%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : HEN009-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:19:00 AM UTC 2026
% Result : Unsatisfiable 1.23s 0.68s
% Output : Proof 2.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN009-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 10:51:06 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.23/0.68 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 1.23/0.68
% 1.23/0.68 % SZS status Unsatisfiable
% 1.23/0.68
% 1.76/0.80 % SZS output start Proof
% 1.76/0.80 Axiom 1 (id_divide_a_is_b): divide(identity, a) = b.
% 1.76/0.80 Axiom 2 (id_divide_b_is_c): divide(identity, b) = c.
% 1.76/0.80 Axiom 3 (id_divide_c_is_d): divide(identity, c) = d.
% 1.76/0.80 Axiom 4 (identity_is_largest): less_equal(X, identity) = true.
% 1.76/0.80 Axiom 5 (zero_is_smallest): less_equal(zero, X) = true.
% 1.76/0.80 Axiom 6 (quotient_smaller_than_numerator): less_equal(divide(X, Y), X) = true.
% 1.76/0.80 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 1.76/0.80 Axiom 8 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 1.76/0.80 Axiom 9 (quotient_less_equal1): ifeq(less_equal(X, Y), true, divide(X, Y), zero) = zero.
% 1.76/0.80 Axiom 10 (quotient_less_equal2): ifeq2(divide(X, Y), zero, less_equal(X, Y), true) = true.
% 1.76/0.80 Axiom 11 (quotient_property): less_equal(divide(divide(X, Y), divide(Z, Y)), divide(divide(X, Z), Y)) = true.
% 1.76/0.80 Axiom 12 (less_equal_and_equal): ifeq(less_equal(X, Y), true, ifeq(less_equal(Y, X), true, Y, X), X) = X.
% 1.76/0.80
% 1.76/0.80 Lemma 13: divide(zero, X) = zero.
% 1.76/0.80 Proof:
% 1.76/0.80 divide(zero, X)
% 1.76/0.80 = { by axiom 7 (ifeq_axiom) R->L }
% 1.76/0.80 ifeq(true, true, divide(zero, X), zero)
% 1.76/0.80 = { by axiom 5 (zero_is_smallest) R->L }
% 1.76/0.80 ifeq(less_equal(zero, X), true, divide(zero, X), zero)
% 1.76/0.80 = { by axiom 9 (quotient_less_equal1) }
% 1.76/0.80 zero
% 1.76/0.80
% 1.76/0.80 Lemma 14: divide(divide(X, Y), X) = zero.
% 1.76/0.80 Proof:
% 1.76/0.80 divide(divide(X, Y), X)
% 1.76/0.80 = { by axiom 7 (ifeq_axiom) R->L }
% 1.76/0.80 ifeq(true, true, divide(divide(X, Y), X), zero)
% 1.76/0.80 = { by axiom 6 (quotient_smaller_than_numerator) R->L }
% 1.76/0.80 ifeq(less_equal(divide(X, Y), X), true, divide(divide(X, Y), X), zero)
% 2.46/0.80 = { by axiom 9 (quotient_less_equal1) }
% 2.46/0.80 zero
% 2.46/0.80
% 2.46/0.80 Lemma 15: divide(divide(divide(X, Y), Z), divide(X, Z)) = zero.
% 2.46/0.80 Proof:
% 2.46/0.80 divide(divide(divide(X, Y), Z), divide(X, Z))
% 2.46/0.80 = { by axiom 12 (less_equal_and_equal) R->L }
% 2.46/0.80 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)))
% 2.46/0.80 = { by lemma 13 R->L }
% 2.46/0.80 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)))
% 2.46/0.80 = { by lemma 14 R->L }
% 2.46/0.80 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)))
% 2.46/0.80 = { by axiom 11 (quotient_property) }
% 2.46/0.80 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)))
% 2.46/0.80 = { by axiom 7 (ifeq_axiom) }
% 2.46/0.80 ifeq(less_equal(zero, divide(divide(divide(X, Y), Z), divide(X, Z))), true, zero, divide(divide(divide(X, Y), Z), divide(X, Z)))
% 2.46/0.80 = { by axiom 5 (zero_is_smallest) }
% 2.46/0.80 ifeq(true, true, zero, divide(divide(divide(X, Y), Z), divide(X, Z)))
% 2.46/0.80 = { by axiom 7 (ifeq_axiom) }
% 2.46/0.80 zero
% 2.46/0.80
% 2.46/0.80 Lemma 16: divide(X, X) = zero.
