%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : NUM017-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:09:49 PM UTC 2026
% Result : Unsatisfiable 69.32s 9.25s
% Output : Proof 70.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM017-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n006.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sun Sep 27 18:39:10 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 69.32/9.25 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 69.32/9.25
% 69.32/9.25 % SZS status Unsatisfiable
% 69.32/9.25
% 70.11/9.33 % SZS output start Proof
% 70.11/9.33 Axiom 1 (a_is_prime): prime(a) = true.
% 70.11/9.33 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 70.11/9.33 Axiom 3 (closure_of_product): product(X, Y, multiply(X, Y)) = true.
% 70.11/9.33 Axiom 4 (product_divisible_by_operand): ifeq(product(X, Y, Z), true, divides(X, Z), true) = true.
% 70.11/9.33 Axiom 5 (divides_implies_product): ifeq(divides(X, Y), true, product(X, second_divided_by_1st(X, Y), Y), true) = true.
% 70.11/9.33 Axiom 6 (divides_substitution1): ifeq(divides(X, Y), true, ifeq(equalish(Y, Z), true, divides(X, Z), true), true) = true.
% 70.11/9.33 Axiom 7 (product_left_cancellation): ifeq(product(X, Y, Z), true, ifeq(product(X, W, Z), true, equalish(W, Y), true), true) = true.
% 70.11/9.33 Axiom 8 (primes_lemma1): ifeq(prime(X), true, ifeq(divides(X, Y), true, ifeq(product(Z, Z, Y), true, divides(X, Z), true), true), true) = true.
% 70.11/9.33 Axiom 9 (product_associativity2): ifeq(product(X, Y, Z), true, ifeq(product(Y, W, V), true, ifeq(product(Z, W, U), true, product(X, V, U), true), true), true) = true.
% 70.11/9.33
% 70.11/9.33 Goal 1 (prove_there_is_no_common_divisor): tuple(divides(X, b), divides(X, c)) = tuple(true, true).
% 70.11/9.33 The goal is true when:
% 70.11/9.34 X = second_divided_by_1st(a, a)
% 70.11/9.34
% 70.11/9.34 Proof:
% 70.11/9.34 tuple(divides(second_divided_by_1st(a, a), b), divides(second_divided_by_1st(a, a), c))
% 70.11/9.34 = { by axiom 2 (ifeq_axiom) R->L }
% 70.11/9.34 tuple(ifeq(true, true, divides(second_divided_by_1st(a, a), b), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.34 = { by axiom 7 (product_left_cancellation) R->L }
% 70.11/9.34 tuple(ifeq(ifeq(product(a, b, multiply(a, b)), true, ifeq(product(a, multiply(second_divided_by_1st(a, a), b), multiply(a, b)), true, equalish(multiply(second_divided_by_1st(a, a), b), b), true), true), true, divides(second_divided_by_1st(a, a), b), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.34 = { by axiom 3 (closure_of_product) }
% 70.11/9.34 tuple(ifeq(ifeq(true, true, ifeq(product(a, multiply(second_divided_by_1st(a, a), b), multiply(a, b)), true, equalish(multiply(second_divided_by_1st(a, a), b), b), true), true), true, divides(second_divided_by_1st(a, a), b), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.34 = { by axiom 2 (ifeq_axiom) }
% 70.11/9.34 tuple(ifeq(ifeq(product(a, multiply(second_divided_by_1st(a, a), b), multiply(a, b)), true, equalish(multiply(second_divided_by_1st(a, a), b), b), true), true, divides(second_divided_by_1st(a, a), b), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.34 = { by axiom 2 (ifeq_axiom) R->L }
% 70.11/9.34 tuple(ifeq(ifeq(ifeq(true, true, product(a, multiply(second_divided_by_1st(a, a), b), multiply(a, b)), true), true, equalish(multiply(second_divided_by_1st(a, a), b), b), true), true, divides(second_divided_by_1st(a, a), b), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.34 = { by axiom 5 (divides_implies_product) R->L }
