TSTP Solution File: SWV733-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SWV733-1 : TPTP v8.1.2. Released v4.1.0.
% 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 : n024.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 23:06:03 EDT 2023
% Result : Unsatisfiable 111.05s 14.59s
% Output : Proof 112.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV733-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 06:57:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 111.05/14.59 Command-line arguments: --flatten
% 111.05/14.59
% 111.05/14.59 % SZS status Unsatisfiable
% 111.05/14.59
% 111.34/14.67 % SZS output start Proof
% 111.34/14.67 Take the following subset of the input axioms:
% 111.34/14.67 fof(cls_UnCI_0, axiom, ![V_A, V_B, V_c, T_a]: (c_in(V_c, c_Lattices_Oupper__semilattice__class_Osup(V_A, V_B, tc_fun(T_a, tc_bool)), T_a) | ~c_in(V_c, V_B, T_a))).
% 111.34/14.67 fof(cls_Un__commute_0, axiom, ![T_a2, V_A2, V_B2]: c_Lattices_Oupper__semilattice__class_Osup(V_A2, V_B2, tc_fun(T_a2, tc_bool))=c_Lattices_Oupper__semilattice__class_Osup(V_B2, V_A2, tc_fun(T_a2, tc_bool))).
% 111.34/14.67 fof(cls_Un__empty__left_0, axiom, ![T_a2, V_B2]: c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(T_a2, tc_bool)), V_B2, tc_fun(T_a2, tc_bool))=V_B2).
% 111.34/14.67 fof(cls_Un__insert__left_0, axiom, ![V_C, V_a, T_a2, V_B2]: c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(V_a, V_B2, T_a2), V_C, tc_fun(T_a2, tc_bool))=c_Set_Oinsert(V_a, c_Lattices_Oupper__semilattice__class_Osup(V_B2, V_C, tc_fun(T_a2, tc_bool)), T_a2)).
% 111.34/14.67 fof(cls_Un__insert__right_0, axiom, ![T_a2, V_A2, V_a2, V_B2]: c_Lattices_Oupper__semilattice__class_Osup(V_A2, c_Set_Oinsert(V_a2, V_B2, T_a2), tc_fun(T_a2, tc_bool))=c_Set_Oinsert(V_a2, c_Lattices_Oupper__semilattice__class_Osup(V_A2, V_B2, tc_fun(T_a2, tc_bool)), T_a2)).
% 111.34/14.67 fof(cls_analz_OInj_0, axiom, ![V_X, V_H]: (c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg) | ~c_in(V_X, V_H, tc_Message_Omsg))).
% 111.34/14.67 fof(cls_analz__empty_0, axiom, c_Message_Oanalz(c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)))=c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool))).
% 111.34/14.67 fof(cls_analz__parts_0, axiom, ![V_H2]: c_Message_Oanalz(c_Message_Oparts(V_H2))=c_Message_Oparts(V_H2)).
% 111.34/14.67 fof(cls_conjecture_2, negated_conjecture, c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)).
% 111.34/14.67 fof(cls_conjecture_3, negated_conjecture, c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg)).
% 111.34/14.67 fof(cls_conjecture_4, negated_conjecture, ~c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)).
% 111.34/14.67 fof(cls_insert__absorb_0, axiom, ![T_a2, V_A2, V_a2]: (c_Set_Oinsert(V_a2, V_A2, T_a2)=V_A2 | ~c_in(V_a2, V_A2, T_a2))).
% 111.34/14.67 fof(cls_mem__def_0, axiom, ![V_S, V_x, T_a2]: (hBOOL(hAPP(V_S, V_x)) | ~c_in(V_x, V_S, T_a2))).
% 111.34/14.67 fof(cls_mem__def_1, axiom, ![V_S2, T_a2, V_x2]: (c_in(V_x2, V_S2, T_a2) | ~hBOOL(hAPP(V_S2, V_x2)))).
% 111.34/14.67 fof(cls_ns__sharedp_ONil_0, axiom, c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent))).
% 111.34/14.67 fof(cls_parts__Un_0, axiom, ![V_G, V_H2]: c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(V_G, V_H2, tc_fun(tc_Message_Omsg, tc_bool)))=c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(V_G), c_Message_Oparts(V_H2), tc_fun(tc_Message_Omsg, tc_bool))).
% 111.34/14.67 fof(cls_parts__idem_0, axiom, ![V_H2]: c_Message_Oparts(c_Message_Oparts(V_H2))=c_Message_Oparts(V_H2)).
% 111.34/14.67 fof(cls_parts__insert_0, axiom, ![V_X2, V_H2]: c_Message_Oparts(c_Set_Oinsert(V_X2, V_H2, tc_Message_Omsg))=c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(V_X2, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), c_Message_Oparts(V_H2), tc_fun(tc_Message_Omsg, tc_bool))).
% 111.34/14.67 fof(cls_parts__insert__Crypt_0, axiom, ![V_K, V_X2, V_H2]: c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OCrypt(V_K, V_X2), V_H2, tc_Message_Omsg))=c_Set_Oinsert(c_Message_Omsg_OCrypt(V_K, V_X2), c_Message_Oparts(c_Set_Oinsert(V_X2, V_H2, tc_Message_Omsg)), tc_Message_Omsg)).
% 111.34/14.67 fof(clsarity_bool__HOL_Oord, axiom, class_HOL_Oord(tc_bool)).
% 111.34/14.67 fof(clsarity_bool__Lattices_Odistrib__lattice, axiom, class_Lattices_Odistrib__lattice(tc_bool)).
% 111.34/14.67 fof(clsarity_bool__Lattices_Olower__semilattice, axiom, class_Lattices_Olower__semilattice(tc_bool)).
% 111.34/14.67 fof(clsarity_bool__Orderings_Opreorder, axiom, class_Orderings_Opreorder(tc_bool)).
% 111.34/14.67 fof(clsarity_bool__Orderings_Otop, axiom, class_Orderings_Otop(tc_bool)).
% 111.34/14.67 fof(clsarity_nat__HOL_Oord, axiom, class_HOL_Oord(tc_nat)).
% 111.34/14.67 fof(clsarity_nat__Lattices_Odistrib__lattice, axiom, class_Lattices_Odistrib__lattice(tc_nat)).
% 111.34/14.67 fof(clsarity_nat__Lattices_Olower__semilattice, axiom, class_Lattices_Olower__semilattice(tc_nat)).
% 111.34/14.67 fof(clsarity_nat__Orderings_Olinorder, axiom, class_Orderings_Olinorder(tc_nat)).