% 2.46/0.80 Proof:
% 2.46/0.80 divide(X, X)
% 2.46/0.80 = { by axiom 12 (less_equal_and_equal) R->L }
% 2.46/0.80 ifeq(less_equal(divide(X, X), zero), true, ifeq(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 2.46/0.80 = { by axiom 8 (ifeq_axiom) R->L }
% 2.46/0.80 ifeq(ifeq2(zero, zero, less_equal(divide(X, X), zero), true), true, ifeq(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 2.46/0.81 = { by axiom 7 (ifeq_axiom) R->L }
% 2.46/0.81 ifeq(ifeq2(ifeq(true, true, zero, divide(divide(X, X), divide(zero, X))), zero, less_equal(divide(X, X), zero), true), true, ifeq(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 2.46/0.81 = { by axiom 5 (zero_is_smallest) R->L }
% 2.46/0.81 ifeq(ifeq2(ifeq(less_equal(zero, divide(divide(X, X), divide(zero, X))), true, zero, divide(divide(X, X), divide(zero, X))), zero, less_equal(divide(X, X), zero), true), true, ifeq(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 2.46/0.81 = { by axiom 7 (ifeq_axiom) R->L }
% 2.46/0.81 ifeq(ifeq2(ifeq(true, true, ifeq(less_equal(zero, divide(divide(X, X), divide(zero, X))), true, zero, divide(divide(X, X), divide(zero, X))), divide(divide(X, X), divide(zero, X))), zero, less_equal(divide(X, X), zero), true), true, ifeq(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 2.46/0.81 = { by axiom 11 (quotient_property) R->L }
% 2.46/0.81 ifeq(ifeq2(ifeq(less_equal(divide(divide(X, X), divide(zero, X)), divide(divide(X, zero), X)), true, ifeq(less_equal(zero, divide(divide(X, X), divide(zero, X))), true, zero, divide(divide(X, X), divide(zero, X))), divide(divide(X, X), divide(zero, X))), zero, less_equal(divide(X, X), zero), true), true, ifeq(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 2.46/0.81 = { by lemma 14 }
% 2.46/0.81 ifeq(ifeq2(ifeq(less_equal(divide(divide(X, X), divide(zero, X)), zero), true, ifeq(less_equal(zero, divide(divide(X, X), divide(zero, X))), true, zero, divide(divide(X, X), divide(zero, X))), divide(divide(X, X), divide(zero, X))), zero, less_equal(divide(X, X), zero), true), true, ifeq(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 2.46/0.81 = { by axiom 12 (less_equal_and_equal) }
% 2.46/0.81 ifeq(ifeq2(divide(divide(X, X), divide(zero, X)), zero, less_equal(divide(X, X), zero), true), true, ifeq(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 2.46/0.81 = { by lemma 13 }
% 2.46/0.81 ifeq(ifeq2(divide(divide(X, X), zero), zero, less_equal(divide(X, X), zero), true), true, ifeq(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 2.46/0.81 = { by axiom 10 (quotient_less_equal2) }
% 2.46/0.81 ifeq(true, true, ifeq(less_equal(zero, divide(X, X)), true, zero, divide(X, X)), divide(X, X))
% 2.46/0.81 = { by axiom 7 (ifeq_axiom) }
% 2.46/0.81 ifeq(less_equal(zero, divide(X, X)), true, zero, divide(X, X))
% 2.46/0.81 = { by axiom 5 (zero_is_smallest) }
% 2.46/0.81 ifeq(true, true, zero, divide(X, X))
% 2.46/0.81 = { by axiom 7 (ifeq_axiom) }
% 2.46/0.81 zero
% 2.46/0.81
% 2.46/0.81 Lemma 17: divide(d, divide(b, c)) = zero.
