%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : HEN010-3 : 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 10:19:01 AM UTC 2026
% Result : Unsatisfiable 0.30s 0.67s
% Output : Proof 0.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HEN010-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.45 % Computer : n010.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Sun Sep 27 10:51:31 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.30/0.67 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.30/0.67
% 0.30/0.67 % SZS status Unsatisfiable
% 0.30/0.67
% 0.30/0.77 % SZS output start Proof
% 0.30/0.77 Axiom 1 (identity_is_largest): less_equal(X, identity) = true.
% 0.30/0.77 Axiom 2 (zero_is_smallest): less_equal(zero, X) = true.
% 0.30/0.77 Axiom 3 (quotient_smaller_than_numerator): less_equal(divide(X, Y), X) = true.
% 0.30/0.77 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.30/0.77 Axiom 5 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.30/0.77 Axiom 6 (quotient_less_equal1): ifeq(less_equal(X, Y), true, divide(X, Y), zero) = zero.
% 0.30/0.77 Axiom 7 (quotient_less_equal2): ifeq2(divide(X, Y), zero, less_equal(X, Y), true) = true.
% 0.30/0.77 Axiom 8 (quotient_property): less_equal(divide(divide(X, Y), divide(Z, Y)), divide(divide(X, Z), Y)) = true.
% 0.30/0.77 Axiom 9 (less_equal_and_equal): ifeq(less_equal(X, Y), true, ifeq(less_equal(Y, X), true, Y, X), X) = X.
% 0.30/0.77
% 0.30/0.77 Lemma 10: divide(zero, X) = zero.
% 0.30/0.77 Proof:
% 0.30/0.77 divide(zero, X)
% 0.30/0.77 = { by axiom 4 (ifeq_axiom) R->L }
% 0.30/0.77 ifeq(true, true, divide(zero, X), zero)
% 0.30/0.77 = { by axiom 2 (zero_is_smallest) R->L }
% 0.30/0.77 ifeq(less_equal(zero, X), true, divide(zero, X), zero)
% 0.30/0.77 = { by axiom 6 (quotient_less_equal1) }
% 0.30/0.77 zero
% 0.30/0.77
% 0.30/0.78 Lemma 11: divide(divide(X, Y), X) = zero.
% 0.30/0.78 Proof:
% 0.30/0.78 divide(divide(X, Y), X)
% 0.30/0.78 = { by axiom 4 (ifeq_axiom) R->L }
% 0.30/0.78 ifeq(true, true, divide(divide(X, Y), X), zero)
% 0.30/0.78 = { by axiom 3 (quotient_smaller_than_numerator) R->L }
% 0.30/0.78 ifeq(less_equal(divide(X, Y), X), true, divide(divide(X, Y), X), zero)
% 0.30/0.78 = { by axiom 6 (quotient_less_equal1) }
% 0.30/0.78 zero
% 0.30/0.78
% 0.30/0.78 Lemma 12: divide(divide(divide(X, Y), Z), divide(X, Z)) = zero.