% 111.34/14.67 fof(clsarity_nat__Orderings_Opreorder, axiom, class_Orderings_Opreorder(tc_nat)).
% 111.34/14.67
% 111.34/14.67 Now clausify the problem and encode Horn clauses using encoding 3 of
% 111.34/14.67 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 111.34/14.67 We repeatedly replace C & s=t => u=v by the two clauses:
% 111.34/14.67 fresh(y, y, x1...xn) = u
% 111.34/14.67 C => fresh(s, t, x1...xn) = v
% 111.34/14.67 where fresh is a fresh function symbol and x1..xn are the free
% 111.34/14.67 variables of u and v.
% 111.34/14.67 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 111.34/14.67 input problem has no model of domain size 1).
% 111.34/14.67
% 111.34/14.67 The encoding turns the above axioms into the following unit equations and goals:
% 111.34/14.67
% 111.34/14.67 Axiom 1 (clsarity_nat__Orderings_Olinorder): class_Orderings_Olinorder(tc_nat) = true2.
% 111.34/14.67 Axiom 2 (clsarity_bool__Orderings_Otop): class_Orderings_Otop(tc_bool) = true2.
% 111.34/14.67 Axiom 3 (clsarity_nat__HOL_Oord): class_HOL_Oord(tc_nat) = true2.
% 111.34/14.67 Axiom 4 (clsarity_bool__HOL_Oord): class_HOL_Oord(tc_bool) = true2.
% 111.34/14.67 Axiom 5 (clsarity_nat__Orderings_Opreorder): class_Orderings_Opreorder(tc_nat) = true2.
% 111.34/14.67 Axiom 6 (clsarity_bool__Orderings_Opreorder): class_Orderings_Opreorder(tc_bool) = true2.
% 111.34/14.67 Axiom 7 (clsarity_nat__Lattices_Odistrib__lattice): class_Lattices_Odistrib__lattice(tc_nat) = true2.
% 111.34/14.67 Axiom 8 (clsarity_bool__Lattices_Odistrib__lattice): class_Lattices_Odistrib__lattice(tc_bool) = true2.
% 111.34/14.67 Axiom 9 (clsarity_nat__Lattices_Olower__semilattice): class_Lattices_Olower__semilattice(tc_nat) = true2.
% 111.34/14.67 Axiom 10 (clsarity_bool__Lattices_Olower__semilattice): class_Lattices_Olower__semilattice(tc_bool) = true2.
% 111.34/14.67 Axiom 11 (cls_ns__sharedp_ONil_0): c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)) = true2.
% 111.34/14.67 Axiom 12 (cls_parts__idem_0): c_Message_Oparts(c_Message_Oparts(X)) = c_Message_Oparts(X).
% 111.34/14.67 Axiom 13 (cls_analz__parts_0): c_Message_Oanalz(c_Message_Oparts(X)) = c_Message_Oparts(X).
% 111.34/14.67 Axiom 14 (cls_analz_OInj_0): fresh382(X, X, Y, Z) = true2.
% 111.34/14.67 Axiom 15 (cls_mem__def_0): fresh227(X, X, Y, Z) = true2.
% 111.34/14.67 Axiom 16 (cls_analz__empty_0): c_Message_Oanalz(c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)).
% 111.34/14.67 Axiom 17 (cls_parts__insert__eq__I_1): fresh206(X, X, Y, Z) = c_Set_Oinsert(Y, c_Message_Oparts(Z), tc_Message_Omsg).
% 111.34/14.67 Axiom 18 (cls_mem__def_1): fresh226(X, X, Y, Z, W) = true2.
% 111.34/14.67 Axiom 19 (cls_insert__absorb_0): fresh28(X, X, Y, Z, W) = Z.
% 111.34/14.67 Axiom 20 (cls_Un__commute_0): c_Lattices_Oupper__semilattice__class_Osup(X, Y, tc_fun(Z, tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(Y, X, tc_fun(Z, tc_bool)).
% 111.34/14.67 Axiom 21 (cls_UnCI_0): fresh395(X, X, Y, Z, W, V) = true2.
% 111.34/14.67 Axiom 22 (cls_image__constant_0): fresh338(X, X, Y, Z, W, V) = c_Set_Oinsert(Y, c_Orderings_Obot__class_Obot(tc_fun(Z, tc_bool)), Z).
% 111.34/14.67 Axiom 23 (cls_analz_OInj_0): fresh382(c_in(X, Y, tc_Message_Omsg), true2, X, Y) = c_in(X, c_Message_Oanalz(Y), tc_Message_Omsg).
% 111.34/14.67 Axiom 24 (cls_mem__def_0): fresh227(c_in(X, Y, Z), true2, Y, X) = hBOOL(hAPP(Y, X)).
% 111.34/14.67 Axiom 25 (cls_parts__Un_0): c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(X, Y, tc_fun(tc_Message_Omsg, tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(X), c_Message_Oparts(Y), tc_fun(tc_Message_Omsg, tc_bool)).
% 111.34/14.67 Axiom 26 (cls_mem__def_1): fresh226(hBOOL(hAPP(X, Y)), true2, Y, X, Z) = c_in(Y, X, Z).
% 111.34/14.67 Axiom 27 (cls_insert__absorb_0): fresh28(c_in(X, Y, Z), true2, X, Y, Z) = c_Set_Oinsert(X, Y, Z).
% 111.34/14.67 Axiom 28 (cls_Un__empty__left_0): c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X, tc_bool)), Y, tc_fun(X, tc_bool)) = Y.
% 111.34/14.67 Axiom 29 (cls_Un__insert__left_0): c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X, Y, Z), W, tc_fun(Z, tc_bool)) = c_Set_Oinsert(X, c_Lattices_Oupper__semilattice__class_Osup(Y, W, tc_fun(Z, tc_bool)), Z).
% 111.34/14.67 Axiom 30 (cls_Un__insert__right_0): c_Lattices_Oupper__semilattice__class_Osup(X, c_Set_Oinsert(Y, Z, W), tc_fun(W, tc_bool)) = c_Set_Oinsert(Y, c_Lattices_Oupper__semilattice__class_Osup(X, Z, tc_fun(W, tc_bool)), W).
% 111.34/14.67 Axiom 31 (cls_conjecture_2): c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg) = true2.
% 111.34/14.67 Axiom 32 (cls_UnCI_0): fresh395(c_in(X, Y, Z), true2, X, W, Y, Z) = c_in(X, c_Lattices_Oupper__semilattice__class_Osup(W, Y, tc_fun(Z, tc_bool)), Z).
