%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : HEN006-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 10:18:57 AM UTC 2026
% Result : Unsatisfiable 18.85s 2.89s
% Output : Proof 19.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n007.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 27 10:48:45 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.85/2.89 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
% 18.85/2.89
% 18.85/2.89 % SZS status Unsatisfiable
% 18.85/2.89
% 19.65/2.93 % SZS output start Proof
% 19.65/2.93 Axiom 1 (zero_is_smallest): less_equal(zero, X) = true.
% 19.65/2.93 Axiom 2 (xQyLEz): less_equal(xQy, z) = true.
% 19.65/2.93 Axiom 3 (xQy): quotient(x, y, xQy) = true.
% 19.65/2.93 Axiom 4 (xQz): quotient(x, z, xQz) = true.
% 19.65/2.93 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 19.65/2.93 Axiom 6 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 19.65/2.93 Axiom 7 (closure): quotient(X, Y, divide(X, Y)) = true.
% 19.65/2.93 Axiom 8 (quotient_less_equal): ifeq(less_equal(X, Y), true, quotient(X, Y, zero), true) = true.
% 19.65/2.93 Axiom 9 (divisor_existence): ifeq(quotient(X, Y, Z), true, less_equal(Z, X), true) = true.
% 19.65/2.93 Axiom 10 (less_equal_quotient): ifeq(quotient(X, Y, zero), true, less_equal(X, Y), true) = true.
% 19.65/2.93 Axiom 11 (less_equal_and_equal): ifeq2(less_equal(X, Y), true, ifeq2(less_equal(Y, X), true, Y, X), X) = X.
% 19.65/2.93 Axiom 12 (well_defined): ifeq2(quotient(X, Y, Z), true, ifeq2(quotient(X, Y, W), true, W, Z), Z) = Z.
% 19.65/2.93 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.
% 19.65/2.93
% 19.65/2.93 Goal 1 (prove_xQzLEy): less_equal(xQz, y) = true.
% 19.65/2.93 Proof:
% 19.65/2.93 less_equal(xQz, y)
% 19.65/2.93 = { by axiom 5 (ifeq_axiom) R->L }
% 19.65/2.93 ifeq(true, true, less_equal(xQz, y), true)
% 19.65/2.93 = { by axiom 7 (closure) R->L }
% 19.65/2.93 ifeq(quotient(xQz, y, divide(xQz, y)), true, less_equal(xQz, y), true)
% 19.65/2.93 = { by axiom 11 (less_equal_and_equal) R->L }
% 19.65/2.93 ifeq(quotient(xQz, y, ifeq2(less_equal(divide(xQz, y), zero), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.93 = { by axiom 5 (ifeq_axiom) R->L }
% 19.65/2.93 ifeq(quotient(xQz, y, ifeq2(ifeq(true, true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.93 = { by axiom 7 (closure) R->L }
% 19.65/2.93 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, divide(divide(xQz, y), zero)), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.93 = { by axiom 11 (less_equal_and_equal) R->L }
% 19.65/2.93 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(less_equal(divide(divide(xQz, y), zero), zero), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.93 = { by axiom 5 (ifeq_axiom) R->L }
% 19.65/2.93 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(true, true, less_equal(divide(divide(xQz, y), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.93 = { by axiom 7 (closure) R->L }
% 19.65/2.93 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), divide(xQz, divide(y, z))), true, less_equal(divide(divide(xQz, y), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.94 = { by axiom 11 (less_equal_and_equal) R->L }
% 19.65/2.94 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), ifeq2(less_equal(divide(xQz, divide(y, z)), zero), true, ifeq2(less_equal(zero, divide(xQz, divide(y, z))), true, zero, divide(xQz, divide(y, z))), divide(xQz, divide(y, z)))), true, less_equal(divide(divide(xQz, y), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.94 = { by axiom 5 (ifeq_axiom) R->L }
% 19.65/2.94 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), ifeq2(ifeq(true, true, less_equal(divide(xQz, divide(y, z)), zero), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, z))), true, zero, divide(xQz, divide(y, z))), divide(xQz, divide(y, z)))), true, less_equal(divide(divide(xQz, y), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.94 = { by axiom 7 (closure) R->L }
% 19.65/2.94 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), ifeq2(ifeq(quotient(y, z, divide(y, z)), true, less_equal(divide(xQz, divide(y, z)), zero), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, z))), true, zero, divide(xQz, divide(y, z))), divide(xQz, divide(y, z)))), true, less_equal(divide(divide(xQz, y), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.94 = { by axiom 5 (ifeq_axiom) R->L }
% 19.65/2.94 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), ifeq2(ifeq(true, true, ifeq(quotient(y, z, divide(y, z)), true, less_equal(divide(xQz, divide(y, z)), zero), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, z))), true, zero, divide(xQz, divide(y, z))), divide(xQz, divide(y, z)))), true, less_equal(divide(divide(xQz, y), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.94 = { by axiom 7 (closure) R->L }
