% 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_157__5229198_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:23:44.526

% Could-be-implicit typings (11)
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__Message__Omsg_J, type,
    list_msg : $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 (69)
thf(sy_c_Event_Obad, type,
    bad : set_agent).
thf(sy_c_Event_Oevent_OGets, type,
    gets : agent > msg > event).
thf(sy_c_Event_Oevent_ONotes, type,
    notes : agent > msg > event).
thf(sy_c_Event_Oevent_OSays, type,
    says : agent > agent > msg > event).
thf(sy_c_Event_OinitState, type,
    initState : agent > set_msg).
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_OCons_001t__Message__Omsg, type,
    cons_msg : msg > list_msg > list_msg).
thf(sy_c_List_Olist_Oset_001t__Event__Oevent, type,
    set_event2 : list_event > set_event).
thf(sy_c_List_Olist_Oset_001t__Message__Omsg, type,
    set_msg2 : list_msg > set_msg).
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_NS__Shared__Mirabelle__xwdrtqxrux_Ons__sharedp, type,
    nS_Sha1092415543haredp : list_event > $o).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Event__Oevent_M_Eo_J, type,
    top_top_event_o : event > $o).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__List__Olist_It__Event__Oevent_J_M_Eo_J, type,
    top_top_list_event_o : list_event > $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__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__Event__Oevent, type,
    image_event_event : (event > event) > set_event > set_event).
thf(sy_c_Set_Oimage_001t__Event__Oevent_001t__Message__Oagent, type,
    image_event_agent : (event > agent) > set_event > set_agent).
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__Message__Oagent_001t__Event__Oevent, type,
    image_agent_event : (agent > event) > set_agent > set_event).
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__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__Message__Omsg, type,
    insert_msg : msg > set_msg > set_msg).
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_B, type,
    b : agent).
thf(sy_v_K, type,
    k : nat).
thf(sy_v_K_H, type,
    k2 : nat).
thf(sy_v_N, type,
    n : msg).
thf(sy_v_X, type,
    x : msg).
thf(sy_v_evs, type,
    evs : list_event).

% Relevant facts (249)
thf(fact_0_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_1_shrK__injective, axiom,
    ((![X : agent, Y : agent]: (((shrK @ X) = (shrK @ Y)) = (X = Y))))). % shrK_injective
thf(fact_2_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_3_msg_Oinject_I1_J, axiom,
    ((![X1 : agent, Y1 : agent]: (((agent2 @ X1) = (agent2 @ Y1)) = (X1 = Y1))))). % msg.inject(1)
thf(fact_4_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_5_msg_Oinject_I4_J, axiom,
    ((![X4 : nat, Y4 : nat]: (((key @ X4) = (key @ Y4)) = (X4 = Y4))))). % msg.inject(4)
thf(fact_6_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_7_UNIV__I, axiom,
    ((![X : event]: (member_event @ X @ top_top_set_event)))). % UNIV_I
thf(fact_8_UNIV__I, axiom,
    ((![X : list_event]: (member_list_event @ X @ top_to1178833912_event)))). % UNIV_I
thf(fact_9_UNIV__I, axiom,
    ((![X : nat]: (member_nat @ X @ top_top_set_nat)))). % UNIV_I
thf(fact_10_UNIV__I, axiom,
    ((![X : msg]: (member_msg @ X @ top_top_set_msg)))). % UNIV_I
thf(fact_11_UNIV__I, axiom,
    ((![X : agent]: (member_agent @ X @ top_top_set_agent)))). % UNIV_I
thf(fact_12_iso__tuple__UNIV__I, axiom,
    ((![X : event]: (member_event @ X @ top_top_set_event)))). % iso_tuple_UNIV_I
thf(fact_13_iso__tuple__UNIV__I, axiom,
    ((![X : list_event]: (member_list_event @ X @ top_to1178833912_event)))). % iso_tuple_UNIV_I
thf(fact_14_iso__tuple__UNIV__I, axiom,
    ((![X : nat]: (member_nat @ X @ top_top_set_nat)))). % iso_tuple_UNIV_I
thf(fact_15_iso__tuple__UNIV__I, axiom,
    ((![X : msg]: (member_msg @ X @ top_top_set_msg)))). % iso_tuple_UNIV_I
thf(fact_16_iso__tuple__UNIV__I, axiom,
    ((![X : agent]: (member_agent @ X @ top_top_set_agent)))). % iso_tuple_UNIV_I
thf(fact_17_image__eqI, axiom,
    ((![B : event, F : event > event, X : event, A : set_event]: ((B = (F @ X)) => ((member_event @ X @ A) => (member_event @ B @ (image_event_event @ F @ A))))))). % image_eqI
thf(fact_18_image__eqI, axiom,
    ((![B : nat, F : event > nat, X : event, A : set_event]: ((B = (F @ X)) => ((member_event @ X @ A) => (member_nat @ B @ (image_event_nat @ F @ A))))))). % image_eqI
thf(fact_19_image__eqI, axiom,
    ((![B : agent, F : event > agent, X : event, A : set_event]: ((B = (F @ X)) => ((member_event @ X @ A) => (member_agent @ B @ (image_event_agent @ F @ A))))))). % image_eqI
thf(fact_20_image__eqI, axiom,
    ((![B : msg, F : event > msg, X : event, A : set_event]: ((B = (F @ X)) => ((member_event @ X @ A) => (member_msg @ B @ (image_event_msg @ F @ A))))))). % image_eqI
thf(fact_21_image__eqI, axiom,
    ((![B : event, F : nat > event, X : nat, A : set_nat]: ((B = (F @ X)) => ((member_nat @ X @ A) => (member_event @ B @ (image_nat_event @ F @ A))))))). % image_eqI
thf(fact_22_image__eqI, axiom,
    ((![B : nat, F : nat > nat, X : nat, A : set_nat]: ((B = (F @ X)) => ((member_nat @ X @ A) => (member_nat @ B @ (image_nat_nat @ F @ A))))))). % image_eqI
thf(fact_23_image__eqI, axiom,
    ((![B : agent, F : nat > agent, X : nat, A : set_nat]: ((B = (F @ X)) => ((member_nat @ X @ A) => (member_agent @ B @ (image_nat_agent @ F @ A))))))). % image_eqI
thf(fact_24_image__eqI, axiom,
    ((![B : msg, F : nat > msg, X : nat, A : set_nat]: ((B = (F @ X)) => ((member_nat @ X @ A) => (member_msg @ B @ (image_nat_msg @ F @ A))))))). % image_eqI
thf(fact_25_image__eqI, axiom,
    ((![B : event, F : agent > event, X : agent, A : set_agent]: ((B = (F @ X)) => ((member_agent @ X @ A) => (member_event @ B @ (image_agent_event @ F @ A))))))). % image_eqI
thf(fact_26_image__eqI, axiom,
    ((![B : nat, F : agent > nat, X : agent, A : set_agent]: ((B = (F @ X)) => ((member_agent @ X @ A) => (member_nat @ B @ (image_agent_nat @ F @ A))))))). % image_eqI
thf(fact_27_msg_Odistinct_I11_J, axiom,
    ((![X1 : agent, X71 : nat, X72 : msg]: (~ (((agent2 @ X1) = (crypt @ X71 @ X72))))))). % msg.distinct(11)
thf(fact_28_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_29_top__set__def, axiom,
