% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/NS_Shared/prob_232__5229896_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:23:56.475

% Could-be-implicit typings (7)
thf(ty_n_t__Set__Oset_It__Message__Oagent_J, type,
    set_agent : $tType).
thf(ty_n_t__List__Olist_It__Event__Oevent_J, type,
    list_event : $tType).
thf(ty_n_t__Set__Oset_It__Message__Omsg_J, type,
    set_msg : $tType).
thf(ty_n_t__Set__Oset_It__Nat__Onat_J, type,
    set_nat : $tType).
thf(ty_n_t__Message__Oagent, type,
    agent : $tType).
thf(ty_n_t__Message__Omsg, type,
    msg : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (42)
thf(sy_c_Event_Oknows, type,
    knows : agent > list_event > set_msg).
thf(sy_c_Groups_Ouminus__class_Ouminus_001_062_It__Message__Oagent_M_Eo_J, type,
    uminus875686828gent_o : (agent > $o) > agent > $o).
thf(sy_c_Groups_Ouminus__class_Ouminus_001_062_It__Message__Omsg_M_Eo_J, type,
    uminus_uminus_msg_o : (msg > $o) > msg > $o).
thf(sy_c_Groups_Ouminus__class_Ouminus_001_062_It__Nat__Onat_M_Eo_J, type,
    uminus_uminus_nat_o : (nat > $o) > nat > $o).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Message__Oagent_J, type,
    uminus1992895513_agent : set_agent > set_agent).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Message__Omsg_J, type,
    uminus676873109et_msg : set_msg > set_msg).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Nat__Onat_J, type,
    uminus814679503et_nat : set_nat > set_nat).
thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Message__Oagent_M_Eo_J, type,
    sup_sup_agent_o : (agent > $o) > (agent > $o) > agent > $o).
thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Message__Omsg_M_Eo_J, type,
    sup_sup_msg_o : (msg > $o) > (msg > $o) > msg > $o).
thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Nat__Onat_M_Eo_J, type,
    sup_sup_nat_o : (nat > $o) > (nat > $o) > nat > $o).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Message__Oagent_J, type,
    sup_sup_set_agent : set_agent > set_agent > set_agent).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Message__Omsg_J, type,
    sup_sup_set_msg : set_msg > set_msg > set_msg).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J, type,
    sup_sup_set_nat : set_nat > set_nat > set_nat).
thf(sy_c_List_Olist_ONil_001t__Event__Oevent, type,
    nil_event : list_event).
thf(sy_c_Message_Oagent_OSpy, type,
    spy : agent).
thf(sy_c_Message_Oanalz, type,
    analz : set_msg > set_msg).
thf(sy_c_Message_Omsg_OKey, type,
    key : nat > msg).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Message__Oagent_J, type,
    ord_le722097072_agent : set_agent > set_agent > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Message__Omsg_J, type,
    ord_less_eq_set_msg : set_msg > set_msg > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J, type,
    ord_less_eq_set_nat : set_nat > set_nat > $o).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Message__Oagent_M_Eo_J, type,
    top_top_agent_o : agent > $o).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Message__Omsg_M_Eo_J, type,
    top_top_msg_o : msg > $o).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Nat__Onat_M_Eo_J, type,
    top_top_nat_o : nat > $o).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Message__Oagent_J, type,
    top_top_set_agent : set_agent).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Message__Omsg_J, type,
    top_top_set_msg : set_msg).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J, type,
    top_top_set_nat : set_nat).
thf(sy_c_Public_OshrK, type,
    shrK : agent > nat).
thf(sy_c_Set_OCollect_001t__Message__Oagent, type,
    collect_agent : (agent > $o) > set_agent).
thf(sy_c_Set_OCollect_001t__Message__Omsg, type,
    collect_msg : (msg > $o) > set_msg).
thf(sy_c_Set_OCollect_001t__Nat__Onat, type,
    collect_nat : (nat > $o) > set_nat).
thf(sy_c_Set_Oimage_001t__Message__Oagent_001t__Message__Oagent, type,
    image_agent_agent : (agent > agent) > set_agent > set_agent).
thf(sy_c_Set_Oimage_001t__Message__Oagent_001t__Message__Omsg, type,
    image_agent_msg : (agent > msg) > set_agent > set_msg).
thf(sy_c_Set_Oimage_001t__Message__Oagent_001t__Nat__Onat, type,
    image_agent_nat : (agent > nat) > set_agent > set_nat).
thf(sy_c_Set_Oimage_001t__Message__Omsg_001t__Message__Oagent, type,
    image_msg_agent : (msg > agent) > set_msg > set_agent).
thf(sy_c_Set_Oimage_001t__Message__Omsg_001t__Message__Omsg, type,
    image_msg_msg : (msg > msg) > set_msg > set_msg).
thf(sy_c_Set_Oimage_001t__Message__Omsg_001t__Nat__Onat, type,
    image_msg_nat : (msg > nat) > set_msg > set_nat).
thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Message__Oagent, type,
    image_nat_agent : (nat > agent) > set_nat > set_agent).
thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Message__Omsg, type,
    image_nat_msg : (nat > msg) > set_nat > set_msg).
thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat, type,
    image_nat_nat : (nat > nat) > set_nat > set_nat).
thf(sy_c_member_001t__Message__Oagent, type,
    member_agent : agent > set_agent > $o).
thf(sy_c_member_001t__Message__Omsg, type,
    member_msg : msg > set_msg > $o).
thf(sy_c_member_001t__Nat__Onat, type,
    member_nat : nat > set_nat > $o).

% Relevant facts (249)
thf(fact_0_analz__image__Key, axiom,
    ((![N : set_nat]: ((analz @ (image_nat_msg @ key @ N)) = (image_nat_msg @ key @ N))))). % analz_image_Key
thf(fact_1_shrK__in__knows, axiom,
    ((![A : agent, Evs : list_event]: (member_msg @ (key @ (shrK @ A)) @ (knows @ A @ Evs))))). % shrK_in_knows
thf(fact_2_compl__sup__top, axiom,
    ((![X : set_msg]: ((sup_sup_set_msg @ (uminus676873109et_msg @ X) @ X) = top_top_set_msg)))). % compl_sup_top
thf(fact_3_compl__sup__top, axiom,
    ((![X : set_agent]: ((sup_sup_set_agent @ (uminus1992895513_agent @ X) @ X) = top_top_set_agent)))). % compl_sup_top
thf(fact_4_compl__sup__top, axiom,
    ((![X : set_nat]: ((sup_sup_set_nat @ (uminus814679503et_nat @ X) @ X) = top_top_set_nat)))). % compl_sup_top
thf(fact_5_sup__compl__top, axiom,
    ((![X : set_msg]: ((sup_sup_set_msg @ X @ (uminus676873109et_msg @ X)) = top_top_set_msg)))). % sup_compl_top
thf(fact_6_sup__compl__top, axiom,
    ((![X : set_agent]: ((sup_sup_set_agent @ X @ (uminus1992895513_agent @ X)) = top_top_set_agent)))). % sup_compl_top
thf(fact_7_sup__compl__top, axiom,
    ((![X : set_nat]: ((sup_sup_set_nat @ X @ (uminus814679503et_nat @ X)) = top_top_set_nat)))). % sup_compl_top
