/36.05 Axiom 10 (product_associativity2): fresh31(X, X, Y, Z, W) = true2.
% 280.32/36.05 Axiom 11 (divides_substitution1): fresh27(X, X, Y, Z, W) = divides(W, Z).
% 280.32/36.05 Axiom 12 (primes_lemma1): fresh20(X, X, Y, Z, W) = divides(Y, W).
% 280.32/36.05 Axiom 13 (product_substitution3): fresh8(X, X, Y, Z, W) = true2.
% 280.32/36.05 Axiom 14 (closure_of_product): product(X, Y, multiply(X, Y)) = true2.
% 280.32/36.05 Axiom 15 (divides_implies_product): fresh26(divides(X, Y), true2, X, Y) = product(X, second_divided_by_1st(X, Y), Y).
% 280.32/36.05 Axiom 16 (product_left_cancellation): fresh15(X, X, Y, Z, W, V) = equalish(Z, V).
% 280.32/36.05 Axiom 17 (product_substitution3): fresh9(X, X, Y, Z, W, V) = product(Z, W, V).
% 280.32/36.05 Axiom 18 (symmetry): fresh7(equalish(X, Y), true2, X, Y) = equalish(Y, X).
% 280.32/36.05 Axiom 19 (well_defined_product): fresh2(X, X, Y, Z, W, V) = equalish(V, W).
% 280.32/36.05 Axiom 20 (primes_lemma1): fresh28(X, X, Y, Z, W) = fresh29(product(W, W, Z), true2, Y, W).
% 280.32/36.05 Axiom 21 (divides_substitution1): fresh27(divides(X, Y), true2, Y, Z, X) = fresh25(equalish(Y, Z), true2, Z, X).
% 280.32/36.05 Axiom 22 (primes_lemma1): fresh28(prime(X), true2, X, Y, Z) = fresh20(divides(X, Y), true2, X, Y, Z).
% 280.32/36.05 Axiom 23 (product_associativity2): fresh18(X, X, Y, Z, W, V, U) = product(U, V, W).
% 280.32/36.05 Axiom 24 (product_divisible_by_operand): fresh16(product(X, Y, Z), true2, X, Z) = divides(X, Z).
% 280.32/36.05 Axiom 25 (product_associativity2): fresh30(X, X, Y, Z, W, V, U, T) = fresh31(product(Y, Z, W), true2, W, U, T).
% 280.32/36.05 Axiom 26 (product_left_cancellation): fresh15(product(X, Y, Z), true2, X, W, Z, Y) = fresh14(product(X, W, Z), true2, W, Y).
% 280.32/36.05 Axiom 27 (product_substitution3): fresh9(product(X, Y, Z), true2, X, W, Y, Z) = fresh8(equalish(X, W), true2, W, Y, Z).
% 280.32/36.05 Axiom 28 (well_defined_product): fresh2(product(X, Y, Z), true2, X, Y, W, Z) = fresh(product(X, Y, W), true2, W, Z).
% 280.32/36.05 Axiom 29 (product_associativity2): fresh30(product(X, Y, Z), true2, Z, W, V, Y, U, X) = fresh18(product(Y, W, U), true2, Z, W, V, U, X).
% 280.32/36.05
% 280.32/36.05 Lemma 30: product(b, b, d) = prime(a).
% 280.32/36.05 Proof:
% 280.32/36.05 product(b, b, d)
% 280.32/36.05 = { by axiom 2 (b_squared) }
% 280.32/36.05 true2
% 280.32/36.05 = { by axiom 1 (a_is_prime) R->L }
% 280.32/36.05 prime(a)
% 280.32/36.05
% 280.32/36.05 Lemma 31: product(X, Y, multiply(X, Y)) = product(b, b, d).
% 280.32/36.05 Proof:
% 280.32/36.05 product(X, Y, multiply(X, Y))
% 280.32/36.05 = { by axiom 14 (closure_of_product) }
% 280.32/36.05 true2
% 280.32/36.05 = { by axiom 1 (a_is_prime) R->L }
% 280.32/36.05 prime(a)
% 280.32/36.05 = { by lemma 30 R->L }
% 280.32/36.05 product(b, b, d)
% 280.32/36.05
% 280.32/36.05 Lemma 32: divides(X, multiply(X, Y)) = product(b, b, d).
