% 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_217__5229656_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:23:53.308

% Could-be-implicit typings (10)
thf(ty_n_t__Set__Oset_It__List__Olist_It__Event__Oevent_J_J, type,
    set_list_event : $tType).
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__Event__Oevent_J, type,
    set_event : $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__Event__Oevent, type,
    event : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (68)
thf(sy_c_Event_Obad, type,
    bad : set_agent).
thf(sy_c_Event_Oevent_OSays, type,
    says : agent > agent > msg > event).
thf(sy_c_Event_Oknows, type,
    knows : agent > list_event > set_msg).
thf(sy_c_Event_Oused, type,
    used : list_event > set_msg).
thf(sy_c_List_Olist_OCons_001t__Event__Oevent, type,
    cons_event : event > list_event > list_event).
thf(sy_c_List_Olist_Oset_001t__Event__Oevent, type,
    set_event2 : list_event > set_event).
thf(sy_c_Message_Oagent_OServer, type,
    server : agent).
thf(sy_c_Message_Oagent_OSpy, type,
    spy : agent).
thf(sy_c_Message_Oanalz, type,
    analz : set_msg > set_msg).
thf(sy_c_Message_OkeysFor, type,
    keysFor : set_msg > set_nat).
thf(sy_c_Message_Omsg_OAgent, type,
    agent2 : agent > msg).
thf(sy_c_Message_Omsg_OCrypt, type,
    crypt : nat > msg > msg).
thf(sy_c_Message_Omsg_OKey, type,
    key : nat > msg).
thf(sy_c_Message_Omsg_OMPair, type,
    mPair : msg > msg > msg).
thf(sy_c_Message_Omsg_ONonce, type,
    nonce : nat > msg).
thf(sy_c_Message_Oparts, type,
    parts : set_msg > set_msg).
thf(sy_c_Message_OsymKeys, type,
    symKeys : set_nat).
thf(sy_c_NS__Shared__Mirabelle__xwdrtqxrux_Ons__shared, type,
    nS_Sha1061662329shared : set_list_event).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Event__Oevent_J, type,
    bot_bot_set_event : set_event).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__List__Olist_It__Event__Oevent_J_J, type,
    bot_bo1693714908_event : set_list_event).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Message__Oagent_J, type,
    bot_bot_set_agent : set_agent).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Message__Omsg_J, type,
    bot_bot_set_msg : set_msg).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J, type,
    bot_bot_set_nat : set_nat).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Event__Oevent_J, type,
    top_top_set_event : set_event).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__List__Olist_It__Event__Oevent_J_J, type,
    top_to1178833912_event : set_list_event).
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__Event__Oevent, type,
    collect_event : (event > $o) > set_event).
thf(sy_c_Set_OCollect_001t__List__Olist_It__Event__Oevent_J, type,
    collect_list_event : (list_event > $o) > set_list_event).
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__Event__Oevent_001t__Message__Omsg, type,
    image_event_msg : (event > msg) > set_event > set_msg).
thf(sy_c_Set_Oimage_001t__Event__Oevent_001t__Nat__Onat, type,
    image_event_nat : (event > nat) > set_event > set_nat).
thf(sy_c_Set_Oimage_001t__List__Olist_It__Event__Oevent_J_001t__Message__Omsg, type,
    image_list_event_msg : (list_event > msg) > set_list_event > set_msg).
thf(sy_c_Set_Oimage_001t__List__Olist_It__Event__Oevent_J_001t__Nat__Onat, type,
    image_list_event_nat : (list_event > nat) > set_list_event > set_nat).
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__Event__Oevent, type,
    image_msg_event : (msg > event) > set_msg > set_event).
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__Event__Oevent, type,
    image_nat_event : (nat > event) > set_nat > set_event).
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_Set_Oinsert_001t__Event__Oevent, type,
    insert_event : event > set_event > set_event).
thf(sy_c_Set_Oinsert_001t__List__Olist_It__Event__Oevent_J, type,
    insert_list_event : list_event > set_list_event > set_list_event).
thf(sy_c_Set_Oinsert_001t__Message__Oagent, type,
    insert_agent : agent > set_agent > set_agent).
thf(sy_c_Set_Oinsert_001t__Message__Omsg, type,
    insert_msg : msg > set_msg > set_msg).
thf(sy_c_Set_Oinsert_001t__Nat__Onat, type,
    insert_nat : nat > set_nat > set_nat).
thf(sy_c_member_001t__Event__Oevent, type,
    member_event : event > set_event > $o).
thf(sy_c_member_001t__List__Olist_It__Event__Oevent_J, type,
    member_list_event : list_event > set_list_event > $o).
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).
thf(sy_v_A, type,
    a : agent).
thf(sy_v_A_H, type,
    a2 : agent).
thf(sy_v_B, type,
    b : agent).
thf(sy_v_K, type,
    k : nat).
thf(sy_v_KAB, type,
    kab : nat).
thf(sy_v_KABa, type,
    kABa : nat).
thf(sy_v_Kab, type,
    kab2 : nat).
thf(sy_v_NA, type,
    na : nat).
thf(sy_v_X, type,
    x : msg).
thf(sy_v_evs2, type,
    evs2 : list_event).

% Relevant facts (249)
thf(fact_0_Oops__parts__spies, axiom,
    ((![A : agent, NA : msg, B : msg, K : msg, X : msg, Evs : list_event]: ((member_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ NA @ (mPair @ B @ (mPair @ K @ X))))) @ (set_event2 @ Evs)) => (member_msg @ K @ (parts @ (knows @ spy @ Evs))))))). % Oops_parts_spies
thf(fact_1_NS3__msg__in__parts__spies, axiom,
    ((![S : agent, A : agent, KA : nat, N : msg, B : msg, K : msg, X : msg, Evs : list_event]: ((member_event @ (says @ S @ A @ (crypt @ KA @ (mPair @ N @ (mPair @ B @ (mPair @ K @ X))))) @ (set_event2 @ Evs)) => (member_msg @ X @ (parts @ (knows @ spy @ Evs))))))). % NS3_msg_in_parts_spies
thf(fact_2_Says__Server__message__form, axiom,
    ((![A : agent, K2 : nat, N : msg, B : agent, K : nat, X : msg, Evs : list_event]: ((member_event @ (says @ server @ A @ (crypt @ K2 @ (mPair @ N @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (set_event2 @ Evs)) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => ((~ ((member_nat @ K @ (image_agent_nat @ shrK @ top_top_set_agent)))) & ((X = (crypt @ (shrK @ B) @ (mPair @ (key @ K) @ (agent2 @ A)))) & (K2 = (shrK @ A))))))))). % Says_Server_message_form
thf(fact_3_usedI, axiom,
    ((![C : msg, Evs : list_event]: ((member_msg @ C @ (parts @ (knows @ spy @ Evs))) => (member_msg @ C @ (used @ Evs)))))). % usedI
thf(fact_4_range__constant, axiom,
    ((![X2 : nat]: ((image_nat_nat @ (^[Uu : nat]: X2) @ top_top_set_nat) = (insert_nat @ X2 @ bot_bot_set_nat))))). % range_constant
thf(fact_5_range__constant, axiom,
    ((![X2 : msg]: ((image_nat_msg @ (^[Uu : nat]: X2) @ top_top_set_nat) = (insert_msg @ X2 @ bot_bot_set_msg))))). % range_constant
thf(fact_6_range__constant, axiom,
    ((![X2 : nat]: ((image_agent_nat @ (^[Uu : agent]: X2) @ top_top_set_agent) = (insert_nat @ X2 @ bot_bot_set_nat))))). % range_constant
thf(fact_7_range__constant, axiom,
    ((![X2 : msg]: ((image_agent_msg @ (^[Uu : agent]: X2) @ top_top_set_agent) = (insert_msg @ X2 @ bot_bot_set_msg))))). % range_constant
thf(fact_8_shrK__in__used, axiom,
