%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : HEN010-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 10:19:00 AM UTC 2026
% Result : Unsatisfiable 155.52s 20.12s
% Output : Proof 158.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : HEN010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n010.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sun Sep 27 10:51:16 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 155.52/20.12 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
% 155.52/20.12
% 155.52/20.12 % SZS status Unsatisfiable
% 155.52/20.12
% 157.11/20.37 % SZS output start Proof
% 157.11/20.37 Axiom 1 (identity_is_largest): less_equal(X, identity) = true.
% 157.11/20.37 Axiom 2 (zero_is_smallest): less_equal(zero, X) = true.
% 157.11/20.38 Axiom 3 (identity_divide_idQ_idQa): quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa) = true.
% 157.11/20.38 Axiom 4 (identity_divide_idQa): quotient(identity, idQa, idQ_idQa) = true.
% 157.11/20.38 Axiom 5 (identity_divide_a): quotient(identity, a, idQa) = true.
% 157.11/20.38 Axiom 6 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 157.11/20.38 Axiom 7 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 157.11/20.38 Axiom 8 (closure): quotient(X, Y, divide(X, Y)) = true.
% 157.11/20.38 Axiom 9 (quotient_less_equal): ifeq(less_equal(X, Y), true, quotient(X, Y, zero), true) = true.
% 157.11/20.38 Axiom 10 (divisor_existence): ifeq(quotient(X, Y, Z), true, less_equal(Z, X), true) = true.
% 157.11/20.38 Axiom 11 (less_equal_quotient): ifeq(quotient(X, Y, zero), true, less_equal(X, Y), true) = true.
% 157.11/20.38 Axiom 12 (less_equal_and_equal): ifeq2(less_equal(X, Y), true, ifeq2(less_equal(Y, X), true, Y, X), X) = X.
% 157.11/20.38 Axiom 13 (well_defined): ifeq2(quotient(X, Y, Z), true, ifeq2(quotient(X, Y, W), true, W, Z), Z) = Z.
% 157.11/20.38 Axiom 14 (quotient_property): ifeq(quotient(X, Y, Z), true, ifeq(quotient(W, V, U), true, ifeq(quotient(T, V, Y), true, ifeq(quotient(S, V, X), true, ifeq(quotient(S, T, W), true, less_equal(Z, U), true), true), true), true), true) = true.
% 157.11/20.38
% 157.11/20.38 Lemma 15: divide(X, X) = zero.
% 157.11/20.38 Proof:
% 157.11/20.38 divide(X, X)
% 157.11/20.38 = { by axiom 12 (less_equal_and_equal) R->L }
% 157.11/20.38 ifeq2(less_equal(divide(X, X), zero), true, ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 157.11/20.38 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.38 ifeq2(ifeq(true, true, less_equal(divide(X, X), zero), true), true, ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 157.11/20.38 = { by axiom 8 (closure) R->L }
% 157.11/20.38 ifeq2(ifeq(quotient(divide(X, X), zero, divide(divide(X, X), zero)), true, less_equal(divide(X, X), zero), true), true, ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 157.11/20.38 = { by axiom 12 (less_equal_and_equal) R->L }
% 157.11/20.38 ifeq2(ifeq(quotient(divide(X, X), zero, ifeq2(less_equal(divide(divide(X, X), zero), zero), true, ifeq2(less_equal(zero, divide(divide(X, X), zero)), true, zero, divide(divide(X, X), zero)), divide(divide(X, X), zero))), true, less_equal(divide(X, X), zero), true), true, ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 157.11/20.38 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.38 ifeq2(ifeq(quotient(divide(X, X), zero, ifeq2(ifeq(true, true, less_equal(divide(divide(X, X), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(X, X), zero)), true, zero, divide(divide(X, X), zero)), divide(divide(X, X), zero))), true, less_equal(divide(X, X), zero), true), true, ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 157.11/20.38 = { by axiom 8 (closure) R->L }
% 157.11/20.38 ifeq2(ifeq(quotient(divide(X, X), zero, ifeq2(ifeq(quotient(X, X, divide(X, X)), true, less_equal(divide(divide(X, X), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(X, X), zero)), true, zero, divide(divide(X, X), zero)), divide(divide(X, X), zero))), true, less_equal(divide(X, X), zero), true), true, ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 157.11/20.38 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.38 ifeq2(ifeq(quotient(divide(X, X), zero, ifeq2(ifeq(true, true, ifeq(quotient(X, X, divide(X, X)), true, less_equal(divide(divide(X, X), zero), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(X, X), zero)), true, zero, divide(divide(X, X), zero)), divide(divide(X, X), zero))), true, less_equal(divide(X, X), zero), true), true, ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 157.11/20.38 = { by axiom 9 (quotient_less_equal) R->L }
% 157.11/20.38 ifeq2(ifeq(quotient(divide(X, X), zero, ifeq2(ifeq(ifeq(less_equal(divide(X, zero), X), true, quotient(divide(X, zero), X, zero), true), true, ifeq(quotient(X, X, divide(X, X)), true, less_equal(divide(divide(X, X), zero), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(X, X), zero)), true, zero, divide(divide(X, X), zero)), divide(divide(X, X), zero))), true, less_equal(divide(X, X), zero), true), true, ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 157.11/20.38 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.38 ifeq2(ifeq(quotient(divide(X, X), zero, ifeq2(ifeq(ifeq(ifeq(true, true, less_equal(divide(X, zero), X), true), true, quotient(divide(X, zero), X, zero), true), true, ifeq(quotient(X, X, divide(X, X)), true, less_equal(divide(divide(X, X), zero), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(X, X), zero)), true, zero, divide(divide(X, X), zero)), divide(divide(X, X), zero))), true, less_equal(divide(X, X), zero), true), true, ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 157.11/20.38 = { by axiom 8 (closure) R->L }
% 157.11/20.38 ifeq2(ifeq(quotient(divide(X, X), zero, ifeq2(ifeq(ifeq(ifeq(quotient(X, zero, divide(X, zero)), true, less_equal(divide(X, zero), X), true), true, quotient(divide(X, zero), X, zero), true), true, ifeq(quotient(X, X, divide(X, X)), true, less_equal(divide(divide(X, X), zero), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(X, X), zero)), true, zero, divide(divide(X, X), zero)), divide(divide(X, X), zero))), true, less_equal(divide(X, X), zero), true), true, ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 157.11/20.38 = { by axiom 10 (divisor_existence) }
% 157.11/20.38 ifeq2(ifeq(quotient(divide(X, X), zero, ifeq2(ifeq(ifeq(true, true, quotient(divide(X, zero), X, zero), true), true, ifeq(quotient(X, X, divide(X, X)), true, less_equal(divide(divide(X, X), zero), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(X, X), zero)), true, zero, divide(divide(X, X), zero)), divide(divide(X, X), zero))), true, less_equal(divide(X, X), zero), true), true, ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 157.11/20.38 = { by axiom 6 (ifeq_axiom) }
% 157.11/20.38 ifeq2(ifeq(quotient(divide(X, X), zero, ifeq2(ifeq(quotient(divide(X, zero), X, zero), true, ifeq(quotient(X, X, divide(X, X)), true, less_equal(divide(divide(X, X), zero), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(X, X), zero)), true, zero, divide(divide(X, X), zero)), divide(divide(X, X), zero))), true, less_equal(divide(X, X), zero), true), true, ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 157.11/20.38 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.38 ifeq2(ifeq(quotient(divide(X, X), zero, ifeq2(ifeq(quotient(divide(X, zero), X, zero), true, ifeq(quotient(X, X, divide(X, X)), true, ifeq(true, true, less_equal(divide(divide(X, X), zero), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(X, X), zero)), true, zero, divide(divide(X, X), zero)), divide(divide(X, X), zero))), true, less_equal(divide(X, X), zero), true), true, ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 157.11/20.38 = { by axiom 8 (closure) R->L }
% 157.11/20.38 ifeq2(ifeq(quotient(divide(X, X), zero, ifeq2(ifeq(quotient(divide(X, zero), X, zero), true, ifeq(quotient(X, X, divide(X, X)), true, ifeq(quotient(X, zero, divide(X, zero)), true, less_equal(divide(divide(X, X), zero), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(X, X), zero)), true, zero, divide(divide(X, X), zero)), divide(divide(X, X), zero))), true, less_equal(divide(X, X), zero), true), true, ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 157.11/20.38 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.38 ifeq2(ifeq(quotient(divide(X, X), zero, ifeq2(ifeq(quotient(divide(X, zero), X, zero), true, ifeq(true, true, ifeq(quotient(X, X, divide(X, X)), true, ifeq(quotient(X, zero, divide(X, zero)), true, less_equal(divide(divide(X, X), zero), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(X, X), zero)), true, zero, divide(divide(X, X), zero)), divide(divide(X, X), zero))), true, less_equal(divide(X, X), zero), true), true, ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 157.11/20.38 = { by axiom 9 (quotient_less_equal) R->L }
% 157.11/20.38 ifeq2(ifeq(quotient(divide(X, X), zero, ifeq2(ifeq(quotient(divide(X, zero), X, zero), true, ifeq(ifeq(less_equal(zero, X), true, quotient(zero, X, zero), true), true, ifeq(quotient(X, X, divide(X, X)), true, ifeq(quotient(X, zero, divide(X, zero)), true, less_equal(divide(divide(X, X), zero), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(X, X), zero)), true, zero, divide(divide(X, X), zero)), divide(divide(X, X), zero))), true, less_equal(divide(X, X), zero), true), true, ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 157.11/20.38 = { by axiom 2 (zero_is_smallest) }
% 157.11/20.38 ifeq2(ifeq(quotient(divide(X, X), zero, ifeq2(ifeq(quotient(divide(X, zero), X, zero), true, ifeq(ifeq(true, true, quotient(zero, X, zero), true), true, ifeq(quotient(X, X, divide(X, X)), true, ifeq(quotient(X, zero, divide(X, zero)), true, less_equal(divide(divide(X, X), zero), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(X, X), zero)), true, zero, divide(divide(X, X), zero)), divide(divide(X, X), zero))), true, less_equal(divide(X, X), zero), true), true, ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 157.11/20.38 = { by axiom 6 (ifeq_axiom) }
% 157.11/20.38 ifeq2(ifeq(quotient(divide(X, X), zero, ifeq2(ifeq(quotient(divide(X, zero), X, zero), true, ifeq(quotient(zero, X, zero), true, ifeq(quotient(X, X, divide(X, X)), true, ifeq(quotient(X, zero, divide(X, zero)), true, less_equal(divide(divide(X, X), zero), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(X, X), zero)), true, zero, divide(divide(X, X), zero)), divide(divide(X, X), zero))), true, less_equal(divide(X, X), zero), true), true, ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 157.11/20.38 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.38 ifeq2(ifeq(quotient(divide(X, X), zero, ifeq2(ifeq(true, true, ifeq(quotient(divide(X, zero), X, zero), true, ifeq(quotient(zero, X, zero), true, ifeq(quotient(X, X, divide(X, X)), true, ifeq(quotient(X, zero, divide(X, zero)), true, less_equal(divide(divide(X, X), zero), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(X, X), zero)), true, zero, divide(divide(X, X), zero)), divide(divide(X, X), zero))), true, less_equal(divide(X, X), zero), true), true, ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 157.11/20.38 = { by axiom 8 (closure) R->L }
% 157.11/20.38 ifeq2(ifeq(quotient(divide(X, X), zero, ifeq2(ifeq(quotient(divide(X, X), zero, divide(divide(X, X), zero)), true, ifeq(quotient(divide(X, zero), X, zero), true, ifeq(quotient(zero, X, zero), true, ifeq(quotient(X, X, divide(X, X)), true, ifeq(quotient(X, zero, divide(X, zero)), true, less_equal(divide(divide(X, X), zero), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(X, X), zero)), true, zero, divide(divide(X, X), zero)), divide(divide(X, X), zero))), true, less_equal(divide(X, X), zero), true), true, ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 157.11/20.38 = { by axiom 14 (quotient_property) }
% 157.11/20.38 ifeq2(ifeq(quotient(divide(X, X), zero, ifeq2(true, true, ifeq2(less_equal(zero, divide(divide(X, X), zero)), true, zero, divide(divide(X, X), zero)), divide(divide(X, X), zero))), true, less_equal(divide(X, X), zero), true), true, ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 157.11/20.38 = { by axiom 7 (ifeq_axiom) }
% 157.11/20.38 ifeq2(ifeq(quotient(divide(X, X), zero, ifeq2(less_equal(zero, divide(divide(X, X), zero)), true, zero, divide(divide(X, X), zero))), true, less_equal(divide(X, X), zero), true), true, ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 157.11/20.38 = { by axiom 2 (zero_is_smallest) }
% 157.11/20.38 ifeq2(ifeq(quotient(divide(X, X), zero, ifeq2(true, true, zero, divide(divide(X, X), zero))), true, less_equal(divide(X, X), zero), true), true, ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 157.11/20.38 = { by axiom 7 (ifeq_axiom) }
% 157.11/20.38 ifeq2(ifeq(quotient(divide(X, X), zero, zero), true, less_equal(divide(X, X), zero), true), true, ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 157.11/20.38 = { by axiom 11 (less_equal_quotient) }
% 157.11/20.38 ifeq2(true, true, ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 157.11/20.38 = { by axiom 7 (ifeq_axiom) }
% 157.11/20.38 ifeq2(less_equal(zero, divide(X, X)), true, zero, divide(X, X))
% 157.11/20.38 = { by axiom 2 (zero_is_smallest) }
% 157.11/20.38 ifeq2(true, true, zero, divide(X, X))
% 157.11/20.38 = { by axiom 7 (ifeq_axiom) }
% 157.11/20.39 zero
% 157.11/20.39
% 157.11/20.39 Lemma 16: divide(idQa, a) = divide(idQa, zero).