% 0.30/0.78 Proof:
% 0.30/0.78 divide(divide(divide(X, Y), Z), divide(X, Z))
% 0.30/0.78 = { by axiom 9 (less_equal_and_equal) R->L }
% 0.30/0.78 ifeq(less_equal(divide(divide(divide(X, Y), Z), divide(X, Z)), zero), true, ifeq(less_equal(zero, divide(divide(divide(X, Y), Z), divide(X, Z))), true, zero, divide(divide(divide(X, Y), Z), divide(X, Z))), divide(divide(divide(X, Y), Z), divide(X, Z)))
% 0.30/0.78 = { by lemma 10 R->L }
% 0.30/0.78 ifeq(less_equal(divide(divide(divide(X, Y), Z), divide(X, Z)), divide(zero, Z)), true, ifeq(less_equal(zero, divide(divide(divide(X, Y), Z), divide(X, Z))), true, zero, divide(divide(divide(X, Y), Z), divide(X, Z))), divide(divide(divide(X, Y), Z), divide(X, Z)))
% 0.30/0.78 = { by lemma 11 R->L }
% 0.30/0.78 ifeq(less_equal(divide(divide(divide(X, Y), Z), divide(X, Z)), divide(divide(divide(X, Y), X), Z)), true, ifeq(less_equal(zero, divide(divide(divide(X, Y), Z), divide(X, Z))), true, zero, divide(divide(divide(X, Y), Z), divide(X, Z))), divide(divide(divide(X, Y), Z), divide(X, Z)))
% 0.30/0.78 = { by axiom 8 (quotient_property) }
% 0.30/0.78 ifeq(true, true, ifeq(less_equal(zero, divide(divide(divide(X, Y), Z), divide(X, Z))), true, zero, divide(divide(divide(X, Y), Z), divide(X, Z))), divide(divide(divide(X, Y), Z), divide(X, Z)))
% 0.30/0.78 = { by axiom 4 (ifeq_axiom) }
% 0.30/0.78 ifeq(less_equal(zero, divide(divide(divide(X, Y), Z), divide(X, Z))), true, zero, divide(divide(divide(X, Y), Z), divide(X, Z)))
% 0.30/0.78 = { by axiom 2 (zero_is_smallest) }
% 0.30/0.78 ifeq(true, true, zero, divide(divide(divide(X, Y), Z), divide(X, Z)))
% 0.30/0.78 = { by axiom 4 (ifeq_axiom) }
% 0.30/0.78 zero
% 0.30/0.78
% 0.30/0.78 Lemma 13: divide(divide(divide(X, Y), Z), X) = zero.
% 0.30/0.78 Proof:
% 0.30/0.78 divide(divide(divide(X, Y), Z), X)
% 0.30/0.78 = { by axiom 9 (less_equal_and_equal) R->L }
% 0.30/0.78 ifeq(less_equal(divide(divide(divide(X, Y), Z), X), zero), true, ifeq(less_equal(zero, divide(divide(divide(X, Y), Z), X)), true, zero, divide(divide(divide(X, Y), Z), X)), divide(divide(divide(X, Y), Z), X))
% 0.30/0.78 = { by axiom 5 (ifeq_axiom) R->L }
% 0.30/0.78 ifeq(ifeq2(zero, zero, less_equal(divide(divide(divide(X, Y), Z), X), zero), true), true, ifeq(less_equal(zero, divide(divide(divide(X, Y), Z), X)), true, zero, divide(divide(divide(X, Y), Z), X)), divide(divide(divide(X, Y), Z), X))
% 0.30/0.78 = { by lemma 12 R->L }
% 0.30/0.78 ifeq(ifeq2(divide(divide(divide(divide(X, Y), Z), X), divide(divide(X, Y), X)), zero, less_equal(divide(divide(divide(X, Y), Z), X), zero), true), true, ifeq(less_equal(zero, divide(divide(divide(X, Y), Z), X)), true, zero, divide(divide(divide(X, Y), Z), X)), divide(divide(divide(X, Y), Z), X))
% 0.30/0.78 = { by lemma 11 }
% 0.30/0.78 ifeq(ifeq2(divide(divide(divide(divide(X, Y), Z), X), zero), zero, less_equal(divide(divide(divide(X, Y), Z), X), zero), true), true, ifeq(less_equal(zero, divide(divide(divide(X, Y), Z), X)), true, zero, divide(divide(divide(X, Y), Z), X)), divide(divide(divide(X, Y), Z), X))
% 0.30/0.78 = { by axiom 7 (quotient_less_equal2) }
% 0.30/0.78 ifeq(true, true, ifeq(less_equal(zero, divide(divide(divide(X, Y), Z), X)), true, zero, divide(divide(divide(X, Y), Z), X)), divide(divide(divide(X, Y), Z), X))
% 0.30/0.78 = { by axiom 4 (ifeq_axiom) }
% 0.30/0.78 ifeq(less_equal(zero, divide(divide(divide(X, Y), Z), X)), true, zero, divide(divide(divide(X, Y), Z), X))
% 0.30/0.78 = { by axiom 2 (zero_is_smallest) }
% 0.30/0.78 ifeq(true, true, zero, divide(divide(divide(X, Y), Z), X))
% 0.30/0.78 = { by axiom 4 (ifeq_axiom) }
% 0.30/0.78 zero
% 0.30/0.78
% 0.30/0.78 Lemma 14: divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))) = zero.
