TSTP Solution File: SWV099+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV099+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 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 : n007.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 23:02:35 EDT 2023
% Result : Theorem 4.61s 0.96s
% Output : Proof 7.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV099+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.10/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 09:58:13 EDT 2023
% 0.14/0.34 % CPUTime :
% 4.61/0.96 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 4.61/0.96
% 4.61/0.96 % SZS status Theorem
% 4.61/0.96
% 5.30/1.07 % SZS output start Proof
% 5.30/1.07 Take the following subset of the input axioms:
% 7.60/1.30 fof(pred_minus_1, axiom, ![X]: minus(X, n1)=pred(X)).
% 7.60/1.31 fof(quaternion_ds1_inuse_0011, conjecture, (a_select2(rho_defuse, n0)=use & (a_select2(rho_defuse, n1)=use & (a_select2(rho_defuse, n2)=use & (a_select2(sigma_defuse, n0)=use & (a_select2(sigma_defuse, n1)=use & (a_select2(sigma_defuse, n2)=use & (a_select2(sigma_defuse, n3)=use & (a_select2(sigma_defuse, n4)=use & (a_select2(sigma_defuse, n5)=use & (a_select3(u_defuse, n0, n0)=use & (a_select3(u_defuse, n1, n0)=use & (a_select3(u_defuse, n2, n0)=use & (a_select2(xinit_defuse, n3)=use & (a_select2(xinit_defuse, n4)=use & (a_select2(xinit_defuse, n5)=use & (a_select2(xinit_mean_defuse, n0)=use & (a_select2(xinit_mean_defuse, n1)=use & (a_select2(xinit_mean_defuse, n2)=use & (a_select2(xinit_mean_defuse, n3)=use & (a_select2(xinit_mean_defuse, n4)=use & (a_select2(xinit_mean_defuse, n5)=use & (a_select2(xinit_noise_defuse, n0)=use & (a_select2(xinit_noise_defuse, n1)=use & (a_select2(xinit_noise_defuse, n2)=use & (a_select2(xinit_noise_defuse, n3)=use & (a_select2(xinit_noise_defuse, n4)=use & (a_select2(xinit_noise_defuse, n5)=use & (leq(n0, pv5) & (leq(pv5, minus(n999, n1)) & ![B, A2]: ((leq(n0, A2) & (leq(n0, B) & (leq(A2, n2) & leq(B, minus(pv5, n1))))) => (a_select3(u_defuse, A2, B)=use & a_select3(z_defuse, A2, B)=use))))))))))))))))))))))))))))))) => (a_select2(rho_defuse, n0)=use & (a_select2(rho_defuse, n1)=use & (a_select2(rho_defuse, n2)=use & (a_select2(sigma_defuse, n0)=use & (a_select2(sigma_defuse, n1)=use & (a_select2(sigma_defuse, n2)=use & (a_select2(sigma_defuse, n3)=use & (a_select2(sigma_defuse, n4)=use & (a_select2(sigma_defuse, n5)=use & (a_select3(u_defuse, n0, n0)=use & (a_select3(u_defuse, n1, n0)=use & (a_select3(u_defuse, n2, n0)=use & (a_select2(xinit_defuse, n3)=use & (a_select2(xinit_defuse, n4)=use & (a_select2(xinit_defuse, n5)=use & (a_select2(xinit_mean_defuse, n0)=use & (a_select2(xinit_mean_defuse, n1)=use & (a_select2(xinit_mean_defuse, n2)=use & (a_select2(xinit_mean_defuse, n3)=use & (a_select2(xinit_mean_defuse, n4)=use & (a_select2(xinit_mean_defuse, n5)=use & (a_select2(xinit_noise_defuse, n0)=use & (a_select2(xinit_noise_defuse, n1)=use & (a_select2(xinit_noise_defuse, n2)=use & (a_select2(xinit_noise_defuse, n3)=use & (a_select2(xinit_noise_defuse, n4)=use & (a_select2(xinit_noise_defuse, n5)=use & (leq(n0, pv5) & (leq(pv5, minus(n999, n1)) & ![C, D]: ((leq(n0, C) & (leq(n0, D) & (leq(C, n2) & leq(D, minus(pv5, n1))))) => (a_select3(u_defuse, C, D)=use & a_select3(z_defuse, C, D)=use)))))))))))))))))))))))))))))))).
% 7.60/1.31
% 7.60/1.31 Now clausify the problem and encode Horn clauses using encoding 3 of
% 7.60/1.31 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 7.60/1.31 We repeatedly replace C & s=t => u=v by the two clauses:
% 7.60/1.31 fresh(y, y, x1...xn) = u
% 7.60/1.31 C => fresh(s, t, x1...xn) = v
% 7.60/1.31 where fresh is a fresh function symbol and x1..xn are the free
% 7.60/1.31 variables of u and v.
% 7.60/1.31 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 7.60/1.31 input problem has no model of domain size 1).
% 7.60/1.31
% 7.60/1.31 The encoding turns the above axioms into the following unit equations and goals:
% 7.60/1.31
% 7.60/1.31 Axiom 1 (quaternion_ds1_inuse_0011_3): a_select2(sigma_defuse, n0) = use.
% 7.60/1.31 Axiom 2 (quaternion_ds1_inuse_0011_4): a_select2(sigma_defuse, n1) = use.
% 7.60/1.31 Axiom 3 (quaternion_ds1_inuse_0011_5): a_select2(sigma_defuse, n2) = use.
% 7.60/1.31 Axiom 4 (quaternion_ds1_inuse_0011_6): a_select2(sigma_defuse, n3) = use.
% 7.60/1.31 Axiom 5 (quaternion_ds1_inuse_0011_7): a_select2(sigma_defuse, n4) = use.
% 7.60/1.31 Axiom 6 (quaternion_ds1_inuse_0011_8): a_select2(sigma_defuse, n5) = use.
% 7.60/1.31 Axiom 7 (quaternion_ds1_inuse_0011_12): a_select2(xinit_mean_defuse, n0) = use.
% 7.60/1.31 Axiom 8 (quaternion_ds1_inuse_0011_13): a_select2(xinit_mean_defuse, n1) = use.
% 7.60/1.31 Axiom 9 (quaternion_ds1_inuse_0011_14): a_select2(xinit_mean_defuse, n2) = use.
% 7.60/1.31 Axiom 10 (quaternion_ds1_inuse_0011_15): a_select2(xinit_mean_defuse, n3) = use.
% 7.60/1.31 Axiom 11 (quaternion_ds1_inuse_0011_16): a_select2(xinit_mean_defuse, n4) = use.
% 7.60/1.31 Axiom 12 (quaternion_ds1_inuse_0011_17): a_select2(xinit_mean_defuse, n5) = use.
% 7.60/1.31 Axiom 13 (quaternion_ds1_inuse_0011_18): a_select2(xinit_noise_defuse, n0) = use.
% 7.60/1.31 Axiom 14 (quaternion_ds1_inuse_0011_19): a_select2(xinit_noise_defuse, n1) = use.
% 7.60/1.31 Axiom 15 (quaternion_ds1_inuse_0011_20): a_select2(xinit_noise_defuse, n2) = use.
% 7.60/1.31 Axiom 16 (quaternion_ds1_inuse_0011_21): a_select2(xinit_noise_defuse, n3) = use.
% 7.60/1.31 Axiom 17 (quaternion_ds1_inuse_0011_22): a_select2(xinit_noise_defuse, n4) = use.
% 7.60/1.31 Axiom 18 (quaternion_ds1_inuse_0011_23): a_select2(xinit_noise_defuse, n5) = use.
% 7.60/1.31 Axiom 19 (quaternion_ds1_inuse_0011): a_select2(rho_defuse, n0) = use.
% 7.60/1.31 Axiom 20 (quaternion_ds1_inuse_0011_1): a_select2(rho_defuse, n1) = use.
% 7.60/1.31 Axiom 21 (quaternion_ds1_inuse_0011_2): a_select2(rho_defuse, n2) = use.
% 7.60/1.31 Axiom 22 (quaternion_ds1_inuse_0011_9): a_select2(xinit_defuse, n3) = use.
% 7.60/1.31 Axiom 23 (quaternion_ds1_inuse_0011_10): a_select2(xinit_defuse, n4) = use.
% 7.60/1.31 Axiom 24 (quaternion_ds1_inuse_0011_11): a_select2(xinit_defuse, n5) = use.
% 7.60/1.31 Axiom 25 (quaternion_ds1_inuse_0011_27): leq(n0, pv5) = true3.
% 7.60/1.31 Axiom 26 (pred_minus_1): minus(X, n1) = pred(X).
% 7.60/1.31 Axiom 27 (quaternion_ds1_inuse_0011_30): fresh164(X, X) = true3.
% 7.60/1.31 Axiom 28 (quaternion_ds1_inuse_0011_30): fresh162(X, X) = leq(n0, d).
% 7.60/1.31 Axiom 29 (quaternion_ds1_inuse_0011_31): fresh135(X, X) = true3.
% 7.60/1.31 Axiom 30 (quaternion_ds1_inuse_0011_31): fresh133(X, X) = leq(n0, c).
% 7.60/1.31 Axiom 31 (quaternion_ds1_inuse_0011_32): fresh106(X, X) = true3.
% 7.60/1.31 Axiom 32 (quaternion_ds1_inuse_0011_33): fresh77(X, X) = true3.
% 7.60/1.31 Axiom 33 (quaternion_ds1_inuse_0011_33): fresh75(X, X) = leq(c, n2).
% 7.60/1.31 Axiom 34 (quaternion_ds1_inuse_0011_24): a_select3(u_defuse, n0, n0) = use.
% 7.60/1.31 Axiom 35 (quaternion_ds1_inuse_0011_25): a_select3(u_defuse, n1, n0) = use.
% 7.60/1.31 Axiom 36 (quaternion_ds1_inuse_0011_26): a_select3(u_defuse, n2, n0) = use.
% 7.60/1.31 Axiom 37 (quaternion_ds1_inuse_0011_28): leq(pv5, minus(n999, n1)) = true3.
% 7.60/1.31 Axiom 38 (quaternion_ds1_inuse_0011_32): fresh104(X, X) = leq(d, minus(pv5, n1)).
% 7.60/1.31 Axiom 39 (quaternion_ds1_inuse_0011_30): fresh163(X, X) = fresh164(a_select2(rho_defuse, n0), use).
% 7.60/1.31 Axiom 40 (quaternion_ds1_inuse_0011_30): fresh160(X, X) = fresh163(a_select2(rho_defuse, n2), use).
% 7.60/1.31 Axiom 41 (quaternion_ds1_inuse_0011_30): fresh161(X, X) = fresh162(a_select2(rho_defuse, n1), use).
% 7.60/1.31 Axiom 42 (quaternion_ds1_inuse_0011_30): fresh159(X, X) = fresh161(a_select2(sigma_defuse, n0), use).
% 7.60/1.31 Axiom 43 (quaternion_ds1_inuse_0011_30): fresh158(X, X) = fresh160(a_select2(sigma_defuse, n1), use).
% 7.60/1.31 Axiom 44 (quaternion_ds1_inuse_0011_30): fresh157(X, X) = fresh159(a_select2(sigma_defuse, n2), use).
% 7.60/1.31 Axiom 45 (quaternion_ds1_inuse_0011_30): fresh156(X, X) = fresh158(a_select2(sigma_defuse, n3), use).
% 7.60/1.31 Axiom 46 (quaternion_ds1_inuse_0011_30): fresh155(X, X) = fresh157(a_select2(sigma_defuse, n4), use).
% 7.60/1.31 Axiom 47 (quaternion_ds1_inuse_0011_30): fresh154(X, X) = fresh156(a_select2(sigma_defuse, n5), use).