% 70.11/9.34 tuple(ifeq(ifeq(ifeq(ifeq(divides(a, a), true, product(a, second_divided_by_1st(a, a), a), true), true, product(a, multiply(second_divided_by_1st(a, a), b), multiply(a, b)), true), true, equalish(multiply(second_divided_by_1st(a, a), b), b), true), true, divides(second_divided_by_1st(a, a), b), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.34 = { by axiom 2 (ifeq_axiom) R->L }
% 70.11/9.34 tuple(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, divides(a, a), true), true, product(a, second_divided_by_1st(a, a), a), true), true, product(a, multiply(second_divided_by_1st(a, a), b), multiply(a, b)), true), true, equalish(multiply(second_divided_by_1st(a, a), b), b), true), true, divides(second_divided_by_1st(a, a), b), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.34 = { by axiom 1 (a_is_prime) R->L }
% 70.11/9.34 tuple(ifeq(ifeq(ifeq(ifeq(ifeq(prime(a), true, divides(a, a), true), true, product(a, second_divided_by_1st(a, a), a), true), true, product(a, multiply(second_divided_by_1st(a, a), b), multiply(a, b)), true), true, equalish(multiply(second_divided_by_1st(a, a), b), b), true), true, divides(second_divided_by_1st(a, a), b), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.34 = { by axiom 2 (ifeq_axiom) R->L }
% 70.11/9.34 tuple(ifeq(ifeq(ifeq(ifeq(ifeq(prime(a), true, ifeq(true, true, divides(a, a), true), true), true, product(a, second_divided_by_1st(a, a), a), true), true, product(a, multiply(second_divided_by_1st(a, a), b), multiply(a, b)), true), true, equalish(multiply(second_divided_by_1st(a, a), b), b), true), true, divides(second_divided_by_1st(a, a), b), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.34 = { by axiom 4 (product_divisible_by_operand) R->L }
% 70.11/9.34 tuple(ifeq(ifeq(ifeq(ifeq(ifeq(prime(a), true, ifeq(ifeq(product(a, a, multiply(a, a)), true, divides(a, multiply(a, a)), true), true, divides(a, a), true), true), true, product(a, second_divided_by_1st(a, a), a), true), true, product(a, multiply(second_divided_by_1st(a, a), b), multiply(a, b)), true), true, equalish(multiply(second_divided_by_1st(a, a), b), b), true), true, divides(second_divided_by_1st(a, a), b), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.34 = { by axiom 3 (closure_of_product) }
% 70.11/9.34 tuple(ifeq(ifeq(ifeq(ifeq(ifeq(prime(a), true, ifeq(ifeq(true, true, divides(a, multiply(a, a)), true), true, divides(a, a), true), true), true, product(a, second_divided_by_1st(a, a), a), true), true, product(a, multiply(second_divided_by_1st(a, a), b), multiply(a, b)), true), true, equalish(multiply(second_divided_by_1st(a, a), b), b), true), true, divides(second_divided_by_1st(a, a), b), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.34 = { by axiom 2 (ifeq_axiom) }
% 70.11/9.34 tuple(ifeq(ifeq(ifeq(ifeq(ifeq(prime(a), true, ifeq(divides(a, multiply(a, a)), true, divides(a, a), true), true), true, product(a, second_divided_by_1st(a, a), a), true), true, product(a, multiply(second_divided_by_1st(a, a), b), multiply(a, b)), true), true, equalish(multiply(second_divided_by_1st(a, a), b), b), true), true, divides(second_divided_by_1st(a, a), b), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.35 = { by axiom 2 (ifeq_axiom) R->L }
% 70.11/9.35 tuple(ifeq(ifeq(ifeq(ifeq(ifeq(prime(a), true, ifeq(divides(a, multiply(a, a)), true, ifeq(true, true, divides(a, a), true), true), true), true, product(a, second_divided_by_1st(a, a), a), true), true, product(a, multiply(second_divided_by_1st(a, a), b), multiply(a, b)), true), true, equalish(multiply(second_divided_by_1st(a, a), b), b), true), true, divides(second_divided_by_1st(a, a), b), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.35 = { by axiom 3 (closure_of_product) R->L }