thf(fact_8_sup__compl__top__left1, axiom,
    ((![X : set_msg, Y : set_msg]: ((sup_sup_set_msg @ (uminus676873109et_msg @ X) @ (sup_sup_set_msg @ X @ Y)) = top_top_set_msg)))). % sup_compl_top_left1
thf(fact_9_sup__compl__top__left1, axiom,
    ((![X : set_agent, Y : set_agent]: ((sup_sup_set_agent @ (uminus1992895513_agent @ X) @ (sup_sup_set_agent @ X @ Y)) = top_top_set_agent)))). % sup_compl_top_left1
thf(fact_10_sup__compl__top__left1, axiom,
    ((![X : set_nat, Y : set_nat]: ((sup_sup_set_nat @ (uminus814679503et_nat @ X) @ (sup_sup_set_nat @ X @ Y)) = top_top_set_nat)))). % sup_compl_top_left1
thf(fact_11_sup__compl__top__left2, axiom,
    ((![X : set_msg, Y : set_msg]: ((sup_sup_set_msg @ X @ (sup_sup_set_msg @ (uminus676873109et_msg @ X) @ Y)) = top_top_set_msg)))). % sup_compl_top_left2
thf(fact_12_sup__compl__top__left2, axiom,
    ((![X : set_agent, Y : set_agent]: ((sup_sup_set_agent @ X @ (sup_sup_set_agent @ (uminus1992895513_agent @ X) @ Y)) = top_top_set_agent)))). % sup_compl_top_left2
thf(fact_13_sup__compl__top__left2, axiom,
    ((![X : set_nat, Y : set_nat]: ((sup_sup_set_nat @ X @ (sup_sup_set_nat @ (uminus814679503et_nat @ X) @ Y)) = top_top_set_nat)))). % sup_compl_top_left2
thf(fact_14_shrK__image__eq, axiom,
    ((![X : agent, AA : set_agent]: ((member_nat @ (shrK @ X) @ (image_agent_nat @ shrK @ AA)) = (member_agent @ X @ AA))))). % shrK_image_eq
thf(fact_15_Key__image__eq, axiom,
    ((![X : nat, A : set_nat]: ((member_msg @ (key @ X) @ (image_nat_msg @ key @ A)) = (member_nat @ X @ A))))). % Key_image_eq
thf(fact_16_analz__analz__Un, axiom,
    ((![G : set_msg, H : set_msg]: ((analz @ (sup_sup_set_msg @ (analz @ G) @ H)) = (analz @ (sup_sup_set_msg @ G @ H)))))). % analz_analz_Un
thf(fact_17_Compl__anti__mono, axiom,
    ((![A : set_agent, B : set_agent]: ((ord_le722097072_agent @ A @ B) => (ord_le722097072_agent @ (uminus1992895513_agent @ B) @ (uminus1992895513_agent @ A)))))). % Compl_anti_mono
thf(fact_18_Compl__anti__mono, axiom,
    ((![A : set_nat, B : set_nat]: ((ord_less_eq_set_nat @ A @ B) => (ord_less_eq_set_nat @ (uminus814679503et_nat @ B) @ (uminus814679503et_nat @ A)))))). % Compl_anti_mono
thf(fact_19_Compl__anti__mono, axiom,
    ((![A : set_msg, B : set_msg]: ((ord_less_eq_set_msg @ A @ B) => (ord_less_eq_set_msg @ (uminus676873109et_msg @ B) @ (uminus676873109et_msg @ A)))))). % Compl_anti_mono
thf(fact_20_Compl__subset__Compl__iff, axiom,
    ((![A : set_agent, B : set_agent]: ((ord_le722097072_agent @ (uminus1992895513_agent @ A) @ (uminus1992895513_agent @ B)) = (ord_le722097072_agent @ B @ A))))). % Compl_subset_Compl_iff
thf(fact_21_Compl__subset__Compl__iff, axiom,
    ((![A : set_nat, B : set_nat]: ((ord_less_eq_set_nat @ (uminus814679503et_nat @ A) @ (uminus814679503et_nat @ B)) = (ord_less_eq_set_nat @ B @ A))))). % Compl_subset_Compl_iff
thf(fact_22_Compl__subset__Compl__iff, axiom,
    ((![A : set_msg, B : set_msg]: ((ord_less_eq_set_msg @ (uminus676873109et_msg @ A) @ (uminus676873109et_msg @ B)) = (ord_less_eq_set_msg @ B @ A))))). % Compl_subset_Compl_iff
thf(fact_23_Un__subset__iff, axiom,
    ((![A : set_agent, B : set_agent, C : set_agent]: ((ord_le722097072_agent @ (sup_sup_set_agent @ A @ B) @ C) = (((ord_le722097072_agent @ A @ C)) & ((ord_le722097072_agent @ B @ C))))))). % Un_subset_iff
thf(fact_24_Un__subset__iff, axiom,
    ((![A : set_nat, B : set_nat, C : set_nat]: ((ord_less_eq_set_nat @ (sup_sup_set_nat @ A @ B) @ C) = (((ord_less_eq_set_nat @ A @ C)) & ((ord_less_eq_set_nat @ B @ C))))))). % Un_subset_iff
thf(fact_25_Un__subset__iff, axiom,
    ((![A : set_msg, B : set_msg, C : set_msg]: ((ord_less_eq_set_msg @ (sup_sup_set_msg @ A @ B) @ C) = (((ord_less_eq_set_msg @ A @ C)) & ((ord_less_eq_set_msg @ B @ C))))))). % Un_subset_iff
thf(fact_26_image__eqI, axiom,
    ((![B2 : msg, F : msg > msg, X : msg, A : set_msg]: ((B2 = (F @ X)) => ((member_msg @ X @ A) => (member_msg @ B2 @ (image_msg_msg @ F @ A))))))). % image_eqI
thf(fact_27_image__eqI, axiom,
    ((![B2 : nat, F : msg > nat, X : msg, A : set_msg]: ((B2 = (F @ X)) => ((member_msg @ X @ A) => (member_nat @ B2 @ (image_msg_nat @ F @ A))))))). % image_eqI
thf(fact_28_image__eqI, axiom,
    ((![B2 : agent, F : msg > agent, X : msg, A : set_msg]: ((B2 = (F @ X)) => ((member_msg @ X @ A) => (member_agent @ B2 @ (image_msg_agent @ F @ A))))))). % image_eqI
thf(fact_29_image__eqI, axiom,
    ((![B2 : msg, F : nat > msg, X : nat, A : set_nat]: ((B2 = (F @ X)) => ((member_nat @ X @ A) => (member_msg @ B2 @ (image_nat_msg @ F @ A))))))). % image_eqI
thf(fact_30_image__eqI, axiom,
    ((![B2 : nat, F : nat > nat, X : nat, A : set_nat]: ((B2 = (F @ X)) => ((member_nat @ X @ A) => (member_nat @ B2 @ (image_nat_nat @ F @ A))))))). % image_eqI
thf(fact_31_image__eqI, axiom,
    ((![B2 : agent, F : nat > agent, X : nat, A : set_nat]: ((B2 = (F @ X)) => ((member_nat @ X @ A) => (member_agent @ B2 @ (image_nat_agent @ F @ A))))))). % image_eqI
thf(fact_32_image__eqI, axiom,
    ((![B2 : msg, F : agent > msg, X : agent, A : set_agent]: ((B2 = (F @ X)) => ((member_agent @ X @ A) => (member_msg @ B2 @ (image_agent_msg @ F @ A))))))). % image_eqI
thf(fact_33_image__eqI, axiom,
    ((![B2 : nat, F : agent > nat, X : agent, A : set_agent]: ((B2 = (F @ X)) => ((member_agent @ X @ A) => (member_nat @ B2 @ (image_agent_nat @ F @ A))))))). % image_eqI
thf(fact_34_image__eqI, axiom,
    ((![B2 : agent, F : agent > agent, X : agent, A : set_agent]: ((B2 = (F @ X)) => ((member_agent @ X @ A) => (member_agent @ B2 @ (image_agent_agent @ F @ A))))))). % image_eqI
thf(fact_35_compl__eq__compl__iff, axiom,
    ((![X : set_nat, Y : set_nat]: (((uminus814679503et_nat @ X) = (uminus814679503et_nat @ Y)) = (X = Y))))). % compl_eq_compl_iff
thf(fact_36_compl__eq__compl__iff, axiom,
    ((![X : set_agent, Y : set_agent]: (((uminus1992895513_agent @ X) = (uminus1992895513_agent @ Y)) = (X = Y))))). % compl_eq_compl_iff
thf(fact_37_compl__eq__compl__iff, axiom,
    ((![X : set_msg, Y : set_msg]: (((uminus676873109et_msg @ X) = (uminus676873109et_msg @ Y)) = (X = Y))))). % compl_eq_compl_iff
thf(fact_38_double__compl, axiom,
    ((![X : set_nat]: ((uminus814679503et_nat @ (uminus814679503et_nat @ X)) = X)))). % double_compl
thf(fact_39_double__compl, axiom,
    ((![X : set_agent]: ((uminus1992895513_agent @ (uminus1992895513_agent @ X)) = X)))). % double_compl