% 2.46/0.81 Proof:
% 2.46/0.81 divide(d, divide(b, c))
% 2.46/0.81 = { by axiom 12 (less_equal_and_equal) R->L }
% 2.46/0.81 ifeq(less_equal(divide(d, divide(b, c)), zero), true, ifeq(less_equal(zero, divide(d, divide(b, c))), true, zero, divide(d, divide(b, c))), divide(d, divide(b, c)))
% 2.46/0.81 = { by lemma 16 R->L }
% 2.46/0.81 ifeq(less_equal(divide(d, divide(b, c)), divide(c, c)), true, ifeq(less_equal(zero, divide(d, divide(b, c))), true, zero, divide(d, divide(b, c))), divide(d, divide(b, c)))
% 2.46/0.81 = { by axiom 3 (id_divide_c_is_d) R->L }
% 2.46/0.81 ifeq(less_equal(divide(divide(identity, c), divide(b, c)), divide(c, c)), true, ifeq(less_equal(zero, divide(d, divide(b, c))), true, zero, divide(d, divide(b, c))), divide(d, divide(b, c)))
% 2.46/0.81 = { by axiom 2 (id_divide_b_is_c) R->L }
% 2.46/0.81 ifeq(less_equal(divide(divide(identity, c), divide(b, c)), divide(divide(identity, b), c)), true, ifeq(less_equal(zero, divide(d, divide(b, c))), true, zero, divide(d, divide(b, c))), divide(d, divide(b, c)))
% 2.46/0.81 = { by axiom 11 (quotient_property) }
% 2.46/0.81 ifeq(true, true, ifeq(less_equal(zero, divide(d, divide(b, c))), true, zero, divide(d, divide(b, c))), divide(d, divide(b, c)))
% 2.46/0.81 = { by axiom 7 (ifeq_axiom) }
% 2.46/0.81 ifeq(less_equal(zero, divide(d, divide(b, c))), true, zero, divide(d, divide(b, c)))
% 2.46/0.81 = { by axiom 5 (zero_is_smallest) }
% 2.46/0.81 ifeq(true, true, zero, divide(d, divide(b, c)))
% 2.46/0.81 = { by axiom 7 (ifeq_axiom) }
% 2.46/0.81 zero
% 2.46/0.81
% 2.46/0.81 Lemma 18: divide(b, c) = d.
% 2.46/0.81 Proof:
% 2.46/0.81 divide(b, c)
% 2.46/0.81 = { by axiom 7 (ifeq_axiom) R->L }
% 2.46/0.81 ifeq(true, true, divide(b, c), d)
% 2.46/0.81 = { by axiom 10 (quotient_less_equal2) R->L }
% 2.46/0.81 ifeq(ifeq2(divide(divide(b, c), d), zero, less_equal(divide(b, c), d), true), true, divide(b, c), d)
% 2.46/0.81 = { by axiom 3 (id_divide_c_is_d) R->L }
% 2.46/0.81 ifeq(ifeq2(divide(divide(b, c), divide(identity, c)), zero, less_equal(divide(b, c), d), true), true, divide(b, c), d)
% 2.46/0.81 = { by axiom 1 (id_divide_a_is_b) R->L }
% 2.46/0.81 ifeq(ifeq2(divide(divide(divide(identity, a), c), divide(identity, c)), zero, less_equal(divide(b, c), d), true), true, divide(b, c), d)
% 2.46/0.81 = { by lemma 15 }
% 2.46/0.81 ifeq(ifeq2(zero, zero, less_equal(divide(b, c), d), true), true, divide(b, c), d)
% 2.46/0.81 = { by axiom 8 (ifeq_axiom) }
% 2.46/0.81 ifeq(less_equal(divide(b, c), d), true, divide(b, c), d)
% 2.46/0.81 = { by axiom 7 (ifeq_axiom) R->L }
% 2.46/0.81 ifeq(true, true, ifeq(less_equal(divide(b, c), d), true, divide(b, c), d), d)
% 2.46/0.81 = { by axiom 10 (quotient_less_equal2) R->L }
% 2.46/0.81 ifeq(ifeq2(divide(d, divide(b, c)), zero, less_equal(d, divide(b, c)), true), true, ifeq(less_equal(divide(b, c), d), true, divide(b, c), d), d)
% 2.46/0.81 = { by lemma 17 }
% 2.46/0.81 ifeq(ifeq2(zero, zero, less_equal(d, divide(b, c)), true), true, ifeq(less_equal(divide(b, c), d), true, divide(b, c), d), d)
% 2.46/0.81 = { by axiom 8 (ifeq_axiom) }
% 2.46/0.81 ifeq(less_equal(d, divide(b, c)), true, ifeq(less_equal(divide(b, c), d), true, divide(b, c), d), d)
% 2.46/0.81 = { by axiom 12 (less_equal_and_equal) }
% 2.46/0.81 d
% 2.46/0.81
% 2.46/0.81 Lemma 19: divide(d, a) = b.
