%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : HEN007-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/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 10:18:58 AM UTC 2026
% Result : Unsatisfiable 94.82s 12.43s
% Output : Proof 96.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.39 % Computer : n010.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 10:51:07 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 94.82/12.43 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 94.82/12.43
% 94.82/12.43 % SZS status Unsatisfiable
% 94.82/12.43
% 95.50/12.53 % SZS output start Proof
% 95.50/12.53 Axiom 1 (zero_is_smallest): less_equal(zero, X) = true.
% 95.50/12.53 Axiom 2 (xLEy): less_equal(x, y) = true.
% 95.50/12.53 Axiom 3 (zQx): quotient(z, x, zQx) = true.
% 95.50/12.53 Axiom 4 (zQy): quotient(z, y, zQy) = true.
% 95.50/12.53 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 95.50/12.53 Axiom 6 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 95.50/12.53 Axiom 7 (closure): quotient(X, Y, divide(X, Y)) = true.
% 95.50/12.54 Axiom 8 (quotient_less_equal): ifeq(less_equal(X, Y), true, quotient(X, Y, zero), true) = true.
% 95.50/12.54 Axiom 9 (divisor_existence): ifeq(quotient(X, Y, Z), true, less_equal(Z, X), true) = true.
% 95.50/12.54 Axiom 10 (less_equal_quotient): ifeq(quotient(X, Y, zero), true, less_equal(X, Y), true) = true.
% 95.50/12.54 Axiom 11 (less_equal_and_equal): ifeq2(less_equal(X, Y), true, ifeq2(less_equal(Y, X), true, Y, X), X) = X.
% 95.50/12.54 Axiom 12 (well_defined): ifeq2(quotient(X, Y, Z), true, ifeq2(quotient(X, Y, W), true, W, Z), Z) = Z.
% 95.50/12.54 Axiom 13 (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.
% 95.50/12.54
% 95.50/12.54 Goal 1 (prove_zQyLEzQx): less_equal(zQy, zQx) = true.
% 95.50/12.54 Proof:
% 95.50/12.54 less_equal(zQy, zQx)
% 95.50/12.54 = { by axiom 11 (less_equal_and_equal) R->L }
% 95.50/12.54 less_equal(ifeq2(less_equal(zQy, divide(zQx, y)), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.54 = { by axiom 5 (ifeq_axiom) R->L }
% 95.50/12.54 less_equal(ifeq2(ifeq(true, true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.54 = { by axiom 7 (closure) R->L }
% 95.50/12.54 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), divide(zQy, divide(zQx, y))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.54 = { by axiom 11 (less_equal_and_equal) R->L }
% 95.50/12.54 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(less_equal(divide(zQy, divide(zQx, y)), zero), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.54 = { by axiom 5 (ifeq_axiom) R->L }
% 95.50/12.54 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(true, true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.54 = { by axiom 7 (closure) R->L }
% 95.50/12.54 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, divide(divide(zQy, divide(zQx, y)), zero)), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.54 = { by axiom 11 (less_equal_and_equal) R->L }
% 95.50/12.54 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.55 = { by axiom 5 (ifeq_axiom) R->L }
% 95.50/12.55 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(true, true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.55 = { by axiom 8 (quotient_less_equal) R->L }
% 95.50/12.55 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(ifeq(less_equal(divide(zQy, zero), divide(zQx, y)), true, quotient(divide(zQy, zero), divide(zQx, y), zero), true), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.55 = { by axiom 5 (ifeq_axiom) R->L }