% 157.11/20.39 Proof:
% 157.11/20.39 divide(idQa, a)
% 157.11/20.39 = { by axiom 12 (less_equal_and_equal) R->L }
% 157.11/20.39 ifeq2(less_equal(divide(idQa, a), divide(idQa, divide(a, a))), true, ifeq2(less_equal(divide(idQa, divide(a, a)), divide(idQa, a)), true, divide(idQa, divide(a, a)), divide(idQa, a)), divide(idQa, a))
% 157.11/20.39 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.39 ifeq2(less_equal(divide(idQa, a), divide(idQa, divide(a, a))), true, ifeq2(ifeq(true, true, less_equal(divide(idQa, divide(a, a)), divide(idQa, a)), true), true, divide(idQa, divide(a, a)), divide(idQa, a)), divide(idQa, a))
% 157.11/20.39 = { by axiom 8 (closure) R->L }
% 157.11/20.39 ifeq2(less_equal(divide(idQa, a), divide(idQa, divide(a, a))), true, ifeq2(ifeq(quotient(a, a, divide(a, a)), true, less_equal(divide(idQa, divide(a, a)), divide(idQa, a)), true), true, divide(idQa, divide(a, a)), divide(idQa, a)), divide(idQa, a))
% 157.11/20.39 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.39 ifeq2(less_equal(divide(idQa, a), divide(idQa, divide(a, a))), true, ifeq2(ifeq(true, true, ifeq(quotient(a, a, divide(a, a)), true, less_equal(divide(idQa, divide(a, a)), divide(idQa, a)), true), true), true, divide(idQa, divide(a, a)), divide(idQa, a)), divide(idQa, a))
% 157.11/20.39 = { by axiom 8 (closure) R->L }
% 157.11/20.39 ifeq2(less_equal(divide(idQa, a), divide(idQa, divide(a, a))), true, ifeq2(ifeq(quotient(idQa, divide(a, a), divide(idQa, divide(a, a))), true, ifeq(quotient(a, a, divide(a, a)), true, less_equal(divide(idQa, divide(a, a)), divide(idQa, a)), true), true), true, divide(idQa, divide(a, a)), divide(idQa, a)), divide(idQa, a))
% 157.11/20.39 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.39 ifeq2(less_equal(divide(idQa, a), divide(idQa, divide(a, a))), true, ifeq2(ifeq(quotient(idQa, divide(a, a), divide(idQa, divide(a, a))), true, ifeq(true, true, ifeq(quotient(a, a, divide(a, a)), true, less_equal(divide(idQa, divide(a, a)), divide(idQa, a)), true), true), true), true, divide(idQa, divide(a, a)), divide(idQa, a)), divide(idQa, a))
% 157.11/20.39 = { by axiom 8 (closure) R->L }
% 157.11/20.39 ifeq2(less_equal(divide(idQa, a), divide(idQa, divide(a, a))), true, ifeq2(ifeq(quotient(idQa, divide(a, a), divide(idQa, divide(a, a))), true, ifeq(quotient(idQa, a, divide(idQa, a)), true, ifeq(quotient(a, a, divide(a, a)), true, less_equal(divide(idQa, divide(a, a)), divide(idQa, a)), true), true), true), true, divide(idQa, divide(a, a)), divide(idQa, a)), divide(idQa, a))
% 157.11/20.39 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.39 ifeq2(less_equal(divide(idQa, a), divide(idQa, divide(a, a))), true, ifeq2(ifeq(quotient(idQa, divide(a, a), divide(idQa, divide(a, a))), true, ifeq(quotient(idQa, a, divide(idQa, a)), true, ifeq(quotient(a, a, divide(a, a)), true, ifeq(true, true, less_equal(divide(idQa, divide(a, a)), divide(idQa, a)), true), true), true), true), true, divide(idQa, divide(a, a)), divide(idQa, a)), divide(idQa, a))
% 157.11/20.39 = { by axiom 5 (identity_divide_a) R->L }
% 157.11/20.39 ifeq2(less_equal(divide(idQa, a), divide(idQa, divide(a, a))), true, ifeq2(ifeq(quotient(idQa, divide(a, a), divide(idQa, divide(a, a))), true, ifeq(quotient(idQa, a, divide(idQa, a)), true, ifeq(quotient(a, a, divide(a, a)), true, ifeq(quotient(identity, a, idQa), true, less_equal(divide(idQa, divide(a, a)), divide(idQa, a)), true), true), true), true), true, divide(idQa, divide(a, a)), divide(idQa, a)), divide(idQa, a))
% 157.11/20.39 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.39 ifeq2(less_equal(divide(idQa, a), divide(idQa, divide(a, a))), true, ifeq2(ifeq(quotient(idQa, divide(a, a), divide(idQa, divide(a, a))), true, ifeq(quotient(idQa, a, divide(idQa, a)), true, ifeq(quotient(a, a, divide(a, a)), true, ifeq(quotient(identity, a, idQa), true, ifeq(true, true, less_equal(divide(idQa, divide(a, a)), divide(idQa, a)), true), true), true), true), true), true, divide(idQa, divide(a, a)), divide(idQa, a)), divide(idQa, a))
% 157.11/20.39 = { by axiom 5 (identity_divide_a) R->L }
% 157.11/20.39 ifeq2(less_equal(divide(idQa, a), divide(idQa, divide(a, a))), true, ifeq2(ifeq(quotient(idQa, divide(a, a), divide(idQa, divide(a, a))), true, ifeq(quotient(idQa, a, divide(idQa, a)), true, ifeq(quotient(a, a, divide(a, a)), true, ifeq(quotient(identity, a, idQa), true, ifeq(quotient(identity, a, idQa), true, less_equal(divide(idQa, divide(a, a)), divide(idQa, a)), true), true), true), true), true), true, divide(idQa, divide(a, a)), divide(idQa, a)), divide(idQa, a))
% 157.11/20.39 = { by axiom 14 (quotient_property) }
% 157.11/20.39 ifeq2(less_equal(divide(idQa, a), divide(idQa, divide(a, a))), true, ifeq2(true, true, divide(idQa, divide(a, a)), divide(idQa, a)), divide(idQa, a))
% 157.11/20.39 = { by axiom 7 (ifeq_axiom) }
% 157.11/20.39 ifeq2(less_equal(divide(idQa, a), divide(idQa, divide(a, a))), true, divide(idQa, divide(a, a)), divide(idQa, a))
% 157.11/20.39 = { by lemma 15 }
% 157.11/20.39 ifeq2(less_equal(divide(idQa, a), divide(idQa, zero)), true, divide(idQa, divide(a, a)), divide(idQa, a))
% 157.11/20.39 = { by lemma 15 }
% 157.11/20.39 ifeq2(less_equal(divide(idQa, a), divide(idQa, zero)), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.39 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.39 ifeq2(ifeq(true, true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.39 = { by axiom 8 (closure) R->L }
% 157.11/20.39 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), divide(divide(idQa, a), divide(idQa, zero))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.39 = { by axiom 12 (less_equal_and_equal) R->L }
% 157.11/20.39 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.39 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.39 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(true, true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.39 = { by axiom 8 (closure) R->L }
% 157.11/20.39 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.39 = { by axiom 12 (less_equal_and_equal) R->L }
% 157.11/20.39 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), zero), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.39 = { by axiom 7 (ifeq_axiom) R->L }
% 157.11/20.40 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), ifeq2(true, true, zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero)))), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.40 = { by axiom 2 (zero_is_smallest) R->L }
% 157.11/20.40 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), ifeq2(less_equal(zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero)))), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.40 = { by axiom 7 (ifeq_axiom) R->L }
% 157.11/20.40 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), ifeq2(true, true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), divide(divide(divide(idQa, a), zero), divide(idQa, zero)))), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.40 = { by axiom 14 (quotient_property) R->L }
% 157.11/20.40 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), zero), divide(idQa, zero), divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, ifeq(quotient(zero, zero, zero), true, ifeq(quotient(idQa, zero, divide(idQa, zero)), true, ifeq(quotient(divide(idQa, a), zero, divide(divide(idQa, a), zero)), true, ifeq(quotient(divide(idQa, a), idQa, zero), true, less_equal(divide(divide(divide(idQa, a), zero), divide(idQa, zero)), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), divide(divide(divide(idQa, a), zero), divide(idQa, zero)))), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.40 = { by axiom 8 (closure) }
% 157.11/20.40 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), ifeq2(ifeq(true, true, ifeq(quotient(zero, zero, zero), true, ifeq(quotient(idQa, zero, divide(idQa, zero)), true, ifeq(quotient(divide(idQa, a), zero, divide(divide(idQa, a), zero)), true, ifeq(quotient(divide(idQa, a), idQa, zero), true, less_equal(divide(divide(divide(idQa, a), zero), divide(idQa, zero)), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), divide(divide(divide(idQa, a), zero), divide(idQa, zero)))), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.40 = { by axiom 6 (ifeq_axiom) }
% 157.11/20.40 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), ifeq2(ifeq(quotient(zero, zero, zero), true, ifeq(quotient(idQa, zero, divide(idQa, zero)), true, ifeq(quotient(divide(idQa, a), zero, divide(divide(idQa, a), zero)), true, ifeq(quotient(divide(idQa, a), idQa, zero), true, less_equal(divide(divide(divide(idQa, a), zero), divide(idQa, zero)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), divide(divide(divide(idQa, a), zero), divide(idQa, zero)))), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.40 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.40 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), ifeq2(ifeq(ifeq(true, true, quotient(zero, zero, zero), true), true, ifeq(quotient(idQa, zero, divide(idQa, zero)), true, ifeq(quotient(divide(idQa, a), zero, divide(divide(idQa, a), zero)), true, ifeq(quotient(divide(idQa, a), idQa, zero), true, less_equal(divide(divide(divide(idQa, a), zero), divide(idQa, zero)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), divide(divide(divide(idQa, a), zero), divide(idQa, zero)))), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.41 = { by axiom 2 (zero_is_smallest) R->L }
% 157.11/20.41 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), ifeq2(ifeq(ifeq(less_equal(zero, zero), true, quotient(zero, zero, zero), true), true, ifeq(quotient(idQa, zero, divide(idQa, zero)), true, ifeq(quotient(divide(idQa, a), zero, divide(divide(idQa, a), zero)), true, ifeq(quotient(divide(idQa, a), idQa, zero), true, less_equal(divide(divide(divide(idQa, a), zero), divide(idQa, zero)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), divide(divide(divide(idQa, a), zero), divide(idQa, zero)))), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.41 = { by axiom 9 (quotient_less_equal) }
% 157.11/20.41 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), ifeq2(ifeq(true, true, ifeq(quotient(idQa, zero, divide(idQa, zero)), true, ifeq(quotient(divide(idQa, a), zero, divide(divide(idQa, a), zero)), true, ifeq(quotient(divide(idQa, a), idQa, zero), true, less_equal(divide(divide(divide(idQa, a), zero), divide(idQa, zero)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), divide(divide(divide(idQa, a), zero), divide(idQa, zero)))), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.41 = { by axiom 6 (ifeq_axiom) }
% 157.11/20.41 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), ifeq2(ifeq(quotient(idQa, zero, divide(idQa, zero)), true, ifeq(quotient(divide(idQa, a), zero, divide(divide(idQa, a), zero)), true, ifeq(quotient(divide(idQa, a), idQa, zero), true, less_equal(divide(divide(divide(idQa, a), zero), divide(idQa, zero)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), divide(divide(divide(idQa, a), zero), divide(idQa, zero)))), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.41 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.41 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), ifeq2(ifeq(quotient(idQa, zero, divide(idQa, zero)), true, ifeq(quotient(divide(idQa, a), zero, divide(divide(idQa, a), zero)), true, ifeq(ifeq(true, true, quotient(divide(idQa, a), idQa, zero), true), true, less_equal(divide(divide(divide(idQa, a), zero), divide(idQa, zero)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), divide(divide(divide(idQa, a), zero), divide(idQa, zero)))), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.41 = { by axiom 10 (divisor_existence) R->L }
% 157.11/20.41 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), ifeq2(ifeq(quotient(idQa, zero, divide(idQa, zero)), true, ifeq(quotient(divide(idQa, a), zero, divide(divide(idQa, a), zero)), true, ifeq(ifeq(ifeq(quotient(idQa, a, divide(idQa, a)), true, less_equal(divide(idQa, a), idQa), true), true, quotient(divide(idQa, a), idQa, zero), true), true, less_equal(divide(divide(divide(idQa, a), zero), divide(idQa, zero)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), divide(divide(divide(idQa, a), zero), divide(idQa, zero)))), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.41 = { by axiom 8 (closure) }
% 157.11/20.41 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), ifeq2(ifeq(quotient(idQa, zero, divide(idQa, zero)), true, ifeq(quotient(divide(idQa, a), zero, divide(divide(idQa, a), zero)), true, ifeq(ifeq(ifeq(true, true, less_equal(divide(idQa, a), idQa), true), true, quotient(divide(idQa, a), idQa, zero), true), true, less_equal(divide(divide(divide(idQa, a), zero), divide(idQa, zero)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), divide(divide(divide(idQa, a), zero), divide(idQa, zero)))), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.41 = { by axiom 6 (ifeq_axiom) }
% 157.11/20.41 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), ifeq2(ifeq(quotient(idQa, zero, divide(idQa, zero)), true, ifeq(quotient(divide(idQa, a), zero, divide(divide(idQa, a), zero)), true, ifeq(ifeq(less_equal(divide(idQa, a), idQa), true, quotient(divide(idQa, a), idQa, zero), true), true, less_equal(divide(divide(divide(idQa, a), zero), divide(idQa, zero)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), divide(divide(divide(idQa, a), zero), divide(idQa, zero)))), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.41 = { by axiom 9 (quotient_less_equal) }
% 157.11/20.42 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), ifeq2(ifeq(quotient(idQa, zero, divide(idQa, zero)), true, ifeq(quotient(divide(idQa, a), zero, divide(divide(idQa, a), zero)), true, ifeq(true, true, less_equal(divide(divide(divide(idQa, a), zero), divide(idQa, zero)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), divide(divide(divide(idQa, a), zero), divide(idQa, zero)))), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.42 = { by axiom 6 (ifeq_axiom) }
% 157.11/20.42 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), ifeq2(ifeq(quotient(idQa, zero, divide(idQa, zero)), true, ifeq(quotient(divide(idQa, a), zero, divide(divide(idQa, a), zero)), true, less_equal(divide(divide(divide(idQa, a), zero), divide(idQa, zero)), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), divide(divide(divide(idQa, a), zero), divide(idQa, zero)))), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.42 = { by axiom 8 (closure) }
% 157.11/20.42 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), ifeq2(ifeq(quotient(idQa, zero, divide(idQa, zero)), true, ifeq(true, true, less_equal(divide(divide(divide(idQa, a), zero), divide(idQa, zero)), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), divide(divide(divide(idQa, a), zero), divide(idQa, zero)))), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.42 = { by axiom 6 (ifeq_axiom) }
% 157.11/20.42 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), ifeq2(ifeq(quotient(idQa, zero, divide(idQa, zero)), true, less_equal(divide(divide(divide(idQa, a), zero), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), divide(divide(divide(idQa, a), zero), divide(idQa, zero)))), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.42 = { by axiom 8 (closure) }
% 157.11/20.42 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), ifeq2(ifeq(true, true, less_equal(divide(divide(divide(idQa, a), zero), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), divide(divide(divide(idQa, a), zero), divide(idQa, zero)))), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.42 = { by axiom 6 (ifeq_axiom) }
% 157.11/20.42 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), ifeq2(less_equal(divide(divide(divide(idQa, a), zero), divide(idQa, zero)), zero), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, zero, divide(divide(divide(idQa, a), zero), divide(idQa, zero))), divide(divide(divide(idQa, a), zero), divide(idQa, zero)))), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.42 = { by axiom 12 (less_equal_and_equal) }
% 157.11/20.42 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.42 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.42 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(ifeq(true, true, less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.42 = { by axiom 8 (closure) R->L }
% 157.11/20.42 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), divide(divide(idQa, a), divide(idQa, zero))), true, less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.42 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.42 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(ifeq(true, true, ifeq(quotient(divide(idQa, a), divide(idQa, zero), divide(divide(idQa, a), divide(idQa, zero))), true, less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.42 = { by axiom 8 (closure) R->L }
% 157.11/20.43 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(ifeq(quotient(divide(divide(idQa, a), zero), divide(idQa, zero), divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, ifeq(quotient(divide(idQa, a), divide(idQa, zero), divide(divide(idQa, a), divide(idQa, zero))), true, less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.43 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.43 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(ifeq(quotient(divide(divide(idQa, a), zero), divide(idQa, zero), divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, ifeq(quotient(divide(idQa, a), divide(idQa, zero), divide(divide(idQa, a), divide(idQa, zero))), true, ifeq(true, true, less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.43 = { by axiom 8 (closure) R->L }
% 157.11/20.43 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(ifeq(quotient(divide(divide(idQa, a), zero), divide(idQa, zero), divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, ifeq(quotient(divide(idQa, a), divide(idQa, zero), divide(divide(idQa, a), divide(idQa, zero))), true, ifeq(quotient(divide(idQa, a), zero, divide(divide(idQa, a), zero)), true, less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.44 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.44 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(ifeq(quotient(divide(divide(idQa, a), zero), divide(idQa, zero), divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, ifeq(true, true, ifeq(quotient(divide(idQa, a), divide(idQa, zero), divide(divide(idQa, a), divide(idQa, zero))), true, ifeq(quotient(divide(idQa, a), zero, divide(divide(idQa, a), zero)), true, less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.44 = { by axiom 9 (quotient_less_equal) R->L }
% 157.11/20.44 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(ifeq(quotient(divide(divide(idQa, a), zero), divide(idQa, zero), divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, ifeq(ifeq(less_equal(zero, divide(idQa, zero)), true, quotient(zero, divide(idQa, zero), zero), true), true, ifeq(quotient(divide(idQa, a), divide(idQa, zero), divide(divide(idQa, a), divide(idQa, zero))), true, ifeq(quotient(divide(idQa, a), zero, divide(divide(idQa, a), zero)), true, less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.44 = { by axiom 2 (zero_is_smallest) }
% 157.11/20.44 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(ifeq(quotient(divide(divide(idQa, a), zero), divide(idQa, zero), divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, ifeq(ifeq(true, true, quotient(zero, divide(idQa, zero), zero), true), true, ifeq(quotient(divide(idQa, a), divide(idQa, zero), divide(divide(idQa, a), divide(idQa, zero))), true, ifeq(quotient(divide(idQa, a), zero, divide(divide(idQa, a), zero)), true, less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.44 = { by axiom 6 (ifeq_axiom) }
% 157.11/20.44 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(ifeq(quotient(divide(divide(idQa, a), zero), divide(idQa, zero), divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, ifeq(quotient(zero, divide(idQa, zero), zero), true, ifeq(quotient(divide(idQa, a), divide(idQa, zero), divide(divide(idQa, a), divide(idQa, zero))), true, ifeq(quotient(divide(idQa, a), zero, divide(divide(idQa, a), zero)), true, less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.44 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.44 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(ifeq(true, true, ifeq(quotient(divide(divide(idQa, a), zero), divide(idQa, zero), divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, ifeq(quotient(zero, divide(idQa, zero), zero), true, ifeq(quotient(divide(idQa, a), divide(idQa, zero), divide(divide(idQa, a), divide(idQa, zero))), true, ifeq(quotient(divide(idQa, a), zero, divide(divide(idQa, a), zero)), true, less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.44 = { by axiom 8 (closure) R->L }
% 157.11/20.44 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, ifeq(quotient(divide(divide(idQa, a), zero), divide(idQa, zero), divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true, ifeq(quotient(zero, divide(idQa, zero), zero), true, ifeq(quotient(divide(idQa, a), divide(idQa, zero), divide(divide(idQa, a), divide(idQa, zero))), true, ifeq(quotient(divide(idQa, a), zero, divide(divide(idQa, a), zero)), true, less_equal(divide(divide(divide(idQa, a), divide(idQa, zero)), zero), divide(divide(divide(idQa, a), zero), divide(idQa, zero))), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.44 = { by axiom 14 (quotient_property) }
% 157.11/20.44 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(true, true, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.44 = { by axiom 7 (ifeq_axiom) }
% 157.11/20.44 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(less_equal(zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero)), true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.44 = { by axiom 2 (zero_is_smallest) }
% 157.11/20.44 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, ifeq2(true, true, zero, divide(divide(divide(idQa, a), divide(idQa, zero)), zero))), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.44 = { by axiom 7 (ifeq_axiom) }
% 157.11/20.44 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(ifeq(quotient(divide(divide(idQa, a), divide(idQa, zero)), zero, zero), true, less_equal(divide(divide(idQa, a), divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.44 = { by axiom 11 (less_equal_quotient) }
% 157.11/20.44 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(true, true, ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero))), divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.44 = { by axiom 7 (ifeq_axiom) }
% 157.11/20.44 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(less_equal(zero, divide(divide(idQa, a), divide(idQa, zero))), true, zero, divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.44 = { by axiom 2 (zero_is_smallest) }
% 157.11/20.44 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), ifeq2(true, true, zero, divide(divide(idQa, a), divide(idQa, zero)))), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.44 = { by axiom 7 (ifeq_axiom) }
% 157.11/20.44 ifeq2(ifeq(quotient(divide(idQa, a), divide(idQa, zero), zero), true, less_equal(divide(idQa, a), divide(idQa, zero)), true), true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.44 = { by axiom 11 (less_equal_quotient) }
% 157.11/20.44 ifeq2(true, true, divide(idQa, zero), divide(idQa, a))
% 157.11/20.44 = { by axiom 7 (ifeq_axiom) }
% 157.11/20.44 divide(idQa, zero)
% 157.11/20.44
% 157.11/20.44 Lemma 17: divide(divide(X, idQa), idQ_idQa) = zero.