% 70.11/9.35 tuple(ifeq(ifeq(ifeq(ifeq(ifeq(prime(a), true, ifeq(divides(a, multiply(a, a)), true, ifeq(product(a, a, multiply(a, a)), true, divides(a, a), true), true), true), true, product(a, second_divided_by_1st(a, a), a), true), true, product(a, multiply(second_divided_by_1st(a, a), b), multiply(a, b)), true), true, equalish(multiply(second_divided_by_1st(a, a), b), b), true), true, divides(second_divided_by_1st(a, a), b), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.35 = { by axiom 8 (primes_lemma1) }
% 70.11/9.35 tuple(ifeq(ifeq(ifeq(ifeq(true, true, product(a, second_divided_by_1st(a, a), a), true), true, product(a, multiply(second_divided_by_1st(a, a), b), multiply(a, b)), true), true, equalish(multiply(second_divided_by_1st(a, a), b), b), true), true, divides(second_divided_by_1st(a, a), b), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.35 = { by axiom 2 (ifeq_axiom) }
% 70.11/9.35 tuple(ifeq(ifeq(ifeq(product(a, second_divided_by_1st(a, a), a), true, product(a, multiply(second_divided_by_1st(a, a), b), multiply(a, b)), true), true, equalish(multiply(second_divided_by_1st(a, a), b), b), true), true, divides(second_divided_by_1st(a, a), b), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.35 = { by axiom 2 (ifeq_axiom) R->L }
% 70.11/9.35 tuple(ifeq(ifeq(ifeq(product(a, second_divided_by_1st(a, a), a), true, ifeq(true, true, product(a, multiply(second_divided_by_1st(a, a), b), multiply(a, b)), true), true), true, equalish(multiply(second_divided_by_1st(a, a), b), b), true), true, divides(second_divided_by_1st(a, a), b), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.35 = { by axiom 3 (closure_of_product) R->L }
% 70.11/9.35 tuple(ifeq(ifeq(ifeq(product(a, second_divided_by_1st(a, a), a), true, ifeq(product(a, b, multiply(a, b)), true, product(a, multiply(second_divided_by_1st(a, a), b), multiply(a, b)), true), true), true, equalish(multiply(second_divided_by_1st(a, a), b), b), true), true, divides(second_divided_by_1st(a, a), b), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.35 = { by axiom 2 (ifeq_axiom) R->L }
% 70.11/9.35 tuple(ifeq(ifeq(ifeq(product(a, second_divided_by_1st(a, a), a), true, ifeq(true, true, ifeq(product(a, b, multiply(a, b)), true, product(a, multiply(second_divided_by_1st(a, a), b), multiply(a, b)), true), true), true), true, equalish(multiply(second_divided_by_1st(a, a), b), b), true), true, divides(second_divided_by_1st(a, a), b), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.35 = { by axiom 3 (closure_of_product) R->L }
% 70.11/9.35 tuple(ifeq(ifeq(ifeq(product(a, second_divided_by_1st(a, a), a), true, ifeq(product(second_divided_by_1st(a, a), b, multiply(second_divided_by_1st(a, a), b)), true, ifeq(product(a, b, multiply(a, b)), true, product(a, multiply(second_divided_by_1st(a, a), b), multiply(a, b)), true), true), true), true, equalish(multiply(second_divided_by_1st(a, a), b), b), true), true, divides(second_divided_by_1st(a, a), b), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.35 = { by axiom 9 (product_associativity2) }
% 70.11/9.35 tuple(ifeq(ifeq(true, true, equalish(multiply(second_divided_by_1st(a, a), b), b), true), true, divides(second_divided_by_1st(a, a), b), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.35 = { by axiom 2 (ifeq_axiom) }
% 70.11/9.35 tuple(ifeq(equalish(multiply(second_divided_by_1st(a, a), b), b), true, divides(second_divided_by_1st(a, a), b), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.35 = { by axiom 2 (ifeq_axiom) R->L }
