%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : HEN006-7 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 10:18:58 AM UTC 2026
% Result : Unsatisfiable 27.48s 3.82s
% Output : Proof 28.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : HEN006-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sun Sep 27 10:50:25 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.48/3.82 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
% 27.48/3.82
% 27.48/3.82 % SZS status Unsatisfiable
% 27.48/3.82
% 28.27/3.91 % SZS output start Proof
% 28.27/3.91 Axiom 1 (zero_is_smallest): less_equal(zero, X) = true.
% 28.27/3.91 Axiom 2 (xQyLEz): less_equal(xQy, z) = true.
% 28.27/3.91 Axiom 3 (x_divide_x_is_zero): quotient(X, X, zero) = true.
% 28.27/3.91 Axiom 4 (x_divde_zero_is_x): quotient(X, zero, X) = true.
% 28.27/3.91 Axiom 5 (zero_divide_anything_is_zero): quotient(zero, X, zero) = true.
% 28.27/3.91 Axiom 6 (xQy): quotient(x, y, xQy) = true.
% 28.27/3.91 Axiom 7 (xQz): quotient(x, z, xQz) = true.
% 28.27/3.91 Axiom 8 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 28.27/3.91 Axiom 9 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 28.27/3.91 Axiom 10 (closure): quotient(X, Y, divide(X, Y)) = true.
% 28.27/3.91 Axiom 11 (quotient_less_equal): ifeq(less_equal(X, Y), true, quotient(X, Y, zero), true) = true.
% 28.27/3.91 Axiom 12 (divisor_existence): ifeq(quotient(X, Y, Z), true, less_equal(Z, X), true) = true.
% 28.27/3.91 Axiom 13 (less_equal_quotient): ifeq(quotient(X, Y, zero), true, less_equal(X, Y), true) = true.
% 28.27/3.91 Axiom 14 (less_equal_and_equal): ifeq2(less_equal(X, Y), true, ifeq2(less_equal(Y, X), true, Y, X), X) = X.
% 28.27/3.91 Axiom 15 (well_defined): ifeq2(quotient(X, Y, Z), true, ifeq2(quotient(X, Y, W), true, W, Z), Z) = Z.
% 28.27/3.91 Axiom 16 (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.
% 28.27/3.91
% 28.27/3.91 Lemma 17: divide(X, zero) = X.
% 28.27/3.91 Proof:
% 28.27/3.91 divide(X, zero)
% 28.27/3.91 = { by axiom 9 (ifeq_axiom) R->L }
% 28.27/3.91 ifeq2(true, true, divide(X, zero), X)
% 28.27/3.91 = { by axiom 10 (closure) R->L }
% 28.27/3.91 ifeq2(quotient(X, zero, divide(X, zero)), true, divide(X, zero), X)
% 28.27/3.91 = { by axiom 9 (ifeq_axiom) R->L }
% 28.27/3.91 ifeq2(true, true, ifeq2(quotient(X, zero, divide(X, zero)), true, divide(X, zero), X), X)
% 28.27/3.91 = { by axiom 4 (x_divde_zero_is_x) R->L }
% 28.27/3.91 ifeq2(quotient(X, zero, X), true, ifeq2(quotient(X, zero, divide(X, zero)), true, divide(X, zero), X), X)
% 28.27/3.91 = { by axiom 15 (well_defined) }
% 28.27/3.91 X
% 28.27/3.91
% 28.27/3.91 Lemma 18: divide(zero, X) = zero.
% 28.27/3.91 Proof:
% 28.27/3.91 divide(zero, X)
% 28.27/3.91 = { by axiom 14 (less_equal_and_equal) R->L }
% 28.27/3.91 ifeq2(less_equal(divide(zero, X), zero), true, ifeq2(less_equal(zero, divide(zero, X)), true, zero, divide(zero, X)), divide(zero, X))
% 28.27/3.91 = { by axiom 1 (zero_is_smallest) }
% 28.27/3.91 ifeq2(less_equal(divide(zero, X), zero), true, ifeq2(true, true, zero, divide(zero, X)), divide(zero, X))
% 28.27/3.92 = { by axiom 9 (ifeq_axiom) }
% 28.27/3.92 ifeq2(less_equal(divide(zero, X), zero), true, zero, divide(zero, X))
% 28.27/3.92 = { by axiom 8 (ifeq_axiom) R->L }
% 28.27/3.92 ifeq2(ifeq(true, true, less_equal(divide(zero, X), zero), true), true, zero, divide(zero, X))
% 28.27/3.92 = { by axiom 10 (closure) R->L }
% 28.27/3.92 ifeq2(ifeq(quotient(zero, X, divide(zero, X)), true, less_equal(divide(zero, X), zero), true), true, zero, divide(zero, X))
% 28.27/3.92 = { by axiom 12 (divisor_existence) }
% 28.27/3.92 ifeq2(true, true, zero, divide(zero, X))
% 28.27/3.92 = { by axiom 9 (ifeq_axiom) }
% 28.27/3.92 zero
% 28.27/3.92
% 28.27/3.92 Lemma 19: divide(xQz, y) = zero.