% 111.34/14.67 Axiom 33 (cls_parts__insert__Crypt_0): c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OCrypt(X, Y), Z, tc_Message_Omsg)) = c_Set_Oinsert(c_Message_Omsg_OCrypt(X, Y), c_Message_Oparts(c_Set_Oinsert(Y, Z, tc_Message_Omsg)), tc_Message_Omsg).
% 111.34/14.67 Axiom 34 (cls_conjecture_3): c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg) = true2.
% 111.34/14.67 Axiom 35 (cls_parts__insert_0): c_Message_Oparts(c_Set_Oinsert(X, Y, tc_Message_Omsg)) = c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), c_Message_Oparts(Y), tc_fun(tc_Message_Omsg, tc_bool)).
% 111.34/14.67
% 111.34/14.67 Lemma 36: class_Orderings_Otop(tc_bool) = class_Orderings_Olinorder(tc_nat).
% 111.34/14.67 Proof:
% 111.34/14.67 class_Orderings_Otop(tc_bool)
% 111.34/14.67 = { by axiom 2 (clsarity_bool__Orderings_Otop) }
% 111.34/14.67 true2
% 111.34/14.67 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 111.34/14.67 class_Orderings_Olinorder(tc_nat)
% 111.34/14.67
% 111.34/14.67 Lemma 37: class_HOL_Oord(tc_nat) = class_Orderings_Otop(tc_bool).
% 111.34/14.67 Proof:
% 111.34/14.67 class_HOL_Oord(tc_nat)
% 111.34/14.67 = { by axiom 3 (clsarity_nat__HOL_Oord) }
% 111.34/14.67 true2
% 111.34/14.67 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 111.34/14.67 class_Orderings_Olinorder(tc_nat)
% 111.34/14.67 = { by lemma 36 R->L }
% 111.34/14.67 class_Orderings_Otop(tc_bool)
% 111.34/14.67
% 111.34/14.67 Lemma 38: class_HOL_Oord(tc_bool) = class_HOL_Oord(tc_nat).
% 111.34/14.67 Proof:
% 111.34/14.67 class_HOL_Oord(tc_bool)
% 111.34/14.67 = { by axiom 4 (clsarity_bool__HOL_Oord) }
% 111.34/14.67 true2
% 111.34/14.67 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 111.34/14.67 class_Orderings_Olinorder(tc_nat)
% 111.34/14.67 = { by lemma 36 R->L }
% 111.34/14.67 class_Orderings_Otop(tc_bool)
% 111.34/14.67 = { by lemma 37 R->L }
% 111.34/14.67 class_HOL_Oord(tc_nat)
% 111.34/14.67
% 111.34/14.67 Lemma 39: class_Orderings_Opreorder(tc_nat) = class_HOL_Oord(tc_bool).
% 111.34/14.67 Proof:
% 111.34/14.67 class_Orderings_Opreorder(tc_nat)
% 111.34/14.67 = { by axiom 5 (clsarity_nat__Orderings_Opreorder) }
% 111.34/14.67 true2
% 111.34/14.67 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 111.34/14.67 class_Orderings_Olinorder(tc_nat)
% 111.34/14.67 = { by lemma 36 R->L }
% 111.34/14.67 class_Orderings_Otop(tc_bool)
% 111.34/14.67 = { by lemma 37 R->L }
% 111.34/14.67 class_HOL_Oord(tc_nat)
% 111.34/14.67 = { by lemma 38 R->L }
% 111.34/14.67 class_HOL_Oord(tc_bool)
% 111.34/14.67
% 111.34/14.67 Lemma 40: class_Orderings_Opreorder(tc_bool) = class_Orderings_Opreorder(tc_nat).
% 111.34/14.67 Proof:
% 111.34/14.67 class_Orderings_Opreorder(tc_bool)
% 111.34/14.67 = { by axiom 6 (clsarity_bool__Orderings_Opreorder) }
% 111.34/14.67 true2
% 111.34/14.67 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 111.34/14.67 class_Orderings_Olinorder(tc_nat)
% 111.34/14.67 = { by lemma 36 R->L }
% 111.34/14.67 class_Orderings_Otop(tc_bool)
% 111.34/14.67 = { by lemma 37 R->L }
% 111.34/14.67 class_HOL_Oord(tc_nat)
% 111.34/14.67 = { by lemma 38 R->L }
% 111.34/14.67 class_HOL_Oord(tc_bool)
% 111.34/14.67 = { by lemma 39 R->L }
% 111.34/14.67 class_Orderings_Opreorder(tc_nat)
% 111.34/14.67
% 111.34/14.67 Lemma 41: class_Lattices_Odistrib__lattice(tc_nat) = class_Orderings_Opreorder(tc_bool).
% 111.34/14.67 Proof:
% 111.34/14.67 class_Lattices_Odistrib__lattice(tc_nat)
% 111.34/14.67 = { by axiom 7 (clsarity_nat__Lattices_Odistrib__lattice) }
% 111.34/14.67 true2
% 111.34/14.67 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 111.34/14.67 class_Orderings_Olinorder(tc_nat)
% 111.34/14.67 = { by lemma 36 R->L }
% 111.34/14.67 class_Orderings_Otop(tc_bool)
% 111.34/14.67 = { by lemma 37 R->L }
% 111.34/14.67 class_HOL_Oord(tc_nat)
% 111.34/14.68 = { by lemma 38 R->L }
% 111.34/14.68 class_HOL_Oord(tc_bool)
% 111.34/14.68 = { by lemma 39 R->L }
% 111.34/14.68 class_Orderings_Opreorder(tc_nat)
% 111.34/14.68 = { by lemma 40 R->L }
% 111.34/14.68 class_Orderings_Opreorder(tc_bool)
% 111.34/14.68
% 111.34/14.68 Lemma 42: class_Lattices_Odistrib__lattice(tc_bool) = class_Lattices_Odistrib__lattice(tc_nat).
% 111.34/14.68 Proof:
% 111.34/14.68 class_Lattices_Odistrib__lattice(tc_bool)
% 111.34/14.68 = { by axiom 8 (clsarity_bool__Lattices_Odistrib__lattice) }
% 111.34/14.68 true2
% 111.34/14.68 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 111.34/14.68 class_Orderings_Olinorder(tc_nat)
% 111.34/14.68 = { by lemma 36 R->L }
% 111.34/14.68 class_Orderings_Otop(tc_bool)
% 111.34/14.68 = { by lemma 37 R->L }
% 111.34/14.68 class_HOL_Oord(tc_nat)
% 111.34/14.68 = { by lemma 38 R->L }
% 111.34/14.68 class_HOL_Oord(tc_bool)
% 111.34/14.68 = { by lemma 39 R->L }
% 111.34/14.68 class_Orderings_Opreorder(tc_nat)
% 111.34/14.68 = { by lemma 40 R->L }
% 111.34/14.68 class_Orderings_Opreorder(tc_bool)
% 111.34/14.68 = { by lemma 41 R->L }
% 111.34/14.68 class_Lattices_Odistrib__lattice(tc_nat)
% 111.34/14.68
% 111.34/14.68 Lemma 43: class_Lattices_Olower__semilattice(tc_nat) = class_Lattices_Odistrib__lattice(tc_bool).
