% 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_438__5232520_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:24:52.511

% Could-be-implicit typings (12)
thf(ty_n_t__List__Olist_It__List__Olist_It__Event__Oevent_J_J, type,
    list_list_event : $tType).
thf(ty_n_t__Set__Oset_It__List__Olist_It__Event__Oevent_J_J, type,
    set_list_event : $tType).
thf(ty_n_t__List__Olist_It__Message__Oagent_J, type,
    list_agent : $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__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 (54)
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_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__List__Olist_It__Event__Oevent_J, type,
    cons_list_event : list_event > list_list_event > list_list_event).
thf(sy_c_List_Olist_OCons_001t__Message__Oagent, type,
    cons_agent : agent > list_agent > list_agent).
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__List__Olist_It__Event__Oevent_J, type,
    set_list_event2 : list_list_event > set_list_event).
thf(sy_c_List_Olist_Oset_001t__Message__Oagent, type,
    set_agent2 : list_agent > set_agent).
thf(sy_c_List_Olist_Oset_001t__Message__Omsg, type,
    set_msg2 : list_msg > set_msg).
thf(sy_c_List_Orev_001t__Event__Oevent, type,
    rev_event : list_event > list_event).
thf(sy_c_List_OtakeWhile_001t__Event__Oevent, type,
    takeWhile_event : (event > $o) > list_event > list_event).
thf(sy_c_List_OtakeWhile_001t__List__Olist_It__Event__Oevent_J, type,
    takeWhile_list_event : (list_event > $o) > list_list_event > list_list_event).
thf(sy_c_List_OtakeWhile_001t__Message__Oagent, type,
    takeWhile_agent : (agent > $o) > list_agent > list_agent).
thf(sy_c_List_OtakeWhile_001t__Message__Omsg, type,
    takeWhile_msg : (msg > $o) > list_msg > list_msg).
thf(sy_c_Message_Oagent_OSpy, type,
    spy : agent).
thf(sy_c_Message_Oanalz, type,
    analz : set_msg > set_msg).
thf(sy_c_Message_Omsg_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_NS__Shared__Mirabelle__xwdrtqxrux_OIssues, type,
    nS_Sha1425748201Issues : agent > agent > msg > list_event > $o).
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_Oord__class_Oless__eq_001t__Set__Oset_It__Event__Oevent_J, type,
    ord_le152226328_event : set_event > set_event > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_It__Event__Oevent_J_J, type,
    ord_le119303592_event : set_list_event > set_list_event > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Message__Oagent_J, type,
    ord_le722097072_agent : set_agent > set_agent > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Message__Omsg_J, type,
    ord_less_eq_set_msg : set_msg > set_msg > $o).
thf(sy_c_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_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_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_v_A, type,
    a : agent).
thf(sy_v_B, type,
    b : agent).
thf(sy_v_K, type,
    k : nat).
thf(sy_v_Nb, type,
    nb : nat).
thf(sy_v_evs, type,
    evs : list_event).

% Relevant facts (196)
thf(fact_0_spies__evs__rev, axiom,
    ((![Evs : list_event]: ((knows @ spy @ Evs) = (knows @ spy @ (rev_event @ Evs)))))). % spies_evs_rev
thf(fact_1_Spy__in__bad, axiom,
    ((member_agent @ spy @ bad))). % Spy_in_bad
thf(fact_2_Says__imp__analz__Spy, axiom,
    ((![A : agent, B : agent, X : msg, Evs : list_event]: ((member_event @ (says @ A @ B @ X) @ (set_event2 @ Evs)) => (member_msg @ X @ (analz @ (knows @ spy @ Evs))))))). % Says_imp_analz_Spy
thf(fact_3_takeWhile__eq__all__conv, axiom,
    ((![P : event > $o, Xs : list_event]: (((takeWhile_event @ P @ Xs) = Xs) = (![X2 : event]: (((member_event @ X2 @ (set_event2 @ Xs))) => ((P @ X2)))))))). % takeWhile_eq_all_conv
thf(fact_4_analz__parts, axiom,
    ((![H : set_msg]: ((analz @ (parts @ H)) = (parts @ H))))). % analz_parts
thf(fact_5_parts__analz, axiom,
    ((![H : set_msg]: ((parts @ (analz @ H)) = (parts @ H))))). % parts_analz
thf(fact_6_analz__conj__parts, axiom,