    ((top_top_set_agent = (collect_agent @ top_top_agent_o)))). % top_set_def
thf(fact_30_top__set__def, axiom,
    ((top_top_set_msg = (collect_msg @ top_top_msg_o)))). % top_set_def
thf(fact_31_top__set__def, axiom,
    ((top_top_set_nat = (collect_nat @ top_top_nat_o)))). % top_set_def
thf(fact_32_top__set__def, axiom,
    ((top_to1178833912_event = (collect_list_event @ top_top_list_event_o)))). % top_set_def
thf(fact_33_top__set__def, axiom,
    ((top_top_set_event = (collect_event @ top_top_event_o)))). % top_set_def
thf(fact_34_Crypt__notin__image__Key, axiom,
    ((![K : nat, X2 : msg, A : set_nat]: (~ ((member_msg @ (crypt @ K @ X2) @ (image_nat_msg @ key @ A))))))). % Crypt_notin_image_Key
thf(fact_35_rev__image__eqI, axiom,
    ((![X : event, A : set_event, B : event, F : event > event]: ((member_event @ X @ A) => ((B = (F @ X)) => (member_event @ B @ (image_event_event @ F @ A))))))). % rev_image_eqI
thf(fact_36_rev__image__eqI, axiom,
    ((![X : event, A : set_event, B : nat, F : event > nat]: ((member_event @ X @ A) => ((B = (F @ X)) => (member_nat @ B @ (image_event_nat @ F @ A))))))). % rev_image_eqI
thf(fact_37_rev__image__eqI, axiom,
    ((![X : event, A : set_event, B : agent, F : event > agent]: ((member_event @ X @ A) => ((B = (F @ X)) => (member_agent @ B @ (image_event_agent @ F @ A))))))). % rev_image_eqI
thf(fact_38_rev__image__eqI, axiom,
    ((![X : event, A : set_event, B : msg, F : event > msg]: ((member_event @ X @ A) => ((B = (F @ X)) => (member_msg @ B @ (image_event_msg @ F @ A))))))). % rev_image_eqI
thf(fact_39_rev__image__eqI, axiom,
    ((![X : nat, A : set_nat, B : event, F : nat > event]: ((member_nat @ X @ A) => ((B = (F @ X)) => (member_event @ B @ (image_nat_event @ F @ A))))))). % rev_image_eqI
thf(fact_40_rev__image__eqI, axiom,
    ((![X : nat, A : set_nat, B : nat, F : nat > nat]: ((member_nat @ X @ A) => ((B = (F @ X)) => (member_nat @ B @ (image_nat_nat @ F @ A))))))). % rev_image_eqI
thf(fact_41_rev__image__eqI, axiom,
    ((![X : nat, A : set_nat, B : agent, F : nat > agent]: ((member_nat @ X @ A) => ((B = (F @ X)) => (member_agent @ B @ (image_nat_agent @ F @ A))))))). % rev_image_eqI
thf(fact_42_rev__image__eqI, axiom,
    ((![X : nat, A : set_nat, B : msg, F : nat > msg]: ((member_nat @ X @ A) => ((B = (F @ X)) => (member_msg @ B @ (image_nat_msg @ F @ A))))))). % rev_image_eqI
thf(fact_43_rev__image__eqI, axiom,
    ((![X : agent, A : set_agent, B : event, F : agent > event]: ((member_agent @ X @ A) => ((B = (F @ X)) => (member_event @ B @ (image_agent_event @ F @ A))))))). % rev_image_eqI
thf(fact_44_rev__image__eqI, axiom,
    ((![X : agent, A : set_agent, B : nat, F : agent > nat]: ((member_agent @ X @ A) => ((B = (F @ X)) => (member_nat @ B @ (image_agent_nat @ F @ A))))))). % rev_image_eqI
thf(fact_45_ball__imageD, axiom,
    ((![F : agent > nat, A : set_agent, P : nat > $o]: ((![X3 : nat]: ((member_nat @ X3 @ (image_agent_nat @ F @ A)) => (P @ X3))) => (![X5 : agent]: ((member_agent @ X5 @ A) => (P @ (F @ X5)))))))). % ball_imageD
thf(fact_46_ball__imageD, axiom,
    ((![F : nat > msg, A : set_nat, P : msg > $o]: ((![X3 : msg]: ((member_msg @ X3 @ (image_nat_msg @ F @ A)) => (P @ X3))) => (![X5 : nat]: ((member_nat @ X5 @ A) => (P @ (F @ X5)))))))). % ball_imageD
thf(fact_47_image__cong, axiom,
    ((![M : set_nat, N : set_nat, F : nat > msg, G : nat > msg]: ((M = N) => ((![X3 : nat]: ((member_nat @ X3 @ N) => ((F @ X3) = (G @ X3)))) => ((image_nat_msg @ F @ M) = (image_nat_msg @ G @ N))))))). % image_cong
thf(fact_48_image__cong, axiom,
    ((![M : set_agent, N : set_agent, F : agent > nat, G : agent > nat]: ((M = N) => ((![X3 : agent]: ((member_agent @ X3 @ N) => ((F @ X3) = (G @ X3)))) => ((image_agent_nat @ F @ M) = (image_agent_nat @ G @ N))))))). % image_cong
thf(fact_49_bex__imageD, axiom,
    ((![F : agent > nat, A : set_agent, P : nat > $o]: ((?[X5 : nat]: ((member_nat @ X5 @ (image_agent_nat @ F @ A)) & (P @ X5))) => (?[X3 : agent]: ((member_agent @ X3 @ A) & (P @ (F @ X3)))))))). % bex_imageD
thf(fact_50_bex__imageD, axiom,
    ((![F : nat > msg, A : set_nat, P : msg > $o]: ((?[X5 : msg]: ((member_msg @ X5 @ (image_nat_msg @ F @ A)) & (P @ X5))) => (?[X3 : nat]: ((member_nat @ X3 @ A) & (P @ (F @ X3)))))))). % bex_imageD
thf(fact_51_image__iff, axiom,
    ((![Z : nat, F : agent > nat, A : set_agent]: ((member_nat @ Z @ (image_agent_nat @ F @ A)) = (?[X6 : agent]: (((member_agent @ X6 @ A)) & ((Z = (F @ X6))))))))). % image_iff
thf(fact_52_image__iff, axiom,
    ((![Z : msg, F : nat > msg, A : set_nat]: ((member_msg @ Z @ (image_nat_msg @ F @ A)) = (?[X6 : nat]: (((member_nat @ X6 @ A)) & ((Z = (F @ X6))))))))). % image_iff
thf(fact_53_imageI, axiom,
    ((![X : event, A : set_event, F : event > event]: ((member_event @ X @ A) => (member_event @ (F @ X) @ (image_event_event @ F @ A)))))). % imageI
thf(fact_54_imageI, axiom,
    ((![X : event, A : set_event, F : event > nat]: ((member_event @ X @ A) => (member_nat @ (F @ X) @ (image_event_nat @ F @ A)))))). % imageI
thf(fact_55_imageI, axiom,
    ((![X : event, A : set_event, F : event > agent]: ((member_event @ X @ A) => (member_agent @ (F @ X) @ (image_event_agent @ F @ A)))))). % imageI
thf(fact_56_imageI, axiom,
    ((![X : event, A : set_event, F : event > msg]: ((member_event @ X @ A) => (member_msg @ (F @ X) @ (image_event_msg @ F @ A)))))). % imageI
thf(fact_57_imageI, axiom,
    ((![X : nat, A : set_nat, F : nat > event]: ((member_nat @ X @ A) => (member_event @ (F @ X) @ (image_nat_event @ F @ A)))))). % imageI
thf(fact_58_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_59_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_60_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_61_imageI, axiom,
    ((![X : agent, A : set_agent, F : agent > event]: ((member_agent @ X @ A) => (member_event @ (F @ X) @ (image_agent_event @ F @ A)))))). % imageI
thf(fact_62_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_63_UNIV__witness, axiom,
    ((?[X3 : agent]: (member_agent @ X3 @ top_top_set_agent)))). % UNIV_witness
thf(fact_64_UNIV__witness, axiom,
    ((?[X3 : msg]: (member_msg @ X3 @ top_top_set_msg)))). % UNIV_witness
thf(fact_65_UNIV__witness, axiom,
    ((?[X3 : nat]: (member_nat @ X3 @ top_top_set_nat)))). % UNIV_witness