% 28.27/3.92 Proof:
% 28.27/3.92 divide(xQz, y)
% 28.27/3.92 = { by lemma 17 R->L }
% 28.27/3.92 divide(divide(xQz, y), zero)
% 28.27/3.92 = { by lemma 18 R->L }
% 28.27/3.92 divide(divide(xQz, y), divide(zero, y))
% 28.27/3.92 = { by axiom 9 (ifeq_axiom) R->L }
% 28.27/3.92 divide(divide(xQz, y), divide(ifeq2(true, true, zero, divide(xQz, divide(y, xQy))), y))
% 28.27/3.92 = { by axiom 1 (zero_is_smallest) R->L }
% 28.27/3.92 divide(divide(xQz, y), divide(ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), y))
% 28.27/3.92 = { by axiom 9 (ifeq_axiom) R->L }
% 28.27/3.92 divide(divide(xQz, y), divide(ifeq2(true, true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.92 = { by axiom 16 (quotient_property) R->L }
% 28.27/3.92 divide(divide(xQz, y), divide(ifeq2(ifeq(quotient(divide(xQz, divide(y, xQy)), zero, divide(xQz, divide(y, xQy))), true, ifeq(quotient(divide(xQz, divide(x, xQy)), divide(y, xQy), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true, ifeq(quotient(divide(x, xQy), divide(y, xQy), zero), true, ifeq(quotient(xQz, divide(y, xQy), divide(xQz, divide(y, xQy))), true, ifeq(quotient(xQz, divide(x, xQy), divide(xQz, divide(x, xQy))), true, less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.92 = { by axiom 4 (x_divde_zero_is_x) }
% 28.27/3.92 divide(divide(xQz, y), divide(ifeq2(ifeq(true, true, ifeq(quotient(divide(xQz, divide(x, xQy)), divide(y, xQy), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true, ifeq(quotient(divide(x, xQy), divide(y, xQy), zero), true, ifeq(quotient(xQz, divide(y, xQy), divide(xQz, divide(y, xQy))), true, ifeq(quotient(xQz, divide(x, xQy), divide(xQz, divide(x, xQy))), true, less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.92 = { by axiom 8 (ifeq_axiom) }
% 28.27/3.92 divide(divide(xQz, y), divide(ifeq2(ifeq(quotient(divide(xQz, divide(x, xQy)), divide(y, xQy), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true, ifeq(quotient(divide(x, xQy), divide(y, xQy), zero), true, ifeq(quotient(xQz, divide(y, xQy), divide(xQz, divide(y, xQy))), true, ifeq(quotient(xQz, divide(x, xQy), divide(xQz, divide(x, xQy))), true, less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true), true), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.92 = { by axiom 10 (closure) }
% 28.27/3.92 divide(divide(xQz, y), divide(ifeq2(ifeq(true, true, ifeq(quotient(divide(x, xQy), divide(y, xQy), zero), true, ifeq(quotient(xQz, divide(y, xQy), divide(xQz, divide(y, xQy))), true, ifeq(quotient(xQz, divide(x, xQy), divide(xQz, divide(x, xQy))), true, less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true), true), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 8 (ifeq_axiom) }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(ifeq(quotient(divide(x, xQy), divide(y, xQy), zero), true, ifeq(quotient(xQz, divide(y, xQy), divide(xQz, divide(y, xQy))), true, ifeq(quotient(xQz, divide(x, xQy), divide(xQz, divide(x, xQy))), true, less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 10 (closure) }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(ifeq(quotient(divide(x, xQy), divide(y, xQy), zero), true, ifeq(true, true, ifeq(quotient(xQz, divide(x, xQy), divide(xQz, divide(x, xQy))), true, less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 8 (ifeq_axiom) }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(ifeq(quotient(divide(x, xQy), divide(y, xQy), zero), true, ifeq(quotient(xQz, divide(x, xQy), divide(xQz, divide(x, xQy))), true, less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 10 (closure) }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(ifeq(quotient(divide(x, xQy), divide(y, xQy), zero), true, ifeq(true, true, less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 8 (ifeq_axiom) }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(ifeq(quotient(divide(x, xQy), divide(y, xQy), zero), true, less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 9 (ifeq_axiom) R->L }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(ifeq(quotient(divide(x, xQy), divide(y, xQy), ifeq2(true, true, zero, divide(divide(x, xQy), divide(y, xQy)))), true, less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 1 (zero_is_smallest) R->L }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(ifeq(quotient(divide(x, xQy), divide(y, xQy), ifeq2(less_equal(zero, divide(divide(x, xQy), divide(y, xQy))), true, zero, divide(divide(x, xQy), divide(y, xQy)))), true, less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 9 (ifeq_axiom) R->L }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(ifeq(quotient(divide(x, xQy), divide(y, xQy), ifeq2(true, true, ifeq2(less_equal(zero, divide(divide(x, xQy), divide(y, xQy))), true, zero, divide(divide(x, xQy), divide(y, xQy))), divide(divide(x, xQy), divide(y, xQy)))), true, less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 16 (quotient_property) R->L }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(ifeq(quotient(divide(x, xQy), divide(y, xQy), ifeq2(ifeq(quotient(divide(x, xQy), divide(y, xQy), divide(divide(x, xQy), divide(y, xQy))), true, ifeq(quotient(xQy, xQy, zero), true, ifeq(quotient(y, xQy, divide(y, xQy)), true, ifeq(quotient(x, xQy, divide(x, xQy)), true, ifeq(quotient(x, y, xQy), true, less_equal(divide(divide(x, xQy), divide(y, xQy)), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, xQy), divide(y, xQy))), true, zero, divide(divide(x, xQy), divide(y, xQy))), divide(divide(x, xQy), divide(y, xQy)))), true, less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 