TSTP Solution File: SWV092+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV092+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 : n004.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 23:02:33 EDT 2023
% Result : Theorem 2.82s 0.74s
% Output : Proof 4.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV092+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 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 : n004.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 : Tue Aug 29 03:56:52 EDT 2023
% 0.19/0.34 % CPUTime :
% 2.82/0.74 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 2.82/0.74
% 2.82/0.74 % SZS status Theorem
% 2.82/0.74
% 3.28/0.78 % SZS output start Proof
% 3.28/0.78 Take the following subset of the input axioms:
% 4.53/0.93 fof(finite_domain_0, axiom, ![X]: ((leq(n0, X) & leq(X, n0)) => X=n0)).
% 4.53/0.93 fof(irreflexivity_gt, axiom, ![X2]: ~gt(X2, X2)).
% 4.53/0.93 fof(leq_succ, axiom, ![Y, X2]: (leq(X2, Y) => leq(X2, succ(Y)))).
% 4.53/0.93 fof(leq_succ_gt_equiv, axiom, ![X2, Y2]: (leq(X2, Y2) <=> gt(succ(Y2), X2))).
% 4.53/0.93 fof(matrix_symm_joseph_update, axiom, ![C, N, B, M, D, E, F, A2]: ((![I, J]: ((leq(n0, I) & (leq(I, M) & (leq(n0, J) & leq(J, M)))) => a_select3(D, I, J)=a_select3(D, J, I)) & (![I2, J2]: ((leq(n0, I2) & (leq(I2, N) & (leq(n0, J2) & leq(J2, N)))) => a_select3(A2, I2, J2)=a_select3(A2, J2, I2)) & ![I2, J2]: ((leq(n0, I2) & (leq(I2, N) & (leq(n0, J2) & leq(J2, N)))) => a_select3(F, I2, J2)=a_select3(F, J2, I2)))) => ![I2, J2]: ((leq(n0, I2) & (leq(I2, N) & (leq(n0, J2) & leq(J2, N)))) => a_select3(tptp_madd(A2, tptp_mmul(B, tptp_mmul(tptp_madd(tptp_mmul(C, tptp_mmul(D, trans(C))), tptp_mmul(E, tptp_mmul(F, trans(E)))), trans(B)))), I2, J2)=a_select3(tptp_madd(A2, tptp_mmul(B, tptp_mmul(tptp_madd(tptp_mmul(C, tptp_mmul(D, trans(C))), tptp_mmul(E, tptp_mmul(F, trans(E)))), trans(B)))), J2, I2)))).
% 4.53/0.93 fof(pred_minus_1, axiom, ![X2]: minus(X2, n1)=pred(X2)).
% 4.53/0.93 fof(quaternion_ds1_inuse_0004, 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)))))))))))))))))))))))))) => (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 & ![A, B2]: ((leq(n0, A) & (leq(n0, B2) & (leq(A, n2) & leq(B2, minus(n0, n1))))) => (a_select3(u_defuse, A, B2)=use & a_select3(z_defuse, A, B2)=use)))))))))))))))))))))))))))))).
% 4.53/0.93 fof(succ_pred, axiom, ![X2]: succ(pred(X2))=X2).
% 4.53/0.93
% 4.53/0.93 Now clausify the problem and encode Horn clauses using encoding 3 of
% 4.53/0.93 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 4.53/0.93 We repeatedly replace C & s=t => u=v by the two clauses:
% 4.53/0.93 fresh(y, y, x1...xn) = u
% 4.53/0.93 C => fresh(s, t, x1...xn) = v
% 4.53/0.93 where fresh is a fresh function symbol and x1..xn are the free
% 4.53/0.93 variables of u and v.
% 4.53/0.93 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 4.53/0.93 input problem has no model of domain size 1).
% 4.53/0.93
% 4.53/0.93 The encoding turns the above axioms into the following unit equations and goals:
% 4.53/0.93
% 4.53/0.93 Axiom 1 (quaternion_ds1_inuse_0004_3): a_select2(sigma_defuse, n0) = use.
% 4.53/0.93 Axiom 2 (quaternion_ds1_inuse_0004_4): a_select2(sigma_defuse, n1) = use.
% 4.53/0.93 Axiom 3 (quaternion_ds1_inuse_0004_5): a_select2(sigma_defuse, n2) = use.
% 4.53/0.93 Axiom 4 (quaternion_ds1_inuse_0004_6): a_select2(sigma_defuse, n3) = use.
% 4.53/0.93 Axiom 5 (quaternion_ds1_inuse_0004_7): a_select2(sigma_defuse, n4) = use.
% 4.53/0.93 Axiom 6 (quaternion_ds1_inuse_0004_8): a_select2(sigma_defuse, n5) = use.
% 4.53/0.93 Axiom 7 (quaternion_ds1_inuse_0004_12): a_select2(xinit_mean_defuse, n0) = use.
% 4.53/0.93 Axiom 8 (quaternion_ds1_inuse_0004_13): a_select2(xinit_mean_defuse, n1) = use.
% 4.53/0.93 Axiom 9 (quaternion_ds1_inuse_0004_14): a_select2(xinit_mean_defuse, n2) = use.
% 4.53/0.93 Axiom 10 (quaternion_ds1_inuse_0004_15): a_select2(xinit_mean_defuse, n3) = use.
% 4.53/0.93 Axiom 11 (quaternion_ds1_inuse_0004_16): a_select2(xinit_mean_defuse, n4) = use.