    ((![X : msg, H : set_msg]: ((((member_msg @ X @ (analz @ H))) & ((member_msg @ X @ (parts @ H)))) = (member_msg @ X @ (analz @ H)))))). % analz_conj_parts
thf(fact_7_analz__disj__parts, axiom,
    ((![X : msg, H : set_msg]: ((((member_msg @ X @ (analz @ H))) | ((member_msg @ X @ (parts @ H)))) = (member_msg @ X @ (parts @ H)))))). % analz_disj_parts
thf(fact_8_set__rev, axiom,
    ((![Xs : list_event]: ((set_event2 @ (rev_event @ Xs)) = (set_event2 @ Xs))))). % set_rev
thf(fact_9_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_10_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_11_analz__impI, axiom,
    ((![Y : msg, Evs : list_event, Q : $o]: (((~ ((member_msg @ Y @ (analz @ (knows @ spy @ Evs))))) => Q) => ((~ ((member_msg @ Y @ (analz @ (knows @ spy @ Evs))))) => Q))))). % analz_impI
thf(fact_12_takeWhile__idem, axiom,
    ((![P : event > $o, Xs : list_event]: ((takeWhile_event @ P @ (takeWhile_event @ P @ Xs)) = (takeWhile_event @ P @ Xs))))). % takeWhile_idem
thf(fact_13_analz__idem, axiom,
    ((![H : set_msg]: ((analz @ (analz @ H)) = (analz @ H))))). % analz_idem
thf(fact_14_msg_Oinject_I4_J, axiom,
    ((![X4 : nat, Y4 : nat]: (((key @ X4) = (key @ Y4)) = (X4 = Y4))))). % msg.inject(4)
thf(fact_15_parts__idem, axiom,
    ((![H : set_msg]: ((parts @ (parts @ H)) = (parts @ H))))). % parts_idem
thf(fact_16_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_17_rev__is__rev__conv, axiom,
    ((![Xs : list_event, Ys : list_event]: (((rev_event @ Xs) = (rev_event @ Ys)) = (Xs = Ys))))). % rev_is_rev_conv
thf(fact_18_rev__rev__ident, axiom,
    ((![Xs : list_event]: ((rev_event @ (rev_event @ Xs)) = Xs)))). % rev_rev_ident
thf(fact_19_msg_Oinject_I3_J, axiom,
    ((![X3 : nat, Y3 : nat]: (((nonce @ X3) = (nonce @ Y3)) = (X3 = Y3))))). % msg.inject(3)
thf(fact_20_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_21_analz__analzD, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (analz @ (analz @ H))) => (member_msg @ X @ (analz @ H)))))). % analz_analzD
thf(fact_22_analz_OInj, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ H) => (member_msg @ X @ (analz @ H)))))). % analz.Inj
thf(fact_23_parts__partsD, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (parts @ (parts @ H))) => (member_msg @ X @ (parts @ H)))))). % parts_partsD
thf(fact_24_parts_OInj, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ H) => (member_msg @ X @ (parts @ H)))))). % parts.Inj
thf(fact_25_rev__swap, axiom,
    ((![Xs : list_event, Ys : list_event]: (((rev_event @ Xs) = Ys) = (Xs = (rev_event @ Ys)))))). % rev_swap
thf(fact_26_not__parts__not__analz, axiom,
    ((![C : msg, H : set_msg]: ((~ ((member_msg @ C @ (parts @ H)))) => (~ ((member_msg @ C @ (analz @ H)))))))). % not_parts_not_analz
thf(fact_27_analz__into__parts, axiom,
    ((![C : msg, H : set_msg]: ((member_msg @ C @ (analz @ H)) => (member_msg @ C @ (parts @ H)))))). % analz_into_parts
thf(fact_28_msg_Odistinct_I35_J, axiom,
    ((![X4 : nat, X71 : nat, X72 : msg]: (~ (((key @ X4) = (crypt @ X71 @ X72))))))). % msg.distinct(35)
thf(fact_29_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_30_takeWhile__cong, axiom,
    ((![L : list_agent, K2 : list_agent, P : agent > $o, Q : agent > $o]: ((L = K2) => ((![X5 : agent]: ((member_agent @ X5 @ (set_agent2 @ L)) => ((P @ X5) = (Q @ X5)))) => ((takeWhile_agent @ P @ L) = (takeWhile_agent @ Q @ K2))))))). % takeWhile_cong
thf(fact_31_takeWhile__cong, axiom,
    ((![L : list_list_event, K2 : list_list_event, P : list_event > $o, Q : list_event > $o]: ((L = K2) => ((![X5 : list_event]: ((member_list_event @ X5 @ (set_list_event2 @ L)) => ((P @ X5) = (Q @ X5)))) => ((takeWhile_list_event @ P @ L) = (takeWhile_list_event @ Q @ K2))))))). % takeWhile_cong
thf(fact_32_takeWhile__cong, axiom,
    ((![L : list_msg, K2 : list_msg, P : msg > $o, Q : msg > $o]: ((L = K2) => ((![X5 : msg]: ((member_msg @ X5 @ (set_msg2 @ L)) => ((P @ X5) = (Q @ X5)))) => ((takeWhile_msg @ P @ L) = (takeWhile_msg @ Q @ K2))))))). % takeWhile_cong
thf(fact_33_takeWhile__cong, axiom,