3 (x_divide_x_is_zero) }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(ifeq(quotient(divide(x, xQy), divide(y, xQy), ifeq2(ifeq(quotient(divide(x, xQy), divide(y, xQy), divide(divide(x, xQy), divide(y, xQy))), true, ifeq(true, true, ifeq(quotient(y, xQy, divide(y, xQy)), true, ifeq(quotient(x, xQy, divide(x, xQy)), true, ifeq(quotient(x, y, xQy), true, less_equal(divide(divide(x, xQy), divide(y, xQy)), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, xQy), divide(y, xQy))), true, zero, divide(divide(x, xQy), divide(y, xQy))), divide(divide(x, xQy), divide(y, xQy)))), true, less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 8 (ifeq_axiom) }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(ifeq(quotient(divide(x, xQy), divide(y, xQy), ifeq2(ifeq(quotient(divide(x, xQy), divide(y, xQy), divide(divide(x, xQy), divide(y, xQy))), true, ifeq(quotient(y, xQy, divide(y, xQy)), true, ifeq(quotient(x, xQy, divide(x, xQy)), true, ifeq(quotient(x, y, xQy), true, less_equal(divide(divide(x, xQy), divide(y, xQy)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, xQy), divide(y, xQy))), true, zero, divide(divide(x, xQy), divide(y, xQy))), divide(divide(x, xQy), divide(y, xQy)))), true, less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 6 (xQy) }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(ifeq(quotient(divide(x, xQy), divide(y, xQy), ifeq2(ifeq(quotient(divide(x, xQy), divide(y, xQy), divide(divide(x, xQy), divide(y, xQy))), true, ifeq(quotient(y, xQy, divide(y, xQy)), true, ifeq(quotient(x, xQy, divide(x, xQy)), true, ifeq(true, true, less_equal(divide(divide(x, xQy), divide(y, xQy)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, xQy), divide(y, xQy))), true, zero, divide(divide(x, xQy), divide(y, xQy))), divide(divide(x, xQy), divide(y, xQy)))), true, less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 8 (ifeq_axiom) }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(ifeq(quotient(divide(x, xQy), divide(y, xQy), ifeq2(ifeq(quotient(divide(x, xQy), divide(y, xQy), divide(divide(x, xQy), divide(y, xQy))), true, ifeq(quotient(y, xQy, divide(y, xQy)), true, ifeq(quotient(x, xQy, divide(x, xQy)), true, less_equal(divide(divide(x, xQy), divide(y, xQy)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, xQy), divide(y, xQy))), true, zero, divide(divide(x, xQy), divide(y, xQy))), divide(divide(x, xQy), divide(y, xQy)))), true, less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 10 (closure) }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(ifeq(quotient(divide(x, xQy), divide(y, xQy), ifeq2(ifeq(true, true, ifeq(quotient(y, xQy, divide(y, xQy)), true, ifeq(quotient(x, xQy, divide(x, xQy)), true, less_equal(divide(divide(x, xQy), divide(y, xQy)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(x, xQy), divide(y, xQy))), true, zero, divide(divide(x, xQy), divide(y, xQy))), divide(divide(x, xQy), divide(y, xQy)))), true, less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 8 (ifeq_axiom) }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(ifeq(quotient(divide(x, xQy), divide(y, xQy), ifeq2(ifeq(quotient(y, xQy, divide(y, xQy)), true, ifeq(quotient(x, xQy, divide(x, xQy)), true, less_equal(divide(divide(x, xQy), divide(y, xQy)), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(x, xQy), divide(y, xQy))), true, zero, divide(divide(x, xQy), divide(y, xQy))), divide(divide(x, xQy), divide(y, xQy)))), true, less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 10 (closure) }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(ifeq(quotient(divide(x, xQy), divide(y, xQy), ifeq2(ifeq(true, true, ifeq(quotient(x, xQy, divide(x, xQy)), true, less_equal(divide(divide(x, xQy), divide(y, xQy)), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(x, xQy), divide(y, xQy))), true, zero, divide(divide(x, xQy), divide(y, xQy))), divide(divide(x, xQy), divide(y, xQy)))), true, less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 8 (ifeq_axiom) }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(ifeq(quotient(divide(x, xQy), divide(y, xQy), ifeq2(ifeq(quotient(x, xQy, divide(x, xQy)), true, less_equal(divide(divide(x, xQy), divide(y, xQy)), zero), true), true, ifeq2(less_equal(zero, divide(divide(x, xQy), divide(y, xQy))), true, zero, divide(divide(x, xQy), divide(y, xQy))), divide(divide(x, xQy), divide(y, xQy)))), true, less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 10 (closure) }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(ifeq(quotient(divide(x, xQy), divide(y, xQy), ifeq2(ifeq(true, true, less_equal(divide(divide(x, xQy), divide(y, xQy)), zero), true), true, ifeq2(less_equal(zero, divide(divide(x, xQy), divide(y, xQy))), true, zero, divide(divide(x, xQy), divide(y, xQy))), divide(divide(x, xQy), divide(y, xQy)))), true, less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 8 (ifeq_axiom) }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(ifeq(quotient(divide(x, xQy), divide(y, xQy), ifeq2(less_equal(divide(divide(x, xQy), divide(y, xQy)), zero), true, ifeq2(less_equal(zero, divide(divide(x, xQy), divide(y, xQy))), true, zero, divide(divide(x, xQy), divide(y, xQy))), divide(divide(x, xQy), divide(y, xQy)))), true, less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 