TSTP Solution File: HEN006-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : HEN006-1 : 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 : n023.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 01:56:55 EDT 2023
% Result : Unsatisfiable 4.62s 0.96s
% Output : Proof 5.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN006-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 13:43:42 EDT 2023
% 0.12/0.34 % CPUTime :
% 4.62/0.96 Command-line arguments: --ground-connectedness --complete-subsets
% 4.62/0.96
% 4.62/0.96 % SZS status Unsatisfiable
% 4.62/0.96
% 5.30/1.05 % SZS output start Proof
% 5.30/1.05 Take the following subset of the input axioms:
% 5.30/1.05 fof(closure, axiom, ![X, Y]: quotient(X, Y, divide(X, Y))).
% 5.30/1.05 fof(divisor_existence, axiom, ![Z, X2, Y2]: (~quotient(X2, Y2, Z) | less_equal(Z, X2))).
% 5.30/1.05 fof(identity_is_largest, axiom, ![X2]: less_equal(X2, identity)).
% 5.30/1.05 fof(less_equal_and_equal, axiom, ![X2, Y2]: (~less_equal(X2, Y2) | (~less_equal(Y2, X2) | X2=Y2))).
% 5.30/1.05 fof(less_equal_quotient, axiom, ![X2, Y2]: (~quotient(X2, Y2, zero) | less_equal(X2, Y2))).
% 5.30/1.05 fof(prove_xQzLEy, negated_conjecture, ~less_equal(xQz, y)).
% 5.30/1.05 fof(quotient_less_equal, axiom, ![X2, Y2]: (~less_equal(X2, Y2) | quotient(X2, Y2, zero))).
% 5.30/1.05 fof(quotient_property, axiom, ![V1, V2, V3, V4, V5, X2, Y2, Z2]: (~quotient(X2, Y2, V1) | (~quotient(Y2, Z2, V2) | (~quotient(X2, Z2, V3) | (~quotient(V3, V2, V4) | (~quotient(V1, Z2, V5) | less_equal(V4, V5))))))).
% 5.30/1.05 fof(well_defined, axiom, ![W, X2, Y2, Z2]: (~quotient(X2, Y2, Z2) | (~quotient(X2, Y2, W) | Z2=W))).
% 5.30/1.05 fof(xQy, hypothesis, quotient(x, y, xQy)).
% 5.30/1.05 fof(xQyLEz, hypothesis, less_equal(xQy, z)).
% 5.30/1.05 fof(xQz, hypothesis, quotient(x, z, xQz)).
% 5.30/1.05 fof(zero_is_smallest, axiom, ![X2]: less_equal(zero, X2)).
% 5.30/1.05
% 5.30/1.05 Now clausify the problem and encode Horn clauses using encoding 3 of
% 5.30/1.05 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 5.30/1.05 We repeatedly replace C & s=t => u=v by the two clauses:
% 5.30/1.05 fresh(y, y, x1...xn) = u
% 5.30/1.05 C => fresh(s, t, x1...xn) = v
% 5.30/1.05 where fresh is a fresh function symbol and x1..xn are the free
% 5.30/1.05 variables of u and v.
% 5.30/1.05 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 5.30/1.05 input problem has no model of domain size 1).
% 5.30/1.05
% 5.30/1.05 The encoding turns the above axioms into the following unit equations and goals:
% 5.30/1.05
% 5.30/1.05 Axiom 1 (identity_is_largest): less_equal(X, identity) = true.
% 5.30/1.05 Axiom 2 (xQyLEz): less_equal(xQy, z) = true.
% 5.30/1.05 Axiom 3 (zero_is_smallest): less_equal(zero, X) = true.
% 5.30/1.05 Axiom 4 (xQz): quotient(x, z, xQz) = true.
% 5.30/1.05 Axiom 5 (xQy): quotient(x, y, xQy) = true.
% 5.30/1.05 Axiom 6 (well_defined): fresh(X, X, Y, Z) = Z.
% 5.30/1.05 Axiom 7 (quotient_property): fresh12(X, X, Y, Z) = true.
% 5.30/1.05 Axiom 8 (less_equal_quotient): fresh7(X, X, Y, Z) = true.
% 5.30/1.05 Axiom 9 (divisor_existence): fresh6(X, X, Y, Z) = true.
% 5.30/1.05 Axiom 10 (quotient_less_equal): fresh5(X, X, Y, Z) = true.
% 5.30/1.05 Axiom 11 (less_equal_and_equal): fresh4(X, X, Y, Z) = Y.
% 5.30/1.05 Axiom 12 (less_equal_and_equal): fresh3(X, X, Y, Z) = Z.
% 5.30/1.05 Axiom 13 (closure): quotient(X, Y, divide(X, Y)) = true.