    ((![A : agent, Evs : list_event]: (member_msg @ (key @ (shrK @ A)) @ (used @ Evs))))). % shrK_in_used
thf(fact_9_shrK__in__knows, axiom,
    ((![A : agent, Evs : list_event]: (member_msg @ (key @ (shrK @ A)) @ (knows @ A @ Evs))))). % shrK_in_knows
thf(fact_10_parts__insert__Agent, axiom,
    ((![Agt : agent, H : set_msg]: ((parts @ (insert_msg @ (agent2 @ Agt) @ H)) = (insert_msg @ (agent2 @ Agt) @ (parts @ H)))))). % parts_insert_Agent
thf(fact_11_parts__insert__Nonce, axiom,
    ((![N : nat, H : set_msg]: ((parts @ (insert_msg @ (nonce @ N) @ H)) = (insert_msg @ (nonce @ N) @ (parts @ H)))))). % parts_insert_Nonce
thf(fact_12_parts__insert__Crypt, axiom,
    ((![K : nat, X : msg, H : set_msg]: ((parts @ (insert_msg @ (crypt @ K @ X) @ H)) = (insert_msg @ (crypt @ K @ X) @ (parts @ (insert_msg @ X @ H))))))). % parts_insert_Crypt
thf(fact_13_parts__insert__Key, axiom,
    ((![K : nat, H : set_msg]: ((parts @ (insert_msg @ (key @ K) @ H)) = (insert_msg @ (key @ K) @ (parts @ H)))))). % parts_insert_Key
thf(fact_14_parts__insert__MPair, axiom,
    ((![X : msg, Y : msg, H : set_msg]: ((parts @ (insert_msg @ (mPair @ X @ Y) @ H)) = (insert_msg @ (mPair @ X @ Y) @ (parts @ (insert_msg @ X @ (insert_msg @ Y @ H)))))))). % parts_insert_MPair
thf(fact_15_sym__shrK, axiom,
    ((![X : agent]: (member_nat @ (shrK @ X) @ symKeys)))). % sym_shrK
thf(fact_16_shrK__image__eq, axiom,
    ((![X2 : agent, AA : set_agent]: ((member_nat @ (shrK @ X2) @ (image_agent_nat @ shrK @ AA)) = (member_agent @ X2 @ AA))))). % shrK_image_eq
thf(fact_17_A__trusts__NS2, axiom,
    ((![A : agent, NA : msg, B : agent, K : nat, X : msg, Evs : list_event]: ((member_msg @ (crypt @ (shrK @ A) @ (mPair @ NA @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X)))) @ (parts @ (knows @ spy @ Evs))) => ((~ ((member_agent @ A @ bad))) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => (member_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ NA @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (set_event2 @ Evs)))))))). % A_trusts_NS2
thf(fact_18_image__eqI, axiom,
    ((![B2 : nat, F : nat > nat, X2 : nat, A : set_nat]: ((B2 = (F @ X2)) => ((member_nat @ X2 @ A) => (member_nat @ B2 @ (image_nat_nat @ F @ A))))))). % image_eqI
thf(fact_19_image__eqI, axiom,
    ((![B2 : msg, F : nat > msg, X2 : nat, A : set_nat]: ((B2 = (F @ X2)) => ((member_nat @ X2 @ A) => (member_msg @ B2 @ (image_nat_msg @ F @ A))))))). % image_eqI
thf(fact_20_image__eqI, axiom,
    ((![B2 : event, F : nat > event, X2 : nat, A : set_nat]: ((B2 = (F @ X2)) => ((member_nat @ X2 @ A) => (member_event @ B2 @ (image_nat_event @ F @ A))))))). % image_eqI
thf(fact_21_image__eqI, axiom,
    ((![B2 : agent, F : nat > agent, X2 : nat, A : set_nat]: ((B2 = (F @ X2)) => ((member_nat @ X2 @ A) => (member_agent @ B2 @ (image_nat_agent @ F @ A))))))). % image_eqI
thf(fact_22_image__eqI, axiom,
    ((![B2 : nat, F : msg > nat, X2 : msg, A : set_msg]: ((B2 = (F @ X2)) => ((member_msg @ X2 @ A) => (member_nat @ B2 @ (image_msg_nat @ F @ A))))))). % image_eqI
thf(fact_23_image__eqI, axiom,
    ((![B2 : msg, F : msg > msg, X2 : msg, A : set_msg]: ((B2 = (F @ X2)) => ((member_msg @ X2 @ A) => (member_msg @ B2 @ (image_msg_msg @ F @ A))))))). % image_eqI
thf(fact_24_image__eqI, axiom,
    ((![B2 : event, F : msg > event, X2 : msg, A : set_msg]: ((B2 = (F @ X2)) => ((member_msg @ X2 @ A) => (member_event @ B2 @ (image_msg_event @ F @ A))))))). % image_eqI
thf(fact_25_image__eqI, axiom,
    ((![B2 : agent, F : msg > agent, X2 : msg, A : set_msg]: ((B2 = (F @ X2)) => ((member_msg @ X2 @ A) => (member_agent @ B2 @ (image_msg_agent @ F @ A))))))). % image_eqI
thf(fact_26_image__eqI, axiom,
    ((![B2 : nat, F : event > nat, X2 : event, A : set_event]: ((B2 = (F @ X2)) => ((member_event @ X2 @ A) => (member_nat @ B2 @ (image_event_nat @ F @ A))))))). % image_eqI
thf(fact_27_image__eqI, axiom,
    ((![B2 : msg, F : event > msg, X2 : event, A : set_event]: ((B2 = (F @ X2)) => ((member_event @ X2 @ A) => (member_msg @ B2 @ (image_event_msg @ F @ A))))))). % image_eqI
thf(fact_28_empty__Collect__eq, axiom,
    ((![P : msg > $o]: ((bot_bot_set_msg = (collect_msg @ P)) = (![X3 : msg]: (~ ((P @ X3)))))))). % empty_Collect_eq
thf(fact_29_empty__Collect__eq, axiom,
    ((![P : nat > $o]: ((bot_bot_set_nat = (collect_nat @ P)) = (![X3 : nat]: (~ ((P @ X3)))))))). % empty_Collect_eq
thf(fact_30_Collect__empty__eq, axiom,
    ((![P : msg > $o]: (((collect_msg @ P) = bot_bot_set_msg) = (![X3 : msg]: (~ ((P @ X3)))))))). % Collect_empty_eq
thf(fact_31_Collect__empty__eq, axiom,
    ((![P : nat > $o]: (((collect_nat @ P) = bot_bot_set_nat) = (![X3 : nat]: (~ ((P @ X3)))))))). % Collect_empty_eq
thf(fact_32_all__not__in__conv, axiom,
    ((![A : set_list_event]: ((![X3 : list_event]: (~ ((member_list_event @ X3 @ A)))) = (A = bot_bo1693714908_event))))). % all_not_in_conv
thf(fact_33_all__not__in__conv, axiom,
    ((![A : set_event]: ((![X3 : event]: (~ ((member_event @ X3 @ A)))) = (A = bot_bot_set_event))))). % all_not_in_conv
thf(fact_34_all__not__in__conv, axiom,
    ((![A : set_agent]: ((![X3 : agent]: (~ ((member_agent @ X3 @ A)))) = (A = bot_bot_set_agent))))). % all_not_in_conv
thf(fact_35_all__not__in__conv, axiom,
    ((![A : set_msg]: ((![X3 : msg]: (~ ((member_msg @ X3 @ A)))) = (A = bot_bot_set_msg))))). % all_not_in_conv
thf(fact_36_all__not__in__conv, axiom,
    ((![A : set_nat]: ((![X3 : nat]: (~ ((member_nat @ X3 @ A)))) = (A = bot_bot_set_nat))))). % all_not_in_conv
thf(fact_37_empty__iff, axiom,
    ((![C : list_event]: (~ ((member_list_event @ C @ bot_bo1693714908_event)))))). % empty_iff
thf(fact_38_empty__iff, axiom,
    ((![C : event]: (~ ((member_event @ C @ bot_bot_set_event)))))). % empty_iff
thf(fact_39_empty__iff, axiom,
    ((![C : agent]: (~ ((member_agent @ C @ bot_bot_set_agent)))))). % empty_iff
thf(fact_40_empty__iff, axiom,
    ((![C : msg]: (~ ((member_msg @ C @ bot_bot_set_msg)))))). % empty_iff
thf(fact_41_empty__iff, axiom,
    ((![C : nat]: (~ ((member_nat @ C @ bot_bot_set_nat)))))). % empty_iff
thf(fact_42_insert__absorb2, axiom,
    ((![X2 : msg, A : set_msg]: ((insert_msg @ X2 @ (insert_msg @ X2 @ A)) = (insert_msg @ X2 @ A))))). % insert_absorb2
thf(fact_43_insert__absorb2, axiom,
    ((![X2 : nat, A : set_nat]: ((insert_nat @ X2 @ (insert_nat @ X2 @ A)) = (insert_nat @ X2 @ A))))). % insert_absorb2
thf(fact_44_insert__iff, axiom,
    ((![A2 : nat, B2 : nat, A : set_nat]: ((member_nat @ A2 @ (insert_nat @ B2 @ A)) = (((A2 = B2)) | ((member_nat @ A2 @ A))))))). % insert_iff
thf(fact_45_insert__iff, axiom,
    ((![A2 : list_event, B2 : list_event, A : set_list_event]: ((member_list_event @ A2 @ (insert_list_event @ B2 @ A)) = (((A2 = B2)) | ((member_list_event @ A2 @ A))))))). % insert_iff
thf(fact_46_insert__iff, axiom,
    ((![A2 : msg, B2 : msg, A : set_msg]: ((member_msg @ A2 @ (insert_msg @ B2 @ A)) = (((A2 = B2)) | ((member_msg @ A2 @ A))))))). % insert_iff
thf(fact_47_insert__iff, axiom,
