TSTP Solution File: HEN011-3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : HEN011-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:57:03 EDT 2023
% Result : Unsatisfiable 0.15s 0.65s
% Output : Proof 4.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : HEN011-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.31 % Computer : n032.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu Aug 24 13:31:26 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.15/0.65 Command-line arguments: --ground-connectedness --complete-subsets
% 0.15/0.65
% 0.15/0.65 % SZS status Unsatisfiable
% 0.15/0.65
% 3.96/0.87 % SZS output start Proof
% 3.96/0.87 Take the following subset of the input axioms:
% 3.96/0.87 fof(identity_divide_a, hypothesis, divide(identity, a)=c).
% 3.96/0.87 fof(identity_divide_b, hypothesis, divide(identity, b)=d).
% 3.96/0.87 fof(identity_divide_c, hypothesis, divide(identity, c)=e).
% 3.96/0.87 fof(identity_divide_d, hypothesis, divide(identity, d)=g).
% 3.96/0.87 fof(identity_is_largest, axiom, ![X]: less_equal(X, identity)).
% 3.96/0.87 fof(less_equal_and_equal, axiom, ![Y, X2]: (~less_equal(X2, Y) | (~less_equal(Y, X2) | X2=Y))).
% 3.96/0.87 fof(part_of_theorem, hypothesis, divide(divide(identity, a), divide(identity, divide(identity, b)))!=divide(divide(identity, b), divide(identity, divide(identity, a)))).
% 3.96/0.87 fof(prove_commutativity, negated_conjecture, divide(c, g)!=divide(d, e)).
% 3.96/0.87 fof(quotient_less_equal1, axiom, ![X2, Y2]: (~less_equal(X2, Y2) | divide(X2, Y2)=zero)).
% 3.96/0.87 fof(quotient_less_equal2, axiom, ![X2, Y2]: (divide(X2, Y2)!=zero | less_equal(X2, Y2))).
% 3.96/0.87 fof(quotient_property, axiom, ![Z, X2, Y2]: less_equal(divide(divide(X2, Z), divide(Y2, Z)), divide(divide(X2, Y2), Z))).
% 3.96/0.87 fof(quotient_smaller_than_numerator, axiom, ![X2, Y2]: less_equal(divide(X2, Y2), X2)).
% 3.96/0.87 fof(zero_is_smallest, axiom, ![X2]: less_equal(zero, X2)).
% 3.96/0.87
% 3.96/0.87 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.96/0.87 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.96/0.87 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.96/0.87 fresh(y, y, x1...xn) = u
% 3.96/0.87 C => fresh(s, t, x1...xn) = v
% 3.96/0.87 where fresh is a fresh function symbol and x1..xn are the free
% 3.96/0.87 variables of u and v.
% 3.96/0.87 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.96/0.87 input problem has no model of domain size 1).
% 3.96/0.87
% 3.96/0.87 The encoding turns the above axioms into the following unit equations and goals:
% 3.96/0.87
% 3.96/0.87 Axiom 1 (identity_is_largest): less_equal(X, identity) = true.
% 3.96/0.87 Axiom 2 (zero_is_smallest): less_equal(zero, X) = true.
% 3.96/0.87 Axiom 3 (identity_divide_c): divide(identity, c) = e.
% 3.96/0.87 Axiom 4 (identity_divide_d): divide(identity, d) = g.
% 3.96/0.87 Axiom 5 (identity_divide_a): divide(identity, a) = c.
% 3.96/0.87 Axiom 6 (identity_divide_b): divide(identity, b) = d.
% 3.96/0.87 Axiom 7 (less_equal_and_equal): fresh(X, X, Y, Z) = Z.
% 3.96/0.87 Axiom 8 (quotient_less_equal2): fresh4(X, X, Y, Z) = true.
% 3.96/0.87 Axiom 9 (quotient_less_equal1): fresh3(X, X, Y, Z) = zero.
% 3.96/0.87 Axiom 10 (less_equal_and_equal): fresh2(X, X, Y, Z) = Y.
% 3.96/0.87 Axiom 11 (quotient_smaller_than_numerator): less_equal(divide(X, Y), X) = true.
% 3.96/0.87 Axiom 12 (quotient_less_equal2): fresh4(divide(X, Y), zero, X, Y) = less_equal(X, Y).
% 3.96/0.87 Axiom 13 (quotient_less_equal1): fresh3(less_equal(X, Y), true, X, Y) = divide(X, Y).
% 3.96/0.87 Axiom 14 (less_equal_and_equal): fresh2(less_equal(X, Y), true, Y, X) = fresh(less_equal(Y, X), true, Y, X).
% 3.96/0.87 Axiom 15 (quotient_property): less_equal(divide(divide(X, Y), divide(Z, Y)), divide(divide(X, Z), Y)) = true.
% 3.96/0.87
% 3.96/0.87 Lemma 16: divide(zero, X) = zero.
% 3.96/0.87 Proof:
% 3.96/0.87 divide(zero, X)
% 3.96/0.87 = { by axiom 13 (quotient_less_equal1) R->L }
% 3.96/0.87 fresh3(less_equal(zero, X), true, zero, X)
% 3.96/0.87 = { by axiom 2 (zero_is_smallest) }
% 3.96/0.87 fresh3(true, true, zero, X)
% 3.96/0.87 = { by axiom 9 (quotient_less_equal1) }
% 3.96/0.87 zero
% 3.96/0.87
% 3.96/0.87 Lemma 17: divide(divide(X, Y), X) = zero.
% 3.96/0.87 Proof:
% 3.96/0.87 divide(divide(X, Y), X)
% 3.96/0.87 = { by axiom 13 (quotient_less_equal1) R->L }
% 3.96/0.87 fresh3(less_equal(divide(X, Y), X), true, divide(X, Y), X)
% 3.96/0.87 = { by axiom 11 (quotient_smaller_than_numerator) }
% 3.96/0.87 fresh3(true, true, divide(X, Y), X)
% 3.96/0.87 = { by axiom 9 (quotient_less_equal1) }
% 3.96/0.87 zero
% 3.96/0.87
% 3.96/0.87 Lemma 18: divide(X, X) = zero.