% 7.60/1.31 Axiom 48 (quaternion_ds1_inuse_0011_30): fresh153(X, X) = fresh155(a_select2(xinit_defuse, n3), use).
% 7.60/1.31 Axiom 49 (quaternion_ds1_inuse_0011_30): fresh152(X, X) = fresh154(a_select2(xinit_defuse, n4), use).
% 7.60/1.31 Axiom 50 (quaternion_ds1_inuse_0011_30): fresh151(X, X) = fresh153(a_select2(xinit_defuse, n5), use).
% 7.60/1.31 Axiom 51 (quaternion_ds1_inuse_0011_30): fresh150(X, X) = fresh152(a_select2(xinit_mean_defuse, n0), use).
% 7.60/1.31 Axiom 52 (quaternion_ds1_inuse_0011_30): fresh149(X, X) = fresh151(a_select2(xinit_mean_defuse, n1), use).
% 7.60/1.31 Axiom 53 (quaternion_ds1_inuse_0011_30): fresh148(X, X) = fresh150(a_select2(xinit_mean_defuse, n2), use).
% 7.60/1.31 Axiom 54 (quaternion_ds1_inuse_0011_30): fresh147(X, X) = fresh149(a_select2(xinit_mean_defuse, n3), use).
% 7.60/1.31 Axiom 55 (quaternion_ds1_inuse_0011_30): fresh146(X, X) = fresh148(a_select2(xinit_mean_defuse, n4), use).
% 7.60/1.31 Axiom 56 (quaternion_ds1_inuse_0011_30): fresh145(X, X) = fresh147(a_select2(xinit_mean_defuse, n5), use).
% 7.60/1.31 Axiom 57 (quaternion_ds1_inuse_0011_30): fresh144(X, X) = fresh146(a_select2(xinit_noise_defuse, n0), use).
% 7.60/1.31 Axiom 58 (quaternion_ds1_inuse_0011_30): fresh143(X, X) = fresh145(a_select2(xinit_noise_defuse, n1), use).
% 7.60/1.31 Axiom 59 (quaternion_ds1_inuse_0011_30): fresh142(X, X) = fresh144(a_select2(xinit_noise_defuse, n2), use).
% 7.60/1.31 Axiom 60 (quaternion_ds1_inuse_0011_30): fresh141(X, X) = fresh143(a_select2(xinit_noise_defuse, n3), use).
% 7.60/1.31 Axiom 61 (quaternion_ds1_inuse_0011_30): fresh140(X, X) = fresh142(a_select2(xinit_noise_defuse, n4), use).
% 7.60/1.31 Axiom 62 (quaternion_ds1_inuse_0011_30): fresh139(X, X) = fresh141(a_select2(xinit_noise_defuse, n5), use).
% 7.60/1.31 Axiom 63 (quaternion_ds1_inuse_0011_30): fresh136(X, X) = fresh137(leq(n0, pv5), true3).
% 7.60/1.31 Axiom 64 (quaternion_ds1_inuse_0011_31): fresh134(X, X) = fresh135(a_select2(rho_defuse, n0), use).
% 7.60/1.31 Axiom 65 (quaternion_ds1_inuse_0011_31): fresh131(X, X) = fresh134(a_select2(rho_defuse, n2), use).
% 7.60/1.31 Axiom 66 (quaternion_ds1_inuse_0011_31): fresh132(X, X) = fresh133(a_select2(rho_defuse, n1), use).
% 7.60/1.31 Axiom 67 (quaternion_ds1_inuse_0011_31): fresh130(X, X) = fresh132(a_select2(sigma_defuse, n0), use).
% 7.60/1.31 Axiom 68 (quaternion_ds1_inuse_0011_31): fresh129(X, X) = fresh131(a_select2(sigma_defuse, n1), use).
% 7.60/1.31 Axiom 69 (quaternion_ds1_inuse_0011_31): fresh128(X, X) = fresh130(a_select2(sigma_defuse, n2), use).
% 7.60/1.31 Axiom 70 (quaternion_ds1_inuse_0011_31): fresh127(X, X) = fresh129(a_select2(sigma_defuse, n3), use).
% 7.60/1.31 Axiom 71 (quaternion_ds1_inuse_0011_31): fresh126(X, X) = fresh128(a_select2(sigma_defuse, n4), use).
% 7.60/1.31 Axiom 72 (quaternion_ds1_inuse_0011_31): fresh125(X, X) = fresh127(a_select2(sigma_defuse, n5), use).
% 7.60/1.31 Axiom 73 (quaternion_ds1_inuse_0011_31): fresh124(X, X) = fresh126(a_select2(xinit_defuse, n3), use).
% 7.60/1.31 Axiom 74 (quaternion_ds1_inuse_0011_31): fresh123(X, X) = fresh125(a_select2(xinit_defuse, n4), use).
% 7.60/1.31 Axiom 75 (quaternion_ds1_inuse_0011_31): fresh122(X, X) = fresh124(a_select2(xinit_defuse, n5), use).
% 7.60/1.31 Axiom 76 (quaternion_ds1_inuse_0011_31): fresh121(X, X) = fresh123(a_select2(xinit_mean_defuse, n0), use).
% 7.60/1.31 Axiom 77 (quaternion_ds1_inuse_0011_31): fresh120(X, X) = fresh122(a_select2(xinit_mean_defuse, n1), use).
% 7.60/1.31 Axiom 78 (quaternion_ds1_inuse_0011_31): fresh119(X, X) = fresh121(a_select2(xinit_mean_defuse, n2), use).
% 7.60/1.31 Axiom 79 (quaternion_ds1_inuse_0011_31): fresh118(X, X) = fresh120(a_select2(xinit_mean_defuse, n3), use).
% 7.60/1.31 Axiom 80 (quaternion_ds1_inuse_0011_31): fresh117(X, X) = fresh119(a_select2(xinit_mean_defuse, n4), use).
% 7.60/1.31 Axiom 81 (quaternion_ds1_inuse_0011_31): fresh116(X, X) = fresh118(a_select2(xinit_mean_defuse, n5), use).
% 7.60/1.31 Axiom 82 (quaternion_ds1_inuse_0011_31): fresh115(X, X) = fresh117(a_select2(xinit_noise_defuse, n0), use).
% 7.60/1.31 Axiom 83 (quaternion_ds1_inuse_0011_31): fresh114(X, X) = fresh116(a_select2(xinit_noise_defuse, n1), use).
% 7.60/1.31 Axiom 84 (quaternion_ds1_inuse_0011_31): fresh113(X, X) = fresh115(a_select2(xinit_noise_defuse, n2), use).
% 7.60/1.31 Axiom 85 (quaternion_ds1_inuse_0011_31): fresh112(X, X) = fresh114(a_select2(xinit_noise_defuse, n3), use).
% 7.60/1.31 Axiom 86 (quaternion_ds1_inuse_0011_31): fresh111(X, X) = fresh113(a_select2(xinit_noise_defuse, n4), use).
% 7.60/1.31 Axiom 87 (quaternion_ds1_inuse_0011_31): fresh110(X, X) = fresh112(a_select2(xinit_noise_defuse, n5), use).
% 7.60/1.31 Axiom 88 (quaternion_ds1_inuse_0011_31): fresh107(X, X) = fresh108(leq(n0, pv5), true3).
% 7.60/1.31 Axiom 89 (quaternion_ds1_inuse_0011_32): fresh105(X, X) = fresh106(a_select2(rho_defuse, n0), use).
% 7.60/1.31 Axiom 90 (quaternion_ds1_inuse_0011_32): fresh102(X, X) = fresh105(a_select2(rho_defuse, n2), use).
% 7.60/1.31 Axiom 91 (quaternion_ds1_inuse_0011_32): fresh103(X, X) = fresh104(a_select2(rho_defuse, n1), use).
% 7.60/1.31 Axiom 92 (quaternion_ds1_inuse_0011_32): fresh101(X, X) = fresh103(a_select2(sigma_defuse, n0), use).
% 7.60/1.31 Axiom 93 (quaternion_ds1_inuse_0011_32): fresh100(X, X) = fresh102(a_select2(sigma_defuse, n1), use).
% 7.60/1.31 Axiom 94 (quaternion_ds1_inuse_0011_32): fresh99(X, X) = fresh101(a_select2(sigma_defuse, n2), use).
% 7.60/1.31 Axiom 95 (quaternion_ds1_inuse_0011_32): fresh98(X, X) = fresh100(a_select2(sigma_defuse, n3), use).
% 7.60/1.31 Axiom 96 (quaternion_ds1_inuse_0011_32): fresh97(X, X) = fresh99(a_select2(sigma_defuse, n4), use).
% 7.60/1.31 Axiom 97 (quaternion_ds1_inuse_0011_32): fresh96(X, X) = fresh98(a_select2(sigma_defuse, n5), use).
% 7.60/1.31 Axiom 98 (quaternion_ds1_inuse_0011_32): fresh95(X, X) = fresh97(a_select2(xinit_defuse, n3), use).
% 7.60/1.31 Axiom 99 (quaternion_ds1_inuse_0011_32): fresh94(X, X) = fresh96(a_select2(xinit_defuse, n4), use).
% 7.60/1.31 Axiom 100 (quaternion_ds1_inuse_0011_32): fresh93(X, X) = fresh95(a_select2(xinit_defuse, n5), use).
% 7.60/1.31 Axiom 101 (quaternion_ds1_inuse_0011_32): fresh92(X, X) = fresh94(a_select2(xinit_mean_defuse, n0), use).
% 7.60/1.31 Axiom 102 (quaternion_ds1_inuse_0011_32): fresh91(X, X) = fresh93(a_select2(xinit_mean_defuse, n1), use).
% 7.60/1.31 Axiom 103 (quaternion_ds1_inuse_0011_32): fresh90(X, X) = fresh92(a_select2(xinit_mean_defuse, n2), use).
% 7.60/1.31 Axiom 104 (quaternion_ds1_inuse_0011_32): fresh89(X, X) = fresh91(a_select2(xinit_mean_defuse, n3), use).
% 7.60/1.31 Axiom 105 (quaternion_ds1_inuse_0011_32): fresh88(X, X) = fresh90(a_select2(xinit_mean_defuse, n4), use).
% 7.60/1.31 Axiom 106 (quaternion_ds1_inuse_0011_32): fresh87(X, X) = fresh89(a_select2(xinit_mean_defuse, n5), use).
% 7.60/1.31 Axiom 107 (quaternion_ds1_inuse_0011_32): fresh86(X, X) = fresh88(a_select2(xinit_noise_defuse, n0), use).
% 7.60/1.31 Axiom 108 (quaternion_ds1_inuse_0011_32): fresh85(X, X) = fresh87(a_select2(xinit_noise_defuse, n1), use).
% 7.60/1.31 Axiom 109 (quaternion_ds1_inuse_0011_32): fresh84(X, X) = fresh86(a_select2(xinit_noise_defuse, n2), use).
% 7.60/1.31 Axiom 110 (quaternion_ds1_inuse_0011_32): fresh83(X, X) = fresh85(a_select2(xinit_noise_defuse, n3), use).
% 7.60/1.31 Axiom 111 (quaternion_ds1_inuse_0011_32): fresh82(X, X) = fresh84(a_select2(xinit_noise_defuse, n4), use).
% 7.60/1.31 Axiom 112 (quaternion_ds1_inuse_0011_32): fresh81(X, X) = fresh83(a_select2(xinit_noise_defuse, n5), use).
% 7.60/1.31 Axiom 113 (quaternion_ds1_inuse_0011_32): fresh78(X, X) = fresh79(leq(n0, pv5), true3).
% 7.60/1.31 Axiom 114 (quaternion_ds1_inuse_0011_33): fresh76(X, X) = fresh77(a_select2(rho_defuse, n0), use).