% 4.53/0.93 Axiom 12 (quaternion_ds1_inuse_0004_17): a_select2(xinit_mean_defuse, n5) = use.
% 4.53/0.93 Axiom 13 (quaternion_ds1_inuse_0004_18): a_select2(xinit_noise_defuse, n0) = use.
% 4.53/0.93 Axiom 14 (quaternion_ds1_inuse_0004_19): a_select2(xinit_noise_defuse, n1) = use.
% 4.53/0.93 Axiom 15 (quaternion_ds1_inuse_0004_20): a_select2(xinit_noise_defuse, n2) = use.
% 4.53/0.93 Axiom 16 (quaternion_ds1_inuse_0004_21): a_select2(xinit_noise_defuse, n3) = use.
% 4.53/0.93 Axiom 17 (quaternion_ds1_inuse_0004_22): a_select2(xinit_noise_defuse, n4) = use.
% 4.53/0.93 Axiom 18 (quaternion_ds1_inuse_0004_23): a_select2(xinit_noise_defuse, n5) = use.
% 4.53/0.93 Axiom 19 (quaternion_ds1_inuse_0004): a_select2(rho_defuse, n0) = use.
% 4.53/0.93 Axiom 20 (quaternion_ds1_inuse_0004_1): a_select2(rho_defuse, n1) = use.
% 4.53/0.93 Axiom 21 (quaternion_ds1_inuse_0004_2): a_select2(rho_defuse, n2) = use.
% 4.53/0.93 Axiom 22 (quaternion_ds1_inuse_0004_9): a_select2(xinit_defuse, n3) = use.
% 4.53/0.93 Axiom 23 (quaternion_ds1_inuse_0004_10): a_select2(xinit_defuse, n4) = use.
% 4.53/0.93 Axiom 24 (quaternion_ds1_inuse_0004_11): a_select2(xinit_defuse, n5) = use.
% 4.53/0.93 Axiom 25 (succ_pred): succ(pred(X)) = X.
% 4.53/0.93 Axiom 26 (pred_minus_1): minus(X, n1) = pred(X).
% 4.53/0.93 Axiom 27 (quaternion_ds1_inuse_0004_27): fresh148(X, X) = true3.
% 4.53/0.93 Axiom 28 (quaternion_ds1_inuse_0004_27): fresh146(X, X) = leq(n0, b).
% 4.53/0.93 Axiom 29 (quaternion_ds1_inuse_0004_29): fresh94(X, X) = true3.
% 4.53/0.93 Axiom 30 (quaternion_ds1_inuse_0004_24): a_select3(u_defuse, n0, n0) = use.
% 4.53/0.93 Axiom 31 (quaternion_ds1_inuse_0004_25): a_select3(u_defuse, n1, n0) = use.
% 4.53/0.93 Axiom 32 (quaternion_ds1_inuse_0004_26): a_select3(u_defuse, n2, n0) = use.
% 4.53/0.93 Axiom 33 (finite_domain_0): fresh(X, X, Y) = Y.
% 4.53/0.93 Axiom 34 (finite_domain_0): fresh39(X, X, Y) = n0.
% 4.53/0.93 Axiom 35 (quaternion_ds1_inuse_0004_29): fresh92(X, X) = leq(b, minus(n0, n1)).
% 4.53/0.93 Axiom 36 (quaternion_ds1_inuse_0004_27): fresh147(X, X) = fresh148(a_select2(rho_defuse, n0), use).
% 4.53/0.93 Axiom 37 (quaternion_ds1_inuse_0004_27): fresh144(X, X) = fresh147(a_select2(rho_defuse, n2), use).
% 4.53/0.93 Axiom 38 (quaternion_ds1_inuse_0004_27): fresh145(X, X) = fresh146(a_select2(rho_defuse, n1), use).
% 4.53/0.93 Axiom 39 (quaternion_ds1_inuse_0004_27): fresh143(X, X) = fresh145(a_select2(sigma_defuse, n0), use).
% 4.53/0.93 Axiom 40 (quaternion_ds1_inuse_0004_27): fresh142(X, X) = fresh144(a_select2(sigma_defuse, n1), use).
% 4.53/0.93 Axiom 41 (quaternion_ds1_inuse_0004_27): fresh141(X, X) = fresh143(a_select2(sigma_defuse, n2), use).
% 4.53/0.93 Axiom 42 (quaternion_ds1_inuse_0004_27): fresh140(X, X) = fresh142(a_select2(sigma_defuse, n3), use).
% 4.53/0.93 Axiom 43 (quaternion_ds1_inuse_0004_27): fresh139(X, X) = fresh141(a_select2(sigma_defuse, n4), use).
% 4.53/0.93 Axiom 44 (quaternion_ds1_inuse_0004_27): fresh138(X, X) = fresh140(a_select2(sigma_defuse, n5), use).
% 4.53/0.93 Axiom 45 (quaternion_ds1_inuse_0004_27): fresh137(X, X) = fresh139(a_select2(xinit_defuse, n3), use).
% 4.53/0.93 Axiom 46 (quaternion_ds1_inuse_0004_27): fresh136(X, X) = fresh138(a_select2(xinit_defuse, n4), use).
% 4.53/0.93 Axiom 47 (quaternion_ds1_inuse_0004_27): fresh135(X, X) = fresh137(a_select2(xinit_defuse, n5), use).