thf(fact_40_double__compl, axiom,
    ((![X : set_msg]: ((uminus676873109et_msg @ (uminus676873109et_msg @ X)) = X)))). % double_compl
thf(fact_41_subset__antisym, axiom,
    ((![A : set_nat, B : set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ B @ A) => (A = B)))))). % subset_antisym
thf(fact_42_subset__antisym, axiom,
    ((![A : set_msg, B : set_msg]: ((ord_less_eq_set_msg @ A @ B) => ((ord_less_eq_set_msg @ B @ A) => (A = B)))))). % subset_antisym
thf(fact_43_subsetI, axiom,
    ((![A : set_agent, B : set_agent]: ((![X2 : agent]: ((member_agent @ X2 @ A) => (member_agent @ X2 @ B))) => (ord_le722097072_agent @ A @ B))))). % subsetI
thf(fact_44_subsetI, axiom,
    ((![A : set_nat, B : set_nat]: ((![X2 : nat]: ((member_nat @ X2 @ A) => (member_nat @ X2 @ B))) => (ord_less_eq_set_nat @ A @ B))))). % subsetI
thf(fact_45_subsetI, axiom,
    ((![A : set_msg, B : set_msg]: ((![X2 : msg]: ((member_msg @ X2 @ A) => (member_msg @ X2 @ B))) => (ord_less_eq_set_msg @ A @ B))))). % subsetI
thf(fact_46_sup_Oright__idem, axiom,
    ((![A2 : set_msg, B2 : set_msg]: ((sup_sup_set_msg @ (sup_sup_set_msg @ A2 @ B2) @ B2) = (sup_sup_set_msg @ A2 @ B2))))). % sup.right_idem
thf(fact_47_sup_Oright__idem, axiom,
    ((![A2 : set_nat, B2 : set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ A2 @ B2) @ B2) = (sup_sup_set_nat @ A2 @ B2))))). % sup.right_idem
thf(fact_48_sup_Oright__idem, axiom,
    ((![A2 : set_agent, B2 : set_agent]: ((sup_sup_set_agent @ (sup_sup_set_agent @ A2 @ B2) @ B2) = (sup_sup_set_agent @ A2 @ B2))))). % sup.right_idem
thf(fact_49_sup__left__idem, axiom,
    ((![X : set_msg, Y : set_msg]: ((sup_sup_set_msg @ X @ (sup_sup_set_msg @ X @ Y)) = (sup_sup_set_msg @ X @ Y))))). % sup_left_idem
thf(fact_50_sup__left__idem, axiom,
    ((![X : set_nat, Y : set_nat]: ((sup_sup_set_nat @ X @ (sup_sup_set_nat @ X @ Y)) = (sup_sup_set_nat @ X @ Y))))). % sup_left_idem
thf(fact_51_sup__left__idem, axiom,
    ((![X : set_agent, Y : set_agent]: ((sup_sup_set_agent @ X @ (sup_sup_set_agent @ X @ Y)) = (sup_sup_set_agent @ X @ Y))))). % sup_left_idem
thf(fact_52_sup_Oleft__idem, axiom,
    ((![A2 : set_msg, B2 : set_msg]: ((sup_sup_set_msg @ A2 @ (sup_sup_set_msg @ A2 @ B2)) = (sup_sup_set_msg @ A2 @ B2))))). % sup.left_idem
thf(fact_53_sup_Oleft__idem, axiom,
    ((![A2 : set_nat, B2 : set_nat]: ((sup_sup_set_nat @ A2 @ (sup_sup_set_nat @ A2 @ B2)) = (sup_sup_set_nat @ A2 @ B2))))). % sup.left_idem
thf(fact_54_sup_Oleft__idem, axiom,
    ((![A2 : set_agent, B2 : set_agent]: ((sup_sup_set_agent @ A2 @ (sup_sup_set_agent @ A2 @ B2)) = (sup_sup_set_agent @ A2 @ B2))))). % sup.left_idem
thf(fact_55_sup__idem, axiom,
    ((![X : set_msg]: ((sup_sup_set_msg @ X @ X) = X)))). % sup_idem
thf(fact_56_sup__idem, axiom,
    ((![X : set_nat]: ((sup_sup_set_nat @ X @ X) = X)))). % sup_idem
thf(fact_57_sup__idem, axiom,
    ((![X : set_agent]: ((sup_sup_set_agent @ X @ X) = X)))). % sup_idem
thf(fact_58_sup_Oidem, axiom,
    ((![A2 : set_msg]: ((sup_sup_set_msg @ A2 @ A2) = A2)))). % sup.idem
thf(fact_59_sup_Oidem, axiom,
    ((![A2 : set_nat]: ((sup_sup_set_nat @ A2 @ A2) = A2)))). % sup.idem
thf(fact_60_sup_Oidem, axiom,
    ((![A2 : set_agent]: ((sup_sup_set_agent @ A2 @ A2) = A2)))). % sup.idem
thf(fact_61_UNIV__I, axiom,
    ((![X : agent]: (member_agent @ X @ top_top_set_agent)))). % UNIV_I
thf(fact_62_UNIV__I, axiom,
    ((![X : nat]: (member_nat @ X @ top_top_set_nat)))). % UNIV_I
thf(fact_63_UNIV__I, axiom,
    ((![X : msg]: (member_msg @ X @ top_top_set_msg)))). % UNIV_I
thf(fact_64_Un__iff, axiom,
    ((![C2 : msg, A : set_msg, B : set_msg]: ((member_msg @ C2 @ (sup_sup_set_msg @ A @ B)) = (((member_msg @ C2 @ A)) | ((member_msg @ C2 @ B))))))). % Un_iff
thf(fact_65_Un__iff, axiom,
    ((![C2 : nat, A : set_nat, B : set_nat]: ((member_nat @ C2 @ (sup_sup_set_nat @ A @ B)) = (((member_nat @ C2 @ A)) | ((member_nat @ C2 @ B))))))). % Un_iff
thf(fact_66_Un__iff, axiom,
    ((![C2 : agent, A : set_agent, B : set_agent]: ((member_agent @ C2 @ (sup_sup_set_agent @ A @ B)) = (((member_agent @ C2 @ A)) | ((member_agent @ C2 @ B))))))). % Un_iff
thf(fact_67_UnCI, axiom,
    ((![C2 : msg, B : set_msg, A : set_msg]: (((~ ((member_msg @ C2 @ B))) => (member_msg @ C2 @ A)) => (member_msg @ C2 @ (sup_sup_set_msg @ A @ B)))))). % UnCI
thf(fact_68_UnCI, axiom,
    ((![C2 : nat, B : set_nat, A : set_nat]: (((~ ((member_nat @ C2 @ B))) => (member_nat @ C2 @ A)) => (member_nat @ C2 @ (sup_sup_set_nat @ A @ B)))))). % UnCI
thf(fact_69_UnCI, axiom,
    ((![C2 : agent, B : set_agent, A : set_agent]: (((~ ((member_agent @ C2 @ B))) => (member_agent @ C2 @ A)) => (member_agent @ C2 @ (sup_sup_set_agent @ A @ B)))))). % UnCI
thf(fact_70_analz__subset__iff, axiom,
    ((![G : set_msg, H : set_msg]: ((ord_less_eq_set_msg @ (analz @ G) @ (analz @ H)) = (ord_less_eq_set_msg @ G @ (analz @ H)))))). % analz_subset_iff
thf(fact_71_analz__idem, axiom,
    ((![H : set_msg]: ((analz @ (analz @ H)) = (analz @ H))))). % analz_idem
thf(fact_72_msg_Oinject_I4_J, axiom,
    ((![X4 : nat, Y4 : nat]: (((key @ X4) = (key @ Y4)) = (X4 = Y4))))). % msg.inject(4)
thf(fact_73_Compl__eq__Compl__iff, axiom,
    ((![A : set_nat, B : set_nat]: (((uminus814679503et_nat @ A) = (uminus814679503et_nat @ B)) = (A = B))))). % Compl_eq_Compl_iff
thf(fact_74_Compl__eq__Compl__iff, axiom,
    ((![A : set_agent, B : set_agent]: (((uminus1992895513_agent @ A) = (uminus1992895513_agent @ B)) = (A = B))))). % Compl_eq_Compl_iff
thf(fact_75_Compl__eq__Compl__iff, axiom,
    ((![A : set_msg, B : set_msg]: (((uminus676873109et_msg @ A) = (uminus676873109et_msg @ B)) = (A = B))))). % Compl_eq_Compl_iff
thf(fact_76_Compl__iff, axiom,
    ((![C2 : nat, A : set_nat]: ((member_nat @ C2 @ (uminus814679503et_nat @ A)) = (~ ((member_nat @ C2 @ A))))))). % Compl_iff
thf(fact_77_Compl__iff, axiom,
    ((![C2 : agent, A : set_agent]: ((member_agent @ C2 @ (uminus1992895513_agent @ A)) = (~ ((member_agent @ C2 @ A))))))). % Compl_iff
thf(fact_78_Compl__iff, axiom,
    ((![C2 : msg, A : set_msg]: ((member_msg @ C2 @ (uminus676873109et_msg @ A)) = (~ ((member_msg @ C2 @ A))))))). % Compl_iff
thf(fact_79_ComplI, axiom,
    ((![C2 : nat, A : set_nat]: ((~ ((member_nat @ C2 @ A))) => (member_nat @ C2 @ (uminus814679503et_nat @ A)))))). % ComplI
thf(fact_80_ComplI, axiom,
    ((![C2 : agent, A : set_agent]: ((~ ((member_agent @ C2 @ A))) => (member_agent @ C2 @ (uminus1992895513_agent @ A)))))). % ComplI