% 5.30/1.05 Axiom 14 (quotient_less_equal): fresh5(less_equal(X, Y), true, X, Y) = quotient(X, Y, zero).
% 5.30/1.05 Axiom 15 (less_equal_and_equal): fresh4(less_equal(X, Y), true, Y, X) = fresh3(less_equal(Y, X), true, Y, X).
% 5.30/1.05 Axiom 16 (well_defined): fresh2(X, X, Y, Z, W, V) = W.
% 5.30/1.05 Axiom 17 (quotient_property): fresh10(X, X, Y, Z, W, V, U) = less_equal(V, U).
% 5.30/1.05 Axiom 18 (less_equal_quotient): fresh7(quotient(X, Y, zero), true, X, Y) = less_equal(X, Y).
% 5.30/1.05 Axiom 19 (divisor_existence): fresh6(quotient(X, Y, Z), true, X, Z) = less_equal(Z, X).
% 5.30/1.05 Axiom 20 (quotient_property): fresh11(X, X, Y, Z, W, V, U, T, S) = fresh12(quotient(Y, Z, W), true, T, S).
% 5.30/1.05 Axiom 21 (well_defined): fresh2(quotient(X, Y, Z), true, X, Y, W, Z) = fresh(quotient(X, Y, W), true, W, Z).
% 5.30/1.05 Axiom 22 (quotient_property): fresh9(X, X, Y, Z, W, V, U, T, S, X2) = fresh10(quotient(Y, V, T), true, Y, Z, W, S, X2).
% 5.30/1.05 Axiom 23 (quotient_property): fresh8(X, X, Y, Z, W, V, U, T, S, X2) = fresh11(quotient(Z, V, U), true, Y, Z, W, V, T, S, X2).
% 5.30/1.05 Axiom 24 (quotient_property): fresh8(quotient(X, Y, Z), true, W, V, U, T, Y, X, Z, S) = fresh9(quotient(U, T, S), true, W, V, U, T, Y, X, Z, S).
% 5.30/1.05
% 5.30/1.05 Lemma 25: fresh9(X, X, Y, Z, W, V, U, divide(Y, V), T, S) = less_equal(T, S).
% 5.30/1.05 Proof:
% 5.30/1.05 fresh9(X, X, Y, Z, W, V, U, divide(Y, V), T, S)
% 5.30/1.05 = { by axiom 22 (quotient_property) }
% 5.30/1.05 fresh10(quotient(Y, V, divide(Y, V)), true, Y, Z, W, T, S)
% 5.30/1.05 = { by axiom 13 (closure) }
% 5.30/1.05 fresh10(true, true, Y, Z, W, T, S)
% 5.30/1.05 = { by axiom 17 (quotient_property) }
% 5.30/1.05 less_equal(T, S)
% 5.30/1.05
% 5.30/1.05 Lemma 26: fresh9(quotient(X, Y, Z), true, W, V, X, Y, U, T, divide(T, U), Z) = fresh8(S, S, W, V, X, Y, U, T, divide(T, U), Z).
% 5.30/1.05 Proof:
% 5.30/1.05 fresh9(quotient(X, Y, Z), true, W, V, X, Y, U, T, divide(T, U), Z)
% 5.30/1.05 = { by axiom 24 (quotient_property) R->L }
% 5.30/1.05 fresh8(quotient(T, U, divide(T, U)), true, W, V, X, Y, U, T, divide(T, U), Z)
% 5.30/1.05 = { by axiom 13 (closure) }
% 5.30/1.05 fresh8(true, true, W, V, X, Y, U, T, divide(T, U), Z)
% 5.30/1.05 = { by axiom 23 (quotient_property) }
% 5.30/1.05 fresh11(quotient(V, Y, U), true, W, V, X, Y, T, divide(T, U), Z)
% 5.30/1.05 = { by axiom 23 (quotient_property) R->L }
% 5.30/1.05 fresh8(S, S, W, V, X, Y, U, T, divide(T, U), Z)
% 5.30/1.05
% 5.30/1.05 Lemma 27: less_equal(divide(divide(X, Y), zero), divide(divide(X, zero), Y)) = true.