    ((![L : list_event, K2 : list_event, P : event > $o, Q : event > $o]: ((L = K2) => ((![X5 : event]: ((member_event @ X5 @ (set_event2 @ L)) => ((P @ X5) = (Q @ X5)))) => ((takeWhile_event @ P @ L) = (takeWhile_event @ Q @ K2))))))). % takeWhile_cong
thf(fact_34_set__takeWhileD, axiom,
    ((![X6 : agent, P : agent > $o, Xs : list_agent]: ((member_agent @ X6 @ (set_agent2 @ (takeWhile_agent @ P @ Xs))) => ((member_agent @ X6 @ (set_agent2 @ Xs)) & (P @ X6)))))). % set_takeWhileD
thf(fact_35_set__takeWhileD, axiom,
    ((![X6 : list_event, P : list_event > $o, Xs : list_list_event]: ((member_list_event @ X6 @ (set_list_event2 @ (takeWhile_list_event @ P @ Xs))) => ((member_list_event @ X6 @ (set_list_event2 @ Xs)) & (P @ X6)))))). % set_takeWhileD
thf(fact_36_set__takeWhileD, axiom,
    ((![X6 : msg, P : msg > $o, Xs : list_msg]: ((member_msg @ X6 @ (set_msg2 @ (takeWhile_msg @ P @ Xs))) => ((member_msg @ X6 @ (set_msg2 @ Xs)) & (P @ X6)))))). % set_takeWhileD
thf(fact_37_set__takeWhileD, axiom,
    ((![X6 : event, P : event > $o, Xs : list_event]: ((member_event @ X6 @ (set_event2 @ (takeWhile_event @ P @ Xs))) => ((member_event @ X6 @ (set_event2 @ Xs)) & (P @ X6)))))). % set_takeWhileD
thf(fact_38_msg_Odistinct_I23_J, axiom,
    ((![X3 : nat, X4 : nat]: (~ (((nonce @ X3) = (key @ X4))))))). % msg.distinct(23)
thf(fact_39_msg_Odistinct_I29_J, axiom,
    ((![X3 : nat, X71 : nat, X72 : msg]: (~ (((nonce @ X3) = (crypt @ X71 @ X72))))))). % msg.distinct(29)
thf(fact_40_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_41_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_42_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_43_Notes__imp__knows__Spy, axiom,
    ((![A : agent, X : msg, Evs : list_event]: ((member_event @ (notes @ A @ X) @ (set_event2 @ Evs)) => ((member_agent @ A @ bad) => (member_msg @ X @ (knows @ spy @ Evs))))))). % Notes_imp_knows_Spy
thf(fact_44_parts__spies__takeWhile__mono, axiom,
    ((![P : event > $o, Evs : list_event]: (ord_less_eq_set_msg @ (parts @ (knows @ spy @ (takeWhile_event @ P @ Evs))) @ (parts @ (knows @ spy @ Evs)))))). % parts_spies_takeWhile_mono
thf(fact_45_parts__spies__evs__revD2, axiom,
    ((![Evs : list_event]: (ord_less_eq_set_msg @ (parts @ (knows @ spy @ (rev_event @ Evs))) @ (parts @ (knows @ spy @ Evs)))))). % parts_spies_evs_revD2
thf(fact_46_Gets__imp__knows__agents, axiom,
    ((![A : agent, X : msg, Evs : list_event]: ((~ ((A = spy))) => ((member_event @ (gets @ A @ X) @ (set_event2 @ Evs)) => (member_msg @ X @ (knows @ A @ Evs))))))). % Gets_imp_knows_agents
thf(fact_47_usedI, axiom,
    ((![C : msg, Evs : list_event]: ((member_msg @ C @ (parts @ (knows @ spy @ Evs))) => (member_msg @ C @ (used @ Evs)))))). % usedI
thf(fact_48_Issues__def, axiom,
    ((nS_Sha1425748201Issues = (^[A2 : agent]: (^[B2 : agent]: (^[X7 : msg]: (^[Evs2 : list_event]: (?[Y2 : msg]: (((member_event @ (says @ A2 @ B2 @ Y2) @ (set_event2 @ Evs2))) & ((((member_msg @ X7 @ (parts @ (insert_msg @ Y2 @ bot_bot_set_msg)))) & ((~ ((member_msg @ X7 @ (parts @ (knows @ spy @ (takeWhile_event @ (^[Z : event]: (~ ((Z = (says @ A2 @ B2 @ Y2))))) @ (rev_event @ Evs2))))))))))))))))))). % Issues_def
thf(fact_49_analz__mono__contra_I1_J, axiom,
    ((![C : msg, A : agent, B : agent, X : msg, Evs : list_event]: ((~ ((member_msg @ C @ (analz @ (knows @ spy @ (cons_event @ (says @ A @ B @ X) @ Evs)))))) => (~ ((member_msg @ C @ (analz @ (knows @ spy @ Evs))))))))). % analz_mono_contra(1)
thf(fact_50_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_51_mem__Collect__eq, axiom,
    ((![A3 : agent, P : agent > $o]: ((member_agent @ A3 @ (collect_agent @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_52_mem__Collect__eq, axiom,
    ((![A3 : list_event, P : list_event > $o]: ((member_list_event @ A3 @ (collect_list_event @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_53_mem__Collect__eq, axiom,
    ((![A3 : msg, P : msg > $o]: ((member_msg @ A3 @ (collect_msg @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_54_mem__Collect__eq, axiom,
    ((![A3 : event, P : event > $o]: ((member_event @ A3 @ (collect_event @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_55_Collect__mem__eq, axiom,