thf(fact_66_UNIV__witness, axiom,
    ((?[X3 : list_event]: (member_list_event @ X3 @ top_to1178833912_event)))). % UNIV_witness
thf(fact_67_UNIV__witness, axiom,
    ((?[X3 : event]: (member_event @ X3 @ top_top_set_event)))). % UNIV_witness
thf(fact_68_UNIV__eq__I, axiom,
    ((![A : set_agent]: ((![X3 : agent]: (member_agent @ X3 @ A)) => (top_top_set_agent = A))))). % UNIV_eq_I
thf(fact_69_UNIV__eq__I, axiom,
    ((![A : set_msg]: ((![X3 : msg]: (member_msg @ X3 @ A)) => (top_top_set_msg = A))))). % UNIV_eq_I
thf(fact_70_UNIV__eq__I, axiom,
    ((![A : set_nat]: ((![X3 : nat]: (member_nat @ X3 @ A)) => (top_top_set_nat = A))))). % UNIV_eq_I
thf(fact_71_UNIV__eq__I, axiom,
    ((![A : set_list_event]: ((![X3 : list_event]: (member_list_event @ X3 @ A)) => (top_to1178833912_event = A))))). % UNIV_eq_I
thf(fact_72_UNIV__eq__I, axiom,
    ((![A : set_event]: ((![X3 : event]: (member_event @ X3 @ A)) => (top_top_set_event = A))))). % UNIV_eq_I
thf(fact_73_range__eqI, axiom,
    ((![B : event, F : agent > event, X : agent]: ((B = (F @ X)) => (member_event @ B @ (image_agent_event @ F @ top_top_set_agent)))))). % range_eqI
thf(fact_74_range__eqI, axiom,
    ((![B : nat, F : agent > nat, X : agent]: ((B = (F @ X)) => (member_nat @ B @ (image_agent_nat @ F @ top_top_set_agent)))))). % range_eqI
thf(fact_75_range__eqI, axiom,
    ((![B : agent, F : agent > agent, X : agent]: ((B = (F @ X)) => (member_agent @ B @ (image_agent_agent @ F @ top_top_set_agent)))))). % range_eqI
thf(fact_76_range__eqI, axiom,
    ((![B : msg, F : agent > msg, X : agent]: ((B = (F @ X)) => (member_msg @ B @ (image_agent_msg @ F @ top_top_set_agent)))))). % range_eqI
thf(fact_77_range__eqI, axiom,
    ((![B : event, F : msg > event, X : msg]: ((B = (F @ X)) => (member_event @ B @ (image_msg_event @ F @ top_top_set_msg)))))). % range_eqI
thf(fact_78_range__eqI, axiom,
    ((![B : nat, F : msg > nat, X : msg]: ((B = (F @ X)) => (member_nat @ B @ (image_msg_nat @ F @ top_top_set_msg)))))). % range_eqI
thf(fact_79_range__eqI, axiom,
    ((![B : agent, F : msg > agent, X : msg]: ((B = (F @ X)) => (member_agent @ B @ (image_msg_agent @ F @ top_top_set_msg)))))). % range_eqI
thf(fact_80_range__eqI, axiom,
    ((![B : msg, F : msg > msg, X : msg]: ((B = (F @ X)) => (member_msg @ B @ (image_msg_msg @ F @ top_top_set_msg)))))). % range_eqI
thf(fact_81_range__eqI, axiom,
    ((![B : event, F : nat > event, X : nat]: ((B = (F @ X)) => (member_event @ B @ (image_nat_event @ F @ top_top_set_nat)))))). % range_eqI
thf(fact_82_range__eqI, axiom,
    ((![B : nat, F : nat > nat, X : nat]: ((B = (F @ X)) => (member_nat @ B @ (image_nat_nat @ F @ top_top_set_nat)))))). % range_eqI
thf(fact_83_rangeI, axiom,
    ((![F : agent > event, X : agent]: (member_event @ (F @ X) @ (image_agent_event @ F @ top_top_set_agent))))). % rangeI
thf(fact_84_rangeI, axiom,
    ((![F : agent > nat, X : agent]: (member_nat @ (F @ X) @ (image_agent_nat @ F @ top_top_set_agent))))). % rangeI
thf(fact_85_rangeI, axiom,
    ((![F : agent > agent, X : agent]: (member_agent @ (F @ X) @ (image_agent_agent @ F @ top_top_set_agent))))). % rangeI
thf(fact_86_rangeI, axiom,
    ((![F : agent > msg, X : agent]: (member_msg @ (F @ X) @ (image_agent_msg @ F @ top_top_set_agent))))). % rangeI
thf(fact_87_rangeI, axiom,
    ((![F : msg > event, X : msg]: (member_event @ (F @ X) @ (image_msg_event @ F @ top_top_set_msg))))). % rangeI
thf(fact_88_rangeI, axiom,
    ((![F : msg > nat, X : msg]: (member_nat @ (F @ X) @ (image_msg_nat @ F @ top_top_set_msg))))). % rangeI
thf(fact_89_rangeI, axiom,
    ((![F : msg > agent, X : msg]: (member_agent @ (F @ X) @ (image_msg_agent @ F @ top_top_set_msg))))). % rangeI
thf(fact_90_rangeI, axiom,
    ((![F : msg > msg, X : msg]: (member_msg @ (F @ X) @ (image_msg_msg @ F @ top_top_set_msg))))). % rangeI
thf(fact_91_rangeI, axiom,
    ((![F : nat > event, X : nat]: (member_event @ (F @ X) @ (image_nat_event @ F @ top_top_set_nat))))). % rangeI
thf(fact_92_rangeI, axiom,
    ((![F : nat > nat, X : nat]: (member_nat @ (F @ X) @ (image_nat_nat @ F @ top_top_set_nat))))). % rangeI
thf(fact_93_msg_Odistinct_I33_J, axiom,
    ((![X4 : nat, X61 : msg, X62 : msg]: (~ (((key @ X4) = (mPair @ X61 @ X62))))))). % msg.distinct(33)
thf(fact_94_msg_Odistinct_I41_J, axiom,
    ((![X61 : msg, X62 : msg, X71 : nat, X72 : msg]: (~ (((mPair @ X61 @ X62) = (crypt @ X71 @ X72))))))). % msg.distinct(41)
thf(fact_95_msg_Odistinct_I35_J, axiom,
    ((![X4 : nat, X71 : nat, X72 : msg]: (~ (((key @ X4) = (crypt @ X71 @ X72))))))). % msg.distinct(35)
thf(fact_96_msg_Odistinct_I9_J, axiom,
    ((![X1 : agent, X61 : msg, X62 : msg]: (~ (((agent2 @ X1) = (mPair @ X61 @ X62))))))). % msg.distinct(9)
thf(fact_97_msg_Odistinct_I5_J, axiom,
    ((![X1 : agent, X4 : nat]: (~ (((agent2 @ X1) = (key @ X4))))))). % msg.distinct(5)
thf(fact_98_surj__def, axiom,
    ((![F : agent > agent]: (((image_agent_agent @ F @ top_top_set_agent) = top_top_set_agent) = (![Y2 : agent]: (?[X6 : agent]: (Y2 = (F @ X6)))))))). % surj_def
thf(fact_99_surj__def, axiom,
    ((![F : agent > msg]: (((image_agent_msg @ F @ top_top_set_agent) = top_top_set_msg) = (![Y2 : msg]: (?[X6 : agent]: (Y2 = (F @ X6)))))))). % surj_def
thf(fact_100_surj__def, axiom,
    ((![F : agent > nat]: (((image_agent_nat @ F @ top_top_set_agent) = top_top_set_nat) = (![Y2 : nat]: (?[X6 : agent]: (Y2 = (F @ X6)))))))). % surj_def
thf(fact_101_surj__def, axiom,
    ((![F : agent > event]: (((image_agent_event @ F @ top_top_set_agent) = top_top_set_event) = (![Y2 : event]: (?[X6 : agent]: (Y2 = (F @ X6)))))))). % surj_def
thf(fact_102_surj__def, axiom,
    ((![F : msg > agent]: (((image_msg_agent @ F @ top_top_set_msg) = top_top_set_agent) = (![Y2 : agent]: (?[X6 : msg]: (Y2 = (F @ X6)))))))). % surj_def
thf(fact_103_surj__def, axiom,
    ((![F : msg > msg]: (((image_msg_msg @ F @ top_top_set_msg) = top_top_set_msg) = (![Y2 : msg]: (?[X6 : msg]: (Y2 = (F @ X6)))))))). % surj_def
thf(fact_104_surj__def, axiom,
    ((![F : msg > nat]: (((image_msg_nat @ F @ top_top_set_msg) = top_top_set_nat) = (![Y2 : nat]: (?[X6 : msg]: (Y2 = (F @ X6)))))))). % surj_def
thf(fact_105_surj__def, axiom,
    ((![F : msg > event]: (((image_msg_event @ F @ top_top_set_msg) = top_top_set_event) = (![Y2 : event]: (?[X6 : msg]: (Y2 = (F @ X6)))))))). % surj_def