% 0.30/0.78 Proof:
% 0.30/0.78 divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))
% 0.30/0.78 = { by axiom 9 (less_equal_and_equal) R->L }
% 0.30/0.78 ifeq(less_equal(divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))), zero), true, ifeq(less_equal(zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), true, zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))))
% 0.30/0.78 = { by axiom 4 (ifeq_axiom) R->L }
% 0.30/0.78 ifeq(less_equal(divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))), ifeq(true, true, zero, divide(divide(X, Y), divide(X, Y)))), true, ifeq(less_equal(zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), true, zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))))
% 0.30/0.78 = { by axiom 2 (zero_is_smallest) R->L }
% 0.30/0.78 ifeq(less_equal(divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))), ifeq(less_equal(zero, divide(divide(X, Y), divide(X, Y))), true, zero, divide(divide(X, Y), divide(X, Y)))), true, ifeq(less_equal(zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), true, zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))))
% 0.30/0.78 = { by axiom 4 (ifeq_axiom) R->L }
% 0.30/0.78 ifeq(less_equal(divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))), ifeq(true, true, ifeq(less_equal(zero, divide(divide(X, Y), divide(X, Y))), true, zero, divide(divide(X, Y), divide(X, Y))), divide(divide(X, Y), divide(X, Y)))), true, ifeq(less_equal(zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), true, zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))))
% 0.30/0.78 = { by axiom 7 (quotient_less_equal2) R->L }
% 0.30/0.78 ifeq(less_equal(divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))), ifeq(ifeq2(divide(divide(divide(X, Y), divide(X, Y)), zero), zero, less_equal(divide(divide(X, Y), divide(X, Y)), zero), true), true, ifeq(less_equal(zero, divide(divide(X, Y), divide(X, Y))), true, zero, divide(divide(X, Y), divide(X, Y))), divide(divide(X, Y), divide(X, Y)))), true, ifeq(less_equal(zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), true, zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))))
% 0.30/0.78 = { by lemma 10 R->L }
% 0.30/0.78 ifeq(less_equal(divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))), ifeq(ifeq2(divide(divide(divide(X, Y), divide(X, Y)), divide(zero, divide(X, Y))), zero, less_equal(divide(divide(X, Y), divide(X, Y)), zero), true), true, ifeq(less_equal(zero, divide(divide(X, Y), divide(X, Y))), true, zero, divide(divide(X, Y), divide(X, Y))), divide(divide(X, Y), divide(X, Y)))), true, ifeq(less_equal(zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), true, zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))))
% 0.30/0.78 = { by axiom 9 (less_equal_and_equal) R->L }
% 0.30/0.78 ifeq(less_equal(divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))), ifeq(ifeq2(ifeq(less_equal(divide(divide(divide(X, Y), divide(X, Y)), divide(zero, divide(X, Y))), zero), true, ifeq(less_equal(zero, divide(divide(divide(X, Y), divide(X, Y)), divide(zero, divide(X, Y)))), true, zero, divide(divide(divide(X, Y), divide(X, Y)), divide(zero, divide(X, Y)))), divide(divide(divide(X, Y), divide(X, Y)), divide(zero, divide(X, Y)))), zero, less_equal(divide(divide(X, Y), divide(X, Y)), zero), true), true, ifeq(less_equal(zero, divide(divide(X, Y), divide(X, Y))), true, zero, divide(divide(X, Y), divide(X, Y))), divide(divide(X, Y), divide(X, Y)))), true, ifeq(less_equal(zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), true, zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))))
% 0.30/0.79 = { by lemma 11 R->L }
% 0.30/0.79 ifeq(less_equal(divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))), ifeq(ifeq2(ifeq(less_equal(divide(divide(divide(X, Y), divide(X, Y)), divide(zero, divide(X, Y))), divide(divide(divide(X, Y), zero), divide(X, Y))), true, ifeq(less_equal(zero, divide(divide(divide(X, Y), divide(X, Y)), divide(zero, divide(X, Y)))), true, zero, divide(divide(divide(X, Y), divide(X, Y)), divide(zero, divide(X, Y)))), divide(divide(divide(X, Y), divide(X, Y)), divide(zero, divide(X, Y)))), zero, less_equal(divide(divide(X, Y), divide(X, Y)), zero), true), true, ifeq(less_equal(zero, divide(divide(X, Y), divide(X, Y))), true, zero, divide(divide(X, Y), divide(X, Y))), divide(divide(X, Y), divide(X, Y)))), true, ifeq(less_equal(zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), true, zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))))