% 70.11/9.35 tuple(ifeq(true, true, ifeq(equalish(multiply(second_divided_by_1st(a, a), b), b), true, divides(second_divided_by_1st(a, a), b), true), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.35 = { by axiom 4 (product_divisible_by_operand) R->L }
% 70.11/9.35 tuple(ifeq(ifeq(product(second_divided_by_1st(a, a), b, multiply(second_divided_by_1st(a, a), b)), true, divides(second_divided_by_1st(a, a), multiply(second_divided_by_1st(a, a), b)), true), true, ifeq(equalish(multiply(second_divided_by_1st(a, a), b), b), true, divides(second_divided_by_1st(a, a), b), true), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.35 = { by axiom 3 (closure_of_product) }
% 70.11/9.35 tuple(ifeq(ifeq(true, true, divides(second_divided_by_1st(a, a), multiply(second_divided_by_1st(a, a), b)), true), true, ifeq(equalish(multiply(second_divided_by_1st(a, a), b), b), true, divides(second_divided_by_1st(a, a), b), true), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.35 = { by axiom 2 (ifeq_axiom) }
% 70.11/9.35 tuple(ifeq(divides(second_divided_by_1st(a, a), multiply(second_divided_by_1st(a, a), b)), true, ifeq(equalish(multiply(second_divided_by_1st(a, a), b), b), true, divides(second_divided_by_1st(a, a), b), true), true), divides(second_divided_by_1st(a, a), c))
% 70.11/9.35 = { by axiom 6 (divides_substitution1) }
% 70.11/9.35 tuple(true, divides(second_divided_by_1st(a, a), c))
% 70.11/9.35 = { by axiom 2 (ifeq_axiom) R->L }
% 70.11/9.35 tuple(true, ifeq(true, true, divides(second_divided_by_1st(a, a), c), true))
% 70.11/9.35 = { by axiom 7 (product_left_cancellation) R->L }
% 70.11/9.35 tuple(true, ifeq(ifeq(product(a, c, multiply(a, c)), true, ifeq(product(a, multiply(second_divided_by_1st(a, a), c), multiply(a, c)), true, equalish(multiply(second_divided_by_1st(a, a), c), c), true), true), true, divides(second_divided_by_1st(a, a), c), true))
% 70.11/9.35 = { by axiom 3 (closure_of_product) }
% 70.11/9.35 tuple(true, ifeq(ifeq(true, true, ifeq(product(a, multiply(second_divided_by_1st(a, a), c), multiply(a, c)), true, equalish(multiply(second_divided_by_1st(a, a), c), c), true), true), true, divides(second_divided_by_1st(a, a), c), true))
% 70.11/9.35 = { by axiom 2 (ifeq_axiom) }
% 70.11/9.36 tuple(true, ifeq(ifeq(product(a, multiply(second_divided_by_1st(a, a), c), multiply(a, c)), true, equalish(multiply(second_divided_by_1st(a, a), c), c), true), true, divides(second_divided_by_1st(a, a), c), true))
% 70.11/9.36 = { by axiom 2 (ifeq_axiom) R->L }
% 70.11/9.36 tuple(true, ifeq(ifeq(ifeq(true, true, product(a, multiply(second_divided_by_1st(a, a), c), multiply(a, c)), true), true, equalish(multiply(second_divided_by_1st(a, a), c), c), true), true, divides(second_divided_by_1st(a, a), c), true))
% 70.11/9.36 = { by axiom 5 (divides_implies_product) R->L }
% 70.11/9.36 tuple(true, ifeq(ifeq(ifeq(ifeq(divides(a, a), true, product(a, second_divided_by_1st(a, a), a), true), true, product(a, multiply(second_divided_by_1st(a, a), c), multiply(a, c)), true), true, equalish(multiply(second_divided_by_1st(a, a), c), c), true), true, divides(second_divided_by_1st(a, a), c), true))
% 70.11/9.36 = { by axiom 2 (ifeq_axiom) R->L }
% 70.11/9.36 tuple(true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, divides(a, a), true), true, product(a, second_divided_by_1st(a, a), a), true), true, product(a, multiply(second_divided_by_1st(a, a), c), multiply(a, c)), true), true, equalish(multiply(second_divided_by_1st(a, a), c), c), true), true, divides(second_divided_by_1st(a, a), c), true))
% 70.11/9.36 = { by axiom 1 (a_is_prime) R->L }