% 4.53/0.93 Axiom 48 (quaternion_ds1_inuse_0004_27): fresh134(X, X) = fresh136(a_select2(xinit_mean_defuse, n0), use).
% 4.53/0.93 Axiom 49 (quaternion_ds1_inuse_0004_27): fresh133(X, X) = fresh135(a_select2(xinit_mean_defuse, n1), use).
% 4.53/0.93 Axiom 50 (quaternion_ds1_inuse_0004_27): fresh132(X, X) = fresh134(a_select2(xinit_mean_defuse, n2), use).
% 4.53/0.93 Axiom 51 (quaternion_ds1_inuse_0004_27): fresh131(X, X) = fresh133(a_select2(xinit_mean_defuse, n3), use).
% 4.53/0.93 Axiom 52 (quaternion_ds1_inuse_0004_27): fresh130(X, X) = fresh132(a_select2(xinit_mean_defuse, n4), use).
% 4.53/0.93 Axiom 53 (quaternion_ds1_inuse_0004_27): fresh129(X, X) = fresh131(a_select2(xinit_mean_defuse, n5), use).
% 4.53/0.93 Axiom 54 (quaternion_ds1_inuse_0004_27): fresh128(X, X) = fresh130(a_select2(xinit_noise_defuse, n0), use).
% 4.53/0.93 Axiom 55 (quaternion_ds1_inuse_0004_27): fresh127(X, X) = fresh129(a_select2(xinit_noise_defuse, n1), use).
% 4.53/0.93 Axiom 56 (quaternion_ds1_inuse_0004_27): fresh126(X, X) = fresh128(a_select2(xinit_noise_defuse, n2), use).
% 4.53/0.93 Axiom 57 (quaternion_ds1_inuse_0004_27): fresh125(X, X) = fresh127(a_select2(xinit_noise_defuse, n3), use).
% 4.53/0.93 Axiom 58 (quaternion_ds1_inuse_0004_27): fresh124(X, X) = fresh126(a_select2(xinit_noise_defuse, n4), use).
% 4.53/0.93 Axiom 59 (quaternion_ds1_inuse_0004_27): fresh123(X, X) = fresh125(a_select2(xinit_noise_defuse, n5), use).
% 4.53/0.93 Axiom 60 (quaternion_ds1_inuse_0004_29): fresh93(X, X) = fresh94(a_select2(rho_defuse, n0), use).
% 4.53/0.93 Axiom 61 (quaternion_ds1_inuse_0004_29): fresh90(X, X) = fresh93(a_select2(rho_defuse, n2), use).
% 4.53/0.93 Axiom 62 (quaternion_ds1_inuse_0004_29): fresh91(X, X) = fresh92(a_select2(rho_defuse, n1), use).
% 4.53/0.93 Axiom 63 (quaternion_ds1_inuse_0004_29): fresh89(X, X) = fresh91(a_select2(sigma_defuse, n0), use).
% 4.53/0.93 Axiom 64 (quaternion_ds1_inuse_0004_29): fresh88(X, X) = fresh90(a_select2(sigma_defuse, n1), use).
% 4.53/0.93 Axiom 65 (quaternion_ds1_inuse_0004_29): fresh87(X, X) = fresh89(a_select2(sigma_defuse, n2), use).
% 4.53/0.93 Axiom 66 (quaternion_ds1_inuse_0004_29): fresh86(X, X) = fresh88(a_select2(sigma_defuse, n3), use).
% 4.53/0.93 Axiom 67 (quaternion_ds1_inuse_0004_29): fresh85(X, X) = fresh87(a_select2(sigma_defuse, n4), use).
% 4.53/0.93 Axiom 68 (quaternion_ds1_inuse_0004_29): fresh84(X, X) = fresh86(a_select2(sigma_defuse, n5), use).
% 4.53/0.93 Axiom 69 (quaternion_ds1_inuse_0004_29): fresh83(X, X) = fresh85(a_select2(xinit_defuse, n3), use).
% 4.53/0.93 Axiom 70 (quaternion_ds1_inuse_0004_29): fresh82(X, X) = fresh84(a_select2(xinit_defuse, n4), use).
% 4.53/0.93 Axiom 71 (quaternion_ds1_inuse_0004_29): fresh81(X, X) = fresh83(a_select2(xinit_defuse, n5), use).
% 4.53/0.93 Axiom 72 (quaternion_ds1_inuse_0004_29): fresh80(X, X) = fresh82(a_select2(xinit_mean_defuse, n0), use).
% 4.53/0.93 Axiom 73 (quaternion_ds1_inuse_0004_29): fresh79(X, X) = fresh81(a_select2(xinit_mean_defuse, n1), use).
% 4.53/0.93 Axiom 74 (quaternion_ds1_inuse_0004_29): fresh78(X, X) = fresh80(a_select2(xinit_mean_defuse, n2), use).
% 4.53/0.93 Axiom 75 (quaternion_ds1_inuse_0004_29): fresh77(X, X) = fresh79(a_select2(xinit_mean_defuse, n3), use).
% 4.53/0.93 Axiom 76 (quaternion_ds1_inuse_0004_29): fresh76(X, X) = fresh78(a_select2(xinit_mean_defuse, n4), use).
% 4.53/0.93 Axiom 77 (quaternion_ds1_inuse_0004_29): fresh75(X, X) = fresh77(a_select2(xinit_mean_defuse, n5), use).