% 19.65/2.94 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), ifeq2(ifeq(quotient(xQz, divide(y, z), divide(xQz, divide(y, z))), true, ifeq(quotient(y, z, divide(y, z)), true, less_equal(divide(xQz, divide(y, z)), zero), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, z))), true, zero, divide(xQz, divide(y, z))), divide(xQz, divide(y, z)))), true, less_equal(divide(divide(xQz, y), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.94 = { by axiom 5 (ifeq_axiom) R->L }
% 19.65/2.94 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), ifeq2(ifeq(quotient(xQz, divide(y, z), divide(xQz, divide(y, z))), true, ifeq(quotient(y, z, divide(y, z)), true, ifeq(true, true, less_equal(divide(xQz, divide(y, z)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, z))), true, zero, divide(xQz, divide(y, z))), divide(xQz, divide(y, z)))), true, less_equal(divide(divide(xQz, y), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.94 = { by axiom 4 (xQz) R->L }
% 19.65/2.94 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), ifeq2(ifeq(quotient(xQz, divide(y, z), divide(xQz, divide(y, z))), true, ifeq(quotient(y, z, divide(y, z)), true, ifeq(quotient(x, z, xQz), true, less_equal(divide(xQz, divide(y, z)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, z))), true, zero, divide(xQz, divide(y, z))), divide(xQz, divide(y, z)))), true, less_equal(divide(divide(xQz, y), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.94 = { by axiom 5 (ifeq_axiom) R->L }
% 19.65/2.94 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), ifeq2(ifeq(quotient(xQz, divide(y, z), divide(xQz, divide(y, z))), true, ifeq(true, true, ifeq(quotient(y, z, divide(y, z)), true, ifeq(quotient(x, z, xQz), true, less_equal(divide(xQz, divide(y, z)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, z))), true, zero, divide(xQz, divide(y, z))), divide(xQz, divide(y, z)))), true, less_equal(divide(divide(xQz, y), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.94 = { by axiom 8 (quotient_less_equal) R->L }
% 19.65/2.94 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), ifeq2(ifeq(quotient(xQz, divide(y, z), divide(xQz, divide(y, z))), true, ifeq(ifeq(less_equal(xQy, z), true, quotient(xQy, z, zero), true), true, ifeq(quotient(y, z, divide(y, z)), true, ifeq(quotient(x, z, xQz), true, less_equal(divide(xQz, divide(y, z)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, z))), true, zero, divide(xQz, divide(y, z))), divide(xQz, divide(y, z)))), true, less_equal(divide(divide(xQz, y), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.94 = { by axiom 2 (xQyLEz) }
% 19.65/2.94 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), ifeq2(ifeq(quotient(xQz, divide(y, z), divide(xQz, divide(y, z))), true, ifeq(ifeq(true, true, quotient(xQy, z, zero), true), true, ifeq(quotient(y, z, divide(y, z)), true, ifeq(quotient(x, z, xQz), true, less_equal(divide(xQz, divide(y, z)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, z))), true, zero, divide(xQz, divide(y, z))), divide(xQz, divide(y, z)))), true, less_equal(divide(divide(xQz, y), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.94 = { by axiom 5 (ifeq_axiom) }
% 19.65/2.94 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), ifeq2(ifeq(quotient(xQz, divide(y, z), divide(xQz, divide(y, z))), true, ifeq(quotient(xQy, z, zero), true, ifeq(quotient(y, z, divide(y, z)), true, ifeq(quotient(x, z, xQz), true, less_equal(divide(xQz, divide(y, z)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, z))), true, zero, divide(xQz, divide(y, z))), divide(xQz, divide(y, z)))), true, less_equal(divide(divide(xQz, y), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.94 = { by axiom 5 (ifeq_axiom) R->L }
% 19.65/2.94 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), ifeq2(ifeq(quotient(xQz, divide(y, z), divide(xQz, divide(y, z))), true, ifeq(quotient(xQy, z, zero), true, ifeq(quotient(y, z, divide(y, z)), true, ifeq(quotient(x, z, xQz), true, ifeq(true, true, less_equal(divide(xQz, divide(y, z)), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, z))), true, zero, divide(xQz, divide(y, z))), divide(xQz, divide(y, z)))), true, less_equal(divide(divide(xQz, y), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.95 = { by axiom 3 (xQy) R->L }
% 19.65/2.95 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), ifeq2(ifeq(quotient(xQz, divide(y, z), divide(xQz, divide(y, z))), true, ifeq(quotient(xQy, z, zero), true, ifeq(quotient(y, z, divide(y, z)), true, ifeq(quotient(x, z, xQz), true, ifeq(quotient(x, y, xQy), true, less_equal(divide(xQz, divide(y, z)), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(xQz, divide(y, z))), true, zero, divide(xQz, divide(y, z))), divide(xQz, divide(y, z)))), true, less_equal(divide(divide(xQz, y), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.95 = { by axiom 13 (quotient_property) }