% 95.50/12.55 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(ifeq(ifeq(true, true, less_equal(divide(zQy, zero), divide(zQx, y)), true), true, quotient(divide(zQy, zero), divide(zQx, y), zero), true), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.55 = { by axiom 7 (closure) R->L }
% 95.50/12.55 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(ifeq(ifeq(quotient(zQx, y, divide(zQx, y)), true, less_equal(divide(zQy, zero), divide(zQx, y)), true), true, quotient(divide(zQy, zero), divide(zQx, y), zero), true), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.55 = { by axiom 5 (ifeq_axiom) R->L }
% 95.50/12.55 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(ifeq(ifeq(true, true, ifeq(quotient(zQx, y, divide(zQx, y)), true, less_equal(divide(zQy, zero), divide(zQx, y)), true), true), true, quotient(divide(zQy, zero), divide(zQx, y), zero), true), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.55 = { by axiom 7 (closure) R->L }
% 95.50/12.56 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(ifeq(ifeq(quotient(zQy, zero, divide(zQy, zero)), true, ifeq(quotient(zQx, y, divide(zQx, y)), true, less_equal(divide(zQy, zero), divide(zQx, y)), true), true), true, quotient(divide(zQy, zero), divide(zQx, y), zero), true), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.56 = { by axiom 5 (ifeq_axiom) R->L }
% 95.50/12.56 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(ifeq(ifeq(quotient(zQy, zero, divide(zQy, zero)), true, ifeq(quotient(zQx, y, divide(zQx, y)), true, ifeq(true, true, less_equal(divide(zQy, zero), divide(zQx, y)), true), true), true), true, quotient(divide(zQy, zero), divide(zQx, y), zero), true), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.56 = { by axiom 12 (well_defined) R->L }
% 95.50/12.56 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(ifeq(ifeq(quotient(zQy, ifeq2(quotient(x, y, zero), true, ifeq2(quotient(x, y, divide(x, y)), true, divide(x, y), zero), zero), divide(zQy, zero)), true, ifeq(quotient(zQx, y, divide(zQx, y)), true, ifeq(true, true, less_equal(divide(zQy, zero), divide(zQx, y)), true), true), true), true, quotient(divide(zQy, zero), divide(zQx, y), zero), true), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.56 = { by axiom 7 (closure) }
% 95.50/12.56 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(ifeq(ifeq(quotient(zQy, ifeq2(quotient(x, y, zero), true, ifeq2(true, true, divide(x, y), zero), zero), divide(zQy, zero)), true, ifeq(quotient(zQx, y, divide(zQx, y)), true, ifeq(true, true, less_equal(divide(zQy, zero), divide(zQx, y)), true), true), true), true, quotient(divide(zQy, zero), divide(zQx, y), zero), true), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.56 = { by axiom 6 (ifeq_axiom) }
% 95.50/12.56 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(ifeq(ifeq(quotient(zQy, ifeq2(quotient(x, y, zero), true, divide(x, y), zero), divide(zQy, zero)), true, ifeq(quotient(zQx, y, divide(zQx, y)), true, ifeq(true, true, less_equal(divide(zQy, zero), divide(zQx, y)), true), true), true), true, quotient(divide(zQy, zero), divide(zQx, y), zero), true), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.56 = { by axiom 5 (ifeq_axiom) R->L }
% 95.50/12.56 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(ifeq(ifeq(quotient(zQy, ifeq2(ifeq(true, true, quotient(x, y, zero), true), true, divide(x, y), zero), divide(zQy, zero)), true, ifeq(quotient(zQx, y, divide(zQx, y)), true, ifeq(true, true, less_equal(divide(zQy, zero), divide(zQx, y)), true), true), true), true, quotient(divide(zQy, zero), divide(zQx, y), zero), true), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.57 = { by axiom 2 (xLEy) R->L }