% 0.30/0.79 = { by axiom 8 (quotient_property) }
% 0.30/0.79 ifeq(less_equal(divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))), ifeq(ifeq2(ifeq(true, true, ifeq(less_equal(zero, divide(divide(divide(X, Y), divide(X, Y)), divide(zero, divide(X, Y)))), true, zero, divide(divide(divide(X, Y), divide(X, Y)), divide(zero, divide(X, Y)))), divide(divide(divide(X, Y), divide(X, Y)), divide(zero, divide(X, Y)))), zero, less_equal(divide(divide(X, Y), divide(X, Y)), zero), true), true, ifeq(less_equal(zero, divide(divide(X, Y), divide(X, Y))), true, zero, divide(divide(X, Y), divide(X, Y))), divide(divide(X, Y), divide(X, Y)))), true, ifeq(less_equal(zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), true, zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))))
% 0.30/0.79 = { by axiom 4 (ifeq_axiom) }
% 0.30/0.79 ifeq(less_equal(divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))), ifeq(ifeq2(ifeq(less_equal(zero, divide(divide(divide(X, Y), divide(X, Y)), divide(zero, divide(X, Y)))), true, zero, divide(divide(divide(X, Y), divide(X, Y)), divide(zero, divide(X, Y)))), zero, less_equal(divide(divide(X, Y), divide(X, Y)), zero), true), true, ifeq(less_equal(zero, divide(divide(X, Y), divide(X, Y))), true, zero, divide(divide(X, Y), divide(X, Y))), divide(divide(X, Y), divide(X, Y)))), true, ifeq(less_equal(zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), true, zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))))
% 0.30/0.79 = { by axiom 2 (zero_is_smallest) }
% 0.30/0.79 ifeq(less_equal(divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))), ifeq(ifeq2(ifeq(true, true, zero, divide(divide(divide(X, Y), divide(X, Y)), divide(zero, divide(X, Y)))), zero, less_equal(divide(divide(X, Y), divide(X, Y)), zero), true), true, ifeq(less_equal(zero, divide(divide(X, Y), divide(X, Y))), true, zero, divide(divide(X, Y), divide(X, Y))), divide(divide(X, Y), divide(X, Y)))), true, ifeq(less_equal(zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), true, zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))))
% 0.30/0.79 = { by axiom 4 (ifeq_axiom) }
% 0.30/0.79 ifeq(less_equal(divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))), ifeq(ifeq2(zero, zero, less_equal(divide(divide(X, Y), divide(X, Y)), zero), true), true, ifeq(less_equal(zero, divide(divide(X, Y), divide(X, Y))), true, zero, divide(divide(X, Y), divide(X, Y))), divide(divide(X, Y), divide(X, Y)))), true, ifeq(less_equal(zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), true, zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))))
% 0.30/0.79 = { by axiom 5 (ifeq_axiom) }
% 0.30/0.79 ifeq(less_equal(divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))), ifeq(less_equal(divide(divide(X, Y), divide(X, Y)), zero), true, ifeq(less_equal(zero, divide(divide(X, Y), divide(X, Y))), true, zero, divide(divide(X, Y), divide(X, Y))), divide(divide(X, Y), divide(X, Y)))), true, ifeq(less_equal(zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), true, zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))))
% 0.30/0.79 = { by axiom 9 (less_equal_and_equal) }
% 0.30/0.79 ifeq(less_equal(divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))), divide(divide(X, Y), divide(X, Y))), true, ifeq(less_equal(zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), true, zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))))
% 0.30/0.79 = { by axiom 8 (quotient_property) }
% 0.30/0.79 ifeq(true, true, ifeq(less_equal(zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), true, zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))))
% 0.30/0.79 = { by axiom 4 (ifeq_axiom) }
% 0.30/0.79 ifeq(less_equal(zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y)))), true, zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))))
% 0.30/0.79 = { by axiom 2 (zero_is_smallest) }
% 0.30/0.79 ifeq(true, true, zero, divide(divide(X, divide(X, Y)), divide(Y, divide(X, Y))))
% 0.30/0.79 = { by axiom 4 (ifeq_axiom) }
% 0.30/0.79 zero
% 0.30/0.79
% 0.30/0.79 Lemma 15: divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X) = divide(identity, X).