% 70.11/9.36 tuple(true, ifeq(ifeq(ifeq(ifeq(ifeq(prime(a), true, divides(a, a), true), true, product(a, second_divided_by_1st(a, a), a), true), true, product(a, multiply(second_divided_by_1st(a, a), c), multiply(a, c)), true), true, equalish(multiply(second_divided_by_1st(a, a), c), c), true), true, divides(second_divided_by_1st(a, a), c), true))
% 70.11/9.36 = { by axiom 2 (ifeq_axiom) R->L }
% 70.11/9.36 tuple(true, ifeq(ifeq(ifeq(ifeq(ifeq(prime(a), true, ifeq(true, true, divides(a, a), true), true), true, product(a, second_divided_by_1st(a, a), a), true), true, product(a, multiply(second_divided_by_1st(a, a), c), multiply(a, c)), true), true, equalish(multiply(second_divided_by_1st(a, a), c), c), true), true, divides(second_divided_by_1st(a, a), c), true))
% 70.11/9.36 = { by axiom 4 (product_divisible_by_operand) R->L }
% 70.11/9.36 tuple(true, ifeq(ifeq(ifeq(ifeq(ifeq(prime(a), true, ifeq(ifeq(product(a, a, multiply(a, a)), true, divides(a, multiply(a, a)), true), true, divides(a, a), true), true), true, product(a, second_divided_by_1st(a, a), a), true), true, product(a, multiply(second_divided_by_1st(a, a), c), multiply(a, c)), true), true, equalish(multiply(second_divided_by_1st(a, a), c), c), true), true, divides(second_divided_by_1st(a, a), c), true))
% 70.11/9.36 = { by axiom 3 (closure_of_product) }
% 70.11/9.36 tuple(true, ifeq(ifeq(ifeq(ifeq(ifeq(prime(a), true, ifeq(ifeq(true, true, divides(a, multiply(a, a)), true), true, divides(a, a), true), true), true, product(a, second_divided_by_1st(a, a), a), true), true, product(a, multiply(second_divided_by_1st(a, a), c), multiply(a, c)), true), true, equalish(multiply(second_divided_by_1st(a, a), c), c), true), true, divides(second_divided_by_1st(a, a), c), true))
% 70.11/9.36 = { by axiom 2 (ifeq_axiom) }
% 70.11/9.37 tuple(true, ifeq(ifeq(ifeq(ifeq(ifeq(prime(a), true, ifeq(divides(a, multiply(a, a)), true, divides(a, a), true), true), true, product(a, second_divided_by_1st(a, a), a), true), true, product(a, multiply(second_divided_by_1st(a, a), c), multiply(a, c)), true), true, equalish(multiply(second_divided_by_1st(a, a), c), c), true), true, divides(second_divided_by_1st(a, a), c), true))
% 70.11/9.37 = { by axiom 2 (ifeq_axiom) R->L }
% 70.11/9.37 tuple(true, ifeq(ifeq(ifeq(ifeq(ifeq(prime(a), true, ifeq(divides(a, multiply(a, a)), true, ifeq(true, true, divides(a, a), true), true), true), true, product(a, second_divided_by_1st(a, a), a), true), true, product(a, multiply(second_divided_by_1st(a, a), c), multiply(a, c)), true), true, equalish(multiply(second_divided_by_1st(a, a), c), c), true), true, divides(second_divided_by_1st(a, a), c), true))
% 70.11/9.37 = { by axiom 3 (closure_of_product) R->L }
% 70.11/9.37 tuple(true, ifeq(ifeq(ifeq(ifeq(ifeq(prime(a), true, ifeq(divides(a, multiply(a, a)), true, ifeq(product(a, a, multiply(a, a)), true, divides(a, a), true), true), true), true, product(a, second_divided_by_1st(a, a), a), true), true, product(a, multiply(second_divided_by_1st(a, a), c), multiply(a, c)), true), true, equalish(multiply(second_divided_by_1st(a, a), c), c), true), true, divides(second_divided_by_1st(a, a), c), true))
% 70.11/9.37 = { by axiom 8 (primes_lemma1) }
% 70.11/9.37 tuple(true, ifeq(ifeq(ifeq(ifeq(true, true, product(a, second_divided_by_1st(a, a), a), true), true, product(a, multiply(second_divided_by_1st(a, a), c), multiply(a, c)), true), true, equalish(multiply(second_divided_by_1st(a, a), c), c), true), true, divides(second_divided_by_1st(a, a), c), true))
% 70.11/9.37 = { by axiom 2 (ifeq_axiom) }