% 95.50/12.57 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(ifeq(ifeq(quotient(zQy, ifeq2(ifeq(less_equal(x, y), true, quotient(x, y, zero), true), true, divide(x, y), zero), divide(zQy, zero)), true, ifeq(quotient(zQx, y, divide(zQx, y)), true, ifeq(true, true, less_equal(divide(zQy, zero), divide(zQx, y)), true), true), true), true, quotient(divide(zQy, zero), divide(zQx, y), zero), true), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.57 = { by axiom 8 (quotient_less_equal) }
% 95.50/12.57 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(ifeq(ifeq(quotient(zQy, ifeq2(true, true, divide(x, y), zero), divide(zQy, zero)), true, ifeq(quotient(zQx, y, divide(zQx, y)), true, ifeq(true, true, less_equal(divide(zQy, zero), divide(zQx, y)), true), true), true), true, quotient(divide(zQy, zero), divide(zQx, y), zero), true), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.57 = { by axiom 6 (ifeq_axiom) }
% 95.50/12.57 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(ifeq(ifeq(quotient(zQy, divide(x, y), divide(zQy, zero)), true, ifeq(quotient(zQx, y, divide(zQx, y)), true, ifeq(true, true, less_equal(divide(zQy, zero), divide(zQx, y)), true), true), true), true, quotient(divide(zQy, zero), divide(zQx, y), zero), true), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.57 = { by axiom 7 (closure) R->L }
% 95.50/12.57 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(ifeq(ifeq(quotient(zQy, divide(x, y), divide(zQy, zero)), true, ifeq(quotient(zQx, y, divide(zQx, y)), true, ifeq(quotient(x, y, divide(x, y)), true, less_equal(divide(zQy, zero), divide(zQx, y)), true), true), true), true, quotient(divide(zQy, zero), divide(zQx, y), zero), true), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.57 = { by axiom 5 (ifeq_axiom) R->L }
% 95.50/12.58 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(ifeq(ifeq(quotient(zQy, divide(x, y), divide(zQy, zero)), true, ifeq(quotient(zQx, y, divide(zQx, y)), true, ifeq(quotient(x, y, divide(x, y)), true, ifeq(true, true, less_equal(divide(zQy, zero), divide(zQx, y)), true), true), true), true), true, quotient(divide(zQy, zero), divide(zQx, y), zero), true), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.58 = { by axiom 4 (zQy) R->L }
% 95.50/12.58 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(ifeq(ifeq(quotient(zQy, divide(x, y), divide(zQy, zero)), true, ifeq(quotient(zQx, y, divide(zQx, y)), true, ifeq(quotient(x, y, divide(x, y)), true, ifeq(quotient(z, y, zQy), true, less_equal(divide(zQy, zero), divide(zQx, y)), true), true), true), true), true, quotient(divide(zQy, zero), divide(zQx, y), zero), true), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.58 = { by axiom 5 (ifeq_axiom) R->L }
% 95.50/12.58 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(ifeq(ifeq(quotient(zQy, divide(x, y), divide(zQy, zero)), true, ifeq(quotient(zQx, y, divide(zQx, y)), true, ifeq(quotient(x, y, divide(x, y)), true, ifeq(quotient(z, y, zQy), true, ifeq(true, true, less_equal(divide(zQy, zero), divide(zQx, y)), true), true), true), true), true), true, quotient(divide(zQy, zero), divide(zQx, y), zero), true), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.58 = { by axiom 3 (zQx) R->L }