% 111.34/14.68 Proof:
% 111.34/14.68 class_Lattices_Olower__semilattice(tc_nat)
% 111.34/14.68 = { by axiom 9 (clsarity_nat__Lattices_Olower__semilattice) }
% 111.34/14.68 true2
% 111.34/14.68 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 111.34/14.68 class_Orderings_Olinorder(tc_nat)
% 111.34/14.68 = { by lemma 36 R->L }
% 111.34/14.68 class_Orderings_Otop(tc_bool)
% 111.34/14.68 = { by lemma 37 R->L }
% 111.34/14.68 class_HOL_Oord(tc_nat)
% 111.34/14.68 = { by lemma 38 R->L }
% 111.34/14.68 class_HOL_Oord(tc_bool)
% 111.34/14.68 = { by lemma 39 R->L }
% 111.34/14.68 class_Orderings_Opreorder(tc_nat)
% 111.34/14.68 = { by lemma 40 R->L }
% 111.34/14.68 class_Orderings_Opreorder(tc_bool)
% 111.34/14.68 = { by lemma 41 R->L }
% 111.34/14.68 class_Lattices_Odistrib__lattice(tc_nat)
% 111.34/14.68 = { by lemma 42 R->L }
% 111.34/14.68 class_Lattices_Odistrib__lattice(tc_bool)
% 111.34/14.68
% 111.34/14.68 Lemma 44: class_Lattices_Olower__semilattice(tc_bool) = class_Lattices_Olower__semilattice(tc_nat).
% 111.34/14.68 Proof:
% 111.34/14.68 class_Lattices_Olower__semilattice(tc_bool)
% 111.34/14.68 = { by axiom 10 (clsarity_bool__Lattices_Olower__semilattice) }
% 111.34/14.68 true2
% 111.34/14.68 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 111.34/14.68 class_Orderings_Olinorder(tc_nat)
% 111.34/14.68 = { by lemma 36 R->L }
% 111.34/14.68 class_Orderings_Otop(tc_bool)
% 111.34/14.68 = { by lemma 37 R->L }
% 111.34/14.68 class_HOL_Oord(tc_nat)
% 111.34/14.68 = { by lemma 38 R->L }
% 111.34/14.68 class_HOL_Oord(tc_bool)
% 111.34/14.68 = { by lemma 39 R->L }
% 111.34/14.68 class_Orderings_Opreorder(tc_nat)
% 111.34/14.68 = { by lemma 40 R->L }
% 111.34/14.68 class_Orderings_Opreorder(tc_bool)
% 111.34/14.68 = { by lemma 41 R->L }
% 111.34/14.68 class_Lattices_Odistrib__lattice(tc_nat)
% 111.34/14.68 = { by lemma 42 R->L }
% 111.34/14.68 class_Lattices_Odistrib__lattice(tc_bool)
% 111.34/14.68 = { by lemma 43 R->L }
% 111.34/14.68 class_Lattices_Olower__semilattice(tc_nat)
% 111.34/14.68
% 111.34/14.68 Lemma 45: c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)) = class_Lattices_Olower__semilattice(tc_bool).
% 111.34/14.68 Proof:
% 111.34/14.68 c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent))
% 111.34/14.68 = { by axiom 11 (cls_ns__sharedp_ONil_0) }
% 111.34/14.68 true2
% 111.34/14.68 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 111.34/14.68 class_Orderings_Olinorder(tc_nat)
% 111.34/14.68 = { by lemma 36 R->L }
% 111.34/14.68 class_Orderings_Otop(tc_bool)
% 111.34/14.68 = { by lemma 37 R->L }
% 111.34/14.68 class_HOL_Oord(tc_nat)
% 111.34/14.68 = { by lemma 38 R->L }
% 111.34/14.68 class_HOL_Oord(tc_bool)
% 111.34/14.68 = { by lemma 39 R->L }
% 111.34/14.68 class_Orderings_Opreorder(tc_nat)
% 111.34/14.68 = { by lemma 40 R->L }
% 111.34/14.68 class_Orderings_Opreorder(tc_bool)
% 111.34/14.68 = { by lemma 41 R->L }
% 111.34/14.68 class_Lattices_Odistrib__lattice(tc_nat)
% 111.34/14.68 = { by lemma 42 R->L }
% 111.34/14.68 class_Lattices_Odistrib__lattice(tc_bool)
% 111.34/14.68 = { by lemma 43 R->L }
% 111.34/14.68 class_Lattices_Olower__semilattice(tc_nat)
% 111.34/14.68 = { by lemma 44 R->L }
% 111.34/14.68 class_Lattices_Olower__semilattice(tc_bool)
% 111.34/14.68
% 111.34/14.68 Lemma 46: c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(X), c_Message_Oparts(Y), tc_fun(tc_Message_Omsg, tc_bool)) = c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(Y, X, tc_fun(tc_Message_Omsg, tc_bool))).
% 111.34/14.68 Proof:
% 111.34/14.68 c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(X), c_Message_Oparts(Y), tc_fun(tc_Message_Omsg, tc_bool))
% 111.34/14.68 = { by axiom 25 (cls_parts__Un_0) R->L }
% 111.34/14.68 c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(X, Y, tc_fun(tc_Message_Omsg, tc_bool)))
% 111.34/14.68 = { by axiom 20 (cls_Un__commute_0) R->L }
% 111.34/14.68 c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(Y, X, tc_fun(tc_Message_Omsg, tc_bool)))
% 111.34/14.68
% 111.34/14.68 Lemma 47: c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X, Y, Z), W, tc_fun(Z, tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(Y, c_Set_Oinsert(X, W, Z), tc_fun(Z, tc_bool)).