% 157.11/20.44 Proof:
% 157.11/20.44 divide(divide(X, idQa), idQ_idQa)
% 157.11/20.44 = { by axiom 12 (less_equal_and_equal) R->L }
% 157.11/20.44 ifeq2(less_equal(divide(divide(X, idQa), idQ_idQa), zero), true, ifeq2(less_equal(zero, divide(divide(X, idQa), idQ_idQa)), true, zero, divide(divide(X, idQa), idQ_idQa)), divide(divide(X, idQa), idQ_idQa))
% 157.11/20.44 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.44 ifeq2(ifeq(true, true, less_equal(divide(divide(X, idQa), idQ_idQa), zero), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), idQ_idQa)), true, zero, divide(divide(X, idQa), idQ_idQa)), divide(divide(X, idQa), idQ_idQa))
% 157.11/20.44 = { by axiom 8 (closure) R->L }
% 157.11/20.44 ifeq2(ifeq(quotient(X, idQa, divide(X, idQa)), true, less_equal(divide(divide(X, idQa), idQ_idQa), zero), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), idQ_idQa)), true, zero, divide(divide(X, idQa), idQ_idQa)), divide(divide(X, idQa), idQ_idQa))
% 157.11/20.44 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.44 ifeq2(ifeq(true, true, ifeq(quotient(X, idQa, divide(X, idQa)), true, less_equal(divide(divide(X, idQa), idQ_idQa), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), idQ_idQa)), true, zero, divide(divide(X, idQa), idQ_idQa)), divide(divide(X, idQa), idQ_idQa))
% 157.11/20.44 = { by axiom 8 (closure) R->L }
% 157.11/20.44 ifeq2(ifeq(quotient(divide(X, idQa), idQ_idQa, divide(divide(X, idQa), idQ_idQa)), true, ifeq(quotient(X, idQa, divide(X, idQa)), true, less_equal(divide(divide(X, idQa), idQ_idQa), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), idQ_idQa)), true, zero, divide(divide(X, idQa), idQ_idQa)), divide(divide(X, idQa), idQ_idQa))
% 157.11/20.44 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.44 ifeq2(ifeq(quotient(divide(X, idQa), idQ_idQa, divide(divide(X, idQa), idQ_idQa)), true, ifeq(quotient(X, idQa, divide(X, idQa)), true, ifeq(true, true, less_equal(divide(divide(X, idQa), idQ_idQa), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), idQ_idQa)), true, zero, divide(divide(X, idQa), idQ_idQa)), divide(divide(X, idQa), idQ_idQa))
% 157.11/20.44 = { by axiom 9 (quotient_less_equal) R->L }
% 157.11/20.44 ifeq2(ifeq(quotient(divide(X, idQa), idQ_idQa, divide(divide(X, idQa), idQ_idQa)), true, ifeq(quotient(X, idQa, divide(X, idQa)), true, ifeq(ifeq(less_equal(X, identity), true, quotient(X, identity, zero), true), true, less_equal(divide(divide(X, idQa), idQ_idQa), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), idQ_idQa)), true, zero, divide(divide(X, idQa), idQ_idQa)), divide(divide(X, idQa), idQ_idQa))
% 157.11/20.44 = { by axiom 1 (identity_is_largest) }
% 157.11/20.44 ifeq2(ifeq(quotient(divide(X, idQa), idQ_idQa, divide(divide(X, idQa), idQ_idQa)), true, ifeq(quotient(X, idQa, divide(X, idQa)), true, ifeq(ifeq(true, true, quotient(X, identity, zero), true), true, less_equal(divide(divide(X, idQa), idQ_idQa), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), idQ_idQa)), true, zero, divide(divide(X, idQa), idQ_idQa)), divide(divide(X, idQa), idQ_idQa))
% 157.11/20.44 = { by axiom 6 (ifeq_axiom) }
% 157.11/20.44 ifeq2(ifeq(quotient(divide(X, idQa), idQ_idQa, divide(divide(X, idQa), idQ_idQa)), true, ifeq(quotient(X, idQa, divide(X, idQa)), true, ifeq(quotient(X, identity, zero), true, less_equal(divide(divide(X, idQa), idQ_idQa), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), idQ_idQa)), true, zero, divide(divide(X, idQa), idQ_idQa)), divide(divide(X, idQa), idQ_idQa))
% 157.11/20.44 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.44 ifeq2(ifeq(quotient(divide(X, idQa), idQ_idQa, divide(divide(X, idQa), idQ_idQa)), true, ifeq(true, true, ifeq(quotient(X, idQa, divide(X, idQa)), true, ifeq(quotient(X, identity, zero), true, less_equal(divide(divide(X, idQa), idQ_idQa), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), idQ_idQa)), true, zero, divide(divide(X, idQa), idQ_idQa)), divide(divide(X, idQa), idQ_idQa))
% 157.11/20.44 = { by axiom 9 (quotient_less_equal) R->L }
% 157.11/20.44 ifeq2(ifeq(quotient(divide(X, idQa), idQ_idQa, divide(divide(X, idQa), idQ_idQa)), true, ifeq(ifeq(less_equal(zero, idQa), true, quotient(zero, idQa, zero), true), true, ifeq(quotient(X, idQa, divide(X, idQa)), true, ifeq(quotient(X, identity, zero), true, less_equal(divide(divide(X, idQa), idQ_idQa), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), idQ_idQa)), true, zero, divide(divide(X, idQa), idQ_idQa)), divide(divide(X, idQa), idQ_idQa))
% 157.11/20.44 = { by axiom 2 (zero_is_smallest) }
% 157.11/20.44 ifeq2(ifeq(quotient(divide(X, idQa), idQ_idQa, divide(divide(X, idQa), idQ_idQa)), true, ifeq(ifeq(true, true, quotient(zero, idQa, zero), true), true, ifeq(quotient(X, idQa, divide(X, idQa)), true, ifeq(quotient(X, identity, zero), true, less_equal(divide(divide(X, idQa), idQ_idQa), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), idQ_idQa)), true, zero, divide(divide(X, idQa), idQ_idQa)), divide(divide(X, idQa), idQ_idQa))
% 157.11/20.44 = { by axiom 6 (ifeq_axiom) }
% 157.11/20.44 ifeq2(ifeq(quotient(divide(X, idQa), idQ_idQa, divide(divide(X, idQa), idQ_idQa)), true, ifeq(quotient(zero, idQa, zero), true, ifeq(quotient(X, idQa, divide(X, idQa)), true, ifeq(quotient(X, identity, zero), true, less_equal(divide(divide(X, idQa), idQ_idQa), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), idQ_idQa)), true, zero, divide(divide(X, idQa), idQ_idQa)), divide(divide(X, idQa), idQ_idQa))
% 157.11/20.44 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.44 ifeq2(ifeq(quotient(divide(X, idQa), idQ_idQa, divide(divide(X, idQa), idQ_idQa)), true, ifeq(quotient(zero, idQa, zero), true, ifeq(true, true, ifeq(quotient(X, idQa, divide(X, idQa)), true, ifeq(quotient(X, identity, zero), true, less_equal(divide(divide(X, idQa), idQ_idQa), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), idQ_idQa)), true, zero, divide(divide(X, idQa), idQ_idQa)), divide(divide(X, idQa), idQ_idQa))
% 157.11/20.44 = { by axiom 4 (identity_divide_idQa) R->L }
% 157.11/20.44 ifeq2(ifeq(quotient(divide(X, idQa), idQ_idQa, divide(divide(X, idQa), idQ_idQa)), true, ifeq(quotient(zero, idQa, zero), true, ifeq(quotient(identity, idQa, idQ_idQa), true, ifeq(quotient(X, idQa, divide(X, idQa)), true, ifeq(quotient(X, identity, zero), true, less_equal(divide(divide(X, idQa), idQ_idQa), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), idQ_idQa)), true, zero, divide(divide(X, idQa), idQ_idQa)), divide(divide(X, idQa), idQ_idQa))
% 157.11/20.44 = { by axiom 14 (quotient_property) }
% 157.11/20.44 ifeq2(true, true, ifeq2(less_equal(zero, divide(divide(X, idQa), idQ_idQa)), true, zero, divide(divide(X, idQa), idQ_idQa)), divide(divide(X, idQa), idQ_idQa))
% 157.11/20.44 = { by axiom 7 (ifeq_axiom) }
% 157.11/20.45 ifeq2(less_equal(zero, divide(divide(X, idQa), idQ_idQa)), true, zero, divide(divide(X, idQa), idQ_idQa))
% 157.11/20.45 = { by axiom 2 (zero_is_smallest) }
% 157.11/20.45 ifeq2(true, true, zero, divide(divide(X, idQa), idQ_idQa))
% 157.11/20.45 = { by axiom 7 (ifeq_axiom) }
% 157.11/20.45 zero
% 157.11/20.45
% 157.11/20.45 Lemma 18: divide(idQ_idQa, a) = zero.