14 (less_equal_and_equal) }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(ifeq(quotient(divide(x, xQy), divide(y, xQy), divide(divide(x, xQy), divide(y, xQy))), true, less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 10 (closure) }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(ifeq(true, true, less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 8 (ifeq_axiom) }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(divide(xQz, divide(x, xQy)), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 14 (less_equal_and_equal) R->L }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(less_equal(divide(xQz, divide(x, xQy)), zero), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 8 (ifeq_axiom) R->L }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(true, true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 11 (quotient_less_equal) R->L }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(ifeq(less_equal(xQz, divide(divide(x, xQy), z)), true, quotient(xQz, divide(divide(x, xQy), z), zero), true), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 8 (ifeq_axiom) R->L }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(ifeq(ifeq(true, true, less_equal(xQz, divide(divide(x, xQy), z)), true), true, quotient(xQz, divide(divide(x, xQy), z), zero), true), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.93 = { by axiom 10 (closure) R->L }
% 28.27/3.93 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(ifeq(ifeq(quotient(x, xQy, divide(x, xQy)), true, less_equal(xQz, divide(divide(x, xQy), z)), true), true, quotient(xQz, divide(divide(x, xQy), z), zero), true), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.94 = { by axiom 8 (ifeq_axiom) R->L }
% 28.27/3.94 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(ifeq(ifeq(true, true, ifeq(quotient(x, xQy, divide(x, xQy)), true, less_equal(xQz, divide(divide(x, xQy), z)), true), true), true, quotient(xQz, divide(divide(x, xQy), z), zero), true), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.94 = { by axiom 10 (closure) R->L }
% 28.27/3.94 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(ifeq(ifeq(quotient(divide(x, xQy), z, divide(divide(x, xQy), z)), true, ifeq(quotient(x, xQy, divide(x, xQy)), true, less_equal(xQz, divide(divide(x, xQy), z)), true), true), true, quotient(xQz, divide(divide(x, xQy), z), zero), true), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.94 = { by axiom 8 (ifeq_axiom) R->L }
% 28.27/3.94 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(ifeq(ifeq(quotient(divide(x, xQy), z, divide(divide(x, xQy), z)), true, ifeq(true, true, ifeq(quotient(x, xQy, divide(x, xQy)), true, less_equal(xQz, divide(divide(x, xQy), z)), true), true), true), true, quotient(xQz, divide(divide(x, xQy), z), zero), true), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.94 = { by axiom 7 (xQz) R->L }
% 28.27/3.94 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(ifeq(ifeq(quotient(divide(x, xQy), z, divide(divide(x, xQy), z)), true, ifeq(quotient(x, z, xQz), true, ifeq(quotient(x, xQy, divide(x, xQy)), true, less_equal(xQz, divide(divide(x, xQy), z)), true), true), true), true, quotient(xQz, divide(divide(x, xQy), z), zero), true), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.94 = { by axiom 8 (ifeq_axiom) R->L }
% 28.27/3.94 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(ifeq(ifeq(quotient(divide(x, xQy), z, divide(divide(x, xQy), z)), true, ifeq(true, true, ifeq(quotient(x, z, xQz), true, ifeq(quotient(x, xQy, divide(x, xQy)), true, less_equal(xQz, divide(divide(x, xQy), z)), true), true), true), true), true, quotient(xQz, divide(divide(x, xQy), z), zero), true), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.94 = { by axiom 11 (quotient_less_equal) R->L }
% 28.27/3.94 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(ifeq(ifeq(quotient(divide(x, xQy), z, divide(divide(x, xQy), z)), true, ifeq(ifeq(less_equal(xQy, z), true, quotient(xQy, z, zero), true), true, ifeq(quotient(x, z, xQz), true, ifeq(quotient(x, xQy, divide(x, xQy)), true, less_equal(xQz, divide(divide(x, xQy), z)), true), true), true), true), true, quotient(xQz, divide(divide(x, xQy), z), zero), true), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.94 = { by axiom 2 (xQyLEz) }
% 28.27/3.94 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(ifeq(ifeq(quotient(divide(x, xQy), z, divide(divide(x, xQy), z)), true, ifeq(ifeq(true, true, quotient(xQy, z, zero), true), true, ifeq(quotient(x, z, xQz), true, ifeq(quotient(x, xQy, divide(x, xQy)), true, less_equal(xQz, divide(divide(x, xQy), z)), true), true), true), true), true, quotient(xQz, divide(divide(x, xQy), z), zero), true), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.94 = { by axiom 8 (ifeq_axiom) }
% 28.27/3.94 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(ifeq(ifeq(quotient(divide(x, xQy), z, divide(divide(x, xQy), z)), true, ifeq(quotient(xQy, z, zero), true, ifeq(quotient(x, z, xQz), true, ifeq(quotient(x, xQy, divide(x, xQy)), true, less_equal(xQz, divide(divide(x, xQy), z)), true), true), true), true), true, quotient(xQz, divide(divide(x, xQy), z), zero), true), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.94 = { by axiom 8 (ifeq_axiom) R->L }