% 111.34/14.68 Proof:
% 111.34/14.68 c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(X, Y, Z), W, tc_fun(Z, tc_bool))
% 111.34/14.68 = { by axiom 29 (cls_Un__insert__left_0) }
% 111.34/14.68 c_Set_Oinsert(X, c_Lattices_Oupper__semilattice__class_Osup(Y, W, tc_fun(Z, tc_bool)), Z)
% 111.34/14.68 = { by axiom 30 (cls_Un__insert__right_0) R->L }
% 111.34/14.68 c_Lattices_Oupper__semilattice__class_Osup(Y, c_Set_Oinsert(X, W, Z), tc_fun(Z, tc_bool))
% 111.34/14.68
% 111.34/14.68 Lemma 48: c_Set_Oinsert(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X) = c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)).
% 111.34/14.68 Proof:
% 111.34/14.68 c_Set_Oinsert(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by axiom 27 (cls_insert__absorb_0) R->L }
% 111.34/14.68 fresh28(c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), true2, c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 111.34/14.68 fresh28(c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), class_Orderings_Olinorder(tc_nat), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by lemma 36 R->L }
% 111.34/14.68 fresh28(c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), class_Orderings_Otop(tc_bool), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by lemma 37 R->L }
% 111.34/14.68 fresh28(c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), class_HOL_Oord(tc_nat), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by lemma 38 R->L }
% 111.34/14.68 fresh28(c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), class_HOL_Oord(tc_bool), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by lemma 39 R->L }
% 111.34/14.68 fresh28(c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), class_Orderings_Opreorder(tc_nat), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by lemma 40 R->L }
% 111.34/14.68 fresh28(c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), class_Orderings_Opreorder(tc_bool), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by lemma 41 R->L }
% 111.34/14.68 fresh28(c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), class_Lattices_Odistrib__lattice(tc_nat), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by lemma 42 R->L }
% 111.34/14.68 fresh28(c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), class_Lattices_Odistrib__lattice(tc_bool), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by lemma 43 R->L }
% 111.34/14.68 fresh28(c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), class_Lattices_Olower__semilattice(tc_nat), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by lemma 44 R->L }
% 111.34/14.68 fresh28(c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), class_Lattices_Olower__semilattice(tc_bool), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by lemma 45 R->L }
% 111.34/14.68 fresh28(c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by axiom 26 (cls_mem__def_1) R->L }
% 111.34/14.68 fresh28(fresh226(hBOOL(hAPP(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X))), true2, c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 111.34/14.68 fresh28(fresh226(hBOOL(hAPP(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X))), class_Orderings_Olinorder(tc_nat), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by lemma 36 R->L }
% 111.34/14.68 fresh28(fresh226(hBOOL(hAPP(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X))), class_Orderings_Otop(tc_bool), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by lemma 37 R->L }
% 111.34/14.68 fresh28(fresh226(hBOOL(hAPP(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X))), class_HOL_Oord(tc_nat), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by lemma 38 R->L }
% 111.34/14.68 fresh28(fresh226(hBOOL(hAPP(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X))), class_HOL_Oord(tc_bool), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by lemma 39 R->L }
% 111.34/14.68 fresh28(fresh226(hBOOL(hAPP(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X))), class_Orderings_Opreorder(tc_nat), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by lemma 40 R->L }
% 111.34/14.68 fresh28(fresh226(hBOOL(hAPP(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X))), class_Orderings_Opreorder(tc_bool), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by lemma 41 R->L }
% 111.34/14.68 fresh28(fresh226(hBOOL(hAPP(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X))), class_Lattices_Odistrib__lattice(tc_nat), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by lemma 42 R->L }
% 111.34/14.68 fresh28(fresh226(hBOOL(hAPP(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X))), class_Lattices_Odistrib__lattice(tc_bool), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by lemma 43 R->L }
% 111.34/14.68 fresh28(fresh226(hBOOL(hAPP(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X))), class_Lattices_Olower__semilattice(tc_nat), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by lemma 44 R->L }
% 111.34/14.68 fresh28(fresh226(hBOOL(hAPP(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X))), class_Lattices_Olower__semilattice(tc_bool), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by lemma 45 R->L }
% 111.34/14.68 fresh28(fresh226(hBOOL(hAPP(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X))), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by axiom 24 (cls_mem__def_0) R->L }
% 111.34/14.68 fresh28(fresh226(fresh227(c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg), true2, c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.34/14.68 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 111.34/14.68 fresh28(fresh226(fresh227(c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg), class_Orderings_Olinorder(tc_nat), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.68 = { by lemma 36 R->L }
% 111.94/14.68 fresh28(fresh226(fresh227(c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg), class_Orderings_Otop(tc_bool), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.68 = { by lemma 37 R->L }
% 111.94/14.68 fresh28(fresh226(fresh227(c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg), class_HOL_Oord(tc_nat), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.68 = { by lemma 38 R->L }
% 111.94/14.68 fresh28(fresh226(fresh227(c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg), class_HOL_Oord(tc_bool), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.68 = { by lemma 39 R->L }
% 111.94/14.68 fresh28(fresh226(fresh227(c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg), class_Orderings_Opreorder(tc_nat), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.68 = { by lemma 40 R->L }
% 111.94/14.68 fresh28(fresh226(fresh227(c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg), class_Orderings_Opreorder(tc_bool), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.68 = { by lemma 41 R->L }
% 111.94/14.69 fresh28(fresh226(fresh227(c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg), class_Lattices_Odistrib__lattice(tc_nat), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 42 R->L }
% 111.94/14.69 fresh28(fresh226(fresh227(c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg), class_Lattices_Odistrib__lattice(tc_bool), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 43 R->L }