% 280.32/36.05 Proof:
% 280.32/36.05 divides(X, multiply(X, Y))
% 280.32/36.05 = { by axiom 24 (product_divisible_by_operand) R->L }
% 280.32/36.05 fresh16(product(X, Y, multiply(X, Y)), true2, X, multiply(X, Y))
% 280.32/36.05 = { by axiom 1 (a_is_prime) R->L }
% 280.32/36.05 fresh16(product(X, Y, multiply(X, Y)), prime(a), X, multiply(X, Y))
% 280.32/36.05 = { by lemma 30 R->L }
% 280.32/36.05 fresh16(product(X, Y, multiply(X, Y)), product(b, b, d), X, multiply(X, Y))
% 280.32/36.05 = { by lemma 31 }
% 280.32/36.05 fresh16(product(b, b, d), product(b, b, d), X, multiply(X, Y))
% 280.32/36.05 = { by axiom 7 (product_divisible_by_operand) }
% 280.32/36.05 true2
% 280.32/36.05 = { by axiom 1 (a_is_prime) R->L }
% 280.32/36.05 prime(a)
% 280.32/36.05 = { by lemma 30 R->L }
% 280.85/36.05 product(b, b, d)
% 280.85/36.05
% 280.85/36.05 Lemma 33: divides(second_divided_by_1st(a, a), X) = product(b, b, d).
% 280.85/36.05 Proof:
% 280.85/36.05 divides(second_divided_by_1st(a, a), X)
% 280.85/36.06 = { by axiom 11 (divides_substitution1) R->L }
% 280.85/36.06 fresh27(product(b, b, d), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by lemma 32 R->L }
% 280.85/36.06 fresh27(divides(second_divided_by_1st(a, a), multiply(second_divided_by_1st(a, a), X)), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by lemma 30 }
% 280.85/36.06 fresh27(divides(second_divided_by_1st(a, a), multiply(second_divided_by_1st(a, a), X)), prime(a), multiply(second_divided_by_1st(a, a), X), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by axiom 1 (a_is_prime) }
% 280.85/36.06 fresh27(divides(second_divided_by_1st(a, a), multiply(second_divided_by_1st(a, a), X)), true2, multiply(second_divided_by_1st(a, a), X), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by axiom 21 (divides_substitution1) }
% 280.85/36.06 fresh25(equalish(multiply(second_divided_by_1st(a, a), X), X), true2, X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by axiom 1 (a_is_prime) R->L }
% 280.85/36.06 fresh25(equalish(multiply(second_divided_by_1st(a, a), X), X), prime(a), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by lemma 30 R->L }
% 280.85/36.06 fresh25(equalish(multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by axiom 16 (product_left_cancellation) R->L }
% 280.85/36.06 fresh25(fresh15(product(b, b, d), product(b, b, d), a, multiply(second_divided_by_1st(a, a), X), multiply(a, X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by lemma 31 R->L }
% 280.85/36.06 fresh25(fresh15(product(a, X, multiply(a, X)), product(b, b, d), a, multiply(second_divided_by_1st(a, a), X), multiply(a, X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by lemma 30 }
% 280.85/36.06 fresh25(fresh15(product(a, X, multiply(a, X)), prime(a), a, multiply(second_divided_by_1st(a, a), X), multiply(a, X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by axiom 1 (a_is_prime) }
% 280.85/36.06 fresh25(fresh15(product(a, X, multiply(a, X)), true2, a, multiply(second_divided_by_1st(a, a), X), multiply(a, X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by axiom 26 (product_left_cancellation) }
% 280.85/36.06 fresh25(fresh14(product(a, multiply(second_divided_by_1st(a, a), X), multiply(a, X)), true2, multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by axiom 1 (a_is_prime) R->L }
% 280.85/36.06 fresh25(fresh14(product(a, multiply(second_divided_by_1st(a, a), X), multiply(a, X)), prime(a), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by lemma 30 R->L }
% 280.85/36.06 fresh25(fresh14(product(a, multiply(second_divided_by_1st(a, a), X), multiply(a, X)), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by axiom 23 (product_associativity2) R->L }
% 280.85/36.06 fresh25(fresh14(fresh18(product(b, b, d), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by lemma 31 R->L }
% 280.85/36.06 fresh25(fresh14(fresh18(product(second_divided_by_1st(a, a), X, multiply(second_divided_by_1st(a, a), X)), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by lemma 30 }
% 280.85/36.06 fresh25(fresh14(fresh18(product(second_divided_by_1st(a, a), X, multiply(second_divided_by_1st(a, a), X)), prime(a), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by axiom 1 (a_is_prime) }