% 5.30/1.05 Proof:
% 5.30/1.05 less_equal(divide(divide(X, Y), zero), divide(divide(X, zero), Y))
% 5.30/1.05 = { by lemma 25 R->L }
% 5.30/1.05 fresh9(true, true, X, zero, divide(X, zero), Y, zero, divide(X, Y), divide(divide(X, Y), zero), divide(divide(X, zero), Y))
% 5.30/1.05 = { by axiom 13 (closure) R->L }
% 5.30/1.05 fresh9(quotient(divide(X, zero), Y, divide(divide(X, zero), Y)), true, X, zero, divide(X, zero), Y, zero, divide(X, Y), divide(divide(X, Y), zero), divide(divide(X, zero), Y))
% 5.30/1.05 = { by lemma 26 }
% 5.30/1.05 fresh8(Z, Z, X, zero, divide(X, zero), Y, zero, divide(X, Y), divide(divide(X, Y), zero), divide(divide(X, zero), Y))
% 5.30/1.05 = { by axiom 23 (quotient_property) }
% 5.30/1.05 fresh11(quotient(zero, Y, zero), true, X, zero, divide(X, zero), Y, divide(X, Y), divide(divide(X, Y), zero), divide(divide(X, zero), Y))
% 5.30/1.05 = { by axiom 14 (quotient_less_equal) R->L }
% 5.30/1.05 fresh11(fresh5(less_equal(zero, Y), true, zero, Y), true, X, zero, divide(X, zero), Y, divide(X, Y), divide(divide(X, Y), zero), divide(divide(X, zero), Y))
% 5.30/1.05 = { by axiom 3 (zero_is_smallest) }
% 5.30/1.05 fresh11(fresh5(true, true, zero, Y), true, X, zero, divide(X, zero), Y, divide(X, Y), divide(divide(X, Y), zero), divide(divide(X, zero), Y))
% 5.30/1.05 = { by axiom 10 (quotient_less_equal) }
% 5.30/1.05 fresh11(true, true, X, zero, divide(X, zero), Y, divide(X, Y), divide(divide(X, Y), zero), divide(divide(X, zero), Y))
% 5.30/1.05 = { by axiom 20 (quotient_property) }
% 5.30/1.05 fresh12(quotient(X, zero, divide(X, zero)), true, divide(divide(X, Y), zero), divide(divide(X, zero), Y))
% 5.30/1.05 = { by axiom 13 (closure) }
% 5.30/1.05 fresh12(true, true, divide(divide(X, Y), zero), divide(divide(X, zero), Y))
% 5.30/1.05 = { by axiom 7 (quotient_property) }
% 5.30/1.05 true
% 5.30/1.05
% 5.30/1.05 Lemma 28: less_equal(divide(X, Y), X) = true.
% 5.30/1.05 Proof:
% 5.30/1.05 less_equal(divide(X, Y), X)
% 5.30/1.05 = { by axiom 19 (divisor_existence) R->L }
% 5.30/1.05 fresh6(quotient(X, Y, divide(X, Y)), true, X, divide(X, Y))
% 5.30/1.05 = { by axiom 13 (closure) }
% 5.30/1.05 fresh6(true, true, X, divide(X, Y))
% 5.30/1.05 = { by axiom 9 (divisor_existence) }
% 5.30/1.05 true
% 5.30/1.05
% 5.30/1.05 Lemma 29: quotient(divide(X, Y), X, zero) = true.
% 5.30/1.05 Proof:
% 5.30/1.05 quotient(divide(X, Y), X, zero)
% 5.30/1.05 = { by axiom 14 (quotient_less_equal) R->L }
% 5.30/1.05 fresh5(less_equal(divide(X, Y), X), true, divide(X, Y), X)
% 5.30/1.05 = { by lemma 28 }
% 5.30/1.05 fresh5(true, true, divide(X, Y), X)
% 5.30/1.05 = { by axiom 10 (quotient_less_equal) }
% 5.30/1.06 true
% 5.30/1.06
% 5.30/1.06 Lemma 30: divide(X, zero) = X.