    ((![A2 : event, B2 : event, A : set_event]: ((member_event @ A2 @ (insert_event @ B2 @ A)) = (((A2 = B2)) | ((member_event @ A2 @ A))))))). % insert_iff
thf(fact_48_insert__iff, axiom,
    ((![A2 : agent, B2 : agent, A : set_agent]: ((member_agent @ A2 @ (insert_agent @ B2 @ A)) = (((A2 = B2)) | ((member_agent @ A2 @ A))))))). % insert_iff
thf(fact_49_insertCI, axiom,
    ((![A2 : nat, B : set_nat, B2 : nat]: (((~ ((member_nat @ A2 @ B))) => (A2 = B2)) => (member_nat @ A2 @ (insert_nat @ B2 @ B)))))). % insertCI
thf(fact_50_insertCI, axiom,
    ((![A2 : list_event, B : set_list_event, B2 : list_event]: (((~ ((member_list_event @ A2 @ B))) => (A2 = B2)) => (member_list_event @ A2 @ (insert_list_event @ B2 @ B)))))). % insertCI
thf(fact_51_insertCI, axiom,
    ((![A2 : msg, B : set_msg, B2 : msg]: (((~ ((member_msg @ A2 @ B))) => (A2 = B2)) => (member_msg @ A2 @ (insert_msg @ B2 @ B)))))). % insertCI
thf(fact_52_insertCI, axiom,
    ((![A2 : event, B : set_event, B2 : event]: (((~ ((member_event @ A2 @ B))) => (A2 = B2)) => (member_event @ A2 @ (insert_event @ B2 @ B)))))). % insertCI
thf(fact_53_insertCI, axiom,
    ((![A2 : agent, B : set_agent, B2 : agent]: (((~ ((member_agent @ A2 @ B))) => (A2 = B2)) => (member_agent @ A2 @ (insert_agent @ B2 @ B)))))). % insertCI
thf(fact_54_UNIV__I, axiom,
    ((![X2 : list_event]: (member_list_event @ X2 @ top_to1178833912_event)))). % UNIV_I
thf(fact_55_UNIV__I, axiom,
    ((![X2 : msg]: (member_msg @ X2 @ top_top_set_msg)))). % UNIV_I
thf(fact_56_UNIV__I, axiom,
    ((![X2 : event]: (member_event @ X2 @ top_top_set_event)))). % UNIV_I
thf(fact_57_UNIV__I, axiom,
    ((![X2 : agent]: (member_agent @ X2 @ top_top_set_agent)))). % UNIV_I
thf(fact_58_UNIV__I, axiom,
    ((![X2 : nat]: (member_nat @ X2 @ top_top_set_nat)))). % UNIV_I
thf(fact_59_msg_Oinject_I6_J, axiom,
    ((![X61 : msg, X62 : msg, Y61 : msg, Y62 : msg]: (((mPair @ X61 @ X62) = (mPair @ Y61 @ Y62)) = (((X61 = Y61)) & ((X62 = Y62))))))). % msg.inject(6)
thf(fact_60_parts__idem, axiom,
    ((![H : set_msg]: ((parts @ (parts @ H)) = (parts @ H))))). % parts_idem
thf(fact_61_Key__image__eq, axiom,
    ((![X2 : nat, A : set_nat]: ((member_msg @ (key @ X2) @ (image_nat_msg @ key @ A)) = (member_nat @ X2 @ A))))). % Key_image_eq
thf(fact_62_msg_Oinject_I4_J, axiom,
    ((![X4 : nat, Y4 : nat]: (((key @ X4) = (key @ Y4)) = (X4 = Y4))))). % msg.inject(4)
thf(fact_63_msg_Oinject_I7_J, axiom,
    ((![X71 : nat, X72 : msg, Y71 : nat, Y72 : msg]: (((crypt @ X71 @ X72) = (crypt @ Y71 @ Y72)) = (((X71 = Y71)) & ((X72 = Y72))))))). % msg.inject(7)
thf(fact_64_msg_Oinject_I3_J, axiom,
    ((![X32 : nat, Y3 : nat]: (((nonce @ X32) = (nonce @ Y3)) = (X32 = Y3))))). % msg.inject(3)
thf(fact_65_msg_Oinject_I1_J, axiom,
    ((![X1 : agent, Y1 : agent]: (((agent2 @ X1) = (agent2 @ Y1)) = (X1 = Y1))))). % msg.inject(1)
thf(fact_66_event_Oinject_I1_J, axiom,
    ((![X11 : agent, X12 : agent, X13 : msg, Y11 : agent, Y12 : agent, Y13 : msg]: (((says @ X11 @ X12 @ X13) = (says @ Y11 @ Y12 @ Y13)) = (((X11 = Y11)) & ((((X12 = Y12)) & ((X13 = Y13))))))))). % event.inject(1)
thf(fact_67_shrK__injective, axiom,
    ((![X2 : agent, Y2 : agent]: (((shrK @ X2) = (shrK @ Y2)) = (X2 = Y2))))). % shrK_injective
thf(fact_68_image__is__empty, axiom,
    ((![F : agent > msg, A : set_agent]: (((image_agent_msg @ F @ A) = bot_bot_set_msg) = (A = bot_bot_set_agent))))). % image_is_empty
thf(fact_69_image__is__empty, axiom,
    ((![F : msg > msg, A : set_msg]: (((image_msg_msg @ F @ A) = bot_bot_set_msg) = (A = bot_bot_set_msg))))). % image_is_empty
thf(fact_70_image__is__empty, axiom,
    ((![F : nat > msg, A : set_nat]: (((image_nat_msg @ F @ A) = bot_bot_set_msg) = (A = bot_bot_set_nat))))). % image_is_empty
thf(fact_71_image__is__empty, axiom,
    ((![F : agent > nat, A : set_agent]: (((image_agent_nat @ F @ A) = bot_bot_set_nat) = (A = bot_bot_set_agent))))). % image_is_empty
thf(fact_72_image__is__empty, axiom,
    ((![F : msg > nat, A : set_msg]: (((image_msg_nat @ F @ A) = bot_bot_set_nat) = (A = bot_bot_set_msg))))). % image_is_empty
thf(fact_73_image__is__empty, axiom,
    ((![F : nat > nat, A : set_nat]: (((image_nat_nat @ F @ A) = bot_bot_set_nat) = (A = bot_bot_set_nat))))). % image_is_empty
thf(fact_74_empty__is__image, axiom,
    ((![F : agent > msg, A : set_agent]: ((bot_bot_set_msg = (image_agent_msg @ F @ A)) = (A = bot_bot_set_agent))))). % empty_is_image
thf(fact_75_empty__is__image, axiom,
    ((![F : msg > msg, A : set_msg]: ((bot_bot_set_msg = (image_msg_msg @ F @ A)) = (A = bot_bot_set_msg))))). % empty_is_image
thf(fact_76_empty__is__image, axiom,
    ((![F : nat > msg, A : set_nat]: ((bot_bot_set_msg = (image_nat_msg @ F @ A)) = (A = bot_bot_set_nat))))). % empty_is_image
thf(fact_77_empty__is__image, axiom,
    ((![F : agent > nat, A : set_agent]: ((bot_bot_set_nat = (image_agent_nat @ F @ A)) = (A = bot_bot_set_agent))))). % empty_is_image
thf(fact_78_empty__is__image, axiom,
    ((![F : msg > nat, A : set_msg]: ((bot_bot_set_nat = (image_msg_nat @ F @ A)) = (A = bot_bot_set_msg))))). % empty_is_image
thf(fact_79_empty__is__image, axiom,
    ((![F : nat > nat, A : set_nat]: ((bot_bot_set_nat = (image_nat_nat @ F @ A)) = (A = bot_bot_set_nat))))). % empty_is_image
thf(fact_80_image__empty, axiom,
    ((![F : agent > msg]: ((image_agent_msg @ F @ bot_bot_set_agent) = bot_bot_set_msg)))). % image_empty
thf(fact_81_image__empty, axiom,
    ((![F : agent > nat]: ((image_agent_nat @ F @ bot_bot_set_agent) = bot_bot_set_nat)))). % image_empty
thf(fact_82_image__empty, axiom,
    ((![F : msg > msg]: ((image_msg_msg @ F @ bot_bot_set_msg) = bot_bot_set_msg)))). % image_empty
thf(fact_83_image__empty, axiom,
    ((![F : msg > nat]: ((image_msg_nat @ F @ bot_bot_set_msg) = bot_bot_set_nat)))). % image_empty
thf(fact_84_image__empty, axiom,
    ((![F : nat > msg]: ((image_nat_msg @ F @ bot_bot_set_nat) = bot_bot_set_msg)))). % image_empty
thf(fact_85_image__empty, axiom,
    ((![F : nat > nat]: ((image_nat_nat @ F @ bot_bot_set_nat) = bot_bot_set_nat)))). % image_empty
thf(fact_86_insert__image, axiom,
    ((![X2 : nat, A : set_nat, F : nat > msg]: ((member_nat @ X2 @ A) => ((insert_msg @ (F @ X2) @ (image_nat_msg @ F @ A)) = (image_nat_msg @ F @ A)))))). % insert_image
thf(fact_87_insert__image, axiom,
    ((![X2 : nat, A : set_nat, F : nat > nat]: ((member_nat @ X2 @ A) => ((insert_nat @ (F @ X2) @ (image_nat_nat @ F @ A)) = (image_nat_nat @ F @ A)))))). % insert_image
thf(fact_88_insert__image, axiom,
    ((![X2 : list_event, A : set_list_event, F : list_event > msg]: ((member_list_event @ X2 @ A) => ((insert_msg @ (F @ X2) @ (image_list_event_msg @ F @ A)) = (image_list_event_msg @ F @ A)))))). % insert_image
thf(fact_89_insert__image, axiom,
    ((![X2 : list_event, A : set_list_event, F : list_event > nat]: ((member_list_event @ X2 @ A) => ((insert_nat @ (F @ X2) @ (image_list_event_nat @ F @ A)) = (image_list_event_nat @ F @ A)))))). % insert_image