thf(fact_106_surj__def, axiom,
    ((![F : nat > agent]: (((image_nat_agent @ F @ top_top_set_nat) = top_top_set_agent) = (![Y2 : agent]: (?[X6 : nat]: (Y2 = (F @ X6)))))))). % surj_def
thf(fact_107_surj__def, axiom,
    ((![F : nat > msg]: (((image_nat_msg @ F @ top_top_set_nat) = top_top_set_msg) = (![Y2 : msg]: (?[X6 : nat]: (Y2 = (F @ X6)))))))). % surj_def
thf(fact_108_surjI, axiom,
    ((![G : agent > agent, F : agent > agent]: ((![X3 : agent]: ((G @ (F @ X3)) = X3)) => ((image_agent_agent @ G @ top_top_set_agent) = top_top_set_agent))))). % surjI
thf(fact_109_surjI, axiom,
    ((![G : agent > msg, F : msg > agent]: ((![X3 : msg]: ((G @ (F @ X3)) = X3)) => ((image_agent_msg @ G @ top_top_set_agent) = top_top_set_msg))))). % surjI
thf(fact_110_surjI, axiom,
    ((![G : agent > nat, F : nat > agent]: ((![X3 : nat]: ((G @ (F @ X3)) = X3)) => ((image_agent_nat @ G @ top_top_set_agent) = top_top_set_nat))))). % surjI
thf(fact_111_surjI, axiom,
    ((![G : agent > event, F : event > agent]: ((![X3 : event]: ((G @ (F @ X3)) = X3)) => ((image_agent_event @ G @ top_top_set_agent) = top_top_set_event))))). % surjI
thf(fact_112_surjI, axiom,
    ((![G : msg > agent, F : agent > msg]: ((![X3 : agent]: ((G @ (F @ X3)) = X3)) => ((image_msg_agent @ G @ top_top_set_msg) = top_top_set_agent))))). % surjI
thf(fact_113_surjI, axiom,
    ((![G : msg > msg, F : msg > msg]: ((![X3 : msg]: ((G @ (F @ X3)) = X3)) => ((image_msg_msg @ G @ top_top_set_msg) = top_top_set_msg))))). % surjI
thf(fact_114_surjI, axiom,
    ((![G : msg > nat, F : nat > msg]: ((![X3 : nat]: ((G @ (F @ X3)) = X3)) => ((image_msg_nat @ G @ top_top_set_msg) = top_top_set_nat))))). % surjI
thf(fact_115_surjI, axiom,
    ((![G : msg > event, F : event > msg]: ((![X3 : event]: ((G @ (F @ X3)) = X3)) => ((image_msg_event @ G @ top_top_set_msg) = top_top_set_event))))). % surjI
thf(fact_116_surjI, axiom,
    ((![G : nat > agent, F : agent > nat]: ((![X3 : agent]: ((G @ (F @ X3)) = X3)) => ((image_nat_agent @ G @ top_top_set_nat) = top_top_set_agent))))). % surjI
thf(fact_117_surjI, axiom,
    ((![G : nat > msg, F : msg > nat]: ((![X3 : msg]: ((G @ (F @ X3)) = X3)) => ((image_nat_msg @ G @ top_top_set_nat) = top_top_set_msg))))). % surjI
thf(fact_118_surjE, axiom,
    ((![F : agent > agent, Y : agent]: (((image_agent_agent @ F @ top_top_set_agent) = top_top_set_agent) => (~ ((![X3 : agent]: (~ ((Y = (F @ X3))))))))))). % surjE
thf(fact_119_surjE, axiom,
    ((![F : agent > msg, Y : msg]: (((image_agent_msg @ F @ top_top_set_agent) = top_top_set_msg) => (~ ((![X3 : agent]: (~ ((Y = (F @ X3))))))))))). % surjE
thf(fact_120_surjE, axiom,
    ((![F : agent > nat, Y : nat]: (((image_agent_nat @ F @ top_top_set_agent) = top_top_set_nat) => (~ ((![X3 : agent]: (~ ((Y = (F @ X3))))))))))). % surjE
thf(fact_121_surjE, axiom,
    ((![F : agent > event, Y : event]: (((image_agent_event @ F @ top_top_set_agent) = top_top_set_event) => (~ ((![X3 : agent]: (~ ((Y = (F @ X3))))))))))). % surjE
thf(fact_122_surjE, axiom,
    ((![F : msg > agent, Y : agent]: (((image_msg_agent @ F @ top_top_set_msg) = top_top_set_agent) => (~ ((![X3 : msg]: (~ ((Y = (F @ X3))))))))))). % surjE
thf(fact_123_surjE, axiom,
    ((![F : msg > msg, Y : msg]: (((image_msg_msg @ F @ top_top_set_msg) = top_top_set_msg) => (~ ((![X3 : msg]: (~ ((Y = (F @ X3))))))))))). % surjE
thf(fact_124_surjE, axiom,
    ((![F : msg > nat, Y : nat]: (((image_msg_nat @ F @ top_top_set_msg) = top_top_set_nat) => (~ ((![X3 : msg]: (~ ((Y = (F @ X3))))))))))). % surjE
thf(fact_125_surjE, axiom,
    ((![F : msg > event, Y : event]: (((image_msg_event @ F @ top_top_set_msg) = top_top_set_event) => (~ ((![X3 : msg]: (~ ((Y = (F @ X3))))))))))). % surjE
thf(fact_126_surjE, axiom,
    ((![F : nat > agent, Y : agent]: (((image_nat_agent @ F @ top_top_set_nat) = top_top_set_agent) => (~ ((![X3 : nat]: (~ ((Y = (F @ X3))))))))))). % surjE
thf(fact_127_surjE, axiom,
    ((![F : nat > msg, Y : msg]: (((image_nat_msg @ F @ top_top_set_nat) = top_top_set_msg) => (~ ((![X3 : nat]: (~ ((Y = (F @ X3))))))))))). % surjE
thf(fact_128_surjD, axiom,
    ((![F : agent > agent, Y : agent]: (((image_agent_agent @ F @ top_top_set_agent) = top_top_set_agent) => (?[X3 : agent]: (Y = (F @ X3))))))). % surjD
thf(fact_129_surjD, axiom,
    ((![F : agent > msg, Y : msg]: (((image_agent_msg @ F @ top_top_set_agent) = top_top_set_msg) => (?[X3 : agent]: (Y = (F @ X3))))))). % surjD
thf(fact_130_surjD, axiom,
    ((![F : agent > nat, Y : nat]: (((image_agent_nat @ F @ top_top_set_agent) = top_top_set_nat) => (?[X3 : agent]: (Y = (F @ X3))))))). % surjD
thf(fact_131_surjD, axiom,
    ((![F : agent > event, Y : event]: (((image_agent_event @ F @ top_top_set_agent) = top_top_set_event) => (?[X3 : agent]: (Y = (F @ X3))))))). % surjD
thf(fact_132_surjD, axiom,
    ((![F : msg > agent, Y : agent]: (((image_msg_agent @ F @ top_top_set_msg) = top_top_set_agent) => (?[X3 : msg]: (Y = (F @ X3))))))). % surjD
thf(fact_133_surjD, axiom,
    ((![F : msg > msg, Y : msg]: (((image_msg_msg @ F @ top_top_set_msg) = top_top_set_msg) => (?[X3 : msg]: (Y = (F @ X3))))))). % surjD
thf(fact_134_surjD, axiom,
    ((![F : msg > nat, Y : nat]: (((image_msg_nat @ F @ top_top_set_msg) = top_top_set_nat) => (?[X3 : msg]: (Y = (F @ X3))))))). % surjD
thf(fact_135_surjD, axiom,
    ((![F : msg > event, Y : event]: (((image_msg_event @ F @ top_top_set_msg) = top_top_set_event) => (?[X3 : msg]: (Y = (F @ X3))))))). % surjD
thf(fact_136_surjD, axiom,
    ((![F : nat > agent, Y : agent]: (((image_nat_agent @ F @ top_top_set_nat) = top_top_set_agent) => (?[X3 : nat]: (Y = (F @ X3))))))). % surjD
thf(fact_137_surjD, axiom,
    ((![F : nat > msg, Y : msg]: (((image_nat_msg @ F @ top_top_set_nat) = top_top_set_msg) => (?[X3 : nat]: (Y = (F @ X3))))))). % surjD
thf(fact_138_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_139_ns__shared_ONS3, axiom,
    ((![Evs3 : list_event, A : agent, S : agent, NA : nat, B2 : agent, K : nat, X2 : msg]: ((member_list_event @ Evs3 @ nS_Sha1061662329shared) => ((~ ((A = server))) => ((member_event @ (says @ S @ A @ (crypt @ (shrK @ A) @ (mPair @ (nonce @ NA) @ (mPair @ (agent2 @ B2) @ (mPair @ (key @ K) @ X2))))) @ (set_event2 @ Evs3)) => ((member_event @ (says @ A @ server @ (mPair @ (agent2 @ A) @ (mPair @ (agent2 @ B2) @ (nonce @ NA)))) @ (set_event2 @ Evs3)) => (member_list_event @ (cons_event @ (says @ A @ B2 @ X2) @ Evs3) @ nS_Sha1061662329shared)))))))). % ns_shared.NS3