% 2.46/0.81 Proof:
% 2.46/0.81 divide(d, a)
% 2.46/0.81 = { by axiom 7 (ifeq_axiom) R->L }
% 2.46/0.81 ifeq(true, true, divide(d, a), b)
% 2.46/0.81 = { by axiom 10 (quotient_less_equal2) R->L }
% 2.46/0.81 ifeq(ifeq2(divide(divide(d, a), b), zero, less_equal(divide(d, a), b), true), true, divide(d, a), b)
% 2.46/0.81 = { by axiom 1 (id_divide_a_is_b) R->L }
% 2.46/0.81 ifeq(ifeq2(divide(divide(d, a), divide(identity, a)), zero, less_equal(divide(d, a), b), true), true, divide(d, a), b)
% 2.46/0.81 = { by axiom 3 (id_divide_c_is_d) R->L }
% 2.46/0.81 ifeq(ifeq2(divide(divide(divide(identity, c), a), divide(identity, a)), zero, less_equal(divide(d, a), b), true), true, divide(d, a), b)
% 2.46/0.81 = { by lemma 15 }
% 2.46/0.81 ifeq(ifeq2(zero, zero, less_equal(divide(d, a), b), true), true, divide(d, a), b)
% 2.46/0.81 = { by axiom 8 (ifeq_axiom) }
% 2.46/0.81 ifeq(less_equal(divide(d, a), b), true, divide(d, a), b)
% 2.46/0.81 = { by axiom 7 (ifeq_axiom) R->L }
% 2.46/0.81 ifeq(true, true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.81 = { by axiom 10 (quotient_less_equal2) R->L }
% 2.46/0.81 ifeq(ifeq2(divide(b, divide(d, a)), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.81 = { by axiom 12 (less_equal_and_equal) R->L }
% 2.46/0.82 ifeq(ifeq2(ifeq(less_equal(divide(b, divide(d, a)), zero), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.82 = { by axiom 1 (id_divide_a_is_b) R->L }
% 2.46/0.82 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), zero), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.82 = { by axiom 7 (ifeq_axiom) R->L }
% 2.46/0.82 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), ifeq(true, true, zero, divide(divide(divide(a, b), d), a))), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.82 = { by axiom 5 (zero_is_smallest) R->L }
% 2.46/0.82 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), ifeq(less_equal(zero, divide(divide(divide(a, b), d), a)), true, zero, divide(divide(divide(a, b), d), a))), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.82 = { by axiom 7 (ifeq_axiom) R->L }
% 2.46/0.82 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), ifeq(true, true, ifeq(less_equal(zero, divide(divide(divide(a, b), d), a)), true, zero, divide(divide(divide(a, b), d), a)), divide(divide(divide(a, b), d), a))), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.82 = { by axiom 10 (quotient_less_equal2) R->L }
% 2.46/0.82 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), ifeq(ifeq2(divide(divide(divide(divide(a, b), d), a), divide(divide(a, b), a)), zero, less_equal(divide(divide(divide(a, b), d), a), divide(divide(a, b), a)), true), true, ifeq(less_equal(zero, divide(divide(divide(a, b), d), a)), true, zero, divide(divide(divide(a, b), d), a)), divide(divide(divide(a, b), d), a))), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.82 = { by lemma 15 }
% 2.46/0.82 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), ifeq(ifeq2(zero, zero, less_equal(divide(divide(divide(a, b), d), a), divide(divide(a, b), a)), true), true, ifeq(less_equal(zero, divide(divide(divide(a, b), d), a)), true, zero, divide(divide(divide(a, b), d), a)), divide(divide(divide(a, b), d), a))), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.82 = { by axiom 8 (ifeq_axiom) }
% 2.46/0.82 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), ifeq(less_equal(divide(divide(divide(a, b), d), a), divide(divide(a, b), a)), true, ifeq(less_equal(zero, divide(divide(divide(a, b), d), a)), true, zero, divide(divide(divide(a, b), d), a)), divide(divide(divide(a, b), d), a))), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.82 = { by lemma 14 }
% 2.46/0.82 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), ifeq(less_equal(divide(divide(divide(a, b), d), a), zero), true, ifeq(less_equal(zero, divide(divide(divide(a, b), d), a)), true, zero, divide(divide(divide(a, b), d), a)), divide(divide(divide(a, b), d), a))), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.82 = { by axiom 12 (less_equal_and_equal) }
% 2.46/0.82 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(divide(a, b), d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.82 = { by axiom 7 (ifeq_axiom) R->L }
% 2.46/0.82 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(ifeq(true, true, divide(a, b), c), d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.82 = { by axiom 10 (quotient_less_equal2) R->L }
% 2.46/0.82 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(ifeq(ifeq2(divide(divide(a, b), c), zero, less_equal(divide(a, b), c), true), true, divide(a, b), c), d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.83 = { by axiom 2 (id_divide_b_is_c) R->L }