    ((![A : set_agent]: ((collect_agent @ (^[X2 : agent]: (member_agent @ X2 @ A))) = A)))). % Collect_mem_eq
thf(fact_56_Collect__mem__eq, axiom,
    ((![A : set_list_event]: ((collect_list_event @ (^[X2 : list_event]: (member_list_event @ X2 @ A))) = A)))). % Collect_mem_eq
thf(fact_57_Collect__mem__eq, axiom,
    ((![A : set_msg]: ((collect_msg @ (^[X2 : msg]: (member_msg @ X2 @ A))) = A)))). % Collect_mem_eq
thf(fact_58_Collect__mem__eq, axiom,
    ((![A : set_event]: ((collect_event @ (^[X2 : event]: (member_event @ X2 @ A))) = A)))). % Collect_mem_eq
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_event_Oinject_I3_J, axiom,
    ((![X31 : agent, X32 : msg, Y31 : agent, Y32 : msg]: (((notes @ X31 @ X32) = (notes @ Y31 @ Y32)) = (((X31 = Y31)) & ((X32 = Y32))))))). % event.inject(3)
thf(fact_61_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_62_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_63_analz__subset__iff, axiom,
    ((![G : set_msg, H : set_msg]: ((ord_less_eq_set_msg @ (analz @ G) @ (analz @ H)) = (ord_less_eq_set_msg @ G @ (analz @ H)))))). % analz_subset_iff
thf(fact_64_parts__subset__iff, axiom,
    ((![G : set_msg, H : set_msg]: ((ord_less_eq_set_msg @ (parts @ G) @ (parts @ H)) = (ord_less_eq_set_msg @ G @ (parts @ H)))))). % parts_subset_iff
thf(fact_65_analz__empty, axiom,
    (((analz @ bot_bot_set_msg) = bot_bot_set_msg))). % analz_empty
thf(fact_66_parts__empty, axiom,
    (((parts @ bot_bot_set_msg) = bot_bot_set_msg))). % parts_empty
thf(fact_67_list_Osimps_I15_J, axiom,
    ((![X21 : msg, X22 : list_msg]: ((set_msg2 @ (cons_msg @ X21 @ X22)) = (insert_msg @ X21 @ (set_msg2 @ X22)))))). % list.simps(15)
thf(fact_68_list_Osimps_I15_J, axiom,
    ((![X21 : event, X22 : list_event]: ((set_event2 @ (cons_event @ X21 @ X22)) = (insert_event @ X21 @ (set_event2 @ X22)))))). % list.simps(15)
thf(fact_69_analz__insert__MPair, axiom,
    ((![X : msg, Y : msg, H : set_msg]: ((analz @ (insert_msg @ (mPair @ X @ Y) @ H)) = (insert_msg @ (mPair @ X @ Y) @ (analz @ (insert_msg @ X @ (insert_msg @ Y @ H)))))))). % analz_insert_MPair
thf(fact_70_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_71_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_72_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_73_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_74_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_75_used__Gets, axiom,
    ((![A : agent, X : msg, Evs : list_event]: ((used @ (cons_event @ (gets @ A @ X) @ Evs)) = (used @ Evs))))). % used_Gets
thf(fact_76_knows__Spy__Gets, axiom,
    ((![A : agent, X : msg, Evs : list_event]: ((knows @ spy @ (cons_event @ (gets @ A @ X) @ Evs)) = (knows @ spy @ Evs))))). % knows_Spy_Gets
thf(fact_77_knows__Spy__Says, axiom,
    ((![A : agent, B : agent, X : msg, Evs : list_event]: ((knows @ spy @ (cons_event @ (says @ A @ B @ X) @ Evs)) = (insert_msg @ X @ (knows @ spy @ Evs)))))). % knows_Spy_Says
thf(fact_78_knows__Spy__Notes, axiom,
    ((![A : agent, X : msg, Evs : list_event]: (((member_agent @ A @ bad) => ((knows @ spy @ (cons_event @ (notes @ A @ X) @ Evs)) = (insert_msg @ X @ (knows @ spy @ Evs)))) & ((~ ((member_agent @ A @ bad))) => ((knows @ spy @ (cons_event @ (notes @ A @ X) @ Evs)) = (knows @ spy @ Evs))))))). % knows_Spy_Notes
thf(fact_79_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_80_pushCrypts_I6_J, axiom,
    ((![X : nat, K : msg, X8 : msg, Y : msg, A : set_msg]: ((insert_msg @ (crypt @ X @ K) @ (insert_msg @ (mPair @ X8 @ Y) @ A)) = (insert_msg @ (mPair @ X8 @ Y) @ (insert_msg @ (crypt @ X @ K) @ A)))))). % pushCrypts(6)
thf(fact_81_event_Odistinct_I5_J, axiom,
    ((![X21 : agent, X22 : msg, X31 : agent, X32 : msg]: (~ (((gets @ X21 @ X22) = (notes @ X31 @ X32))))))). % event.distinct(5)
thf(fact_82_not__Cons__self2, axiom,
    ((![X6 : event, Xs : list_event]: (~ (((cons_event @ X6 @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_83_set__subset__Cons, axiom,