% 4.53/0.93 Axiom 78 (quaternion_ds1_inuse_0004_29): fresh74(X, X) = fresh76(a_select2(xinit_noise_defuse, n0), use).
% 4.53/0.93 Axiom 79 (quaternion_ds1_inuse_0004_29): fresh73(X, X) = fresh75(a_select2(xinit_noise_defuse, n1), use).
% 4.53/0.93 Axiom 80 (quaternion_ds1_inuse_0004_29): fresh72(X, X) = fresh74(a_select2(xinit_noise_defuse, n2), use).
% 4.53/0.93 Axiom 81 (quaternion_ds1_inuse_0004_29): fresh71(X, X) = fresh73(a_select2(xinit_noise_defuse, n3), use).
% 4.53/0.93 Axiom 82 (quaternion_ds1_inuse_0004_29): fresh70(X, X) = fresh72(a_select2(xinit_noise_defuse, n4), use).
% 4.53/0.93 Axiom 83 (quaternion_ds1_inuse_0004_29): fresh69(X, X) = fresh71(a_select2(xinit_noise_defuse, n5), use).
% 4.53/0.93 Axiom 84 (leq_succ): fresh32(X, X, Y, Z) = true3.
% 4.53/0.93 Axiom 85 (leq_succ_gt_equiv_1): fresh29(X, X, Y, Z) = true3.
% 4.53/0.93 Axiom 86 (quaternion_ds1_inuse_0004_27): fresh122(X, X) = fresh124(a_select3(u_defuse, n0, n0), use).
% 4.53/0.93 Axiom 87 (quaternion_ds1_inuse_0004_27): fresh122(a_select3(u_defuse, n2, n0), use) = fresh123(a_select3(u_defuse, n1, n0), use).
% 4.53/0.93 Axiom 88 (quaternion_ds1_inuse_0004_29): fresh68(X, X) = fresh70(a_select3(u_defuse, n0, n0), use).
% 4.53/0.93 Axiom 89 (quaternion_ds1_inuse_0004_29): fresh68(a_select3(u_defuse, n2, n0), use) = fresh69(a_select3(u_defuse, n1, n0), use).
% 4.53/0.93 Axiom 90 (finite_domain_0): fresh(leq(n0, X), true3, X) = fresh39(leq(X, n0), true3, X).
% 4.53/0.93 Axiom 91 (leq_succ): fresh32(leq(X, Y), true3, X, Y) = leq(X, succ(Y)).
% 4.53/0.93 Axiom 92 (leq_succ_gt_equiv_1): fresh29(leq(X, Y), true3, X, Y) = gt(succ(Y), X).
% 4.53/0.93
% 4.53/0.93 Lemma 93: fresh92(X, X) = true3.
% 4.53/0.93 Proof:
% 4.53/0.93 fresh92(X, X)
% 4.53/0.93 = { by axiom 35 (quaternion_ds1_inuse_0004_29) }
% 4.53/0.93 leq(b, minus(n0, n1))
% 4.53/0.93 = { by axiom 35 (quaternion_ds1_inuse_0004_29) R->L }
% 4.53/0.93 fresh92(use, use)
% 4.53/0.93 = { by axiom 20 (quaternion_ds1_inuse_0004_1) R->L }
% 4.53/0.93 fresh92(a_select2(rho_defuse, n1), use)
% 4.53/0.93 = { by axiom 62 (quaternion_ds1_inuse_0004_29) R->L }
% 4.53/0.93 fresh91(use, use)
% 4.53/0.93 = { by axiom 1 (quaternion_ds1_inuse_0004_3) R->L }
% 4.53/0.93 fresh91(a_select2(sigma_defuse, n0), use)
% 4.53/0.93 = { by axiom 63 (quaternion_ds1_inuse_0004_29) R->L }
% 4.53/0.93 fresh89(use, use)
% 4.53/0.93 = { by axiom 3 (quaternion_ds1_inuse_0004_5) R->L }
% 4.53/0.93 fresh89(a_select2(sigma_defuse, n2), use)
% 4.53/0.93 = { by axiom 65 (quaternion_ds1_inuse_0004_29) R->L }
% 4.53/0.93 fresh87(use, use)
% 4.53/0.93 = { by axiom 5 (quaternion_ds1_inuse_0004_7) R->L }
% 4.53/0.93 fresh87(a_select2(sigma_defuse, n4), use)
% 4.53/0.93 = { by axiom 67 (quaternion_ds1_inuse_0004_29) R->L }
% 4.53/0.93 fresh85(use, use)
% 4.53/0.93 = { by axiom 22 (quaternion_ds1_inuse_0004_9) R->L }
% 4.53/0.93 fresh85(a_select2(xinit_defuse, n3), use)
% 4.53/0.93 = { by axiom 69 (quaternion_ds1_inuse_0004_29) R->L }
% 4.53/0.93 fresh83(use, use)
% 4.53/0.93 = { by axiom 24 (quaternion_ds1_inuse_0004_11) R->L }
% 4.53/0.93 fresh83(a_select2(xinit_defuse, n5), use)
% 4.53/0.93 = { by axiom 71 (quaternion_ds1_inuse_0004_29) R->L }
% 4.53/0.93 fresh81(use, use)
% 4.53/0.93 = { by axiom 8 (quaternion_ds1_inuse_0004_13) R->L }
% 4.53/0.93 fresh81(a_select2(xinit_mean_defuse, n1), use)