% 2.46/0.83 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(ifeq(ifeq2(divide(divide(a, b), divide(identity, b)), zero, less_equal(divide(a, b), c), true), true, divide(a, b), c), d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.83 = { by axiom 12 (less_equal_and_equal) R->L }
% 2.46/0.83 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(ifeq(ifeq2(ifeq(less_equal(divide(divide(a, b), divide(identity, b)), zero), true, ifeq(less_equal(zero, divide(divide(a, b), divide(identity, b))), true, zero, divide(divide(a, b), divide(identity, b))), divide(divide(a, b), divide(identity, b))), zero, less_equal(divide(a, b), c), true), true, divide(a, b), c), d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.83 = { by lemma 13 R->L }
% 2.46/0.83 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(ifeq(ifeq2(ifeq(less_equal(divide(divide(a, b), divide(identity, b)), divide(zero, b)), true, ifeq(less_equal(zero, divide(divide(a, b), divide(identity, b))), true, zero, divide(divide(a, b), divide(identity, b))), divide(divide(a, b), divide(identity, b))), zero, less_equal(divide(a, b), c), true), true, divide(a, b), c), d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.83 = { by axiom 9 (quotient_less_equal1) R->L }
% 2.46/0.83 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(ifeq(ifeq2(ifeq(less_equal(divide(divide(a, b), divide(identity, b)), divide(ifeq(less_equal(a, identity), true, divide(a, identity), zero), b)), true, ifeq(less_equal(zero, divide(divide(a, b), divide(identity, b))), true, zero, divide(divide(a, b), divide(identity, b))), divide(divide(a, b), divide(identity, b))), zero, less_equal(divide(a, b), c), true), true, divide(a, b), c), d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.83 = { by axiom 4 (identity_is_largest) }
% 2.46/0.83 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(ifeq(ifeq2(ifeq(less_equal(divide(divide(a, b), divide(identity, b)), divide(ifeq(true, true, divide(a, identity), zero), b)), true, ifeq(less_equal(zero, divide(divide(a, b), divide(identity, b))), true, zero, divide(divide(a, b), divide(identity, b))), divide(divide(a, b), divide(identity, b))), zero, less_equal(divide(a, b), c), true), true, divide(a, b), c), d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.83 = { by axiom 7 (ifeq_axiom) }
% 2.46/0.83 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(ifeq(ifeq2(ifeq(less_equal(divide(divide(a, b), divide(identity, b)), divide(divide(a, identity), b)), true, ifeq(less_equal(zero, divide(divide(a, b), divide(identity, b))), true, zero, divide(divide(a, b), divide(identity, b))), divide(divide(a, b), divide(identity, b))), zero, less_equal(divide(a, b), c), true), true, divide(a, b), c), d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.83 = { by axiom 11 (quotient_property) }
% 2.46/0.83 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(ifeq(ifeq2(ifeq(true, true, ifeq(less_equal(zero, divide(divide(a, b), divide(identity, b))), true, zero, divide(divide(a, b), divide(identity, b))), divide(divide(a, b), divide(identity, b))), zero, less_equal(divide(a, b), c), true), true, divide(a, b), c), d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.83 = { by axiom 7 (ifeq_axiom) }
% 2.46/0.83 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(ifeq(ifeq2(ifeq(less_equal(zero, divide(divide(a, b), divide(identity, b))), true, zero, divide(divide(a, b), divide(identity, b))), zero, less_equal(divide(a, b), c), true), true, divide(a, b), c), d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.83 = { by axiom 5 (zero_is_smallest) }
% 2.46/0.83 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(ifeq(ifeq2(ifeq(true, true, zero, divide(divide(a, b), divide(identity, b))), zero, less_equal(divide(a, b), c), true), true, divide(a, b), c), d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.83 = { by axiom 7 (ifeq_axiom) }
% 2.46/0.83 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(ifeq(ifeq2(zero, zero, less_equal(divide(a, b), c), true), true, divide(a, b), c), d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.83 = { by axiom 8 (ifeq_axiom) }
% 2.46/0.83 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(ifeq(less_equal(divide(a, b), c), true, divide(a, b), c), d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.84 = { by axiom 7 (ifeq_axiom) R->L }
% 2.46/0.84 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(ifeq(true, true, ifeq(less_equal(divide(a, b), c), true, divide(a, b), c), c), d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.84 = { by axiom 10 (quotient_less_equal2) R->L }