thf(fact_81_ComplI, axiom,
    ((![C2 : msg, A : set_msg]: ((~ ((member_msg @ C2 @ A))) => (member_msg @ C2 @ (uminus676873109et_msg @ A)))))). % ComplI
thf(fact_82_shrK__injective, axiom,
    ((![X : agent, Y : agent]: (((shrK @ X) = (shrK @ Y)) = (X = Y))))). % shrK_injective
thf(fact_83_compl__le__compl__iff, axiom,
    ((![X : set_agent, Y : set_agent]: ((ord_le722097072_agent @ (uminus1992895513_agent @ X) @ (uminus1992895513_agent @ Y)) = (ord_le722097072_agent @ Y @ X))))). % compl_le_compl_iff
thf(fact_84_compl__le__compl__iff, axiom,
    ((![X : set_nat, Y : set_nat]: ((ord_less_eq_set_nat @ (uminus814679503et_nat @ X) @ (uminus814679503et_nat @ Y)) = (ord_less_eq_set_nat @ Y @ X))))). % compl_le_compl_iff
thf(fact_85_compl__le__compl__iff, axiom,
    ((![X : set_msg, Y : set_msg]: ((ord_less_eq_set_msg @ (uminus676873109et_msg @ X) @ (uminus676873109et_msg @ Y)) = (ord_less_eq_set_msg @ Y @ X))))). % compl_le_compl_iff
thf(fact_86_sup_Obounded__iff, axiom,
    ((![B2 : set_agent, C2 : set_agent, A2 : set_agent]: ((ord_le722097072_agent @ (sup_sup_set_agent @ B2 @ C2) @ A2) = (((ord_le722097072_agent @ B2 @ A2)) & ((ord_le722097072_agent @ C2 @ A2))))))). % sup.bounded_iff
thf(fact_87_sup_Obounded__iff, axiom,
    ((![B2 : set_nat, C2 : set_nat, A2 : set_nat]: ((ord_less_eq_set_nat @ (sup_sup_set_nat @ B2 @ C2) @ A2) = (((ord_less_eq_set_nat @ B2 @ A2)) & ((ord_less_eq_set_nat @ C2 @ A2))))))). % sup.bounded_iff
thf(fact_88_sup_Obounded__iff, axiom,
    ((![B2 : set_msg, C2 : set_msg, A2 : set_msg]: ((ord_less_eq_set_msg @ (sup_sup_set_msg @ B2 @ C2) @ A2) = (((ord_less_eq_set_msg @ B2 @ A2)) & ((ord_less_eq_set_msg @ C2 @ A2))))))). % sup.bounded_iff
thf(fact_89_le__sup__iff, axiom,
    ((![X : set_agent, Y : set_agent, Z : set_agent]: ((ord_le722097072_agent @ (sup_sup_set_agent @ X @ Y) @ Z) = (((ord_le722097072_agent @ X @ Z)) & ((ord_le722097072_agent @ Y @ Z))))))). % le_sup_iff
thf(fact_90_le__sup__iff, axiom,
    ((![X : set_nat, Y : set_nat, Z : set_nat]: ((ord_less_eq_set_nat @ (sup_sup_set_nat @ X @ Y) @ Z) = (((ord_less_eq_set_nat @ X @ Z)) & ((ord_less_eq_set_nat @ Y @ Z))))))). % le_sup_iff
thf(fact_91_le__sup__iff, axiom,
    ((![X : set_msg, Y : set_msg, Z : set_msg]: ((ord_less_eq_set_msg @ (sup_sup_set_msg @ X @ Y) @ Z) = (((ord_less_eq_set_msg @ X @ Z)) & ((ord_less_eq_set_msg @ Y @ Z))))))). % le_sup_iff
thf(fact_92_sup__top__right, axiom,
    ((![X : set_agent]: ((sup_sup_set_agent @ X @ top_top_set_agent) = top_top_set_agent)))). % sup_top_right
thf(fact_93_sup__top__right, axiom,
    ((![X : set_nat]: ((sup_sup_set_nat @ X @ top_top_set_nat) = top_top_set_nat)))). % sup_top_right
thf(fact_94_sup__top__right, axiom,
    ((![X : set_msg]: ((sup_sup_set_msg @ X @ top_top_set_msg) = top_top_set_msg)))). % sup_top_right
thf(fact_95_sup__top__left, axiom,
    ((![X : set_agent]: ((sup_sup_set_agent @ top_top_set_agent @ X) = top_top_set_agent)))). % sup_top_left
thf(fact_96_sup__top__left, axiom,
    ((![X : set_nat]: ((sup_sup_set_nat @ top_top_set_nat @ X) = top_top_set_nat)))). % sup_top_left
thf(fact_97_sup__top__left, axiom,
    ((![X : set_msg]: ((sup_sup_set_msg @ top_top_set_msg @ X) = top_top_set_msg)))). % sup_top_left
thf(fact_98_top__set__def, axiom,
    ((top_top_set_agent = (collect_agent @ top_top_agent_o)))). % top_set_def
thf(fact_99_top__set__def, axiom,
    ((top_top_set_nat = (collect_nat @ top_top_nat_o)))). % top_set_def
thf(fact_100_top__set__def, axiom,
    ((top_top_set_msg = (collect_msg @ top_top_msg_o)))). % top_set_def
thf(fact_101_analz__increasing, axiom,
    ((![H : set_msg]: (ord_less_eq_set_msg @ H @ (analz @ H))))). % analz_increasing
thf(fact_102_analz__trans, axiom,
    ((![X3 : msg, G : set_msg, H : set_msg]: ((member_msg @ X3 @ (analz @ G)) => ((ord_less_eq_set_msg @ G @ (analz @ H)) => (member_msg @ X3 @ (analz @ H))))))). % analz_trans
thf(fact_103_analz__mono, axiom,
    ((![G : set_msg, H : set_msg]: ((ord_less_eq_set_msg @ G @ H) => (ord_less_eq_set_msg @ (analz @ G) @ (analz @ H)))))). % analz_mono
thf(fact_104_sup__set__def, axiom,
    ((sup_sup_set_msg = (^[A3 : set_msg]: (^[B3 : set_msg]: (collect_msg @ (sup_sup_msg_o @ (^[X5 : msg]: (member_msg @ X5 @ A3)) @ (^[X5 : msg]: (member_msg @ X5 @ B3))))))))). % sup_set_def
thf(fact_105_sup__set__def, axiom,
    ((sup_sup_set_nat = (^[A3 : set_nat]: (^[B3 : set_nat]: (collect_nat @ (sup_sup_nat_o @ (^[X5 : nat]: (member_nat @ X5 @ A3)) @ (^[X5 : nat]: (member_nat @ X5 @ B3))))))))). % sup_set_def
thf(fact_106_sup__set__def, axiom,
    ((sup_sup_set_agent = (^[A3 : set_agent]: (^[B3 : set_agent]: (collect_agent @ (sup_sup_agent_o @ (^[X5 : agent]: (member_agent @ X5 @ A3)) @ (^[X5 : agent]: (member_agent @ X5 @ B3))))))))). % sup_set_def
thf(fact_107_mem__Collect__eq, axiom,
    ((![A2 : msg, P : msg > $o]: ((member_msg @ A2 @ (collect_msg @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_108_mem__Collect__eq, axiom,
    ((![A2 : nat, P : nat > $o]: ((member_nat @ A2 @ (collect_nat @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_109_mem__Collect__eq, axiom,
    ((![A2 : agent, P : agent > $o]: ((member_agent @ A2 @ (collect_agent @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_110_Collect__mem__eq, axiom,
    ((![A : set_msg]: ((collect_msg @ (^[X5 : msg]: (member_msg @ X5 @ A))) = A)))). % Collect_mem_eq
thf(fact_111_Collect__mem__eq, axiom,
    ((![A : set_nat]: ((collect_nat @ (^[X5 : nat]: (member_nat @ X5 @ A))) = A)))). % Collect_mem_eq
thf(fact_112_Collect__mem__eq, axiom,
    ((![A : set_agent]: ((collect_agent @ (^[X5 : agent]: (member_agent @ X5 @ A))) = A)))). % Collect_mem_eq
thf(fact_113_uminus__set__def, axiom,
    ((uminus814679503et_nat = (^[A3 : set_nat]: (collect_nat @ (uminus_uminus_nat_o @ (^[X5 : nat]: (member_nat @ X5 @ A3)))))))). % uminus_set_def
thf(fact_114_uminus__set__def, axiom,
    ((uminus1992895513_agent = (^[A3 : set_agent]: (collect_agent @ (uminus875686828gent_o @ (^[X5 : agent]: (member_agent @ X5 @ A3)))))))). % uminus_set_def
thf(fact_115_uminus__set__def, axiom,
    ((uminus676873109et_msg = (^[A3 : set_msg]: (collect_msg @ (uminus_uminus_msg_o @ (^[X5 : msg]: (member_msg @ X5 @ A3)))))))). % uminus_set_def
thf(fact_116_analz__subset__cong, axiom,
    ((![G : set_msg, G2 : set_msg, H : set_msg, H2 : set_msg]: ((ord_less_eq_set_msg @ (analz @ G) @ (analz @ G2)) => ((ord_less_eq_set_msg @ (analz @ H) @ (analz @ H2)) => (ord_less_eq_set_msg @ (analz @ (sup_sup_set_msg @ G @ H)) @ (analz @ (sup_sup_set_msg @ G2 @ H2)))))))). % analz_subset_cong