% 4.53/0.93 = { by axiom 73 (quaternion_ds1_inuse_0004_29) R->L }
% 4.53/0.93 fresh79(use, use)
% 4.53/0.93 = { by axiom 10 (quaternion_ds1_inuse_0004_15) R->L }
% 4.53/0.93 fresh79(a_select2(xinit_mean_defuse, n3), use)
% 4.53/0.93 = { by axiom 75 (quaternion_ds1_inuse_0004_29) R->L }
% 4.53/0.93 fresh77(use, use)
% 4.53/0.93 = { by axiom 12 (quaternion_ds1_inuse_0004_17) R->L }
% 4.53/0.93 fresh77(a_select2(xinit_mean_defuse, n5), use)
% 4.53/0.93 = { by axiom 77 (quaternion_ds1_inuse_0004_29) R->L }
% 4.53/0.93 fresh75(use, use)
% 4.53/0.93 = { by axiom 14 (quaternion_ds1_inuse_0004_19) R->L }
% 4.53/0.93 fresh75(a_select2(xinit_noise_defuse, n1), use)
% 4.53/0.93 = { by axiom 79 (quaternion_ds1_inuse_0004_29) R->L }
% 4.53/0.93 fresh73(use, use)
% 4.53/0.93 = { by axiom 16 (quaternion_ds1_inuse_0004_21) R->L }
% 4.53/0.93 fresh73(a_select2(xinit_noise_defuse, n3), use)
% 4.53/0.93 = { by axiom 81 (quaternion_ds1_inuse_0004_29) R->L }
% 4.53/0.93 fresh71(use, use)
% 4.53/0.93 = { by axiom 18 (quaternion_ds1_inuse_0004_23) R->L }
% 4.53/0.93 fresh71(a_select2(xinit_noise_defuse, n5), use)
% 4.53/0.93 = { by axiom 83 (quaternion_ds1_inuse_0004_29) R->L }
% 4.53/0.93 fresh69(use, use)
% 4.53/0.93 = { by axiom 31 (quaternion_ds1_inuse_0004_25) R->L }
% 4.53/0.93 fresh69(a_select3(u_defuse, n1, n0), use)
% 4.53/0.93 = { by axiom 89 (quaternion_ds1_inuse_0004_29) R->L }
% 4.53/0.93 fresh68(a_select3(u_defuse, n2, n0), use)
% 4.53/0.93 = { by axiom 32 (quaternion_ds1_inuse_0004_26) }
% 4.53/0.93 fresh68(use, use)
% 4.53/0.93 = { by axiom 88 (quaternion_ds1_inuse_0004_29) }
% 4.53/0.93 fresh70(a_select3(u_defuse, n0, n0), use)
% 4.53/0.93 = { by axiom 30 (quaternion_ds1_inuse_0004_24) }
% 4.53/0.93 fresh70(use, use)
% 4.53/0.93 = { by axiom 82 (quaternion_ds1_inuse_0004_29) }
% 4.53/0.93 fresh72(a_select2(xinit_noise_defuse, n4), use)
% 4.53/0.93 = { by axiom 17 (quaternion_ds1_inuse_0004_22) }
% 4.53/0.93 fresh72(use, use)
% 4.53/0.93 = { by axiom 80 (quaternion_ds1_inuse_0004_29) }
% 4.53/0.93 fresh74(a_select2(xinit_noise_defuse, n2), use)
% 4.53/0.93 = { by axiom 15 (quaternion_ds1_inuse_0004_20) }
% 4.53/0.93 fresh74(use, use)
% 4.53/0.93 = { by axiom 78 (quaternion_ds1_inuse_0004_29) }
% 4.53/0.93 fresh76(a_select2(xinit_noise_defuse, n0), use)
% 4.53/0.93 = { by axiom 13 (quaternion_ds1_inuse_0004_18) }
% 4.53/0.93 fresh76(use, use)
% 4.53/0.93 = { by axiom 76 (quaternion_ds1_inuse_0004_29) }
% 4.53/0.93 fresh78(a_select2(xinit_mean_defuse, n4), use)
% 4.53/0.93 = { by axiom 11 (quaternion_ds1_inuse_0004_16) }
% 4.53/0.93 fresh78(use, use)
% 4.53/0.93 = { by axiom 74 (quaternion_ds1_inuse_0004_29) }
% 4.53/0.93 fresh80(a_select2(xinit_mean_defuse, n2), use)
% 4.53/0.93 = { by axiom 9 (quaternion_ds1_inuse_0004_14) }
% 4.53/0.93 fresh80(use, use)
% 4.53/0.93 = { by axiom 72 (quaternion_ds1_inuse_0004_29) }
% 4.53/0.93 fresh82(a_select2(xinit_mean_defuse, n0), use)
% 4.53/0.93 = { by axiom 7 (quaternion_ds1_inuse_0004_12) }
% 4.53/0.93 fresh82(use, use)
% 4.53/0.93 = { by axiom 70 (quaternion_ds1_inuse_0004_29) }
% 4.53/0.93 fresh84(a_select2(xinit_defuse, n4), use)
% 4.53/0.93 = { by axiom 23 (quaternion_ds1_inuse_0004_10) }
% 4.53/0.93 fresh84(use, use)
% 4.53/0.93 = { by axiom 68 (quaternion_ds1_inuse_0004_29) }
% 4.53/0.93 fresh86(a_select2(sigma_defuse, n5), use)