% 2.46/0.84 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(ifeq(ifeq2(divide(c, divide(a, b)), zero, less_equal(c, divide(a, b)), true), true, ifeq(less_equal(divide(a, b), c), true, divide(a, b), c), c), d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.84 = { by axiom 12 (less_equal_and_equal) R->L }
% 2.46/0.84 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(ifeq(ifeq2(ifeq(less_equal(divide(c, divide(a, b)), zero), true, ifeq(less_equal(zero, divide(c, divide(a, b))), true, zero, divide(c, divide(a, b))), divide(c, divide(a, b))), zero, less_equal(c, divide(a, b)), true), true, ifeq(less_equal(divide(a, b), c), true, divide(a, b), c), c), d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.84 = { by lemma 16 R->L }
% 2.46/0.84 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(ifeq(ifeq2(ifeq(less_equal(divide(c, divide(a, b)), divide(b, b)), true, ifeq(less_equal(zero, divide(c, divide(a, b))), true, zero, divide(c, divide(a, b))), divide(c, divide(a, b))), zero, less_equal(c, divide(a, b)), true), true, ifeq(less_equal(divide(a, b), c), true, divide(a, b), c), c), d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.84 = { by axiom 2 (id_divide_b_is_c) R->L }
% 2.46/0.84 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, b), divide(a, b)), divide(b, b)), true, ifeq(less_equal(zero, divide(c, divide(a, b))), true, zero, divide(c, divide(a, b))), divide(c, divide(a, b))), zero, less_equal(c, divide(a, b)), true), true, ifeq(less_equal(divide(a, b), c), true, divide(a, b), c), c), d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.84 = { by axiom 1 (id_divide_a_is_b) R->L }
% 2.46/0.84 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, b), divide(a, b)), divide(divide(identity, a), b)), true, ifeq(less_equal(zero, divide(c, divide(a, b))), true, zero, divide(c, divide(a, b))), divide(c, divide(a, b))), zero, less_equal(c, divide(a, b)), true), true, ifeq(less_equal(divide(a, b), c), true, divide(a, b), c), c), d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.84 = { by axiom 11 (quotient_property) }
% 2.46/0.84 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(ifeq(ifeq2(ifeq(true, true, ifeq(less_equal(zero, divide(c, divide(a, b))), true, zero, divide(c, divide(a, b))), divide(c, divide(a, b))), zero, less_equal(c, divide(a, b)), true), true, ifeq(less_equal(divide(a, b), c), true, divide(a, b), c), c), d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.84 = { by axiom 7 (ifeq_axiom) }
% 2.46/0.84 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(ifeq(ifeq2(ifeq(less_equal(zero, divide(c, divide(a, b))), true, zero, divide(c, divide(a, b))), zero, less_equal(c, divide(a, b)), true), true, ifeq(less_equal(divide(a, b), c), true, divide(a, b), c), c), d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.84 = { by axiom 5 (zero_is_smallest) }
% 2.46/0.84 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(ifeq(ifeq2(ifeq(true, true, zero, divide(c, divide(a, b))), zero, less_equal(c, divide(a, b)), true), true, ifeq(less_equal(divide(a, b), c), true, divide(a, b), c), c), d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.84 = { by axiom 7 (ifeq_axiom) }
% 2.46/0.84 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(ifeq(ifeq2(zero, zero, less_equal(c, divide(a, b)), true), true, ifeq(less_equal(divide(a, b), c), true, divide(a, b), c), c), d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.84 = { by axiom 8 (ifeq_axiom) }
% 2.46/0.84 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(ifeq(less_equal(c, divide(a, b)), true, ifeq(less_equal(divide(a, b), c), true, divide(a, b), c), c), d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.84 = { by axiom 12 (less_equal_and_equal) }
% 2.46/0.84 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(c, d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.84 = { by axiom 7 (ifeq_axiom) R->L }
% 2.46/0.84 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(ifeq(true, true, divide(c, d), divide(identity, d)), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.84 = { by axiom 10 (quotient_less_equal2) R->L }
% 2.46/0.84 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(ifeq(ifeq2(divide(divide(c, d), divide(identity, d)), zero, less_equal(divide(c, d), divide(identity, d)), true), true, divide(c, d), divide(identity, d)), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.85 = { by axiom 2 (id_divide_b_is_c) R->L }