% 111.94/14.69 fresh28(fresh226(fresh227(c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg), class_Lattices_Olower__semilattice(tc_nat), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 44 R->L }
% 111.94/14.69 fresh28(fresh226(fresh227(c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg), class_Lattices_Olower__semilattice(tc_bool), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 45 R->L }
% 111.94/14.69 fresh28(fresh226(fresh227(c_in(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by axiom 31 (cls_conjecture_2) }
% 111.94/14.69 fresh28(fresh226(fresh227(true2, c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 111.94/14.69 fresh28(fresh226(fresh227(class_Orderings_Olinorder(tc_nat), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 36 R->L }
% 111.94/14.69 fresh28(fresh226(fresh227(class_Orderings_Otop(tc_bool), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 37 R->L }
% 111.94/14.69 fresh28(fresh226(fresh227(class_HOL_Oord(tc_nat), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 38 R->L }
% 111.94/14.69 fresh28(fresh226(fresh227(class_HOL_Oord(tc_bool), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 39 R->L }
% 111.94/14.69 fresh28(fresh226(fresh227(class_Orderings_Opreorder(tc_nat), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 40 R->L }
% 111.94/14.69 fresh28(fresh226(fresh227(class_Orderings_Opreorder(tc_bool), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 41 R->L }
% 111.94/14.69 fresh28(fresh226(fresh227(class_Lattices_Odistrib__lattice(tc_nat), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 42 R->L }
% 111.94/14.69 fresh28(fresh226(fresh227(class_Lattices_Odistrib__lattice(tc_bool), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 43 R->L }
% 111.94/14.69 fresh28(fresh226(fresh227(class_Lattices_Olower__semilattice(tc_nat), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 44 R->L }
% 111.94/14.69 fresh28(fresh226(fresh227(class_Lattices_Olower__semilattice(tc_bool), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 45 R->L }
% 111.94/14.69 fresh28(fresh226(fresh227(c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Omsg_OCrypt(v_KAB, v_X)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by axiom 15 (cls_mem__def_0) }
% 111.94/14.69 fresh28(fresh226(true2, c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 111.94/14.69 fresh28(fresh226(class_Orderings_Olinorder(tc_nat), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 36 R->L }
% 111.94/14.69 fresh28(fresh226(class_Orderings_Otop(tc_bool), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 37 R->L }
% 111.94/14.69 fresh28(fresh226(class_HOL_Oord(tc_nat), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 38 R->L }
% 111.94/14.69 fresh28(fresh226(class_HOL_Oord(tc_bool), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 39 R->L }
% 111.94/14.69 fresh28(fresh226(class_Orderings_Opreorder(tc_nat), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 40 R->L }
% 111.94/14.69 fresh28(fresh226(class_Orderings_Opreorder(tc_bool), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 41 R->L }
% 111.94/14.69 fresh28(fresh226(class_Lattices_Odistrib__lattice(tc_nat), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 42 R->L }
% 111.94/14.69 fresh28(fresh226(class_Lattices_Odistrib__lattice(tc_bool), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 43 R->L }
% 111.94/14.69 fresh28(fresh226(class_Lattices_Olower__semilattice(tc_nat), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 44 R->L }
% 111.94/14.69 fresh28(fresh226(class_Lattices_Olower__semilattice(tc_bool), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 45 R->L }
% 111.94/14.69 fresh28(fresh226(c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by axiom 18 (cls_mem__def_1) }
% 111.94/14.69 fresh28(true2, c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 111.94/14.69 fresh28(class_Orderings_Olinorder(tc_nat), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 36 R->L }
% 111.94/14.69 fresh28(class_Orderings_Otop(tc_bool), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 37 R->L }
% 111.94/14.69 fresh28(class_HOL_Oord(tc_nat), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 38 R->L }
% 111.94/14.69 fresh28(class_HOL_Oord(tc_bool), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 39 R->L }
% 111.94/14.69 fresh28(class_Orderings_Opreorder(tc_nat), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 40 R->L }
% 111.94/14.69 fresh28(class_Orderings_Opreorder(tc_bool), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 41 R->L }
% 111.94/14.69 fresh28(class_Lattices_Odistrib__lattice(tc_nat), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 42 R->L }
% 111.94/14.69 fresh28(class_Lattices_Odistrib__lattice(tc_bool), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 43 R->L }
% 111.94/14.69 fresh28(class_Lattices_Olower__semilattice(tc_nat), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 44 R->L }
% 111.94/14.69 fresh28(class_Lattices_Olower__semilattice(tc_bool), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by lemma 45 R->L }
% 111.94/14.69 fresh28(c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), X)
% 111.94/14.69 = { by axiom 19 (cls_insert__absorb_0) }
% 111.94/14.69 c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs))
% 111.94/14.69
% 111.94/14.69 Lemma 49: c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oanalz(c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool))), X, tc_fun(tc_Message_Omsg, tc_bool)) = X.
% 111.94/14.69 Proof:
% 111.94/14.69 c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oanalz(c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool))), X, tc_fun(tc_Message_Omsg, tc_bool))
% 111.94/14.69 = { by axiom 16 (cls_analz__empty_0) }
% 111.94/14.69 c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), X, tc_fun(tc_Message_Omsg, tc_bool))
% 111.94/14.69 = { by axiom 28 (cls_Un__empty__left_0) }
% 111.94/14.69 X
% 111.94/14.69
% 111.94/14.69 Lemma 50: c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(fresh338(X, X, Y, tc_Message_Omsg, Z, W), V, tc_fun(tc_Message_Omsg, tc_bool))) = c_Message_Oparts(c_Set_Oinsert(Y, V, tc_Message_Omsg)).
% 111.94/14.69 Proof:
% 111.94/14.69 c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(fresh338(X, X, Y, tc_Message_Omsg, Z, W), V, tc_fun(tc_Message_Omsg, tc_bool)))
% 111.94/14.69 = { by axiom 25 (cls_parts__Un_0) }
% 111.94/14.69 c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(fresh338(X, X, Y, tc_Message_Omsg, Z, W)), c_Message_Oparts(V), tc_fun(tc_Message_Omsg, tc_bool))
% 111.94/14.69 = { by axiom 22 (cls_image__constant_0) }
% 111.94/14.69 c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(Y, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), c_Message_Oparts(V), tc_fun(tc_Message_Omsg, tc_bool))
% 111.94/14.69 = { by axiom 35 (cls_parts__insert_0) R->L }
% 111.94/14.69 c_Message_Oparts(c_Set_Oinsert(Y, V, tc_Message_Omsg))
% 111.94/14.69
% 111.94/14.69 Goal 1 (cls_conjecture_4): c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg) = true2.