% 3.96/0.87 Proof:
% 3.96/0.87 divide(X, X)
% 3.96/0.87 = { by axiom 7 (less_equal_and_equal) R->L }
% 3.96/0.87 fresh(true, true, zero, divide(X, X))
% 3.96/0.87 = { by axiom 2 (zero_is_smallest) R->L }
% 3.96/0.87 fresh(less_equal(zero, divide(X, X)), true, zero, divide(X, X))
% 3.96/0.87 = { by axiom 14 (less_equal_and_equal) R->L }
% 3.96/0.87 fresh2(less_equal(divide(X, X), zero), true, zero, divide(X, X))
% 3.96/0.87 = { by axiom 12 (quotient_less_equal2) R->L }
% 3.96/0.87 fresh2(fresh4(divide(divide(X, X), zero), zero, divide(X, X), zero), true, zero, divide(X, X))
% 3.96/0.87 = { by lemma 16 R->L }
% 3.96/0.87 fresh2(fresh4(divide(divide(X, X), divide(zero, X)), zero, divide(X, X), zero), true, zero, divide(X, X))
% 3.96/0.88 = { by axiom 7 (less_equal_and_equal) R->L }
% 3.96/0.88 fresh2(fresh4(fresh(true, true, zero, divide(divide(X, X), divide(zero, X))), zero, divide(X, X), zero), true, zero, divide(X, X))
% 3.96/0.88 = { by axiom 2 (zero_is_smallest) R->L }
% 3.96/0.88 fresh2(fresh4(fresh(less_equal(zero, divide(divide(X, X), divide(zero, X))), true, zero, divide(divide(X, X), divide(zero, X))), zero, divide(X, X), zero), true, zero, divide(X, X))
% 3.96/0.88 = { by axiom 14 (less_equal_and_equal) R->L }
% 3.96/0.88 fresh2(fresh4(fresh2(less_equal(divide(divide(X, X), divide(zero, X)), zero), true, zero, divide(divide(X, X), divide(zero, X))), zero, divide(X, X), zero), true, zero, divide(X, X))
% 3.96/0.88 = { by lemma 17 R->L }
% 3.96/0.88 fresh2(fresh4(fresh2(less_equal(divide(divide(X, X), divide(zero, X)), divide(divide(X, zero), X)), true, zero, divide(divide(X, X), divide(zero, X))), zero, divide(X, X), zero), true, zero, divide(X, X))
% 3.96/0.88 = { by axiom 15 (quotient_property) }
% 3.96/0.88 fresh2(fresh4(fresh2(true, true, zero, divide(divide(X, X), divide(zero, X))), zero, divide(X, X), zero), true, zero, divide(X, X))
% 3.96/0.88 = { by axiom 10 (less_equal_and_equal) }
% 3.96/0.88 fresh2(fresh4(zero, zero, divide(X, X), zero), true, zero, divide(X, X))
% 3.96/0.88 = { by axiom 8 (quotient_less_equal2) }
% 3.96/0.88 fresh2(true, true, zero, divide(X, X))
% 3.96/0.88 = { by axiom 10 (less_equal_and_equal) }
% 3.96/0.88 zero
% 3.96/0.88
% 3.96/0.88 Lemma 19: divide(X, zero) = X.
% 3.96/0.88 Proof:
% 3.96/0.88 divide(X, zero)
% 3.96/0.88 = { by axiom 10 (less_equal_and_equal) R->L }
% 3.96/0.88 fresh2(true, true, divide(X, zero), X)
% 3.96/0.88 = { by axiom 8 (quotient_less_equal2) R->L }
% 3.96/0.88 fresh2(fresh4(zero, zero, X, divide(X, zero)), true, divide(X, zero), X)
% 3.96/0.88 = { by axiom 10 (less_equal_and_equal) R->L }
% 3.96/0.88 fresh2(fresh4(fresh2(true, true, zero, divide(X, divide(X, zero))), zero, X, divide(X, zero)), true, divide(X, zero), X)
% 3.96/0.88 = { by axiom 8 (quotient_less_equal2) R->L }
% 3.96/0.88 fresh2(fresh4(fresh2(fresh4(zero, zero, divide(X, divide(X, zero)), zero), true, zero, divide(X, divide(X, zero))), zero, X, divide(X, zero)), true, divide(X, zero), X)
% 3.96/0.88 = { by axiom 10 (less_equal_and_equal) R->L }
% 3.96/0.88 fresh2(fresh4(fresh2(fresh4(fresh2(true, true, zero, divide(divide(X, divide(X, zero)), zero)), zero, divide(X, divide(X, zero)), zero), true, zero, divide(X, divide(X, zero))), zero, X, divide(X, zero)), true, divide(X, zero), X)
% 3.96/0.88 = { by axiom 15 (quotient_property) R->L }
% 3.96/0.88 fresh2(fresh4(fresh2(fresh4(fresh2(less_equal(divide(divide(X, divide(X, zero)), divide(zero, divide(X, zero))), divide(divide(X, zero), divide(X, zero))), true, zero, divide(divide(X, divide(X, zero)), zero)), zero, divide(X, divide(X, zero)), zero), true, zero, divide(X, divide(X, zero))), zero, X, divide(X, zero)), true, divide(X, zero), X)
% 3.96/0.88 = { by lemma 16 }