% 7.60/1.31 Axiom 115 (quaternion_ds1_inuse_0011_33): fresh73(X, X) = fresh76(a_select2(rho_defuse, n2), use).
% 7.60/1.31 Axiom 116 (quaternion_ds1_inuse_0011_33): fresh74(X, X) = fresh75(a_select2(rho_defuse, n1), use).
% 7.60/1.31 Axiom 117 (quaternion_ds1_inuse_0011_33): fresh72(X, X) = fresh74(a_select2(sigma_defuse, n0), use).
% 7.60/1.31 Axiom 118 (quaternion_ds1_inuse_0011_33): fresh71(X, X) = fresh73(a_select2(sigma_defuse, n1), use).
% 7.60/1.31 Axiom 119 (quaternion_ds1_inuse_0011_33): fresh70(X, X) = fresh72(a_select2(sigma_defuse, n2), use).
% 7.60/1.31 Axiom 120 (quaternion_ds1_inuse_0011_33): fresh69(X, X) = fresh71(a_select2(sigma_defuse, n3), use).
% 7.60/1.31 Axiom 121 (quaternion_ds1_inuse_0011_33): fresh68(X, X) = fresh70(a_select2(sigma_defuse, n4), use).
% 7.60/1.31 Axiom 122 (quaternion_ds1_inuse_0011_33): fresh67(X, X) = fresh69(a_select2(sigma_defuse, n5), use).
% 7.60/1.31 Axiom 123 (quaternion_ds1_inuse_0011_33): fresh66(X, X) = fresh68(a_select2(xinit_defuse, n3), use).
% 7.60/1.31 Axiom 124 (quaternion_ds1_inuse_0011_33): fresh65(X, X) = fresh67(a_select2(xinit_defuse, n4), use).
% 7.60/1.31 Axiom 125 (quaternion_ds1_inuse_0011_33): fresh64(X, X) = fresh66(a_select2(xinit_defuse, n5), use).
% 7.60/1.31 Axiom 126 (quaternion_ds1_inuse_0011_33): fresh63(X, X) = fresh65(a_select2(xinit_mean_defuse, n0), use).
% 7.60/1.31 Axiom 127 (quaternion_ds1_inuse_0011_33): fresh62(X, X) = fresh64(a_select2(xinit_mean_defuse, n1), use).
% 7.60/1.31 Axiom 128 (quaternion_ds1_inuse_0011_33): fresh61(X, X) = fresh63(a_select2(xinit_mean_defuse, n2), use).
% 7.60/1.31 Axiom 129 (quaternion_ds1_inuse_0011_33): fresh60(X, X) = fresh62(a_select2(xinit_mean_defuse, n3), use).
% 7.60/1.31 Axiom 130 (quaternion_ds1_inuse_0011_33): fresh59(X, X) = fresh61(a_select2(xinit_mean_defuse, n4), use).
% 7.60/1.31 Axiom 131 (quaternion_ds1_inuse_0011_33): fresh58(X, X) = fresh60(a_select2(xinit_mean_defuse, n5), use).
% 7.60/1.31 Axiom 132 (quaternion_ds1_inuse_0011_33): fresh57(X, X) = fresh59(a_select2(xinit_noise_defuse, n0), use).
% 7.60/1.31 Axiom 133 (quaternion_ds1_inuse_0011_33): fresh56(X, X) = fresh58(a_select2(xinit_noise_defuse, n1), use).
% 7.60/1.31 Axiom 134 (quaternion_ds1_inuse_0011_33): fresh55(X, X) = fresh57(a_select2(xinit_noise_defuse, n2), use).
% 7.60/1.31 Axiom 135 (quaternion_ds1_inuse_0011_33): fresh54(X, X) = fresh56(a_select2(xinit_noise_defuse, n3), use).
% 7.60/1.31 Axiom 136 (quaternion_ds1_inuse_0011_33): fresh53(X, X) = fresh55(a_select2(xinit_noise_defuse, n4), use).
% 7.60/1.31 Axiom 137 (quaternion_ds1_inuse_0011_33): fresh52(X, X) = fresh54(a_select2(xinit_noise_defuse, n5), use).
% 7.60/1.31 Axiom 138 (quaternion_ds1_inuse_0011_33): fresh49(X, X) = fresh50(leq(n0, pv5), true3).
% 7.60/1.31 Axiom 139 (quaternion_ds1_inuse_0011_34): fresh48(X, X, Y, Z) = use.
% 7.60/1.31 Axiom 140 (quaternion_ds1_inuse_0011_35): fresh45(X, X, Y, Z) = use.
% 7.60/1.31 Axiom 141 (quaternion_ds1_inuse_0011_34): fresh12(X, X, Y, Z) = a_select3(u_defuse, Y, Z).
% 7.60/1.31 Axiom 142 (quaternion_ds1_inuse_0011_35): fresh11(X, X, Y, Z) = a_select3(z_defuse, Y, Z).
% 7.60/1.31 Axiom 143 (quaternion_ds1_inuse_0011_30): fresh138(X, X) = fresh140(a_select3(u_defuse, n0, n0), use).
% 7.60/1.31 Axiom 144 (quaternion_ds1_inuse_0011_30): fresh137(X, X) = fresh139(a_select3(u_defuse, n1, n0), use).
% 7.60/1.31 Axiom 145 (quaternion_ds1_inuse_0011_31): fresh109(X, X) = fresh111(a_select3(u_defuse, n0, n0), use).
% 7.60/1.31 Axiom 146 (quaternion_ds1_inuse_0011_31): fresh108(X, X) = fresh110(a_select3(u_defuse, n1, n0), use).
% 7.60/1.31 Axiom 147 (quaternion_ds1_inuse_0011_32): fresh80(X, X) = fresh82(a_select3(u_defuse, n0, n0), use).
% 7.60/1.31 Axiom 148 (quaternion_ds1_inuse_0011_32): fresh79(X, X) = fresh81(a_select3(u_defuse, n1, n0), use).
% 7.60/1.31 Axiom 149 (quaternion_ds1_inuse_0011_33): fresh51(X, X) = fresh53(a_select3(u_defuse, n0, n0), use).
% 7.60/1.31 Axiom 150 (quaternion_ds1_inuse_0011_33): fresh50(X, X) = fresh52(a_select3(u_defuse, n1, n0), use).
% 7.60/1.31 Axiom 151 (quaternion_ds1_inuse_0011_30): fresh136(leq(pv5, minus(n999, n1)), true3) = fresh138(a_select3(u_defuse, n2, n0), use).
% 7.60/1.31 Axiom 152 (quaternion_ds1_inuse_0011_31): fresh107(leq(pv5, minus(n999, n1)), true3) = fresh109(a_select3(u_defuse, n2, n0), use).
% 7.60/1.31 Axiom 153 (quaternion_ds1_inuse_0011_32): fresh78(leq(pv5, minus(n999, n1)), true3) = fresh80(a_select3(u_defuse, n2, n0), use).
% 7.60/1.31 Axiom 154 (quaternion_ds1_inuse_0011_33): fresh49(leq(pv5, minus(n999, n1)), true3) = fresh51(a_select3(u_defuse, n2, n0), use).
% 7.60/1.31 Axiom 155 (quaternion_ds1_inuse_0011_34): fresh47(X, X, Y, Z) = fresh48(leq(Y, n2), true3, Y, Z).
% 7.60/1.31 Axiom 156 (quaternion_ds1_inuse_0011_34): fresh46(X, X, Y, Z) = fresh47(leq(n0, Y), true3, Y, Z).
% 7.60/1.31 Axiom 157 (quaternion_ds1_inuse_0011_35): fresh44(X, X, Y, Z) = fresh45(leq(Y, n2), true3, Y, Z).
% 7.60/1.31 Axiom 158 (quaternion_ds1_inuse_0011_35): fresh43(X, X, Y, Z) = fresh44(leq(n0, Y), true3, Y, Z).
% 7.60/1.31 Axiom 159 (quaternion_ds1_inuse_0011_34): fresh46(leq(n0, X), true3, Y, X) = fresh12(leq(X, minus(pv5, n1)), true3, Y, X).
% 7.60/1.31 Axiom 160 (quaternion_ds1_inuse_0011_35): fresh43(leq(n0, X), true3, Y, X) = fresh11(leq(X, minus(pv5, n1)), true3, Y, X).
% 7.60/1.31
% 7.60/1.31 Lemma 161: leq(n0, d) = true3.