thf(fact_90_insert__image, axiom,
    ((![X2 : msg, A : set_msg, F : msg > msg]: ((member_msg @ X2 @ A) => ((insert_msg @ (F @ X2) @ (image_msg_msg @ F @ A)) = (image_msg_msg @ F @ A)))))). % insert_image
thf(fact_91_insert__image, axiom,
    ((![X2 : msg, A : set_msg, F : msg > nat]: ((member_msg @ X2 @ A) => ((insert_nat @ (F @ X2) @ (image_msg_nat @ F @ A)) = (image_msg_nat @ F @ A)))))). % insert_image
thf(fact_92_insert__image, axiom,
    ((![X2 : event, A : set_event, F : event > msg]: ((member_event @ X2 @ A) => ((insert_msg @ (F @ X2) @ (image_event_msg @ F @ A)) = (image_event_msg @ F @ A)))))). % insert_image
thf(fact_93_insert__image, axiom,
    ((![X2 : event, A : set_event, F : event > nat]: ((member_event @ X2 @ A) => ((insert_nat @ (F @ X2) @ (image_event_nat @ F @ A)) = (image_event_nat @ F @ A)))))). % insert_image
thf(fact_94_insert__image, axiom,
    ((![X2 : agent, A : set_agent, F : agent > msg]: ((member_agent @ X2 @ A) => ((insert_msg @ (F @ X2) @ (image_agent_msg @ F @ A)) = (image_agent_msg @ F @ A)))))). % insert_image
thf(fact_95_insert__image, axiom,
    ((![X2 : agent, A : set_agent, F : agent > nat]: ((member_agent @ X2 @ A) => ((insert_nat @ (F @ X2) @ (image_agent_nat @ F @ A)) = (image_agent_nat @ F @ A)))))). % insert_image
thf(fact_96_image__insert, axiom,
    ((![F : agent > msg, A2 : agent, B : set_agent]: ((image_agent_msg @ F @ (insert_agent @ A2 @ B)) = (insert_msg @ (F @ A2) @ (image_agent_msg @ F @ B)))))). % image_insert
thf(fact_97_image__insert, axiom,
    ((![F : agent > nat, A2 : agent, B : set_agent]: ((image_agent_nat @ F @ (insert_agent @ A2 @ B)) = (insert_nat @ (F @ A2) @ (image_agent_nat @ F @ B)))))). % image_insert
thf(fact_98_image__insert, axiom,
    ((![F : msg > msg, A2 : msg, B : set_msg]: ((image_msg_msg @ F @ (insert_msg @ A2 @ B)) = (insert_msg @ (F @ A2) @ (image_msg_msg @ F @ B)))))). % image_insert
thf(fact_99_image__insert, axiom,
    ((![F : msg > nat, A2 : msg, B : set_msg]: ((image_msg_nat @ F @ (insert_msg @ A2 @ B)) = (insert_nat @ (F @ A2) @ (image_msg_nat @ F @ B)))))). % image_insert
thf(fact_100_image__insert, axiom,
    ((![F : nat > msg, A2 : nat, B : set_nat]: ((image_nat_msg @ F @ (insert_nat @ A2 @ B)) = (insert_msg @ (F @ A2) @ (image_nat_msg @ F @ B)))))). % image_insert
thf(fact_101_image__insert, axiom,
    ((![F : nat > nat, A2 : nat, B : set_nat]: ((image_nat_nat @ F @ (insert_nat @ A2 @ B)) = (insert_nat @ (F @ A2) @ (image_nat_nat @ F @ B)))))). % image_insert
thf(fact_102_singletonI, axiom,
    ((![A2 : list_event]: (member_list_event @ A2 @ (insert_list_event @ A2 @ bot_bo1693714908_event))))). % singletonI
thf(fact_103_singletonI, axiom,
    ((![A2 : event]: (member_event @ A2 @ (insert_event @ A2 @ bot_bot_set_event))))). % singletonI
thf(fact_104_singletonI, axiom,
    ((![A2 : agent]: (member_agent @ A2 @ (insert_agent @ A2 @ bot_bot_set_agent))))). % singletonI
thf(fact_105_singletonI, axiom,
    ((![A2 : msg]: (member_msg @ A2 @ (insert_msg @ A2 @ bot_bot_set_msg))))). % singletonI
thf(fact_106_singletonI, axiom,
    ((![A2 : nat]: (member_nat @ A2 @ (insert_nat @ A2 @ bot_bot_set_nat))))). % singletonI
thf(fact_107_parts__cut__eq, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (parts @ H)) => ((parts @ (insert_msg @ X @ H)) = (parts @ H)))))). % parts_cut_eq
thf(fact_108_parts__image__Key, axiom,
    ((![N : set_nat]: ((parts @ (image_nat_msg @ key @ N)) = (image_nat_msg @ key @ N))))). % parts_image_Key
thf(fact_109_parts__empty, axiom,
    (((parts @ bot_bot_set_msg) = bot_bot_set_msg))). % parts_empty
thf(fact_110_singleton__conv2, axiom,
    ((![A2 : msg]: ((collect_msg @ ((^[Y5 : msg]: (^[Z : msg]: (Y5 = Z))) @ A2)) = (insert_msg @ A2 @ bot_bot_set_msg))))). % singleton_conv2
thf(fact_111_singleton__conv2, axiom,
    ((![A2 : nat]: ((collect_nat @ ((^[Y5 : nat]: (^[Z : nat]: (Y5 = Z))) @ A2)) = (insert_nat @ A2 @ bot_bot_set_nat))))). % singleton_conv2
thf(fact_112_singleton__conv, axiom,
    ((![A2 : msg]: ((collect_msg @ (^[X3 : msg]: (X3 = A2))) = (insert_msg @ A2 @ bot_bot_set_msg))))). % singleton_conv
thf(fact_113_singleton__conv, axiom,
    ((![A2 : nat]: ((collect_nat @ (^[X3 : nat]: (X3 = A2))) = (insert_nat @ A2 @ bot_bot_set_nat))))). % singleton_conv
thf(fact_114_mem__Collect__eq, axiom,
    ((![A2 : nat, P : nat > $o]: ((member_nat @ A2 @ (collect_nat @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_115_mem__Collect__eq, axiom,
    ((![A2 : list_event, P : list_event > $o]: ((member_list_event @ A2 @ (collect_list_event @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_116_mem__Collect__eq, axiom,
    ((![A2 : msg, P : msg > $o]: ((member_msg @ A2 @ (collect_msg @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_117_mem__Collect__eq, axiom,
    ((![A2 : event, P : event > $o]: ((member_event @ A2 @ (collect_event @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_118_mem__Collect__eq, axiom,
    ((![A2 : agent, P : agent > $o]: ((member_agent @ A2 @ (collect_agent @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_119_Collect__mem__eq, axiom,
    ((![A : set_nat]: ((collect_nat @ (^[X3 : nat]: (member_nat @ X3 @ A))) = A)))). % Collect_mem_eq
thf(fact_120_Collect__mem__eq, axiom,
    ((![A : set_list_event]: ((collect_list_event @ (^[X3 : list_event]: (member_list_event @ X3 @ A))) = A)))). % Collect_mem_eq
thf(fact_121_Collect__mem__eq, axiom,
    ((![A : set_msg]: ((collect_msg @ (^[X3 : msg]: (member_msg @ X3 @ A))) = A)))). % Collect_mem_eq
thf(fact_122_Collect__mem__eq, axiom,
    ((![A : set_event]: ((collect_event @ (^[X3 : event]: (member_event @ X3 @ A))) = A)))). % Collect_mem_eq
thf(fact_123_Collect__mem__eq, axiom,
    ((![A : set_agent]: ((collect_agent @ (^[X3 : agent]: (member_agent @ X3 @ A))) = A)))). % Collect_mem_eq
thf(fact_124_Collect__const, axiom,
    ((![P : $o]: ((P => ((collect_msg @ (^[S2 : msg]: P)) = top_top_set_msg)) & ((~ (P)) => ((collect_msg @ (^[S2 : msg]: P)) = bot_bot_set_msg)))))). % Collect_const
thf(fact_125_Collect__const, axiom,
    ((![P : $o]: ((P => ((collect_agent @ (^[S2 : agent]: P)) = top_top_set_agent)) & ((~ (P)) => ((collect_agent @ (^[S2 : agent]: P)) = bot_bot_set_agent)))))). % Collect_const
thf(fact_126_Collect__const, axiom,
    ((![P : $o]: ((P => ((collect_nat @ (^[S2 : nat]: P)) = top_top_set_nat)) & ((~ (P)) => ((collect_nat @ (^[S2 : nat]: P)) = bot_bot_set_nat)))))). % Collect_const
thf(fact_127_Spy__in__bad, axiom,
    ((member_agent @ spy @ bad))). % Spy_in_bad
thf(fact_128_Spy__spies__bad__shrK, axiom,
    ((![A : agent, Evs : list_event]: ((member_agent @ A @ bad) => (member_msg @ (key @ (shrK @ A)) @ (knows @ spy @ Evs)))))). % Spy_spies_bad_shrK
thf(fact_129_Spy__see__shrK, axiom,
    ((![Evs : list_event, A : agent]: ((member_list_event @ Evs @ nS_Sha1061662329shared) => ((member_msg @ (key @ (shrK @ A)) @ (parts @ (knows @ spy @ Evs))) = (member_agent @ A @ bad)))))). % Spy_see_shrK