% 3.96/0.88 fresh2(fresh4(fresh2(fresh4(fresh2(less_equal(divide(divide(X, divide(X, zero)), zero), divide(divide(X, zero), divide(X, zero))), true, zero, divide(divide(X, divide(X, zero)), zero)), zero, divide(X, divide(X, zero)), zero), true, zero, divide(X, divide(X, zero))), zero, X, divide(X, zero)), true, divide(X, zero), X)
% 3.96/0.88 = { by lemma 18 }
% 3.96/0.88 fresh2(fresh4(fresh2(fresh4(fresh2(less_equal(divide(divide(X, divide(X, zero)), zero), zero), true, zero, divide(divide(X, divide(X, zero)), zero)), zero, divide(X, divide(X, zero)), zero), true, zero, divide(X, divide(X, zero))), zero, X, divide(X, zero)), true, divide(X, zero), X)
% 3.96/0.88 = { by axiom 14 (less_equal_and_equal) }
% 3.96/0.88 fresh2(fresh4(fresh2(fresh4(fresh(less_equal(zero, divide(divide(X, divide(X, zero)), zero)), true, zero, divide(divide(X, divide(X, zero)), zero)), zero, divide(X, divide(X, zero)), zero), true, zero, divide(X, divide(X, zero))), zero, X, divide(X, zero)), true, divide(X, zero), X)
% 3.96/0.88 = { by axiom 2 (zero_is_smallest) }
% 3.96/0.88 fresh2(fresh4(fresh2(fresh4(fresh(true, true, zero, divide(divide(X, divide(X, zero)), zero)), zero, divide(X, divide(X, zero)), zero), true, zero, divide(X, divide(X, zero))), zero, X, divide(X, zero)), true, divide(X, zero), X)
% 3.96/0.88 = { by axiom 7 (less_equal_and_equal) }
% 3.96/0.88 fresh2(fresh4(fresh2(fresh4(divide(divide(X, divide(X, zero)), zero), zero, divide(X, divide(X, zero)), zero), true, zero, divide(X, divide(X, zero))), zero, X, divide(X, zero)), true, divide(X, zero), X)
% 3.96/0.88 = { by axiom 12 (quotient_less_equal2) }
% 3.96/0.88 fresh2(fresh4(fresh2(less_equal(divide(X, divide(X, zero)), zero), true, zero, divide(X, divide(X, zero))), zero, X, divide(X, zero)), true, divide(X, zero), X)
% 3.96/0.88 = { by axiom 14 (less_equal_and_equal) }
% 3.96/0.88 fresh2(fresh4(fresh(less_equal(zero, divide(X, divide(X, zero))), true, zero, divide(X, divide(X, zero))), zero, X, divide(X, zero)), true, divide(X, zero), X)
% 3.96/0.88 = { by axiom 2 (zero_is_smallest) }
% 3.96/0.88 fresh2(fresh4(fresh(true, true, zero, divide(X, divide(X, zero))), zero, X, divide(X, zero)), true, divide(X, zero), X)
% 3.96/0.88 = { by axiom 7 (less_equal_and_equal) }
% 3.96/0.88 fresh2(fresh4(divide(X, divide(X, zero)), zero, X, divide(X, zero)), true, divide(X, zero), X)
% 3.96/0.88 = { by axiom 12 (quotient_less_equal2) }
% 3.96/0.88 fresh2(less_equal(X, divide(X, zero)), true, divide(X, zero), X)
% 3.96/0.88 = { by axiom 14 (less_equal_and_equal) }
% 3.96/0.88 fresh(less_equal(divide(X, zero), X), true, divide(X, zero), X)
% 3.96/0.88 = { by axiom 11 (quotient_smaller_than_numerator) }
% 3.96/0.88 fresh(true, true, divide(X, zero), X)
% 3.96/0.88 = { by axiom 7 (less_equal_and_equal) }
% 3.96/0.88 X
% 3.96/0.88
% 3.96/0.88 Lemma 20: divide(X, identity) = zero.
% 3.96/0.88 Proof:
% 3.96/0.88 divide(X, identity)
% 3.96/0.88 = { by axiom 13 (quotient_less_equal1) R->L }
% 3.96/0.88 fresh3(less_equal(X, identity), true, X, identity)
% 3.96/0.88 = { by axiom 1 (identity_is_largest) }
% 3.96/0.88 fresh3(true, true, X, identity)
% 3.96/0.88 = { by axiom 9 (quotient_less_equal1) }
% 3.96/0.88 zero
% 3.96/0.88
% 3.96/0.88 Lemma 21: divide(identity, divide(identity, a)) = e.
% 3.96/0.88 Proof:
% 3.96/0.88 divide(identity, divide(identity, a))
% 3.96/0.88 = { by axiom 5 (identity_divide_a) }
% 3.96/0.88 divide(identity, c)
% 3.96/0.88 = { by axiom 3 (identity_divide_c) }
% 3.96/0.88 e
% 3.96/0.88
% 3.96/0.88 Lemma 22: divide(identity, divide(identity, b)) = g.
% 3.96/0.88 Proof:
% 3.96/0.88 divide(identity, divide(identity, b))
% 3.96/0.88 = { by axiom 6 (identity_divide_b) }
% 3.96/0.88 divide(identity, d)
% 3.96/0.88 = { by axiom 4 (identity_divide_d) }
% 3.96/0.88 g
% 3.96/0.88
% 3.96/0.88 Lemma 23: less_equal(divide(divide(X, Y), Z), divide(X, Z)) = true.