% 0.30/0.79 Proof:
% 0.30/0.79 divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)
% 0.30/0.79 = { by axiom 4 (ifeq_axiom) R->L }
% 0.30/0.79 ifeq(true, true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X))
% 0.30/0.79 = { by axiom 7 (quotient_less_equal2) R->L }
% 0.30/0.79 ifeq(ifeq2(divide(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), zero, less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X))
% 0.30/0.79 = { by lemma 13 }
% 0.30/0.79 ifeq(ifeq2(zero, zero, less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X))
% 0.30/0.79 = { by axiom 5 (ifeq_axiom) }
% 0.30/0.79 ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X))
% 0.30/0.79 = { by axiom 4 (ifeq_axiom) R->L }
% 0.30/0.79 ifeq(true, true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.30/0.79 = { by axiom 7 (quotient_less_equal2) R->L }
% 0.30/0.79 ifeq(ifeq2(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.30/0.79 = { by axiom 9 (less_equal_and_equal) R->L }
% 0.30/0.79 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), zero), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.30/0.80 = { by lemma 13 R->L }
% 0.30/0.80 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(divide(divide(X, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.30/0.80 = { by axiom 4 (ifeq_axiom) R->L }
% 0.30/0.80 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(divide(ifeq(true, true, divide(X, divide(identity, X)), divide(identity, divide(identity, X))), divide(divide(identity, X), divide(identity, divide(identity, X)))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.80 = { by axiom 7 (quotient_less_equal2) R->L }
% 0.31/0.80 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(divide(ifeq(ifeq2(divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X))), zero, less_equal(divide(X, divide(identity, X)), divide(identity, divide(identity, X))), true), true, divide(X, divide(identity, X)), divide(identity, divide(identity, X))), divide(divide(identity, X), divide(identity, divide(identity, X)))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.80 = { by axiom 9 (less_equal_and_equal) R->L }
% 0.31/0.80 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(divide(ifeq(ifeq2(ifeq(less_equal(divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X))), zero), true, ifeq(less_equal(zero, divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X)))), true, zero, divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X)))), divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X)))), zero, less_equal(divide(X, divide(identity, X)), divide(identity, divide(identity, X))), true), true, divide(X, divide(identity, X)), divide(identity, divide(identity, X))), divide(divide(identity, X), divide(identity, divide(identity, X)))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.80 = { by lemma 10 R->L }
% 0.31/0.80 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(divide(ifeq(ifeq2(ifeq(less_equal(divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X))), divide(zero, divide(identity, X))), true, ifeq(less_equal(zero, divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X)))), true, zero, divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X)))), divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X)))), zero, less_equal(divide(X, divide(identity, X)), divide(identity, divide(identity, X))), true), true, divide(X, divide(identity, X)), divide(identity, divide(identity, X))), divide(divide(identity, X), divide(identity, divide(identity, X)))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.80 = { by axiom 6 (quotient_less_equal1) R->L }
% 0.31/0.81 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(divide(ifeq(ifeq2(ifeq(less_equal(divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X))), divide(ifeq(less_equal(X, identity), true, divide(X, identity), zero), divide(identity, X))), true, ifeq(less_equal(zero, divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X)))), true, zero, divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X)))), divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X)))), zero, less_equal(divide(X, divide(identity, X)), divide(identity, divide(identity, X))), true), true, divide(X, divide(identity, X)), divide(identity, divide(identity, X))), divide(divide(identity, X), divide(identity, divide(identity, X)))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.81 = { by axiom 1 (identity_is_largest) }
% 0.31/0.81 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(divide(ifeq(ifeq2(ifeq(less_equal(divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X))), divide(ifeq(true, true, divide(X, identity), zero), divide(identity, X))), true, ifeq(less_equal(zero, divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X)))), true, zero, divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X)))), divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X)))), zero, less_equal(divide(X, divide(identity, X)), divide(identity, divide(identity, X))), true), true, divide(X, divide(identity, X)), divide(identity, divide(identity, X))), divide(divide(identity, X), divide(identity, divide(identity, X)))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.81 = { by axiom 4 (ifeq_axiom) }