thf(fact_130_Server__not__bad, axiom,
    ((~ ((member_agent @ server @ bad))))). % Server_not_bad
thf(fact_131_Crypt__notin__image__Key, axiom,
    ((![K : nat, X : msg, A : set_nat]: (~ ((member_msg @ (crypt @ K @ X) @ (image_nat_msg @ key @ A))))))). % Crypt_notin_image_Key
thf(fact_132_Nonce__Key__image__eq, axiom,
    ((![X2 : nat, A : set_nat]: (~ ((member_msg @ (nonce @ X2) @ (image_nat_msg @ key @ A))))))). % Nonce_Key_image_eq
thf(fact_133_rev__image__eqI, axiom,
    ((![X2 : nat, A : set_nat, B2 : nat, F : nat > nat]: ((member_nat @ X2 @ A) => ((B2 = (F @ X2)) => (member_nat @ B2 @ (image_nat_nat @ F @ A))))))). % rev_image_eqI
thf(fact_134_rev__image__eqI, axiom,
    ((![X2 : nat, A : set_nat, B2 : msg, F : nat > msg]: ((member_nat @ X2 @ A) => ((B2 = (F @ X2)) => (member_msg @ B2 @ (image_nat_msg @ F @ A))))))). % rev_image_eqI
thf(fact_135_rev__image__eqI, axiom,
    ((![X2 : nat, A : set_nat, B2 : event, F : nat > event]: ((member_nat @ X2 @ A) => ((B2 = (F @ X2)) => (member_event @ B2 @ (image_nat_event @ F @ A))))))). % rev_image_eqI
thf(fact_136_rev__image__eqI, axiom,
    ((![X2 : nat, A : set_nat, B2 : agent, F : nat > agent]: ((member_nat @ X2 @ A) => ((B2 = (F @ X2)) => (member_agent @ B2 @ (image_nat_agent @ F @ A))))))). % rev_image_eqI
thf(fact_137_rev__image__eqI, axiom,
    ((![X2 : msg, A : set_msg, B2 : nat, F : msg > nat]: ((member_msg @ X2 @ A) => ((B2 = (F @ X2)) => (member_nat @ B2 @ (image_msg_nat @ F @ A))))))). % rev_image_eqI
thf(fact_138_rev__image__eqI, axiom,
    ((![X2 : msg, A : set_msg, B2 : msg, F : msg > msg]: ((member_msg @ X2 @ A) => ((B2 = (F @ X2)) => (member_msg @ B2 @ (image_msg_msg @ F @ A))))))). % rev_image_eqI
thf(fact_139_rev__image__eqI, axiom,
    ((![X2 : msg, A : set_msg, B2 : event, F : msg > event]: ((member_msg @ X2 @ A) => ((B2 = (F @ X2)) => (member_event @ B2 @ (image_msg_event @ F @ A))))))). % rev_image_eqI
thf(fact_140_rev__image__eqI, axiom,
    ((![X2 : msg, A : set_msg, B2 : agent, F : msg > agent]: ((member_msg @ X2 @ A) => ((B2 = (F @ X2)) => (member_agent @ B2 @ (image_msg_agent @ F @ A))))))). % rev_image_eqI
thf(fact_141_rev__image__eqI, axiom,
    ((![X2 : event, A : set_event, B2 : nat, F : event > nat]: ((member_event @ X2 @ A) => ((B2 = (F @ X2)) => (member_nat @ B2 @ (image_event_nat @ F @ A))))))). % rev_image_eqI
thf(fact_142_rev__image__eqI, axiom,
    ((![X2 : event, A : set_event, B2 : msg, F : event > msg]: ((member_event @ X2 @ A) => ((B2 = (F @ X2)) => (member_msg @ B2 @ (image_event_msg @ F @ A))))))). % rev_image_eqI
thf(fact_143_ball__imageD, axiom,
    ((![F : agent > nat, A : set_agent, P : nat > $o]: ((![X5 : nat]: ((member_nat @ X5 @ (image_agent_nat @ F @ A)) => (P @ X5))) => (![X6 : agent]: ((member_agent @ X6 @ A) => (P @ (F @ X6)))))))). % ball_imageD
thf(fact_144_ball__imageD, axiom,
    ((![F : nat > msg, A : set_nat, P : msg > $o]: ((![X5 : msg]: ((member_msg @ X5 @ (image_nat_msg @ F @ A)) => (P @ X5))) => (![X6 : nat]: ((member_nat @ X6 @ A) => (P @ (F @ X6)))))))). % ball_imageD
thf(fact_145_ball__imageD, axiom,
    ((![F : agent > msg, A : set_agent, P : msg > $o]: ((![X5 : msg]: ((member_msg @ X5 @ (image_agent_msg @ F @ A)) => (P @ X5))) => (![X6 : agent]: ((member_agent @ X6 @ A) => (P @ (F @ X6)))))))). % ball_imageD
thf(fact_146_image__cong, axiom,
    ((![M : set_nat, N : set_nat, F : nat > msg, G : nat > msg]: ((M = N) => ((![X5 : nat]: ((member_nat @ X5 @ N) => ((F @ X5) = (G @ X5)))) => ((image_nat_msg @ F @ M) = (image_nat_msg @ G @ N))))))). % image_cong
thf(fact_147_image__cong, axiom,
    ((![M : set_agent, N : set_agent, F : agent > nat, G : agent > nat]: ((M = N) => ((![X5 : agent]: ((member_agent @ X5 @ N) => ((F @ X5) = (G @ X5)))) => ((image_agent_nat @ F @ M) = (image_agent_nat @ G @ N))))))). % image_cong
thf(fact_148_image__cong, axiom,
    ((![M : set_agent, N : set_agent, F : agent > msg, G : agent > msg]: ((M = N) => ((![X5 : agent]: ((member_agent @ X5 @ N) => ((F @ X5) = (G @ X5)))) => ((image_agent_msg @ F @ M) = (image_agent_msg @ G @ N))))))). % image_cong
thf(fact_149_bex__imageD, axiom,
    ((![F : agent > nat, A : set_agent, P : nat > $o]: ((?[X6 : nat]: ((member_nat @ X6 @ (image_agent_nat @ F @ A)) & (P @ X6))) => (?[X5 : agent]: ((member_agent @ X5 @ A) & (P @ (F @ X5)))))))). % bex_imageD
thf(fact_150_bex__imageD, axiom,
    ((![F : nat > msg, A : set_nat, P : msg > $o]: ((?[X6 : msg]: ((member_msg @ X6 @ (image_nat_msg @ F @ A)) & (P @ X6))) => (?[X5 : nat]: ((member_nat @ X5 @ A) & (P @ (F @ X5)))))))). % bex_imageD
thf(fact_151_bex__imageD, axiom,
    ((![F : agent > msg, A : set_agent, P : msg > $o]: ((?[X6 : msg]: ((member_msg @ X6 @ (image_agent_msg @ F @ A)) & (P @ X6))) => (?[X5 : agent]: ((member_agent @ X5 @ A) & (P @ (F @ X5)))))))). % bex_imageD
thf(fact_152_image__iff, axiom,
    ((![Z2 : nat, F : agent > nat, A : set_agent]: ((member_nat @ Z2 @ (image_agent_nat @ F @ A)) = (?[X3 : agent]: (((member_agent @ X3 @ A)) & ((Z2 = (F @ X3))))))))). % image_iff
thf(fact_153_image__iff, axiom,
    ((![Z2 : msg, F : nat > msg, A : set_nat]: ((member_msg @ Z2 @ (image_nat_msg @ F @ A)) = (?[X3 : nat]: (((member_nat @ X3 @ A)) & ((Z2 = (F @ X3))))))))). % image_iff
thf(fact_154_image__iff, axiom,
    ((![Z2 : msg, F : agent > msg, A : set_agent]: ((member_msg @ Z2 @ (image_agent_msg @ F @ A)) = (?[X3 : agent]: (((member_agent @ X3 @ A)) & ((Z2 = (F @ X3))))))))). % image_iff
thf(fact_155_imageI, axiom,
    ((![X2 : nat, A : set_nat, F : nat > nat]: ((member_nat @ X2 @ A) => (member_nat @ (F @ X2) @ (image_nat_nat @ F @ A)))))). % imageI
thf(fact_156_imageI, axiom,
    ((![X2 : nat, A : set_nat, F : nat > msg]: ((member_nat @ X2 @ A) => (member_msg @ (F @ X2) @ (image_nat_msg @ F @ A)))))). % imageI
thf(fact_157_imageI, axiom,
    ((![X2 : nat, A : set_nat, F : nat > event]: ((member_nat @ X2 @ A) => (member_event @ (F @ X2) @ (image_nat_event @ F @ A)))))). % imageI
thf(fact_158_imageI, axiom,
    ((![X2 : nat, A : set_nat, F : nat > agent]: ((member_nat @ X2 @ A) => (member_agent @ (F @ X2) @ (image_nat_agent @ F @ A)))))). % imageI
thf(fact_159_imageI, axiom,
    ((![X2 : msg, A : set_msg, F : msg > nat]: ((member_msg @ X2 @ A) => (member_nat @ (F @ X2) @ (image_msg_nat @ F @ A)))))). % imageI
thf(fact_160_imageI, axiom,
    ((![X2 : msg, A : set_msg, F : msg > msg]: ((member_msg @ X2 @ A) => (member_msg @ (F @ X2) @ (image_msg_msg @ F @ A)))))). % imageI
thf(fact_161_imageI, axiom,
    ((![X2 : msg, A : set_msg, F : msg > event]: ((member_msg @ X2 @ A) => (member_event @ (F @ X2) @ (image_msg_event @ F @ A)))))). % imageI
thf(fact_162_imageI, axiom,
    ((![X2 : msg, A : set_msg, F : msg > agent]: ((member_msg @ X2 @ A) => (member_agent @ (F @ X2) @ (image_msg_agent @ F @ A)))))). % imageI
thf(fact_163_imageI, axiom,
    ((![X2 : event, A : set_event, F : event > nat]: ((member_event @ X2 @ A) => (member_nat @ (F @ X2) @ (image_event_nat @ F @ A)))))). % imageI