% 3.96/0.88 Proof:
% 3.96/0.88 less_equal(divide(divide(X, Y), Z), divide(X, Z))
% 3.96/0.88 = { by axiom 12 (quotient_less_equal2) R->L }
% 3.96/0.88 fresh4(divide(divide(divide(X, Y), Z), divide(X, Z)), zero, divide(divide(X, Y), Z), divide(X, Z))
% 3.96/0.88 = { by axiom 7 (less_equal_and_equal) R->L }
% 3.96/0.88 fresh4(fresh(true, true, zero, divide(divide(divide(X, Y), Z), divide(X, Z))), zero, divide(divide(X, Y), Z), divide(X, Z))
% 3.96/0.88 = { by axiom 2 (zero_is_smallest) R->L }
% 3.96/0.88 fresh4(fresh(less_equal(zero, divide(divide(divide(X, Y), Z), divide(X, Z))), true, zero, divide(divide(divide(X, Y), Z), divide(X, Z))), zero, divide(divide(X, Y), Z), divide(X, Z))
% 3.96/0.88 = { by axiom 14 (less_equal_and_equal) R->L }
% 3.96/0.88 fresh4(fresh2(less_equal(divide(divide(divide(X, Y), Z), divide(X, Z)), zero), true, zero, divide(divide(divide(X, Y), Z), divide(X, Z))), zero, divide(divide(X, Y), Z), divide(X, Z))
% 3.96/0.88 = { by lemma 16 R->L }
% 3.96/0.88 fresh4(fresh2(less_equal(divide(divide(divide(X, Y), Z), divide(X, Z)), divide(zero, Z)), true, zero, divide(divide(divide(X, Y), Z), divide(X, Z))), zero, divide(divide(X, Y), Z), divide(X, Z))
% 3.96/0.88 = { by lemma 17 R->L }
% 3.96/0.88 fresh4(fresh2(less_equal(divide(divide(divide(X, Y), Z), divide(X, Z)), divide(divide(divide(X, Y), X), Z)), true, zero, divide(divide(divide(X, Y), Z), divide(X, Z))), zero, divide(divide(X, Y), Z), divide(X, Z))
% 3.96/0.88 = { by axiom 15 (quotient_property) }
% 3.96/0.88 fresh4(fresh2(true, true, zero, divide(divide(divide(X, Y), Z), divide(X, Z))), zero, divide(divide(X, Y), Z), divide(X, Z))
% 3.96/0.88 = { by axiom 10 (less_equal_and_equal) }
% 3.96/0.88 fresh4(zero, zero, divide(divide(X, Y), Z), divide(X, Z))
% 3.96/0.88 = { by axiom 8 (quotient_less_equal2) }
% 3.96/0.88 true
% 3.96/0.88
% 3.96/0.88 Lemma 24: divide(divide(X, divide(Y, Z)), Y) = divide(X, Y).
% 3.96/0.88 Proof:
% 3.96/0.88 divide(divide(X, divide(Y, Z)), Y)
% 3.96/0.88 = { by axiom 10 (less_equal_and_equal) R->L }
% 3.96/0.88 fresh2(true, true, divide(divide(X, divide(Y, Z)), Y), divide(X, Y))
% 3.96/0.88 = { by axiom 15 (quotient_property) R->L }
% 3.96/0.88 fresh2(less_equal(divide(divide(X, Y), divide(divide(Y, Z), Y)), divide(divide(X, divide(Y, Z)), Y)), true, divide(divide(X, divide(Y, Z)), Y), divide(X, Y))
% 3.96/0.88 = { by lemma 17 }
% 3.96/0.88 fresh2(less_equal(divide(divide(X, Y), zero), divide(divide(X, divide(Y, Z)), Y)), true, divide(divide(X, divide(Y, Z)), Y), divide(X, Y))
% 3.96/0.88 = { by lemma 19 }
% 3.96/0.88 fresh2(less_equal(divide(X, Y), divide(divide(X, divide(Y, Z)), Y)), true, divide(divide(X, divide(Y, Z)), Y), divide(X, Y))
% 3.96/0.88 = { by axiom 14 (less_equal_and_equal) }
% 3.96/0.88 fresh(less_equal(divide(divide(X, divide(Y, Z)), Y), divide(X, Y)), true, divide(divide(X, divide(Y, Z)), Y), divide(X, Y))
% 3.96/0.88 = { by lemma 23 }
% 3.96/0.88 fresh(true, true, divide(divide(X, divide(Y, Z)), Y), divide(X, Y))
% 3.96/0.88 = { by axiom 7 (less_equal_and_equal) }
% 4.21/0.89 divide(X, Y)
% 4.21/0.89
% 4.21/0.89 Lemma 25: divide(divide(identity, b), divide(identity, divide(identity, a))) = divide(divide(identity, a), divide(identity, divide(identity, b))).
% 4.21/0.89 Proof:
% 4.21/0.89 divide(divide(identity, b), divide(identity, divide(identity, a)))
% 4.21/0.89 = { by axiom 10 (less_equal_and_equal) R->L }
% 4.21/0.89 fresh2(true, true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.21/0.89 = { by axiom 8 (quotient_less_equal2) R->L }
% 4.21/0.89 fresh2(fresh4(zero, zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.21/0.89 = { by lemma 16 R->L }
% 4.21/0.89 fresh2(fresh4(divide(zero, divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.21/0.89 = { by lemma 16 R->L }
% 4.21/0.89 fresh2(fresh4(divide(divide(zero, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.21/0.89 = { by axiom 9 (quotient_less_equal1) R->L }
% 4.21/0.89 fresh2(fresh4(divide(divide(fresh3(true, true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.21/0.89 = { by axiom 15 (quotient_property) R->L }
% 4.21/0.90 fresh2(fresh4(divide(divide(fresh3(less_equal(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(identity, divide(identity, b)))), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.21/0.90 = { by axiom 13 (quotient_less_equal1) }
% 4.21/0.90 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.21/0.90 = { by axiom 10 (less_equal_and_equal) R->L }
% 4.21/0.90 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(true, true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.21/0.90 = { by axiom 15 (quotient_property) R->L }
% 4.21/0.90 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(divide(identity, divide(identity, a)), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.21/0.90 = { by axiom 10 (less_equal_and_equal) R->L }
% 4.21/0.90 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh2(true, true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.21/0.90 = { by axiom 8 (quotient_less_equal2) R->L }
% 4.21/0.90 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh2(fresh4(zero, zero, divide(a, divide(identity, a)), divide(identity, divide(identity, a))), true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.21/0.90 = { by axiom 10 (less_equal_and_equal) R->L }
% 4.21/0.90 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh2(fresh4(fresh2(true, true, zero, divide(divide(a, divide(identity, a)), divide(identity, divide(identity, a)))), zero, divide(a, divide(identity, a)), divide(identity, divide(identity, a))), true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.21/0.90 = { by axiom 15 (quotient_property) R->L }
% 4.21/0.90 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh2(fresh4(fresh2(less_equal(divide(divide(a, c), divide(identity, c)), divide(divide(a, identity), c)), true, zero, divide(divide(a, divide(identity, a)), divide(identity, divide(identity, a)))), zero, divide(a, divide(identity, a)), divide(identity, divide(identity, a))), true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.21/0.91 = { by axiom 3 (identity_divide_c) }
% 4.21/0.91 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh2(fresh4(fresh2(less_equal(divide(divide(a, c), e), divide(divide(a, identity), c)), true, zero, divide(divide(a, divide(identity, a)), divide(identity, divide(identity, a)))), zero, divide(a, divide(identity, a)), divide(identity, divide(identity, a))), true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.21/0.91 = { by axiom 5 (identity_divide_a) R->L }