% 95.50/12.58 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(ifeq(ifeq(quotient(zQy, divide(x, y), divide(zQy, zero)), true, ifeq(quotient(zQx, y, divide(zQx, y)), true, ifeq(quotient(x, y, divide(x, y)), true, ifeq(quotient(z, y, zQy), true, ifeq(quotient(z, x, zQx), true, less_equal(divide(zQy, zero), divide(zQx, y)), true), true), true), true), true), true, quotient(divide(zQy, zero), divide(zQx, y), zero), true), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.58 = { by axiom 13 (quotient_property) }
% 95.50/12.58 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(ifeq(true, true, quotient(divide(zQy, zero), divide(zQx, y), zero), true), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.58 = { by axiom 5 (ifeq_axiom) }
% 95.50/12.58 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(quotient(divide(zQy, zero), divide(zQx, y), zero), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.58 = { by axiom 5 (ifeq_axiom) R->L }
% 95.50/12.59 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(quotient(divide(zQy, zero), divide(zQx, y), zero), true, ifeq(true, true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.59 = { by axiom 7 (closure) R->L }
% 95.50/12.59 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(quotient(divide(zQy, zero), divide(zQx, y), zero), true, ifeq(quotient(zQy, divide(zQx, y), divide(zQy, divide(zQx, y))), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.59 = { by axiom 5 (ifeq_axiom) R->L }
% 95.50/12.59 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(quotient(divide(zQy, zero), divide(zQx, y), zero), true, ifeq(quotient(zQy, divide(zQx, y), divide(zQy, divide(zQx, y))), true, ifeq(true, true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.59 = { by axiom 7 (closure) R->L }
% 95.50/12.59 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(quotient(divide(zQy, zero), divide(zQx, y), zero), true, ifeq(quotient(zQy, divide(zQx, y), divide(zQy, divide(zQx, y))), true, ifeq(quotient(zQy, zero, divide(zQy, zero)), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.59 = { by axiom 5 (ifeq_axiom) R->L }
% 95.50/12.59 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(quotient(divide(zQy, zero), divide(zQx, y), zero), true, ifeq(true, true, ifeq(quotient(zQy, divide(zQx, y), divide(zQy, divide(zQx, y))), true, ifeq(quotient(zQy, zero, divide(zQy, zero)), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.59 = { by axiom 8 (quotient_less_equal) R->L }
% 95.50/12.59 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(quotient(divide(zQy, zero), divide(zQx, y), zero), true, ifeq(ifeq(less_equal(zero, divide(zQx, y)), true, quotient(zero, divide(zQx, y), zero), true), true, ifeq(quotient(zQy, divide(zQx, y), divide(zQy, divide(zQx, y))), true, ifeq(quotient(zQy, zero, divide(zQy, zero)), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.59 = { by axiom 1 (zero_is_smallest) }
% 95.50/12.60 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(quotient(divide(zQy, zero), divide(zQx, y), zero), true, ifeq(ifeq(true, true, quotient(zero, divide(zQx, y), zero), true), true, ifeq(quotient(zQy, divide(zQx, y), divide(zQy, divide(zQx, y))), true, ifeq(quotient(zQy, zero, divide(zQy, zero)), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.60 = { by axiom 5 (ifeq_axiom) }
% 95.50/12.60 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(quotient(divide(zQy, zero), divide(zQx, y), zero), true, ifeq(quotient(zero, divide(zQx, y), zero), true, ifeq(quotient(zQy, divide(zQx, y), divide(zQy, divide(zQx, y))), true, ifeq(quotient(zQy, zero, divide(zQy, zero)), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.60 = { by axiom 5 (ifeq_axiom) R->L }