% 0.31/0.81 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(divide(ifeq(ifeq2(ifeq(less_equal(divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X))), divide(divide(X, identity), divide(identity, X))), true, ifeq(less_equal(zero, divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X)))), true, zero, divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X)))), divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X)))), zero, less_equal(divide(X, divide(identity, X)), divide(identity, divide(identity, X))), true), true, divide(X, divide(identity, X)), divide(identity, divide(identity, X))), divide(divide(identity, X), divide(identity, divide(identity, X)))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.81 = { by axiom 8 (quotient_property) }
% 0.31/0.81 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(divide(ifeq(ifeq2(ifeq(true, true, ifeq(less_equal(zero, divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X)))), true, zero, divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X)))), divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X)))), zero, less_equal(divide(X, divide(identity, X)), divide(identity, divide(identity, X))), true), true, divide(X, divide(identity, X)), divide(identity, divide(identity, X))), divide(divide(identity, X), divide(identity, divide(identity, X)))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.81 = { by axiom 4 (ifeq_axiom) }
% 0.31/0.81 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(divide(ifeq(ifeq2(ifeq(less_equal(zero, divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X)))), true, zero, divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X)))), zero, less_equal(divide(X, divide(identity, X)), divide(identity, divide(identity, X))), true), true, divide(X, divide(identity, X)), divide(identity, divide(identity, X))), divide(divide(identity, X), divide(identity, divide(identity, X)))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.81 = { by axiom 2 (zero_is_smallest) }
% 0.31/0.81 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(divide(ifeq(ifeq2(ifeq(true, true, zero, divide(divide(X, divide(identity, X)), divide(identity, divide(identity, X)))), zero, less_equal(divide(X, divide(identity, X)), divide(identity, divide(identity, X))), true), true, divide(X, divide(identity, X)), divide(identity, divide(identity, X))), divide(divide(identity, X), divide(identity, divide(identity, X)))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.81 = { by axiom 4 (ifeq_axiom) }
% 0.31/0.81 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(divide(ifeq(ifeq2(zero, zero, less_equal(divide(X, divide(identity, X)), divide(identity, divide(identity, X))), true), true, divide(X, divide(identity, X)), divide(identity, divide(identity, X))), divide(divide(identity, X), divide(identity, divide(identity, X)))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.81 = { by axiom 5 (ifeq_axiom) }
% 0.31/0.81 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(divide(ifeq(less_equal(divide(X, divide(identity, X)), divide(identity, divide(identity, X))), true, divide(X, divide(identity, X)), divide(identity, divide(identity, X))), divide(divide(identity, X), divide(identity, divide(identity, X)))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.81 = { by axiom 4 (ifeq_axiom) R->L }
% 0.31/0.82 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(divide(ifeq(true, true, ifeq(less_equal(divide(X, divide(identity, X)), divide(identity, divide(identity, X))), true, divide(X, divide(identity, X)), divide(identity, divide(identity, X))), divide(identity, divide(identity, X))), divide(divide(identity, X), divide(identity, divide(identity, X)))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.82 = { by axiom 7 (quotient_less_equal2) R->L }
% 0.31/0.82 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(divide(ifeq(ifeq2(divide(divide(identity, divide(identity, X)), divide(X, divide(identity, X))), zero, less_equal(divide(identity, divide(identity, X)), divide(X, divide(identity, X))), true), true, ifeq(less_equal(divide(X, divide(identity, X)), divide(identity, divide(identity, X))), true, divide(X, divide(identity, X)), divide(identity, divide(identity, X))), divide(identity, divide(identity, X))), divide(divide(identity, X), divide(identity, divide(identity, X)))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.82 = { by lemma 14 }
% 0.31/0.82 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(divide(ifeq(ifeq2(zero, zero, less_equal(divide(identity, divide(identity, X)), divide(X, divide(identity, X))), true), true, ifeq(less_equal(divide(X, divide(identity, X)), divide(identity, divide(identity, X))), true, divide(X, divide(identity, X)), divide(identity, divide(identity, X))), divide(identity, divide(identity, X))), divide(divide(identity, X), divide(identity, divide(identity, X)))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.82 = { by axiom 5 (ifeq_axiom) }