% 4.34/0.91 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh2(fresh4(fresh2(less_equal(divide(divide(a, c), e), divide(divide(a, identity), divide(identity, a))), true, zero, divide(divide(a, divide(identity, a)), divide(identity, divide(identity, a)))), zero, divide(a, divide(identity, a)), divide(identity, divide(identity, a))), true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.34/0.91 = { by axiom 5 (identity_divide_a) R->L }
% 4.34/0.91 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh2(fresh4(fresh2(less_equal(divide(divide(a, divide(identity, a)), e), divide(divide(a, identity), divide(identity, a))), true, zero, divide(divide(a, divide(identity, a)), divide(identity, divide(identity, a)))), zero, divide(a, divide(identity, a)), divide(identity, divide(identity, a))), true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.34/0.91 = { by lemma 21 R->L }
% 4.34/0.91 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh2(fresh4(fresh2(less_equal(divide(divide(a, divide(identity, a)), divide(identity, divide(identity, a))), divide(divide(a, identity), divide(identity, a))), true, zero, divide(divide(a, divide(identity, a)), divide(identity, divide(identity, a)))), zero, divide(a, divide(identity, a)), divide(identity, divide(identity, a))), true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.34/0.91 = { by lemma 20 }
% 4.34/0.91 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh2(fresh4(fresh2(less_equal(divide(divide(a, divide(identity, a)), divide(identity, divide(identity, a))), divide(zero, divide(identity, a))), true, zero, divide(divide(a, divide(identity, a)), divide(identity, divide(identity, a)))), zero, divide(a, divide(identity, a)), divide(identity, divide(identity, a))), true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.34/0.91 = { by lemma 16 }
% 4.34/0.91 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh2(fresh4(fresh2(less_equal(divide(divide(a, divide(identity, a)), divide(identity, divide(identity, a))), zero), true, zero, divide(divide(a, divide(identity, a)), divide(identity, divide(identity, a)))), zero, divide(a, divide(identity, a)), divide(identity, divide(identity, a))), true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.34/0.91 = { by axiom 14 (less_equal_and_equal) }
% 4.34/0.91 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh2(fresh4(fresh(less_equal(zero, divide(divide(a, divide(identity, a)), divide(identity, divide(identity, a)))), true, zero, divide(divide(a, divide(identity, a)), divide(identity, divide(identity, a)))), zero, divide(a, divide(identity, a)), divide(identity, divide(identity, a))), true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.34/0.91 = { by axiom 2 (zero_is_smallest) }
% 4.34/0.91 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh2(fresh4(fresh(true, true, zero, divide(divide(a, divide(identity, a)), divide(identity, divide(identity, a)))), zero, divide(a, divide(identity, a)), divide(identity, divide(identity, a))), true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.34/0.91 = { by axiom 7 (less_equal_and_equal) }
% 4.34/0.91 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh2(fresh4(divide(divide(a, divide(identity, a)), divide(identity, divide(identity, a))), zero, divide(a, divide(identity, a)), divide(identity, divide(identity, a))), true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.34/0.91 = { by axiom 12 (quotient_less_equal2) }
% 4.34/0.91 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh2(less_equal(divide(a, divide(identity, a)), divide(identity, divide(identity, a))), true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.34/0.91 = { by axiom 14 (less_equal_and_equal) }
% 4.34/0.91 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh(less_equal(divide(identity, divide(identity, a)), divide(a, divide(identity, a))), true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.34/0.92 = { by axiom 12 (quotient_less_equal2) R->L }
% 4.34/0.92 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh(fresh4(divide(divide(identity, divide(identity, a)), divide(a, divide(identity, a))), zero, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.34/0.92 = { by axiom 7 (less_equal_and_equal) R->L }
% 4.34/0.92 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh(fresh4(fresh(true, true, zero, divide(divide(identity, divide(identity, a)), divide(a, divide(identity, a)))), zero, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.34/0.92 = { by axiom 2 (zero_is_smallest) R->L }
% 4.34/0.92 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh(fresh4(fresh(less_equal(zero, divide(divide(identity, divide(identity, a)), divide(a, divide(identity, a)))), true, zero, divide(divide(identity, divide(identity, a)), divide(a, divide(identity, a)))), zero, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.34/0.92 = { by axiom 14 (less_equal_and_equal) R->L }
% 4.34/0.92 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh(fresh4(fresh2(less_equal(divide(divide(identity, divide(identity, a)), divide(a, divide(identity, a))), zero), true, zero, divide(divide(identity, divide(identity, a)), divide(a, divide(identity, a)))), zero, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.34/0.92 = { by lemma 18 R->L }
% 4.34/0.92 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh(fresh4(fresh2(less_equal(divide(divide(identity, divide(identity, a)), divide(a, divide(identity, a))), divide(divide(identity, a), divide(identity, a))), true, zero, divide(divide(identity, divide(identity, a)), divide(a, divide(identity, a)))), zero, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.34/0.92 = { by axiom 5 (identity_divide_a) }
% 4.34/0.92 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh(fresh4(fresh2(less_equal(divide(divide(identity, divide(identity, a)), divide(a, c)), divide(divide(identity, a), divide(identity, a))), true, zero, divide(divide(identity, divide(identity, a)), divide(a, divide(identity, a)))), zero, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.92 = { by axiom 5 (identity_divide_a) }
% 4.42/0.92 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh(fresh4(fresh2(less_equal(divide(divide(identity, divide(identity, a)), divide(a, c)), divide(divide(identity, a), c)), true, zero, divide(divide(identity, divide(identity, a)), divide(a, divide(identity, a)))), zero, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.92 = { by lemma 21 }
% 4.42/0.92 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh(fresh4(fresh2(less_equal(divide(e, divide(a, c)), divide(divide(identity, a), c)), true, zero, divide(divide(identity, divide(identity, a)), divide(a, divide(identity, a)))), zero, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.92 = { by axiom 3 (identity_divide_c) R->L }