thf(fact_117_analz__Un, axiom,
    ((![G : set_msg, H : set_msg]: (ord_less_eq_set_msg @ (sup_sup_set_msg @ (analz @ G) @ (analz @ H)) @ (analz @ (sup_sup_set_msg @ G @ H)))))). % analz_Un
thf(fact_118_rev__image__eqI, axiom,
    ((![X : msg, A : set_msg, B2 : msg, F : msg > msg]: ((member_msg @ X @ A) => ((B2 = (F @ X)) => (member_msg @ B2 @ (image_msg_msg @ F @ A))))))). % rev_image_eqI
thf(fact_119_rev__image__eqI, axiom,
    ((![X : msg, A : set_msg, B2 : nat, F : msg > nat]: ((member_msg @ X @ A) => ((B2 = (F @ X)) => (member_nat @ B2 @ (image_msg_nat @ F @ A))))))). % rev_image_eqI
thf(fact_120_rev__image__eqI, axiom,
    ((![X : msg, A : set_msg, B2 : agent, F : msg > agent]: ((member_msg @ X @ A) => ((B2 = (F @ X)) => (member_agent @ B2 @ (image_msg_agent @ F @ A))))))). % rev_image_eqI
thf(fact_121_rev__image__eqI, axiom,
    ((![X : nat, A : set_nat, B2 : msg, F : nat > msg]: ((member_nat @ X @ A) => ((B2 = (F @ X)) => (member_msg @ B2 @ (image_nat_msg @ F @ A))))))). % rev_image_eqI
thf(fact_122_rev__image__eqI, axiom,
    ((![X : nat, A : set_nat, B2 : nat, F : nat > nat]: ((member_nat @ X @ A) => ((B2 = (F @ X)) => (member_nat @ B2 @ (image_nat_nat @ F @ A))))))). % rev_image_eqI
thf(fact_123_rev__image__eqI, axiom,
    ((![X : nat, A : set_nat, B2 : agent, F : nat > agent]: ((member_nat @ X @ A) => ((B2 = (F @ X)) => (member_agent @ B2 @ (image_nat_agent @ F @ A))))))). % rev_image_eqI
thf(fact_124_rev__image__eqI, axiom,
    ((![X : agent, A : set_agent, B2 : msg, F : agent > msg]: ((member_agent @ X @ A) => ((B2 = (F @ X)) => (member_msg @ B2 @ (image_agent_msg @ F @ A))))))). % rev_image_eqI
thf(fact_125_rev__image__eqI, axiom,
    ((![X : agent, A : set_agent, B2 : nat, F : agent > nat]: ((member_agent @ X @ A) => ((B2 = (F @ X)) => (member_nat @ B2 @ (image_agent_nat @ F @ A))))))). % rev_image_eqI
thf(fact_126_rev__image__eqI, axiom,
    ((![X : agent, A : set_agent, B2 : agent, F : agent > agent]: ((member_agent @ X @ A) => ((B2 = (F @ X)) => (member_agent @ B2 @ (image_agent_agent @ F @ A))))))). % rev_image_eqI
thf(fact_127_ball__imageD, axiom,
    ((![F : agent > nat, A : set_agent, P : nat > $o]: ((![X2 : nat]: ((member_nat @ X2 @ (image_agent_nat @ F @ A)) => (P @ X2))) => (![X6 : agent]: ((member_agent @ X6 @ A) => (P @ (F @ X6)))))))). % ball_imageD
thf(fact_128_ball__imageD, axiom,
    ((![F : nat > msg, A : set_nat, P : msg > $o]: ((![X2 : msg]: ((member_msg @ X2 @ (image_nat_msg @ F @ A)) => (P @ X2))) => (![X6 : nat]: ((member_nat @ X6 @ A) => (P @ (F @ X6)))))))). % ball_imageD
thf(fact_129_image__cong, axiom,
    ((![M : set_nat, N : set_nat, F : nat > msg, G3 : nat > msg]: ((M = N) => ((![X2 : nat]: ((member_nat @ X2 @ N) => ((F @ X2) = (G3 @ X2)))) => ((image_nat_msg @ F @ M) = (image_nat_msg @ G3 @ N))))))). % image_cong
thf(fact_130_image__cong, axiom,
    ((![M : set_agent, N : set_agent, F : agent > nat, G3 : agent > nat]: ((M = N) => ((![X2 : agent]: ((member_agent @ X2 @ N) => ((F @ X2) = (G3 @ X2)))) => ((image_agent_nat @ F @ M) = (image_agent_nat @ G3 @ N))))))). % image_cong
thf(fact_131_bex__imageD, axiom,
    ((![F : agent > nat, A : set_agent, P : nat > $o]: ((?[X6 : nat]: ((member_nat @ X6 @ (image_agent_nat @ F @ A)) & (P @ X6))) => (?[X2 : agent]: ((member_agent @ X2 @ A) & (P @ (F @ X2)))))))). % bex_imageD
thf(fact_132_bex__imageD, axiom,
    ((![F : nat > msg, A : set_nat, P : msg > $o]: ((?[X6 : msg]: ((member_msg @ X6 @ (image_nat_msg @ F @ A)) & (P @ X6))) => (?[X2 : nat]: ((member_nat @ X2 @ A) & (P @ (F @ X2)))))))). % bex_imageD
thf(fact_133_image__iff, axiom,
    ((![Z : msg, F : nat > msg, A : set_nat]: ((member_msg @ Z @ (image_nat_msg @ F @ A)) = (?[X5 : nat]: (((member_nat @ X5 @ A)) & ((Z = (F @ X5))))))))). % image_iff
thf(fact_134_image__iff, axiom,
    ((![Z : nat, F : agent > nat, A : set_agent]: ((member_nat @ Z @ (image_agent_nat @ F @ A)) = (?[X5 : agent]: (((member_agent @ X5 @ A)) & ((Z = (F @ X5))))))))). % image_iff
thf(fact_135_imageI, axiom,
    ((![X : msg, A : set_msg, F : msg > msg]: ((member_msg @ X @ A) => (member_msg @ (F @ X) @ (image_msg_msg @ F @ A)))))). % imageI
thf(fact_136_imageI, axiom,
    ((![X : msg, A : set_msg, F : msg > nat]: ((member_msg @ X @ A) => (member_nat @ (F @ X) @ (image_msg_nat @ F @ A)))))). % imageI
thf(fact_137_imageI, axiom,
    ((![X : msg, A : set_msg, F : msg > agent]: ((member_msg @ X @ A) => (member_agent @ (F @ X) @ (image_msg_agent @ F @ A)))))). % imageI
thf(fact_138_imageI, axiom,
    ((![X : nat, A : set_nat, F : nat > msg]: ((member_nat @ X @ A) => (member_msg @ (F @ X) @ (image_nat_msg @ F @ A)))))). % imageI
thf(fact_139_imageI, axiom,
    ((![X : nat, A : set_nat, F : nat > nat]: ((member_nat @ X @ A) => (member_nat @ (F @ X) @ (image_nat_nat @ F @ A)))))). % imageI
thf(fact_140_imageI, axiom,
    ((![X : nat, A : set_nat, F : nat > agent]: ((member_nat @ X @ A) => (member_agent @ (F @ X) @ (image_nat_agent @ F @ A)))))). % imageI
thf(fact_141_imageI, axiom,
    ((![X : agent, A : set_agent, F : agent > msg]: ((member_agent @ X @ A) => (member_msg @ (F @ X) @ (image_agent_msg @ F @ A)))))). % imageI
thf(fact_142_imageI, axiom,
    ((![X : agent, A : set_agent, F : agent > nat]: ((member_agent @ X @ A) => (member_nat @ (F @ X) @ (image_agent_nat @ F @ A)))))). % imageI
thf(fact_143_imageI, axiom,
    ((![X : agent, A : set_agent, F : agent > agent]: ((member_agent @ X @ A) => (member_agent @ (F @ X) @ (image_agent_agent @ F @ A)))))). % imageI
thf(fact_144_Collect__mono__iff, axiom,
    ((![P : nat > $o, Q : nat > $o]: ((ord_less_eq_set_nat @ (collect_nat @ P) @ (collect_nat @ Q)) = (![X5 : nat]: (((P @ X5)) => ((Q @ X5)))))))). % Collect_mono_iff
thf(fact_145_Collect__mono__iff, axiom,
    ((![P : msg > $o, Q : msg > $o]: ((ord_less_eq_set_msg @ (collect_msg @ P) @ (collect_msg @ Q)) = (![X5 : msg]: (((P @ X5)) => ((Q @ X5)))))))). % Collect_mono_iff
thf(fact_146_set__eq__subset, axiom,
    (((^[Y2 : set_nat]: (^[Z2 : set_nat]: (Y2 = Z2))) = (^[A3 : set_nat]: (^[B3 : set_nat]: (((ord_less_eq_set_nat @ A3 @ B3)) & ((ord_less_eq_set_nat @ B3 @ A3)))))))). % set_eq_subset
thf(fact_147_set__eq__subset, axiom,
    (((^[Y2 : set_msg]: (^[Z2 : set_msg]: (Y2 = Z2))) = (^[A3 : set_msg]: (^[B3 : set_msg]: (((ord_less_eq_set_msg @ A3 @ B3)) & ((ord_less_eq_set_msg @ B3 @ A3)))))))). % set_eq_subset