% 111.94/14.69 Proof:
% 111.94/14.69 c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg)
% 111.94/14.69 = { by axiom 13 (cls_analz__parts_0) R->L }
% 111.94/14.69 c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oanalz(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs))), tc_Message_Omsg)
% 111.94/14.69 = { by axiom 12 (cls_parts__idem_0) R->L }
% 111.94/14.69 c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oanalz(c_Message_Oparts(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)))), tc_Message_Omsg)
% 111.94/14.69 = { by lemma 48 R->L }
% 111.94/14.69 c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oanalz(c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg))), tc_Message_Omsg)
% 111.94/14.69 = { by lemma 50 R->L }
% 111.94/14.69 c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oanalz(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(fresh338(X, X, c_Message_Omsg_OCrypt(v_KAB, v_X), tc_Message_Omsg, Y, Z), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_fun(tc_Message_Omsg, tc_bool)))), tc_Message_Omsg)
% 111.94/14.69 = { by axiom 20 (cls_Un__commute_0) }
% 111.94/14.69 c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oanalz(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), fresh338(X, X, c_Message_Omsg_OCrypt(v_KAB, v_X), tc_Message_Omsg, Y, Z), tc_fun(tc_Message_Omsg, tc_bool)))), tc_Message_Omsg)
% 111.94/14.69 = { by axiom 25 (cls_parts__Un_0) }
% 111.94/14.69 c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oanalz(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs))), c_Message_Oparts(fresh338(X, X, c_Message_Omsg_OCrypt(v_KAB, v_X), tc_Message_Omsg, Y, Z)), tc_fun(tc_Message_Omsg, tc_bool))), tc_Message_Omsg)
% 111.94/14.69 = { by axiom 12 (cls_parts__idem_0) }
% 111.94/14.69 c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oanalz(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(fresh338(X, X, c_Message_Omsg_OCrypt(v_KAB, v_X), tc_Message_Omsg, Y, Z)), tc_fun(tc_Message_Omsg, tc_bool))), tc_Message_Omsg)
% 111.94/14.69 = { by lemma 46 }
% 111.94/14.69 c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oanalz(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(fresh338(X, X, c_Message_Omsg_OCrypt(v_KAB, v_X), tc_Message_Omsg, Y, Z), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs), tc_fun(tc_Message_Omsg, tc_bool)))), tc_Message_Omsg)
% 111.94/14.69 = { by lemma 50 }
% 111.94/14.69 c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oanalz(c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs), tc_Message_Omsg))), tc_Message_Omsg)
% 111.94/14.69 = { by lemma 49 R->L }
% 111.94/14.69 c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oanalz(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oanalz(c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool))), c_Set_Oinsert(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs), tc_Message_Omsg), tc_fun(tc_Message_Omsg, tc_bool)))), tc_Message_Omsg)
% 111.94/14.69 = { by lemma 47 R->L }
% 111.94/14.69 c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oanalz(c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oanalz(c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool))), tc_Message_Omsg), c_Event_Oknows(c_Message_Oagent_OSpy, v_evs), tc_fun(tc_Message_Omsg, tc_bool)))), tc_Message_Omsg)
% 111.94/14.69 = { by lemma 46 R->L }
% 111.94/14.69 c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oanalz(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oanalz(c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool))), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool))), tc_Message_Omsg)
% 111.94/14.69 = { by axiom 33 (cls_parts__insert__Crypt_0) }
% 111.94/14.70 c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oanalz(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Set_Oinsert(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Set_Oinsert(v_X, c_Message_Oanalz(c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool))), tc_Message_Omsg)), tc_Message_Omsg), tc_fun(tc_Message_Omsg, tc_bool))), tc_Message_Omsg)
% 111.94/14.70 = { by axiom 17 (cls_parts__insert__eq__I_1) R->L }
% 111.94/14.70 c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oanalz(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), fresh206(W, W, c_Message_Omsg_OCrypt(v_KAB, v_X), c_Set_Oinsert(v_X, c_Message_Oanalz(c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool))), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool))), tc_Message_Omsg)
% 111.94/14.70 = { by lemma 49 R->L }
% 111.94/14.70 c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oanalz(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), fresh206(W, W, c_Message_Omsg_OCrypt(v_KAB, v_X), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oanalz(c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool))), c_Set_Oinsert(v_X, c_Message_Oanalz(c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool))), tc_Message_Omsg), tc_fun(tc_Message_Omsg, tc_bool))), tc_fun(tc_Message_Omsg, tc_bool))), tc_Message_Omsg)
% 111.94/14.70 = { by lemma 47 R->L }
% 111.94/14.70 c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oanalz(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), fresh206(W, W, c_Message_Omsg_OCrypt(v_KAB, v_X), c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_X, c_Message_Oanalz(c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool))), tc_Message_Omsg), c_Message_Oanalz(c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool))), tc_fun(tc_Message_Omsg, tc_bool))), tc_fun(tc_Message_Omsg, tc_bool))), tc_Message_Omsg)
% 112.03/14.70 = { by axiom 16 (cls_analz__empty_0) }
% 112.03/14.70 c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oanalz(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), fresh206(W, W, c_Message_Omsg_OCrypt(v_KAB, v_X), c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg), c_Message_Oanalz(c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool))), tc_fun(tc_Message_Omsg, tc_bool))), tc_fun(tc_Message_Omsg, tc_bool))), tc_Message_Omsg)
% 112.03/14.70 = { by axiom 20 (cls_Un__commute_0) R->L }
% 112.03/14.70 c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oanalz(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), fresh206(W, W, c_Message_Omsg_OCrypt(v_KAB, v_X), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oanalz(c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool))), c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg), tc_fun(tc_Message_Omsg, tc_bool))), tc_fun(tc_Message_Omsg, tc_bool))), tc_Message_Omsg)
% 112.03/14.70 = { by lemma 49 }
% 112.03/14.70 c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oanalz(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), fresh206(W, W, c_Message_Omsg_OCrypt(v_KAB, v_X), c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool))), tc_Message_Omsg)
% 112.03/14.70 = { by axiom 17 (cls_parts__insert__eq__I_1) }
% 112.03/14.70 c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oanalz(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Set_Oinsert(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), tc_fun(tc_Message_Omsg, tc_bool))), tc_Message_Omsg)
% 112.03/14.70 = { by axiom 20 (cls_Un__commute_0) R->L }
% 112.03/14.70 c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oanalz(c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_fun(tc_Message_Omsg, tc_bool))), tc_Message_Omsg)
% 112.03/14.70 = { by lemma 47 }
% 112.03/14.70 c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oanalz(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), c_Set_Oinsert(c_Message_Omsg_OCrypt(v_KAB, v_X), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_Message_Omsg), tc_fun(tc_Message_Omsg, tc_bool))), tc_Message_Omsg)
% 112.03/14.70 = { by lemma 48 }
% 112.03/14.70 c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oanalz(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), tc_fun(tc_Message_Omsg, tc_bool))), tc_Message_Omsg)
% 112.03/14.70 = { by axiom 20 (cls_Un__commute_0) R->L }
% 112.03/14.70 c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oanalz(c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool))), tc_Message_Omsg)
% 112.03/14.70 = { by axiom 23 (cls_analz_OInj_0) R->L }