% 280.85/36.06 fresh25(fresh14(fresh18(product(second_divided_by_1st(a, a), X, multiply(second_divided_by_1st(a, a), X)), true2, multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by axiom 29 (product_associativity2) R->L }
% 280.85/36.06 fresh25(fresh14(fresh30(product(a, second_divided_by_1st(a, a), multiply(a, second_divided_by_1st(a, a))), true2, multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X), second_divided_by_1st(a, a), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by axiom 1 (a_is_prime) R->L }
% 280.85/36.06 fresh25(fresh14(fresh30(product(a, second_divided_by_1st(a, a), multiply(a, second_divided_by_1st(a, a))), prime(a), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X), second_divided_by_1st(a, a), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by lemma 30 R->L }
% 280.85/36.06 fresh25(fresh14(fresh30(product(a, second_divided_by_1st(a, a), multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X), second_divided_by_1st(a, a), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by lemma 31 }
% 280.85/36.06 fresh25(fresh14(fresh30(product(b, b, d), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X), second_divided_by_1st(a, a), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by axiom 25 (product_associativity2) }
% 280.85/36.06 fresh25(fresh14(fresh31(product(multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), true2, multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by axiom 1 (a_is_prime) R->L }
% 280.85/36.06 fresh25(fresh14(fresh31(product(multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), prime(a), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by lemma 30 R->L }
% 280.85/36.06 fresh25(fresh14(fresh31(product(multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by axiom 17 (product_substitution3) R->L }
% 280.85/36.06 fresh25(fresh14(fresh31(fresh9(product(b, b, d), product(b, b, d), a, multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by lemma 31 R->L }
% 280.85/36.06 fresh25(fresh14(fresh31(fresh9(product(a, X, multiply(a, X)), product(b, b, d), a, multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by lemma 30 }
% 280.85/36.06 fresh25(fresh14(fresh31(fresh9(product(a, X, multiply(a, X)), prime(a), a, multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by axiom 1 (a_is_prime) }
% 280.85/36.06 fresh25(fresh14(fresh31(fresh9(product(a, X, multiply(a, X)), true2, a, multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by axiom 27 (product_substitution3) }
% 280.85/36.06 fresh25(fresh14(fresh31(fresh8(equalish(a, multiply(a, second_divided_by_1st(a, a))), true2, multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by axiom 1 (a_is_prime) R->L }
% 280.85/36.06 fresh25(fresh14(fresh31(fresh8(equalish(a, multiply(a, second_divided_by_1st(a, a))), prime(a), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by lemma 30 R->L }
% 280.85/36.06 fresh25(fresh14(fresh31(fresh8(equalish(a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by axiom 18 (symmetry) R->L }
% 280.85/36.06 fresh25(fresh14(fresh31(fresh8(fresh7(equalish(multiply(a, second_divided_by_1st(a, a)), a), true2, multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by axiom 1 (a_is_prime) R->L }
% 280.85/36.06 fresh25(fresh14(fresh31(fresh8(fresh7(equalish(multiply(a, second_divided_by_1st(a, a)), a), prime(a), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by lemma 30 R->L }
% 280.85/36.06 fresh25(fresh14(fresh31(fresh8(fresh7(equalish(multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by axiom 19 (well_defined_product) R->L }
% 280.85/36.06 fresh25(fresh14(fresh31(fresh8(fresh7(fresh2(product(b, b, d), product(b, b, d), a, second_divided_by_1st(a, a), a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by lemma 31 R->L }
% 280.85/36.06 fresh25(fresh14(fresh31(fresh8(fresh7(fresh2(product(a, second_divided_by_1st(a, a), multiply(a, second_divided_by_1st(a, a))), product(b, b, d), a, second_divided_by_1st(a, a), a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by lemma 30 }
% 280.85/36.06 fresh25(fresh14(fresh31(fresh8(fresh7(fresh2(product(a, second_divided_by_1st(a, a), multiply(a, second_divided_by_1st(a, a))), prime(a), a, second_divided_by_1st(a, a), a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by axiom 1 (a_is_prime) }