% 19.65/2.95 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), ifeq2(true, true, ifeq2(less_equal(zero, divide(xQz, divide(y, z))), true, zero, divide(xQz, divide(y, z))), divide(xQz, divide(y, z)))), true, less_equal(divide(divide(xQz, y), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.95 = { by axiom 6 (ifeq_axiom) }
% 19.65/2.95 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), ifeq2(less_equal(zero, divide(xQz, divide(y, z))), true, zero, divide(xQz, divide(y, z)))), true, less_equal(divide(divide(xQz, y), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.95 = { by axiom 1 (zero_is_smallest) }
% 19.65/2.95 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), ifeq2(true, true, zero, divide(xQz, divide(y, z)))), true, less_equal(divide(divide(xQz, y), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.95 = { by axiom 6 (ifeq_axiom) }
% 19.65/2.95 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), zero), true, less_equal(divide(divide(xQz, y), zero), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.95 = { by axiom 12 (well_defined) R->L }
% 19.65/2.95 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), zero), true, less_equal(divide(divide(xQz, y), ifeq2(quotient(divide(y, z), y, zero), true, ifeq2(quotient(divide(y, z), y, divide(divide(y, z), y)), true, divide(divide(y, z), y), zero), zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.95 = { by axiom 7 (closure) }
% 19.65/2.95 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), zero), true, less_equal(divide(divide(xQz, y), ifeq2(quotient(divide(y, z), y, zero), true, ifeq2(true, true, divide(divide(y, z), y), zero), zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.95 = { by axiom 6 (ifeq_axiom) }
% 19.65/2.95 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), zero), true, less_equal(divide(divide(xQz, y), ifeq2(quotient(divide(y, z), y, zero), true, divide(divide(y, z), y), zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.95 = { by axiom 5 (ifeq_axiom) R->L }
% 19.65/2.95 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), zero), true, less_equal(divide(divide(xQz, y), ifeq2(ifeq(true, true, quotient(divide(y, z), y, zero), true), true, divide(divide(y, z), y), zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.95 = { by axiom 9 (divisor_existence) R->L }
% 19.65/2.95 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), zero), true, less_equal(divide(divide(xQz, y), ifeq2(ifeq(ifeq(quotient(y, z, divide(y, z)), true, less_equal(divide(y, z), y), true), true, quotient(divide(y, z), y, zero), true), true, divide(divide(y, z), y), zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.95 = { by axiom 7 (closure) }
% 19.65/2.95 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), zero), true, less_equal(divide(divide(xQz, y), ifeq2(ifeq(ifeq(true, true, less_equal(divide(y, z), y), true), true, quotient(divide(y, z), y, zero), true), true, divide(divide(y, z), y), zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.95 = { by axiom 5 (ifeq_axiom) }
% 19.65/2.95 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), zero), true, less_equal(divide(divide(xQz, y), ifeq2(ifeq(less_equal(divide(y, z), y), true, quotient(divide(y, z), y, zero), true), true, divide(divide(y, z), y), zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.95 = { by axiom 8 (quotient_less_equal) }
% 19.65/2.95 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), zero), true, less_equal(divide(divide(xQz, y), ifeq2(true, true, divide(divide(y, z), y), zero)), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.95 = { by axiom 6 (ifeq_axiom) }
% 19.65/2.95 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, divide(y, z), zero), true, less_equal(divide(divide(xQz, y), divide(divide(y, z), y)), zero), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.95 = { by axiom 5 (ifeq_axiom) R->L }
% 19.65/2.95 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(true, true, ifeq(quotient(xQz, divide(y, z), zero), true, less_equal(divide(divide(xQz, y), divide(divide(y, z), y)), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.95 = { by axiom 7 (closure) R->L }
% 19.65/2.95 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(xQz, y, divide(xQz, y)), true, ifeq(quotient(xQz, divide(y, z), zero), true, less_equal(divide(divide(xQz, y), divide(divide(y, z), y)), zero), true), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.95 = { by axiom 5 (ifeq_axiom) R->L }
% 19.65/2.95 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(true, true, ifeq(quotient(xQz, y, divide(xQz, y)), true, ifeq(quotient(xQz, divide(y, z), zero), true, less_equal(divide(divide(xQz, y), divide(divide(y, z), y)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.95 = { by axiom 7 (closure) R->L }