thf(fact_148_subset__trans, axiom,
    ((![A : set_nat, B : set_nat, C : set_nat]: ((ord_less_eq_set_nat @ A @ B) => ((ord_less_eq_set_nat @ B @ C) => (ord_less_eq_set_nat @ A @ C)))))). % subset_trans
thf(fact_149_subset__trans, axiom,
    ((![A : set_msg, B : set_msg, C : set_msg]: ((ord_less_eq_set_msg @ A @ B) => ((ord_less_eq_set_msg @ B @ C) => (ord_less_eq_set_msg @ A @ C)))))). % subset_trans
thf(fact_150_Collect__mono, axiom,
    ((![P : nat > $o, Q : nat > $o]: ((![X2 : nat]: ((P @ X2) => (Q @ X2))) => (ord_less_eq_set_nat @ (collect_nat @ P) @ (collect_nat @ Q)))))). % Collect_mono
thf(fact_151_Collect__mono, axiom,
    ((![P : msg > $o, Q : msg > $o]: ((![X2 : msg]: ((P @ X2) => (Q @ X2))) => (ord_less_eq_set_msg @ (collect_msg @ P) @ (collect_msg @ Q)))))). % Collect_mono
thf(fact_152_subset__refl, axiom,
    ((![A : set_nat]: (ord_less_eq_set_nat @ A @ A)))). % subset_refl
thf(fact_153_subset__refl, axiom,
    ((![A : set_msg]: (ord_less_eq_set_msg @ A @ A)))). % subset_refl
thf(fact_154_subset__iff, axiom,
    ((ord_le722097072_agent = (^[A3 : set_agent]: (^[B3 : set_agent]: (![T : agent]: (((member_agent @ T @ A3)) => ((member_agent @ T @ B3))))))))). % subset_iff
thf(fact_155_subset__iff, axiom,
    ((ord_less_eq_set_nat = (^[A3 : set_nat]: (^[B3 : set_nat]: (![T : nat]: (((member_nat @ T @ A3)) => ((member_nat @ T @ B3))))))))). % subset_iff
thf(fact_156_subset__iff, axiom,
    ((ord_less_eq_set_msg = (^[A3 : set_msg]: (^[B3 : set_msg]: (![T : msg]: (((member_msg @ T @ A3)) => ((member_msg @ T @ B3))))))))). % subset_iff
thf(fact_157_equalityD2, axiom,
    ((![A : set_nat, B : set_nat]: ((A = B) => (ord_less_eq_set_nat @ B @ A))))). % equalityD2
thf(fact_158_equalityD2, axiom,
    ((![A : set_msg, B : set_msg]: ((A = B) => (ord_less_eq_set_msg @ B @ A))))). % equalityD2
thf(fact_159_equalityD1, axiom,
    ((![A : set_nat, B : set_nat]: ((A = B) => (ord_less_eq_set_nat @ A @ B))))). % equalityD1
thf(fact_160_equalityD1, axiom,
    ((![A : set_msg, B : set_msg]: ((A = B) => (ord_less_eq_set_msg @ A @ B))))). % equalityD1
thf(fact_161_subset__eq, axiom,
    ((ord_le722097072_agent = (^[A3 : set_agent]: (^[B3 : set_agent]: (![X5 : agent]: (((member_agent @ X5 @ A3)) => ((member_agent @ X5 @ B3))))))))). % subset_eq
thf(fact_162_subset__eq, axiom,
    ((ord_less_eq_set_nat = (^[A3 : set_nat]: (^[B3 : set_nat]: (![X5 : nat]: (((member_nat @ X5 @ A3)) => ((member_nat @ X5 @ B3))))))))). % subset_eq
thf(fact_163_subset__eq, axiom,
    ((ord_less_eq_set_msg = (^[A3 : set_msg]: (^[B3 : set_msg]: (![X5 : msg]: (((member_msg @ X5 @ A3)) => ((member_msg @ X5 @ B3))))))))). % subset_eq
thf(fact_164_equalityE, axiom,
    ((![A : set_nat, B : set_nat]: ((A = B) => (~ (((ord_less_eq_set_nat @ A @ B) => (~ ((ord_less_eq_set_nat @ B @ A)))))))))). % equalityE
thf(fact_165_equalityE, axiom,
    ((![A : set_msg, B : set_msg]: ((A = B) => (~ (((ord_less_eq_set_msg @ A @ B) => (~ ((ord_less_eq_set_msg @ B @ A)))))))))). % equalityE
thf(fact_166_subsetD, axiom,
    ((![A : set_agent, B : set_agent, C2 : agent]: ((ord_le722097072_agent @ A @ B) => ((member_agent @ C2 @ A) => (member_agent @ C2 @ B)))))). % subsetD
thf(fact_167_subsetD, axiom,
    ((![A : set_nat, B : set_nat, C2 : nat]: ((ord_less_eq_set_nat @ A @ B) => ((member_nat @ C2 @ A) => (member_nat @ C2 @ B)))))). % subsetD
thf(fact_168_subsetD, axiom,
    ((![A : set_msg, B : set_msg, C2 : msg]: ((ord_less_eq_set_msg @ A @ B) => ((member_msg @ C2 @ A) => (member_msg @ C2 @ B)))))). % subsetD
thf(fact_169_in__mono, axiom,
    ((![A : set_agent, B : set_agent, X : agent]: ((ord_le722097072_agent @ A @ B) => ((member_agent @ X @ A) => (member_agent @ X @ B)))))). % in_mono
thf(fact_170_in__mono, axiom,
    ((![A : set_nat, B : set_nat, X : nat]: ((ord_less_eq_set_nat @ A @ B) => ((member_nat @ X @ A) => (member_nat @ X @ B)))))). % in_mono
thf(fact_171_in__mono, axiom,
    ((![A : set_msg, B : set_msg, X : msg]: ((ord_less_eq_set_msg @ A @ B) => ((member_msg @ X @ A) => (member_msg @ X @ B)))))). % in_mono
thf(fact_172_sup__left__commute, axiom,
    ((![X : set_msg, Y : set_msg, Z : set_msg]: ((sup_sup_set_msg @ X @ (sup_sup_set_msg @ Y @ Z)) = (sup_sup_set_msg @ Y @ (sup_sup_set_msg @ X @ Z)))))). % sup_left_commute
thf(fact_173_sup__left__commute, axiom,
    ((![X : set_nat, Y : set_nat, Z : set_nat]: ((sup_sup_set_nat @ X @ (sup_sup_set_nat @ Y @ Z)) = (sup_sup_set_nat @ Y @ (sup_sup_set_nat @ X @ Z)))))). % sup_left_commute
thf(fact_174_sup__left__commute, axiom,
    ((![X : set_agent, Y : set_agent, Z : set_agent]: ((sup_sup_set_agent @ X @ (sup_sup_set_agent @ Y @ Z)) = (sup_sup_set_agent @ Y @ (sup_sup_set_agent @ X @ Z)))))). % sup_left_commute
thf(fact_175_sup_Oleft__commute, axiom,
    ((![B2 : set_msg, A2 : set_msg, C2 : set_msg]: ((sup_sup_set_msg @ B2 @ (sup_sup_set_msg @ A2 @ C2)) = (sup_sup_set_msg @ A2 @ (sup_sup_set_msg @ B2 @ C2)))))). % sup.left_commute
thf(fact_176_sup_Oleft__commute, axiom,
    ((![B2 : set_nat, A2 : set_nat, C2 : set_nat]: ((sup_sup_set_nat @ B2 @ (sup_sup_set_nat @ A2 @ C2)) = (sup_sup_set_nat @ A2 @ (sup_sup_set_nat @ B2 @ C2)))))). % sup.left_commute
thf(fact_177_sup_Oleft__commute, axiom,
    ((![B2 : set_agent, A2 : set_agent, C2 : set_agent]: ((sup_sup_set_agent @ B2 @ (sup_sup_set_agent @ A2 @ C2)) = (sup_sup_set_agent @ A2 @ (sup_sup_set_agent @ B2 @ C2)))))). % sup.left_commute
thf(fact_178_sup__commute, axiom,
    ((sup_sup_set_msg = (^[X5 : set_msg]: (^[Y3 : set_msg]: (sup_sup_set_msg @ Y3 @ X5)))))). % sup_commute
thf(fact_179_sup__commute, axiom,
    ((sup_sup_set_nat = (^[X5 : set_nat]: (^[Y3 : set_nat]: (sup_sup_set_nat @ Y3 @ X5)))))). % sup_commute
thf(fact_180_sup__commute, axiom,
    ((sup_sup_set_agent = (^[X5 : set_agent]: (^[Y3 : set_agent]: (sup_sup_set_agent @ Y3 @ X5)))))). % sup_commute
thf(fact_181_sup_Ocommute, axiom,
    ((sup_sup_set_msg = (^[A4 : set_msg]: (^[B4 : set_msg]: (sup_sup_set_msg @ B4 @ A4)))))). % sup.commute
thf(fact_182_sup_Ocommute, axiom,
    ((sup_sup_set_nat = (^[A4 : set_nat]: (^[B4 : set_nat]: (sup_sup_set_nat @ B4 @ A4)))))). % sup.commute
thf(fact_183_sup_Ocommute, axiom,
    ((sup_sup_set_agent = (^[A4 : set_agent]: (^[B4 : set_agent]: (sup_sup_set_agent @ B4 @ A4)))))). % sup.commute
thf(fact_184_sup__assoc, axiom,
    ((![X : set_msg, Y : set_msg, Z : set_msg]: ((sup_sup_set_msg @ (sup_sup_set_msg @ X @ Y) @ Z) = (sup_sup_set_msg @ X @ (sup_sup_set_msg @ Y @ Z)))))). % sup_assoc