% 0.31/0.82 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(divide(ifeq(less_equal(divide(identity, divide(identity, X)), divide(X, divide(identity, X))), true, ifeq(less_equal(divide(X, divide(identity, X)), divide(identity, divide(identity, X))), true, divide(X, divide(identity, X)), divide(identity, divide(identity, X))), divide(identity, divide(identity, X))), divide(divide(identity, X), divide(identity, divide(identity, X)))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.82 = { by axiom 9 (less_equal_and_equal) }
% 0.31/0.82 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.82 = { by axiom 4 (ifeq_axiom) R->L }
% 0.31/0.82 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(ifeq(true, true, divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.82 = { by axiom 7 (quotient_less_equal2) R->L }
% 0.31/0.83 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(ifeq(ifeq2(divide(divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), zero, less_equal(divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), true), true, divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.83 = { by lemma 12 }
% 0.31/0.83 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(ifeq(ifeq2(zero, zero, less_equal(divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), true), true, divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.83 = { by axiom 5 (ifeq_axiom) }
% 0.31/0.83 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(ifeq(less_equal(divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), true, divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.83 = { by axiom 4 (ifeq_axiom) R->L }
% 0.31/0.83 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(ifeq(true, true, ifeq(less_equal(divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), true, divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.83 = { by axiom 7 (quotient_less_equal2) R->L }
% 0.31/0.83 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(ifeq(ifeq2(divide(divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X))))), zero, less_equal(divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X))))), true), true, ifeq(less_equal(divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), true, divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.83 = { by axiom 9 (less_equal_and_equal) R->L }
% 0.31/0.83 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X))))), zero), true, ifeq(less_equal(zero, divide(divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))))), true, zero, divide(divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))))), divide(divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))))), zero, less_equal(divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X))))), true), true, ifeq(less_equal(divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), true, divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.83 = { by lemma 14 R->L }
% 0.31/0.84 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X))))), divide(divide(identity, divide(identity, divide(identity, X))), divide(divide(identity, X), divide(identity, divide(identity, X))))), true, ifeq(less_equal(zero, divide(divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))))), true, zero, divide(divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))))), divide(divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))))), zero, less_equal(divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X))))), true), true, ifeq(less_equal(divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), true, divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.84 = { by axiom 8 (quotient_property) }
% 0.31/0.84 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(ifeq(ifeq2(ifeq(true, true, ifeq(less_equal(zero, divide(divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))))), true, zero, divide(divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))))), divide(divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))))), zero, less_equal(divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X))))), true), true, ifeq(less_equal(divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), true, divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.84 = { by axiom 4 (ifeq_axiom) }
% 0.31/0.84 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(ifeq(ifeq2(ifeq(less_equal(zero, divide(divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))))), true, zero, divide(divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))))), zero, less_equal(divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X))))), true), true, ifeq(less_equal(divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), true, divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.84 = { by axiom 2 (zero_is_smallest) }