% 95.50/12.60 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(true, true, ifeq(quotient(divide(zQy, zero), divide(zQx, y), zero), true, ifeq(quotient(zero, divide(zQx, y), zero), true, ifeq(quotient(zQy, divide(zQx, y), divide(zQy, divide(zQx, y))), true, ifeq(quotient(zQy, zero, divide(zQy, zero)), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.60 = { by axiom 7 (closure) R->L }
% 95.50/12.60 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, divide(divide(zQy, divide(zQx, y)), zero)), true, ifeq(quotient(divide(zQy, zero), divide(zQx, y), zero), true, ifeq(quotient(zero, divide(zQx, y), zero), true, ifeq(quotient(zQy, divide(zQx, y), divide(zQy, divide(zQx, y))), true, ifeq(quotient(zQy, zero, divide(zQy, zero)), true, less_equal(divide(divide(zQy, divide(zQx, y)), zero), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.60 = { by axiom 13 (quotient_property) }
% 95.50/12.60 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(true, true, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero)), divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.60 = { by axiom 6 (ifeq_axiom) }
% 95.50/12.60 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(less_equal(zero, divide(divide(zQy, divide(zQx, y)), zero)), true, zero, divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.60 = { by axiom 1 (zero_is_smallest) }
% 95.50/12.60 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, ifeq2(true, true, zero, divide(divide(zQy, divide(zQx, y)), zero))), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.60 = { by axiom 6 (ifeq_axiom) }
% 95.50/12.60 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(ifeq(quotient(divide(zQy, divide(zQx, y)), zero, zero), true, less_equal(divide(zQy, divide(zQx, y)), zero), true), true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.60 = { by axiom 10 (less_equal_quotient) }
% 95.50/12.60 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(true, true, ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y))), divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.60 = { by axiom 6 (ifeq_axiom) }
% 95.50/12.60 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(less_equal(zero, divide(zQy, divide(zQx, y))), true, zero, divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 95.50/12.60 = { by axiom 1 (zero_is_smallest) }
% 95.50/12.60 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), ifeq2(true, true, zero, divide(zQy, divide(zQx, y)))), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 96.33/12.61 = { by axiom 6 (ifeq_axiom) }
% 96.33/12.61 less_equal(ifeq2(ifeq(quotient(zQy, divide(zQx, y), zero), true, less_equal(zQy, divide(zQx, y)), true), true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 96.33/12.61 = { by axiom 10 (less_equal_quotient) }
% 96.33/12.61 less_equal(ifeq2(true, true, ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQy), zQx)
% 96.33/12.61 = { by axiom 6 (ifeq_axiom) }
% 96.33/12.61 less_equal(ifeq2(less_equal(divide(zQx, y), zQy), true, divide(zQx, y), zQy), zQx)
% 96.33/12.61 = { by axiom 5 (ifeq_axiom) R->L }
% 96.33/12.61 less_equal(ifeq2(ifeq(true, true, less_equal(divide(zQx, y), zQy), true), true, divide(zQx, y), zQy), zQx)
% 96.33/12.61 = { by axiom 7 (closure) R->L }
% 96.33/12.61 less_equal(ifeq2(ifeq(quotient(divide(zQx, y), zQy, divide(divide(zQx, y), zQy)), true, less_equal(divide(zQx, y), zQy), true), true, divide(zQx, y), zQy), zQx)
% 96.33/12.61 = { by axiom 11 (less_equal_and_equal) R->L }