% 4.42/0.92 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh(fresh4(fresh2(less_equal(divide(divide(identity, c), divide(a, c)), divide(divide(identity, a), c)), true, zero, divide(divide(identity, divide(identity, a)), divide(a, divide(identity, a)))), zero, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.92 = { by axiom 15 (quotient_property) }
% 4.42/0.92 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh(fresh4(fresh2(true, true, zero, divide(divide(identity, divide(identity, a)), divide(a, divide(identity, a)))), zero, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.92 = { by axiom 10 (less_equal_and_equal) }
% 4.42/0.92 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh(fresh4(zero, zero, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.92 = { by axiom 8 (quotient_less_equal2) }
% 4.42/0.92 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(fresh(true, true, divide(identity, divide(identity, a)), divide(a, divide(identity, a))), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.92 = { by axiom 7 (less_equal_and_equal) }
% 4.42/0.93 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), divide(divide(a, divide(identity, a)), a)), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.93 = { by lemma 17 }
% 4.42/0.93 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(divide(identity, b), a), zero), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.93 = { by lemma 19 }
% 4.42/0.93 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh2(less_equal(divide(divide(identity, b), a), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.93 = { by axiom 14 (less_equal_and_equal) }
% 4.42/0.93 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh(less_equal(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a)), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.93 = { by lemma 23 }
% 4.42/0.93 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), fresh(true, true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(divide(identity, b), a))), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.93 = { by axiom 7 (less_equal_and_equal) }
% 4.42/0.93 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, a), divide(divide(identity, b), a)), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.93 = { by lemma 24 R->L }
% 4.42/0.93 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(divide(identity, a), divide(divide(identity, b), a)), divide(divide(identity, divide(identity, b)), a)), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.93 = { by axiom 13 (quotient_less_equal1) R->L }
% 4.42/0.93 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(fresh3(less_equal(divide(divide(identity, a), divide(divide(identity, b), a)), divide(divide(identity, divide(identity, b)), a)), true, divide(divide(identity, a), divide(divide(identity, b), a)), divide(divide(identity, divide(identity, b)), a)), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.93 = { by axiom 15 (quotient_property) }
% 4.42/0.93 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(fresh3(true, true, divide(divide(identity, a), divide(divide(identity, b), a)), divide(divide(identity, divide(identity, b)), a)), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.93 = { by axiom 9 (quotient_less_equal1) }
% 4.42/0.93 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(zero, divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.93 = { by lemma 16 }
% 4.42/0.93 fresh2(fresh4(divide(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), zero), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.93 = { by lemma 19 }
% 4.42/0.93 fresh2(fresh4(divide(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a), divide(identity, divide(identity, b)))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.93 = { by lemma 24 }
% 4.42/0.93 fresh2(fresh4(divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(divide(identity, b), divide(identity, divide(identity, a))), a)), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.93 = { by lemma 24 }
% 4.42/0.93 fresh2(fresh4(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), zero, divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.93 = { by axiom 12 (quotient_less_equal2) }
% 4.42/0.93 fresh2(less_equal(divide(divide(identity, a), divide(identity, divide(identity, b))), divide(divide(identity, b), divide(identity, divide(identity, a)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.93 = { by axiom 14 (less_equal_and_equal) }
% 4.42/0.93 fresh(less_equal(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.93 = { by axiom 12 (quotient_less_equal2) R->L }
% 4.42/0.93 fresh(fresh4(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.93 = { by lemma 24 R->L }
% 4.42/0.93 fresh(fresh4(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.93 = { by lemma 24 R->L }
% 4.42/0.93 fresh(fresh4(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.93 = { by lemma 19 R->L }
% 4.42/0.93 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), zero), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.93 = { by lemma 16 R->L }
% 4.42/0.93 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(zero, divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.93 = { by axiom 9 (quotient_less_equal1) R->L }
% 4.42/0.93 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(fresh3(true, true, divide(divide(identity, b), divide(divide(identity, a), b)), divide(divide(identity, divide(identity, a)), b)), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.93 = { by axiom 15 (quotient_property) R->L }
% 4.42/0.93 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(fresh3(less_equal(divide(divide(identity, b), divide(divide(identity, a), b)), divide(divide(identity, divide(identity, a)), b)), true, divide(divide(identity, b), divide(divide(identity, a), b)), divide(divide(identity, divide(identity, a)), b)), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.93 = { by axiom 13 (quotient_less_equal1) }
% 4.42/0.93 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(divide(identity, b), divide(divide(identity, a), b)), divide(divide(identity, divide(identity, a)), b)), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.94 = { by lemma 24 }
% 4.42/0.94 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), divide(divide(identity, a), b)), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.94 = { by axiom 7 (less_equal_and_equal) R->L }
% 4.42/0.94 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh(true, true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.94 = { by lemma 23 R->L }
% 4.42/0.94 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh(less_equal(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.94 = { by axiom 14 (less_equal_and_equal) R->L }