% 5.30/1.06 Proof:
% 5.30/1.06 divide(X, zero)
% 5.30/1.06 = { by axiom 12 (less_equal_and_equal) R->L }
% 5.30/1.06 fresh3(true, true, X, divide(X, zero))
% 5.30/1.06 = { by axiom 8 (less_equal_quotient) R->L }
% 5.30/1.06 fresh3(fresh7(true, true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.06 = { by axiom 13 (closure) R->L }
% 5.30/1.06 fresh3(fresh7(quotient(X, divide(X, zero), divide(X, divide(X, zero))), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.06 = { by axiom 11 (less_equal_and_equal) R->L }
% 5.30/1.06 fresh3(fresh7(quotient(X, divide(X, zero), fresh4(true, true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.06 = { by axiom 3 (zero_is_smallest) R->L }
% 5.30/1.06 fresh3(fresh7(quotient(X, divide(X, zero), fresh4(less_equal(zero, divide(X, divide(X, zero))), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.06 = { by axiom 15 (less_equal_and_equal) }
% 5.30/1.06 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(less_equal(divide(X, divide(X, zero)), zero), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.06 = { by axiom 18 (less_equal_quotient) R->L }
% 5.30/1.06 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(fresh7(quotient(divide(X, divide(X, zero)), zero, zero), true, divide(X, divide(X, zero)), zero), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.06 = { by axiom 12 (less_equal_and_equal) R->L }
% 5.30/1.06 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(fresh7(quotient(divide(X, divide(X, zero)), zero, fresh3(true, true, divide(divide(X, divide(X, zero)), zero), zero)), true, divide(X, divide(X, zero)), zero), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.06 = { by lemma 27 R->L }
% 5.30/1.06 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(fresh7(quotient(divide(X, divide(X, zero)), zero, fresh3(less_equal(divide(divide(X, divide(X, zero)), zero), divide(divide(X, zero), divide(X, zero))), true, divide(divide(X, divide(X, zero)), zero), zero)), true, divide(X, divide(X, zero)), zero), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.06 = { by axiom 11 (less_equal_and_equal) R->L }
% 5.30/1.06 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(fresh7(quotient(divide(X, divide(X, zero)), zero, fresh3(less_equal(divide(divide(X, divide(X, zero)), zero), fresh4(true, true, divide(divide(X, zero), divide(X, zero)), zero)), true, divide(divide(X, divide(X, zero)), zero), zero)), true, divide(X, divide(X, zero)), zero), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.06 = { by axiom 3 (zero_is_smallest) R->L }
% 5.30/1.06 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(fresh7(quotient(divide(X, divide(X, zero)), zero, fresh3(less_equal(divide(divide(X, divide(X, zero)), zero), fresh4(less_equal(zero, divide(divide(X, zero), divide(X, zero))), true, divide(divide(X, zero), divide(X, zero)), zero)), true, divide(divide(X, divide(X, zero)), zero), zero)), true, divide(X, divide(X, zero)), zero), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.06 = { by axiom 15 (less_equal_and_equal) }
% 5.30/1.06 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(fresh7(quotient(divide(X, divide(X, zero)), zero, fresh3(less_equal(divide(divide(X, divide(X, zero)), zero), fresh3(less_equal(divide(divide(X, zero), divide(X, zero)), zero), true, divide(divide(X, zero), divide(X, zero)), zero)), true, divide(divide(X, divide(X, zero)), zero), zero)), true, divide(X, divide(X, zero)), zero), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.06 = { by axiom 18 (less_equal_quotient) R->L }
% 5.30/1.06 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(fresh7(quotient(divide(X, divide(X, zero)), zero, fresh3(less_equal(divide(divide(X, divide(X, zero)), zero), fresh3(fresh7(quotient(divide(divide(X, zero), divide(X, zero)), zero, zero), true, divide(divide(X, zero), divide(X, zero)), zero), true, divide(divide(X, zero), divide(X, zero)), zero)), true, divide(divide(X, divide(X, zero)), zero), zero)), true, divide(X, divide(X, zero)), zero), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.06 = { by axiom 12 (less_equal_and_equal) R->L }
% 5.30/1.06 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(fresh7(quotient(divide(X, divide(X, zero)), zero, fresh3(less_equal(divide(divide(X, divide(X, zero)), zero), fresh3(fresh7(quotient(divide(divide(X, zero), divide(X, zero)), zero, fresh3(true, true, divide(divide(divide(X, zero), divide(X, zero)), zero), zero)), true, divide(divide(X, zero), divide(X, zero)), zero), true, divide(divide(X, zero), divide(X, zero)), zero)), true, divide(divide(X, divide(X, zero)), zero), zero)), true, divide(X, divide(X, zero)), zero), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.06 = { by lemma 27 R->L }