% 96.33/12.61 less_equal(ifeq2(ifeq(quotient(divide(zQx, y), zQy, ifeq2(less_equal(divide(divide(zQx, y), zQy), zero), true, ifeq2(less_equal(zero, divide(divide(zQx, y), zQy)), true, zero, divide(divide(zQx, y), zQy)), divide(divide(zQx, y), zQy))), true, less_equal(divide(zQx, y), zQy), true), true, divide(zQx, y), zQy), zQx)
% 96.33/12.61 = { by axiom 5 (ifeq_axiom) R->L }
% 96.33/12.61 less_equal(ifeq2(ifeq(quotient(divide(zQx, y), zQy, ifeq2(ifeq(true, true, less_equal(divide(divide(zQx, y), zQy), zero), true), true, ifeq2(less_equal(zero, divide(divide(zQx, y), zQy)), true, zero, divide(divide(zQx, y), zQy)), divide(divide(zQx, y), zQy))), true, less_equal(divide(zQx, y), zQy), true), true, divide(zQx, y), zQy), zQx)
% 96.33/12.61 = { by axiom 7 (closure) R->L }
% 96.33/12.61 less_equal(ifeq2(ifeq(quotient(divide(zQx, y), zQy, ifeq2(ifeq(quotient(zQx, y, divide(zQx, y)), true, less_equal(divide(divide(zQx, y), zQy), zero), true), true, ifeq2(less_equal(zero, divide(divide(zQx, y), zQy)), true, zero, divide(divide(zQx, y), zQy)), divide(divide(zQx, y), zQy))), true, less_equal(divide(zQx, y), zQy), true), true, divide(zQx, y), zQy), zQx)
% 96.33/12.61 = { by axiom 5 (ifeq_axiom) R->L }
% 96.33/12.61 less_equal(ifeq2(ifeq(quotient(divide(zQx, y), zQy, ifeq2(ifeq(true, true, ifeq(quotient(zQx, y, divide(zQx, y)), true, less_equal(divide(divide(zQx, y), zQy), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(zQx, y), zQy)), true, zero, divide(divide(zQx, y), zQy)), divide(divide(zQx, y), zQy))), true, less_equal(divide(zQx, y), zQy), true), true, divide(zQx, y), zQy), zQx)
% 96.33/12.61 = { by axiom 7 (closure) R->L }
% 96.33/12.61 less_equal(ifeq2(ifeq(quotient(divide(zQx, y), zQy, ifeq2(ifeq(quotient(divide(zQx, y), zQy, divide(divide(zQx, y), zQy)), true, ifeq(quotient(zQx, y, divide(zQx, y)), true, less_equal(divide(divide(zQx, y), zQy), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(zQx, y), zQy)), true, zero, divide(divide(zQx, y), zQy)), divide(divide(zQx, y), zQy))), true, less_equal(divide(zQx, y), zQy), true), true, divide(zQx, y), zQy), zQx)
% 96.33/12.61 = { by axiom 5 (ifeq_axiom) R->L }
% 96.33/12.61 less_equal(ifeq2(ifeq(quotient(divide(zQx, y), zQy, ifeq2(ifeq(quotient(divide(zQx, y), zQy, divide(divide(zQx, y), zQy)), true, ifeq(quotient(zQx, y, divide(zQx, y)), true, ifeq(true, true, less_equal(divide(divide(zQx, y), zQy), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(zQx, y), zQy)), true, zero, divide(divide(zQx, y), zQy)), divide(divide(zQx, y), zQy))), true, less_equal(divide(zQx, y), zQy), true), true, divide(zQx, y), zQy), zQx)
% 96.33/12.61 = { by axiom 8 (quotient_less_equal) R->L }
% 96.33/12.61 less_equal(ifeq2(ifeq(quotient(divide(zQx, y), zQy, ifeq2(ifeq(quotient(divide(zQx, y), zQy, divide(divide(zQx, y), zQy)), true, ifeq(quotient(zQx, y, divide(zQx, y)), true, ifeq(ifeq(less_equal(zQx, z), true, quotient(zQx, z, zero), true), true, less_equal(divide(divide(zQx, y), zQy), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(zQx, y), zQy)), true, zero, divide(divide(zQx, y), zQy)), divide(divide(zQx, y), zQy))), true, less_equal(divide(zQx, y), zQy), true), true, divide(zQx, y), zQy), zQx)
% 96.33/12.61 = { by axiom 5 (ifeq_axiom) R->L }
% 96.33/12.61 less_equal(ifeq2(ifeq(quotient(divide(zQx, y), zQy, ifeq2(ifeq(quotient(divide(zQx, y), zQy, divide(divide(zQx, y), zQy)), true, ifeq(quotient(zQx, y, divide(zQx, y)), true, ifeq(ifeq(ifeq(true, true, less_equal(zQx, z), true), true, quotient(zQx, z, zero), true), true, less_equal(divide(divide(zQx, y), zQy), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(zQx, y), zQy)), true, zero, divide(divide(zQx, y), zQy)), divide(divide(zQx, y), zQy))), true, less_equal(divide(zQx, y), zQy), true), true, divide(zQx, y), zQy), zQx)