% 28.27/3.94 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(ifeq(ifeq(true, true, ifeq(quotient(divide(x, xQy), z, divide(divide(x, xQy), z)), true, ifeq(quotient(xQy, z, zero), true, ifeq(quotient(x, z, xQz), true, ifeq(quotient(x, xQy, divide(x, xQy)), true, less_equal(xQz, divide(divide(x, xQy), z)), true), true), true), true), true), true, quotient(xQz, divide(divide(x, xQy), z), zero), true), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.94 = { by axiom 4 (x_divde_zero_is_x) R->L }
% 28.27/3.94 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(ifeq(ifeq(quotient(xQz, zero, xQz), true, ifeq(quotient(divide(x, xQy), z, divide(divide(x, xQy), z)), true, ifeq(quotient(xQy, z, zero), true, ifeq(quotient(x, z, xQz), true, ifeq(quotient(x, xQy, divide(x, xQy)), true, less_equal(xQz, divide(divide(x, xQy), z)), true), true), true), true), true), true, quotient(xQz, divide(divide(x, xQy), z), zero), true), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.94 = { by axiom 16 (quotient_property) }
% 28.27/3.94 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(ifeq(true, true, quotient(xQz, divide(divide(x, xQy), z), zero), true), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.94 = { by axiom 8 (ifeq_axiom) }
% 28.27/3.94 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(quotient(xQz, divide(divide(x, xQy), z), zero), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.94 = { by axiom 8 (ifeq_axiom) R->L }
% 28.27/3.94 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(true, true, ifeq(quotient(xQz, divide(divide(x, xQy), z), zero), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.94 = { by axiom 10 (closure) R->L }
% 28.27/3.94 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(quotient(xQz, divide(x, xQy), divide(xQz, divide(x, xQy))), true, ifeq(quotient(xQz, divide(divide(x, xQy), z), zero), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.94 = { by axiom 8 (ifeq_axiom) R->L }
% 28.27/3.94 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(true, true, ifeq(quotient(xQz, divide(x, xQy), divide(xQz, divide(x, xQy))), true, ifeq(quotient(xQz, divide(divide(x, xQy), z), zero), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.94 = { by axiom 11 (quotient_less_equal) R->L }
% 28.27/3.94 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(ifeq(less_equal(divide(divide(x, xQy), z), divide(x, xQy)), true, quotient(divide(divide(x, xQy), z), divide(x, xQy), zero), true), true, ifeq(quotient(xQz, divide(x, xQy), divide(xQz, divide(x, xQy))), true, ifeq(quotient(xQz, divide(divide(x, xQy), z), zero), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.94 = { by axiom 8 (ifeq_axiom) R->L }
% 28.27/3.94 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(ifeq(ifeq(true, true, less_equal(divide(divide(x, xQy), z), divide(x, xQy)), true), true, quotient(divide(divide(x, xQy), z), divide(x, xQy), zero), true), true, ifeq(quotient(xQz, divide(x, xQy), divide(xQz, divide(x, xQy))), true, ifeq(quotient(xQz, divide(divide(x, xQy), z), zero), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.94 = { by axiom 10 (closure) R->L }
% 28.27/3.94 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(ifeq(ifeq(quotient(divide(x, xQy), z, divide(divide(x, xQy), z)), true, less_equal(divide(divide(x, xQy), z), divide(x, xQy)), true), true, quotient(divide(divide(x, xQy), z), divide(x, xQy), zero), true), true, ifeq(quotient(xQz, divide(x, xQy), divide(xQz, divide(x, xQy))), true, ifeq(quotient(xQz, divide(divide(x, xQy), z), zero), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.95 = { by axiom 12 (divisor_existence) }
% 28.27/3.95 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(ifeq(true, true, quotient(divide(divide(x, xQy), z), divide(x, xQy), zero), true), true, ifeq(quotient(xQz, divide(x, xQy), divide(xQz, divide(x, xQy))), true, ifeq(quotient(xQz, divide(divide(x, xQy), z), zero), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.95 = { by axiom 8 (ifeq_axiom) }
% 28.27/3.95 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(quotient(divide(divide(x, xQy), z), divide(x, xQy), zero), true, ifeq(quotient(xQz, divide(x, xQy), divide(xQz, divide(x, xQy))), true, ifeq(quotient(xQz, divide(divide(x, xQy), z), zero), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.95 = { by axiom 8 (ifeq_axiom) R->L }
% 28.27/3.95 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(true, true, ifeq(quotient(divide(divide(x, xQy), z), divide(x, xQy), zero), true, ifeq(quotient(xQz, divide(x, xQy), divide(xQz, divide(x, xQy))), true, ifeq(quotient(xQz, divide(divide(x, xQy), z), zero), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.95 = { by axiom 5 (zero_divide_anything_is_zero) R->L }
% 28.27/3.95 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(quotient(zero, divide(x, xQy), zero), true, ifeq(quotient(divide(divide(x, xQy), z), divide(x, xQy), zero), true, ifeq(quotient(xQz, divide(x, xQy), divide(xQz, divide(x, xQy))), true, ifeq(quotient(xQz, divide(divide(x, xQy), z), zero), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.95 = { by axiom 8 (ifeq_axiom) R->L }