    ((![Xs : list_event, X6 : event]: (ord_le152226328_event @ (set_event2 @ Xs) @ (set_event2 @ (cons_event @ X6 @ Xs)))))). % set_subset_Cons
thf(fact_84_set__subset__Cons, axiom,
    ((![Xs : list_msg, X6 : msg]: (ord_less_eq_set_msg @ (set_msg2 @ Xs) @ (set_msg2 @ (cons_msg @ X6 @ Xs)))))). % set_subset_Cons
thf(fact_85_knows__subset__knows__Gets, axiom,
    ((![A : agent, Evs : list_event, A4 : agent, X : msg]: (ord_less_eq_set_msg @ (knows @ A @ Evs) @ (knows @ A @ (cons_event @ (gets @ A4 @ X) @ Evs)))))). % knows_subset_knows_Gets
thf(fact_86_knows__subset__knows__Notes, axiom,
    ((![A : agent, Evs : list_event, A4 : agent, X : msg]: (ord_less_eq_set_msg @ (knows @ A @ Evs) @ (knows @ A @ (cons_event @ (notes @ A4 @ X) @ Evs)))))). % knows_subset_knows_Notes
thf(fact_87_gen__analz__insert__eq, axiom,
    ((![X : msg, H : set_msg, G : set_msg]: ((member_msg @ X @ (analz @ H)) => ((ord_less_eq_set_msg @ H @ G) => ((analz @ (insert_msg @ X @ G)) = (analz @ G))))))). % gen_analz_insert_eq
thf(fact_88_analz__insert, axiom,
    ((![X : msg, H : set_msg]: (ord_less_eq_set_msg @ (insert_msg @ X @ (analz @ H)) @ (analz @ (insert_msg @ X @ H)))))). % analz_insert
thf(fact_89_parts__insert__subset, axiom,
    ((![X : msg, H : set_msg]: (ord_less_eq_set_msg @ (insert_msg @ X @ (parts @ H)) @ (parts @ (insert_msg @ X @ H)))))). % parts_insert_subset
thf(fact_90_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_91_knows__subset__knows__Cons, axiom,
    ((![A : agent, Evs : list_event, E : event]: (ord_less_eq_set_msg @ (knows @ A @ Evs) @ (knows @ A @ (cons_event @ E @ Evs)))))). % knows_subset_knows_Cons
thf(fact_92_Notes__imp__used, axiom,
    ((![A : agent, X : msg, Evs : list_event]: ((member_event @ (notes @ A @ X) @ (set_event2 @ Evs)) => (member_msg @ X @ (used @ Evs)))))). % Notes_imp_used
thf(fact_93_knows__Spy__subset__knows__Spy__Notes, axiom,
    ((![Evs : list_event, A : agent, X : msg]: (ord_less_eq_set_msg @ (knows @ spy @ Evs) @ (knows @ spy @ (cons_event @ (notes @ A @ X) @ Evs)))))). % knows_Spy_subset_knows_Spy_Notes
thf(fact_94_knows__Spy__subset__knows__Spy__Gets, axiom,
    ((![Evs : list_event, A : agent, X : msg]: (ord_less_eq_set_msg @ (knows @ spy @ Evs) @ (knows @ spy @ (cons_event @ (gets @ A @ X) @ Evs)))))). % knows_Spy_subset_knows_Spy_Gets
thf(fact_95_event_Oinduct, axiom,
    ((![P : event > $o, Event : event]: ((![X1 : agent, X23 : agent, X33 : msg]: (P @ (says @ X1 @ X23 @ X33))) => ((![X1 : agent, X23 : msg]: (P @ (gets @ X1 @ X23))) => ((![X1 : agent, X23 : msg]: (P @ (notes @ X1 @ X23))) => (P @ Event))))))). % event.induct
thf(fact_96_event_Oexhaust, axiom,
    ((![Y5 : event]: ((![X112 : agent, X122 : agent, X132 : msg]: (~ ((Y5 = (says @ X112 @ X122 @ X132))))) => ((![X212 : agent, X222 : msg]: (~ ((Y5 = (gets @ X212 @ X222))))) => (~ ((![X312 : agent, X322 : msg]: (~ ((Y5 = (notes @ X312 @ X322)))))))))))). % event.exhaust
thf(fact_97_analz__insert__Crypt__subset, axiom,
    ((![K : nat, X : msg, H : set_msg]: (ord_less_eq_set_msg @ (analz @ (insert_msg @ (crypt @ K @ X) @ H)) @ (insert_msg @ (crypt @ K @ X) @ (analz @ (insert_msg @ X @ H))))))). % analz_insert_Crypt_subset
thf(fact_98_knows__subset__knows__Says, axiom,
    ((![A : agent, Evs : list_event, A4 : agent, B : agent, X : msg]: (ord_less_eq_set_msg @ (knows @ A @ Evs) @ (knows @ A @ (cons_event @ (says @ A4 @ B @ X) @ Evs)))))). % knows_subset_knows_Says
thf(fact_99_analz_OFst, axiom,
    ((![X : msg, Y : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y) @ (analz @ H)) => (member_msg @ X @ (analz @ H)))))). % analz.Fst
thf(fact_100_analz_OSnd, axiom,
    ((![X : msg, Y : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y) @ (analz @ H)) => (member_msg @ Y @ (analz @ H)))))). % analz.Snd
thf(fact_101_MPair__analz, axiom,
    ((![X : msg, Y : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y) @ (analz @ H)) => (~ (((member_msg @ X @ (analz @ H)) => (~ ((member_msg @ Y @ (analz @ H))))))))))). % MPair_analz
thf(fact_102_msg_Odistinct_I33_J, axiom,
    ((![X4 : nat, X61 : msg, X62 : msg]: (~ (((key @ X4) = (mPair @ X61 @ X62))))))). % msg.distinct(33)