% 280.85/36.06 fresh25(fresh14(fresh31(fresh8(fresh7(fresh2(product(a, second_divided_by_1st(a, a), multiply(a, second_divided_by_1st(a, a))), true2, a, second_divided_by_1st(a, a), a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by axiom 28 (well_defined_product) }
% 280.85/36.06 fresh25(fresh14(fresh31(fresh8(fresh7(fresh(product(a, second_divided_by_1st(a, a), a), true2, a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by axiom 1 (a_is_prime) R->L }
% 280.85/36.06 fresh25(fresh14(fresh31(fresh8(fresh7(fresh(product(a, second_divided_by_1st(a, a), a), prime(a), a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by lemma 30 R->L }
% 280.85/36.06 fresh25(fresh14(fresh31(fresh8(fresh7(fresh(product(a, second_divided_by_1st(a, a), a), product(b, b, d), a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by axiom 15 (divides_implies_product) R->L }
% 280.85/36.06 fresh25(fresh14(fresh31(fresh8(fresh7(fresh(fresh26(divides(a, a), true2, a, a), product(b, b, d), a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by axiom 1 (a_is_prime) R->L }
% 280.85/36.06 fresh25(fresh14(fresh31(fresh8(fresh7(fresh(fresh26(divides(a, a), prime(a), a, a), product(b, b, d), a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.06 = { by lemma 30 R->L }
% 280.85/36.06 fresh25(fresh14(fresh31(fresh8(fresh7(fresh(fresh26(divides(a, a), product(b, b, d), a, a), product(b, b, d), a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by axiom 12 (primes_lemma1) R->L }
% 280.85/36.07 fresh25(fresh14(fresh31(fresh8(fresh7(fresh(fresh26(fresh20(product(b, b, d), product(b, b, d), a, multiply(a, a), a), product(b, b, d), a, a), product(b, b, d), a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by lemma 32 R->L }
% 280.85/36.07 fresh25(fresh14(fresh31(fresh8(fresh7(fresh(fresh26(fresh20(divides(a, multiply(a, a)), product(b, b, d), a, multiply(a, a), a), product(b, b, d), a, a), product(b, b, d), a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by lemma 30 }
% 280.85/36.07 fresh25(fresh14(fresh31(fresh8(fresh7(fresh(fresh26(fresh20(divides(a, multiply(a, a)), prime(a), a, multiply(a, a), a), product(b, b, d), a, a), product(b, b, d), a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by axiom 1 (a_is_prime) }
% 280.85/36.07 fresh25(fresh14(fresh31(fresh8(fresh7(fresh(fresh26(fresh20(divides(a, multiply(a, a)), true2, a, multiply(a, a), a), product(b, b, d), a, a), product(b, b, d), a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by axiom 22 (primes_lemma1) R->L }
% 280.85/36.07 fresh25(fresh14(fresh31(fresh8(fresh7(fresh(fresh26(fresh28(prime(a), true2, a, multiply(a, a), a), product(b, b, d), a, a), product(b, b, d), a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by axiom 1 (a_is_prime) R->L }
% 280.85/36.07 fresh25(fresh14(fresh31(fresh8(fresh7(fresh(fresh26(fresh28(prime(a), prime(a), a, multiply(a, a), a), product(b, b, d), a, a), product(b, b, d), a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by axiom 20 (primes_lemma1) }
% 280.85/36.07 fresh25(fresh14(fresh31(fresh8(fresh7(fresh(fresh26(fresh29(product(a, a, multiply(a, a)), true2, a, a), product(b, b, d), a, a), product(b, b, d), a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by axiom 1 (a_is_prime) R->L }
% 280.85/36.07 fresh25(fresh14(fresh31(fresh8(fresh7(fresh(fresh26(fresh29(product(a, a, multiply(a, a)), prime(a), a, a), product(b, b, d), a, a), product(b, b, d), a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by lemma 30 R->L }
% 280.85/36.07 fresh25(fresh14(fresh31(fresh8(fresh7(fresh(fresh26(fresh29(product(a, a, multiply(a, a)), product(b, b, d), a, a), product(b, b, d), a, a), product(b, b, d), a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by lemma 31 }
% 280.85/36.07 fresh25(fresh14(fresh31(fresh8(fresh7(fresh(fresh26(fresh29(product(b, b, d), product(b, b, d), a, a), product(b, b, d), a, a), product(b, b, d), a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by axiom 4 (primes_lemma1) }
% 280.85/36.07 fresh25(fresh14(fresh31(fresh8(fresh7(fresh(fresh26(true2, product(b, b, d), a, a), product(b, b, d), a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by axiom 1 (a_is_prime) R->L }
% 280.85/36.07 fresh25(fresh14(fresh31(fresh8(fresh7(fresh(fresh26(prime(a), product(b, b, d), a, a), product(b, b, d), a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by lemma 30 R->L }