thf(fact_140_shrK__in__initState, axiom,
    ((![A : agent]: (member_msg @ (key @ (shrK @ A)) @ (initState @ A))))). % shrK_in_initState
thf(fact_141_top__empty__eq, axiom,
    ((top_top_agent_o = (^[X6 : agent]: (member_agent @ X6 @ top_top_set_agent))))). % top_empty_eq
thf(fact_142_top__empty__eq, axiom,
    ((top_top_msg_o = (^[X6 : msg]: (member_msg @ X6 @ top_top_set_msg))))). % top_empty_eq
thf(fact_143_top__empty__eq, axiom,
    ((top_top_nat_o = (^[X6 : nat]: (member_nat @ X6 @ top_top_set_nat))))). % top_empty_eq
thf(fact_144_top__empty__eq, axiom,
    ((top_top_list_event_o = (^[X6 : list_event]: (member_list_event @ X6 @ top_to1178833912_event))))). % top_empty_eq
thf(fact_145_top__empty__eq, axiom,
    ((top_top_event_o = (^[X6 : event]: (member_event @ X6 @ top_top_set_event))))). % top_empty_eq
thf(fact_146_Sup_OSUP__cong, axiom,
    ((![A : set_nat, B2 : set_nat, C : nat > msg, D : nat > msg, Sup : set_msg > msg]: ((A = B2) => ((![X3 : nat]: ((member_nat @ X3 @ B2) => ((C @ X3) = (D @ X3)))) => ((Sup @ (image_nat_msg @ C @ A)) = (Sup @ (image_nat_msg @ D @ B2)))))))). % Sup.SUP_cong
thf(fact_147_Sup_OSUP__cong, axiom,
    ((![A : set_agent, B2 : set_agent, C : agent > nat, D : agent > nat, Sup : set_nat > nat]: ((A = B2) => ((![X3 : agent]: ((member_agent @ X3 @ B2) => ((C @ X3) = (D @ X3)))) => ((Sup @ (image_agent_nat @ C @ A)) = (Sup @ (image_agent_nat @ D @ B2)))))))). % Sup.SUP_cong
thf(fact_148_msg_Oinject_I3_J, axiom,
    ((![X32 : nat, Y3 : nat]: (((nonce @ X32) = (nonce @ Y3)) = (X32 = Y3))))). % msg.inject(3)
thf(fact_149_shrK__in__used, axiom,
    ((![A : agent, Evs : list_event]: (member_msg @ (key @ (shrK @ A)) @ (used @ Evs))))). % shrK_in_used
thf(fact_150_Nonce__supply1, axiom,
    ((![Evs : list_event]: (?[N2 : nat]: (~ ((member_msg @ (nonce @ N2) @ (used @ Evs)))))))). % Nonce_supply1
thf(fact_151_msg_Odistinct_I27_J, axiom,
    ((![X32 : nat, X61 : msg, X62 : msg]: (~ (((nonce @ X32) = (mPair @ X61 @ X62))))))). % msg.distinct(27)
thf(fact_152_mem__Collect__eq, axiom,
    ((![A2 : event, P : event > $o]: ((member_event @ A2 @ (collect_event @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_153_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_154_mem__Collect__eq, axiom,
    ((![A2 : nat, P : nat > $o]: ((member_nat @ A2 @ (collect_nat @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_155_mem__Collect__eq, axiom,
    ((![A2 : agent, P : agent > $o]: ((member_agent @ A2 @ (collect_agent @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_156_mem__Collect__eq, axiom,
    ((![A2 : msg, P : msg > $o]: ((member_msg @ A2 @ (collect_msg @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_157_Collect__mem__eq, axiom,
    ((![A : set_event]: ((collect_event @ (^[X6 : event]: (member_event @ X6 @ A))) = A)))). % Collect_mem_eq
thf(fact_158_Collect__mem__eq, axiom,
    ((![A : set_list_event]: ((collect_list_event @ (^[X6 : list_event]: (member_list_event @ X6 @ A))) = A)))). % Collect_mem_eq
thf(fact_159_Collect__mem__eq, axiom,
    ((![A : set_nat]: ((collect_nat @ (^[X6 : nat]: (member_nat @ X6 @ A))) = A)))). % Collect_mem_eq
thf(fact_160_Collect__mem__eq, axiom,
    ((![A : set_agent]: ((collect_agent @ (^[X6 : agent]: (member_agent @ X6 @ A))) = A)))). % Collect_mem_eq
thf(fact_161_Collect__mem__eq, axiom,
    ((![A : set_msg]: ((collect_msg @ (^[X6 : msg]: (member_msg @ X6 @ A))) = A)))). % Collect_mem_eq
thf(fact_162_msg_Odistinct_I23_J, axiom,
    ((![X32 : nat, X4 : nat]: (~ (((nonce @ X32) = (key @ X4))))))). % msg.distinct(23)
thf(fact_163_Nonce__Key__image__eq, axiom,
    ((![X : nat, A : set_nat]: (~ ((member_msg @ (nonce @ X) @ (image_nat_msg @ key @ A))))))). % Nonce_Key_image_eq
thf(fact_164_msg_Odistinct_I29_J, axiom,
    ((![X32 : nat, X71 : nat, X72 : msg]: (~ (((nonce @ X32) = (crypt @ X71 @ X72))))))). % msg.distinct(29)
thf(fact_165_msg_Odistinct_I3_J, axiom,
    ((![X1 : agent, X32 : nat]: (~ (((agent2 @ X1) = (nonce @ X32))))))). % msg.distinct(3)
thf(fact_166_MPair__used, axiom,
    ((![X2 : msg, Y5 : msg, H : list_event]: ((member_msg @ (mPair @ X2 @ Y5) @ (used @ H)) => (~ (((member_msg @ X2 @ (used @ H)) => (~ ((member_msg @ Y5 @ (used @ H))))))))))). % MPair_used
thf(fact_167_MPair__used__D, axiom,
    ((![X2 : msg, Y5 : msg, H : list_event]: ((member_msg @ (mPair @ X2 @ Y5) @ (used @ H)) => ((member_msg @ X2 @ (used @ H)) & (member_msg @ Y5 @ (used @ H))))))). % MPair_used_D
thf(fact_168_ns__shared_ONS1, axiom,
    ((![Evs1 : list_event, NA : nat, A : agent, B2 : agent]: ((member_list_event @ Evs1 @ nS_Sha1061662329shared) => ((~ ((member_msg @ (nonce @ NA) @ (used @ Evs1)))) => (member_list_event @ (cons_event @ (says @ A @ server @ (mPair @ (agent2 @ A) @ (mPair @ (agent2 @ B2) @ (nonce @ NA)))) @ Evs1) @ nS_Sha1061662329shared)))))). % ns_shared.NS1
thf(fact_169_neq__shrK, axiom,
    ((![S2 : nat, Evs : list_event, B2 : agent]: ((~ ((member_msg @ (key @ S2) @ (used @ Evs)))) => (~ ((S2 = (shrK @ B2)))))))). % neq_shrK
thf(fact_170_shrK__neq, axiom,
    ((![K : nat, Evs : list_event, B2 : agent]: ((~ ((member_msg @ (key @ K) @ (used @ Evs)))) => (~ (((shrK @ B2) = K))))))). % shrK_neq
thf(fact_171_Says__imp__used, axiom,
    ((![A : agent, B2 : agent, X2 : msg, Evs : list_event]: ((member_event @ (says @ A @ B2 @ X2) @ (set_event2 @ Evs)) => (member_msg @ X2 @ (used @ Evs)))))). % Says_imp_used
thf(fact_172_Inf_OINF__cong, axiom,
    ((![A : set_nat, B2 : set_nat, C : nat > msg, D : nat > msg, Inf : set_msg > msg]: ((A = B2) => ((![X3 : nat]: ((member_nat @ X3 @ B2) => ((C @ X3) = (D @ X3)))) => ((Inf @ (image_nat_msg @ C @ A)) = (Inf @ (image_nat_msg @ D @ B2)))))))). % Inf.INF_cong
thf(fact_173_Inf_OINF__cong, axiom,
    ((![A : set_agent, B2 : set_agent, C : agent > nat, D : agent > nat, Inf : set_nat > nat]: ((A = B2) => ((![X3 : agent]: ((member_agent @ X3 @ B2) => ((C @ X3) = (D @ X3)))) => ((Inf @ (image_agent_nat @ C @ A)) = (Inf @ (image_agent_nat @ D @ B2)))))))). % Inf.INF_cong
thf(fact_174_ns__shared_ONS2, axiom,