thf(fact_164_imageI, axiom,
    ((![X2 : event, A : set_event, F : event > msg]: ((member_event @ X2 @ A) => (member_msg @ (F @ X2) @ (image_event_msg @ F @ A)))))). % imageI
thf(fact_165_ex__in__conv, axiom,
    ((![A : set_list_event]: ((?[X3 : list_event]: (member_list_event @ X3 @ A)) = (~ ((A = bot_bo1693714908_event))))))). % ex_in_conv
thf(fact_166_ex__in__conv, axiom,
    ((![A : set_event]: ((?[X3 : event]: (member_event @ X3 @ A)) = (~ ((A = bot_bot_set_event))))))). % ex_in_conv
thf(fact_167_ex__in__conv, axiom,
    ((![A : set_agent]: ((?[X3 : agent]: (member_agent @ X3 @ A)) = (~ ((A = bot_bot_set_agent))))))). % ex_in_conv
thf(fact_168_ex__in__conv, axiom,
    ((![A : set_msg]: ((?[X3 : msg]: (member_msg @ X3 @ A)) = (~ ((A = bot_bot_set_msg))))))). % ex_in_conv
thf(fact_169_ex__in__conv, axiom,
    ((![A : set_nat]: ((?[X3 : nat]: (member_nat @ X3 @ A)) = (~ ((A = bot_bot_set_nat))))))). % ex_in_conv
thf(fact_170_equals0I, axiom,
    ((![A : set_list_event]: ((![Y6 : list_event]: (~ ((member_list_event @ Y6 @ A)))) => (A = bot_bo1693714908_event))))). % equals0I
thf(fact_171_equals0I, axiom,
    ((![A : set_event]: ((![Y6 : event]: (~ ((member_event @ Y6 @ A)))) => (A = bot_bot_set_event))))). % equals0I
thf(fact_172_equals0I, axiom,
    ((![A : set_agent]: ((![Y6 : agent]: (~ ((member_agent @ Y6 @ A)))) => (A = bot_bot_set_agent))))). % equals0I
thf(fact_173_equals0I, axiom,
    ((![A : set_msg]: ((![Y6 : msg]: (~ ((member_msg @ Y6 @ A)))) => (A = bot_bot_set_msg))))). % equals0I
thf(fact_174_equals0I, axiom,
    ((![A : set_nat]: ((![Y6 : nat]: (~ ((member_nat @ Y6 @ A)))) => (A = bot_bot_set_nat))))). % equals0I
thf(fact_175_equals0D, axiom,
    ((![A : set_list_event, A2 : list_event]: ((A = bot_bo1693714908_event) => (~ ((member_list_event @ A2 @ A))))))). % equals0D
thf(fact_176_equals0D, axiom,
    ((![A : set_event, A2 : event]: ((A = bot_bot_set_event) => (~ ((member_event @ A2 @ A))))))). % equals0D
thf(fact_177_equals0D, axiom,
    ((![A : set_agent, A2 : agent]: ((A = bot_bot_set_agent) => (~ ((member_agent @ A2 @ A))))))). % equals0D
thf(fact_178_equals0D, axiom,
    ((![A : set_msg, A2 : msg]: ((A = bot_bot_set_msg) => (~ ((member_msg @ A2 @ A))))))). % equals0D
thf(fact_179_equals0D, axiom,
    ((![A : set_nat, A2 : nat]: ((A = bot_bot_set_nat) => (~ ((member_nat @ A2 @ A))))))). % equals0D
thf(fact_180_emptyE, axiom,
    ((![A2 : list_event]: (~ ((member_list_event @ A2 @ bot_bo1693714908_event)))))). % emptyE
thf(fact_181_emptyE, axiom,
    ((![A2 : event]: (~ ((member_event @ A2 @ bot_bot_set_event)))))). % emptyE
thf(fact_182_emptyE, axiom,
    ((![A2 : agent]: (~ ((member_agent @ A2 @ bot_bot_set_agent)))))). % emptyE
thf(fact_183_emptyE, axiom,
    ((![A2 : msg]: (~ ((member_msg @ A2 @ bot_bot_set_msg)))))). % emptyE
thf(fact_184_emptyE, axiom,
    ((![A2 : nat]: (~ ((member_nat @ A2 @ bot_bot_set_nat)))))). % emptyE
thf(fact_185_mk__disjoint__insert, axiom,
    ((![A2 : nat, A : set_nat]: ((member_nat @ A2 @ A) => (?[B3 : set_nat]: ((A = (insert_nat @ A2 @ B3)) & (~ ((member_nat @ A2 @ B3))))))))). % mk_disjoint_insert
thf(fact_186_mk__disjoint__insert, axiom,
    ((![A2 : list_event, A : set_list_event]: ((member_list_event @ A2 @ A) => (?[B3 : set_list_event]: ((A = (insert_list_event @ A2 @ B3)) & (~ ((member_list_event @ A2 @ B3))))))))). % mk_disjoint_insert
thf(fact_187_mk__disjoint__insert, axiom,
    ((![A2 : msg, A : set_msg]: ((member_msg @ A2 @ A) => (?[B3 : set_msg]: ((A = (insert_msg @ A2 @ B3)) & (~ ((member_msg @ A2 @ B3))))))))). % mk_disjoint_insert
thf(fact_188_mk__disjoint__insert, axiom,
    ((![A2 : event, A : set_event]: ((member_event @ A2 @ A) => (?[B3 : set_event]: ((A = (insert_event @ A2 @ B3)) & (~ ((member_event @ A2 @ B3))))))))). % mk_disjoint_insert
thf(fact_189_mk__disjoint__insert, axiom,
    ((![A2 : agent, A : set_agent]: ((member_agent @ A2 @ A) => (?[B3 : set_agent]: ((A = (insert_agent @ A2 @ B3)) & (~ ((member_agent @ A2 @ B3))))))))). % mk_disjoint_insert
thf(fact_190_insert__commute, axiom,
    ((![X2 : msg, Y2 : msg, A : set_msg]: ((insert_msg @ X2 @ (insert_msg @ Y2 @ A)) = (insert_msg @ Y2 @ (insert_msg @ X2 @ A)))))). % insert_commute
thf(fact_191_insert__commute, axiom,
    ((![X2 : nat, Y2 : nat, A : set_nat]: ((insert_nat @ X2 @ (insert_nat @ Y2 @ A)) = (insert_nat @ Y2 @ (insert_nat @ X2 @ A)))))). % insert_commute
thf(fact_192_insert__eq__iff, axiom,
    ((![A2 : nat, A : set_nat, B2 : nat, B : set_nat]: ((~ ((member_nat @ A2 @ A))) => ((~ ((member_nat @ B2 @ B))) => (((insert_nat @ A2 @ A) = (insert_nat @ B2 @ B)) = (((((A2 = B2)) => ((A = B)))) & ((((~ ((A2 = B2)))) => ((?[C2 : set_nat]: (((A = (insert_nat @ B2 @ C2))) & ((((~ ((member_nat @ B2 @ C2)))) & ((((B = (insert_nat @ A2 @ C2))) & ((~ ((member_nat @ A2 @ C2)))))))))))))))))))). % insert_eq_iff
thf(fact_193_insert__eq__iff, axiom,
    ((![A2 : list_event, A : set_list_event, B2 : list_event, B : set_list_event]: ((~ ((member_list_event @ A2 @ A))) => ((~ ((member_list_event @ B2 @ B))) => (((insert_list_event @ A2 @ A) = (insert_list_event @ B2 @ B)) = (((((A2 = B2)) => ((A = B)))) & ((((~ ((A2 = B2)))) => ((?[C2 : set_list_event]: (((A = (insert_list_event @ B2 @ C2))) & ((((~ ((member_list_event @ B2 @ C2)))) & ((((B = (insert_list_event @ A2 @ C2))) & ((~ ((member_list_event @ A2 @ C2)))))))))))))))))))). % insert_eq_iff
thf(fact_194_insert__eq__iff, axiom,
    ((![A2 : msg, A : set_msg, B2 : msg, B : set_msg]: ((~ ((member_msg @ A2 @ A))) => ((~ ((member_msg @ B2 @ B))) => (((insert_msg @ A2 @ A) = (insert_msg @ B2 @ B)) = (((((A2 = B2)) => ((A = B)))) & ((((~ ((A2 = B2)))) => ((?[C2 : set_msg]: (((A = (insert_msg @ B2 @ C2))) & ((((~ ((member_msg @ B2 @ C2)))) & ((((B = (insert_msg @ A2 @ C2))) & ((~ ((member_msg @ A2 @ C2)))))))))))))))))))). % insert_eq_iff
thf(fact_195_insert__eq__iff, axiom,
    ((![A2 : event, A : set_event, B2 : event, B : set_event]: ((~ ((member_event @ A2 @ A))) => ((~ ((member_event @ B2 @ B))) => (((insert_event @ A2 @ A) = (insert_event @ B2 @ B)) = (((((A2 = B2)) => ((A = B)))) & ((((~ ((A2 = B2)))) => ((?[C2 : set_event]: (((A = (insert_event @ B2 @ C2))) & ((((~ ((member_event @ B2 @ C2)))) & ((((B = (insert_event @ A2 @ C2))) & ((~ ((member_event @ A2 @ C2)))))))))))))))))))). % insert_eq_iff
thf(fact_196_insert__eq__iff, axiom,
    ((![A2 : agent, A : set_agent, B2 : agent, B : set_agent]: ((~ ((member_agent @ A2 @ A))) => ((~ ((member_agent @ B2 @ B))) => (((insert_agent @ A2 @ A) = (insert_agent @ B2 @ B)) = (((((A2 = B2)) => ((A = B)))) & ((((~ ((A2 = B2)))) => ((?[C2 : set_agent]: (((A = (insert_agent @ B2 @ C2))) & ((((~ ((member_agent @ B2 @ C2)))) & ((((B = (insert_agent @ A2 @ C2))) & ((~ ((member_agent @ A2 @ C2)))))))))))))))))))). % insert_eq_iff
thf(fact_197_insert__absorb, axiom,
    ((![A2 : list_event, A : set_list_event]: ((member_list_event @ A2 @ A) => ((insert_list_event @ A2 @ A) = A))))). % insert_absorb