% 2.46/0.85 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(ifeq(ifeq2(divide(divide(divide(identity, b), d), divide(identity, d)), zero, less_equal(divide(c, d), divide(identity, d)), true), true, divide(c, d), divide(identity, d)), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.85 = { by lemma 15 }
% 2.46/0.85 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(ifeq(ifeq2(zero, zero, less_equal(divide(c, d), divide(identity, d)), true), true, divide(c, d), divide(identity, d)), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.85 = { by axiom 8 (ifeq_axiom) }
% 2.46/0.85 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(ifeq(less_equal(divide(c, d), divide(identity, d)), true, divide(c, d), divide(identity, d)), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.85 = { by axiom 7 (ifeq_axiom) R->L }
% 2.46/0.85 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(ifeq(true, true, ifeq(less_equal(divide(c, d), divide(identity, d)), true, divide(c, d), divide(identity, d)), divide(identity, d)), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.85 = { by axiom 10 (quotient_less_equal2) R->L }
% 2.46/0.85 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(ifeq(ifeq2(divide(divide(identity, d), divide(c, d)), zero, less_equal(divide(identity, d), divide(c, d)), true), true, ifeq(less_equal(divide(c, d), divide(identity, d)), true, divide(c, d), divide(identity, d)), divide(identity, d)), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.85 = { by axiom 12 (less_equal_and_equal) R->L }
% 2.46/0.85 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, d), divide(c, d)), zero), true, ifeq(less_equal(zero, divide(divide(identity, d), divide(c, d))), true, zero, divide(divide(identity, d), divide(c, d))), divide(divide(identity, d), divide(c, d))), zero, less_equal(divide(identity, d), divide(c, d)), true), true, ifeq(less_equal(divide(c, d), divide(identity, d)), true, divide(c, d), divide(identity, d)), divide(identity, d)), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.85 = { by lemma 18 R->L }
% 2.46/0.85 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, divide(b, c)), divide(c, d)), zero), true, ifeq(less_equal(zero, divide(divide(identity, d), divide(c, d))), true, zero, divide(divide(identity, d), divide(c, d))), divide(divide(identity, d), divide(c, d))), zero, less_equal(divide(identity, d), divide(c, d)), true), true, ifeq(less_equal(divide(c, d), divide(identity, d)), true, divide(c, d), divide(identity, d)), divide(identity, d)), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.85 = { by lemma 18 R->L }
% 2.46/0.85 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, divide(b, c)), divide(c, divide(b, c))), zero), true, ifeq(less_equal(zero, divide(divide(identity, d), divide(c, d))), true, zero, divide(divide(identity, d), divide(c, d))), divide(divide(identity, d), divide(c, d))), zero, less_equal(divide(identity, d), divide(c, d)), true), true, ifeq(less_equal(divide(c, d), divide(identity, d)), true, divide(c, d), divide(identity, d)), divide(identity, d)), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.85 = { by lemma 17 R->L }
% 2.46/0.85 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, divide(b, c)), divide(c, divide(b, c))), divide(d, divide(b, c))), true, ifeq(less_equal(zero, divide(divide(identity, d), divide(c, d))), true, zero, divide(divide(identity, d), divide(c, d))), divide(divide(identity, d), divide(c, d))), zero, less_equal(divide(identity, d), divide(c, d)), true), true, ifeq(less_equal(divide(c, d), divide(identity, d)), true, divide(c, d), divide(identity, d)), divide(identity, d)), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.85 = { by axiom 3 (id_divide_c_is_d) R->L }
% 2.46/0.85 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, divide(b, c)), divide(c, divide(b, c))), divide(divide(identity, c), divide(b, c))), true, ifeq(less_equal(zero, divide(divide(identity, d), divide(c, d))), true, zero, divide(divide(identity, d), divide(c, d))), divide(divide(identity, d), divide(c, d))), zero, less_equal(divide(identity, d), divide(c, d)), true), true, ifeq(less_equal(divide(c, d), divide(identity, d)), true, divide(c, d), divide(identity, d)), divide(identity, d)), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.85 = { by axiom 11 (quotient_property) }
% 2.46/0.85 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(ifeq(ifeq2(ifeq(true, true, ifeq(less_equal(zero, divide(divide(identity, d), divide(c, d))), true, zero, divide(divide(identity, d), divide(c, d))), divide(divide(identity, d), divide(c, d))), zero, less_equal(divide(identity, d), divide(c, d)), true), true, ifeq(less_equal(divide(c, d), divide(identity, d)), true, divide(c, d), divide(identity, d)), divide(identity, d)), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.85 = { by axiom 7 (ifeq_axiom) }