% 0.31/0.84 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(ifeq(ifeq2(ifeq(true, true, zero, divide(divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))))), zero, less_equal(divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X))))), true), true, ifeq(less_equal(divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), true, divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.84 = { by axiom 4 (ifeq_axiom) }
% 0.31/0.84 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(ifeq(ifeq2(zero, zero, less_equal(divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X))))), true), true, ifeq(less_equal(divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), true, divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.84 = { by axiom 5 (ifeq_axiom) }
% 0.31/0.84 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(ifeq(less_equal(divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X))))), true, ifeq(less_equal(divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), true, divide(divide(identity, divide(identity, X)), divide(divide(identity, X), divide(identity, divide(identity, X)))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X))))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.84 = { by axiom 9 (less_equal_and_equal) }
% 0.31/0.84 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), divide(divide(identity, divide(divide(identity, X), divide(identity, divide(identity, X)))), X)), true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.84 = { by axiom 8 (quotient_property) }
% 0.31/0.84 ifeq(ifeq2(ifeq(true, true, ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.85 = { by axiom 4 (ifeq_axiom) }
% 0.31/0.85 ifeq(ifeq2(ifeq(less_equal(zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.85 = { by axiom 2 (zero_is_smallest) }
% 0.31/0.85 ifeq(ifeq2(ifeq(true, true, zero, divide(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X))), zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.85 = { by axiom 4 (ifeq_axiom) }
% 0.31/0.85 ifeq(ifeq2(zero, zero, less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.85 = { by axiom 5 (ifeq_axiom) }
% 0.31/0.85 ifeq(less_equal(divide(identity, X), divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X)), true, ifeq(less_equal(divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), true, divide(divide(divide(identity, X), divide(identity, divide(identity, X))), X), divide(identity, X)), divide(identity, X))
% 0.31/0.85 = { by axiom 9 (less_equal_and_equal) }
% 0.31/0.85 divide(identity, X)
% 0.31/0.85
% 0.31/0.85 Goal 1 (prove_property_of_inversion): divide(identity, a) = divide(divide(identity, a), divide(identity, divide(identity, a))).
% 0.31/0.85 Proof:
% 0.31/0.85 divide(identity, a)
% 0.31/0.85 = { by lemma 15 R->L }
% 0.31/0.85 divide(divide(divide(identity, a), divide(identity, divide(identity, a))), a)
% 0.31/0.85 = { by axiom 4 (ifeq_axiom) R->L }
% 0.31/0.85 ifeq(true, true, divide(divide(divide(identity, a), divide(identity, divide(identity, a))), a), divide(divide(identity, a), divide(identity, divide(identity, a))))
% 0.31/0.85 = { by axiom 3 (quotient_smaller_than_numerator) R->L }
% 0.31/0.85 ifeq(less_equal(divide(divide(identity, a), divide(identity, divide(identity, a))), divide(identity, a)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, a))), a), divide(divide(identity, a), divide(identity, divide(identity, a))))
% 0.31/0.85 = { by lemma 15 R->L }
% 0.31/0.85 ifeq(less_equal(divide(divide(identity, a), divide(identity, divide(identity, a))), divide(divide(divide(identity, a), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, a))), a), divide(divide(identity, a), divide(identity, divide(identity, a))))
% 0.31/0.85 = { by axiom 4 (ifeq_axiom) R->L }
% 0.31/0.85 ifeq(less_equal(divide(divide(identity, a), divide(identity, divide(identity, a))), divide(divide(divide(identity, a), divide(identity, divide(identity, a))), a)), true, ifeq(true, true, divide(divide(divide(identity, a), divide(identity, divide(identity, a))), a), divide(divide(identity, a), divide(identity, divide(identity, a)))), divide(divide(identity, a), divide(identity, divide(identity, a))))
% 0.31/0.85 = { by axiom 3 (quotient_smaller_than_numerator) R->L }
% 0.31/0.85 ifeq(less_equal(divide(divide(identity, a), divide(identity, divide(identity, a))), divide(divide(divide(identity, a), divide(identity, divide(identity, a))), a)), true, ifeq(less_equal(divide(divide(divide(identity, a), divide(identity, divide(identity, a))), a), divide(divide(identity, a), divide(identity, divide(identity, a)))), true, divide(divide(divide(identity, a), divide(identity, divide(identity, a))), a), divide(divide(identity, a), divide(identity, divide(identity, a)))), divide(divide(identity, a), divide(identity, divide(identity, a))))
% 0.31/0.85 = { by axiom 9 (less_equal_and_equal) }
% 0.31/0.85 divide(divide(identity, a), divide(identity, divide(identity, a)))
% 0.31/0.85 % SZS output end Proof
% 0.31/0.85
% 0.31/0.85 RESULT: Unsatisfiable (the axioms are contradictory).
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