% 19.65/2.95 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(divide(y, z), y, divide(divide(y, z), y)), true, ifeq(quotient(xQz, y, divide(xQz, y)), true, ifeq(quotient(xQz, divide(y, z), zero), true, less_equal(divide(divide(xQz, y), divide(divide(y, z), y)), zero), true), true), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.95 = { by axiom 5 (ifeq_axiom) R->L }
% 19.65/2.95 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(true, true, ifeq(quotient(divide(y, z), y, divide(divide(y, z), y)), true, ifeq(quotient(xQz, y, divide(xQz, y)), true, ifeq(quotient(xQz, divide(y, z), zero), true, less_equal(divide(divide(xQz, y), divide(divide(y, z), y)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.95 = { by axiom 8 (quotient_less_equal) R->L }
% 19.65/2.95 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(ifeq(less_equal(zero, y), true, quotient(zero, y, zero), true), true, ifeq(quotient(divide(y, z), y, divide(divide(y, z), y)), true, ifeq(quotient(xQz, y, divide(xQz, y)), true, ifeq(quotient(xQz, divide(y, z), zero), true, less_equal(divide(divide(xQz, y), divide(divide(y, z), y)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.95 = { by axiom 1 (zero_is_smallest) }
% 19.65/2.95 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(ifeq(true, true, quotient(zero, y, zero), true), true, ifeq(quotient(divide(y, z), y, divide(divide(y, z), y)), true, ifeq(quotient(xQz, y, divide(xQz, y)), true, ifeq(quotient(xQz, divide(y, z), zero), true, less_equal(divide(divide(xQz, y), divide(divide(y, z), y)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.96 = { by axiom 5 (ifeq_axiom) }
% 19.65/2.96 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(zero, y, zero), true, ifeq(quotient(divide(y, z), y, divide(divide(y, z), y)), true, ifeq(quotient(xQz, y, divide(xQz, y)), true, ifeq(quotient(xQz, divide(y, z), zero), true, less_equal(divide(divide(xQz, y), divide(divide(y, z), y)), zero), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.96 = { by axiom 5 (ifeq_axiom) R->L }
% 19.65/2.96 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(true, true, ifeq(quotient(zero, y, zero), true, ifeq(quotient(divide(y, z), y, divide(divide(y, z), y)), true, ifeq(quotient(xQz, y, divide(xQz, y)), true, ifeq(quotient(xQz, divide(y, z), zero), true, less_equal(divide(divide(xQz, y), divide(divide(y, z), y)), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.96 = { by axiom 7 (closure) R->L }
% 19.65/2.96 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(ifeq(quotient(divide(xQz, y), divide(divide(y, z), y), divide(divide(xQz, y), divide(divide(y, z), y))), true, ifeq(quotient(zero, y, zero), true, ifeq(quotient(divide(y, z), y, divide(divide(y, z), y)), true, ifeq(quotient(xQz, y, divide(xQz, y)), true, ifeq(quotient(xQz, divide(y, z), zero), true, less_equal(divide(divide(xQz, y), divide(divide(y, z), y)), zero), true), true), true), true), true), true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.96 = { by axiom 13 (quotient_property) }
% 19.65/2.96 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(true, true, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero)), divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.96 = { by axiom 6 (ifeq_axiom) }
% 19.65/2.96 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(less_equal(zero, divide(divide(xQz, y), zero)), true, zero, divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.96 = { by axiom 1 (zero_is_smallest) }
% 19.65/2.96 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, ifeq2(true, true, zero, divide(divide(xQz, y), zero))), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.96 = { by axiom 6 (ifeq_axiom) }
% 19.65/2.96 ifeq(quotient(xQz, y, ifeq2(ifeq(quotient(divide(xQz, y), zero, zero), true, less_equal(divide(xQz, y), zero), true), true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.96 = { by axiom 10 (less_equal_quotient) }
% 19.65/2.96 ifeq(quotient(xQz, y, ifeq2(true, true, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y)), divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.96 = { by axiom 6 (ifeq_axiom) }
% 19.65/2.96 ifeq(quotient(xQz, y, ifeq2(less_equal(zero, divide(xQz, y)), true, zero, divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.96 = { by axiom 1 (zero_is_smallest) }
% 19.65/2.96 ifeq(quotient(xQz, y, ifeq2(true, true, zero, divide(xQz, y))), true, less_equal(xQz, y), true)
% 19.65/2.96 = { by axiom 6 (ifeq_axiom) }
% 19.65/2.96 ifeq(quotient(xQz, y, zero), true, less_equal(xQz, y), true)
% 19.65/2.96 = { by axiom 10 (less_equal_quotient) }
% 19.65/2.96 true
% 19.65/2.96 % SZS output end Proof
% 19.65/2.96
% 19.65/2.96 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------