% 2.46/0.85 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(ifeq(ifeq2(ifeq(less_equal(zero, divide(divide(identity, d), divide(c, d))), true, zero, divide(divide(identity, d), divide(c, d))), zero, less_equal(divide(identity, d), divide(c, d)), true), true, ifeq(less_equal(divide(c, d), divide(identity, d)), true, divide(c, d), divide(identity, d)), divide(identity, d)), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.85 = { by axiom 5 (zero_is_smallest) }
% 2.46/0.85 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(ifeq(ifeq2(ifeq(true, true, zero, divide(divide(identity, d), divide(c, d))), zero, less_equal(divide(identity, d), divide(c, d)), true), true, ifeq(less_equal(divide(c, d), divide(identity, d)), true, divide(c, d), divide(identity, d)), divide(identity, d)), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.85 = { by axiom 7 (ifeq_axiom) }
% 2.46/0.85 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(ifeq(ifeq2(zero, zero, less_equal(divide(identity, d), divide(c, d)), true), true, ifeq(less_equal(divide(c, d), divide(identity, d)), true, divide(c, d), divide(identity, d)), divide(identity, d)), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.85 = { by axiom 8 (ifeq_axiom) }
% 2.46/0.85 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(ifeq(less_equal(divide(identity, d), divide(c, d)), true, ifeq(less_equal(divide(c, d), divide(identity, d)), true, divide(c, d), divide(identity, d)), divide(identity, d)), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.85 = { by axiom 12 (less_equal_and_equal) }
% 2.46/0.85 ifeq(ifeq2(ifeq(less_equal(divide(divide(identity, a), divide(d, a)), divide(divide(identity, d), a)), true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.85 = { by axiom 11 (quotient_property) }
% 2.46/0.85 ifeq(ifeq2(ifeq(true, true, ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.85 = { by axiom 7 (ifeq_axiom) }
% 2.46/0.85 ifeq(ifeq2(ifeq(less_equal(zero, divide(b, divide(d, a))), true, zero, divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.85 = { by axiom 5 (zero_is_smallest) }
% 2.46/0.85 ifeq(ifeq2(ifeq(true, true, zero, divide(b, divide(d, a))), zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.85 = { by axiom 7 (ifeq_axiom) }
% 2.46/0.85 ifeq(ifeq2(zero, zero, less_equal(b, divide(d, a)), true), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.85 = { by axiom 8 (ifeq_axiom) }
% 2.46/0.85 ifeq(less_equal(b, divide(d, a)), true, ifeq(less_equal(divide(d, a), b), true, divide(d, a), b), b)
% 2.46/0.85 = { by axiom 12 (less_equal_and_equal) }
% 2.46/0.85 b
% 2.46/0.85
% 2.46/0.85 Lemma 20: d = b.
% 2.46/0.85 Proof:
% 2.46/0.85 d
% 2.46/0.85 = { by axiom 12 (less_equal_and_equal) R->L }
% 2.46/0.85 ifeq(less_equal(d, divide(d, a)), true, ifeq(less_equal(divide(d, a), d), true, divide(d, a), d), d)
% 2.46/0.85 = { by axiom 6 (quotient_smaller_than_numerator) }
% 2.46/0.85 ifeq(less_equal(d, divide(d, a)), true, ifeq(true, true, divide(d, a), d), d)
% 2.46/0.85 = { by axiom 7 (ifeq_axiom) }
% 2.46/0.86 ifeq(less_equal(d, divide(d, a)), true, divide(d, a), d)
% 2.46/0.86 = { by lemma 19 }
% 2.46/0.86 ifeq(less_equal(d, b), true, divide(d, a), d)
% 2.46/0.86 = { by lemma 18 R->L }
% 2.46/0.86 ifeq(less_equal(divide(b, c), b), true, divide(d, a), d)
% 2.46/0.86 = { by axiom 6 (quotient_smaller_than_numerator) }
% 2.46/0.86 ifeq(true, true, divide(d, a), d)
% 2.46/0.86 = { by axiom 7 (ifeq_axiom) }
% 2.46/0.86 divide(d, a)
% 2.46/0.86 = { by lemma 19 }
% 2.46/0.86 b
% 2.46/0.86
% 2.46/0.86 Goal 1 (prove_b_equals_d): b = d.
% 2.46/0.86 Proof:
% 2.46/0.86 b
% 2.46/0.86 = { by lemma 20 R->L }
% 2.46/0.86 d
% 2.46/0.86
% 2.46/0.86 Goal 2 (part_of_theorem): divide(identity, a) = divide(identity, divide(identity, divide(identity, a))).
% 2.46/0.86 Proof:
% 2.46/0.86 divide(identity, a)
% 2.46/0.86 = { by axiom 1 (id_divide_a_is_b) }
% 2.46/0.86 b
% 2.46/0.86 = { by lemma 20 R->L }
% 2.46/0.86 d
% 2.46/0.86 = { by axiom 3 (id_divide_c_is_d) R->L }
% 2.46/0.86 divide(identity, c)
% 2.46/0.86 = { by axiom 2 (id_divide_b_is_c) R->L }
% 2.46/0.86 divide(identity, divide(identity, b))
% 2.46/0.86 = { by axiom 1 (id_divide_a_is_b) R->L }
% 2.46/0.86 divide(identity, divide(identity, divide(identity, a)))
% 2.46/0.86 % SZS output end Proof
% 2.46/0.86
% 2.46/0.86 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------