% 28.27/3.95 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(true, true, ifeq(quotient(zero, divide(x, xQy), zero), true, ifeq(quotient(divide(divide(x, xQy), z), divide(x, xQy), zero), true, ifeq(quotient(xQz, divide(x, xQy), divide(xQz, divide(x, xQy))), true, ifeq(quotient(xQz, divide(divide(x, xQy), z), zero), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.95 = { by axiom 4 (x_divde_zero_is_x) R->L }
% 28.27/3.95 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(ifeq(quotient(divide(xQz, divide(x, xQy)), zero, divide(xQz, divide(x, xQy))), true, ifeq(quotient(zero, divide(x, xQy), zero), true, ifeq(quotient(divide(divide(x, xQy), z), divide(x, xQy), zero), true, ifeq(quotient(xQz, divide(x, xQy), divide(xQz, divide(x, xQy))), true, ifeq(quotient(xQz, divide(divide(x, xQy), z), zero), true, less_equal(divide(xQz, divide(x, xQy)), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.95 = { by axiom 16 (quotient_property) }
% 28.27/3.95 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(true, true, ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.95 = { by axiom 9 (ifeq_axiom) }
% 28.27/3.95 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(less_equal(zero, divide(xQz, divide(x, xQy))), true, zero, divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.95 = { by axiom 1 (zero_is_smallest) }
% 28.27/3.95 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(ifeq2(true, true, zero, divide(xQz, divide(x, xQy))), divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.95 = { by axiom 9 (ifeq_axiom) }
% 28.27/3.95 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), divide(zero, divide(y, xQy))), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.95 = { by lemma 18 }
% 28.27/3.95 divide(divide(xQz, y), divide(ifeq2(less_equal(divide(xQz, divide(y, xQy)), zero), true, ifeq2(less_equal(zero, divide(xQz, divide(y, xQy))), true, zero, divide(xQz, divide(y, xQy))), divide(xQz, divide(y, xQy))), y))
% 28.27/3.95 = { by axiom 14 (less_equal_and_equal) }
% 28.27/3.95 divide(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y))
% 28.27/3.95 = { by axiom 9 (ifeq_axiom) R->L }
% 28.27/3.95 ifeq2(true, true, divide(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), zero)
% 28.27/3.95 = { by axiom 11 (quotient_less_equal) R->L }
% 28.27/3.95 ifeq2(ifeq(less_equal(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), true, quotient(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y), zero), true), true, divide(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), zero)
% 28.27/3.95 = { by axiom 8 (ifeq_axiom) R->L }
% 28.27/3.95 ifeq2(ifeq(ifeq(true, true, less_equal(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), true), true, quotient(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y), zero), true), true, divide(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), zero)
% 28.27/3.95 = { by axiom 10 (closure) R->L }
% 28.27/3.95 ifeq2(ifeq(ifeq(quotient(xQz, divide(y, xQy), divide(xQz, divide(y, xQy))), true, less_equal(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), true), true, quotient(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y), zero), true), true, divide(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), zero)
% 28.27/3.95 = { by axiom 8 (ifeq_axiom) R->L }
% 28.27/3.95 ifeq2(ifeq(ifeq(true, true, ifeq(quotient(xQz, divide(y, xQy), divide(xQz, divide(y, xQy))), true, less_equal(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), true), true), true, quotient(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y), zero), true), true, divide(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), zero)
% 28.27/3.95 = { by axiom 10 (closure) R->L }
% 28.27/3.95 ifeq2(ifeq(ifeq(quotient(xQz, y, divide(xQz, y)), true, ifeq(quotient(xQz, divide(y, xQy), divide(xQz, divide(y, xQy))), true, less_equal(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), true), true), true, quotient(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y), zero), true), true, divide(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), zero)
% 28.27/3.95 = { by axiom 8 (ifeq_axiom) R->L }
% 28.27/3.95 ifeq2(ifeq(ifeq(true, true, ifeq(quotient(xQz, y, divide(xQz, y)), true, ifeq(quotient(xQz, divide(y, xQy), divide(xQz, divide(y, xQy))), true, less_equal(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), true), true), true), true, quotient(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y), zero), true), true, divide(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), zero)
% 28.27/3.95 = { by axiom 11 (quotient_less_equal) R->L }
% 28.27/3.95 ifeq2(ifeq(ifeq(ifeq(less_equal(divide(y, xQy), y), true, quotient(divide(y, xQy), y, zero), true), true, ifeq(quotient(xQz, y, divide(xQz, y)), true, ifeq(quotient(xQz, divide(y, xQy), divide(xQz, divide(y, xQy))), true, less_equal(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), true), true), true), true, quotient(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y), zero), true), true, divide(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), zero)
% 28.27/3.95 = { by axiom 8 (ifeq_axiom) R->L }
% 28.27/3.95 ifeq2(ifeq(ifeq(ifeq(ifeq(true, true, less_equal(divide(y, xQy), y), true), true, quotient(divide(y, xQy), y, zero), true), true, ifeq(quotient(xQz, y, divide(xQz, y)), true, ifeq(quotient(xQz, divide(y, xQy), divide(xQz, divide(y, xQy))), true, less_equal(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), true), true), true), true, quotient(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y), zero), true), true, divide(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), zero)