thf(fact_185_sup__assoc, axiom,
    ((![X : set_nat, Y : set_nat, Z : set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ X @ Y) @ Z) = (sup_sup_set_nat @ X @ (sup_sup_set_nat @ Y @ Z)))))). % sup_assoc
thf(fact_186_sup__assoc, axiom,
    ((![X : set_agent, Y : set_agent, Z : set_agent]: ((sup_sup_set_agent @ (sup_sup_set_agent @ X @ Y) @ Z) = (sup_sup_set_agent @ X @ (sup_sup_set_agent @ Y @ Z)))))). % sup_assoc
thf(fact_187_sup_Oassoc, axiom,
    ((![A2 : set_msg, B2 : set_msg, C2 : set_msg]: ((sup_sup_set_msg @ (sup_sup_set_msg @ A2 @ B2) @ C2) = (sup_sup_set_msg @ A2 @ (sup_sup_set_msg @ B2 @ C2)))))). % sup.assoc
thf(fact_188_sup_Oassoc, axiom,
    ((![A2 : set_nat, B2 : set_nat, C2 : set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ A2 @ B2) @ C2) = (sup_sup_set_nat @ A2 @ (sup_sup_set_nat @ B2 @ C2)))))). % sup.assoc
thf(fact_189_sup_Oassoc, axiom,
    ((![A2 : set_agent, B2 : set_agent, C2 : set_agent]: ((sup_sup_set_agent @ (sup_sup_set_agent @ A2 @ B2) @ C2) = (sup_sup_set_agent @ A2 @ (sup_sup_set_agent @ B2 @ C2)))))). % sup.assoc
thf(fact_190_boolean__algebra__cancel_Osup2, axiom,
    ((![B : set_msg, K : set_msg, B2 : set_msg, A2 : set_msg]: ((B = (sup_sup_set_msg @ K @ B2)) => ((sup_sup_set_msg @ A2 @ B) = (sup_sup_set_msg @ K @ (sup_sup_set_msg @ A2 @ B2))))))). % boolean_algebra_cancel.sup2
thf(fact_191_boolean__algebra__cancel_Osup2, axiom,
    ((![B : set_nat, K : set_nat, B2 : set_nat, A2 : set_nat]: ((B = (sup_sup_set_nat @ K @ B2)) => ((sup_sup_set_nat @ A2 @ B) = (sup_sup_set_nat @ K @ (sup_sup_set_nat @ A2 @ B2))))))). % boolean_algebra_cancel.sup2
thf(fact_192_boolean__algebra__cancel_Osup2, axiom,
    ((![B : set_agent, K : set_agent, B2 : set_agent, A2 : set_agent]: ((B = (sup_sup_set_agent @ K @ B2)) => ((sup_sup_set_agent @ A2 @ B) = (sup_sup_set_agent @ K @ (sup_sup_set_agent @ A2 @ B2))))))). % boolean_algebra_cancel.sup2
thf(fact_193_boolean__algebra__cancel_Osup1, axiom,
    ((![A : set_msg, K : set_msg, A2 : set_msg, B2 : set_msg]: ((A = (sup_sup_set_msg @ K @ A2)) => ((sup_sup_set_msg @ A @ B2) = (sup_sup_set_msg @ K @ (sup_sup_set_msg @ A2 @ B2))))))). % boolean_algebra_cancel.sup1
thf(fact_194_boolean__algebra__cancel_Osup1, axiom,
    ((![A : set_nat, K : set_nat, A2 : set_nat, B2 : set_nat]: ((A = (sup_sup_set_nat @ K @ A2)) => ((sup_sup_set_nat @ A @ B2) = (sup_sup_set_nat @ K @ (sup_sup_set_nat @ A2 @ B2))))))). % boolean_algebra_cancel.sup1
thf(fact_195_boolean__algebra__cancel_Osup1, axiom,
    ((![A : set_agent, K : set_agent, A2 : set_agent, B2 : set_agent]: ((A = (sup_sup_set_agent @ K @ A2)) => ((sup_sup_set_agent @ A @ B2) = (sup_sup_set_agent @ K @ (sup_sup_set_agent @ A2 @ B2))))))). % boolean_algebra_cancel.sup1
thf(fact_196_inf__sup__aci_I5_J, axiom,
    ((sup_sup_set_msg = (^[X5 : set_msg]: (^[Y3 : set_msg]: (sup_sup_set_msg @ Y3 @ X5)))))). % inf_sup_aci(5)
thf(fact_197_inf__sup__aci_I5_J, axiom,
    ((sup_sup_set_nat = (^[X5 : set_nat]: (^[Y3 : set_nat]: (sup_sup_set_nat @ Y3 @ X5)))))). % inf_sup_aci(5)
thf(fact_198_inf__sup__aci_I5_J, axiom,
    ((sup_sup_set_agent = (^[X5 : set_agent]: (^[Y3 : set_agent]: (sup_sup_set_agent @ Y3 @ X5)))))). % inf_sup_aci(5)
thf(fact_199_inf__sup__aci_I6_J, axiom,
    ((![X : set_msg, Y : set_msg, Z : set_msg]: ((sup_sup_set_msg @ (sup_sup_set_msg @ X @ Y) @ Z) = (sup_sup_set_msg @ X @ (sup_sup_set_msg @ Y @ Z)))))). % inf_sup_aci(6)
thf(fact_200_inf__sup__aci_I6_J, axiom,
    ((![X : set_nat, Y : set_nat, Z : set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ X @ Y) @ Z) = (sup_sup_set_nat @ X @ (sup_sup_set_nat @ Y @ Z)))))). % inf_sup_aci(6)
thf(fact_201_inf__sup__aci_I6_J, axiom,
    ((![X : set_agent, Y : set_agent, Z : set_agent]: ((sup_sup_set_agent @ (sup_sup_set_agent @ X @ Y) @ Z) = (sup_sup_set_agent @ X @ (sup_sup_set_agent @ Y @ Z)))))). % inf_sup_aci(6)
thf(fact_202_inf__sup__aci_I7_J, axiom,
    ((![X : set_msg, Y : set_msg, Z : set_msg]: ((sup_sup_set_msg @ X @ (sup_sup_set_msg @ Y @ Z)) = (sup_sup_set_msg @ Y @ (sup_sup_set_msg @ X @ Z)))))). % inf_sup_aci(7)
thf(fact_203_inf__sup__aci_I7_J, axiom,
    ((![X : set_nat, Y : set_nat, Z : set_nat]: ((sup_sup_set_nat @ X @ (sup_sup_set_nat @ Y @ Z)) = (sup_sup_set_nat @ Y @ (sup_sup_set_nat @ X @ Z)))))). % inf_sup_aci(7)
thf(fact_204_inf__sup__aci_I7_J, axiom,
    ((![X : set_agent, Y : set_agent, Z : set_agent]: ((sup_sup_set_agent @ X @ (sup_sup_set_agent @ Y @ Z)) = (sup_sup_set_agent @ Y @ (sup_sup_set_agent @ X @ Z)))))). % inf_sup_aci(7)
thf(fact_205_inf__sup__aci_I8_J, axiom,
    ((![X : set_msg, Y : set_msg]: ((sup_sup_set_msg @ X @ (sup_sup_set_msg @ X @ Y)) = (sup_sup_set_msg @ X @ Y))))). % inf_sup_aci(8)
thf(fact_206_inf__sup__aci_I8_J, axiom,
    ((![X : set_nat, Y : set_nat]: ((sup_sup_set_nat @ X @ (sup_sup_set_nat @ X @ Y)) = (sup_sup_set_nat @ X @ Y))))). % inf_sup_aci(8)
thf(fact_207_inf__sup__aci_I8_J, axiom,
    ((![X : set_agent, Y : set_agent]: ((sup_sup_set_agent @ X @ (sup_sup_set_agent @ X @ Y)) = (sup_sup_set_agent @ X @ Y))))). % inf_sup_aci(8)
thf(fact_208_UNIV__witness, axiom,
    ((?[X2 : agent]: (member_agent @ X2 @ top_top_set_agent)))). % UNIV_witness
thf(fact_209_UNIV__witness, axiom,
    ((?[X2 : nat]: (member_nat @ X2 @ top_top_set_nat)))). % UNIV_witness
thf(fact_210_UNIV__witness, axiom,
    ((?[X2 : msg]: (member_msg @ X2 @ top_top_set_msg)))). % UNIV_witness
thf(fact_211_UNIV__eq__I, axiom,
    ((![A : set_agent]: ((![X2 : agent]: (member_agent @ X2 @ A)) => (top_top_set_agent = A))))). % UNIV_eq_I
thf(fact_212_UNIV__eq__I, axiom,
    ((![A : set_nat]: ((![X2 : nat]: (member_nat @ X2 @ A)) => (top_top_set_nat = A))))). % UNIV_eq_I
thf(fact_213_UNIV__eq__I, axiom,
    ((![A : set_msg]: ((![X2 : msg]: (member_msg @ X2 @ A)) => (top_top_set_msg = A))))). % UNIV_eq_I
thf(fact_214_Un__left__commute, axiom,
    ((![A : set_msg, B : set_msg, C : set_msg]: ((sup_sup_set_msg @ A @ (sup_sup_set_msg @ B @ C)) = (sup_sup_set_msg @ B @ (sup_sup_set_msg @ A @ C)))))). % Un_left_commute
thf(fact_215_Un__left__commute, axiom,
    ((![A : set_nat, B : set_nat, C : set_nat]: ((sup_sup_set_nat @ A @ (sup_sup_set_nat @ B @ C)) = (sup_sup_set_nat @ B @ (sup_sup_set_nat @ A @ C)))))). % Un_left_commute
thf(fact_216_Un__left__commute, axiom,
    ((![A : set_agent, B : set_agent, C : set_agent]: ((sup_sup_set_agent @ A @ (sup_sup_set_agent @ B @ C)) = (sup_sup_set_agent @ B @ (sup_sup_set_agent @ A @ C)))))). % Un_left_commute