thf(fact_103_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_104_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_105_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_106_msg_Odistinct_I41_J, axiom,
    ((![X61 : msg, X62 : msg, X71 : nat, X72 : msg]: (~ (((mPair @ X61 @ X62) = (crypt @ X71 @ X72))))))). % msg.distinct(41)
thf(fact_107_list_Oset__intros_I2_J, axiom,
    ((![Y5 : agent, X22 : list_agent, X21 : agent]: ((member_agent @ Y5 @ (set_agent2 @ X22)) => (member_agent @ Y5 @ (set_agent2 @ (cons_agent @ X21 @ X22))))))). % list.set_intros(2)
thf(fact_108_list_Oset__intros_I2_J, axiom,
    ((![Y5 : list_event, X22 : list_list_event, X21 : list_event]: ((member_list_event @ Y5 @ (set_list_event2 @ X22)) => (member_list_event @ Y5 @ (set_list_event2 @ (cons_list_event @ X21 @ X22))))))). % list.set_intros(2)
thf(fact_109_list_Oset__intros_I2_J, axiom,
    ((![Y5 : msg, X22 : list_msg, X21 : msg]: ((member_msg @ Y5 @ (set_msg2 @ X22)) => (member_msg @ Y5 @ (set_msg2 @ (cons_msg @ X21 @ X22))))))). % list.set_intros(2)
thf(fact_110_list_Oset__intros_I2_J, axiom,
    ((![Y5 : event, X22 : list_event, X21 : event]: ((member_event @ Y5 @ (set_event2 @ X22)) => (member_event @ Y5 @ (set_event2 @ (cons_event @ X21 @ X22))))))). % list.set_intros(2)
thf(fact_111_list_Oset__intros_I1_J, axiom,
    ((![X21 : agent, X22 : list_agent]: (member_agent @ X21 @ (set_agent2 @ (cons_agent @ X21 @ X22)))))). % list.set_intros(1)
thf(fact_112_list_Oset__intros_I1_J, axiom,
    ((![X21 : list_event, X22 : list_list_event]: (member_list_event @ X21 @ (set_list_event2 @ (cons_list_event @ X21 @ X22)))))). % list.set_intros(1)
thf(fact_113_list_Oset__intros_I1_J, axiom,
    ((![X21 : msg, X22 : list_msg]: (member_msg @ X21 @ (set_msg2 @ (cons_msg @ X21 @ X22)))))). % list.set_intros(1)
thf(fact_114_list_Oset__intros_I1_J, axiom,
    ((![X21 : event, X22 : list_event]: (member_event @ X21 @ (set_event2 @ (cons_event @ X21 @ X22)))))). % list.set_intros(1)
thf(fact_115_set__ConsD, axiom,
    ((![Y5 : agent, X6 : agent, Xs : list_agent]: ((member_agent @ Y5 @ (set_agent2 @ (cons_agent @ X6 @ Xs))) => ((Y5 = X6) | (member_agent @ Y5 @ (set_agent2 @ Xs))))))). % set_ConsD
thf(fact_116_set__ConsD, axiom,
    ((![Y5 : list_event, X6 : list_event, Xs : list_list_event]: ((member_list_event @ Y5 @ (set_list_event2 @ (cons_list_event @ X6 @ Xs))) => ((Y5 = X6) | (member_list_event @ Y5 @ (set_list_event2 @ Xs))))))). % set_ConsD
thf(fact_117_set__ConsD, axiom,
    ((![Y5 : msg, X6 : msg, Xs : list_msg]: ((member_msg @ Y5 @ (set_msg2 @ (cons_msg @ X6 @ Xs))) => ((Y5 = X6) | (member_msg @ Y5 @ (set_msg2 @ Xs))))))). % set_ConsD
thf(fact_118_set__ConsD, axiom,
    ((![Y5 : event, X6 : event, Xs : list_event]: ((member_event @ Y5 @ (set_event2 @ (cons_event @ X6 @ Xs))) => ((Y5 = X6) | (member_event @ Y5 @ (set_event2 @ Xs))))))). % set_ConsD
thf(fact_119_list_Oset__cases, axiom,
    ((![E : agent, A3 : list_agent]: ((member_agent @ E @ (set_agent2 @ A3)) => ((![Z2 : list_agent]: (~ ((A3 = (cons_agent @ E @ Z2))))) => (~ ((![Z1 : agent, Z2 : list_agent]: ((A3 = (cons_agent @ Z1 @ Z2)) => (~ ((member_agent @ E @ (set_agent2 @ Z2))))))))))))). % list.set_cases
thf(fact_120_list_Oset__cases, axiom,
    ((![E : list_event, A3 : list_list_event]: ((member_list_event @ E @ (set_list_event2 @ A3)) => ((![Z2 : list_list_event]: (~ ((A3 = (cons_list_event @ E @ Z2))))) => (~ ((![Z1 : list_event, Z2 : list_list_event]: ((A3 = (cons_list_event @ Z1 @ Z2)) => (~ ((member_list_event @ E @ (set_list_event2 @ Z2))))))))))))). % list.set_cases
thf(fact_121_list_Oset__cases, axiom,
    ((![E : msg, A3 : list_msg]: ((member_msg @ E @ (set_msg2 @ A3)) => ((![Z2 : list_msg]: (~ ((A3 = (cons_msg @ E @ Z2))))) => (~ ((![Z1 : msg, Z2 : list_msg]: ((A3 = (cons_msg @ Z1 @ Z2)) => (~ ((member_msg @ E @ (set_msg2 @ Z2))))))))))))). % list.set_cases
thf(fact_122_list_Oset__cases, axiom,