% 96.33/12.61 = { by axiom 3 (zQx) R->L }
% 96.33/12.61 less_equal(ifeq2(ifeq(quotient(divide(zQx, y), zQy, ifeq2(ifeq(quotient(divide(zQx, y), zQy, divide(divide(zQx, y), zQy)), true, ifeq(quotient(zQx, y, divide(zQx, y)), true, ifeq(ifeq(ifeq(quotient(z, x, zQx), true, less_equal(zQx, z), true), true, quotient(zQx, z, zero), true), true, less_equal(divide(divide(zQx, y), zQy), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(zQx, y), zQy)), true, zero, divide(divide(zQx, y), zQy)), divide(divide(zQx, y), zQy))), true, less_equal(divide(zQx, y), zQy), true), true, divide(zQx, y), zQy), zQx)
% 96.33/12.61 = { by axiom 9 (divisor_existence) }
% 96.33/12.62 less_equal(ifeq2(ifeq(quotient(divide(zQx, y), zQy, ifeq2(ifeq(quotient(divide(zQx, y), zQy, divide(divide(zQx, y), zQy)), true, ifeq(quotient(zQx, y, divide(zQx, y)), true, ifeq(ifeq(true, true, quotient(zQx, z, zero), true), true, less_equal(divide(divide(zQx, y), zQy), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(zQx, y), zQy)), true, zero, divide(divide(zQx, y), zQy)), divide(divide(zQx, y), zQy))), true, less_equal(divide(zQx, y), zQy), true), true, divide(zQx, y), zQy), zQx)
% 96.33/12.62 = { by axiom 5 (ifeq_axiom) }
% 96.33/12.62 less_equal(ifeq2(ifeq(quotient(divide(zQx, y), zQy, ifeq2(ifeq(quotient(divide(zQx, y), zQy, divide(divide(zQx, y), zQy)), true, ifeq(quotient(zQx, y, divide(zQx, y)), true, ifeq(quotient(zQx, z, zero), true, less_equal(divide(divide(zQx, y), zQy), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(zQx, y), zQy)), true, zero, divide(divide(zQx, y), zQy)), divide(divide(zQx, y), zQy))), true, less_equal(divide(zQx, y), zQy), true), true, divide(zQx, y), zQy), zQx)
% 96.33/12.62 = { by axiom 5 (ifeq_axiom) R->L }
% 96.33/12.62 less_equal(ifeq2(ifeq(quotient(divide(zQx, y), zQy, ifeq2(ifeq(quotient(divide(zQx, y), zQy, divide(divide(zQx, y), zQy)), true, ifeq(true, true, ifeq(quotient(zQx, y, divide(zQx, y)), true, ifeq(quotient(zQx, z, zero), true, less_equal(divide(divide(zQx, y), zQy), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(zQx, y), zQy)), true, zero, divide(divide(zQx, y), zQy)), divide(divide(zQx, y), zQy))), true, less_equal(divide(zQx, y), zQy), true), true, divide(zQx, y), zQy), zQx)
% 96.33/12.62 = { by axiom 8 (quotient_less_equal) R->L }
% 96.33/12.62 less_equal(ifeq2(ifeq(quotient(divide(zQx, y), zQy, ifeq2(ifeq(quotient(divide(zQx, y), zQy, divide(divide(zQx, y), zQy)), true, ifeq(ifeq(less_equal(zero, y), true, quotient(zero, y, zero), true), true, ifeq(quotient(zQx, y, divide(zQx, y)), true, ifeq(quotient(zQx, z, zero), true, less_equal(divide(divide(zQx, y), zQy), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(zQx, y), zQy)), true, zero, divide(divide(zQx, y), zQy)), divide(divide(zQx, y), zQy))), true, less_equal(divide(zQx, y), zQy), true), true, divide(zQx, y), zQy), zQx)
% 96.33/12.62 = { by axiom 1 (zero_is_smallest) }
% 96.33/12.62 less_equal(ifeq2(ifeq(quotient(divide(zQx, y), zQy, ifeq2(ifeq(quotient(divide(zQx, y), zQy, divide(divide(zQx, y), zQy)), true, ifeq(ifeq(true, true, quotient(zero, y, zero), true), true, ifeq(quotient(zQx, y, divide(zQx, y)), true, ifeq(quotient(zQx, z, zero), true, less_equal(divide(divide(zQx, y), zQy), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(zQx, y), zQy)), true, zero, divide(divide(zQx, y), zQy)), divide(divide(zQx, y), zQy))), true, less_equal(divide(zQx, y), zQy), true), true, divide(zQx, y), zQy), zQx)