% 4.53/0.93 = { by axiom 6 (quaternion_ds1_inuse_0004_8) }
% 4.53/0.93 fresh86(use, use)
% 4.53/0.93 = { by axiom 66 (quaternion_ds1_inuse_0004_29) }
% 4.53/0.93 fresh88(a_select2(sigma_defuse, n3), use)
% 4.53/0.93 = { by axiom 4 (quaternion_ds1_inuse_0004_6) }
% 4.53/0.93 fresh88(use, use)
% 4.53/0.93 = { by axiom 64 (quaternion_ds1_inuse_0004_29) }
% 4.53/0.93 fresh90(a_select2(sigma_defuse, n1), use)
% 4.53/0.93 = { by axiom 2 (quaternion_ds1_inuse_0004_4) }
% 4.53/0.93 fresh90(use, use)
% 4.53/0.93 = { by axiom 61 (quaternion_ds1_inuse_0004_29) }
% 4.53/0.93 fresh93(a_select2(rho_defuse, n2), use)
% 4.53/0.93 = { by axiom 21 (quaternion_ds1_inuse_0004_2) }
% 4.53/0.93 fresh93(use, use)
% 4.53/0.93 = { by axiom 60 (quaternion_ds1_inuse_0004_29) }
% 4.53/0.93 fresh94(a_select2(rho_defuse, n0), use)
% 4.53/0.93 = { by axiom 19 (quaternion_ds1_inuse_0004) }
% 4.53/0.93 fresh94(use, use)
% 4.53/0.93 = { by axiom 29 (quaternion_ds1_inuse_0004_29) }
% 4.53/0.93 true3
% 4.53/0.93
% 4.53/0.93 Lemma 94: leq(b, pred(n0)) = fresh92(X, X).
% 4.53/0.93 Proof:
% 4.53/0.93 leq(b, pred(n0))
% 4.53/0.93 = { by axiom 26 (pred_minus_1) R->L }
% 4.53/0.93 leq(b, minus(n0, n1))
% 4.53/0.93 = { by axiom 35 (quaternion_ds1_inuse_0004_29) R->L }
% 4.53/0.94 fresh92(X, X)
% 4.53/0.94
% 4.53/0.94 Goal 1 (irreflexivity_gt): gt(X, X) = true3.
% 4.53/0.94 The goal is true when:
% 4.53/0.94 X = n0
% 4.53/0.94
% 4.53/0.94 Proof:
% 4.53/0.94 gt(n0, n0)
% 4.53/0.94 = { by axiom 34 (finite_domain_0) R->L }
% 4.53/0.94 gt(n0, fresh39(true3, true3, b))
% 4.53/0.94 = { by axiom 84 (leq_succ) R->L }
% 4.53/0.94 gt(n0, fresh39(fresh32(true3, true3, b, pred(n0)), true3, b))
% 4.53/0.94 = { by lemma 93 R->L }
% 4.53/0.94 gt(n0, fresh39(fresh32(fresh92(Y, Y), true3, b, pred(n0)), true3, b))
% 4.53/0.94 = { by lemma 94 R->L }
% 4.53/0.94 gt(n0, fresh39(fresh32(leq(b, pred(n0)), true3, b, pred(n0)), true3, b))
% 4.53/0.94 = { by axiom 91 (leq_succ) }
% 4.53/0.94 gt(n0, fresh39(leq(b, succ(pred(n0))), true3, b))
% 4.53/0.94 = { by axiom 25 (succ_pred) }
% 4.53/0.94 gt(n0, fresh39(leq(b, n0), true3, b))
% 4.53/0.94 = { by axiom 90 (finite_domain_0) R->L }
% 4.53/0.94 gt(n0, fresh(leq(n0, b), true3, b))
% 4.53/0.94 = { by axiom 28 (quaternion_ds1_inuse_0004_27) R->L }
% 4.53/0.94 gt(n0, fresh(fresh146(use, use), true3, b))
% 4.53/0.94 = { by axiom 20 (quaternion_ds1_inuse_0004_1) R->L }
% 4.53/0.94 gt(n0, fresh(fresh146(a_select2(rho_defuse, n1), use), true3, b))
% 4.53/0.94 = { by axiom 38 (quaternion_ds1_inuse_0004_27) R->L }
% 4.53/0.94 gt(n0, fresh(fresh145(use, use), true3, b))
% 4.53/0.94 = { by axiom 1 (quaternion_ds1_inuse_0004_3) R->L }
% 4.53/0.94 gt(n0, fresh(fresh145(a_select2(sigma_defuse, n0), use), true3, b))
% 4.53/0.94 = { by axiom 39 (quaternion_ds1_inuse_0004_27) R->L }
% 4.53/0.94 gt(n0, fresh(fresh143(use, use), true3, b))
% 4.53/0.94 = { by axiom 3 (quaternion_ds1_inuse_0004_5) R->L }
% 4.53/0.94 gt(n0, fresh(fresh143(a_select2(sigma_defuse, n2), use), true3, b))
% 4.53/0.94 = { by axiom 41 (quaternion_ds1_inuse_0004_27) R->L }
% 4.53/0.94 gt(n0, fresh(fresh141(use, use), true3, b))
% 4.53/0.94 = { by axiom 5 (quaternion_ds1_inuse_0004_7) R->L }
% 4.53/0.94 gt(n0, fresh(fresh141(a_select2(sigma_defuse, n4), use), true3, b))
% 4.53/0.94 = { by axiom 43 (quaternion_ds1_inuse_0004_27) R->L }
% 4.53/0.94 gt(n0, fresh(fresh139(use, use), true3, b))