thf(fact_217_Un__left__absorb, axiom,
    ((![A : set_msg, B : set_msg]: ((sup_sup_set_msg @ A @ (sup_sup_set_msg @ A @ B)) = (sup_sup_set_msg @ A @ B))))). % Un_left_absorb
thf(fact_218_Un__left__absorb, axiom,
    ((![A : set_nat, B : set_nat]: ((sup_sup_set_nat @ A @ (sup_sup_set_nat @ A @ B)) = (sup_sup_set_nat @ A @ B))))). % Un_left_absorb
thf(fact_219_Un__left__absorb, axiom,
    ((![A : set_agent, B : set_agent]: ((sup_sup_set_agent @ A @ (sup_sup_set_agent @ A @ B)) = (sup_sup_set_agent @ A @ B))))). % Un_left_absorb
thf(fact_220_Un__commute, axiom,
    ((sup_sup_set_msg = (^[A3 : set_msg]: (^[B3 : set_msg]: (sup_sup_set_msg @ B3 @ A3)))))). % Un_commute
thf(fact_221_Un__commute, axiom,
    ((sup_sup_set_nat = (^[A3 : set_nat]: (^[B3 : set_nat]: (sup_sup_set_nat @ B3 @ A3)))))). % Un_commute
thf(fact_222_Un__commute, axiom,
    ((sup_sup_set_agent = (^[A3 : set_agent]: (^[B3 : set_agent]: (sup_sup_set_agent @ B3 @ A3)))))). % Un_commute
thf(fact_223_Un__absorb, axiom,
    ((![A : set_msg]: ((sup_sup_set_msg @ A @ A) = A)))). % Un_absorb
thf(fact_224_Un__absorb, axiom,
    ((![A : set_nat]: ((sup_sup_set_nat @ A @ A) = A)))). % Un_absorb
thf(fact_225_Un__absorb, axiom,
    ((![A : set_agent]: ((sup_sup_set_agent @ A @ A) = A)))). % Un_absorb
thf(fact_226_Un__assoc, axiom,
    ((![A : set_msg, B : set_msg, C : set_msg]: ((sup_sup_set_msg @ (sup_sup_set_msg @ A @ B) @ C) = (sup_sup_set_msg @ A @ (sup_sup_set_msg @ B @ C)))))). % Un_assoc
thf(fact_227_Un__assoc, axiom,
    ((![A : set_nat, B : set_nat, C : set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ A @ B) @ C) = (sup_sup_set_nat @ A @ (sup_sup_set_nat @ B @ C)))))). % Un_assoc
thf(fact_228_Un__assoc, axiom,
    ((![A : set_agent, B : set_agent, C : set_agent]: ((sup_sup_set_agent @ (sup_sup_set_agent @ A @ B) @ C) = (sup_sup_set_agent @ A @ (sup_sup_set_agent @ B @ C)))))). % Un_assoc
thf(fact_229_ball__Un, axiom,
    ((![A : set_msg, B : set_msg, P : msg > $o]: ((![X5 : msg]: (((member_msg @ X5 @ (sup_sup_set_msg @ A @ B))) => ((P @ X5)))) = (((![X5 : msg]: (((member_msg @ X5 @ A)) => ((P @ X5))))) & ((![X5 : msg]: (((member_msg @ X5 @ B)) => ((P @ X5)))))))))). % ball_Un
thf(fact_230_ball__Un, axiom,
    ((![A : set_nat, B : set_nat, P : nat > $o]: ((![X5 : nat]: (((member_nat @ X5 @ (sup_sup_set_nat @ A @ B))) => ((P @ X5)))) = (((![X5 : nat]: (((member_nat @ X5 @ A)) => ((P @ X5))))) & ((![X5 : nat]: (((member_nat @ X5 @ B)) => ((P @ X5)))))))))). % ball_Un
thf(fact_231_ball__Un, axiom,
    ((![A : set_agent, B : set_agent, P : agent > $o]: ((![X5 : agent]: (((member_agent @ X5 @ (sup_sup_set_agent @ A @ B))) => ((P @ X5)))) = (((![X5 : agent]: (((member_agent @ X5 @ A)) => ((P @ X5))))) & ((![X5 : agent]: (((member_agent @ X5 @ B)) => ((P @ X5)))))))))). % ball_Un
thf(fact_232_bex__Un, axiom,
    ((![A : set_msg, B : set_msg, P : msg > $o]: ((?[X5 : msg]: (((member_msg @ X5 @ (sup_sup_set_msg @ A @ B))) & ((P @ X5)))) = (((?[X5 : msg]: (((member_msg @ X5 @ A)) & ((P @ X5))))) | ((?[X5 : msg]: (((member_msg @ X5 @ B)) & ((P @ X5)))))))))). % bex_Un
thf(fact_233_bex__Un, axiom,
    ((![A : set_nat, B : set_nat, P : nat > $o]: ((?[X5 : nat]: (((member_nat @ X5 @ (sup_sup_set_nat @ A @ B))) & ((P @ X5)))) = (((?[X5 : nat]: (((member_nat @ X5 @ A)) & ((P @ X5))))) | ((?[X5 : nat]: (((member_nat @ X5 @ B)) & ((P @ X5)))))))))). % bex_Un
thf(fact_234_bex__Un, axiom,
    ((![A : set_agent, B : set_agent, P : agent > $o]: ((?[X5 : agent]: (((member_agent @ X5 @ (sup_sup_set_agent @ A @ B))) & ((P @ X5)))) = (((?[X5 : agent]: (((member_agent @ X5 @ A)) & ((P @ X5))))) | ((?[X5 : agent]: (((member_agent @ X5 @ B)) & ((P @ X5)))))))))). % bex_Un
thf(fact_235_UnI2, axiom,
    ((![C2 : msg, B : set_msg, A : set_msg]: ((member_msg @ C2 @ B) => (member_msg @ C2 @ (sup_sup_set_msg @ A @ B)))))). % UnI2
thf(fact_236_UnI2, axiom,
    ((![C2 : nat, B : set_nat, A : set_nat]: ((member_nat @ C2 @ B) => (member_nat @ C2 @ (sup_sup_set_nat @ A @ B)))))). % UnI2
thf(fact_237_UnI2, axiom,
    ((![C2 : agent, B : set_agent, A : set_agent]: ((member_agent @ C2 @ B) => (member_agent @ C2 @ (sup_sup_set_agent @ A @ B)))))). % UnI2
thf(fact_238_UnI1, axiom,
    ((![C2 : msg, A : set_msg, B : set_msg]: ((member_msg @ C2 @ A) => (member_msg @ C2 @ (sup_sup_set_msg @ A @ B)))))). % UnI1
thf(fact_239_UnI1, axiom,
    ((![C2 : nat, A : set_nat, B : set_nat]: ((member_nat @ C2 @ A) => (member_nat @ C2 @ (sup_sup_set_nat @ A @ B)))))). % UnI1
thf(fact_240_UnI1, axiom,
    ((![C2 : agent, A : set_agent, B : set_agent]: ((member_agent @ C2 @ A) => (member_agent @ C2 @ (sup_sup_set_agent @ A @ B)))))). % UnI1
thf(fact_241_UnE, axiom,
    ((![C2 : msg, A : set_msg, B : set_msg]: ((member_msg @ C2 @ (sup_sup_set_msg @ A @ B)) => ((~ ((member_msg @ C2 @ A))) => (member_msg @ C2 @ B)))))). % UnE
thf(fact_242_UnE, axiom,
    ((![C2 : nat, A : set_nat, B : set_nat]: ((member_nat @ C2 @ (sup_sup_set_nat @ A @ B)) => ((~ ((member_nat @ C2 @ A))) => (member_nat @ C2 @ B)))))). % UnE
thf(fact_243_UnE, axiom,
    ((![C2 : agent, A : set_agent, B : set_agent]: ((member_agent @ C2 @ (sup_sup_set_agent @ A @ B)) => ((~ ((member_agent @ C2 @ A))) => (member_agent @ C2 @ B)))))). % UnE
thf(fact_244_analz__analzD, axiom,
    ((![X3 : msg, H : set_msg]: ((member_msg @ X3 @ (analz @ (analz @ H))) => (member_msg @ X3 @ (analz @ H)))))). % analz_analzD
thf(fact_245_analz_OInj, axiom,
    ((![X3 : msg, H : set_msg]: ((member_msg @ X3 @ H) => (member_msg @ X3 @ (analz @ H)))))). % analz.Inj
thf(fact_246_double__complement, axiom,
    ((![A : set_nat]: ((uminus814679503et_nat @ (uminus814679503et_nat @ A)) = A)))). % double_complement
thf(fact_247_double__complement, axiom,
    ((![A : set_agent]: ((uminus1992895513_agent @ (uminus1992895513_agent @ A)) = A)))). % double_complement
thf(fact_248_double__complement, axiom,
    ((![A : set_msg]: ((uminus676873109et_msg @ (uminus676873109et_msg @ A)) = A)))). % double_complement

% Conjectures (1)
thf(conj_0, conjecture,
    ((![K2 : nat, KK : set_nat]: ((~ ((ord_less_eq_set_nat @ KK @ (uminus814679503et_nat @ (image_agent_nat @ shrK @ top_top_set_agent))))) | ((member_msg @ (key @ K2) @ (analz @ (sup_sup_set_msg @ (image_nat_msg @ key @ KK) @ (knows @ spy @ nil_event)))) = (((member_nat @ K2 @ KK)) | ((member_msg @ (key @ K2) @ (analz @ (knows @ spy @ nil_event)))))))))).