% 5.30/1.06 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(fresh7(quotient(divide(X, divide(X, zero)), zero, fresh3(less_equal(divide(divide(X, divide(X, zero)), zero), fresh3(fresh7(quotient(divide(divide(X, zero), divide(X, zero)), zero, fresh3(less_equal(divide(divide(divide(X, zero), divide(X, zero)), zero), divide(divide(divide(X, zero), zero), divide(X, zero))), true, divide(divide(divide(X, zero), divide(X, zero)), zero), zero)), true, divide(divide(X, zero), divide(X, zero)), zero), true, divide(divide(X, zero), divide(X, zero)), zero)), true, divide(divide(X, divide(X, zero)), zero), zero)), true, divide(X, divide(X, zero)), zero), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.06 = { by axiom 6 (well_defined) R->L }
% 5.30/1.06 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(fresh7(quotient(divide(X, divide(X, zero)), zero, fresh3(less_equal(divide(divide(X, divide(X, zero)), zero), fresh3(fresh7(quotient(divide(divide(X, zero), divide(X, zero)), zero, fresh3(less_equal(divide(divide(divide(X, zero), divide(X, zero)), zero), fresh(true, true, zero, divide(divide(divide(X, zero), zero), divide(X, zero)))), true, divide(divide(divide(X, zero), divide(X, zero)), zero), zero)), true, divide(divide(X, zero), divide(X, zero)), zero), true, divide(divide(X, zero), divide(X, zero)), zero)), true, divide(divide(X, divide(X, zero)), zero), zero)), true, divide(X, divide(X, zero)), zero), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.06 = { by lemma 29 R->L }
% 5.30/1.06 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(fresh7(quotient(divide(X, divide(X, zero)), zero, fresh3(less_equal(divide(divide(X, divide(X, zero)), zero), fresh3(fresh7(quotient(divide(divide(X, zero), divide(X, zero)), zero, fresh3(less_equal(divide(divide(divide(X, zero), divide(X, zero)), zero), fresh(quotient(divide(divide(X, zero), zero), divide(X, zero), zero), true, zero, divide(divide(divide(X, zero), zero), divide(X, zero)))), true, divide(divide(divide(X, zero), divide(X, zero)), zero), zero)), true, divide(divide(X, zero), divide(X, zero)), zero), true, divide(divide(X, zero), divide(X, zero)), zero)), true, divide(divide(X, divide(X, zero)), zero), zero)), true, divide(X, divide(X, zero)), zero), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.06 = { by axiom 21 (well_defined) R->L }
% 5.30/1.06 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(fresh7(quotient(divide(X, divide(X, zero)), zero, fresh3(less_equal(divide(divide(X, divide(X, zero)), zero), fresh3(fresh7(quotient(divide(divide(X, zero), divide(X, zero)), zero, fresh3(less_equal(divide(divide(divide(X, zero), divide(X, zero)), zero), fresh2(quotient(divide(divide(X, zero), zero), divide(X, zero), divide(divide(divide(X, zero), zero), divide(X, zero))), true, divide(divide(X, zero), zero), divide(X, zero), zero, divide(divide(divide(X, zero), zero), divide(X, zero)))), true, divide(divide(divide(X, zero), divide(X, zero)), zero), zero)), true, divide(divide(X, zero), divide(X, zero)), zero), true, divide(divide(X, zero), divide(X, zero)), zero)), true, divide(divide(X, divide(X, zero)), zero), zero)), true, divide(X, divide(X, zero)), zero), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.06 = { by axiom 13 (closure) }
% 5.30/1.07 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(fresh7(quotient(divide(X, divide(X, zero)), zero, fresh3(less_equal(divide(divide(X, divide(X, zero)), zero), fresh3(fresh7(quotient(divide(divide(X, zero), divide(X, zero)), zero, fresh3(less_equal(divide(divide(divide(X, zero), divide(X, zero)), zero), fresh2(true, true, divide(divide(X, zero), zero), divide(X, zero), zero, divide(divide(divide(X, zero), zero), divide(X, zero)))), true, divide(divide(divide(X, zero), divide(X, zero)), zero), zero)), true, divide(divide(X, zero), divide(X, zero)), zero), true, divide(divide(X, zero), divide(X, zero)), zero)), true, divide(divide(X, divide(X, zero)), zero), zero)), true, divide(X, divide(X, zero)), zero), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.07 = { by axiom 16 (well_defined) }
% 5.30/1.07 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(fresh7(quotient(divide(X, divide(X, zero)), zero, fresh3(less_equal(divide(divide(X, divide(X, zero)), zero), fresh3(fresh7(quotient(divide(divide(X, zero), divide(X, zero)), zero, fresh3(less_equal(divide(divide(divide(X, zero), divide(X, zero)), zero), zero), true, divide(divide(divide(X, zero), divide(X, zero)), zero), zero)), true, divide(divide(X, zero), divide(X, zero)), zero), true, divide(divide(X, zero), divide(X, zero)), zero)), true, divide(divide(X, divide(X, zero)), zero), zero)), true, divide(X, divide(X, zero)), zero), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.07 = { by axiom 15 (less_equal_and_equal) R->L }