% 4.42/0.94 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(identity, a), b), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.94 = { by lemma 19 R->L }
% 4.42/0.94 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), zero), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.94 = { by lemma 17 R->L }
% 4.42/0.94 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(divide(b, divide(identity, b)), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.94 = { by axiom 7 (less_equal_and_equal) R->L }
% 4.42/0.94 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh(true, true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.94 = { by axiom 8 (quotient_less_equal2) R->L }
% 4.42/0.94 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh(fresh4(zero, zero, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.94 = { by axiom 10 (less_equal_and_equal) R->L }
% 4.42/0.94 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh(fresh4(fresh2(true, true, zero, divide(divide(identity, divide(identity, b)), divide(b, divide(identity, b)))), zero, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.95 = { by axiom 15 (quotient_property) R->L }
% 4.42/0.95 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh(fresh4(fresh2(less_equal(divide(divide(identity, d), divide(b, d)), divide(divide(identity, b), d)), true, zero, divide(divide(identity, divide(identity, b)), divide(b, divide(identity, b)))), zero, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.95 = { by axiom 4 (identity_divide_d) }
% 4.42/0.95 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh(fresh4(fresh2(less_equal(divide(g, divide(b, d)), divide(divide(identity, b), d)), true, zero, divide(divide(identity, divide(identity, b)), divide(b, divide(identity, b)))), zero, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.95 = { by lemma 22 R->L }
% 4.42/0.95 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh(fresh4(fresh2(less_equal(divide(divide(identity, divide(identity, b)), divide(b, d)), divide(divide(identity, b), d)), true, zero, divide(divide(identity, divide(identity, b)), divide(b, divide(identity, b)))), zero, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.95 = { by axiom 6 (identity_divide_b) R->L }
% 4.42/0.95 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh(fresh4(fresh2(less_equal(divide(divide(identity, divide(identity, b)), divide(b, d)), divide(divide(identity, b), divide(identity, b))), true, zero, divide(divide(identity, divide(identity, b)), divide(b, divide(identity, b)))), zero, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.95 = { by axiom 6 (identity_divide_b) R->L }
% 4.42/0.95 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh(fresh4(fresh2(less_equal(divide(divide(identity, divide(identity, b)), divide(b, divide(identity, b))), divide(divide(identity, b), divide(identity, b))), true, zero, divide(divide(identity, divide(identity, b)), divide(b, divide(identity, b)))), zero, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.95 = { by lemma 18 }
% 4.42/0.95 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh(fresh4(fresh2(less_equal(divide(divide(identity, divide(identity, b)), divide(b, divide(identity, b))), zero), true, zero, divide(divide(identity, divide(identity, b)), divide(b, divide(identity, b)))), zero, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.95 = { by axiom 14 (less_equal_and_equal) }
% 4.42/0.95 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh(fresh4(fresh(less_equal(zero, divide(divide(identity, divide(identity, b)), divide(b, divide(identity, b)))), true, zero, divide(divide(identity, divide(identity, b)), divide(b, divide(identity, b)))), zero, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.96 = { by axiom 2 (zero_is_smallest) }
% 4.42/0.96 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh(fresh4(fresh(true, true, zero, divide(divide(identity, divide(identity, b)), divide(b, divide(identity, b)))), zero, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.96 = { by axiom 7 (less_equal_and_equal) }
% 4.42/0.96 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh(fresh4(divide(divide(identity, divide(identity, b)), divide(b, divide(identity, b))), zero, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.96 = { by axiom 12 (quotient_less_equal2) }
% 4.42/0.96 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh(less_equal(divide(identity, divide(identity, b)), divide(b, divide(identity, b))), true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.96 = { by axiom 14 (less_equal_and_equal) R->L }
% 4.42/0.96 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh2(less_equal(divide(b, divide(identity, b)), divide(identity, divide(identity, b))), true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.96 = { by axiom 12 (quotient_less_equal2) R->L }
% 4.42/0.96 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh2(fresh4(divide(divide(b, divide(identity, b)), divide(identity, divide(identity, b))), zero, divide(b, divide(identity, b)), divide(identity, divide(identity, b))), true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.96 = { by axiom 7 (less_equal_and_equal) R->L }
% 4.42/0.96 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh2(fresh4(fresh(true, true, zero, divide(divide(b, divide(identity, b)), divide(identity, divide(identity, b)))), zero, divide(b, divide(identity, b)), divide(identity, divide(identity, b))), true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.96 = { by axiom 2 (zero_is_smallest) R->L }
% 4.42/0.96 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh2(fresh4(fresh(less_equal(zero, divide(divide(b, divide(identity, b)), divide(identity, divide(identity, b)))), true, zero, divide(divide(b, divide(identity, b)), divide(identity, divide(identity, b)))), zero, divide(b, divide(identity, b)), divide(identity, divide(identity, b))), true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.96 = { by axiom 14 (less_equal_and_equal) R->L }
% 4.42/0.96 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh2(fresh4(fresh2(less_equal(divide(divide(b, divide(identity, b)), divide(identity, divide(identity, b))), zero), true, zero, divide(divide(b, divide(identity, b)), divide(identity, divide(identity, b)))), zero, divide(b, divide(identity, b)), divide(identity, divide(identity, b))), true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.97 = { by lemma 16 R->L }
% 4.42/0.97 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh2(fresh4(fresh2(less_equal(divide(divide(b, divide(identity, b)), divide(identity, divide(identity, b))), divide(zero, divide(identity, b))), true, zero, divide(divide(b, divide(identity, b)), divide(identity, divide(identity, b)))), zero, divide(b, divide(identity, b)), divide(identity, divide(identity, b))), true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.97 = { by lemma 20 R->L }