% 4.53/0.94 = { by axiom 22 (quaternion_ds1_inuse_0004_9) R->L }
% 4.53/0.94 gt(n0, fresh(fresh139(a_select2(xinit_defuse, n3), use), true3, b))
% 4.53/0.94 = { by axiom 45 (quaternion_ds1_inuse_0004_27) R->L }
% 4.53/0.94 gt(n0, fresh(fresh137(use, use), true3, b))
% 4.53/0.94 = { by axiom 24 (quaternion_ds1_inuse_0004_11) R->L }
% 4.53/0.94 gt(n0, fresh(fresh137(a_select2(xinit_defuse, n5), use), true3, b))
% 4.53/0.94 = { by axiom 47 (quaternion_ds1_inuse_0004_27) R->L }
% 4.53/0.94 gt(n0, fresh(fresh135(use, use), true3, b))
% 4.53/0.94 = { by axiom 8 (quaternion_ds1_inuse_0004_13) R->L }
% 4.53/0.94 gt(n0, fresh(fresh135(a_select2(xinit_mean_defuse, n1), use), true3, b))
% 4.53/0.94 = { by axiom 49 (quaternion_ds1_inuse_0004_27) R->L }
% 4.53/0.94 gt(n0, fresh(fresh133(use, use), true3, b))
% 4.53/0.94 = { by axiom 10 (quaternion_ds1_inuse_0004_15) R->L }
% 4.53/0.94 gt(n0, fresh(fresh133(a_select2(xinit_mean_defuse, n3), use), true3, b))
% 4.53/0.94 = { by axiom 51 (quaternion_ds1_inuse_0004_27) R->L }
% 4.53/0.94 gt(n0, fresh(fresh131(use, use), true3, b))
% 4.53/0.94 = { by axiom 12 (quaternion_ds1_inuse_0004_17) R->L }
% 4.53/0.94 gt(n0, fresh(fresh131(a_select2(xinit_mean_defuse, n5), use), true3, b))
% 4.53/0.94 = { by axiom 53 (quaternion_ds1_inuse_0004_27) R->L }
% 4.53/0.94 gt(n0, fresh(fresh129(use, use), true3, b))
% 4.53/0.94 = { by axiom 14 (quaternion_ds1_inuse_0004_19) R->L }
% 4.53/0.94 gt(n0, fresh(fresh129(a_select2(xinit_noise_defuse, n1), use), true3, b))
% 4.53/0.94 = { by axiom 55 (quaternion_ds1_inuse_0004_27) R->L }
% 4.53/0.94 gt(n0, fresh(fresh127(use, use), true3, b))
% 4.53/0.94 = { by axiom 16 (quaternion_ds1_inuse_0004_21) R->L }
% 4.53/0.94 gt(n0, fresh(fresh127(a_select2(xinit_noise_defuse, n3), use), true3, b))
% 4.53/0.94 = { by axiom 57 (quaternion_ds1_inuse_0004_27) R->L }
% 4.53/0.94 gt(n0, fresh(fresh125(use, use), true3, b))
% 4.53/0.94 = { by axiom 18 (quaternion_ds1_inuse_0004_23) R->L }
% 4.53/0.94 gt(n0, fresh(fresh125(a_select2(xinit_noise_defuse, n5), use), true3, b))
% 4.53/0.94 = { by axiom 59 (quaternion_ds1_inuse_0004_27) R->L }
% 4.53/0.94 gt(n0, fresh(fresh123(use, use), true3, b))
% 4.63/0.94 = { by axiom 31 (quaternion_ds1_inuse_0004_25) R->L }
% 4.63/0.94 gt(n0, fresh(fresh123(a_select3(u_defuse, n1, n0), use), true3, b))
% 4.63/0.94 = { by axiom 87 (quaternion_ds1_inuse_0004_27) R->L }
% 4.63/0.94 gt(n0, fresh(fresh122(a_select3(u_defuse, n2, n0), use), true3, b))
% 4.63/0.94 = { by axiom 32 (quaternion_ds1_inuse_0004_26) }
% 4.63/0.94 gt(n0, fresh(fresh122(use, use), true3, b))
% 4.63/0.94 = { by axiom 86 (quaternion_ds1_inuse_0004_27) }
% 4.63/0.94 gt(n0, fresh(fresh124(a_select3(u_defuse, n0, n0), use), true3, b))
% 4.63/0.94 = { by axiom 30 (quaternion_ds1_inuse_0004_24) }
% 4.63/0.94 gt(n0, fresh(fresh124(use, use), true3, b))
% 4.63/0.94 = { by axiom 58 (quaternion_ds1_inuse_0004_27) }
% 4.63/0.94 gt(n0, fresh(fresh126(a_select2(xinit_noise_defuse, n4), use), true3, b))
% 4.63/0.94 = { by axiom 17 (quaternion_ds1_inuse_0004_22) }
% 4.63/0.94 gt(n0, fresh(fresh126(use, use), true3, b))
% 4.63/0.94 = { by axiom 56 (quaternion_ds1_inuse_0004_27) }
% 4.63/0.94 gt(n0, fresh(fresh128(a_select2(xinit_noise_defuse, n2), use), true3, b))
% 4.63/0.94 = { by axiom 15 (quaternion_ds1_inuse_0004_20) }