% 28.27/3.95 = { by axiom 10 (closure) R->L }
% 28.27/3.95 ifeq2(ifeq(ifeq(ifeq(ifeq(quotient(y, xQy, divide(y, xQy)), true, less_equal(divide(y, xQy), y), true), true, quotient(divide(y, xQy), y, zero), true), true, ifeq(quotient(xQz, y, divide(xQz, y)), true, ifeq(quotient(xQz, divide(y, xQy), divide(xQz, divide(y, xQy))), true, less_equal(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), true), true), true), true, quotient(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y), zero), true), true, divide(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), zero)
% 28.27/3.95 = { by axiom 12 (divisor_existence) }
% 28.27/3.95 ifeq2(ifeq(ifeq(ifeq(true, true, quotient(divide(y, xQy), y, zero), true), true, ifeq(quotient(xQz, y, divide(xQz, y)), true, ifeq(quotient(xQz, divide(y, xQy), divide(xQz, divide(y, xQy))), true, less_equal(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), true), true), true), true, quotient(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y), zero), true), true, divide(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), zero)
% 28.27/3.95 = { by axiom 8 (ifeq_axiom) }
% 28.27/3.95 ifeq2(ifeq(ifeq(quotient(divide(y, xQy), y, zero), true, ifeq(quotient(xQz, y, divide(xQz, y)), true, ifeq(quotient(xQz, divide(y, xQy), divide(xQz, divide(y, xQy))), true, less_equal(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), true), true), true), true, quotient(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y), zero), true), true, divide(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), zero)
% 28.27/3.95 = { by axiom 8 (ifeq_axiom) R->L }
% 28.27/3.95 ifeq2(ifeq(ifeq(true, true, ifeq(quotient(divide(y, xQy), y, zero), true, ifeq(quotient(xQz, y, divide(xQz, y)), true, ifeq(quotient(xQz, divide(y, xQy), divide(xQz, divide(y, xQy))), true, less_equal(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), true), true), true), true), true, quotient(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y), zero), true), true, divide(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), zero)
% 28.27/3.95 = { by axiom 10 (closure) R->L }
% 28.27/3.95 ifeq2(ifeq(ifeq(quotient(divide(xQz, divide(y, xQy)), y, divide(divide(xQz, divide(y, xQy)), y)), true, ifeq(quotient(divide(y, xQy), y, zero), true, ifeq(quotient(xQz, y, divide(xQz, y)), true, ifeq(quotient(xQz, divide(y, xQy), divide(xQz, divide(y, xQy))), true, less_equal(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), true), true), true), true), true, quotient(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y), zero), true), true, divide(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), zero)
% 28.27/3.95 = { by axiom 8 (ifeq_axiom) R->L }
% 28.27/3.95 ifeq2(ifeq(ifeq(true, true, ifeq(quotient(divide(xQz, divide(y, xQy)), y, divide(divide(xQz, divide(y, xQy)), y)), true, ifeq(quotient(divide(y, xQy), y, zero), true, ifeq(quotient(xQz, y, divide(xQz, y)), true, ifeq(quotient(xQz, divide(y, xQy), divide(xQz, divide(y, xQy))), true, less_equal(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), true), true), true), true), true), true, quotient(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y), zero), true), true, divide(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), zero)
% 28.27/3.95 = { by axiom 4 (x_divde_zero_is_x) R->L }
% 28.27/3.95 ifeq2(ifeq(ifeq(quotient(divide(xQz, y), zero, divide(xQz, y)), true, ifeq(quotient(divide(xQz, divide(y, xQy)), y, divide(divide(xQz, divide(y, xQy)), y)), true, ifeq(quotient(divide(y, xQy), y, zero), true, ifeq(quotient(xQz, y, divide(xQz, y)), true, ifeq(quotient(xQz, divide(y, xQy), divide(xQz, divide(y, xQy))), true, less_equal(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), true), true), true), true), true), true, quotient(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y), zero), true), true, divide(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), zero)
% 28.27/3.95 = { by axiom 16 (quotient_property) }
% 28.27/3.95 ifeq2(ifeq(true, true, quotient(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y), zero), true), true, divide(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), zero)
% 28.27/3.95 = { by axiom 8 (ifeq_axiom) }
% 28.27/3.95 ifeq2(quotient(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y), zero), true, divide(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), zero)
% 28.27/3.95 = { by axiom 9 (ifeq_axiom) R->L }
% 28.27/3.95 ifeq2(quotient(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y), zero), true, ifeq2(true, true, divide(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), zero), zero)
% 28.27/3.95 = { by axiom 10 (closure) R->L }
% 28.27/3.95 ifeq2(quotient(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y), zero), true, ifeq2(quotient(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y), divide(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y))), true, divide(divide(xQz, y), divide(divide(xQz, divide(y, xQy)), y)), zero), zero)
% 28.27/3.95 = { by axiom 15 (well_defined) }
% 28.27/3.95 zero
% 28.27/3.95
% 28.27/3.95 Goal 1 (prove_xQzLEy): less_equal(xQz, y) = true.