    ((![E : event, A3 : list_event]: ((member_event @ E @ (set_event2 @ A3)) => ((![Z2 : list_event]: (~ ((A3 = (cons_event @ E @ Z2))))) => (~ ((![Z1 : event, Z2 : list_event]: ((A3 = (cons_event @ Z1 @ Z2)) => (~ ((member_event @ E @ (set_event2 @ Z2))))))))))))). % list.set_cases
thf(fact_123_msg_Odistinct_I27_J, axiom,
    ((![X3 : nat, X61 : msg, X62 : msg]: (~ (((nonce @ X3) = (mPair @ X61 @ X62))))))). % msg.distinct(27)
thf(fact_124_subset__code_I1_J, axiom,
    ((![Xs : list_agent, B : set_agent]: ((ord_le722097072_agent @ (set_agent2 @ Xs) @ B) = (![X2 : agent]: (((member_agent @ X2 @ (set_agent2 @ Xs))) => ((member_agent @ X2 @ B)))))))). % subset_code(1)
thf(fact_125_subset__code_I1_J, axiom,
    ((![Xs : list_list_event, B : set_list_event]: ((ord_le119303592_event @ (set_list_event2 @ Xs) @ B) = (![X2 : list_event]: (((member_list_event @ X2 @ (set_list_event2 @ Xs))) => ((member_list_event @ X2 @ B)))))))). % subset_code(1)
thf(fact_126_subset__code_I1_J, axiom,
    ((![Xs : list_event, B : set_event]: ((ord_le152226328_event @ (set_event2 @ Xs) @ B) = (![X2 : event]: (((member_event @ X2 @ (set_event2 @ Xs))) => ((member_event @ X2 @ B)))))))). % subset_code(1)
thf(fact_127_subset__code_I1_J, axiom,
    ((![Xs : list_msg, B : set_msg]: ((ord_less_eq_set_msg @ (set_msg2 @ Xs) @ B) = (![X2 : msg]: (((member_msg @ X2 @ (set_msg2 @ Xs))) => ((member_msg @ X2 @ B)))))))). % subset_code(1)
thf(fact_128_analz__cut, axiom,
    ((![Y : msg, X : msg, H : set_msg]: ((member_msg @ Y @ (analz @ (insert_msg @ X @ H))) => ((member_msg @ X @ (analz @ H)) => (member_msg @ Y @ (analz @ H))))))). % analz_cut
thf(fact_129_analz__insertI, axiom,
    ((![C : msg, G : set_msg, A3 : msg]: ((member_msg @ C @ (analz @ G)) => (member_msg @ C @ (analz @ (insert_msg @ A3 @ G))))))). % analz_insertI
thf(fact_130_analz__insert__eq, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (analz @ H)) => ((analz @ (insert_msg @ X @ H)) = (analz @ H)))))). % analz_insert_eq
thf(fact_131_analz__insert__cong, axiom,
    ((![H : set_msg, H2 : set_msg, X : msg]: (((analz @ H) = (analz @ H2)) => ((analz @ (insert_msg @ X @ H)) = (analz @ (insert_msg @ X @ H2))))))). % analz_insert_cong
thf(fact_132_analz__insert__eq__I, axiom,
    ((![X : msg, H : set_msg]: ((![X5 : msg]: ((member_msg @ X5 @ (analz @ (insert_msg @ X @ H))) => (member_msg @ X5 @ (insert_msg @ X @ (analz @ H))))) => ((analz @ (insert_msg @ X @ H)) = (insert_msg @ X @ (analz @ H))))))). % analz_insert_eq_I
thf(fact_133_parts__insertI, axiom,
    ((![C : msg, G : set_msg, A3 : msg]: ((member_msg @ C @ (parts @ G)) => (member_msg @ C @ (parts @ (insert_msg @ A3 @ G))))))). % parts_insertI
thf(fact_134_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_135_analz__mono, axiom,
    ((![G : set_msg, H : set_msg]: ((ord_less_eq_set_msg @ G @ H) => (ord_less_eq_set_msg @ (analz @ G) @ (analz @ H)))))). % analz_mono
thf(fact_136_analz__trans, axiom,
    ((![X : msg, G : set_msg, H : set_msg]: ((member_msg @ X @ (analz @ G)) => ((ord_less_eq_set_msg @ G @ (analz @ H)) => (member_msg @ X @ (analz @ H))))))). % analz_trans
thf(fact_137_analz__increasing, axiom,
    ((![H : set_msg]: (ord_less_eq_set_msg @ H @ (analz @ H))))). % analz_increasing
thf(fact_138_parts__mono, axiom,
    ((![G : set_msg, H : set_msg]: ((ord_less_eq_set_msg @ G @ H) => (ord_less_eq_set_msg @ (parts @ G) @ (parts @ H)))))). % parts_mono
thf(fact_139_parts__trans, axiom,
    ((![X : msg, G : set_msg, H : set_msg]: ((member_msg @ X @ (parts @ G)) => ((ord_less_eq_set_msg @ G @ (parts @ H)) => (member_msg @ X @ (parts @ H))))))). % parts_trans
thf(fact_140_parts__increasing, axiom,
    ((![H : set_msg]: (ord_less_eq_set_msg @ H @ (parts @ H))))). % parts_increasing
thf(fact_141_parts__emptyE, axiom,
    ((![X : msg]: (~ ((member_msg @ X @ (parts @ bot_bot_set_msg))))))). % parts_emptyE
thf(fact_142_knows__Spy__subset__knows__Spy__Says, axiom,
    ((![Evs : list_event, A : agent, B : agent, X : msg]: (ord_less_eq_set_msg @ (knows @ spy @ Evs) @ (knows @ spy @ (cons_event @ (says @ A @ B @ X) @ Evs)))))). % knows_Spy_subset_knows_Spy_Says
thf(fact_143_event_Odistinct_I3_J, axiom,