% 4.42/0.97 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh2(fresh4(fresh2(less_equal(divide(divide(b, divide(identity, b)), divide(identity, divide(identity, b))), divide(divide(b, identity), divide(identity, b))), true, zero, divide(divide(b, divide(identity, b)), divide(identity, divide(identity, b)))), zero, divide(b, divide(identity, b)), divide(identity, divide(identity, b))), true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.97 = { by lemma 22 }
% 4.42/0.97 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh2(fresh4(fresh2(less_equal(divide(divide(b, divide(identity, b)), g), divide(divide(b, identity), divide(identity, b))), true, zero, divide(divide(b, divide(identity, b)), divide(identity, divide(identity, b)))), zero, divide(b, divide(identity, b)), divide(identity, divide(identity, b))), true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.97 = { by axiom 6 (identity_divide_b) }
% 4.42/0.97 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh2(fresh4(fresh2(less_equal(divide(divide(b, d), g), divide(divide(b, identity), divide(identity, b))), true, zero, divide(divide(b, divide(identity, b)), divide(identity, divide(identity, b)))), zero, divide(b, divide(identity, b)), divide(identity, divide(identity, b))), true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.97 = { by axiom 6 (identity_divide_b) }
% 4.42/0.97 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh2(fresh4(fresh2(less_equal(divide(divide(b, d), g), divide(divide(b, identity), d)), true, zero, divide(divide(b, divide(identity, b)), divide(identity, divide(identity, b)))), zero, divide(b, divide(identity, b)), divide(identity, divide(identity, b))), true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.97 = { by axiom 4 (identity_divide_d) R->L }
% 4.42/0.97 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh2(fresh4(fresh2(less_equal(divide(divide(b, d), divide(identity, d)), divide(divide(b, identity), d)), true, zero, divide(divide(b, divide(identity, b)), divide(identity, divide(identity, b)))), zero, divide(b, divide(identity, b)), divide(identity, divide(identity, b))), true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.97 = { by axiom 15 (quotient_property) }
% 4.42/0.97 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh2(fresh4(fresh2(true, true, zero, divide(divide(b, divide(identity, b)), divide(identity, divide(identity, b)))), zero, divide(b, divide(identity, b)), divide(identity, divide(identity, b))), true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.97 = { by axiom 10 (less_equal_and_equal) }
% 4.42/0.97 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh2(fresh4(zero, zero, divide(b, divide(identity, b)), divide(identity, divide(identity, b))), true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.97 = { by axiom 8 (quotient_less_equal2) }
% 4.42/0.98 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(fresh2(true, true, divide(identity, divide(identity, b)), divide(b, divide(identity, b))), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.98 = { by axiom 10 (less_equal_and_equal) }
% 4.42/0.98 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(less_equal(divide(divide(divide(identity, a), b), divide(divide(identity, divide(identity, b)), b)), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.98 = { by axiom 15 (quotient_property) }
% 4.42/0.98 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), fresh2(true, true, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(divide(identity, a), b))), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.98 = { by axiom 10 (less_equal_and_equal) }
% 4.42/0.98 fresh(fresh4(divide(divide(divide(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.98 = { by axiom 13 (quotient_less_equal1) R->L }
% 4.42/0.98 fresh(fresh4(divide(divide(fresh3(less_equal(divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(identity, divide(identity, a)))), true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.98 = { by axiom 15 (quotient_property) }
% 4.42/0.98 fresh(fresh4(divide(divide(fresh3(true, true, divide(divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b), divide(identity, divide(identity, a)))), divide(divide(divide(identity, b), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(identity, divide(identity, a)))), divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.98 = { by axiom 9 (quotient_less_equal1) }
% 4.42/0.98 fresh(fresh4(divide(divide(zero, divide(divide(divide(identity, a), divide(identity, divide(identity, b))), b)), divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.98 = { by lemma 16 }
% 4.42/0.98 fresh(fresh4(divide(zero, divide(divide(identity, a), divide(identity, divide(identity, b)))), zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.98 = { by lemma 16 }
% 4.42/0.98 fresh(fresh4(zero, zero, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b)))), true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.98 = { by axiom 8 (quotient_less_equal2) }
% 4.42/0.98 fresh(true, true, divide(divide(identity, b), divide(identity, divide(identity, a))), divide(divide(identity, a), divide(identity, divide(identity, b))))
% 4.42/0.98 = { by axiom 7 (less_equal_and_equal) }
% 4.42/0.98 divide(divide(identity, a), divide(identity, divide(identity, b)))
% 4.42/0.98
% 4.42/0.98 Goal 1 (prove_commutativity): divide(c, g) = divide(d, e).
% 4.42/0.98 Proof:
% 4.42/0.98 divide(c, g)
% 4.42/0.98 = { by lemma 22 R->L }
% 4.42/0.98 divide(c, divide(identity, divide(identity, b)))
% 4.42/0.98 = { by axiom 5 (identity_divide_a) R->L }
% 4.42/0.98 divide(divide(identity, a), divide(identity, divide(identity, b)))
% 4.42/0.98 = { by lemma 25 R->L }
% 4.42/0.98 divide(divide(identity, b), divide(identity, divide(identity, a)))
% 4.42/0.98 = { by axiom 6 (identity_divide_b) }
% 4.42/0.98 divide(d, divide(identity, divide(identity, a)))
% 4.42/0.98 = { by lemma 21 }
% 4.42/0.98 divide(d, e)
% 4.42/0.98
% 4.42/0.98 Goal 2 (part_of_theorem): divide(divide(identity, a), divide(identity, divide(identity, b))) = divide(divide(identity, b), divide(identity, divide(identity, a))).
% 4.42/0.98 Proof:
% 4.42/0.98 divide(divide(identity, a), divide(identity, divide(identity, b)))
% 4.42/0.98 = { by lemma 25 R->L }
% 4.42/0.98 divide(divide(identity, b), divide(identity, divide(identity, a)))
% 4.42/0.98 % SZS output end Proof
% 4.42/0.98
% 4.42/0.98 RESULT: Unsatisfiable (the axioms are contradictory).
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