% 157.11/20.45 Proof:
% 157.11/20.45 divide(idQ_idQa, a)
% 157.11/20.45 = { by axiom 12 (less_equal_and_equal) R->L }
% 157.11/20.45 divide(ifeq2(less_equal(idQ_idQa, divide(a, idQa)), true, ifeq2(less_equal(divide(a, idQa), idQ_idQa), true, divide(a, idQa), idQ_idQa), idQ_idQa), a)
% 157.11/20.45 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.45 divide(ifeq2(ifeq(true, true, less_equal(idQ_idQa, divide(a, idQa)), true), true, ifeq2(less_equal(divide(a, idQa), idQ_idQa), true, divide(a, idQa), idQ_idQa), idQ_idQa), a)
% 157.11/20.45 = { by axiom 8 (closure) R->L }
% 157.11/20.45 divide(ifeq2(ifeq(quotient(idQ_idQa, divide(a, idQa), divide(idQ_idQa, divide(a, idQa))), true, less_equal(idQ_idQa, divide(a, idQa)), true), true, ifeq2(less_equal(divide(a, idQa), idQ_idQa), true, divide(a, idQa), idQ_idQa), idQ_idQa), a)
% 157.11/20.45 = { by axiom 7 (ifeq_axiom) R->L }
% 157.11/20.45 divide(ifeq2(ifeq(quotient(idQ_idQa, divide(a, idQa), ifeq2(true, true, divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa))), true, less_equal(idQ_idQa, divide(a, idQa)), true), true, ifeq2(less_equal(divide(a, idQa), idQ_idQa), true, divide(a, idQa), idQ_idQa), idQ_idQa), a)
% 157.11/20.45 = { by axiom 2 (zero_is_smallest) R->L }
% 157.11/20.45 divide(ifeq2(ifeq(quotient(idQ_idQa, divide(a, idQa), ifeq2(less_equal(zero, divide(idQ_idQa, divide(a, idQa))), true, divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa))), true, less_equal(idQ_idQa, divide(a, idQa)), true), true, ifeq2(less_equal(divide(a, idQa), idQ_idQa), true, divide(a, idQa), idQ_idQa), idQ_idQa), a)
% 157.11/20.45 = { by lemma 15 R->L }
% 157.11/20.45 divide(ifeq2(ifeq(quotient(idQ_idQa, divide(a, idQa), ifeq2(less_equal(divide(idQa, idQa), divide(idQ_idQa, divide(a, idQa))), true, divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa))), true, less_equal(idQ_idQa, divide(a, idQa)), true), true, ifeq2(less_equal(divide(a, idQa), idQ_idQa), true, divide(a, idQa), idQ_idQa), idQ_idQa), a)
% 157.11/20.45 = { by axiom 7 (ifeq_axiom) R->L }
% 157.11/20.45 divide(ifeq2(ifeq(quotient(idQ_idQa, divide(a, idQa), ifeq2(less_equal(divide(idQa, idQa), divide(idQ_idQa, divide(a, idQa))), true, ifeq2(true, true, divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa)), divide(idQa, idQa))), true, less_equal(idQ_idQa, divide(a, idQa)), true), true, ifeq2(less_equal(divide(a, idQa), idQ_idQa), true, divide(a, idQa), idQ_idQa), idQ_idQa), a)
% 157.11/20.45 = { by axiom 14 (quotient_property) R->L }
% 157.11/20.45 divide(ifeq2(ifeq(quotient(idQ_idQa, divide(a, idQa), ifeq2(less_equal(divide(idQa, idQa), divide(idQ_idQa, divide(a, idQa))), true, ifeq2(ifeq(quotient(idQ_idQa, divide(a, idQa), divide(idQ_idQa, divide(a, idQa))), true, ifeq(quotient(idQa, idQa, divide(idQa, idQa)), true, ifeq(quotient(a, idQa, divide(a, idQa)), true, ifeq(quotient(identity, idQa, idQ_idQa), true, ifeq(quotient(identity, a, idQa), true, less_equal(divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa)), true), true), true), true), true), true, divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa)), divide(idQa, idQa))), true, less_equal(idQ_idQa, divide(a, idQa)), true), true, ifeq2(less_equal(divide(a, idQa), idQ_idQa), true, divide(a, idQa), idQ_idQa), idQ_idQa), a)
% 157.11/20.45 = { by axiom 5 (identity_divide_a) }
% 157.11/20.45 divide(ifeq2(ifeq(quotient(idQ_idQa, divide(a, idQa), ifeq2(less_equal(divide(idQa, idQa), divide(idQ_idQa, divide(a, idQa))), true, ifeq2(ifeq(quotient(idQ_idQa, divide(a, idQa), divide(idQ_idQa, divide(a, idQa))), true, ifeq(quotient(idQa, idQa, divide(idQa, idQa)), true, ifeq(quotient(a, idQa, divide(a, idQa)), true, ifeq(quotient(identity, idQa, idQ_idQa), true, ifeq(true, true, less_equal(divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa)), true), true), true), true), true), true, divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa)), divide(idQa, idQa))), true, less_equal(idQ_idQa, divide(a, idQa)), true), true, ifeq2(less_equal(divide(a, idQa), idQ_idQa), true, divide(a, idQa), idQ_idQa), idQ_idQa), a)
% 157.11/20.45 = { by axiom 6 (ifeq_axiom) }
% 157.11/20.45 divide(ifeq2(ifeq(quotient(idQ_idQa, divide(a, idQa), ifeq2(less_equal(divide(idQa, idQa), divide(idQ_idQa, divide(a, idQa))), true, ifeq2(ifeq(quotient(idQ_idQa, divide(a, idQa), divide(idQ_idQa, divide(a, idQa))), true, ifeq(quotient(idQa, idQa, divide(idQa, idQa)), true, ifeq(quotient(a, idQa, divide(a, idQa)), true, ifeq(quotient(identity, idQa, idQ_idQa), true, less_equal(divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa)), true), true), true), true), true, divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa)), divide(idQa, idQa))), true, less_equal(idQ_idQa, divide(a, idQa)), true), true, ifeq2(less_equal(divide(a, idQa), idQ_idQa), true, divide(a, idQa), idQ_idQa), idQ_idQa), a)
% 157.11/20.45 = { by axiom 4 (identity_divide_idQa) }
% 157.11/20.45 divide(ifeq2(ifeq(quotient(idQ_idQa, divide(a, idQa), ifeq2(less_equal(divide(idQa, idQa), divide(idQ_idQa, divide(a, idQa))), true, ifeq2(ifeq(quotient(idQ_idQa, divide(a, idQa), divide(idQ_idQa, divide(a, idQa))), true, ifeq(quotient(idQa, idQa, divide(idQa, idQa)), true, ifeq(quotient(a, idQa, divide(a, idQa)), true, ifeq(true, true, less_equal(divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa)), true), true), true), true), true, divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa)), divide(idQa, idQa))), true, less_equal(idQ_idQa, divide(a, idQa)), true), true, ifeq2(less_equal(divide(a, idQa), idQ_idQa), true, divide(a, idQa), idQ_idQa), idQ_idQa), a)
% 157.11/20.45 = { by axiom 6 (ifeq_axiom) }
% 157.11/20.45 divide(ifeq2(ifeq(quotient(idQ_idQa, divide(a, idQa), ifeq2(less_equal(divide(idQa, idQa), divide(idQ_idQa, divide(a, idQa))), true, ifeq2(ifeq(quotient(idQ_idQa, divide(a, idQa), divide(idQ_idQa, divide(a, idQa))), true, ifeq(quotient(idQa, idQa, divide(idQa, idQa)), true, ifeq(quotient(a, idQa, divide(a, idQa)), true, less_equal(divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa)), true), true), true), true, divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa)), divide(idQa, idQa))), true, less_equal(idQ_idQa, divide(a, idQa)), true), true, ifeq2(less_equal(divide(a, idQa), idQ_idQa), true, divide(a, idQa), idQ_idQa), idQ_idQa), a)
% 157.11/20.45 = { by axiom 8 (closure) }
% 157.11/20.45 divide(ifeq2(ifeq(quotient(idQ_idQa, divide(a, idQa), ifeq2(less_equal(divide(idQa, idQa), divide(idQ_idQa, divide(a, idQa))), true, ifeq2(ifeq(quotient(idQ_idQa, divide(a, idQa), divide(idQ_idQa, divide(a, idQa))), true, ifeq(true, true, ifeq(quotient(a, idQa, divide(a, idQa)), true, less_equal(divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa)), true), true), true), true, divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa)), divide(idQa, idQa))), true, less_equal(idQ_idQa, divide(a, idQa)), true), true, ifeq2(less_equal(divide(a, idQa), idQ_idQa), true, divide(a, idQa), idQ_idQa), idQ_idQa), a)
% 157.11/20.45 = { by axiom 6 (ifeq_axiom) }
% 157.11/20.45 divide(ifeq2(ifeq(quotient(idQ_idQa, divide(a, idQa), ifeq2(less_equal(divide(idQa, idQa), divide(idQ_idQa, divide(a, idQa))), true, ifeq2(ifeq(quotient(idQ_idQa, divide(a, idQa), divide(idQ_idQa, divide(a, idQa))), true, ifeq(quotient(a, idQa, divide(a, idQa)), true, less_equal(divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa)), true), true), true, divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa)), divide(idQa, idQa))), true, less_equal(idQ_idQa, divide(a, idQa)), true), true, ifeq2(less_equal(divide(a, idQa), idQ_idQa), true, divide(a, idQa), idQ_idQa), idQ_idQa), a)
% 157.11/20.45 = { by axiom 8 (closure) }
% 157.11/20.45 divide(ifeq2(ifeq(quotient(idQ_idQa, divide(a, idQa), ifeq2(less_equal(divide(idQa, idQa), divide(idQ_idQa, divide(a, idQa))), true, ifeq2(ifeq(true, true, ifeq(quotient(a, idQa, divide(a, idQa)), true, less_equal(divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa)), true), true), true, divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa)), divide(idQa, idQa))), true, less_equal(idQ_idQa, divide(a, idQa)), true), true, ifeq2(less_equal(divide(a, idQa), idQ_idQa), true, divide(a, idQa), idQ_idQa), idQ_idQa), a)
% 157.11/20.45 = { by axiom 6 (ifeq_axiom) }
% 157.11/20.45 divide(ifeq2(ifeq(quotient(idQ_idQa, divide(a, idQa), ifeq2(less_equal(divide(idQa, idQa), divide(idQ_idQa, divide(a, idQa))), true, ifeq2(ifeq(quotient(a, idQa, divide(a, idQa)), true, less_equal(divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa)), true), true, divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa)), divide(idQa, idQa))), true, less_equal(idQ_idQa, divide(a, idQa)), true), true, ifeq2(less_equal(divide(a, idQa), idQ_idQa), true, divide(a, idQa), idQ_idQa), idQ_idQa), a)
% 157.11/20.45 = { by axiom 8 (closure) }
% 157.11/20.45 divide(ifeq2(ifeq(quotient(idQ_idQa, divide(a, idQa), ifeq2(less_equal(divide(idQa, idQa), divide(idQ_idQa, divide(a, idQa))), true, ifeq2(ifeq(true, true, less_equal(divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa)), true), true, divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa)), divide(idQa, idQa))), true, less_equal(idQ_idQa, divide(a, idQa)), true), true, ifeq2(less_equal(divide(a, idQa), idQ_idQa), true, divide(a, idQa), idQ_idQa), idQ_idQa), a)
% 157.11/20.45 = { by axiom 6 (ifeq_axiom) }
% 157.11/20.45 divide(ifeq2(ifeq(quotient(idQ_idQa, divide(a, idQa), ifeq2(less_equal(divide(idQa, idQa), divide(idQ_idQa, divide(a, idQa))), true, ifeq2(less_equal(divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa)), true, divide(idQ_idQa, divide(a, idQa)), divide(idQa, idQa)), divide(idQa, idQa))), true, less_equal(idQ_idQa, divide(a, idQa)), true), true, ifeq2(less_equal(divide(a, idQa), idQ_idQa), true, divide(a, idQa), idQ_idQa), idQ_idQa), a)
% 157.11/20.46 = { by axiom 12 (less_equal_and_equal) }
% 157.11/20.46 divide(ifeq2(ifeq(quotient(idQ_idQa, divide(a, idQa), divide(idQa, idQa)), true, less_equal(idQ_idQa, divide(a, idQa)), true), true, ifeq2(less_equal(divide(a, idQa), idQ_idQa), true, divide(a, idQa), idQ_idQa), idQ_idQa), a)
% 157.11/20.46 = { by lemma 15 }
% 157.11/20.46 divide(ifeq2(ifeq(quotient(idQ_idQa, divide(a, idQa), zero), true, less_equal(idQ_idQa, divide(a, idQa)), true), true, ifeq2(less_equal(divide(a, idQa), idQ_idQa), true, divide(a, idQa), idQ_idQa), idQ_idQa), a)
% 157.11/20.46 = { by axiom 11 (less_equal_quotient) }
% 157.11/20.46 divide(ifeq2(true, true, ifeq2(less_equal(divide(a, idQa), idQ_idQa), true, divide(a, idQa), idQ_idQa), idQ_idQa), a)
% 157.11/20.46 = { by axiom 7 (ifeq_axiom) }
% 157.11/20.46 divide(ifeq2(less_equal(divide(a, idQa), idQ_idQa), true, divide(a, idQa), idQ_idQa), a)
% 157.11/20.46 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.46 divide(ifeq2(ifeq(true, true, less_equal(divide(a, idQa), idQ_idQa), true), true, divide(a, idQa), idQ_idQa), a)
% 157.11/20.46 = { by axiom 8 (closure) R->L }
% 157.11/20.46 divide(ifeq2(ifeq(quotient(divide(a, idQa), idQ_idQa, divide(divide(a, idQa), idQ_idQa)), true, less_equal(divide(a, idQa), idQ_idQa), true), true, divide(a, idQa), idQ_idQa), a)
% 157.11/20.46 = { by lemma 17 }
% 157.11/20.46 divide(ifeq2(ifeq(quotient(divide(a, idQa), idQ_idQa, zero), true, less_equal(divide(a, idQa), idQ_idQa), true), true, divide(a, idQa), idQ_idQa), a)
% 157.11/20.46 = { by axiom 11 (less_equal_quotient) }
% 157.11/20.46 divide(ifeq2(true, true, divide(a, idQa), idQ_idQa), a)
% 157.11/20.46 = { by axiom 7 (ifeq_axiom) }
% 157.11/20.46 divide(divide(a, idQa), a)
% 157.11/20.46 = { by axiom 7 (ifeq_axiom) R->L }
% 157.11/20.46 ifeq2(true, true, divide(divide(a, idQa), a), zero)
% 157.11/20.46 = { by axiom 9 (quotient_less_equal) R->L }
% 157.11/20.46 ifeq2(ifeq(less_equal(divide(a, idQa), a), true, quotient(divide(a, idQa), a, zero), true), true, divide(divide(a, idQa), a), zero)
% 157.11/20.46 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.46 ifeq2(ifeq(ifeq(true, true, less_equal(divide(a, idQa), a), true), true, quotient(divide(a, idQa), a, zero), true), true, divide(divide(a, idQa), a), zero)
% 157.11/20.46 = { by axiom 8 (closure) R->L }
% 157.11/20.46 ifeq2(ifeq(ifeq(quotient(a, idQa, divide(a, idQa)), true, less_equal(divide(a, idQa), a), true), true, quotient(divide(a, idQa), a, zero), true), true, divide(divide(a, idQa), a), zero)
% 157.11/20.46 = { by axiom 10 (divisor_existence) }
% 157.11/20.46 ifeq2(ifeq(true, true, quotient(divide(a, idQa), a, zero), true), true, divide(divide(a, idQa), a), zero)
% 157.11/20.46 = { by axiom 6 (ifeq_axiom) }
% 157.11/20.46 ifeq2(quotient(divide(a, idQa), a, zero), true, divide(divide(a, idQa), a), zero)
% 157.11/20.46 = { by axiom 7 (ifeq_axiom) R->L }
% 157.11/20.46 ifeq2(quotient(divide(a, idQa), a, zero), true, ifeq2(true, true, divide(divide(a, idQa), a), zero), zero)
% 157.11/20.46 = { by axiom 8 (closure) R->L }
% 157.11/20.46 ifeq2(quotient(divide(a, idQa), a, zero), true, ifeq2(quotient(divide(a, idQa), a, divide(divide(a, idQa), a)), true, divide(divide(a, idQa), a), zero), zero)
% 157.11/20.46 = { by axiom 13 (well_defined) }
% 157.11/20.46 zero
% 157.11/20.46
% 157.11/20.46 Lemma 19: divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)) = zero.
% 157.11/20.46 Proof:
% 157.11/20.46 divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))
% 157.11/20.46 = { by axiom 12 (less_equal_and_equal) R->L }
% 157.11/20.46 ifeq2(less_equal(divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)), zero), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), true, zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)))
% 157.11/20.46 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.46 ifeq2(ifeq(true, true, less_equal(divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), true, zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)))
% 157.11/20.46 = { by axiom 8 (closure) R->L }
% 157.11/20.46 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, X, divide(idQa_Q__idQ_idQa, X)), true, less_equal(divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), true, zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)))
% 157.11/20.46 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.46 ifeq2(ifeq(true, true, ifeq(quotient(idQa_Q__idQ_idQa, X, divide(idQa_Q__idQ_idQa, X)), true, less_equal(divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), true, zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)))
% 157.11/20.46 = { by axiom 8 (closure) R->L }
% 157.11/20.46 ifeq2(ifeq(quotient(idQa, X, divide(idQa, X)), true, ifeq(quotient(idQa_Q__idQ_idQa, X, divide(idQa_Q__idQ_idQa, X)), true, less_equal(divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), true, zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)))
% 157.11/20.46 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.46 ifeq2(ifeq(quotient(idQa, X, divide(idQa, X)), true, ifeq(quotient(idQa_Q__idQ_idQa, X, divide(idQa_Q__idQ_idQa, X)), true, ifeq(true, true, less_equal(divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), true, zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)))
% 157.11/20.46 = { by axiom 9 (quotient_less_equal) R->L }
% 157.11/20.46 ifeq2(ifeq(quotient(idQa, X, divide(idQa, X)), true, ifeq(quotient(idQa_Q__idQ_idQa, X, divide(idQa_Q__idQ_idQa, X)), true, ifeq(ifeq(less_equal(idQa_Q__idQ_idQa, idQa), true, quotient(idQa_Q__idQ_idQa, idQa, zero), true), true, less_equal(divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), true, zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)))
% 157.11/20.46 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.46 ifeq2(ifeq(quotient(idQa, X, divide(idQa, X)), true, ifeq(quotient(idQa_Q__idQ_idQa, X, divide(idQa_Q__idQ_idQa, X)), true, ifeq(ifeq(ifeq(true, true, less_equal(idQa_Q__idQ_idQa, idQa), true), true, quotient(idQa_Q__idQ_idQa, idQa, zero), true), true, less_equal(divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), true, zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)))
% 157.11/20.46 = { by axiom 3 (identity_divide_idQ_idQa) R->L }
% 157.11/20.46 ifeq2(ifeq(quotient(idQa, X, divide(idQa, X)), true, ifeq(quotient(idQa_Q__idQ_idQa, X, divide(idQa_Q__idQ_idQa, X)), true, ifeq(ifeq(ifeq(quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa), true, less_equal(idQa_Q__idQ_idQa, idQa), true), true, quotient(idQa_Q__idQ_idQa, idQa, zero), true), true, less_equal(divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), true, zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)))
% 157.11/20.46 = { by axiom 10 (divisor_existence) }
% 157.11/20.46 ifeq2(ifeq(quotient(idQa, X, divide(idQa, X)), true, ifeq(quotient(idQa_Q__idQ_idQa, X, divide(idQa_Q__idQ_idQa, X)), true, ifeq(ifeq(true, true, quotient(idQa_Q__idQ_idQa, idQa, zero), true), true, less_equal(divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), true, zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)))
% 157.11/20.46 = { by axiom 6 (ifeq_axiom) }
% 157.11/20.46 ifeq2(ifeq(quotient(idQa, X, divide(idQa, X)), true, ifeq(quotient(idQa_Q__idQ_idQa, X, divide(idQa_Q__idQ_idQa, X)), true, ifeq(quotient(idQa_Q__idQ_idQa, idQa, zero), true, less_equal(divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), true, zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)))
% 157.11/20.46 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.46 ifeq2(ifeq(true, true, ifeq(quotient(idQa, X, divide(idQa, X)), true, ifeq(quotient(idQa_Q__idQ_idQa, X, divide(idQa_Q__idQ_idQa, X)), true, ifeq(quotient(idQa_Q__idQ_idQa, idQa, zero), true, less_equal(divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), true, zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)))
% 157.11/20.46 = { by axiom 9 (quotient_less_equal) R->L }
% 157.11/20.46 ifeq2(ifeq(ifeq(less_equal(zero, X), true, quotient(zero, X, zero), true), true, ifeq(quotient(idQa, X, divide(idQa, X)), true, ifeq(quotient(idQa_Q__idQ_idQa, X, divide(idQa_Q__idQ_idQa, X)), true, ifeq(quotient(idQa_Q__idQ_idQa, idQa, zero), true, less_equal(divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), true, zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)))
% 157.11/20.46 = { by axiom 2 (zero_is_smallest) }
% 157.11/20.46 ifeq2(ifeq(ifeq(true, true, quotient(zero, X, zero), true), true, ifeq(quotient(idQa, X, divide(idQa, X)), true, ifeq(quotient(idQa_Q__idQ_idQa, X, divide(idQa_Q__idQ_idQa, X)), true, ifeq(quotient(idQa_Q__idQ_idQa, idQa, zero), true, less_equal(divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), true, zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)))
% 157.11/20.46 = { by axiom 6 (ifeq_axiom) }
% 157.11/20.46 ifeq2(ifeq(quotient(zero, X, zero), true, ifeq(quotient(idQa, X, divide(idQa, X)), true, ifeq(quotient(idQa_Q__idQ_idQa, X, divide(idQa_Q__idQ_idQa, X)), true, ifeq(quotient(idQa_Q__idQ_idQa, idQa, zero), true, less_equal(divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), true, zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)))
% 157.11/20.46 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.46 ifeq2(ifeq(true, true, ifeq(quotient(zero, X, zero), true, ifeq(quotient(idQa, X, divide(idQa, X)), true, ifeq(quotient(idQa_Q__idQ_idQa, X, divide(idQa_Q__idQ_idQa, X)), true, ifeq(quotient(idQa_Q__idQ_idQa, idQa, zero), true, less_equal(divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), true, zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)))
% 157.11/20.46 = { by axiom 8 (closure) R->L }
% 157.11/20.46 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, X), divide(idQa, X), divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), true, ifeq(quotient(zero, X, zero), true, ifeq(quotient(idQa, X, divide(idQa, X)), true, ifeq(quotient(idQa_Q__idQ_idQa, X, divide(idQa_Q__idQ_idQa, X)), true, ifeq(quotient(idQa_Q__idQ_idQa, idQa, zero), true, less_equal(divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), true, zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)))
% 157.11/20.46 = { by axiom 14 (quotient_property) }
% 157.11/20.46 ifeq2(true, true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), true, zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)))
% 157.11/20.46 = { by axiom 7 (ifeq_axiom) }
% 157.11/20.46 ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X))), true, zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)))
% 157.11/20.46 = { by axiom 2 (zero_is_smallest) }
% 157.11/20.46 ifeq2(true, true, zero, divide(divide(idQa_Q__idQ_idQa, X), divide(idQa, X)))
% 157.11/20.46 = { by axiom 7 (ifeq_axiom) }
% 157.11/20.46 zero
% 157.11/20.46
% 157.11/20.46 Lemma 20: divide(idQa_Q__idQ_idQa, a) = divide(idQa, zero).