    ((![Evs2 : list_event, KAB : nat, A3 : agent, A : agent, B2 : 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 @ B2) @ (nonce @ NA)))) @ (set_event2 @ Evs2)) => (member_list_event @ (cons_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ (nonce @ NA) @ (mPair @ (agent2 @ B2) @ (mPair @ (key @ KAB) @ (crypt @ (shrK @ B2) @ (mPair @ (key @ KAB) @ (agent2 @ A)))))))) @ Evs2) @ nS_Sha1061662329shared)))))))). % ns_shared.NS2
thf(fact_175_ns__shared_ONS4, axiom,
    ((![Evs4 : list_event, NB : nat, K : nat, A3 : agent, B2 : agent, A : agent]: ((member_list_event @ Evs4 @ nS_Sha1061662329shared) => ((~ ((member_msg @ (nonce @ NB) @ (used @ Evs4)))) => ((member_nat @ K @ symKeys) => ((member_event @ (says @ A3 @ B2 @ (crypt @ (shrK @ B2) @ (mPair @ (key @ K) @ (agent2 @ A)))) @ (set_event2 @ Evs4)) => (member_list_event @ (cons_event @ (says @ B2 @ A @ (crypt @ K @ (nonce @ NB))) @ Evs4) @ nS_Sha1061662329shared)))))))). % ns_shared.NS4
thf(fact_176_ns__shared_ONS5, axiom,
    ((![Evs5 : list_event, K : nat, B3 : agent, A : agent, NB : nat, S : agent, NA : nat, B2 : agent, X2 : msg]: ((member_list_event @ Evs5 @ nS_Sha1061662329shared) => ((member_nat @ K @ symKeys) => ((member_event @ (says @ B3 @ A @ (crypt @ K @ (nonce @ NB))) @ (set_event2 @ Evs5)) => ((member_event @ (says @ S @ A @ (crypt @ (shrK @ A) @ (mPair @ (nonce @ NA) @ (mPair @ (agent2 @ B2) @ (mPair @ (key @ K) @ X2))))) @ (set_event2 @ Evs5)) => (member_list_event @ (cons_event @ (says @ A @ B2 @ (crypt @ K @ (mPair @ (nonce @ NB) @ (nonce @ NB)))) @ Evs5) @ nS_Sha1061662329shared)))))))). % ns_shared.NS5
thf(fact_177_ns__sharedp_ONS3, axiom,
    ((![Evs3 : list_event, A : agent, S : agent, NA : nat, B2 : agent, K : nat, X2 : msg]: ((nS_Sha1092415543haredp @ Evs3) => ((~ ((A = server))) => ((member_event @ (says @ S @ A @ (crypt @ (shrK @ A) @ (mPair @ (nonce @ NA) @ (mPair @ (agent2 @ B2) @ (mPair @ (key @ K) @ X2))))) @ (set_event2 @ Evs3)) => ((member_event @ (says @ A @ server @ (mPair @ (agent2 @ A) @ (mPair @ (agent2 @ B2) @ (nonce @ NA)))) @ (set_event2 @ Evs3)) => (nS_Sha1092415543haredp @ (cons_event @ (says @ A @ B2 @ X2) @ Evs3))))))))). % ns_sharedp.NS3
thf(fact_178_ns__sharedp_ONS1, axiom,
    ((![Evs1 : list_event, NA : nat, A : agent, B2 : agent]: ((nS_Sha1092415543haredp @ Evs1) => ((~ ((member_msg @ (nonce @ NA) @ (used @ Evs1)))) => (nS_Sha1092415543haredp @ (cons_event @ (says @ A @ server @ (mPair @ (agent2 @ A) @ (mPair @ (agent2 @ B2) @ (nonce @ NA)))) @ Evs1))))))). % ns_sharedp.NS1
thf(fact_179_ns__sharedp_ONS2, axiom,
    ((![Evs2 : list_event, KAB : nat, A3 : agent, A : agent, B2 : agent, NA : nat]: ((nS_Sha1092415543haredp @ Evs2) => ((~ ((member_msg @ (key @ KAB) @ (used @ Evs2)))) => ((member_nat @ KAB @ symKeys) => ((member_event @ (says @ A3 @ server @ (mPair @ (agent2 @ A) @ (mPair @ (agent2 @ B2) @ (nonce @ NA)))) @ (set_event2 @ Evs2)) => (nS_Sha1092415543haredp @ (cons_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ (nonce @ NA) @ (mPair @ (agent2 @ B2) @ (mPair @ (key @ KAB) @ (crypt @ (shrK @ B2) @ (mPair @ (key @ KAB) @ (agent2 @ A)))))))) @ Evs2))))))))). % ns_sharedp.NS2
thf(fact_180_sym__shrK, axiom,
    ((![X2 : agent]: (member_nat @ (shrK @ X2) @ symKeys)))). % sym_shrK
thf(fact_181_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_182_ns__sharedp__ns__shared__eq, axiom,
    ((nS_Sha1092415543haredp = (^[X6 : list_event]: (member_list_event @ X6 @ nS_Sha1061662329shared))))). % ns_sharedp_ns_shared_eq
thf(fact_183_ns__sharedp_ONS5, axiom,
    ((![Evs5 : list_event, K : nat, B3 : agent, A : agent, NB : nat, S : agent, NA : nat, B2 : agent, X2 : msg]: ((nS_Sha1092415543haredp @ Evs5) => ((member_nat @ K @ symKeys) => ((member_event @ (says @ B3 @ A @ (crypt @ K @ (nonce @ NB))) @ (set_event2 @ Evs5)) => ((member_event @ (says @ S @ A @ (crypt @ (shrK @ A) @ (mPair @ (nonce @ NA) @ (mPair @ (agent2 @ B2) @ (mPair @ (key @ K) @ X2))))) @ (set_event2 @ Evs5)) => (nS_Sha1092415543haredp @ (cons_event @ (says @ A @ B2 @ (crypt @ K @ (mPair @ (nonce @ NB) @ (nonce @ NB)))) @ Evs5))))))))). % ns_sharedp.NS5
thf(fact_184_ns__sharedp_ONS4, axiom,
    ((![Evs4 : list_event, NB : nat, K : nat, A3 : agent, B2 : agent, A : agent]: ((nS_Sha1092415543haredp @ Evs4) => ((~ ((member_msg @ (nonce @ NB) @ (used @ Evs4)))) => ((member_nat @ K @ symKeys) => ((member_event @ (says @ A3 @ B2 @ (crypt @ (shrK @ B2) @ (mPair @ (key @ K) @ (agent2 @ A)))) @ (set_event2 @ Evs4)) => (nS_Sha1092415543haredp @ (cons_event @ (says @ B2 @ A @ (crypt @ K @ (nonce @ NB))) @ Evs4))))))))). % ns_sharedp.NS4
thf(fact_185_list_Oinject, axiom,
    ((![X21 : event, X22 : list_event, Y21 : event, Y22 : list_event]: (((cons_event @ X21 @ X22) = (cons_event @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_186_ns__sharedp_OOops, axiom,
    ((![Evso : list_event, B2 : agent, A : agent, K : nat, NB : nat, NA : nat, X2 : msg]: ((nS_Sha1092415543haredp @ Evso) => ((member_event @ (says @ B2 @ A @ (crypt @ K @ (nonce @ NB))) @ (set_event2 @ Evso)) => ((member_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ (nonce @ NA) @ (mPair @ (agent2 @ B2) @ (mPair @ (key @ K) @ X2))))) @ (set_event2 @ Evso)) => (nS_Sha1092415543haredp @ (cons_event @ (notes @ spy @ (mPair @ (nonce @ NA) @ (mPair @ (nonce @ NB) @ (key @ K)))) @ Evso)))))))). % ns_sharedp.Oops
thf(fact_187_ns__shared_OOops, axiom,
    ((![Evso : list_event, B2 : agent, A : agent, K : nat, NB : nat, NA : nat, X2 : msg]: ((member_list_event @ Evso @ nS_Sha1061662329shared) => ((member_event @ (says @ B2 @ A @ (crypt @ K @ (nonce @ NB))) @ (set_event2 @ Evso)) => ((member_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ (nonce @ NA) @ (mPair @ (agent2 @ B2) @ (mPair @ (key @ K) @ X2))))) @ (set_event2 @ Evso)) => (member_list_event @ (cons_event @ (notes @ spy @ (mPair @ (nonce @ NA) @ (mPair @ (nonce @ NB) @ (key @ K)))) @ Evso) @ nS_Sha1061662329shared))))))). % ns_shared.Oops
thf(fact_188_list_Oset__cases, axiom,
    ((![E : msg, A2 : list_msg]: ((member_msg @ E @ (set_msg2 @ A2)) => ((![Z2 : list_msg]: (~ ((A2 = (cons_msg @ E @ Z2))))) => (~ ((![Z1 : msg, Z2 : list_msg]: ((A2 = (cons_msg @ Z1 @ Z2)) => (~ ((member_msg @ E @ (set_msg2 @ Z2))))))))))))). % list.set_cases
thf(fact_189_list_Oset__cases, axiom,