% 28.27/3.95 Proof:
% 28.27/3.95 less_equal(xQz, y)
% 28.27/3.95 = { by lemma 17 R->L }
% 28.27/3.95 less_equal(xQz, divide(y, zero))
% 28.27/3.95 = { by lemma 19 R->L }
% 28.27/3.95 less_equal(xQz, divide(y, divide(xQz, y)))
% 28.27/3.95 = { by lemma 17 R->L }
% 28.27/3.95 less_equal(divide(xQz, zero), divide(y, divide(xQz, y)))
% 28.27/3.95 = { by lemma 19 R->L }
% 28.27/3.95 less_equal(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))
% 28.27/3.95 = { by axiom 8 (ifeq_axiom) R->L }
% 28.27/3.95 ifeq(true, true, less_equal(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), true)
% 28.27/3.95 = { by axiom 10 (closure) R->L }
% 28.27/3.95 ifeq(quotient(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)), divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), true, less_equal(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), true)
% 28.27/3.95 = { by axiom 14 (less_equal_and_equal) R->L }
% 28.27/3.95 ifeq(quotient(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)), ifeq2(less_equal(divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), zero), true, ifeq2(less_equal(zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), true, zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))))), true, less_equal(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), true)
% 28.27/3.95 = { by axiom 8 (ifeq_axiom) R->L }
% 28.27/3.95 ifeq(quotient(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)), ifeq2(ifeq(true, true, less_equal(divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), true, zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))))), true, less_equal(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), true)
% 28.27/3.95 = { by axiom 10 (closure) R->L }
% 28.27/3.95 ifeq(quotient(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)), ifeq2(ifeq(quotient(xQz, y, divide(xQz, y)), true, less_equal(divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), true, zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))))), true, less_equal(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), true)
% 28.27/3.95 = { by axiom 8 (ifeq_axiom) R->L }
% 28.27/3.95 ifeq(quotient(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)), ifeq2(ifeq(true, true, ifeq(quotient(xQz, y, divide(xQz, y)), true, less_equal(divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), true, zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))))), true, less_equal(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), true)
% 28.27/3.96 = { by axiom 10 (closure) R->L }
% 28.27/3.96 ifeq(quotient(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)), ifeq2(ifeq(quotient(xQz, divide(xQz, y), divide(xQz, divide(xQz, y))), true, ifeq(quotient(xQz, y, divide(xQz, y)), true, less_equal(divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), true, zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))))), true, less_equal(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), true)
% 28.27/3.96 = { by axiom 8 (ifeq_axiom) R->L }
% 28.27/3.96 ifeq(quotient(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)), ifeq2(ifeq(true, true, ifeq(quotient(xQz, divide(xQz, y), divide(xQz, divide(xQz, y))), true, ifeq(quotient(xQz, y, divide(xQz, y)), true, less_equal(divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), true, zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))))), true, less_equal(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), true)
% 28.27/3.96 = { by axiom 10 (closure) R->L }
% 28.27/3.96 ifeq(quotient(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)), ifeq2(ifeq(quotient(y, divide(xQz, y), divide(y, divide(xQz, y))), true, ifeq(quotient(xQz, divide(xQz, y), divide(xQz, divide(xQz, y))), true, ifeq(quotient(xQz, y, divide(xQz, y)), true, less_equal(divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), true, zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))))), true, less_equal(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), true)
% 28.27/3.96 = { by axiom 8 (ifeq_axiom) R->L }
% 28.27/3.96 ifeq(quotient(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)), ifeq2(ifeq(true, true, ifeq(quotient(y, divide(xQz, y), divide(y, divide(xQz, y))), true, ifeq(quotient(xQz, divide(xQz, y), divide(xQz, divide(xQz, y))), true, ifeq(quotient(xQz, y, divide(xQz, y)), true, less_equal(divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), true, zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))))), true, less_equal(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), true)
% 28.27/3.96 = { by axiom 10 (closure) R->L }
% 28.27/3.96 ifeq(quotient(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)), ifeq2(ifeq(quotient(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)), divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), true, ifeq(quotient(y, divide(xQz, y), divide(y, divide(xQz, y))), true, ifeq(quotient(xQz, divide(xQz, y), divide(xQz, divide(xQz, y))), true, ifeq(quotient(xQz, y, divide(xQz, y)), true, less_equal(divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), true, zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))))), true, less_equal(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), true)
% 28.27/3.96 = { by axiom 8 (ifeq_axiom) R->L }
% 28.27/3.96 ifeq(quotient(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)), ifeq2(ifeq(quotient(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)), divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), true, ifeq(true, true, ifeq(quotient(y, divide(xQz, y), divide(y, divide(xQz, y))), true, ifeq(quotient(xQz, divide(xQz, y), divide(xQz, divide(xQz, y))), true, ifeq(quotient(xQz, y, divide(xQz, y)), true, less_equal(divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), true, zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))))), true, less_equal(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), true)
% 28.27/3.96 = { by axiom 3 (x_divide_x_is_zero) R->L }
% 28.27/3.96 ifeq(quotient(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)), ifeq2(ifeq(quotient(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)), divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), true, ifeq(quotient(divide(xQz, y), divide(xQz, y), zero), true, ifeq(quotient(y, divide(xQz, y), divide(y, divide(xQz, y))), true, ifeq(quotient(xQz, divide(xQz, y), divide(xQz, divide(xQz, y))), true, ifeq(quotient(xQz, y, divide(xQz, y)), true, less_equal(divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), true, zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))))), true, less_equal(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), true)
% 28.27/3.96 = { by axiom 16 (quotient_property) }
% 28.27/3.96 ifeq(quotient(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)), ifeq2(true, true, ifeq2(less_equal(zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), true, zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))))), true, less_equal(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), true)
% 28.27/3.96 = { by axiom 9 (ifeq_axiom) }
% 28.27/3.96 ifeq(quotient(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)), ifeq2(less_equal(zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)))), true, zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))))), true, less_equal(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), true)
% 28.27/3.96 = { by axiom 1 (zero_is_smallest) }
% 28.27/3.96 ifeq(quotient(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)), ifeq2(true, true, zero, divide(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))))), true, less_equal(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), true)
% 28.27/3.96 = { by axiom 9 (ifeq_axiom) }
% 28.27/3.96 ifeq(quotient(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y)), zero), true, less_equal(divide(xQz, divide(xQz, y)), divide(y, divide(xQz, y))), true)
% 28.27/3.96 = { by axiom 13 (less_equal_quotient) }
% 28.27/3.96 true
% 28.27/3.96 % SZS output end Proof
% 28.27/3.96
% 28.27/3.96 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------