thf(fact_198_insert__absorb, axiom,
    ((![A2 : msg, A : set_msg]: ((member_msg @ A2 @ A) => ((insert_msg @ A2 @ A) = A))))). % insert_absorb
thf(fact_199_insert__absorb, axiom,
    ((![A2 : event, A : set_event]: ((member_event @ A2 @ A) => ((insert_event @ A2 @ A) = A))))). % insert_absorb
thf(fact_200_insert__absorb, axiom,
    ((![A2 : agent, A : set_agent]: ((member_agent @ A2 @ A) => ((insert_agent @ A2 @ A) = A))))). % insert_absorb
thf(fact_201_parts__partsD, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (parts @ (parts @ H))) => (member_msg @ X @ (parts @ H)))))). % parts_partsD
thf(fact_202_parts_OInj, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ H) => (member_msg @ X @ (parts @ H)))))). % parts.Inj
thf(fact_203_symKeys__neq__imp__neq, axiom,
    ((![K : nat, K2 : nat]: ((~ (((member_nat @ K @ symKeys) = (member_nat @ K2 @ symKeys)))) => (~ ((K = K2))))))). % symKeys_neq_imp_neq
thf(fact_204_parts__insert__eq__I, axiom,
    ((![X : msg, H : set_msg]: ((![X5 : msg]: ((member_msg @ X5 @ (parts @ (insert_msg @ X @ H))) => (member_msg @ X5 @ (insert_msg @ X @ (parts @ H))))) => ((parts @ (insert_msg @ X @ H)) = (insert_msg @ X @ (parts @ H))))))). % parts_insert_eq_I
thf(fact_205_parts__insertI, axiom,
    ((![C : msg, G2 : set_msg, A2 : msg]: ((member_msg @ C @ (parts @ G2)) => (member_msg @ C @ (parts @ (insert_msg @ A2 @ G2))))))). % parts_insertI
thf(fact_206_MPair__parts, axiom,
    ((![X : msg, Y : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y) @ (parts @ H)) => (~ (((member_msg @ X @ (parts @ H)) => (~ ((member_msg @ Y @ (parts @ H))))))))))). % MPair_parts
thf(fact_207_parts_OSnd, axiom,
    ((![X : msg, Y : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y) @ (parts @ H)) => (member_msg @ Y @ (parts @ H)))))). % parts.Snd
thf(fact_208_parts_OFst, axiom,
    ((![X : msg, Y : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y) @ (parts @ H)) => (member_msg @ X @ (parts @ H)))))). % parts.Fst
thf(fact_209_msg_Odistinct_I33_J, axiom,
    ((![X4 : nat, X61 : msg, X62 : msg]: (~ (((key @ X4) = (mPair @ X61 @ X62))))))). % msg.distinct(33)
thf(fact_210_msg_Odistinct_I41_J, axiom,
    ((![X61 : msg, X62 : msg, X71 : nat, X72 : msg]: (~ (((mPair @ X61 @ X62) = (crypt @ X71 @ X72))))))). % msg.distinct(41)
thf(fact_211_parts_OBody, axiom,
    ((![K : nat, X : msg, H : set_msg]: ((member_msg @ (crypt @ K @ X) @ (parts @ H)) => (member_msg @ X @ (parts @ H)))))). % parts.Body
thf(fact_212_msg_Odistinct_I35_J, axiom,
    ((![X4 : nat, X71 : nat, X72 : msg]: (~ (((key @ X4) = (crypt @ X71 @ X72))))))). % msg.distinct(35)
thf(fact_213_msg_Odistinct_I27_J, axiom,
    ((![X32 : nat, X61 : msg, X62 : msg]: (~ (((nonce @ X32) = (mPair @ X61 @ X62))))))). % msg.distinct(27)
thf(fact_214_msg_Odistinct_I9_J, axiom,
    ((![X1 : agent, X61 : msg, X62 : msg]: (~ (((agent2 @ X1) = (mPair @ X61 @ X62))))))). % msg.distinct(9)
thf(fact_215_msg_Odistinct_I23_J, axiom,
    ((![X32 : nat, X4 : nat]: (~ (((nonce @ X32) = (key @ X4))))))). % msg.distinct(23)
thf(fact_216_msg_Odistinct_I5_J, axiom,
    ((![X1 : agent, X4 : nat]: (~ (((agent2 @ X1) = (key @ X4))))))). % msg.distinct(5)
thf(fact_217_msg_Odistinct_I29_J, axiom,
    ((![X32 : nat, X71 : nat, X72 : msg]: (~ (((nonce @ X32) = (crypt @ X71 @ X72))))))). % msg.distinct(29)
thf(fact_218_msg_Odistinct_I11_J, axiom,
    ((![X1 : agent, X71 : nat, X72 : msg]: (~ (((agent2 @ X1) = (crypt @ X71 @ X72))))))). % msg.distinct(11)
thf(fact_219_MPair__used__D, axiom,
    ((![X : msg, Y : msg, H : list_event]: ((member_msg @ (mPair @ X @ Y) @ (used @ H)) => ((member_msg @ X @ (used @ H)) & (member_msg @ Y @ (used @ H))))))). % MPair_used_D
thf(fact_220_MPair__used, axiom,
    ((![X : msg, Y : msg, H : list_event]: ((member_msg @ (mPair @ X @ Y) @ (used @ H)) => (~ (((member_msg @ X @ (used @ H)) => (~ ((member_msg @ Y @ (used @ H))))))))))). % MPair_used
thf(fact_221_msg_Odistinct_I3_J, axiom,
    ((![X1 : agent, X32 : nat]: (~ (((agent2 @ X1) = (nonce @ X32))))))). % msg.distinct(3)
thf(fact_222_Nonce__supply1, axiom,
    ((![Evs : list_event]: (?[N2 : nat]: (~ ((member_msg @ (nonce @ N2) @ (used @ Evs)))))))). % Nonce_supply1
thf(fact_223_parts__emptyE, axiom,
    ((![X : msg]: (~ ((member_msg @ X @ (parts @ bot_bot_set_msg))))))). % parts_emptyE
thf(fact_224_agent_Odistinct_I3_J, axiom,
    ((~ ((server = spy))))). % agent.distinct(3)
thf(fact_225_pushKeys_I5_J, axiom,
    ((![K : nat, X : msg, Y : msg, A : set_msg]: ((insert_msg @ (key @ K) @ (insert_msg @ (mPair @ X @ Y) @ A)) = (insert_msg @ (mPair @ X @ Y) @ (insert_msg @ (key @ K) @ A)))))). % pushKeys(5)
thf(fact_226_pushCrypts_I6_J, axiom,
    ((![X : nat, K : msg, X7 : msg, Y : msg, A : set_msg]: ((insert_msg @ (crypt @ X @ K) @ (insert_msg @ (mPair @ X7 @ Y) @ A)) = (insert_msg @ (mPair @ X7 @ Y) @ (insert_msg @ (crypt @ X @ K) @ A)))))). % pushCrypts(6)
thf(fact_227_parts_Oinducts, axiom,
    ((![X2 : msg, H : set_msg, P : msg > $o]: ((member_msg @ X2 @ (parts @ H)) => ((![X8 : msg]: ((member_msg @ X8 @ H) => (P @ X8))) => ((![X8 : msg, Y7 : msg]: ((member_msg @ (mPair @ X8 @ Y7) @ (parts @ H)) => ((P @ (mPair @ X8 @ Y7)) => (P @ X8)))) => ((![X8 : msg, Y7 : msg]: ((member_msg @ (mPair @ X8 @ Y7) @ (parts @ H)) => ((P @ (mPair @ X8 @ Y7)) => (P @ Y7)))) => ((![K3 : nat, X8 : msg]: ((member_msg @ (crypt @ K3 @ X8) @ (parts @ H)) => ((P @ (crypt @ K3 @ X8)) => (P @ X8)))) => (P @ X2))))))))). % parts.inducts
thf(fact_228_parts_Osimps, axiom,
    ((![A2 : msg, H : set_msg]: ((member_msg @ A2 @ (parts @ H)) = (((?[X9 : msg]: (((A2 = X9)) & ((member_msg @ X9 @ H))))) | ((((?[X9 : msg]: (?[Y8 : msg]: (((A2 = X9)) & ((member_msg @ (mPair @ X9 @ Y8) @ (parts @ H))))))) | ((((?[X9 : msg]: (?[Y8 : msg]: (((A2 = Y8)) & ((member_msg @ (mPair @ X9 @ Y8) @ (parts @ H))))))) | ((?[K4 : nat]: (?[X9 : msg]: (((A2 = X9)) & ((member_msg @ (crypt @ K4 @ X9) @ (parts @ H)))))))))))))))). % parts.simps
thf(fact_229_parts_Ocases, axiom,
    ((![A2 : msg, H : set_msg]: ((member_msg @ A2 @ (parts @ H)) => ((~ ((member_msg @ A2 @ H))) => ((![Y7 : msg]: (~ ((member_msg @ (mPair @ A2 @ Y7) @ (parts @ H))))) => ((![X8 : msg]: (~ ((member_msg @ (mPair @ X8 @ A2) @ (parts @ H))))) => (~ ((![K3 : nat]: (~ ((member_msg @ (crypt @ K3 @ A2) @ (parts @ H)))))))))))))). % parts.cases
thf(fact_230_pushKeys_I6_J, axiom,
    ((![K : nat, X : nat, K2 : msg, A : set_msg]: ((insert_msg @ (key @ K) @ (insert_msg @ (crypt @ X @ K2) @ A)) = (insert_msg @ (crypt @ X @ K2) @ (insert_msg @ (key @ K) @ A)))))). % pushKeys(6)
thf(fact_231_pushKeys_I2_J, axiom,
    ((![K : nat, N : nat, A : set_msg]: ((insert_msg @ (key @ K) @ (insert_msg @ (nonce @ N) @ A)) = (insert_msg @ (nonce @ N) @ (insert_msg @ (key @ K) @ A)))))). % pushKeys(2)
thf(fact_232_pushKeys_I1_J, axiom,
    ((![K : nat, C3 : agent, A : set_msg]: ((insert_msg @ (key @ K) @ (insert_msg @ (agent2 @ C3) @ A)) = (insert_msg @ (agent2 @ C3) @ (insert_msg @ (key @ K) @ A)))))). % pushKeys(1)