% 7.60/1.31 Proof:
% 7.60/1.31 leq(n0, d)
% 7.60/1.31 = { by axiom 28 (quaternion_ds1_inuse_0011_30) R->L }
% 7.60/1.31 fresh162(use, use)
% 7.60/1.31 = { by axiom 20 (quaternion_ds1_inuse_0011_1) R->L }
% 7.60/1.31 fresh162(a_select2(rho_defuse, n1), use)
% 7.60/1.31 = { by axiom 41 (quaternion_ds1_inuse_0011_30) R->L }
% 7.60/1.31 fresh161(use, use)
% 7.60/1.31 = { by axiom 1 (quaternion_ds1_inuse_0011_3) R->L }
% 7.60/1.31 fresh161(a_select2(sigma_defuse, n0), use)
% 7.60/1.31 = { by axiom 42 (quaternion_ds1_inuse_0011_30) R->L }
% 7.60/1.31 fresh159(use, use)
% 7.60/1.31 = { by axiom 3 (quaternion_ds1_inuse_0011_5) R->L }
% 7.60/1.31 fresh159(a_select2(sigma_defuse, n2), use)
% 7.60/1.31 = { by axiom 44 (quaternion_ds1_inuse_0011_30) R->L }
% 7.60/1.31 fresh157(use, use)
% 7.60/1.31 = { by axiom 5 (quaternion_ds1_inuse_0011_7) R->L }
% 7.60/1.31 fresh157(a_select2(sigma_defuse, n4), use)
% 7.60/1.31 = { by axiom 46 (quaternion_ds1_inuse_0011_30) R->L }
% 7.60/1.31 fresh155(use, use)
% 7.60/1.31 = { by axiom 22 (quaternion_ds1_inuse_0011_9) R->L }
% 7.60/1.31 fresh155(a_select2(xinit_defuse, n3), use)
% 7.60/1.31 = { by axiom 48 (quaternion_ds1_inuse_0011_30) R->L }
% 7.60/1.31 fresh153(use, use)
% 7.60/1.31 = { by axiom 24 (quaternion_ds1_inuse_0011_11) R->L }
% 7.60/1.31 fresh153(a_select2(xinit_defuse, n5), use)
% 7.60/1.31 = { by axiom 50 (quaternion_ds1_inuse_0011_30) R->L }
% 7.60/1.31 fresh151(use, use)
% 7.60/1.31 = { by axiom 8 (quaternion_ds1_inuse_0011_13) R->L }
% 7.60/1.31 fresh151(a_select2(xinit_mean_defuse, n1), use)
% 7.60/1.31 = { by axiom 52 (quaternion_ds1_inuse_0011_30) R->L }
% 7.60/1.31 fresh149(use, use)
% 7.60/1.31 = { by axiom 10 (quaternion_ds1_inuse_0011_15) R->L }
% 7.60/1.31 fresh149(a_select2(xinit_mean_defuse, n3), use)
% 7.60/1.31 = { by axiom 54 (quaternion_ds1_inuse_0011_30) R->L }
% 7.60/1.31 fresh147(use, use)
% 7.60/1.31 = { by axiom 12 (quaternion_ds1_inuse_0011_17) R->L }
% 7.60/1.31 fresh147(a_select2(xinit_mean_defuse, n5), use)
% 7.60/1.31 = { by axiom 56 (quaternion_ds1_inuse_0011_30) R->L }
% 7.60/1.31 fresh145(use, use)
% 7.60/1.31 = { by axiom 14 (quaternion_ds1_inuse_0011_19) R->L }
% 7.60/1.31 fresh145(a_select2(xinit_noise_defuse, n1), use)
% 7.60/1.31 = { by axiom 58 (quaternion_ds1_inuse_0011_30) R->L }
% 7.60/1.31 fresh143(use, use)
% 7.60/1.31 = { by axiom 16 (quaternion_ds1_inuse_0011_21) R->L }
% 7.60/1.31 fresh143(a_select2(xinit_noise_defuse, n3), use)
% 7.60/1.31 = { by axiom 60 (quaternion_ds1_inuse_0011_30) R->L }
% 7.60/1.31 fresh141(use, use)
% 7.60/1.31 = { by axiom 18 (quaternion_ds1_inuse_0011_23) R->L }
% 7.60/1.31 fresh141(a_select2(xinit_noise_defuse, n5), use)
% 7.60/1.31 = { by axiom 62 (quaternion_ds1_inuse_0011_30) R->L }
% 7.60/1.31 fresh139(use, use)
% 7.60/1.31 = { by axiom 35 (quaternion_ds1_inuse_0011_25) R->L }
% 7.60/1.31 fresh139(a_select3(u_defuse, n1, n0), use)
% 7.60/1.31 = { by axiom 144 (quaternion_ds1_inuse_0011_30) R->L }
% 7.60/1.31 fresh137(true3, true3)
% 7.60/1.31 = { by axiom 25 (quaternion_ds1_inuse_0011_27) R->L }
% 7.60/1.31 fresh137(leq(n0, pv5), true3)
% 7.60/1.31 = { by axiom 63 (quaternion_ds1_inuse_0011_30) R->L }
% 7.60/1.31 fresh136(true3, true3)
% 7.60/1.31 = { by axiom 37 (quaternion_ds1_inuse_0011_28) R->L }
% 7.60/1.31 fresh136(leq(pv5, minus(n999, n1)), true3)
% 7.60/1.31 = { by axiom 151 (quaternion_ds1_inuse_0011_30) }
% 7.60/1.31 fresh138(a_select3(u_defuse, n2, n0), use)
% 7.60/1.31 = { by axiom 36 (quaternion_ds1_inuse_0011_26) }
% 7.60/1.31 fresh138(use, use)
% 7.60/1.31 = { by axiom 143 (quaternion_ds1_inuse_0011_30) }
% 7.60/1.31 fresh140(a_select3(u_defuse, n0, n0), use)
% 7.60/1.31 = { by axiom 34 (quaternion_ds1_inuse_0011_24) }
% 7.60/1.31 fresh140(use, use)
% 7.60/1.31 = { by axiom 61 (quaternion_ds1_inuse_0011_30) }
% 7.60/1.31 fresh142(a_select2(xinit_noise_defuse, n4), use)
% 7.60/1.31 = { by axiom 17 (quaternion_ds1_inuse_0011_22) }
% 7.60/1.31 fresh142(use, use)
% 7.60/1.31 = { by axiom 59 (quaternion_ds1_inuse_0011_30) }
% 7.60/1.31 fresh144(a_select2(xinit_noise_defuse, n2), use)
% 7.60/1.31 = { by axiom 15 (quaternion_ds1_inuse_0011_20) }
% 7.60/1.31 fresh144(use, use)
% 7.60/1.31 = { by axiom 57 (quaternion_ds1_inuse_0011_30) }
% 7.60/1.31 fresh146(a_select2(xinit_noise_defuse, n0), use)
% 7.60/1.31 = { by axiom 13 (quaternion_ds1_inuse_0011_18) }
% 7.60/1.31 fresh146(use, use)
% 7.60/1.31 = { by axiom 55 (quaternion_ds1_inuse_0011_30) }
% 7.60/1.31 fresh148(a_select2(xinit_mean_defuse, n4), use)
% 7.60/1.31 = { by axiom 11 (quaternion_ds1_inuse_0011_16) }
% 7.60/1.31 fresh148(use, use)
% 7.60/1.31 = { by axiom 53 (quaternion_ds1_inuse_0011_30) }
% 7.60/1.31 fresh150(a_select2(xinit_mean_defuse, n2), use)
% 7.60/1.31 = { by axiom 9 (quaternion_ds1_inuse_0011_14) }
% 7.60/1.31 fresh150(use, use)
% 7.60/1.31 = { by axiom 51 (quaternion_ds1_inuse_0011_30) }
% 7.60/1.31 fresh152(a_select2(xinit_mean_defuse, n0), use)
% 7.60/1.31 = { by axiom 7 (quaternion_ds1_inuse_0011_12) }
% 7.60/1.31 fresh152(use, use)
% 7.60/1.31 = { by axiom 49 (quaternion_ds1_inuse_0011_30) }
% 7.60/1.31 fresh154(a_select2(xinit_defuse, n4), use)
% 7.60/1.31 = { by axiom 23 (quaternion_ds1_inuse_0011_10) }
% 7.60/1.31 fresh154(use, use)
% 7.60/1.31 = { by axiom 47 (quaternion_ds1_inuse_0011_30) }
% 7.60/1.31 fresh156(a_select2(sigma_defuse, n5), use)
% 7.60/1.31 = { by axiom 6 (quaternion_ds1_inuse_0011_8) }
% 7.60/1.31 fresh156(use, use)
% 7.60/1.31 = { by axiom 45 (quaternion_ds1_inuse_0011_30) }
% 7.60/1.31 fresh158(a_select2(sigma_defuse, n3), use)
% 7.60/1.31 = { by axiom 4 (quaternion_ds1_inuse_0011_6) }
% 7.60/1.31 fresh158(use, use)
% 7.60/1.31 = { by axiom 43 (quaternion_ds1_inuse_0011_30) }
% 7.60/1.32 fresh160(a_select2(sigma_defuse, n1), use)
% 7.60/1.32 = { by axiom 2 (quaternion_ds1_inuse_0011_4) }
% 7.60/1.32 fresh160(use, use)
% 7.60/1.32 = { by axiom 40 (quaternion_ds1_inuse_0011_30) }
% 7.60/1.32 fresh163(a_select2(rho_defuse, n2), use)
% 7.60/1.32 = { by axiom 21 (quaternion_ds1_inuse_0011_2) }
% 7.60/1.32 fresh163(use, use)
% 7.60/1.32 = { by axiom 39 (quaternion_ds1_inuse_0011_30) }
% 7.60/1.32 fresh164(a_select2(rho_defuse, n0), use)
% 7.60/1.32 = { by axiom 19 (quaternion_ds1_inuse_0011) }
% 7.60/1.32 fresh164(use, use)
% 7.60/1.32 = { by axiom 27 (quaternion_ds1_inuse_0011_30) }
% 7.60/1.32 true3
% 7.60/1.32
% 7.60/1.32 Lemma 162: leq(n0, c) = true3.
% 7.60/1.32 Proof:
% 7.60/1.32 leq(n0, c)
% 7.60/1.32 = { by axiom 30 (quaternion_ds1_inuse_0011_31) R->L }
% 7.60/1.32 fresh133(use, use)
% 7.60/1.32 = { by axiom 20 (quaternion_ds1_inuse_0011_1) R->L }
% 7.60/1.32 fresh133(a_select2(rho_defuse, n1), use)
% 7.60/1.32 = { by axiom 66 (quaternion_ds1_inuse_0011_31) R->L }
% 7.60/1.32 fresh132(use, use)
% 7.60/1.32 = { by axiom 1 (quaternion_ds1_inuse_0011_3) R->L }
% 7.60/1.32 fresh132(a_select2(sigma_defuse, n0), use)
% 7.60/1.32 = { by axiom 67 (quaternion_ds1_inuse_0011_31) R->L }
% 7.60/1.32 fresh130(use, use)
% 7.60/1.32 = { by axiom 3 (quaternion_ds1_inuse_0011_5) R->L }
% 7.60/1.32 fresh130(a_select2(sigma_defuse, n2), use)
% 7.60/1.32 = { by axiom 69 (quaternion_ds1_inuse_0011_31) R->L }
% 7.60/1.32 fresh128(use, use)
% 7.60/1.32 = { by axiom 5 (quaternion_ds1_inuse_0011_7) R->L }
% 7.60/1.32 fresh128(a_select2(sigma_defuse, n4), use)
% 7.60/1.32 = { by axiom 71 (quaternion_ds1_inuse_0011_31) R->L }
% 7.60/1.32 fresh126(use, use)
% 7.60/1.32 = { by axiom 22 (quaternion_ds1_inuse_0011_9) R->L }
% 7.60/1.32 fresh126(a_select2(xinit_defuse, n3), use)
% 7.60/1.32 = { by axiom 73 (quaternion_ds1_inuse_0011_31) R->L }
% 7.60/1.32 fresh124(use, use)
% 7.60/1.32 = { by axiom 24 (quaternion_ds1_inuse_0011_11) R->L }
% 7.60/1.32 fresh124(a_select2(xinit_defuse, n5), use)
% 7.60/1.32 = { by axiom 75 (quaternion_ds1_inuse_0011_31) R->L }
% 7.60/1.32 fresh122(use, use)
% 7.60/1.32 = { by axiom 8 (quaternion_ds1_inuse_0011_13) R->L }
% 7.60/1.32 fresh122(a_select2(xinit_mean_defuse, n1), use)
% 7.60/1.32 = { by axiom 77 (quaternion_ds1_inuse_0011_31) R->L }
% 7.60/1.32 fresh120(use, use)
% 7.60/1.32 = { by axiom 10 (quaternion_ds1_inuse_0011_15) R->L }
% 7.60/1.32 fresh120(a_select2(xinit_mean_defuse, n3), use)
% 7.60/1.32 = { by axiom 79 (quaternion_ds1_inuse_0011_31) R->L }
% 7.60/1.32 fresh118(use, use)
% 7.60/1.32 = { by axiom 12 (quaternion_ds1_inuse_0011_17) R->L }
% 7.60/1.32 fresh118(a_select2(xinit_mean_defuse, n5), use)
% 7.60/1.32 = { by axiom 81 (quaternion_ds1_inuse_0011_31) R->L }
% 7.60/1.32 fresh116(use, use)
% 7.60/1.32 = { by axiom 14 (quaternion_ds1_inuse_0011_19) R->L }