% 157.11/20.46 Proof:
% 157.11/20.46 divide(idQa_Q__idQ_idQa, a)
% 157.11/20.46 = { by axiom 12 (less_equal_and_equal) R->L }
% 157.11/20.46 ifeq2(less_equal(divide(idQa_Q__idQ_idQa, a), divide(idQa, a)), true, ifeq2(less_equal(divide(idQa, a), divide(idQa_Q__idQ_idQa, a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 157.11/20.46 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.46 ifeq2(ifeq(true, true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(idQa, a)), true), true, ifeq2(less_equal(divide(idQa, a), divide(idQa_Q__idQ_idQa, a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 157.11/20.46 = { by axiom 8 (closure) R->L }
% 157.11/20.46 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(idQa, a), divide(divide(idQa_Q__idQ_idQa, a), divide(idQa, a))), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(idQa, a)), true), true, ifeq2(less_equal(divide(idQa, a), divide(idQa_Q__idQ_idQa, a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 157.11/20.46 = { by lemma 19 }
% 157.11/20.46 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(idQa, a), zero), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(idQa, a)), true), true, ifeq2(less_equal(divide(idQa, a), divide(idQa_Q__idQ_idQa, a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 157.11/20.46 = { by axiom 11 (less_equal_quotient) }
% 157.11/20.46 ifeq2(true, true, ifeq2(less_equal(divide(idQa, a), divide(idQa_Q__idQ_idQa, a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 157.11/20.46 = { by axiom 7 (ifeq_axiom) }
% 157.11/20.46 ifeq2(less_equal(divide(idQa, a), divide(idQa_Q__idQ_idQa, a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 157.11/20.46 = { by lemma 16 }
% 157.11/20.46 ifeq2(less_equal(divide(idQa, zero), divide(idQa_Q__idQ_idQa, a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 157.11/20.46 = { by lemma 18 R->L }
% 157.11/20.46 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 157.11/20.46 = { by axiom 12 (less_equal_and_equal) R->L }
% 157.11/20.46 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(less_equal(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), true, ifeq2(less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 157.11/20.46 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.46 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(true, true, less_equal(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), true), true, ifeq2(less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 157.11/20.46 = { by axiom 8 (closure) R->L }
% 157.11/20.46 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, less_equal(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), true), true, ifeq2(less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 157.11/20.46 = { by axiom 12 (less_equal_and_equal) R->L }
% 157.11/20.46 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), ifeq2(less_equal(divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), zero), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)))), true, less_equal(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), true), true, ifeq2(less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 157.11/20.46 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.46 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), ifeq2(ifeq(true, true, less_equal(divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), zero), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)))), true, less_equal(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), true), true, ifeq2(less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 157.11/20.46 = { by axiom 8 (closure) R->L }
% 157.11/20.46 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), ifeq2(ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, less_equal(divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), zero), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)))), true, less_equal(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), true), true, ifeq2(less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 157.11/20.47 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.47 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), ifeq2(ifeq(true, true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, less_equal(divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), zero), true), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)))), true, less_equal(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), true), true, ifeq2(less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 157.11/20.47 = { by axiom 8 (closure) R->L }
% 157.11/20.47 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, less_equal(divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), zero), true), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)))), true, less_equal(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), true), true, ifeq2(less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 157.11/20.47 = { by axiom 6 (ifeq_axiom) R->L }
% 157.11/20.47 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, ifeq(true, true, less_equal(divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)))), true, less_equal(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), true), true, ifeq2(less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 157.11/20.47 = { by axiom 9 (quotient_less_equal) R->L }
% 157.11/20.47 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, ifeq(ifeq(less_equal(idQa, identity), true, quotient(idQa, identity, zero), true), true, less_equal(divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)))), true, less_equal(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), true), true, ifeq2(less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 157.11/20.47 = { by axiom 1 (identity_is_largest) }
% 157.11/20.47 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, ifeq(ifeq(true, true, quotient(idQa, identity, zero), true), true, less_equal(divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)))), true, less_equal(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), true), true, ifeq2(less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 157.11/20.47 = { by axiom 6 (ifeq_axiom) }
% 157.11/20.47 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, ifeq(quotient(idQa, identity, zero), true, less_equal(divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)))), true, less_equal(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), true), true, ifeq2(less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.47 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.47 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, ifeq(true, true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, ifeq(quotient(idQa, identity, zero), true, less_equal(divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)))), true, less_equal(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), true), true, ifeq2(less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.47 = { by axiom 9 (quotient_less_equal) R->L }
% 158.37/20.47 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, ifeq(ifeq(less_equal(zero, idQ_idQa), true, quotient(zero, idQ_idQa, zero), true), true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, ifeq(quotient(idQa, identity, zero), true, less_equal(divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)))), true, less_equal(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), true), true, ifeq2(less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.47 = { by axiom 2 (zero_is_smallest) }
% 158.37/20.47 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, ifeq(ifeq(true, true, quotient(zero, idQ_idQa, zero), true), true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, ifeq(quotient(idQa, identity, zero), true, less_equal(divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)))), true, less_equal(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), true), true, ifeq2(less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.47 = { by axiom 6 (ifeq_axiom) }
% 158.37/20.47 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, ifeq(quotient(zero, idQ_idQa, zero), true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, ifeq(quotient(idQa, identity, zero), true, less_equal(divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)))), true, less_equal(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), true), true, ifeq2(less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.47 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.47 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, ifeq(quotient(zero, idQ_idQa, zero), true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, ifeq(true, true, ifeq(quotient(idQa, identity, zero), true, less_equal(divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)))), true, less_equal(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), true), true, ifeq2(less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.47 = { by axiom 3 (identity_divide_idQ_idQa) R->L }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, ifeq(quotient(zero, idQ_idQa, zero), true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, ifeq(quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa), true, ifeq(quotient(idQa, identity, zero), true, less_equal(divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)))), true, less_equal(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), true), true, ifeq2(less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 14 (quotient_property) }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), ifeq2(true, true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)))), true, less_equal(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), true), true, ifeq2(less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 7 (ifeq_axiom) }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa))), true, zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)))), true, less_equal(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), true), true, ifeq2(less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 2 (zero_is_smallest) }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), ifeq2(true, true, zero, divide(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)))), true, less_equal(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), true), true, ifeq2(less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 7 (ifeq_axiom) }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(identity, idQ_idQa), zero), true, less_equal(idQa_Q__idQ_idQa, divide(identity, idQ_idQa)), true), true, ifeq2(less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 11 (less_equal_quotient) }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(true, true, ifeq2(less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 7 (ifeq_axiom) }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(true, true, less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 8 (closure) R->L }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(divide(identity, idQ_idQa), idQa_Q__idQ_idQa, divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), true, less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 12 (less_equal_and_equal) R->L }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(divide(identity, idQ_idQa), idQa_Q__idQ_idQa, ifeq2(less_equal(divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), divide(divide(identity, idQa), idQ_idQa)), true, ifeq2(less_equal(divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), true, divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa))), true, less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(divide(identity, idQ_idQa), idQa_Q__idQ_idQa, ifeq2(ifeq(true, true, less_equal(divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), divide(divide(identity, idQa), idQ_idQa)), true), true, ifeq2(less_equal(divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), true, divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa))), true, less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 8 (closure) R->L }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(divide(identity, idQ_idQa), idQa_Q__idQ_idQa, ifeq2(ifeq(quotient(identity, idQa, divide(identity, idQa)), true, less_equal(divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), divide(divide(identity, idQa), idQ_idQa)), true), true, ifeq2(less_equal(divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), true, divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa))), true, less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(divide(identity, idQ_idQa), idQa_Q__idQ_idQa, ifeq2(ifeq(true, true, ifeq(quotient(identity, idQa, divide(identity, idQa)), true, less_equal(divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), divide(divide(identity, idQa), idQ_idQa)), true), true), true, ifeq2(less_equal(divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), true, divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa))), true, less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 8 (closure) R->L }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(divide(identity, idQ_idQa), idQa_Q__idQ_idQa, ifeq2(ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, ifeq(quotient(identity, idQa, divide(identity, idQa)), true, less_equal(divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), divide(divide(identity, idQa), idQ_idQa)), true), true), true, ifeq2(less_equal(divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), true, divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa))), true, less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(divide(identity, idQ_idQa), idQa_Q__idQ_idQa, ifeq2(ifeq(true, true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, ifeq(quotient(identity, idQa, divide(identity, idQa)), true, less_equal(divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), divide(divide(identity, idQa), idQ_idQa)), true), true), true), true, ifeq2(less_equal(divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), true, divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa))), true, less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 8 (closure) R->L }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(divide(identity, idQ_idQa), idQa_Q__idQ_idQa, ifeq2(ifeq(quotient(divide(identity, idQa), idQ_idQa, divide(divide(identity, idQa), idQ_idQa)), true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, ifeq(quotient(identity, idQa, divide(identity, idQa)), true, less_equal(divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), divide(divide(identity, idQa), idQ_idQa)), true), true), true), true, ifeq2(less_equal(divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), true, divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa))), true, less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(divide(identity, idQ_idQa), idQa_Q__idQ_idQa, ifeq2(ifeq(true, true, ifeq(quotient(divide(identity, idQa), idQ_idQa, divide(divide(identity, idQa), idQ_idQa)), true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, ifeq(quotient(identity, idQa, divide(identity, idQa)), true, less_equal(divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), divide(divide(identity, idQa), idQ_idQa)), true), true), true), true), true, ifeq2(less_equal(divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), true, divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa))), true, less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 8 (closure) R->L }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(divide(identity, idQ_idQa), idQa_Q__idQ_idQa, ifeq2(ifeq(quotient(divide(identity, idQ_idQa), idQa_Q__idQ_idQa, divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), true, ifeq(quotient(divide(identity, idQa), idQ_idQa, divide(divide(identity, idQa), idQ_idQa)), true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, ifeq(quotient(identity, idQa, divide(identity, idQa)), true, less_equal(divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), divide(divide(identity, idQa), idQ_idQa)), true), true), true), true), true, ifeq2(less_equal(divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), true, divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa))), true, less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(divide(identity, idQ_idQa), idQa_Q__idQ_idQa, ifeq2(ifeq(quotient(divide(identity, idQ_idQa), idQa_Q__idQ_idQa, divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), true, ifeq(quotient(divide(identity, idQa), idQ_idQa, divide(divide(identity, idQa), idQ_idQa)), true, ifeq(true, true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, ifeq(quotient(identity, idQa, divide(identity, idQa)), true, less_equal(divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), divide(divide(identity, idQa), idQ_idQa)), true), true), true), true), true), true, ifeq2(less_equal(divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), true, divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa))), true, less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 3 (identity_divide_idQ_idQa) R->L }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(divide(identity, idQ_idQa), idQa_Q__idQ_idQa, ifeq2(ifeq(quotient(divide(identity, idQ_idQa), idQa_Q__idQ_idQa, divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), true, ifeq(quotient(divide(identity, idQa), idQ_idQa, divide(divide(identity, idQa), idQ_idQa)), true, ifeq(quotient(idQa, idQ_idQa, idQa_Q__idQ_idQa), true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, ifeq(quotient(identity, idQa, divide(identity, idQa)), true, less_equal(divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), divide(divide(identity, idQa), idQ_idQa)), true), true), true), true), true), true, ifeq2(less_equal(divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), true, divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa))), true, less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 14 (quotient_property) }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(divide(identity, idQ_idQa), idQa_Q__idQ_idQa, ifeq2(true, true, ifeq2(less_equal(divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), true, divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa))), true, less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 7 (ifeq_axiom) }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(divide(identity, idQ_idQa), idQa_Q__idQ_idQa, ifeq2(less_equal(divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), true, divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa))), true, less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by lemma 17 }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(divide(identity, idQ_idQa), idQa_Q__idQ_idQa, ifeq2(less_equal(zero, divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa)), true, divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa))), true, less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 2 (zero_is_smallest) }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(divide(identity, idQ_idQa), idQa_Q__idQ_idQa, ifeq2(true, true, divide(divide(identity, idQa), idQ_idQa), divide(divide(identity, idQ_idQa), idQa_Q__idQ_idQa))), true, less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 7 (ifeq_axiom) }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(divide(identity, idQ_idQa), idQa_Q__idQ_idQa, divide(divide(identity, idQa), idQ_idQa)), true, less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by lemma 17 }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(ifeq(quotient(divide(identity, idQ_idQa), idQa_Q__idQ_idQa, zero), true, less_equal(divide(identity, idQ_idQa), idQa_Q__idQ_idQa), true), true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 11 (less_equal_quotient) }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(ifeq2(true, true, divide(identity, idQ_idQa), idQa_Q__idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 7 (ifeq_axiom) }
% 158.37/20.48 ifeq2(less_equal(divide(idQa, divide(idQ_idQa, a)), divide(divide(identity, idQ_idQa), a)), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.48 ifeq2(ifeq(true, true, less_equal(divide(idQa, divide(idQ_idQa, a)), divide(divide(identity, idQ_idQa), a)), true), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 8 (closure) R->L }
% 158.37/20.48 ifeq2(ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, less_equal(divide(idQa, divide(idQ_idQa, a)), divide(divide(identity, idQ_idQa), a)), true), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.48 ifeq2(ifeq(true, true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, less_equal(divide(idQa, divide(idQ_idQa, a)), divide(divide(identity, idQ_idQa), a)), true), true), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 8 (closure) R->L }
% 158.37/20.48 ifeq2(ifeq(quotient(idQ_idQa, a, divide(idQ_idQa, a)), true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, less_equal(divide(idQa, divide(idQ_idQa, a)), divide(divide(identity, idQ_idQa), a)), true), true), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.48 ifeq2(ifeq(true, true, ifeq(quotient(idQ_idQa, a, divide(idQ_idQa, a)), true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, less_equal(divide(idQa, divide(idQ_idQa, a)), divide(divide(identity, idQ_idQa), a)), true), true), true), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 8 (closure) R->L }
% 158.37/20.48 ifeq2(ifeq(quotient(divide(identity, idQ_idQa), a, divide(divide(identity, idQ_idQa), a)), true, ifeq(quotient(idQ_idQa, a, divide(idQ_idQa, a)), true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, less_equal(divide(idQa, divide(idQ_idQa, a)), divide(divide(identity, idQ_idQa), a)), true), true), true), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.48 ifeq2(ifeq(true, true, ifeq(quotient(divide(identity, idQ_idQa), a, divide(divide(identity, idQ_idQa), a)), true, ifeq(quotient(idQ_idQa, a, divide(idQ_idQa, a)), true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, less_equal(divide(idQa, divide(idQ_idQa, a)), divide(divide(identity, idQ_idQa), a)), true), true), true), true), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.48 = { by axiom 8 (closure) R->L }
% 158.37/20.48 ifeq2(ifeq(quotient(idQa, divide(idQ_idQa, a), divide(idQa, divide(idQ_idQa, a))), true, ifeq(quotient(divide(identity, idQ_idQa), a, divide(divide(identity, idQ_idQa), a)), true, ifeq(quotient(idQ_idQa, a, divide(idQ_idQa, a)), true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, less_equal(divide(idQa, divide(idQ_idQa, a)), divide(divide(identity, idQ_idQa), a)), true), true), true), true), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.49 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.49 ifeq2(ifeq(quotient(idQa, divide(idQ_idQa, a), divide(idQa, divide(idQ_idQa, a))), true, ifeq(quotient(divide(identity, idQ_idQa), a, divide(divide(identity, idQ_idQa), a)), true, ifeq(quotient(idQ_idQa, a, divide(idQ_idQa, a)), true, ifeq(true, true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, less_equal(divide(idQa, divide(idQ_idQa, a)), divide(divide(identity, idQ_idQa), a)), true), true), true), true), true), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.49 = { by axiom 5 (identity_divide_a) R->L }
% 158.37/20.49 ifeq2(ifeq(quotient(idQa, divide(idQ_idQa, a), divide(idQa, divide(idQ_idQa, a))), true, ifeq(quotient(divide(identity, idQ_idQa), a, divide(divide(identity, idQ_idQa), a)), true, ifeq(quotient(idQ_idQa, a, divide(idQ_idQa, a)), true, ifeq(quotient(identity, a, idQa), true, ifeq(quotient(identity, idQ_idQa, divide(identity, idQ_idQa)), true, less_equal(divide(idQa, divide(idQ_idQa, a)), divide(divide(identity, idQ_idQa), a)), true), true), true), true), true), true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.49 = { by axiom 14 (quotient_property) }
% 158.37/20.49 ifeq2(true, true, divide(idQa, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.49 = { by axiom 7 (ifeq_axiom) }
% 158.37/20.49 divide(idQa, a)
% 158.37/20.49 = { by lemma 16 }
% 158.37/20.49 divide(idQa, zero)
% 158.37/20.49
% 158.37/20.49 Lemma 21: divide(divide(X, idQa), a) = zero.