% 96.33/12.62 = { by axiom 5 (ifeq_axiom) }
% 96.33/12.62 less_equal(ifeq2(ifeq(quotient(divide(zQx, y), zQy, ifeq2(ifeq(quotient(divide(zQx, y), zQy, divide(divide(zQx, y), zQy)), true, ifeq(quotient(zero, y, zero), true, ifeq(quotient(zQx, y, divide(zQx, y)), true, ifeq(quotient(zQx, z, zero), true, less_equal(divide(divide(zQx, y), zQy), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(zQx, y), zQy)), true, zero, divide(divide(zQx, y), zQy)), divide(divide(zQx, y), zQy))), true, less_equal(divide(zQx, y), zQy), true), true, divide(zQx, y), zQy), zQx)
% 96.33/12.62 = { by axiom 5 (ifeq_axiom) R->L }
% 96.33/12.62 less_equal(ifeq2(ifeq(quotient(divide(zQx, y), zQy, ifeq2(ifeq(quotient(divide(zQx, y), zQy, divide(divide(zQx, y), zQy)), true, ifeq(quotient(zero, y, zero), true, ifeq(true, true, ifeq(quotient(zQx, y, divide(zQx, y)), true, ifeq(quotient(zQx, z, zero), true, less_equal(divide(divide(zQx, y), zQy), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(zQx, y), zQy)), true, zero, divide(divide(zQx, y), zQy)), divide(divide(zQx, y), zQy))), true, less_equal(divide(zQx, y), zQy), true), true, divide(zQx, y), zQy), zQx)
% 96.33/12.62 = { by axiom 4 (zQy) R->L }
% 96.33/12.62 less_equal(ifeq2(ifeq(quotient(divide(zQx, y), zQy, ifeq2(ifeq(quotient(divide(zQx, y), zQy, divide(divide(zQx, y), zQy)), true, ifeq(quotient(zero, y, zero), true, ifeq(quotient(z, y, zQy), true, ifeq(quotient(zQx, y, divide(zQx, y)), true, ifeq(quotient(zQx, z, zero), true, less_equal(divide(divide(zQx, y), zQy), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(zQx, y), zQy)), true, zero, divide(divide(zQx, y), zQy)), divide(divide(zQx, y), zQy))), true, less_equal(divide(zQx, y), zQy), true), true, divide(zQx, y), zQy), zQx)
% 96.33/12.62 = { by axiom 13 (quotient_property) }
% 96.33/12.62 less_equal(ifeq2(ifeq(quotient(divide(zQx, y), zQy, ifeq2(true, true, ifeq2(less_equal(zero, divide(divide(zQx, y), zQy)), true, zero, divide(divide(zQx, y), zQy)), divide(divide(zQx, y), zQy))), true, less_equal(divide(zQx, y), zQy), true), true, divide(zQx, y), zQy), zQx)
% 96.33/12.62 = { by axiom 6 (ifeq_axiom) }
% 96.33/12.62 less_equal(ifeq2(ifeq(quotient(divide(zQx, y), zQy, ifeq2(less_equal(zero, divide(divide(zQx, y), zQy)), true, zero, divide(divide(zQx, y), zQy))), true, less_equal(divide(zQx, y), zQy), true), true, divide(zQx, y), zQy), zQx)
% 96.33/12.62 = { by axiom 1 (zero_is_smallest) }
% 96.33/12.62 less_equal(ifeq2(ifeq(quotient(divide(zQx, y), zQy, ifeq2(true, true, zero, divide(divide(zQx, y), zQy))), true, less_equal(divide(zQx, y), zQy), true), true, divide(zQx, y), zQy), zQx)
% 96.33/12.62 = { by axiom 6 (ifeq_axiom) }
% 96.33/12.62 less_equal(ifeq2(ifeq(quotient(divide(zQx, y), zQy, zero), true, less_equal(divide(zQx, y), zQy), true), true, divide(zQx, y), zQy), zQx)
% 96.33/12.62 = { by axiom 10 (less_equal_quotient) }
% 96.33/12.62 less_equal(ifeq2(true, true, divide(zQx, y), zQy), zQx)
% 96.33/12.62 = { by axiom 6 (ifeq_axiom) }
% 96.33/12.62 less_equal(divide(zQx, y), zQx)
% 96.33/12.62 = { by axiom 5 (ifeq_axiom) R->L }
% 96.33/12.62 ifeq(true, true, less_equal(divide(zQx, y), zQx), true)
% 96.33/12.62 = { by axiom 7 (closure) R->L }
% 96.33/12.62 ifeq(quotient(zQx, y, divide(zQx, y)), true, less_equal(divide(zQx, y), zQx), true)
% 96.33/12.62 = { by axiom 9 (divisor_existence) }
% 96.33/12.62 true
% 96.33/12.62 % SZS output end Proof
% 96.33/12.62
% 96.33/12.62 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------