thf(fact_233_pushCrypts_I3_J, axiom,
    ((![X : nat, K : msg, N : nat, A : set_msg]: ((insert_msg @ (crypt @ X @ K) @ (insert_msg @ (nonce @ N) @ A)) = (insert_msg @ (nonce @ N) @ (insert_msg @ (crypt @ X @ K) @ A)))))). % pushCrypts(3)
thf(fact_234_pushCrypts_I1_J, axiom,
    ((![X : nat, K : msg, C3 : agent, A : set_msg]: ((insert_msg @ (crypt @ X @ K) @ (insert_msg @ (agent2 @ C3) @ A)) = (insert_msg @ (agent2 @ C3) @ (insert_msg @ (crypt @ X @ K) @ A)))))). % pushCrypts(1)
thf(fact_235_parts__singleton, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (parts @ H)) => (?[X5 : msg]: ((member_msg @ X5 @ H) & (member_msg @ X @ (parts @ (insert_msg @ X5 @ bot_bot_set_msg))))))))). % parts_singleton
thf(fact_236_shrK__neq, axiom,
    ((![K : nat, Evs : list_event, B : agent]: ((~ ((member_msg @ (key @ K) @ (used @ Evs)))) => (~ (((shrK @ B) = K))))))). % shrK_neq
thf(fact_237_neq__shrK, axiom,
    ((![S3 : nat, Evs : list_event, B : agent]: ((~ ((member_msg @ (key @ S3) @ (used @ Evs)))) => (~ ((S3 = (shrK @ B)))))))). % neq_shrK
thf(fact_238_Says__imp__knows, axiom,
    ((![A : agent, B : agent, X : msg, Evs : list_event]: ((member_event @ (says @ A @ B @ X) @ (set_event2 @ Evs)) => (member_msg @ X @ (knows @ A @ Evs)))))). % Says_imp_knows
thf(fact_239_Says__imp__used, axiom,
    ((![A : agent, B : agent, X : msg, Evs : list_event]: ((member_event @ (says @ A @ B @ X) @ (set_event2 @ Evs)) => (member_msg @ X @ (used @ Evs)))))). % Says_imp_used
thf(fact_240_Says__imp__knows__Spy, axiom,
    ((![A : agent, B : agent, X : msg, Evs : list_event]: ((member_event @ (says @ A @ B @ X) @ (set_event2 @ Evs)) => (member_msg @ X @ (knows @ spy @ Evs)))))). % Says_imp_knows_Spy
thf(fact_241_cert__A__form, axiom,
    ((![A : agent, NA : msg, B : agent, K : nat, X : msg, Evs : list_event]: ((member_msg @ (crypt @ (shrK @ A) @ (mPair @ NA @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X)))) @ (parts @ (knows @ spy @ Evs))) => ((~ ((member_agent @ A @ bad))) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => ((~ ((member_nat @ K @ (image_agent_nat @ shrK @ top_top_set_agent)))) & (X = (crypt @ (shrK @ B) @ (mPair @ (key @ K) @ (agent2 @ A))))))))))). % cert_A_form
thf(fact_242_Key__not__used, axiom,
    ((![K : nat, Evs : list_event]: ((~ ((member_msg @ (key @ K) @ (used @ Evs)))) => (~ ((member_nat @ K @ (image_agent_nat @ shrK @ top_top_set_agent)))))))). % Key_not_used
thf(fact_243_Says__S__message__form, axiom,
    ((![S : agent, A : agent, NA : nat, B : agent, K : nat, X : msg, Evs : list_event]: ((member_event @ (says @ S @ A @ (crypt @ (shrK @ A) @ (mPair @ (nonce @ NA) @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (set_event2 @ Evs)) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => (((~ ((member_nat @ K @ (image_agent_nat @ shrK @ top_top_set_agent)))) & (X = (crypt @ (shrK @ B) @ (mPair @ (key @ K) @ (agent2 @ A))))) | (member_msg @ X @ (analz @ (knows @ spy @ Evs))))))))). % Says_S_message_form
thf(fact_244_ns__shared_ONS2, axiom,
    ((![Evs2 : list_event, KAB : nat, A3 : agent, A : agent, B : agent, NA : nat]: ((member_list_event @ Evs2 @ nS_Sha1061662329shared) => ((~ ((member_msg @ (key @ KAB) @ (used @ Evs2)))) => ((member_nat @ KAB @ symKeys) => ((member_event @ (says @ A3 @ server @ (mPair @ (agent2 @ A) @ (mPair @ (agent2 @ B) @ (nonce @ NA)))) @ (set_event2 @ Evs2)) => (member_list_event @ (cons_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ (nonce @ NA) @ (mPair @ (agent2 @ B) @ (mPair @ (key @ KAB) @ (crypt @ (shrK @ B) @ (mPair @ (key @ KAB) @ (agent2 @ A)))))))) @ Evs2) @ nS_Sha1061662329shared)))))))). % ns_shared.NS2
thf(fact_245_ns__shared_ONS4, axiom,
    ((![Evs4 : list_event, NB : nat, K : nat, A3 : agent, B : agent, A : agent]: ((member_list_event @ Evs4 @ nS_Sha1061662329shared) => ((~ ((member_msg @ (nonce @ NB) @ (used @ Evs4)))) => ((member_nat @ K @ symKeys) => ((member_event @ (says @ A3 @ B @ (crypt @ (shrK @ B) @ (mPair @ (key @ K) @ (agent2 @ A)))) @ (set_event2 @ Evs4)) => (member_list_event @ (cons_event @ (says @ B @ A @ (crypt @ K @ (nonce @ NB))) @ Evs4) @ nS_Sha1061662329shared)))))))). % ns_shared.NS4
thf(fact_246_ns__shared_ONS5, axiom,
    ((![Evs5 : list_event, K : nat, B4 : agent, A : agent, NB : nat, S : agent, NA : nat, B : agent, X : msg]: ((member_list_event @ Evs5 @ nS_Sha1061662329shared) => ((member_nat @ K @ symKeys) => ((member_event @ (says @ B4 @ A @ (crypt @ K @ (nonce @ NB))) @ (set_event2 @ Evs5)) => ((member_event @ (says @ S @ A @ (crypt @ (shrK @ A) @ (mPair @ (nonce @ NA) @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (set_event2 @ Evs5)) => (member_list_event @ (cons_event @ (says @ A @ B @ (crypt @ K @ (mPair @ (nonce @ NB) @ (nonce @ NB)))) @ Evs5) @ nS_Sha1061662329shared)))))))). % ns_shared.NS5
thf(fact_247_ns__shared_ONS3, axiom,
    ((![Evs3 : list_event, A : agent, S : agent, NA : nat, B : agent, K : nat, X : msg]: ((member_list_event @ Evs3 @ nS_Sha1061662329shared) => ((~ ((A = server))) => ((member_event @ (says @ S @ A @ (crypt @ (shrK @ A) @ (mPair @ (nonce @ NA) @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (set_event2 @ Evs3)) => ((member_event @ (says @ A @ server @ (mPair @ (agent2 @ A) @ (mPair @ (agent2 @ B) @ (nonce @ NA)))) @ (set_event2 @ Evs3)) => (member_list_event @ (cons_event @ (says @ A @ B @ X) @ Evs3) @ nS_Sha1061662329shared)))))))). % ns_shared.NS3
thf(fact_248_new__keys__not__used, axiom,
    ((![K : nat, Evs : list_event]: ((~ ((member_msg @ (key @ K) @ (used @ Evs)))) => ((member_nat @ K @ symKeys) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => (~ ((member_nat @ K @ (keysFor @ (parts @ (knows @ spy @ Evs)))))))))))). % new_keys_not_used

% Conjectures (7)
thf(conj_0, hypothesis,
    ((~ ((member_nat @ kab2 @ (image_agent_nat @ shrK @ top_top_set_agent)))))).
thf(conj_1, hypothesis,
    ((member_list_event @ evs2 @ nS_Sha1061662329shared))).
thf(conj_2, hypothesis,
    ((((member_msg @ (crypt @ kab @ x) @ (parts @ (knows @ spy @ evs2))) & (member_msg @ (key @ k) @ (parts @ (insert_msg @ x @ bot_bot_set_msg)))) => (member_msg @ (key @ k) @ (parts @ (knows @ spy @ evs2)))))).
thf(conj_3, hypothesis,
    ((~ ((member_msg @ (key @ kABa) @ (used @ evs2)))))).
thf(conj_4, hypothesis,
    ((member_nat @ kABa @ symKeys))).
thf(conj_5, hypothesis,
    ((member_event @ (says @ a2 @ server @ (mPair @ (agent2 @ a) @ (mPair @ (agent2 @ b) @ (nonce @ na)))) @ (set_event2 @ evs2)))).
thf(conj_6, conjecture,
    ((((((~ ((kab = (shrK @ a)))) | (~ ((x = (mPair @ (nonce @ na) @ (mPair @ (agent2 @ b) @ (mPair @ (key @ kABa) @ (crypt @ (shrK @ b) @ (mPair @ (key @ kABa) @ (agent2 @ a)))))))))) & (((~ ((kab = (shrK @ b)))) | (~ ((x = (mPair @ (key @ kABa) @ (agent2 @ a)))))) & (~ ((member_msg @ (crypt @ kab @ x) @ (parts @ (knows @ spy @ evs2))))))) | (~ ((member_msg @ (key @ k) @ (parts @ (insert_msg @ x @ bot_bot_set_msg)))))) | ((k = kABa) | (member_msg @ (key @ k) @ (parts @ (knows @ spy @ evs2))))))).