% 5.30/1.07 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(fresh7(quotient(divide(X, divide(X, zero)), zero, fresh3(less_equal(divide(divide(X, divide(X, zero)), zero), fresh3(fresh7(quotient(divide(divide(X, zero), divide(X, zero)), zero, fresh4(less_equal(zero, divide(divide(divide(X, zero), divide(X, zero)), zero)), true, divide(divide(divide(X, zero), divide(X, zero)), zero), zero)), true, divide(divide(X, zero), divide(X, zero)), zero), true, divide(divide(X, zero), divide(X, zero)), zero)), true, divide(divide(X, divide(X, zero)), zero), zero)), true, divide(X, divide(X, zero)), zero), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.07 = { by axiom 3 (zero_is_smallest) }
% 5.30/1.07 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(fresh7(quotient(divide(X, divide(X, zero)), zero, fresh3(less_equal(divide(divide(X, divide(X, zero)), zero), fresh3(fresh7(quotient(divide(divide(X, zero), divide(X, zero)), zero, fresh4(true, true, divide(divide(divide(X, zero), divide(X, zero)), zero), zero)), true, divide(divide(X, zero), divide(X, zero)), zero), true, divide(divide(X, zero), divide(X, zero)), zero)), true, divide(divide(X, divide(X, zero)), zero), zero)), true, divide(X, divide(X, zero)), zero), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.07 = { by axiom 11 (less_equal_and_equal) }
% 5.30/1.07 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(fresh7(quotient(divide(X, divide(X, zero)), zero, fresh3(less_equal(divide(divide(X, divide(X, zero)), zero), fresh3(fresh7(quotient(divide(divide(X, zero), divide(X, zero)), zero, divide(divide(divide(X, zero), divide(X, zero)), zero)), true, divide(divide(X, zero), divide(X, zero)), zero), true, divide(divide(X, zero), divide(X, zero)), zero)), true, divide(divide(X, divide(X, zero)), zero), zero)), true, divide(X, divide(X, zero)), zero), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.07 = { by axiom 13 (closure) }
% 5.30/1.07 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(fresh7(quotient(divide(X, divide(X, zero)), zero, fresh3(less_equal(divide(divide(X, divide(X, zero)), zero), fresh3(fresh7(true, true, divide(divide(X, zero), divide(X, zero)), zero), true, divide(divide(X, zero), divide(X, zero)), zero)), true, divide(divide(X, divide(X, zero)), zero), zero)), true, divide(X, divide(X, zero)), zero), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.07 = { by axiom 8 (less_equal_quotient) }
% 5.30/1.07 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(fresh7(quotient(divide(X, divide(X, zero)), zero, fresh3(less_equal(divide(divide(X, divide(X, zero)), zero), fresh3(true, true, divide(divide(X, zero), divide(X, zero)), zero)), true, divide(divide(X, divide(X, zero)), zero), zero)), true, divide(X, divide(X, zero)), zero), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.07 = { by axiom 12 (less_equal_and_equal) }
% 5.30/1.07 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(fresh7(quotient(divide(X, divide(X, zero)), zero, fresh3(less_equal(divide(divide(X, divide(X, zero)), zero), zero), true, divide(divide(X, divide(X, zero)), zero), zero)), true, divide(X, divide(X, zero)), zero), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.07 = { by axiom 15 (less_equal_and_equal) R->L }
% 5.30/1.07 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(fresh7(quotient(divide(X, divide(X, zero)), zero, fresh4(less_equal(zero, divide(divide(X, divide(X, zero)), zero)), true, divide(divide(X, divide(X, zero)), zero), zero)), true, divide(X, divide(X, zero)), zero), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.07 = { by axiom 3 (zero_is_smallest) }
% 5.30/1.07 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(fresh7(quotient(divide(X, divide(X, zero)), zero, fresh4(true, true, divide(divide(X, divide(X, zero)), zero), zero)), true, divide(X, divide(X, zero)), zero), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.07 = { by axiom 11 (less_equal_and_equal) }
% 5.30/1.07 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(fresh7(quotient(divide(X, divide(X, zero)), zero, divide(divide(X, divide(X, zero)), zero)), true, divide(X, divide(X, zero)), zero), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.07 = { by axiom 13 (closure) }
% 5.30/1.07 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(fresh7(true, true, divide(X, divide(X, zero)), zero), true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.07 = { by axiom 8 (less_equal_quotient) }
% 5.30/1.07 fresh3(fresh7(quotient(X, divide(X, zero), fresh3(true, true, divide(X, divide(X, zero)), zero)), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.07 = { by axiom 12 (less_equal_and_equal) }
% 5.30/1.07 fresh3(fresh7(quotient(X, divide(X, zero), zero), true, X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.07 = { by axiom 18 (less_equal_quotient) }
% 5.30/1.07 fresh3(less_equal(X, divide(X, zero)), true, X, divide(X, zero))
% 5.30/1.07 = { by axiom 15 (less_equal_and_equal) R->L }
% 5.30/1.07 fresh4(less_equal(divide(X, zero), X), true, X, divide(X, zero))
% 5.30/1.07 = { by lemma 28 }
% 5.30/1.07 fresh4(true, true, X, divide(X, zero))
% 5.30/1.07 = { by axiom 11 (less_equal_and_equal) }
% 5.30/1.07 X
% 5.30/1.07
% 5.30/1.07 Goal 1 (prove_xQzLEy): less_equal(xQz, y) = true.