% 280.85/36.07 fresh25(fresh14(fresh31(fresh8(fresh7(fresh(fresh26(product(b, b, d), product(b, b, d), a, a), product(b, b, d), a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by axiom 5 (divides_implies_product) }
% 280.85/36.07 fresh25(fresh14(fresh31(fresh8(fresh7(fresh(true2, product(b, b, d), a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by axiom 1 (a_is_prime) R->L }
% 280.85/36.07 fresh25(fresh14(fresh31(fresh8(fresh7(fresh(prime(a), product(b, b, d), a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by lemma 30 R->L }
% 280.85/36.07 fresh25(fresh14(fresh31(fresh8(fresh7(fresh(product(b, b, d), product(b, b, d), a, multiply(a, second_divided_by_1st(a, a))), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by axiom 3 (well_defined_product) }
% 280.85/36.07 fresh25(fresh14(fresh31(fresh8(fresh7(true2, product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by axiom 1 (a_is_prime) R->L }
% 280.85/36.07 fresh25(fresh14(fresh31(fresh8(fresh7(prime(a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by lemma 30 R->L }
% 280.85/36.07 fresh25(fresh14(fresh31(fresh8(fresh7(product(b, b, d), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by axiom 9 (symmetry) }
% 280.85/36.07 fresh25(fresh14(fresh31(fresh8(true2, product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by axiom 1 (a_is_prime) R->L }
% 280.85/36.07 fresh25(fresh14(fresh31(fresh8(prime(a), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by lemma 30 R->L }
% 280.85/36.07 fresh25(fresh14(fresh31(fresh8(product(b, b, d), product(b, b, d), multiply(a, second_divided_by_1st(a, a)), X, multiply(a, X)), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by axiom 13 (product_substitution3) }
% 280.85/36.07 fresh25(fresh14(fresh31(true2, product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by axiom 1 (a_is_prime) R->L }
% 280.85/36.07 fresh25(fresh14(fresh31(prime(a), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by lemma 30 R->L }
% 280.85/36.07 fresh25(fresh14(fresh31(product(b, b, d), product(b, b, d), multiply(a, X), multiply(second_divided_by_1st(a, a), X), a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by axiom 10 (product_associativity2) }
% 280.85/36.07 fresh25(fresh14(true2, product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by axiom 1 (a_is_prime) R->L }
% 280.85/36.07 fresh25(fresh14(prime(a), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by lemma 30 R->L }
% 280.85/36.07 fresh25(fresh14(product(b, b, d), product(b, b, d), multiply(second_divided_by_1st(a, a), X), X), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by axiom 8 (product_left_cancellation) }
% 280.85/36.07 fresh25(true2, product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by axiom 1 (a_is_prime) R->L }
% 280.85/36.07 fresh25(prime(a), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by lemma 30 R->L }
% 280.85/36.07 fresh25(product(b, b, d), product(b, b, d), X, second_divided_by_1st(a, a))
% 280.85/36.07 = { by axiom 6 (divides_substitution1) }
% 280.85/36.07 true2
% 280.85/36.07 = { by axiom 1 (a_is_prime) R->L }
% 280.85/36.07 prime(a)
% 280.85/36.07 = { by lemma 30 R->L }
% 280.85/36.07 product(b, b, d)
% 280.85/36.07
% 280.85/36.07 Goal 1 (prove_there_is_no_common_divisor): tuple(divides(X, b), divides(X, c)) = tuple(true2, true2).
% 280.85/36.07 The goal is true when:
% 280.85/36.07 X = second_divided_by_1st(a, a)
% 280.85/36.07
% 280.85/36.07 Proof:
% 280.85/36.07 tuple(divides(second_divided_by_1st(a, a), b), divides(second_divided_by_1st(a, a), c))
% 280.85/36.07 = { by lemma 33 }
% 280.85/36.07 tuple(product(b, b, d), divides(second_divided_by_1st(a, a), c))
% 280.85/36.07 = { by lemma 33 }
% 280.85/36.07 tuple(product(b, b, d), product(b, b, d))
% 280.85/36.07 = { by lemma 30 }
% 280.85/36.07 tuple(product(b, b, d), prime(a))
% 280.85/36.07 = { by lemma 30 }
% 280.85/36.07 tuple(prime(a), prime(a))
% 280.85/36.07 = { by axiom 1 (a_is_prime) }
% 280.85/36.07 tuple(true2, prime(a))
% 280.85/36.07 = { by axiom 1 (a_is_prime) }
% 280.85/36.07 tuple(true2, true2)
% 280.85/36.07 % SZS output end Proof
% 280.85/36.07
% 280.85/36.07 RESULT: Unsatisfiable (the axioms are contradictory).
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