% 4.63/0.94 gt(n0, fresh(fresh128(use, use), true3, b))
% 4.63/0.94 = { by axiom 54 (quaternion_ds1_inuse_0004_27) }
% 4.63/0.94 gt(n0, fresh(fresh130(a_select2(xinit_noise_defuse, n0), use), true3, b))
% 4.63/0.94 = { by axiom 13 (quaternion_ds1_inuse_0004_18) }
% 4.63/0.94 gt(n0, fresh(fresh130(use, use), true3, b))
% 4.63/0.94 = { by axiom 52 (quaternion_ds1_inuse_0004_27) }
% 4.63/0.94 gt(n0, fresh(fresh132(a_select2(xinit_mean_defuse, n4), use), true3, b))
% 4.63/0.94 = { by axiom 11 (quaternion_ds1_inuse_0004_16) }
% 4.63/0.94 gt(n0, fresh(fresh132(use, use), true3, b))
% 4.63/0.94 = { by axiom 50 (quaternion_ds1_inuse_0004_27) }
% 4.63/0.94 gt(n0, fresh(fresh134(a_select2(xinit_mean_defuse, n2), use), true3, b))
% 4.63/0.94 = { by axiom 9 (quaternion_ds1_inuse_0004_14) }
% 4.63/0.94 gt(n0, fresh(fresh134(use, use), true3, b))
% 4.63/0.94 = { by axiom 48 (quaternion_ds1_inuse_0004_27) }
% 4.63/0.94 gt(n0, fresh(fresh136(a_select2(xinit_mean_defuse, n0), use), true3, b))
% 4.63/0.94 = { by axiom 7 (quaternion_ds1_inuse_0004_12) }
% 4.63/0.94 gt(n0, fresh(fresh136(use, use), true3, b))
% 4.63/0.94 = { by axiom 46 (quaternion_ds1_inuse_0004_27) }
% 4.63/0.94 gt(n0, fresh(fresh138(a_select2(xinit_defuse, n4), use), true3, b))
% 4.63/0.94 = { by axiom 23 (quaternion_ds1_inuse_0004_10) }
% 4.63/0.94 gt(n0, fresh(fresh138(use, use), true3, b))
% 4.63/0.94 = { by axiom 44 (quaternion_ds1_inuse_0004_27) }
% 4.63/0.94 gt(n0, fresh(fresh140(a_select2(sigma_defuse, n5), use), true3, b))
% 4.63/0.94 = { by axiom 6 (quaternion_ds1_inuse_0004_8) }
% 4.63/0.94 gt(n0, fresh(fresh140(use, use), true3, b))
% 4.63/0.94 = { by axiom 42 (quaternion_ds1_inuse_0004_27) }
% 4.63/0.94 gt(n0, fresh(fresh142(a_select2(sigma_defuse, n3), use), true3, b))
% 4.63/0.94 = { by axiom 4 (quaternion_ds1_inuse_0004_6) }
% 4.63/0.94 gt(n0, fresh(fresh142(use, use), true3, b))
% 4.63/0.94 = { by axiom 40 (quaternion_ds1_inuse_0004_27) }
% 4.63/0.94 gt(n0, fresh(fresh144(a_select2(sigma_defuse, n1), use), true3, b))
% 4.63/0.94 = { by axiom 2 (quaternion_ds1_inuse_0004_4) }
% 4.63/0.94 gt(n0, fresh(fresh144(use, use), true3, b))
% 4.63/0.94 = { by axiom 37 (quaternion_ds1_inuse_0004_27) }
% 4.63/0.94 gt(n0, fresh(fresh147(a_select2(rho_defuse, n2), use), true3, b))
% 4.63/0.94 = { by axiom 21 (quaternion_ds1_inuse_0004_2) }
% 4.63/0.94 gt(n0, fresh(fresh147(use, use), true3, b))
% 4.63/0.94 = { by axiom 36 (quaternion_ds1_inuse_0004_27) }
% 4.63/0.94 gt(n0, fresh(fresh148(a_select2(rho_defuse, n0), use), true3, b))
% 4.63/0.94 = { by axiom 19 (quaternion_ds1_inuse_0004) }
% 4.63/0.94 gt(n0, fresh(fresh148(use, use), true3, b))
% 4.63/0.94 = { by axiom 27 (quaternion_ds1_inuse_0004_27) }
% 4.63/0.94 gt(n0, fresh(true3, true3, b))
% 4.63/0.94 = { by axiom 33 (finite_domain_0) }
% 4.63/0.94 gt(n0, b)
% 4.63/0.94 = { by axiom 25 (succ_pred) R->L }
% 4.63/0.94 gt(succ(pred(n0)), b)
% 4.63/0.94 = { by axiom 92 (leq_succ_gt_equiv_1) R->L }
% 4.63/0.94 fresh29(leq(b, pred(n0)), true3, b, pred(n0))
% 4.63/0.94 = { by lemma 94 }
% 4.63/0.94 fresh29(fresh92(X, X), true3, b, pred(n0))
% 4.63/0.94 = { by lemma 93 }
% 4.63/0.94 fresh29(true3, true3, b, pred(n0))
% 4.63/0.94 = { by axiom 85 (leq_succ_gt_equiv_1) }
% 4.63/0.94 true3
% 4.63/0.94 % SZS output end Proof
% 4.63/0.94
% 4.63/0.94 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------