% 158.37/20.49 Proof:
% 158.37/20.49 divide(divide(X, idQa), a)
% 158.37/20.49 = { by axiom 12 (less_equal_and_equal) R->L }
% 158.37/20.49 ifeq2(less_equal(divide(divide(X, idQa), a), zero), true, ifeq2(less_equal(zero, divide(divide(X, idQa), a)), true, zero, divide(divide(X, idQa), a)), divide(divide(X, idQa), a))
% 158.37/20.49 = { by lemma 18 R->L }
% 158.37/20.49 ifeq2(less_equal(divide(divide(X, idQa), a), divide(idQ_idQa, a)), true, ifeq2(less_equal(zero, divide(divide(X, idQa), a)), true, zero, divide(divide(X, idQa), a)), divide(divide(X, idQa), a))
% 158.37/20.49 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.49 ifeq2(ifeq(true, true, less_equal(divide(divide(X, idQa), a), divide(idQ_idQa, a)), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), a)), true, zero, divide(divide(X, idQa), a)), divide(divide(X, idQa), a))
% 158.37/20.49 = { by axiom 8 (closure) R->L }
% 158.37/20.49 ifeq2(ifeq(quotient(divide(divide(X, idQa), a), divide(idQ_idQa, a), divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), true, less_equal(divide(divide(X, idQa), a), divide(idQ_idQa, a)), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), a)), true, zero, divide(divide(X, idQa), a)), divide(divide(X, idQa), a))
% 158.37/20.49 = { by axiom 12 (less_equal_and_equal) R->L }
% 158.37/20.49 ifeq2(ifeq(quotient(divide(divide(X, idQa), a), divide(idQ_idQa, a), ifeq2(less_equal(divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)), zero), true, ifeq2(less_equal(zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), true, zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)))), true, less_equal(divide(divide(X, idQa), a), divide(idQ_idQa, a)), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), a)), true, zero, divide(divide(X, idQa), a)), divide(divide(X, idQa), a))
% 158.37/20.49 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.49 ifeq2(ifeq(quotient(divide(divide(X, idQa), a), divide(idQ_idQa, a), ifeq2(ifeq(true, true, less_equal(divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)), zero), true), true, ifeq2(less_equal(zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), true, zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)))), true, less_equal(divide(divide(X, idQa), a), divide(idQ_idQa, a)), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), a)), true, zero, divide(divide(X, idQa), a)), divide(divide(X, idQa), a))
% 158.37/20.49 = { by axiom 8 (closure) R->L }
% 158.37/20.49 ifeq2(ifeq(quotient(divide(divide(X, idQa), a), divide(idQ_idQa, a), ifeq2(ifeq(quotient(divide(X, idQa), idQ_idQa, divide(divide(X, idQa), idQ_idQa)), true, less_equal(divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)), zero), true), true, ifeq2(less_equal(zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), true, zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)))), true, less_equal(divide(divide(X, idQa), a), divide(idQ_idQa, a)), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), a)), true, zero, divide(divide(X, idQa), a)), divide(divide(X, idQa), a))
% 158.37/20.49 = { by lemma 17 }
% 158.37/20.49 ifeq2(ifeq(quotient(divide(divide(X, idQa), a), divide(idQ_idQa, a), ifeq2(ifeq(quotient(divide(X, idQa), idQ_idQa, zero), true, less_equal(divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)), zero), true), true, ifeq2(less_equal(zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), true, zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)))), true, less_equal(divide(divide(X, idQa), a), divide(idQ_idQa, a)), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), a)), true, zero, divide(divide(X, idQa), a)), divide(divide(X, idQa), a))
% 158.37/20.49 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.49 ifeq2(ifeq(quotient(divide(divide(X, idQa), a), divide(idQ_idQa, a), ifeq2(ifeq(true, true, ifeq(quotient(divide(X, idQa), idQ_idQa, zero), true, less_equal(divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), true, zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)))), true, less_equal(divide(divide(X, idQa), a), divide(idQ_idQa, a)), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), a)), true, zero, divide(divide(X, idQa), a)), divide(divide(X, idQa), a))
% 158.37/20.49 = { by axiom 8 (closure) R->L }
% 158.37/20.49 ifeq2(ifeq(quotient(divide(divide(X, idQa), a), divide(idQ_idQa, a), ifeq2(ifeq(quotient(divide(X, idQa), a, divide(divide(X, idQa), a)), true, ifeq(quotient(divide(X, idQa), idQ_idQa, zero), true, less_equal(divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), true, zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)))), true, less_equal(divide(divide(X, idQa), a), divide(idQ_idQa, a)), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), a)), true, zero, divide(divide(X, idQa), a)), divide(divide(X, idQa), a))
% 158.37/20.49 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.49 ifeq2(ifeq(quotient(divide(divide(X, idQa), a), divide(idQ_idQa, a), ifeq2(ifeq(true, true, ifeq(quotient(divide(X, idQa), a, divide(divide(X, idQa), a)), true, ifeq(quotient(divide(X, idQa), idQ_idQa, zero), true, less_equal(divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), true, zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)))), true, less_equal(divide(divide(X, idQa), a), divide(idQ_idQa, a)), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), a)), true, zero, divide(divide(X, idQa), a)), divide(divide(X, idQa), a))
% 158.37/20.49 = { by axiom 8 (closure) R->L }
% 158.37/20.49 ifeq2(ifeq(quotient(divide(divide(X, idQa), a), divide(idQ_idQa, a), ifeq2(ifeq(quotient(idQ_idQa, a, divide(idQ_idQa, a)), true, ifeq(quotient(divide(X, idQa), a, divide(divide(X, idQa), a)), true, ifeq(quotient(divide(X, idQa), idQ_idQa, zero), true, less_equal(divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), true, zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)))), true, less_equal(divide(divide(X, idQa), a), divide(idQ_idQa, a)), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), a)), true, zero, divide(divide(X, idQa), a)), divide(divide(X, idQa), a))
% 158.37/20.49 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.49 ifeq2(ifeq(quotient(divide(divide(X, idQa), a), divide(idQ_idQa, a), ifeq2(ifeq(true, true, ifeq(quotient(idQ_idQa, a, divide(idQ_idQa, a)), true, ifeq(quotient(divide(X, idQa), a, divide(divide(X, idQa), a)), true, ifeq(quotient(divide(X, idQa), idQ_idQa, zero), true, less_equal(divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), true, zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)))), true, less_equal(divide(divide(X, idQa), a), divide(idQ_idQa, a)), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), a)), true, zero, divide(divide(X, idQa), a)), divide(divide(X, idQa), a))
% 158.37/20.49 = { by axiom 9 (quotient_less_equal) R->L }
% 158.37/20.49 ifeq2(ifeq(quotient(divide(divide(X, idQa), a), divide(idQ_idQa, a), ifeq2(ifeq(ifeq(less_equal(zero, a), true, quotient(zero, a, zero), true), true, ifeq(quotient(idQ_idQa, a, divide(idQ_idQa, a)), true, ifeq(quotient(divide(X, idQa), a, divide(divide(X, idQa), a)), true, ifeq(quotient(divide(X, idQa), idQ_idQa, zero), true, less_equal(divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), true, zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)))), true, less_equal(divide(divide(X, idQa), a), divide(idQ_idQa, a)), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), a)), true, zero, divide(divide(X, idQa), a)), divide(divide(X, idQa), a))
% 158.37/20.49 = { by axiom 2 (zero_is_smallest) }
% 158.37/20.49 ifeq2(ifeq(quotient(divide(divide(X, idQa), a), divide(idQ_idQa, a), ifeq2(ifeq(ifeq(true, true, quotient(zero, a, zero), true), true, ifeq(quotient(idQ_idQa, a, divide(idQ_idQa, a)), true, ifeq(quotient(divide(X, idQa), a, divide(divide(X, idQa), a)), true, ifeq(quotient(divide(X, idQa), idQ_idQa, zero), true, less_equal(divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), true, zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)))), true, less_equal(divide(divide(X, idQa), a), divide(idQ_idQa, a)), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), a)), true, zero, divide(divide(X, idQa), a)), divide(divide(X, idQa), a))
% 158.37/20.49 = { by axiom 6 (ifeq_axiom) }
% 158.37/20.49 ifeq2(ifeq(quotient(divide(divide(X, idQa), a), divide(idQ_idQa, a), ifeq2(ifeq(quotient(zero, a, zero), true, ifeq(quotient(idQ_idQa, a, divide(idQ_idQa, a)), true, ifeq(quotient(divide(X, idQa), a, divide(divide(X, idQa), a)), true, ifeq(quotient(divide(X, idQa), idQ_idQa, zero), true, less_equal(divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), true, zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)))), true, less_equal(divide(divide(X, idQa), a), divide(idQ_idQa, a)), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), a)), true, zero, divide(divide(X, idQa), a)), divide(divide(X, idQa), a))
% 158.37/20.49 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.49 ifeq2(ifeq(quotient(divide(divide(X, idQa), a), divide(idQ_idQa, a), ifeq2(ifeq(true, true, ifeq(quotient(zero, a, zero), true, ifeq(quotient(idQ_idQa, a, divide(idQ_idQa, a)), true, ifeq(quotient(divide(X, idQa), a, divide(divide(X, idQa), a)), true, ifeq(quotient(divide(X, idQa), idQ_idQa, zero), true, less_equal(divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), true, zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)))), true, less_equal(divide(divide(X, idQa), a), divide(idQ_idQa, a)), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), a)), true, zero, divide(divide(X, idQa), a)), divide(divide(X, idQa), a))
% 158.37/20.49 = { by axiom 8 (closure) R->L }
% 158.37/20.49 ifeq2(ifeq(quotient(divide(divide(X, idQa), a), divide(idQ_idQa, a), ifeq2(ifeq(quotient(divide(divide(X, idQa), a), divide(idQ_idQa, a), divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), true, ifeq(quotient(zero, a, zero), true, ifeq(quotient(idQ_idQa, a, divide(idQ_idQa, a)), true, ifeq(quotient(divide(X, idQa), a, divide(divide(X, idQa), a)), true, ifeq(quotient(divide(X, idQa), idQ_idQa, zero), true, less_equal(divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), true, zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)))), true, less_equal(divide(divide(X, idQa), a), divide(idQ_idQa, a)), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), a)), true, zero, divide(divide(X, idQa), a)), divide(divide(X, idQa), a))
% 158.37/20.49 = { by axiom 14 (quotient_property) }
% 158.37/20.49 ifeq2(ifeq(quotient(divide(divide(X, idQa), a), divide(idQ_idQa, a), ifeq2(true, true, ifeq2(less_equal(zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), true, zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)))), true, less_equal(divide(divide(X, idQa), a), divide(idQ_idQa, a)), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), a)), true, zero, divide(divide(X, idQa), a)), divide(divide(X, idQa), a))
% 158.37/20.49 = { by axiom 7 (ifeq_axiom) }
% 158.37/20.49 ifeq2(ifeq(quotient(divide(divide(X, idQa), a), divide(idQ_idQa, a), ifeq2(less_equal(zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a))), true, zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)))), true, less_equal(divide(divide(X, idQa), a), divide(idQ_idQa, a)), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), a)), true, zero, divide(divide(X, idQa), a)), divide(divide(X, idQa), a))
% 158.37/20.49 = { by axiom 2 (zero_is_smallest) }
% 158.37/20.49 ifeq2(ifeq(quotient(divide(divide(X, idQa), a), divide(idQ_idQa, a), ifeq2(true, true, zero, divide(divide(divide(X, idQa), a), divide(idQ_idQa, a)))), true, less_equal(divide(divide(X, idQa), a), divide(idQ_idQa, a)), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), a)), true, zero, divide(divide(X, idQa), a)), divide(divide(X, idQa), a))
% 158.37/20.49 = { by axiom 7 (ifeq_axiom) }
% 158.37/20.49 ifeq2(ifeq(quotient(divide(divide(X, idQa), a), divide(idQ_idQa, a), zero), true, less_equal(divide(divide(X, idQa), a), divide(idQ_idQa, a)), true), true, ifeq2(less_equal(zero, divide(divide(X, idQa), a)), true, zero, divide(divide(X, idQa), a)), divide(divide(X, idQa), a))
% 158.37/20.50 = { by axiom 11 (less_equal_quotient) }
% 158.37/20.50 ifeq2(true, true, ifeq2(less_equal(zero, divide(divide(X, idQa), a)), true, zero, divide(divide(X, idQa), a)), divide(divide(X, idQa), a))
% 158.37/20.50 = { by axiom 7 (ifeq_axiom) }
% 158.37/20.50 ifeq2(less_equal(zero, divide(divide(X, idQa), a)), true, zero, divide(divide(X, idQa), a))
% 158.37/20.50 = { by axiom 2 (zero_is_smallest) }
% 158.37/20.50 ifeq2(true, true, zero, divide(divide(X, idQa), a))
% 158.37/20.50 = { by axiom 7 (ifeq_axiom) }
% 158.37/20.50 zero
% 158.37/20.50
% 158.37/20.50 Goal 1 (prove_idQa_equals_idQa_Q__idQ_idQa): idQa = idQa_Q__idQ_idQa.