    ((![E : event, A2 : list_event]: ((member_event @ E @ (set_event2 @ A2)) => ((![Z2 : list_event]: (~ ((A2 = (cons_event @ E @ Z2))))) => (~ ((![Z1 : event, Z2 : list_event]: ((A2 = (cons_event @ Z1 @ Z2)) => (~ ((member_event @ E @ (set_event2 @ Z2))))))))))))). % list.set_cases
thf(fact_190_event_Oinject_I3_J, axiom,
    ((![X31 : agent, X322 : msg, Y31 : agent, Y32 : msg]: (((notes @ X31 @ X322) = (notes @ Y31 @ Y32)) = (((X31 = Y31)) & ((X322 = Y32))))))). % event.inject(3)
thf(fact_191_agent_Odistinct_I3_J, axiom,
    ((~ ((server = spy))))). % agent.distinct(3)
thf(fact_192_event_Odistinct_I3_J, axiom,
    ((![X11 : agent, X12 : agent, X13 : msg, X31 : agent, X322 : msg]: (~ (((says @ X11 @ X12 @ X13) = (notes @ X31 @ X322))))))). % event.distinct(3)
thf(fact_193_Notes__imp__used, axiom,
    ((![A : agent, X2 : msg, Evs : list_event]: ((member_event @ (notes @ A @ X2) @ (set_event2 @ Evs)) => (member_msg @ X2 @ (used @ Evs)))))). % Notes_imp_used
thf(fact_194_knows__Spy__imp__Says__Notes__initState, axiom,
    ((![X2 : msg, Evs : list_event]: ((member_msg @ X2 @ (knows @ spy @ Evs)) => (?[A4 : agent, B4 : agent]: ((member_event @ (says @ A4 @ B4 @ X2) @ (set_event2 @ Evs)) | ((member_event @ (notes @ A4 @ X2) @ (set_event2 @ Evs)) | (member_msg @ X2 @ (initState @ spy))))))))). % knows_Spy_imp_Says_Notes_initState
thf(fact_195_used__Gets, axiom,
    ((![A : agent, X2 : msg, Evs : list_event]: ((used @ (cons_event @ (gets @ A @ X2) @ Evs)) = (used @ Evs))))). % used_Gets
thf(fact_196_event_Oinject_I2_J, axiom,
    ((![X21 : agent, X22 : msg, Y21 : agent, Y22 : msg]: (((gets @ X21 @ X22) = (gets @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % event.inject(2)
thf(fact_197_shrK__in__knows, axiom,
    ((![A : agent, Evs : list_event]: (member_msg @ (key @ (shrK @ A)) @ (knows @ A @ Evs))))). % shrK_in_knows
thf(fact_198_knows__Spy__Gets, axiom,
    ((![A : agent, X2 : msg, Evs : list_event]: ((knows @ spy @ (cons_event @ (gets @ A @ X2) @ Evs)) = (knows @ spy @ Evs))))). % knows_Spy_Gets
thf(fact_199_Gets__imp__knows__agents, axiom,
    ((![A : agent, X2 : msg, Evs : list_event]: ((~ ((A = spy))) => ((member_event @ (gets @ A @ X2) @ (set_event2 @ Evs)) => (member_msg @ X2 @ (knows @ A @ Evs))))))). % Gets_imp_knows_agents
thf(fact_200_event_Odistinct_I1_J, axiom,
    ((![X11 : agent, X12 : agent, X13 : msg, X21 : agent, X22 : msg]: (~ (((says @ X11 @ X12 @ X13) = (gets @ X21 @ X22))))))). % event.distinct(1)
thf(fact_201_event_Odistinct_I5_J, axiom,
    ((![X21 : agent, X22 : msg, X31 : agent, X322 : msg]: (~ (((gets @ X21 @ X22) = (notes @ X31 @ X322))))))). % event.distinct(5)
thf(fact_202_Says__imp__knows, axiom,
    ((![A : agent, B2 : agent, X2 : msg, Evs : list_event]: ((member_event @ (says @ A @ B2 @ X2) @ (set_event2 @ Evs)) => (member_msg @ X2 @ (knows @ A @ Evs)))))). % Says_imp_knows
thf(fact_203_Notes__imp__knows, axiom,
    ((![A : agent, X2 : msg, Evs : list_event]: ((member_event @ (notes @ A @ X2) @ (set_event2 @ Evs)) => (member_msg @ X2 @ (knows @ A @ Evs)))))). % Notes_imp_knows
thf(fact_204_knows__imp__Says__Gets__Notes__initState, axiom,
    ((![X2 : msg, A : agent, Evs : list_event]: ((member_msg @ X2 @ (knows @ A @ Evs)) => ((~ ((A = spy))) => (?[B4 : agent]: ((member_event @ (says @ A @ B4 @ X2) @ (set_event2 @ Evs)) | ((member_event @ (gets @ A @ X2) @ (set_event2 @ Evs)) | ((member_event @ (notes @ A @ X2) @ (set_event2 @ Evs)) | (member_msg @ X2 @ (initState @ A))))))))))). % knows_imp_Says_Gets_Notes_initState
thf(fact_205_Says__imp__knows__Spy, axiom,
    ((![A : agent, B2 : agent, X2 : msg, Evs : list_event]: ((member_event @ (says @ A @ B2 @ X2) @ (set_event2 @ Evs)) => (member_msg @ X2 @ (knows @ spy @ Evs)))))). % Says_imp_knows_Spy
thf(fact_206_event_Oinduct, axiom,
    ((![P : event > $o, Event : event]: ((![X14 : agent, X23 : agent, X33 : msg]: (P @ (says @ X14 @ X23 @ X33))) => ((![X14 : agent, X23 : msg]: (P @ (gets @ X14 @ X23))) => ((![X14 : agent, X23 : msg]: (P @ (notes @ X14 @ X23))) => (P @ Event))))))). % event.induct
thf(fact_207_event_Oexhaust, axiom,
    ((![Y : event]: ((![X112 : agent, X122 : agent, X132 : msg]: (~ ((Y = (says @ X112 @ X122 @ X132))))) => ((![X212 : agent, X222 : msg]: (~ ((Y = (gets @ X212 @ X222))))) => (~ ((![X312 : agent, X323 : msg]: (~ ((Y = (notes @ X312 @ X323)))))))))))). % event.exhaust
thf(fact_208_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_209_Oops__parts__spies, axiom,
    ((![A : agent, NA : msg, B2 : msg, K : msg, X2 : msg, Evs : list_event]: ((member_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ NA @ (mPair @ B2 @ (mPair @ K @ X2))))) @ (set_event2 @ Evs)) => (member_msg @ K @ (parts @ (knows @ spy @ Evs))))))). % Oops_parts_spies
thf(fact_210_Notes__imp__knows__Spy, axiom,
    ((![A : agent, X2 : msg, Evs : list_event]: ((member_event @ (notes @ A @ X2) @ (set_event2 @ Evs)) => ((member_agent @ A @ bad) => (member_msg @ X2 @ (knows @ spy @ Evs))))))). % Notes_imp_knows_Spy
thf(fact_211_parts__idem, axiom,
    ((![H : set_msg]: ((parts @ (parts @ H)) = (parts @ H))))). % parts_idem
thf(fact_212_Spy__in__bad, axiom,
    ((member_agent @ spy @ bad))). % Spy_in_bad
thf(fact_213_parts__image__Key, axiom,
    ((![N : set_nat]: ((parts @ (image_nat_msg @ key @ N)) = (image_nat_msg @ key @ N))))). % parts_image_Key
thf(fact_214_usedI, axiom,
    ((![C2 : msg, Evs : list_event]: ((member_msg @ C2 @ (parts @ (knows @ spy @ Evs))) => (member_msg @ C2 @ (used @ Evs)))))). % usedI
thf(fact_215_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_216_MPair__parts, axiom,
    ((![X2 : msg, Y5 : msg, H : set_msg]: ((member_msg @ (mPair @ X2 @ Y5) @ (parts @ H)) => (~ (((member_msg @ X2 @ (parts @ H)) => (~ ((member_msg @ Y5 @ (parts @ H))))))))))). % MPair_parts
thf(fact_217_parts_OSnd, axiom,
    ((![X2 : msg, Y5 : msg, H : set_msg]: ((member_msg @ (mPair @ X2 @ Y5) @ (parts @ H)) => (member_msg @ Y5 @ (parts @ H)))))). % parts.Snd
thf(fact_218_parts_OFst, axiom,
    ((![X2 : msg, Y5 : msg, H : set_msg]: ((member_msg @ (mPair @ X2 @ Y5) @ (parts @ H)) => (member_msg @ X2 @ (parts @ H)))))). % parts.Fst
thf(fact_219_parts_OBody, axiom,
    ((![K : nat, X2 : msg, H : set_msg]: ((member_msg @ (crypt @ K @ X2) @ (parts @ H)) => (member_msg @ X2 @ (parts @ H)))))). % parts.Body
thf(fact_220_parts_OInj, axiom,