% 70.11/9.37 tuple(true, ifeq(ifeq(ifeq(product(a, second_divided_by_1st(a, a), a), true, product(a, multiply(second_divided_by_1st(a, a), c), multiply(a, c)), true), true, equalish(multiply(second_divided_by_1st(a, a), c), c), true), true, divides(second_divided_by_1st(a, a), c), true))
% 70.11/9.37 = { by axiom 2 (ifeq_axiom) R->L }
% 70.11/9.37 tuple(true, ifeq(ifeq(ifeq(product(a, second_divided_by_1st(a, a), a), true, ifeq(true, true, product(a, multiply(second_divided_by_1st(a, a), c), multiply(a, c)), true), true), true, equalish(multiply(second_divided_by_1st(a, a), c), c), true), true, divides(second_divided_by_1st(a, a), c), true))
% 70.11/9.37 = { by axiom 3 (closure_of_product) R->L }
% 70.11/9.37 tuple(true, ifeq(ifeq(ifeq(product(a, second_divided_by_1st(a, a), a), true, ifeq(product(a, c, multiply(a, c)), true, product(a, multiply(second_divided_by_1st(a, a), c), multiply(a, c)), true), true), true, equalish(multiply(second_divided_by_1st(a, a), c), c), true), true, divides(second_divided_by_1st(a, a), c), true))
% 70.11/9.37 = { by axiom 2 (ifeq_axiom) R->L }
% 70.11/9.37 tuple(true, ifeq(ifeq(ifeq(product(a, second_divided_by_1st(a, a), a), true, ifeq(true, true, ifeq(product(a, c, multiply(a, c)), true, product(a, multiply(second_divided_by_1st(a, a), c), multiply(a, c)), true), true), true), true, equalish(multiply(second_divided_by_1st(a, a), c), c), true), true, divides(second_divided_by_1st(a, a), c), true))
% 70.11/9.37 = { by axiom 3 (closure_of_product) R->L }
% 70.11/9.37 tuple(true, ifeq(ifeq(ifeq(product(a, second_divided_by_1st(a, a), a), true, ifeq(product(second_divided_by_1st(a, a), c, multiply(second_divided_by_1st(a, a), c)), true, ifeq(product(a, c, multiply(a, c)), true, product(a, multiply(second_divided_by_1st(a, a), c), multiply(a, c)), true), true), true), true, equalish(multiply(second_divided_by_1st(a, a), c), c), true), true, divides(second_divided_by_1st(a, a), c), true))
% 70.11/9.37 = { by axiom 9 (product_associativity2) }
% 70.11/9.37 tuple(true, ifeq(ifeq(true, true, equalish(multiply(second_divided_by_1st(a, a), c), c), true), true, divides(second_divided_by_1st(a, a), c), true))
% 70.11/9.37 = { by axiom 2 (ifeq_axiom) }
% 70.11/9.37 tuple(true, ifeq(equalish(multiply(second_divided_by_1st(a, a), c), c), true, divides(second_divided_by_1st(a, a), c), true))
% 70.11/9.37 = { by axiom 2 (ifeq_axiom) R->L }
% 70.11/9.37 tuple(true, ifeq(true, true, ifeq(equalish(multiply(second_divided_by_1st(a, a), c), c), true, divides(second_divided_by_1st(a, a), c), true), true))
% 70.11/9.37 = { by axiom 4 (product_divisible_by_operand) R->L }
% 70.11/9.37 tuple(true, ifeq(ifeq(product(second_divided_by_1st(a, a), c, multiply(second_divided_by_1st(a, a), c)), true, divides(second_divided_by_1st(a, a), multiply(second_divided_by_1st(a, a), c)), true), true, ifeq(equalish(multiply(second_divided_by_1st(a, a), c), c), true, divides(second_divided_by_1st(a, a), c), true), true))
% 70.11/9.37 = { by axiom 3 (closure_of_product) }
% 70.11/9.37 tuple(true, ifeq(ifeq(true, true, divides(second_divided_by_1st(a, a), multiply(second_divided_by_1st(a, a), c)), true), true, ifeq(equalish(multiply(second_divided_by_1st(a, a), c), c), true, divides(second_divided_by_1st(a, a), c), true), true))
% 70.11/9.37 = { by axiom 2 (ifeq_axiom) }
% 70.11/9.37 tuple(true, ifeq(divides(second_divided_by_1st(a, a), multiply(second_divided_by_1st(a, a), c)), true, ifeq(equalish(multiply(second_divided_by_1st(a, a), c), c), true, divides(second_divided_by_1st(a, a), c), true), true))
% 70.11/9.37 = { by axiom 6 (divides_substitution1) }
% 70.11/9.37 tuple(true, true)
% 70.11/9.37 % SZS output end Proof
% 70.11/9.37
% 70.11/9.37 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------