% 158.37/20.50 Proof:
% 158.37/20.50 idQa
% 158.37/20.50 = { by axiom 7 (ifeq_axiom) R->L }
% 158.37/20.50 ifeq2(true, true, idQa, divide(identity, a))
% 158.37/20.50 = { by axiom 8 (closure) R->L }
% 158.37/20.50 ifeq2(quotient(identity, a, divide(identity, a)), true, idQa, divide(identity, a))
% 158.37/20.50 = { by axiom 7 (ifeq_axiom) R->L }
% 158.37/20.50 ifeq2(quotient(identity, a, divide(identity, a)), true, ifeq2(true, true, idQa, divide(identity, a)), divide(identity, a))
% 158.37/20.50 = { by axiom 5 (identity_divide_a) R->L }
% 158.37/20.50 ifeq2(quotient(identity, a, divide(identity, a)), true, ifeq2(quotient(identity, a, idQa), true, idQa, divide(identity, a)), divide(identity, a))
% 158.37/20.50 = { by axiom 13 (well_defined) }
% 158.37/20.50 divide(identity, a)
% 158.37/20.50 = { by axiom 7 (ifeq_axiom) R->L }
% 158.37/20.50 ifeq2(true, true, divide(identity, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.50 = { by axiom 11 (less_equal_quotient) R->L }
% 158.37/20.50 ifeq2(ifeq(quotient(divide(identity, a), divide(idQa, zero), zero), true, less_equal(divide(identity, a), divide(idQa, zero)), true), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.50 = { by lemma 21 R->L }
% 158.37/20.50 ifeq2(ifeq(quotient(divide(identity, a), divide(idQa, zero), divide(divide(identity, idQa), a)), true, less_equal(divide(identity, a), divide(idQa, zero)), true), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.50 = { by axiom 12 (less_equal_and_equal) R->L }
% 158.37/20.50 ifeq2(ifeq(quotient(divide(identity, a), divide(idQa, zero), ifeq2(less_equal(divide(divide(identity, idQa), a), divide(divide(identity, a), divide(idQa, a))), true, ifeq2(less_equal(divide(divide(identity, a), divide(idQa, a)), divide(divide(identity, idQa), a)), true, divide(divide(identity, a), divide(idQa, a)), divide(divide(identity, idQa), a)), divide(divide(identity, idQa), a))), true, less_equal(divide(identity, a), divide(idQa, zero)), true), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.50 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.50 ifeq2(ifeq(quotient(divide(identity, a), divide(idQa, zero), ifeq2(less_equal(divide(divide(identity, idQa), a), divide(divide(identity, a), divide(idQa, a))), true, ifeq2(ifeq(true, true, less_equal(divide(divide(identity, a), divide(idQa, a)), divide(divide(identity, idQa), a)), true), true, divide(divide(identity, a), divide(idQa, a)), divide(divide(identity, idQa), a)), divide(divide(identity, idQa), a))), true, less_equal(divide(identity, a), divide(idQa, zero)), true), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.50 = { by axiom 8 (closure) R->L }
% 158.37/20.50 ifeq2(ifeq(quotient(divide(identity, a), divide(idQa, zero), ifeq2(less_equal(divide(divide(identity, idQa), a), divide(divide(identity, a), divide(idQa, a))), true, ifeq2(ifeq(quotient(identity, idQa, divide(identity, idQa)), true, less_equal(divide(divide(identity, a), divide(idQa, a)), divide(divide(identity, idQa), a)), true), true, divide(divide(identity, a), divide(idQa, a)), divide(divide(identity, idQa), a)), divide(divide(identity, idQa), a))), true, less_equal(divide(identity, a), divide(idQa, zero)), true), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.50 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.50 ifeq2(ifeq(quotient(divide(identity, a), divide(idQa, zero), ifeq2(less_equal(divide(divide(identity, idQa), a), divide(divide(identity, a), divide(idQa, a))), true, ifeq2(ifeq(true, true, ifeq(quotient(identity, idQa, divide(identity, idQa)), true, less_equal(divide(divide(identity, a), divide(idQa, a)), divide(divide(identity, idQa), a)), true), true), true, divide(divide(identity, a), divide(idQa, a)), divide(divide(identity, idQa), a)), divide(divide(identity, idQa), a))), true, less_equal(divide(identity, a), divide(idQa, zero)), true), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.50 = { by axiom 8 (closure) R->L }
% 158.37/20.50 ifeq2(ifeq(quotient(divide(identity, a), divide(idQa, zero), ifeq2(less_equal(divide(divide(identity, idQa), a), divide(divide(identity, a), divide(idQa, a))), true, ifeq2(ifeq(quotient(identity, a, divide(identity, a)), true, ifeq(quotient(identity, idQa, divide(identity, idQa)), true, less_equal(divide(divide(identity, a), divide(idQa, a)), divide(divide(identity, idQa), a)), true), true), true, divide(divide(identity, a), divide(idQa, a)), divide(divide(identity, idQa), a)), divide(divide(identity, idQa), a))), true, less_equal(divide(identity, a), divide(idQa, zero)), true), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.50 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.50 ifeq2(ifeq(quotient(divide(identity, a), divide(idQa, zero), ifeq2(less_equal(divide(divide(identity, idQa), a), divide(divide(identity, a), divide(idQa, a))), true, ifeq2(ifeq(true, true, ifeq(quotient(identity, a, divide(identity, a)), true, ifeq(quotient(identity, idQa, divide(identity, idQa)), true, less_equal(divide(divide(identity, a), divide(idQa, a)), divide(divide(identity, idQa), a)), true), true), true), true, divide(divide(identity, a), divide(idQa, a)), divide(divide(identity, idQa), a)), divide(divide(identity, idQa), a))), true, less_equal(divide(identity, a), divide(idQa, zero)), true), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.50 = { by axiom 8 (closure) R->L }
% 158.37/20.50 ifeq2(ifeq(quotient(divide(identity, a), divide(idQa, zero), ifeq2(less_equal(divide(divide(identity, idQa), a), divide(divide(identity, a), divide(idQa, a))), true, ifeq2(ifeq(quotient(idQa, a, divide(idQa, a)), true, ifeq(quotient(identity, a, divide(identity, a)), true, ifeq(quotient(identity, idQa, divide(identity, idQa)), true, less_equal(divide(divide(identity, a), divide(idQa, a)), divide(divide(identity, idQa), a)), true), true), true), true, divide(divide(identity, a), divide(idQa, a)), divide(divide(identity, idQa), a)), divide(divide(identity, idQa), a))), true, less_equal(divide(identity, a), divide(idQa, zero)), true), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.50 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.50 ifeq2(ifeq(quotient(divide(identity, a), divide(idQa, zero), ifeq2(less_equal(divide(divide(identity, idQa), a), divide(divide(identity, a), divide(idQa, a))), true, ifeq2(ifeq(true, true, ifeq(quotient(idQa, a, divide(idQa, a)), true, ifeq(quotient(identity, a, divide(identity, a)), true, ifeq(quotient(identity, idQa, divide(identity, idQa)), true, less_equal(divide(divide(identity, a), divide(idQa, a)), divide(divide(identity, idQa), a)), true), true), true), true), true, divide(divide(identity, a), divide(idQa, a)), divide(divide(identity, idQa), a)), divide(divide(identity, idQa), a))), true, less_equal(divide(identity, a), divide(idQa, zero)), true), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.50 = { by axiom 8 (closure) R->L }
% 158.37/20.51 ifeq2(ifeq(quotient(divide(identity, a), divide(idQa, zero), ifeq2(less_equal(divide(divide(identity, idQa), a), divide(divide(identity, a), divide(idQa, a))), true, ifeq2(ifeq(quotient(divide(identity, idQa), a, divide(divide(identity, idQa), a)), true, ifeq(quotient(idQa, a, divide(idQa, a)), true, ifeq(quotient(identity, a, divide(identity, a)), true, ifeq(quotient(identity, idQa, divide(identity, idQa)), true, less_equal(divide(divide(identity, a), divide(idQa, a)), divide(divide(identity, idQa), a)), true), true), true), true), true, divide(divide(identity, a), divide(idQa, a)), divide(divide(identity, idQa), a)), divide(divide(identity, idQa), a))), true, less_equal(divide(identity, a), divide(idQa, zero)), true), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.51 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.51 ifeq2(ifeq(quotient(divide(identity, a), divide(idQa, zero), ifeq2(less_equal(divide(divide(identity, idQa), a), divide(divide(identity, a), divide(idQa, a))), true, ifeq2(ifeq(true, true, ifeq(quotient(divide(identity, idQa), a, divide(divide(identity, idQa), a)), true, ifeq(quotient(idQa, a, divide(idQa, a)), true, ifeq(quotient(identity, a, divide(identity, a)), true, ifeq(quotient(identity, idQa, divide(identity, idQa)), true, less_equal(divide(divide(identity, a), divide(idQa, a)), divide(divide(identity, idQa), a)), true), true), true), true), true), true, divide(divide(identity, a), divide(idQa, a)), divide(divide(identity, idQa), a)), divide(divide(identity, idQa), a))), true, less_equal(divide(identity, a), divide(idQa, zero)), true), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.51 = { by axiom 8 (closure) R->L }
% 158.37/20.51 ifeq2(ifeq(quotient(divide(identity, a), divide(idQa, zero), ifeq2(less_equal(divide(divide(identity, idQa), a), divide(divide(identity, a), divide(idQa, a))), true, ifeq2(ifeq(quotient(divide(identity, a), divide(idQa, a), divide(divide(identity, a), divide(idQa, a))), true, ifeq(quotient(divide(identity, idQa), a, divide(divide(identity, idQa), a)), true, ifeq(quotient(idQa, a, divide(idQa, a)), true, ifeq(quotient(identity, a, divide(identity, a)), true, ifeq(quotient(identity, idQa, divide(identity, idQa)), true, less_equal(divide(divide(identity, a), divide(idQa, a)), divide(divide(identity, idQa), a)), true), true), true), true), true), true, divide(divide(identity, a), divide(idQa, a)), divide(divide(identity, idQa), a)), divide(divide(identity, idQa), a))), true, less_equal(divide(identity, a), divide(idQa, zero)), true), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.51 = { by axiom 14 (quotient_property) }
% 158.37/20.51 ifeq2(ifeq(quotient(divide(identity, a), divide(idQa, zero), ifeq2(less_equal(divide(divide(identity, idQa), a), divide(divide(identity, a), divide(idQa, a))), true, ifeq2(true, true, divide(divide(identity, a), divide(idQa, a)), divide(divide(identity, idQa), a)), divide(divide(identity, idQa), a))), true, less_equal(divide(identity, a), divide(idQa, zero)), true), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.51 = { by axiom 7 (ifeq_axiom) }
% 158.37/20.51 ifeq2(ifeq(quotient(divide(identity, a), divide(idQa, zero), ifeq2(less_equal(divide(divide(identity, idQa), a), divide(divide(identity, a), divide(idQa, a))), true, divide(divide(identity, a), divide(idQa, a)), divide(divide(identity, idQa), a))), true, less_equal(divide(identity, a), divide(idQa, zero)), true), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.51 = { by lemma 16 }
% 158.37/20.51 ifeq2(ifeq(quotient(divide(identity, a), divide(idQa, zero), ifeq2(less_equal(divide(divide(identity, idQa), a), divide(divide(identity, a), divide(idQa, zero))), true, divide(divide(identity, a), divide(idQa, a)), divide(divide(identity, idQa), a))), true, less_equal(divide(identity, a), divide(idQa, zero)), true), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.51 = { by lemma 21 }
% 158.37/20.51 ifeq2(ifeq(quotient(divide(identity, a), divide(idQa, zero), ifeq2(less_equal(divide(divide(identity, idQa), a), divide(divide(identity, a), divide(idQa, zero))), true, divide(divide(identity, a), divide(idQa, a)), zero)), true, less_equal(divide(identity, a), divide(idQa, zero)), true), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.51 = { by lemma 21 }
% 158.37/20.51 ifeq2(ifeq(quotient(divide(identity, a), divide(idQa, zero), ifeq2(less_equal(zero, divide(divide(identity, a), divide(idQa, zero))), true, divide(divide(identity, a), divide(idQa, a)), zero)), true, less_equal(divide(identity, a), divide(idQa, zero)), true), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.51 = { by axiom 2 (zero_is_smallest) }
% 158.37/20.51 ifeq2(ifeq(quotient(divide(identity, a), divide(idQa, zero), ifeq2(true, true, divide(divide(identity, a), divide(idQa, a)), zero)), true, less_equal(divide(identity, a), divide(idQa, zero)), true), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.51 = { by axiom 7 (ifeq_axiom) }
% 158.37/20.51 ifeq2(ifeq(quotient(divide(identity, a), divide(idQa, zero), divide(divide(identity, a), divide(idQa, a))), true, less_equal(divide(identity, a), divide(idQa, zero)), true), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.51 = { by lemma 16 }
% 158.37/20.51 ifeq2(ifeq(quotient(divide(identity, a), divide(idQa, zero), divide(divide(identity, a), divide(idQa, zero))), true, less_equal(divide(identity, a), divide(idQa, zero)), true), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.51 = { by axiom 8 (closure) }
% 158.37/20.51 ifeq2(ifeq(true, true, less_equal(divide(identity, a), divide(idQa, zero)), true), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.51 = { by axiom 6 (ifeq_axiom) }
% 158.37/20.51 ifeq2(less_equal(divide(identity, a), divide(idQa, zero)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.51 = { by lemma 20 R->L }
% 158.37/20.51 ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.51 = { by axiom 7 (ifeq_axiom) R->L }
% 158.37/20.51 ifeq2(true, true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.51 = { by axiom 11 (less_equal_quotient) R->L }
% 158.37/20.51 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), zero), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.51 = { by axiom 7 (ifeq_axiom) R->L }
% 158.37/20.51 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), ifeq2(true, true, zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)))), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.51 = { by axiom 2 (zero_is_smallest) R->L }
% 158.37/20.51 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), true, zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)))), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.51 = { by axiom 7 (ifeq_axiom) R->L }
% 158.37/20.51 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), ifeq2(true, true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), true, zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)))), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.51 = { by axiom 14 (quotient_property) R->L }
% 158.37/20.51 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), true, ifeq(quotient(zero, a, divide(zero, a)), true, ifeq(quotient(identity, a, divide(identity, a)), true, ifeq(quotient(idQa_Q__idQ_idQa, a, divide(idQa_Q__idQ_idQa, a)), true, ifeq(quotient(idQa_Q__idQ_idQa, identity, zero), true, less_equal(divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), divide(zero, a)), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), true, zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)))), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.51 = { by axiom 8 (closure) }
% 158.37/20.51 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), ifeq2(ifeq(true, true, ifeq(quotient(zero, a, divide(zero, a)), true, ifeq(quotient(identity, a, divide(identity, a)), true, ifeq(quotient(idQa_Q__idQ_idQa, a, divide(idQa_Q__idQ_idQa, a)), true, ifeq(quotient(idQa_Q__idQ_idQa, identity, zero), true, less_equal(divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), divide(zero, a)), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), true, zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)))), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.51 = { by axiom 6 (ifeq_axiom) }
% 158.37/20.51 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), ifeq2(ifeq(quotient(zero, a, divide(zero, a)), true, ifeq(quotient(identity, a, divide(identity, a)), true, ifeq(quotient(idQa_Q__idQ_idQa, a, divide(idQa_Q__idQ_idQa, a)), true, ifeq(quotient(idQa_Q__idQ_idQa, identity, zero), true, less_equal(divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), divide(zero, a)), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), true, zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)))), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.51 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.51 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), ifeq2(ifeq(quotient(zero, a, divide(zero, a)), true, ifeq(quotient(identity, a, divide(identity, a)), true, ifeq(quotient(idQa_Q__idQ_idQa, a, divide(idQa_Q__idQ_idQa, a)), true, ifeq(ifeq(true, true, quotient(idQa_Q__idQ_idQa, identity, zero), true), true, less_equal(divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), divide(zero, a)), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), true, zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)))), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.51 = { by axiom 1 (identity_is_largest) R->L }
% 158.37/20.51 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), ifeq2(ifeq(quotient(zero, a, divide(zero, a)), true, ifeq(quotient(identity, a, divide(identity, a)), true, ifeq(quotient(idQa_Q__idQ_idQa, a, divide(idQa_Q__idQ_idQa, a)), true, ifeq(ifeq(less_equal(idQa_Q__idQ_idQa, identity), true, quotient(idQa_Q__idQ_idQa, identity, zero), true), true, less_equal(divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), divide(zero, a)), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), true, zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)))), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.51 = { by axiom 9 (quotient_less_equal) }
% 158.37/20.51 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), ifeq2(ifeq(quotient(zero, a, divide(zero, a)), true, ifeq(quotient(identity, a, divide(identity, a)), true, ifeq(quotient(idQa_Q__idQ_idQa, a, divide(idQa_Q__idQ_idQa, a)), true, ifeq(true, true, less_equal(divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), divide(zero, a)), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), true, zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)))), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.52 = { by axiom 6 (ifeq_axiom) }
% 158.37/20.52 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), ifeq2(ifeq(quotient(zero, a, divide(zero, a)), true, ifeq(quotient(identity, a, divide(identity, a)), true, ifeq(quotient(idQa_Q__idQ_idQa, a, divide(idQa_Q__idQ_idQa, a)), true, less_equal(divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), divide(zero, a)), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), true, zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)))), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.52 = { by axiom 8 (closure) }
% 158.37/20.52 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), ifeq2(ifeq(true, true, ifeq(quotient(identity, a, divide(identity, a)), true, ifeq(quotient(idQa_Q__idQ_idQa, a, divide(idQa_Q__idQ_idQa, a)), true, less_equal(divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), divide(zero, a)), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), true, zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)))), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.52 = { by axiom 6 (ifeq_axiom) }
% 158.37/20.52 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), ifeq2(ifeq(quotient(identity, a, divide(identity, a)), true, ifeq(quotient(idQa_Q__idQ_idQa, a, divide(idQa_Q__idQ_idQa, a)), true, less_equal(divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), divide(zero, a)), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), true, zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)))), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.52 = { by axiom 12 (less_equal_and_equal) R->L }
% 158.37/20.52 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), ifeq2(ifeq(quotient(identity, a, divide(identity, a)), true, ifeq(quotient(idQa_Q__idQ_idQa, a, divide(idQa_Q__idQ_idQa, a)), true, less_equal(divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), ifeq2(less_equal(divide(zero, a), zero), true, ifeq2(less_equal(zero, divide(zero, a)), true, zero, divide(zero, a)), divide(zero, a))), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), true, zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)))), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.52 = { by axiom 2 (zero_is_smallest) }
% 158.37/20.52 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), ifeq2(ifeq(quotient(identity, a, divide(identity, a)), true, ifeq(quotient(idQa_Q__idQ_idQa, a, divide(idQa_Q__idQ_idQa, a)), true, less_equal(divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), ifeq2(less_equal(divide(zero, a), zero), true, ifeq2(true, true, zero, divide(zero, a)), divide(zero, a))), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), true, zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)))), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.52 = { by axiom 7 (ifeq_axiom) }