% 5.30/1.07 Proof:
% 5.30/1.07 less_equal(xQz, y)
% 5.30/1.07 = { by axiom 18 (less_equal_quotient) R->L }
% 5.30/1.07 fresh7(quotient(xQz, y, zero), true, xQz, y)
% 5.30/1.07 = { by axiom 12 (less_equal_and_equal) R->L }
% 5.30/1.07 fresh7(quotient(xQz, y, fresh3(true, true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.07 = { by axiom 7 (quotient_property) R->L }
% 5.30/1.07 fresh7(quotient(xQz, y, fresh3(fresh12(true, true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.07 = { by axiom 13 (closure) R->L }
% 5.30/1.07 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), divide(xQz, divide(y, z))), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.07 = { by axiom 11 (less_equal_and_equal) R->L }
% 5.30/1.07 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), fresh4(true, true, divide(xQz, divide(y, z)), zero)), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.07 = { by axiom 3 (zero_is_smallest) R->L }
% 5.30/1.07 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), fresh4(less_equal(zero, divide(xQz, divide(y, z))), true, divide(xQz, divide(y, z)), zero)), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.07 = { by axiom 15 (less_equal_and_equal) }
% 5.30/1.07 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), fresh3(less_equal(divide(xQz, divide(y, z)), zero), true, divide(xQz, divide(y, z)), zero)), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.07 = { by axiom 6 (well_defined) R->L }
% 5.30/1.07 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), fresh3(less_equal(divide(fresh(true, true, divide(x, z), xQz), divide(y, z)), zero), true, divide(xQz, divide(y, z)), zero)), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.07 = { by axiom 13 (closure) R->L }
% 5.30/1.07 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), fresh3(less_equal(divide(fresh(quotient(x, z, divide(x, z)), true, divide(x, z), xQz), divide(y, z)), zero), true, divide(xQz, divide(y, z)), zero)), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.07 = { by axiom 21 (well_defined) R->L }
% 5.30/1.07 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), fresh3(less_equal(divide(fresh2(quotient(x, z, xQz), true, x, z, divide(x, z), xQz), divide(y, z)), zero), true, divide(xQz, divide(y, z)), zero)), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.07 = { by axiom 4 (xQz) }
% 5.30/1.07 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), fresh3(less_equal(divide(fresh2(true, true, x, z, divide(x, z), xQz), divide(y, z)), zero), true, divide(xQz, divide(y, z)), zero)), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.07 = { by axiom 16 (well_defined) }
% 5.30/1.07 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), fresh3(less_equal(divide(divide(x, z), divide(y, z)), zero), true, divide(xQz, divide(y, z)), zero)), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.07 = { by lemma 25 R->L }
% 5.30/1.07 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), fresh3(fresh9(true, true, x, y, xQy, z, divide(y, z), divide(x, z), divide(divide(x, z), divide(y, z)), zero), true, divide(xQz, divide(y, z)), zero)), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.07 = { by axiom 10 (quotient_less_equal) R->L }
% 5.30/1.07 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), fresh3(fresh9(fresh5(true, true, xQy, z), true, x, y, xQy, z, divide(y, z), divide(x, z), divide(divide(x, z), divide(y, z)), zero), true, divide(xQz, divide(y, z)), zero)), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.07 = { by axiom 2 (xQyLEz) R->L }
% 5.30/1.07 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), fresh3(fresh9(fresh5(less_equal(xQy, z), true, xQy, z), true, x, y, xQy, z, divide(y, z), divide(x, z), divide(divide(x, z), divide(y, z)), zero), true, divide(xQz, divide(y, z)), zero)), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.07 = { by axiom 14 (quotient_less_equal) }
% 5.30/1.07 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), fresh3(fresh9(quotient(xQy, z, zero), true, x, y, xQy, z, divide(y, z), divide(x, z), divide(divide(x, z), divide(y, z)), zero), true, divide(xQz, divide(y, z)), zero)), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.07 = { by lemma 26 }
% 5.30/1.08 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), fresh3(fresh8(X, X, x, y, xQy, z, divide(y, z), divide(x, z), divide(divide(x, z), divide(y, z)), zero), true, divide(xQz, divide(y, z)), zero)), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.08 = { by axiom 23 (quotient_property) }
% 5.30/1.08 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), fresh3(fresh11(quotient(y, z, divide(y, z)), true, x, y, xQy, z, divide(x, z), divide(divide(x, z), divide(y, z)), zero), true, divide(xQz, divide(y, z)), zero)), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.08 = { by axiom 13 (closure) }
% 5.30/1.08 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), fresh3(fresh11(true, true, x, y, xQy, z, divide(x, z), divide(divide(x, z), divide(y, z)), zero), true, divide(xQz, divide(y, z)), zero)), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.08 = { by axiom 20 (quotient_property) }