% 7.60/1.32 fresh116(a_select2(xinit_noise_defuse, n1), use)
% 7.60/1.32 = { by axiom 83 (quaternion_ds1_inuse_0011_31) R->L }
% 7.60/1.32 fresh114(use, use)
% 7.60/1.32 = { by axiom 16 (quaternion_ds1_inuse_0011_21) R->L }
% 7.60/1.32 fresh114(a_select2(xinit_noise_defuse, n3), use)
% 7.60/1.32 = { by axiom 85 (quaternion_ds1_inuse_0011_31) R->L }
% 7.60/1.32 fresh112(use, use)
% 7.60/1.32 = { by axiom 18 (quaternion_ds1_inuse_0011_23) R->L }
% 7.60/1.32 fresh112(a_select2(xinit_noise_defuse, n5), use)
% 7.60/1.32 = { by axiom 87 (quaternion_ds1_inuse_0011_31) R->L }
% 7.60/1.32 fresh110(use, use)
% 7.60/1.32 = { by axiom 35 (quaternion_ds1_inuse_0011_25) R->L }
% 7.60/1.32 fresh110(a_select3(u_defuse, n1, n0), use)
% 7.60/1.32 = { by axiom 146 (quaternion_ds1_inuse_0011_31) R->L }
% 7.60/1.32 fresh108(true3, true3)
% 7.60/1.32 = { by axiom 25 (quaternion_ds1_inuse_0011_27) R->L }
% 7.60/1.32 fresh108(leq(n0, pv5), true3)
% 7.60/1.32 = { by axiom 88 (quaternion_ds1_inuse_0011_31) R->L }
% 7.60/1.32 fresh107(true3, true3)
% 7.60/1.32 = { by axiom 37 (quaternion_ds1_inuse_0011_28) R->L }
% 7.60/1.32 fresh107(leq(pv5, minus(n999, n1)), true3)
% 7.60/1.32 = { by axiom 152 (quaternion_ds1_inuse_0011_31) }
% 7.60/1.32 fresh109(a_select3(u_defuse, n2, n0), use)
% 7.60/1.32 = { by axiom 36 (quaternion_ds1_inuse_0011_26) }
% 7.60/1.32 fresh109(use, use)
% 7.60/1.32 = { by axiom 145 (quaternion_ds1_inuse_0011_31) }
% 7.60/1.32 fresh111(a_select3(u_defuse, n0, n0), use)
% 7.60/1.32 = { by axiom 34 (quaternion_ds1_inuse_0011_24) }
% 7.60/1.32 fresh111(use, use)
% 7.60/1.32 = { by axiom 86 (quaternion_ds1_inuse_0011_31) }
% 7.60/1.32 fresh113(a_select2(xinit_noise_defuse, n4), use)
% 7.60/1.32 = { by axiom 17 (quaternion_ds1_inuse_0011_22) }
% 7.60/1.32 fresh113(use, use)
% 7.60/1.32 = { by axiom 84 (quaternion_ds1_inuse_0011_31) }
% 7.60/1.32 fresh115(a_select2(xinit_noise_defuse, n2), use)
% 7.60/1.32 = { by axiom 15 (quaternion_ds1_inuse_0011_20) }
% 7.60/1.32 fresh115(use, use)
% 7.60/1.32 = { by axiom 82 (quaternion_ds1_inuse_0011_31) }
% 7.60/1.32 fresh117(a_select2(xinit_noise_defuse, n0), use)
% 7.60/1.32 = { by axiom 13 (quaternion_ds1_inuse_0011_18) }
% 7.60/1.32 fresh117(use, use)
% 7.60/1.32 = { by axiom 80 (quaternion_ds1_inuse_0011_31) }
% 7.60/1.32 fresh119(a_select2(xinit_mean_defuse, n4), use)
% 7.60/1.32 = { by axiom 11 (quaternion_ds1_inuse_0011_16) }
% 7.60/1.32 fresh119(use, use)
% 7.60/1.32 = { by axiom 78 (quaternion_ds1_inuse_0011_31) }
% 7.60/1.32 fresh121(a_select2(xinit_mean_defuse, n2), use)
% 7.60/1.32 = { by axiom 9 (quaternion_ds1_inuse_0011_14) }
% 7.60/1.32 fresh121(use, use)
% 7.60/1.32 = { by axiom 76 (quaternion_ds1_inuse_0011_31) }
% 7.60/1.32 fresh123(a_select2(xinit_mean_defuse, n0), use)
% 7.60/1.32 = { by axiom 7 (quaternion_ds1_inuse_0011_12) }
% 7.60/1.32 fresh123(use, use)
% 7.60/1.32 = { by axiom 74 (quaternion_ds1_inuse_0011_31) }
% 7.60/1.32 fresh125(a_select2(xinit_defuse, n4), use)
% 7.60/1.32 = { by axiom 23 (quaternion_ds1_inuse_0011_10) }
% 7.60/1.32 fresh125(use, use)
% 7.60/1.32 = { by axiom 72 (quaternion_ds1_inuse_0011_31) }
% 7.60/1.32 fresh127(a_select2(sigma_defuse, n5), use)
% 7.60/1.32 = { by axiom 6 (quaternion_ds1_inuse_0011_8) }
% 7.60/1.32 fresh127(use, use)
% 7.60/1.32 = { by axiom 70 (quaternion_ds1_inuse_0011_31) }
% 7.60/1.32 fresh129(a_select2(sigma_defuse, n3), use)
% 7.60/1.32 = { by axiom 4 (quaternion_ds1_inuse_0011_6) }
% 7.60/1.32 fresh129(use, use)
% 7.60/1.32 = { by axiom 68 (quaternion_ds1_inuse_0011_31) }
% 7.60/1.32 fresh131(a_select2(sigma_defuse, n1), use)
% 7.60/1.32 = { by axiom 2 (quaternion_ds1_inuse_0011_4) }
% 7.60/1.32 fresh131(use, use)
% 7.60/1.32 = { by axiom 65 (quaternion_ds1_inuse_0011_31) }
% 7.60/1.32 fresh134(a_select2(rho_defuse, n2), use)
% 7.60/1.32 = { by axiom 21 (quaternion_ds1_inuse_0011_2) }
% 7.60/1.32 fresh134(use, use)
% 7.60/1.32 = { by axiom 64 (quaternion_ds1_inuse_0011_31) }
% 7.60/1.32 fresh135(a_select2(rho_defuse, n0), use)
% 7.60/1.32 = { by axiom 19 (quaternion_ds1_inuse_0011) }
% 7.60/1.32 fresh135(use, use)
% 7.60/1.32 = { by axiom 29 (quaternion_ds1_inuse_0011_31) }
% 7.60/1.32 true3
% 7.60/1.32
% 7.60/1.32 Lemma 163: leq(c, n2) = true3.
% 7.60/1.32 Proof:
% 7.60/1.32 leq(c, n2)
% 7.60/1.32 = { by axiom 33 (quaternion_ds1_inuse_0011_33) R->L }
% 7.60/1.32 fresh75(use, use)
% 7.60/1.32 = { by axiom 20 (quaternion_ds1_inuse_0011_1) R->L }
% 7.60/1.32 fresh75(a_select2(rho_defuse, n1), use)
% 7.60/1.32 = { by axiom 116 (quaternion_ds1_inuse_0011_33) R->L }
% 7.60/1.32 fresh74(use, use)
% 7.60/1.32 = { by axiom 1 (quaternion_ds1_inuse_0011_3) R->L }
% 7.60/1.32 fresh74(a_select2(sigma_defuse, n0), use)
% 7.60/1.32 = { by axiom 117 (quaternion_ds1_inuse_0011_33) R->L }
% 7.60/1.32 fresh72(use, use)
% 7.60/1.32 = { by axiom 3 (quaternion_ds1_inuse_0011_5) R->L }
% 7.60/1.32 fresh72(a_select2(sigma_defuse, n2), use)
% 7.60/1.32 = { by axiom 119 (quaternion_ds1_inuse_0011_33) R->L }
% 7.60/1.32 fresh70(use, use)
% 7.60/1.32 = { by axiom 5 (quaternion_ds1_inuse_0011_7) R->L }
% 7.60/1.32 fresh70(a_select2(sigma_defuse, n4), use)
% 7.60/1.32 = { by axiom 121 (quaternion_ds1_inuse_0011_33) R->L }
% 7.60/1.32 fresh68(use, use)
% 7.60/1.32 = { by axiom 22 (quaternion_ds1_inuse_0011_9) R->L }
% 7.60/1.32 fresh68(a_select2(xinit_defuse, n3), use)
% 7.60/1.32 = { by axiom 123 (quaternion_ds1_inuse_0011_33) R->L }
% 7.60/1.32 fresh66(use, use)
% 7.60/1.32 = { by axiom 24 (quaternion_ds1_inuse_0011_11) R->L }
% 7.60/1.32 fresh66(a_select2(xinit_defuse, n5), use)
% 7.60/1.32 = { by axiom 125 (quaternion_ds1_inuse_0011_33) R->L }
% 7.60/1.32 fresh64(use, use)
% 7.60/1.32 = { by axiom 8 (quaternion_ds1_inuse_0011_13) R->L }
% 7.60/1.32 fresh64(a_select2(xinit_mean_defuse, n1), use)
% 7.60/1.32 = { by axiom 127 (quaternion_ds1_inuse_0011_33) R->L }
% 7.60/1.32 fresh62(use, use)
% 7.60/1.32 = { by axiom 10 (quaternion_ds1_inuse_0011_15) R->L }
% 7.60/1.32 fresh62(a_select2(xinit_mean_defuse, n3), use)
% 7.60/1.32 = { by axiom 129 (quaternion_ds1_inuse_0011_33) R->L }
% 7.60/1.32 fresh60(use, use)
% 7.60/1.32 = { by axiom 12 (quaternion_ds1_inuse_0011_17) R->L }
% 7.60/1.32 fresh60(a_select2(xinit_mean_defuse, n5), use)
% 7.60/1.32 = { by axiom 131 (quaternion_ds1_inuse_0011_33) R->L }
% 7.60/1.32 fresh58(use, use)
% 7.60/1.32 = { by axiom 14 (quaternion_ds1_inuse_0011_19) R->L }
% 7.60/1.32 fresh58(a_select2(xinit_noise_defuse, n1), use)
% 7.60/1.32 = { by axiom 133 (quaternion_ds1_inuse_0011_33) R->L }
% 7.60/1.32 fresh56(use, use)
% 7.60/1.32 = { by axiom 16 (quaternion_ds1_inuse_0011_21) R->L }
% 7.60/1.32 fresh56(a_select2(xinit_noise_defuse, n3), use)
% 7.60/1.32 = { by axiom 135 (quaternion_ds1_inuse_0011_33) R->L }
% 7.60/1.32 fresh54(use, use)
% 7.60/1.32 = { by axiom 18 (quaternion_ds1_inuse_0011_23) R->L }
% 7.60/1.32 fresh54(a_select2(xinit_noise_defuse, n5), use)
% 7.60/1.32 = { by axiom 137 (quaternion_ds1_inuse_0011_33) R->L }
% 7.60/1.32 fresh52(use, use)
% 7.60/1.32 = { by axiom 35 (quaternion_ds1_inuse_0011_25) R->L }
% 7.60/1.32 fresh52(a_select3(u_defuse, n1, n0), use)
% 7.60/1.32 = { by axiom 150 (quaternion_ds1_inuse_0011_33) R->L }
% 7.60/1.32 fresh50(true3, true3)
% 7.60/1.32 = { by axiom 25 (quaternion_ds1_inuse_0011_27) R->L }
% 7.60/1.32 fresh50(leq(n0, pv5), true3)
% 7.60/1.32 = { by axiom 138 (quaternion_ds1_inuse_0011_33) R->L }
% 7.60/1.32 fresh49(true3, true3)
% 7.60/1.32 = { by axiom 37 (quaternion_ds1_inuse_0011_28) R->L }
% 7.60/1.32 fresh49(leq(pv5, minus(n999, n1)), true3)
% 7.60/1.32 = { by axiom 154 (quaternion_ds1_inuse_0011_33) }
% 7.60/1.32 fresh51(a_select3(u_defuse, n2, n0), use)
% 7.60/1.32 = { by axiom 36 (quaternion_ds1_inuse_0011_26) }
% 7.60/1.32 fresh51(use, use)
% 7.60/1.32 = { by axiom 149 (quaternion_ds1_inuse_0011_33) }
% 7.60/1.32 fresh53(a_select3(u_defuse, n0, n0), use)
% 7.60/1.32 = { by axiom 34 (quaternion_ds1_inuse_0011_24) }
% 7.60/1.32 fresh53(use, use)
% 7.60/1.32 = { by axiom 136 (quaternion_ds1_inuse_0011_33) }
% 7.60/1.32 fresh55(a_select2(xinit_noise_defuse, n4), use)
% 7.60/1.32 = { by axiom 17 (quaternion_ds1_inuse_0011_22) }
% 7.60/1.32 fresh55(use, use)
% 7.60/1.32 = { by axiom 134 (quaternion_ds1_inuse_0011_33) }
% 7.60/1.32 fresh57(a_select2(xinit_noise_defuse, n2), use)
% 7.60/1.32 = { by axiom 15 (quaternion_ds1_inuse_0011_20) }
% 7.60/1.32 fresh57(use, use)
% 7.60/1.32 = { by axiom 132 (quaternion_ds1_inuse_0011_33) }
% 7.60/1.32 fresh59(a_select2(xinit_noise_defuse, n0), use)