    ((![X2 : msg, H : set_msg]: ((member_msg @ X2 @ H) => (member_msg @ X2 @ (parts @ H)))))). % parts.Inj
thf(fact_221_parts__partsD, axiom,
    ((![X2 : msg, H : set_msg]: ((member_msg @ X2 @ (parts @ (parts @ H))) => (member_msg @ X2 @ (parts @ H)))))). % parts_partsD
thf(fact_222_parts_Ocases, axiom,
    ((![A2 : msg, H : set_msg]: ((member_msg @ A2 @ (parts @ H)) => ((~ ((member_msg @ A2 @ H))) => ((![Y6 : msg]: (~ ((member_msg @ (mPair @ A2 @ Y6) @ (parts @ H))))) => ((![X7 : msg]: (~ ((member_msg @ (mPair @ X7 @ A2) @ (parts @ H))))) => (~ ((![K3 : nat]: (~ ((member_msg @ (crypt @ K3 @ A2) @ (parts @ H)))))))))))))). % parts.cases
thf(fact_223_parts_Osimps, axiom,
    ((![A2 : msg, H : set_msg]: ((member_msg @ A2 @ (parts @ H)) = (((?[X8 : msg]: (((A2 = X8)) & ((member_msg @ X8 @ H))))) | ((((?[X8 : msg]: (?[Y7 : msg]: (((A2 = X8)) & ((member_msg @ (mPair @ X8 @ Y7) @ (parts @ H))))))) | ((((?[X8 : msg]: (?[Y7 : msg]: (((A2 = Y7)) & ((member_msg @ (mPair @ X8 @ Y7) @ (parts @ H))))))) | ((?[K4 : nat]: (?[X8 : msg]: (((A2 = X8)) & ((member_msg @ (crypt @ K4 @ X8) @ (parts @ H)))))))))))))))). % parts.simps
thf(fact_224_parts_Oinducts, axiom,
    ((![X : msg, H : set_msg, P : msg > $o]: ((member_msg @ X @ (parts @ H)) => ((![X7 : msg]: ((member_msg @ X7 @ H) => (P @ X7))) => ((![X7 : msg, Y6 : msg]: ((member_msg @ (mPair @ X7 @ Y6) @ (parts @ H)) => ((P @ (mPair @ X7 @ Y6)) => (P @ X7)))) => ((![X7 : msg, Y6 : msg]: ((member_msg @ (mPair @ X7 @ Y6) @ (parts @ H)) => ((P @ (mPair @ X7 @ Y6)) => (P @ Y6)))) => ((![K3 : nat, X7 : msg]: ((member_msg @ (crypt @ K3 @ X7) @ (parts @ H)) => ((P @ (crypt @ K3 @ X7)) => (P @ X7)))) => (P @ X))))))))). % parts.inducts
thf(fact_225_Crypt__notin__initState, axiom,
    ((![K : nat, X2 : msg, B2 : agent]: (~ ((member_msg @ (crypt @ K @ X2) @ (parts @ (initState @ B2)))))))). % Crypt_notin_initState
thf(fact_226_Server__not__bad, axiom,
    ((~ ((member_agent @ server @ bad))))). % Server_not_bad
thf(fact_227_Nonce__notin__initState, axiom,
    ((![N : nat, B2 : agent]: (~ ((member_msg @ (nonce @ N) @ (parts @ (initState @ B2)))))))). % Nonce_notin_initState
thf(fact_228_initState__into__used, axiom,
    ((![X2 : msg, B2 : agent, Evs : list_event]: ((member_msg @ X2 @ (parts @ (initState @ B2))) => (member_msg @ X2 @ (used @ Evs)))))). % initState_into_used
thf(fact_229_NS3__msg__in__parts__spies, axiom,
    ((![S : agent, A : agent, KA : nat, N : msg, B2 : msg, K : msg, X2 : msg, Evs : list_event]: ((member_event @ (says @ S @ A @ (crypt @ KA @ (mPair @ N @ (mPair @ B2 @ (mPair @ K @ X2))))) @ (set_event2 @ Evs)) => (member_msg @ X2 @ (parts @ (knows @ spy @ Evs))))))). % NS3_msg_in_parts_spies
thf(fact_230_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
thf(fact_231_Spy__analz__shrK, axiom,
    ((![Evs : list_event, A : agent]: ((member_list_event @ Evs @ nS_Sha1061662329shared) => ((member_msg @ (key @ (shrK @ A)) @ (analz @ (knows @ spy @ Evs))) = (member_agent @ A @ bad)))))). % Spy_analz_shrK
thf(fact_232_knows__Spy__Notes, axiom,
    ((![A : agent, X2 : msg, Evs : list_event]: (((member_agent @ A @ bad) => ((knows @ spy @ (cons_event @ (notes @ A @ X2) @ Evs)) = (insert_msg @ X2 @ (knows @ spy @ Evs)))) & ((~ ((member_agent @ A @ bad))) => ((knows @ spy @ (cons_event @ (notes @ A @ X2) @ Evs)) = (knows @ spy @ Evs))))))). % knows_Spy_Notes
thf(fact_233_analz__idem, axiom,
    ((![H : set_msg]: ((analz @ (analz @ H)) = (analz @ H))))). % analz_idem
thf(fact_234_analz__parts, axiom,
    ((![H : set_msg]: ((analz @ (parts @ H)) = (parts @ H))))). % analz_parts
thf(fact_235_parts__analz, axiom,
    ((![H : set_msg]: ((parts @ (analz @ H)) = (parts @ H))))). % parts_analz
thf(fact_236_analz__conj__parts, axiom,
    ((![X2 : msg, H : set_msg]: ((((member_msg @ X2 @ (analz @ H))) & ((member_msg @ X2 @ (parts @ H)))) = (member_msg @ X2 @ (analz @ H)))))). % analz_conj_parts
thf(fact_237_analz__disj__parts, axiom,
    ((![X2 : msg, H : set_msg]: ((((member_msg @ X2 @ (analz @ H))) | ((member_msg @ X2 @ (parts @ H)))) = (member_msg @ X2 @ (parts @ H)))))). % analz_disj_parts
thf(fact_238_parts__cut__eq, axiom,
    ((![X2 : msg, H : set_msg]: ((member_msg @ X2 @ (parts @ H)) => ((parts @ (insert_msg @ X2 @ H)) = (parts @ H)))))). % parts_cut_eq
thf(fact_239_analz__insert__MPair, axiom,
    ((![X2 : msg, Y5 : msg, H : set_msg]: ((analz @ (insert_msg @ (mPair @ X2 @ Y5) @ H)) = (insert_msg @ (mPair @ X2 @ Y5) @ (analz @ (insert_msg @ X2 @ (insert_msg @ Y5 @ H)))))))). % analz_insert_MPair
thf(fact_240_parts__insert__MPair, axiom,
    ((![X2 : msg, Y5 : msg, H : set_msg]: ((parts @ (insert_msg @ (mPair @ X2 @ Y5) @ H)) = (insert_msg @ (mPair @ X2 @ Y5) @ (parts @ (insert_msg @ X2 @ (insert_msg @ Y5 @ H)))))))). % parts_insert_MPair
thf(fact_241_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_242_parts__insert__Crypt, axiom,
    ((![K : nat, X2 : msg, H : set_msg]: ((parts @ (insert_msg @ (crypt @ K @ X2) @ H)) = (insert_msg @ (crypt @ K @ X2) @ (parts @ (insert_msg @ X2 @ H))))))). % parts_insert_Crypt
thf(fact_243_analz__insert__Nonce, axiom,
    ((![N : nat, H : set_msg]: ((analz @ (insert_msg @ (nonce @ N) @ H)) = (insert_msg @ (nonce @ N) @ (analz @ H)))))). % analz_insert_Nonce
thf(fact_244_analz__insert__Agent, axiom,
    ((![Agt : agent, H : set_msg]: ((analz @ (insert_msg @ (agent2 @ Agt) @ H)) = (insert_msg @ (agent2 @ Agt) @ (analz @ H)))))). % analz_insert_Agent
thf(fact_245_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_246_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_247_keysFor__insert__MPair, axiom,
    ((![X2 : msg, Y5 : msg, H : set_msg]: ((keysFor @ (insert_msg @ (mPair @ X2 @ Y5) @ H)) = (keysFor @ H))))). % keysFor_insert_MPair
thf(fact_248_keysFor__insert__Key, axiom,
    ((![K : nat, H : set_msg]: ((keysFor @ (insert_msg @ (key @ K) @ H)) = (keysFor @ H))))). % keysFor_insert_Key

% Conjectures (3)
thf(conj_0, hypothesis,
    ((member_event @ (says @ server @ a @ (crypt @ k2 @ (mPair @ n @ (mPair @ (agent2 @ b) @ (mPair @ (key @ k) @ x))))) @ (set_event2 @ evs)))).
thf(conj_1, hypothesis,
    ((member_list_event @ evs @ nS_Sha1061662329shared))).
thf(conj_2, conjecture,
    (((~ ((member_nat @ k @ (image_agent_nat @ shrK @ top_top_set_agent)))) & ((x = (crypt @ (shrK @ b) @ (mPair @ (key @ k) @ (agent2 @ a)))) & (k2 = (shrK @ a)))))).