% 5.30/1.08 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), fresh3(fresh12(quotient(x, y, xQy), true, divide(divide(x, z), divide(y, z)), zero), true, divide(xQz, divide(y, z)), zero)), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.08 = { by axiom 5 (xQy) }
% 5.30/1.08 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), fresh3(fresh12(true, true, divide(divide(x, z), divide(y, z)), zero), true, divide(xQz, divide(y, z)), zero)), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.08 = { by axiom 7 (quotient_property) }
% 5.30/1.08 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), fresh3(true, true, divide(xQz, divide(y, z)), zero)), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.08 = { by axiom 12 (less_equal_and_equal) }
% 5.30/1.08 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), zero), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.08 = { by axiom 6 (well_defined) R->L }
% 5.30/1.08 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), fresh(true, true, divide(y, identity), zero)), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.08 = { by axiom 13 (closure) R->L }
% 5.30/1.08 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), fresh(quotient(y, identity, divide(y, identity)), true, divide(y, identity), zero)), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.08 = { by axiom 21 (well_defined) R->L }
% 5.30/1.08 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), fresh2(quotient(y, identity, zero), true, y, identity, divide(y, identity), zero)), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.08 = { by axiom 14 (quotient_less_equal) R->L }
% 5.30/1.08 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), fresh2(fresh5(less_equal(y, identity), true, y, identity), true, y, identity, divide(y, identity), zero)), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.08 = { by axiom 1 (identity_is_largest) }
% 5.30/1.08 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), fresh2(fresh5(true, true, y, identity), true, y, identity, divide(y, identity), zero)), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.08 = { by axiom 10 (quotient_less_equal) }
% 5.30/1.08 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), fresh2(true, true, y, identity, divide(y, identity), zero)), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.08 = { by axiom 16 (well_defined) }
% 5.30/1.08 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), divide(y, identity)), true, divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.08 = { by lemma 30 R->L }
% 5.30/1.08 fresh7(quotient(xQz, y, fresh3(fresh12(quotient(xQz, divide(y, z), divide(y, identity)), true, divide(divide(xQz, y), zero), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.08 = { by axiom 20 (quotient_property) R->L }
% 5.30/1.08 fresh7(quotient(xQz, y, fresh3(fresh11(true, true, xQz, divide(y, z), divide(y, identity), y, divide(xQz, y), divide(divide(xQz, y), zero), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.08 = { by lemma 29 R->L }
% 5.30/1.08 fresh7(quotient(xQz, y, fresh3(fresh11(quotient(divide(y, z), y, zero), true, xQz, divide(y, z), divide(y, identity), y, divide(xQz, y), divide(divide(xQz, y), zero), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.08 = { by axiom 23 (quotient_property) R->L }
% 5.30/1.08 fresh7(quotient(xQz, y, fresh3(fresh8(Y, Y, xQz, divide(y, z), divide(y, identity), y, zero, divide(xQz, y), divide(divide(xQz, y), zero), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.08 = { by lemma 26 R->L }
% 5.30/1.08 fresh7(quotient(xQz, y, fresh3(fresh9(quotient(divide(y, identity), y, zero), true, xQz, divide(y, z), divide(y, identity), y, zero, divide(xQz, y), divide(divide(xQz, y), zero), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.30/1.08 = { by lemma 29 }
% 5.81/1.08 fresh7(quotient(xQz, y, fresh3(fresh9(true, true, xQz, divide(y, z), divide(y, identity), y, zero, divide(xQz, y), divide(divide(xQz, y), zero), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.81/1.08 = { by lemma 30 }
% 5.81/1.08 fresh7(quotient(xQz, y, fresh3(fresh9(true, true, xQz, divide(y, z), divide(y, identity), y, zero, divide(xQz, y), divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.81/1.08 = { by lemma 25 }
% 5.81/1.08 fresh7(quotient(xQz, y, fresh3(less_equal(divide(xQz, y), zero), true, divide(xQz, y), zero)), true, xQz, y)
% 5.81/1.08 = { by axiom 15 (less_equal_and_equal) R->L }
% 5.81/1.08 fresh7(quotient(xQz, y, fresh4(less_equal(zero, divide(xQz, y)), true, divide(xQz, y), zero)), true, xQz, y)
% 5.81/1.08 = { by axiom 3 (zero_is_smallest) }
% 5.81/1.08 fresh7(quotient(xQz, y, fresh4(true, true, divide(xQz, y), zero)), true, xQz, y)
% 5.81/1.08 = { by axiom 11 (less_equal_and_equal) }
% 5.81/1.08 fresh7(quotient(xQz, y, divide(xQz, y)), true, xQz, y)
% 5.81/1.08 = { by axiom 13 (closure) }
% 5.81/1.08 fresh7(true, true, xQz, y)
% 5.81/1.08 = { by axiom 8 (less_equal_quotient) }
% 5.81/1.08 true
% 5.81/1.08 % SZS output end Proof
% 5.81/1.08
% 5.81/1.08 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------