% 7.60/1.32 = { by axiom 13 (quaternion_ds1_inuse_0011_18) }
% 7.60/1.32 fresh59(use, use)
% 7.60/1.32 = { by axiom 130 (quaternion_ds1_inuse_0011_33) }
% 7.60/1.32 fresh61(a_select2(xinit_mean_defuse, n4), use)
% 7.60/1.32 = { by axiom 11 (quaternion_ds1_inuse_0011_16) }
% 7.60/1.32 fresh61(use, use)
% 7.60/1.32 = { by axiom 128 (quaternion_ds1_inuse_0011_33) }
% 7.60/1.32 fresh63(a_select2(xinit_mean_defuse, n2), use)
% 7.60/1.32 = { by axiom 9 (quaternion_ds1_inuse_0011_14) }
% 7.60/1.32 fresh63(use, use)
% 7.60/1.32 = { by axiom 126 (quaternion_ds1_inuse_0011_33) }
% 7.60/1.32 fresh65(a_select2(xinit_mean_defuse, n0), use)
% 7.60/1.32 = { by axiom 7 (quaternion_ds1_inuse_0011_12) }
% 7.60/1.32 fresh65(use, use)
% 7.60/1.32 = { by axiom 124 (quaternion_ds1_inuse_0011_33) }
% 7.60/1.32 fresh67(a_select2(xinit_defuse, n4), use)
% 7.60/1.32 = { by axiom 23 (quaternion_ds1_inuse_0011_10) }
% 7.60/1.32 fresh67(use, use)
% 7.60/1.32 = { by axiom 122 (quaternion_ds1_inuse_0011_33) }
% 7.60/1.32 fresh69(a_select2(sigma_defuse, n5), use)
% 7.60/1.32 = { by axiom 6 (quaternion_ds1_inuse_0011_8) }
% 7.60/1.32 fresh69(use, use)
% 7.60/1.32 = { by axiom 120 (quaternion_ds1_inuse_0011_33) }
% 7.60/1.32 fresh71(a_select2(sigma_defuse, n3), use)
% 7.60/1.32 = { by axiom 4 (quaternion_ds1_inuse_0011_6) }
% 7.60/1.32 fresh71(use, use)
% 7.60/1.32 = { by axiom 118 (quaternion_ds1_inuse_0011_33) }
% 7.60/1.32 fresh73(a_select2(sigma_defuse, n1), use)
% 7.60/1.32 = { by axiom 2 (quaternion_ds1_inuse_0011_4) }
% 7.60/1.32 fresh73(use, use)
% 7.60/1.32 = { by axiom 115 (quaternion_ds1_inuse_0011_33) }
% 7.60/1.32 fresh76(a_select2(rho_defuse, n2), use)
% 7.60/1.32 = { by axiom 21 (quaternion_ds1_inuse_0011_2) }
% 7.60/1.32 fresh76(use, use)
% 7.60/1.32 = { by axiom 114 (quaternion_ds1_inuse_0011_33) }
% 7.60/1.32 fresh77(a_select2(rho_defuse, n0), use)
% 7.60/1.32 = { by axiom 19 (quaternion_ds1_inuse_0011) }
% 7.60/1.32 fresh77(use, use)
% 7.60/1.32 = { by axiom 32 (quaternion_ds1_inuse_0011_33) }
% 7.60/1.32 true3
% 7.60/1.32
% 7.60/1.32 Lemma 164: fresh104(X, X) = true3.
% 7.60/1.32 Proof:
% 7.60/1.32 fresh104(X, X)
% 7.60/1.32 = { by axiom 38 (quaternion_ds1_inuse_0011_32) }
% 7.60/1.32 leq(d, minus(pv5, n1))
% 7.60/1.32 = { by axiom 38 (quaternion_ds1_inuse_0011_32) R->L }
% 7.60/1.32 fresh104(use, use)
% 7.60/1.32 = { by axiom 20 (quaternion_ds1_inuse_0011_1) R->L }
% 7.60/1.32 fresh104(a_select2(rho_defuse, n1), use)
% 7.60/1.32 = { by axiom 91 (quaternion_ds1_inuse_0011_32) R->L }
% 7.60/1.32 fresh103(use, use)
% 7.60/1.32 = { by axiom 1 (quaternion_ds1_inuse_0011_3) R->L }
% 7.60/1.32 fresh103(a_select2(sigma_defuse, n0), use)
% 7.60/1.32 = { by axiom 92 (quaternion_ds1_inuse_0011_32) R->L }
% 7.60/1.32 fresh101(use, use)
% 7.60/1.32 = { by axiom 3 (quaternion_ds1_inuse_0011_5) R->L }
% 7.60/1.32 fresh101(a_select2(sigma_defuse, n2), use)
% 7.60/1.32 = { by axiom 94 (quaternion_ds1_inuse_0011_32) R->L }
% 7.60/1.32 fresh99(use, use)
% 7.60/1.32 = { by axiom 5 (quaternion_ds1_inuse_0011_7) R->L }
% 7.60/1.32 fresh99(a_select2(sigma_defuse, n4), use)
% 7.60/1.32 = { by axiom 96 (quaternion_ds1_inuse_0011_32) R->L }
% 7.60/1.32 fresh97(use, use)
% 7.60/1.32 = { by axiom 22 (quaternion_ds1_inuse_0011_9) R->L }
% 7.60/1.32 fresh97(a_select2(xinit_defuse, n3), use)
% 7.60/1.32 = { by axiom 98 (quaternion_ds1_inuse_0011_32) R->L }
% 7.60/1.32 fresh95(use, use)
% 7.60/1.32 = { by axiom 24 (quaternion_ds1_inuse_0011_11) R->L }
% 7.60/1.32 fresh95(a_select2(xinit_defuse, n5), use)
% 7.60/1.32 = { by axiom 100 (quaternion_ds1_inuse_0011_32) R->L }
% 7.60/1.32 fresh93(use, use)
% 7.60/1.32 = { by axiom 8 (quaternion_ds1_inuse_0011_13) R->L }
% 7.60/1.32 fresh93(a_select2(xinit_mean_defuse, n1), use)
% 7.60/1.32 = { by axiom 102 (quaternion_ds1_inuse_0011_32) R->L }
% 7.60/1.32 fresh91(use, use)
% 7.60/1.32 = { by axiom 10 (quaternion_ds1_inuse_0011_15) R->L }
% 7.60/1.32 fresh91(a_select2(xinit_mean_defuse, n3), use)
% 7.60/1.32 = { by axiom 104 (quaternion_ds1_inuse_0011_32) R->L }
% 7.60/1.32 fresh89(use, use)
% 7.60/1.32 = { by axiom 12 (quaternion_ds1_inuse_0011_17) R->L }
% 7.60/1.32 fresh89(a_select2(xinit_mean_defuse, n5), use)
% 7.60/1.32 = { by axiom 106 (quaternion_ds1_inuse_0011_32) R->L }
% 7.60/1.32 fresh87(use, use)
% 7.60/1.32 = { by axiom 14 (quaternion_ds1_inuse_0011_19) R->L }
% 7.60/1.32 fresh87(a_select2(xinit_noise_defuse, n1), use)
% 7.60/1.32 = { by axiom 108 (quaternion_ds1_inuse_0011_32) R->L }
% 7.60/1.32 fresh85(use, use)
% 7.60/1.32 = { by axiom 16 (quaternion_ds1_inuse_0011_21) R->L }
% 7.60/1.32 fresh85(a_select2(xinit_noise_defuse, n3), use)
% 7.60/1.32 = { by axiom 110 (quaternion_ds1_inuse_0011_32) R->L }
% 7.60/1.32 fresh83(use, use)
% 7.60/1.32 = { by axiom 18 (quaternion_ds1_inuse_0011_23) R->L }
% 7.60/1.32 fresh83(a_select2(xinit_noise_defuse, n5), use)
% 7.60/1.32 = { by axiom 112 (quaternion_ds1_inuse_0011_32) R->L }
% 7.60/1.32 fresh81(use, use)
% 7.60/1.32 = { by axiom 35 (quaternion_ds1_inuse_0011_25) R->L }
% 7.60/1.32 fresh81(a_select3(u_defuse, n1, n0), use)
% 7.60/1.32 = { by axiom 148 (quaternion_ds1_inuse_0011_32) R->L }
% 7.60/1.32 fresh79(true3, true3)
% 7.60/1.32 = { by axiom 25 (quaternion_ds1_inuse_0011_27) R->L }
% 7.60/1.32 fresh79(leq(n0, pv5), true3)
% 7.60/1.32 = { by axiom 113 (quaternion_ds1_inuse_0011_32) R->L }
% 7.60/1.32 fresh78(true3, true3)
% 7.60/1.32 = { by axiom 37 (quaternion_ds1_inuse_0011_28) R->L }
% 7.60/1.32 fresh78(leq(pv5, minus(n999, n1)), true3)
% 7.60/1.32 = { by axiom 153 (quaternion_ds1_inuse_0011_32) }
% 7.60/1.32 fresh80(a_select3(u_defuse, n2, n0), use)
% 7.60/1.32 = { by axiom 36 (quaternion_ds1_inuse_0011_26) }
% 7.60/1.32 fresh80(use, use)
% 7.60/1.32 = { by axiom 147 (quaternion_ds1_inuse_0011_32) }
% 7.60/1.32 fresh82(a_select3(u_defuse, n0, n0), use)
% 7.60/1.32 = { by axiom 34 (quaternion_ds1_inuse_0011_24) }
% 7.60/1.32 fresh82(use, use)
% 7.60/1.32 = { by axiom 111 (quaternion_ds1_inuse_0011_32) }
% 7.60/1.32 fresh84(a_select2(xinit_noise_defuse, n4), use)
% 7.60/1.32 = { by axiom 17 (quaternion_ds1_inuse_0011_22) }
% 7.60/1.32 fresh84(use, use)
% 7.60/1.32 = { by axiom 109 (quaternion_ds1_inuse_0011_32) }
% 7.60/1.32 fresh86(a_select2(xinit_noise_defuse, n2), use)
% 7.60/1.32 = { by axiom 15 (quaternion_ds1_inuse_0011_20) }
% 7.60/1.32 fresh86(use, use)
% 7.60/1.32 = { by axiom 107 (quaternion_ds1_inuse_0011_32) }
% 7.60/1.32 fresh88(a_select2(xinit_noise_defuse, n0), use)
% 7.60/1.32 = { by axiom 13 (quaternion_ds1_inuse_0011_18) }
% 7.60/1.32 fresh88(use, use)
% 7.60/1.32 = { by axiom 105 (quaternion_ds1_inuse_0011_32) }
% 7.60/1.32 fresh90(a_select2(xinit_mean_defuse, n4), use)
% 7.60/1.32 = { by axiom 11 (quaternion_ds1_inuse_0011_16) }
% 7.60/1.32 fresh90(use, use)
% 7.60/1.32 = { by axiom 103 (quaternion_ds1_inuse_0011_32) }
% 7.60/1.32 fresh92(a_select2(xinit_mean_defuse, n2), use)
% 7.60/1.32 = { by axiom 9 (quaternion_ds1_inuse_0011_14) }
% 7.60/1.32 fresh92(use, use)
% 7.60/1.32 = { by axiom 101 (quaternion_ds1_inuse_0011_32) }
% 7.60/1.32 fresh94(a_select2(xinit_mean_defuse, n0), use)
% 7.60/1.32 = { by axiom 7 (quaternion_ds1_inuse_0011_12) }
% 7.60/1.32 fresh94(use, use)
% 7.60/1.32 = { by axiom 99 (quaternion_ds1_inuse_0011_32) }
% 7.60/1.32 fresh96(a_select2(xinit_defuse, n4), use)
% 7.60/1.32 = { by axiom 23 (quaternion_ds1_inuse_0011_10) }
% 7.60/1.32 fresh96(use, use)
% 7.60/1.32 = { by axiom 97 (quaternion_ds1_inuse_0011_32) }
% 7.60/1.32 fresh98(a_select2(sigma_defuse, n5), use)
% 7.60/1.32 = { by axiom 6 (quaternion_ds1_inuse_0011_8) }
% 7.60/1.32 fresh98(use, use)
% 7.60/1.32 = { by axiom 95 (quaternion_ds1_inuse_0011_32) }
% 7.60/1.32 fresh100(a_select2(sigma_defuse, n3), use)
% 7.60/1.32 = { by axiom 4 (quaternion_ds1_inuse_0011_6) }
% 7.60/1.32 fresh100(use, use)
% 7.60/1.32 = { by axiom 93 (quaternion_ds1_inuse_0011_32) }
% 7.60/1.32 fresh102(a_select2(sigma_defuse, n1), use)
% 7.60/1.32 = { by axiom 2 (quaternion_ds1_inuse_0011_4) }
% 7.60/1.32 fresh102(use, use)
% 7.60/1.32 = { by axiom 90 (quaternion_ds1_inuse_0011_32) }
% 7.60/1.32 fresh105(a_select2(rho_defuse, n2), use)
% 7.60/1.32 = { by axiom 21 (quaternion_ds1_inuse_0011_2) }
% 7.60/1.32 fresh105(use, use)
% 7.60/1.32 = { by axiom 89 (quaternion_ds1_inuse_0011_32) }
% 7.60/1.32 fresh106(a_select2(rho_defuse, n0), use)
% 7.60/1.32 = { by axiom 19 (quaternion_ds1_inuse_0011) }
% 7.60/1.32 fresh106(use, use)
% 7.60/1.32 = { by axiom 31 (quaternion_ds1_inuse_0011_32) }
% 7.60/1.32 true3
% 7.60/1.32
% 7.60/1.32 Lemma 165: leq(d, pred(pv5)) = fresh104(X, X).