% 112.03/14.70 fresh382(c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg), true2, hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 112.03/14.70 fresh382(c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg), class_Orderings_Olinorder(tc_nat), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by lemma 36 R->L }
% 112.03/14.70 fresh382(c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg), class_Orderings_Otop(tc_bool), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by lemma 37 R->L }
% 112.03/14.70 fresh382(c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg), class_HOL_Oord(tc_nat), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by lemma 38 R->L }
% 112.03/14.70 fresh382(c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg), class_HOL_Oord(tc_bool), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by lemma 39 R->L }
% 112.03/14.70 fresh382(c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg), class_Orderings_Opreorder(tc_nat), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by lemma 40 R->L }
% 112.03/14.70 fresh382(c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg), class_Orderings_Opreorder(tc_bool), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by lemma 41 R->L }
% 112.03/14.70 fresh382(c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg), class_Lattices_Odistrib__lattice(tc_nat), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by lemma 42 R->L }
% 112.03/14.70 fresh382(c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg), class_Lattices_Odistrib__lattice(tc_bool), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by lemma 43 R->L }
% 112.03/14.70 fresh382(c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg), class_Lattices_Olower__semilattice(tc_nat), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by lemma 44 R->L }
% 112.03/14.70 fresh382(c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg), class_Lattices_Olower__semilattice(tc_bool), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by lemma 45 R->L }
% 112.03/14.70 fresh382(c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by axiom 32 (cls_UnCI_0) R->L }
% 112.03/14.70 fresh382(fresh395(c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), true2, hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 112.03/14.70 fresh382(fresh395(c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), class_Orderings_Olinorder(tc_nat), hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by lemma 36 R->L }
% 112.03/14.70 fresh382(fresh395(c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), class_Orderings_Otop(tc_bool), hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by lemma 37 R->L }
% 112.03/14.70 fresh382(fresh395(c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), class_HOL_Oord(tc_nat), hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by lemma 38 R->L }
% 112.03/14.70 fresh382(fresh395(c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), class_HOL_Oord(tc_bool), hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by lemma 39 R->L }
% 112.03/14.70 fresh382(fresh395(c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), class_Orderings_Opreorder(tc_nat), hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by lemma 40 R->L }
% 112.03/14.70 fresh382(fresh395(c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), class_Orderings_Opreorder(tc_bool), hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by lemma 41 R->L }
% 112.03/14.70 fresh382(fresh395(c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), class_Lattices_Odistrib__lattice(tc_nat), hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by lemma 42 R->L }
% 112.03/14.70 fresh382(fresh395(c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), class_Lattices_Odistrib__lattice(tc_bool), hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by lemma 43 R->L }
% 112.03/14.70 fresh382(fresh395(c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), class_Lattices_Olower__semilattice(tc_nat), hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by lemma 44 R->L }
% 112.03/14.70 fresh382(fresh395(c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), class_Lattices_Olower__semilattice(tc_bool), hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by lemma 45 R->L }
% 112.03/14.70 fresh382(fresh395(c_in(hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by axiom 34 (cls_conjecture_3) }
% 112.03/14.70 fresh382(fresh395(true2, c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 112.03/14.70 fresh382(fresh395(class_Orderings_Olinorder(tc_nat), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by lemma 36 R->L }
% 112.03/14.70 fresh382(fresh395(class_Orderings_Otop(tc_bool), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by lemma 37 R->L }
% 112.03/14.70 fresh382(fresh395(class_HOL_Oord(tc_nat), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.70 = { by lemma 38 R->L }
% 112.03/14.71 fresh382(fresh395(class_HOL_Oord(tc_bool), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.71 = { by lemma 39 R->L }
% 112.03/14.71 fresh382(fresh395(class_Orderings_Opreorder(tc_nat), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.71 = { by lemma 40 R->L }
% 112.03/14.71 fresh382(fresh395(class_Orderings_Opreorder(tc_bool), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.71 = { by lemma 41 R->L }
% 112.03/14.71 fresh382(fresh395(class_Lattices_Odistrib__lattice(tc_nat), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.71 = { by lemma 42 R->L }
% 112.03/14.71 fresh382(fresh395(class_Lattices_Odistrib__lattice(tc_bool), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.71 = { by lemma 43 R->L }
% 112.03/14.71 fresh382(fresh395(class_Lattices_Olower__semilattice(tc_nat), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.71 = { by lemma 44 R->L }
% 112.03/14.71 fresh382(fresh395(class_Lattices_Olower__semilattice(tc_bool), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.71 = { by lemma 45 R->L }
% 112.03/14.71 fresh382(fresh395(c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_Message_Omsg), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.71 = { by axiom 21 (cls_UnCI_0) }
% 112.03/14.71 fresh382(true2, c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.71 = { by axiom 1 (clsarity_nat__Orderings_Olinorder) R->L }
% 112.03/14.71 fresh382(class_Orderings_Olinorder(tc_nat), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.71 = { by lemma 36 R->L }
% 112.03/14.71 fresh382(class_Orderings_Otop(tc_bool), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.71 = { by lemma 37 R->L }
% 112.03/14.71 fresh382(class_HOL_Oord(tc_nat), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.71 = { by lemma 38 R->L }
% 112.03/14.71 fresh382(class_HOL_Oord(tc_bool), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.71 = { by lemma 39 R->L }
% 112.03/14.71 fresh382(class_Orderings_Opreorder(tc_nat), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.71 = { by lemma 40 R->L }
% 112.03/14.71 fresh382(class_Orderings_Opreorder(tc_bool), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.71 = { by lemma 41 R->L }
% 112.03/14.71 fresh382(class_Lattices_Odistrib__lattice(tc_nat), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.71 = { by lemma 42 R->L }
% 112.03/14.71 fresh382(class_Lattices_Odistrib__lattice(tc_bool), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.71 = { by lemma 43 R->L }
% 112.03/14.71 fresh382(class_Lattices_Olower__semilattice(tc_nat), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.71 = { by lemma 44 R->L }
% 112.03/14.71 fresh382(class_Lattices_Olower__semilattice(tc_bool), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.71 = { by lemma 45 R->L }
% 112.03/14.71 fresh382(c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), c_NS__Shared__Mirabelle_Ons__sharedp(c_List_Olist_ONil(tc_Event_Oevent)), hAPP(c_Message_Omsg_OKey, v_K), c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy, v_evs)), c_Message_Oparts(c_Set_Oinsert(v_X, c_Orderings_Obot__class_Obot(tc_fun(tc_Message_Omsg, tc_bool)), tc_Message_Omsg)), tc_fun(tc_Message_Omsg, tc_bool)))
% 112.03/14.71 = { by axiom 14 (cls_analz_OInj_0) }
% 112.03/14.71 true2
% 112.03/14.71 % SZS output end Proof
% 112.03/14.71
% 112.03/14.71 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------