% 158.37/20.52 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), ifeq2(ifeq(quotient(identity, a, divide(identity, a)), true, ifeq(quotient(idQa_Q__idQ_idQa, a, divide(idQa_Q__idQ_idQa, a)), true, less_equal(divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), ifeq2(less_equal(divide(zero, a), zero), true, zero, divide(zero, a))), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), true, zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)))), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.52 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.52 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), ifeq2(ifeq(quotient(identity, a, divide(identity, a)), true, ifeq(quotient(idQa_Q__idQ_idQa, a, divide(idQa_Q__idQ_idQa, a)), true, less_equal(divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), ifeq2(ifeq(true, true, less_equal(divide(zero, a), zero), true), true, zero, divide(zero, a))), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), true, zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)))), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.52 = { by axiom 8 (closure) R->L }
% 158.37/20.52 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), ifeq2(ifeq(quotient(identity, a, divide(identity, a)), true, ifeq(quotient(idQa_Q__idQ_idQa, a, divide(idQa_Q__idQ_idQa, a)), true, less_equal(divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), ifeq2(ifeq(quotient(zero, a, divide(zero, a)), true, less_equal(divide(zero, a), zero), true), true, zero, divide(zero, a))), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), true, zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)))), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.52 = { by axiom 10 (divisor_existence) }
% 158.37/20.52 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), ifeq2(ifeq(quotient(identity, a, divide(identity, a)), true, ifeq(quotient(idQa_Q__idQ_idQa, a, divide(idQa_Q__idQ_idQa, a)), true, less_equal(divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), ifeq2(true, true, zero, divide(zero, a))), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), true, zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)))), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.52 = { by axiom 7 (ifeq_axiom) }
% 158.37/20.52 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), ifeq2(ifeq(quotient(identity, a, divide(identity, a)), true, ifeq(quotient(idQa_Q__idQ_idQa, a, divide(idQa_Q__idQ_idQa, a)), true, less_equal(divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), true, zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)))), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.52 = { by axiom 8 (closure) }
% 158.37/20.52 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), ifeq2(ifeq(true, true, ifeq(quotient(idQa_Q__idQ_idQa, a, divide(idQa_Q__idQ_idQa, a)), true, less_equal(divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), true, zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)))), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.52 = { by axiom 6 (ifeq_axiom) }
% 158.37/20.52 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, a, divide(idQa_Q__idQ_idQa, a)), true, less_equal(divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), true, zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)))), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.52 = { by axiom 8 (closure) }
% 158.37/20.52 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), ifeq2(ifeq(true, true, less_equal(divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), zero), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), true, zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)))), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.52 = { by axiom 6 (ifeq_axiom) }
% 158.37/20.52 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), ifeq2(less_equal(divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), zero), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), true, zero, divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a)))), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.52 = { by axiom 12 (less_equal_and_equal) }
% 158.37/20.52 ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, a), divide(identity, a), divide(divide(idQa_Q__idQ_idQa, a), divide(identity, a))), true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.52 = { by axiom 8 (closure) }
% 158.37/20.52 ifeq2(ifeq(true, true, less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.52 = { by axiom 6 (ifeq_axiom) }
% 158.37/20.52 ifeq2(less_equal(divide(idQa_Q__idQ_idQa, a), divide(identity, a)), true, ifeq2(less_equal(divide(identity, a), divide(idQa_Q__idQ_idQa, a)), true, divide(identity, a), divide(idQa_Q__idQ_idQa, a)), divide(idQa_Q__idQ_idQa, a))
% 158.37/20.52 = { by axiom 12 (less_equal_and_equal) }
% 158.37/20.52 divide(idQa_Q__idQ_idQa, a)
% 158.37/20.52 = { by axiom 7 (ifeq_axiom) R->L }
% 158.37/20.52 ifeq2(true, true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.52 = { by axiom 11 (less_equal_quotient) R->L }
% 158.37/20.52 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), zero), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.52 = { by axiom 7 (ifeq_axiom) R->L }
% 158.37/20.52 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), ifeq2(true, true, zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero)))), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.52 = { by axiom 2 (zero_is_smallest) R->L }
% 158.37/20.52 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero)))), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.52 = { by axiom 7 (ifeq_axiom) R->L }
% 158.37/20.52 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), ifeq2(true, true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), divide(idQa_Q__idQ_idQa, divide(idQa, zero)))), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.52 = { by axiom 11 (less_equal_quotient) R->L }
% 158.37/20.52 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero, zero), true, less_equal(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), divide(idQa_Q__idQ_idQa, divide(idQa, zero)))), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.52 = { by axiom 7 (ifeq_axiom) R->L }
% 158.37/20.52 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero, ifeq2(true, true, zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero))), true, less_equal(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), divide(idQa_Q__idQ_idQa, divide(idQa, zero)))), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.52 = { by axiom 2 (zero_is_smallest) R->L }
% 158.37/20.52 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), true, zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero))), true, less_equal(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), divide(idQa_Q__idQ_idQa, divide(idQa, zero)))), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.52 = { by axiom 7 (ifeq_axiom) R->L }
% 158.37/20.52 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero, ifeq2(true, true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), true, zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero))), true, less_equal(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), divide(idQa_Q__idQ_idQa, divide(idQa, zero)))), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.52 = { by axiom 14 (quotient_property) R->L }
% 158.37/20.52 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero, ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), true, ifeq(quotient(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero), divide(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero))), true, ifeq(quotient(zero, divide(idQa, zero), zero), true, ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, ifeq(quotient(idQa_Q__idQ_idQa, zero, divide(idQa_Q__idQ_idQa, zero)), true, less_equal(divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), divide(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero))), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), true, zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero))), true, less_equal(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), divide(idQa_Q__idQ_idQa, divide(idQa, zero)))), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.52 = { by axiom 8 (closure) }
% 158.37/20.52 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero, ifeq2(ifeq(true, true, ifeq(quotient(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero), divide(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero))), true, ifeq(quotient(zero, divide(idQa, zero), zero), true, ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, ifeq(quotient(idQa_Q__idQ_idQa, zero, divide(idQa_Q__idQ_idQa, zero)), true, less_equal(divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), divide(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero))), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), true, zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero))), true, less_equal(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), divide(idQa_Q__idQ_idQa, divide(idQa, zero)))), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.53 = { by axiom 6 (ifeq_axiom) }
% 158.37/20.53 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero, ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero), divide(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero))), true, ifeq(quotient(zero, divide(idQa, zero), zero), true, ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, ifeq(quotient(idQa_Q__idQ_idQa, zero, divide(idQa_Q__idQ_idQa, zero)), true, less_equal(divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), divide(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero))), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), true, zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero))), true, less_equal(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), divide(idQa_Q__idQ_idQa, divide(idQa, zero)))), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.53 = { by axiom 6 (ifeq_axiom) R->L }
% 158.37/20.53 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero, ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero), divide(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero))), true, ifeq(ifeq(true, true, quotient(zero, divide(idQa, zero), zero), true), true, ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, ifeq(quotient(idQa_Q__idQ_idQa, zero, divide(idQa_Q__idQ_idQa, zero)), true, less_equal(divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), divide(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero))), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), true, zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero))), true, less_equal(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), divide(idQa_Q__idQ_idQa, divide(idQa, zero)))), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.53 = { by axiom 2 (zero_is_smallest) R->L }
% 158.37/20.53 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero, ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero), divide(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero))), true, ifeq(ifeq(less_equal(zero, divide(idQa, zero)), true, quotient(zero, divide(idQa, zero), zero), true), true, ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, ifeq(quotient(idQa_Q__idQ_idQa, zero, divide(idQa_Q__idQ_idQa, zero)), true, less_equal(divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), divide(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero))), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), true, zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero))), true, less_equal(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), divide(idQa_Q__idQ_idQa, divide(idQa, zero)))), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.53 = { by axiom 9 (quotient_less_equal) }
% 158.37/20.53 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero, ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero), divide(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero))), true, ifeq(true, true, ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, ifeq(quotient(idQa_Q__idQ_idQa, zero, divide(idQa_Q__idQ_idQa, zero)), true, less_equal(divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), divide(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero))), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), true, zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero))), true, less_equal(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), divide(idQa_Q__idQ_idQa, divide(idQa, zero)))), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.53 = { by axiom 6 (ifeq_axiom) }
% 158.37/20.53 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero, ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero), divide(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero))), true, ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, ifeq(quotient(idQa_Q__idQ_idQa, zero, divide(idQa_Q__idQ_idQa, zero)), true, less_equal(divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), divide(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero))), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), true, zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero))), true, less_equal(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), divide(idQa_Q__idQ_idQa, divide(idQa, zero)))), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.53 = { by axiom 8 (closure) }
% 158.37/20.53 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero, ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero), divide(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero))), true, ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, ifeq(true, true, less_equal(divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), divide(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero))), true), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), true, zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero))), true, less_equal(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), divide(idQa_Q__idQ_idQa, divide(idQa, zero)))), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.53 = { by axiom 6 (ifeq_axiom) }
% 158.37/20.53 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero, ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero), divide(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero))), true, ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, less_equal(divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), divide(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero))), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), true, zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero))), true, less_equal(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), divide(idQa_Q__idQ_idQa, divide(idQa, zero)))), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.53 = { by axiom 8 (closure) }
% 158.37/20.53 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero, ifeq2(ifeq(true, true, ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, less_equal(divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), divide(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero))), true), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), true, zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero))), true, less_equal(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), divide(idQa_Q__idQ_idQa, divide(idQa, zero)))), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.53 = { by axiom 6 (ifeq_axiom) }
% 158.37/20.53 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero, ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, less_equal(divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), divide(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero))), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), true, zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero))), true, less_equal(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), divide(idQa_Q__idQ_idQa, divide(idQa, zero)))), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.53 = { by axiom 8 (closure) }
% 158.37/20.53 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero, ifeq2(ifeq(true, true, less_equal(divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), divide(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero))), true), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), true, zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero))), true, less_equal(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), divide(idQa_Q__idQ_idQa, divide(idQa, zero)))), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.53 = { by axiom 6 (ifeq_axiom) }
% 158.37/20.53 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero, ifeq2(less_equal(divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), divide(divide(idQa_Q__idQ_idQa, zero), divide(idQa, zero))), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), true, zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero))), true, less_equal(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), divide(idQa_Q__idQ_idQa, divide(idQa, zero)))), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.54 = { by lemma 19 }
% 158.37/20.54 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero, ifeq2(less_equal(divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), zero), true, ifeq2(less_equal(zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), true, zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero))), true, less_equal(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), divide(idQa_Q__idQ_idQa, divide(idQa, zero)))), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.54 = { by axiom 12 (less_equal_and_equal) }
% 158.37/20.54 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), ifeq2(ifeq(quotient(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero, divide(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero)), true, less_equal(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), divide(idQa_Q__idQ_idQa, divide(idQa, zero)))), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.54 = { by axiom 8 (closure) }
% 158.37/20.54 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), ifeq2(ifeq(true, true, less_equal(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), true), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), divide(idQa_Q__idQ_idQa, divide(idQa, zero)))), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.54 = { by axiom 6 (ifeq_axiom) }
% 158.37/20.54 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), ifeq2(less_equal(divide(idQa_Q__idQ_idQa, divide(idQa, zero)), zero), true, ifeq2(less_equal(zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, zero, divide(idQa_Q__idQ_idQa, divide(idQa, zero))), divide(idQa_Q__idQ_idQa, divide(idQa, zero)))), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.54 = { by axiom 12 (less_equal_and_equal) }
% 158.37/20.54 ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, divide(idQa, zero), divide(idQa_Q__idQ_idQa, divide(idQa, zero))), true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.54 = { by axiom 8 (closure) }
% 158.37/20.54 ifeq2(ifeq(true, true, less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.54 = { by axiom 6 (ifeq_axiom) }
% 158.37/20.54 ifeq2(less_equal(idQa_Q__idQ_idQa, divide(idQa, zero)), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.54 = { by lemma 20 R->L }
% 158.37/20.54 ifeq2(less_equal(idQa_Q__idQ_idQa, divide(idQa_Q__idQ_idQa, a)), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa)
% 158.37/20.54 = { by axiom 7 (ifeq_axiom) R->L }
% 158.37/20.54 ifeq2(less_equal(idQa_Q__idQ_idQa, divide(idQa_Q__idQ_idQa, a)), true, ifeq2(true, true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa)
% 158.37/20.54 = { by axiom 10 (divisor_existence) R->L }
% 158.37/20.54 ifeq2(less_equal(idQa_Q__idQ_idQa, divide(idQa_Q__idQ_idQa, a)), true, ifeq2(ifeq(quotient(idQa_Q__idQ_idQa, a, divide(idQa_Q__idQ_idQa, a)), true, less_equal(divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa)
% 158.37/20.54 = { by axiom 8 (closure) }
% 158.37/20.54 ifeq2(less_equal(idQa_Q__idQ_idQa, divide(idQa_Q__idQ_idQa, a)), true, ifeq2(ifeq(true, true, less_equal(divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa), true), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa)
% 158.37/20.54 = { by axiom 6 (ifeq_axiom) }
% 158.37/20.54 ifeq2(less_equal(idQa_Q__idQ_idQa, divide(idQa_Q__idQ_idQa, a)), true, ifeq2(less_equal(divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa), true, divide(idQa_Q__idQ_idQa, a), idQa_Q__idQ_idQa), idQa_Q__idQ_idQa)
% 158.37/20.54 = { by axiom 12 (less_equal_and_equal) }
% 158.37/20.54 idQa_Q__idQ_idQa
% 158.37/20.54 % SZS output end Proof
% 158.37/20.54
% 158.37/20.54 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------