% 7.60/1.32 Proof:
% 7.60/1.32 leq(d, pred(pv5))
% 7.60/1.32 = { by axiom 26 (pred_minus_1) R->L }
% 7.60/1.32 leq(d, minus(pv5, n1))
% 7.60/1.32 = { by axiom 38 (quaternion_ds1_inuse_0011_32) R->L }
% 7.60/1.33 fresh104(X, X)
% 7.60/1.33
% 7.60/1.33 Goal 1 (quaternion_ds1_inuse_0011_29): tuple2(a_select2(rho_defuse, n0), a_select2(rho_defuse, n1), a_select2(rho_defuse, n2), a_select2(sigma_defuse, n0), a_select2(sigma_defuse, n1), a_select2(sigma_defuse, n2), a_select2(sigma_defuse, n3), a_select2(sigma_defuse, n4), a_select2(sigma_defuse, n5), a_select2(xinit_defuse, n3), a_select2(xinit_defuse, n4), a_select2(xinit_defuse, n5), a_select2(xinit_mean_defuse, n0), a_select2(xinit_mean_defuse, n1), a_select2(xinit_mean_defuse, n2), a_select2(xinit_mean_defuse, n3), a_select2(xinit_mean_defuse, n4), a_select2(xinit_mean_defuse, n5), a_select2(xinit_noise_defuse, n0), a_select2(xinit_noise_defuse, n1), a_select2(xinit_noise_defuse, n2), a_select2(xinit_noise_defuse, n3), a_select2(xinit_noise_defuse, n4), a_select2(xinit_noise_defuse, n5), a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1))) = tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, true3, true3).
% 7.60/1.33 Proof:
% 7.60/1.33 tuple2(a_select2(rho_defuse, n0), a_select2(rho_defuse, n1), a_select2(rho_defuse, n2), a_select2(sigma_defuse, n0), a_select2(sigma_defuse, n1), a_select2(sigma_defuse, n2), a_select2(sigma_defuse, n3), a_select2(sigma_defuse, n4), a_select2(sigma_defuse, n5), a_select2(xinit_defuse, n3), a_select2(xinit_defuse, n4), a_select2(xinit_defuse, n5), a_select2(xinit_mean_defuse, n0), a_select2(xinit_mean_defuse, n1), a_select2(xinit_mean_defuse, n2), a_select2(xinit_mean_defuse, n3), a_select2(xinit_mean_defuse, n4), a_select2(xinit_mean_defuse, n5), a_select2(xinit_noise_defuse, n0), a_select2(xinit_noise_defuse, n1), a_select2(xinit_noise_defuse, n2), a_select2(xinit_noise_defuse, n3), a_select2(xinit_noise_defuse, n4), a_select2(xinit_noise_defuse, n5), a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 19 (quaternion_ds1_inuse_0011) }
% 7.60/1.33 tuple2(use, a_select2(rho_defuse, n1), a_select2(rho_defuse, n2), a_select2(sigma_defuse, n0), a_select2(sigma_defuse, n1), a_select2(sigma_defuse, n2), a_select2(sigma_defuse, n3), a_select2(sigma_defuse, n4), a_select2(sigma_defuse, n5), a_select2(xinit_defuse, n3), a_select2(xinit_defuse, n4), a_select2(xinit_defuse, n5), a_select2(xinit_mean_defuse, n0), a_select2(xinit_mean_defuse, n1), a_select2(xinit_mean_defuse, n2), a_select2(xinit_mean_defuse, n3), a_select2(xinit_mean_defuse, n4), a_select2(xinit_mean_defuse, n5), a_select2(xinit_noise_defuse, n0), a_select2(xinit_noise_defuse, n1), a_select2(xinit_noise_defuse, n2), a_select2(xinit_noise_defuse, n3), a_select2(xinit_noise_defuse, n4), a_select2(xinit_noise_defuse, n5), a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 20 (quaternion_ds1_inuse_0011_1) }
% 7.60/1.33 tuple2(use, use, a_select2(rho_defuse, n2), a_select2(sigma_defuse, n0), a_select2(sigma_defuse, n1), a_select2(sigma_defuse, n2), a_select2(sigma_defuse, n3), a_select2(sigma_defuse, n4), a_select2(sigma_defuse, n5), a_select2(xinit_defuse, n3), a_select2(xinit_defuse, n4), a_select2(xinit_defuse, n5), a_select2(xinit_mean_defuse, n0), a_select2(xinit_mean_defuse, n1), a_select2(xinit_mean_defuse, n2), a_select2(xinit_mean_defuse, n3), a_select2(xinit_mean_defuse, n4), a_select2(xinit_mean_defuse, n5), a_select2(xinit_noise_defuse, n0), a_select2(xinit_noise_defuse, n1), a_select2(xinit_noise_defuse, n2), a_select2(xinit_noise_defuse, n3), a_select2(xinit_noise_defuse, n4), a_select2(xinit_noise_defuse, n5), a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 21 (quaternion_ds1_inuse_0011_2) }
% 7.60/1.33 tuple2(use, use, use, a_select2(sigma_defuse, n0), a_select2(sigma_defuse, n1), a_select2(sigma_defuse, n2), a_select2(sigma_defuse, n3), a_select2(sigma_defuse, n4), a_select2(sigma_defuse, n5), a_select2(xinit_defuse, n3), a_select2(xinit_defuse, n4), a_select2(xinit_defuse, n5), a_select2(xinit_mean_defuse, n0), a_select2(xinit_mean_defuse, n1), a_select2(xinit_mean_defuse, n2), a_select2(xinit_mean_defuse, n3), a_select2(xinit_mean_defuse, n4), a_select2(xinit_mean_defuse, n5), a_select2(xinit_noise_defuse, n0), a_select2(xinit_noise_defuse, n1), a_select2(xinit_noise_defuse, n2), a_select2(xinit_noise_defuse, n3), a_select2(xinit_noise_defuse, n4), a_select2(xinit_noise_defuse, n5), a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 1 (quaternion_ds1_inuse_0011_3) }
% 7.60/1.33 tuple2(use, use, use, use, a_select2(sigma_defuse, n1), a_select2(sigma_defuse, n2), a_select2(sigma_defuse, n3), a_select2(sigma_defuse, n4), a_select2(sigma_defuse, n5), a_select2(xinit_defuse, n3), a_select2(xinit_defuse, n4), a_select2(xinit_defuse, n5), a_select2(xinit_mean_defuse, n0), a_select2(xinit_mean_defuse, n1), a_select2(xinit_mean_defuse, n2), a_select2(xinit_mean_defuse, n3), a_select2(xinit_mean_defuse, n4), a_select2(xinit_mean_defuse, n5), a_select2(xinit_noise_defuse, n0), a_select2(xinit_noise_defuse, n1), a_select2(xinit_noise_defuse, n2), a_select2(xinit_noise_defuse, n3), a_select2(xinit_noise_defuse, n4), a_select2(xinit_noise_defuse, n5), a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 2 (quaternion_ds1_inuse_0011_4) }
% 7.60/1.33 tuple2(use, use, use, use, use, a_select2(sigma_defuse, n2), a_select2(sigma_defuse, n3), a_select2(sigma_defuse, n4), a_select2(sigma_defuse, n5), a_select2(xinit_defuse, n3), a_select2(xinit_defuse, n4), a_select2(xinit_defuse, n5), a_select2(xinit_mean_defuse, n0), a_select2(xinit_mean_defuse, n1), a_select2(xinit_mean_defuse, n2), a_select2(xinit_mean_defuse, n3), a_select2(xinit_mean_defuse, n4), a_select2(xinit_mean_defuse, n5), a_select2(xinit_noise_defuse, n0), a_select2(xinit_noise_defuse, n1), a_select2(xinit_noise_defuse, n2), a_select2(xinit_noise_defuse, n3), a_select2(xinit_noise_defuse, n4), a_select2(xinit_noise_defuse, n5), a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 3 (quaternion_ds1_inuse_0011_5) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, a_select2(sigma_defuse, n3), a_select2(sigma_defuse, n4), a_select2(sigma_defuse, n5), a_select2(xinit_defuse, n3), a_select2(xinit_defuse, n4), a_select2(xinit_defuse, n5), a_select2(xinit_mean_defuse, n0), a_select2(xinit_mean_defuse, n1), a_select2(xinit_mean_defuse, n2), a_select2(xinit_mean_defuse, n3), a_select2(xinit_mean_defuse, n4), a_select2(xinit_mean_defuse, n5), a_select2(xinit_noise_defuse, n0), a_select2(xinit_noise_defuse, n1), a_select2(xinit_noise_defuse, n2), a_select2(xinit_noise_defuse, n3), a_select2(xinit_noise_defuse, n4), a_select2(xinit_noise_defuse, n5), a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 4 (quaternion_ds1_inuse_0011_6) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, a_select2(sigma_defuse, n4), a_select2(sigma_defuse, n5), a_select2(xinit_defuse, n3), a_select2(xinit_defuse, n4), a_select2(xinit_defuse, n5), a_select2(xinit_mean_defuse, n0), a_select2(xinit_mean_defuse, n1), a_select2(xinit_mean_defuse, n2), a_select2(xinit_mean_defuse, n3), a_select2(xinit_mean_defuse, n4), a_select2(xinit_mean_defuse, n5), a_select2(xinit_noise_defuse, n0), a_select2(xinit_noise_defuse, n1), a_select2(xinit_noise_defuse, n2), a_select2(xinit_noise_defuse, n3), a_select2(xinit_noise_defuse, n4), a_select2(xinit_noise_defuse, n5), a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 5 (quaternion_ds1_inuse_0011_7) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, a_select2(sigma_defuse, n5), a_select2(xinit_defuse, n3), a_select2(xinit_defuse, n4), a_select2(xinit_defuse, n5), a_select2(xinit_mean_defuse, n0), a_select2(xinit_mean_defuse, n1), a_select2(xinit_mean_defuse, n2), a_select2(xinit_mean_defuse, n3), a_select2(xinit_mean_defuse, n4), a_select2(xinit_mean_defuse, n5), a_select2(xinit_noise_defuse, n0), a_select2(xinit_noise_defuse, n1), a_select2(xinit_noise_defuse, n2), a_select2(xinit_noise_defuse, n3), a_select2(xinit_noise_defuse, n4), a_select2(xinit_noise_defuse, n5), a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 6 (quaternion_ds1_inuse_0011_8) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, a_select2(xinit_defuse, n3), a_select2(xinit_defuse, n4), a_select2(xinit_defuse, n5), a_select2(xinit_mean_defuse, n0), a_select2(xinit_mean_defuse, n1), a_select2(xinit_mean_defuse, n2), a_select2(xinit_mean_defuse, n3), a_select2(xinit_mean_defuse, n4), a_select2(xinit_mean_defuse, n5), a_select2(xinit_noise_defuse, n0), a_select2(xinit_noise_defuse, n1), a_select2(xinit_noise_defuse, n2), a_select2(xinit_noise_defuse, n3), a_select2(xinit_noise_defuse, n4), a_select2(xinit_noise_defuse, n5), a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 22 (quaternion_ds1_inuse_0011_9) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, a_select2(xinit_defuse, n4), a_select2(xinit_defuse, n5), a_select2(xinit_mean_defuse, n0), a_select2(xinit_mean_defuse, n1), a_select2(xinit_mean_defuse, n2), a_select2(xinit_mean_defuse, n3), a_select2(xinit_mean_defuse, n4), a_select2(xinit_mean_defuse, n5), a_select2(xinit_noise_defuse, n0), a_select2(xinit_noise_defuse, n1), a_select2(xinit_noise_defuse, n2), a_select2(xinit_noise_defuse, n3), a_select2(xinit_noise_defuse, n4), a_select2(xinit_noise_defuse, n5), a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 23 (quaternion_ds1_inuse_0011_10) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, a_select2(xinit_defuse, n5), a_select2(xinit_mean_defuse, n0), a_select2(xinit_mean_defuse, n1), a_select2(xinit_mean_defuse, n2), a_select2(xinit_mean_defuse, n3), a_select2(xinit_mean_defuse, n4), a_select2(xinit_mean_defuse, n5), a_select2(xinit_noise_defuse, n0), a_select2(xinit_noise_defuse, n1), a_select2(xinit_noise_defuse, n2), a_select2(xinit_noise_defuse, n3), a_select2(xinit_noise_defuse, n4), a_select2(xinit_noise_defuse, n5), a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 24 (quaternion_ds1_inuse_0011_11) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, a_select2(xinit_mean_defuse, n0), a_select2(xinit_mean_defuse, n1), a_select2(xinit_mean_defuse, n2), a_select2(xinit_mean_defuse, n3), a_select2(xinit_mean_defuse, n4), a_select2(xinit_mean_defuse, n5), a_select2(xinit_noise_defuse, n0), a_select2(xinit_noise_defuse, n1), a_select2(xinit_noise_defuse, n2), a_select2(xinit_noise_defuse, n3), a_select2(xinit_noise_defuse, n4), a_select2(xinit_noise_defuse, n5), a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 7 (quaternion_ds1_inuse_0011_12) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, a_select2(xinit_mean_defuse, n1), a_select2(xinit_mean_defuse, n2), a_select2(xinit_mean_defuse, n3), a_select2(xinit_mean_defuse, n4), a_select2(xinit_mean_defuse, n5), a_select2(xinit_noise_defuse, n0), a_select2(xinit_noise_defuse, n1), a_select2(xinit_noise_defuse, n2), a_select2(xinit_noise_defuse, n3), a_select2(xinit_noise_defuse, n4), a_select2(xinit_noise_defuse, n5), a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 8 (quaternion_ds1_inuse_0011_13) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select2(xinit_mean_defuse, n2), a_select2(xinit_mean_defuse, n3), a_select2(xinit_mean_defuse, n4), a_select2(xinit_mean_defuse, n5), a_select2(xinit_noise_defuse, n0), a_select2(xinit_noise_defuse, n1), a_select2(xinit_noise_defuse, n2), a_select2(xinit_noise_defuse, n3), a_select2(xinit_noise_defuse, n4), a_select2(xinit_noise_defuse, n5), a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 9 (quaternion_ds1_inuse_0011_14) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select2(xinit_mean_defuse, n3), a_select2(xinit_mean_defuse, n4), a_select2(xinit_mean_defuse, n5), a_select2(xinit_noise_defuse, n0), a_select2(xinit_noise_defuse, n1), a_select2(xinit_noise_defuse, n2), a_select2(xinit_noise_defuse, n3), a_select2(xinit_noise_defuse, n4), a_select2(xinit_noise_defuse, n5), a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 10 (quaternion_ds1_inuse_0011_15) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select2(xinit_mean_defuse, n4), a_select2(xinit_mean_defuse, n5), a_select2(xinit_noise_defuse, n0), a_select2(xinit_noise_defuse, n1), a_select2(xinit_noise_defuse, n2), a_select2(xinit_noise_defuse, n3), a_select2(xinit_noise_defuse, n4), a_select2(xinit_noise_defuse, n5), a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 11 (quaternion_ds1_inuse_0011_16) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select2(xinit_mean_defuse, n5), a_select2(xinit_noise_defuse, n0), a_select2(xinit_noise_defuse, n1), a_select2(xinit_noise_defuse, n2), a_select2(xinit_noise_defuse, n3), a_select2(xinit_noise_defuse, n4), a_select2(xinit_noise_defuse, n5), a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 12 (quaternion_ds1_inuse_0011_17) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select2(xinit_noise_defuse, n0), a_select2(xinit_noise_defuse, n1), a_select2(xinit_noise_defuse, n2), a_select2(xinit_noise_defuse, n3), a_select2(xinit_noise_defuse, n4), a_select2(xinit_noise_defuse, n5), a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 13 (quaternion_ds1_inuse_0011_18) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select2(xinit_noise_defuse, n1), a_select2(xinit_noise_defuse, n2), a_select2(xinit_noise_defuse, n3), a_select2(xinit_noise_defuse, n4), a_select2(xinit_noise_defuse, n5), a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 14 (quaternion_ds1_inuse_0011_19) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select2(xinit_noise_defuse, n2), a_select2(xinit_noise_defuse, n3), a_select2(xinit_noise_defuse, n4), a_select2(xinit_noise_defuse, n5), a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 15 (quaternion_ds1_inuse_0011_20) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select2(xinit_noise_defuse, n3), a_select2(xinit_noise_defuse, n4), a_select2(xinit_noise_defuse, n5), a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 16 (quaternion_ds1_inuse_0011_21) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select2(xinit_noise_defuse, n4), a_select2(xinit_noise_defuse, n5), a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 17 (quaternion_ds1_inuse_0011_22) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select2(xinit_noise_defuse, n5), a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 18 (quaternion_ds1_inuse_0011_23) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select3(u_defuse, n0, n0), a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 34 (quaternion_ds1_inuse_0011_24) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select3(u_defuse, n1, n0), a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 35 (quaternion_ds1_inuse_0011_25) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select3(u_defuse, n2, n0), a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 36 (quaternion_ds1_inuse_0011_26) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), leq(n0, pv5), leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 25 (quaternion_ds1_inuse_0011_27) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), true3, leq(pv5, minus(n999, n1)))
% 7.60/1.33 = { by axiom 37 (quaternion_ds1_inuse_0011_28) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select3(u_defuse, c, d), a_select3(z_defuse, c, d), true3, true3)
% 7.60/1.33 = { by axiom 142 (quaternion_ds1_inuse_0011_35) R->L }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select3(u_defuse, c, d), fresh11(true3, true3, c, d), true3, true3)
% 7.60/1.33 = { by lemma 164 R->L }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select3(u_defuse, c, d), fresh11(fresh104(X, X), true3, c, d), true3, true3)
% 7.60/1.33 = { by lemma 165 R->L }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select3(u_defuse, c, d), fresh11(leq(d, pred(pv5)), true3, c, d), true3, true3)
% 7.60/1.33 = { by axiom 26 (pred_minus_1) R->L }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select3(u_defuse, c, d), fresh11(leq(d, minus(pv5, n1)), true3, c, d), true3, true3)
% 7.60/1.33 = { by axiom 160 (quaternion_ds1_inuse_0011_35) R->L }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select3(u_defuse, c, d), fresh43(leq(n0, d), true3, c, d), true3, true3)
% 7.60/1.33 = { by lemma 161 }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select3(u_defuse, c, d), fresh43(true3, true3, c, d), true3, true3)
% 7.60/1.33 = { by axiom 158 (quaternion_ds1_inuse_0011_35) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select3(u_defuse, c, d), fresh44(leq(n0, c), true3, c, d), true3, true3)
% 7.60/1.33 = { by lemma 162 }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select3(u_defuse, c, d), fresh44(true3, true3, c, d), true3, true3)
% 7.60/1.33 = { by axiom 157 (quaternion_ds1_inuse_0011_35) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select3(u_defuse, c, d), fresh45(leq(c, n2), true3, c, d), true3, true3)
% 7.60/1.33 = { by lemma 163 }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select3(u_defuse, c, d), fresh45(true3, true3, c, d), true3, true3)
% 7.60/1.33 = { by axiom 140 (quaternion_ds1_inuse_0011_35) }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, a_select3(u_defuse, c, d), use, true3, true3)
% 7.60/1.33 = { by axiom 141 (quaternion_ds1_inuse_0011_34) R->L }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, fresh12(true3, true3, c, d), use, true3, true3)
% 7.60/1.33 = { by lemma 164 R->L }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, fresh12(fresh104(Y, Y), true3, c, d), use, true3, true3)
% 7.60/1.33 = { by lemma 165 R->L }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, fresh12(leq(d, pred(pv5)), true3, c, d), use, true3, true3)
% 7.60/1.33 = { by axiom 26 (pred_minus_1) R->L }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, fresh12(leq(d, minus(pv5, n1)), true3, c, d), use, true3, true3)
% 7.60/1.33 = { by axiom 159 (quaternion_ds1_inuse_0011_34) R->L }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, fresh46(leq(n0, d), true3, c, d), use, true3, true3)
% 7.60/1.33 = { by lemma 161 }
% 7.60/1.33 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, fresh46(true3, true3, c, d), use, true3, true3)
% 7.60/1.34 = { by axiom 156 (quaternion_ds1_inuse_0011_34) }
% 7.60/1.34 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, fresh47(leq(n0, c), true3, c, d), use, true3, true3)
% 7.60/1.34 = { by lemma 162 }
% 7.60/1.34 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, fresh47(true3, true3, c, d), use, true3, true3)
% 7.60/1.34 = { by axiom 155 (quaternion_ds1_inuse_0011_34) }
% 7.60/1.34 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, fresh48(leq(c, n2), true3, c, d), use, true3, true3)
% 7.60/1.34 = { by lemma 163 }
% 7.60/1.34 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, fresh48(true3, true3, c, d), use, true3, true3)
% 7.60/1.34 = { by axiom 139 (quaternion_ds1_inuse_0011_34) }
% 7.60/1.34 tuple2(use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, use, true3, true3)
% 7.60/1.34 % SZS output end Proof
% 7.60/1.34
% 7.60/1.34 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------