    ((![X11 : agent, X12 : agent, X13 : msg, X31 : agent, X32 : msg]: (~ (((says @ X11 @ X12 @ X13) = (notes @ X31 @ X32))))))). % event.distinct(3)
thf(fact_144_parts__knows__Spy__subset__used, axiom,
    ((![Evs : list_event]: (ord_less_eq_set_msg @ (parts @ (knows @ spy @ Evs)) @ (used @ Evs))))). % parts_knows_Spy_subset_used
thf(fact_145_analz__mono__contra_I2_J, axiom,
    ((![C : msg, A : agent, X : msg, Evs : list_event]: ((~ ((member_msg @ C @ (analz @ (knows @ spy @ (cons_event @ (notes @ A @ X) @ Evs)))))) => (~ ((member_msg @ C @ (analz @ (knows @ spy @ Evs))))))))). % analz_mono_contra(2)
thf(fact_146_analz__mono__contra_I3_J, axiom,
    ((![C : msg, A : agent, X : msg, Evs : list_event]: ((~ ((member_msg @ C @ (analz @ (knows @ spy @ (cons_event @ (gets @ A @ X) @ Evs)))))) => (~ ((member_msg @ C @ (analz @ (knows @ spy @ Evs))))))))). % analz_mono_contra(3)
thf(fact_147_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_148_analz__trivial, axiom,
    ((![H : set_msg]: ((![X9 : msg, Y6 : msg]: (~ ((member_msg @ (mPair @ X9 @ Y6) @ H)))) => ((![X9 : msg, K3 : nat]: (~ ((member_msg @ (crypt @ K3 @ X9) @ H)))) => ((analz @ H) = H)))))). % analz_trivial
thf(fact_149_parts_Ocases, axiom,
    ((![A3 : msg, H : set_msg]: ((member_msg @ A3 @ (parts @ H)) => ((~ ((member_msg @ A3 @ H))) => ((![Y6 : msg]: (~ ((member_msg @ (mPair @ A3 @ Y6) @ (parts @ H))))) => ((![X9 : msg]: (~ ((member_msg @ (mPair @ X9 @ A3) @ (parts @ H))))) => (~ ((![K3 : nat]: (~ ((member_msg @ (crypt @ K3 @ A3) @ (parts @ H)))))))))))))). % parts.cases
thf(fact_150_parts_Osimps, axiom,
    ((![A3 : msg, H : set_msg]: ((member_msg @ A3 @ (parts @ H)) = (((?[X7 : msg]: (((A3 = X7)) & ((member_msg @ X7 @ H))))) | ((((?[X7 : msg]: (?[Y2 : msg]: (((A3 = X7)) & ((member_msg @ (mPair @ X7 @ Y2) @ (parts @ H))))))) | ((((?[X7 : msg]: (?[Y2 : msg]: (((A3 = Y2)) & ((member_msg @ (mPair @ X7 @ Y2) @ (parts @ H))))))) | ((?[K4 : nat]: (?[X7 : msg]: (((A3 = X7)) & ((member_msg @ (crypt @ K4 @ X7) @ (parts @ H)))))))))))))))). % parts.simps
thf(fact_151_parts_Oinducts, axiom,
    ((![X6 : msg, H : set_msg, P : msg > $o]: ((member_msg @ X6 @ (parts @ H)) => ((![X9 : msg]: ((member_msg @ X9 @ H) => (P @ X9))) => ((![X9 : msg, Y6 : msg]: ((member_msg @ (mPair @ X9 @ Y6) @ (parts @ H)) => ((P @ (mPair @ X9 @ Y6)) => (P @ X9)))) => ((![X9 : msg, Y6 : msg]: ((member_msg @ (mPair @ X9 @ Y6) @ (parts @ H)) => ((P @ (mPair @ X9 @ Y6)) => (P @ Y6)))) => ((![K3 : nat, X9 : msg]: ((member_msg @ (crypt @ K3 @ X9) @ (parts @ H)) => ((P @ (crypt @ K3 @ X9)) => (P @ X9)))) => (P @ X6))))))))). % parts.inducts
thf(fact_152_pushKeys_I6_J, axiom,
    ((![K : nat, X : nat, K5 : msg, A : set_msg]: ((insert_msg @ (key @ K) @ (insert_msg @ (crypt @ X @ K5) @ A)) = (insert_msg @ (crypt @ X @ K5) @ (insert_msg @ (key @ K) @ A)))))). % pushKeys(6)
thf(fact_153_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_154_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_155_analz__subset__parts, axiom,
    ((![H : set_msg]: (ord_less_eq_set_msg @ (analz @ H) @ (parts @ H))))). % analz_subset_parts
thf(fact_156_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_157_Notes__imp__knows, axiom,
    ((![A : agent, X : msg, Evs : list_event]: ((member_event @ (notes @ A @ X) @ (set_event2 @ Evs)) => (member_msg @ X @ (knows @ A @ Evs)))))). % Notes_imp_knows
thf(fact_158_spies__takeWhile, axiom,
    ((![P : event > $o, Evs : list_event]: (ord_less_eq_set_msg @ (knows @ spy @ (takeWhile_event @ P @ Evs)) @ (knows @ spy @ Evs))))). % spies_takeWhile
thf(fact_159_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_160_shrK__in__used, axiom,
    ((![A : agent, Evs : list_event]: (member_msg @ (key @ (shrK @ A)) @ (used @ Evs))))). % shrK_in_used
thf(fact_161_shrK__in__knows, axiom,
    ((![A : agent, Evs : list_event]: (member_msg @ (key @ (shrK @ A)) @ (knows @ A @ Evs))))). % shrK_in_knows
thf(fact_162_singleton__insert__inj__eq_H, axiom,
    ((![A3 : msg, A : set_msg, B3 : msg]: (((insert_msg @ A3 @ A) = (insert_msg @ B3 @ bot_bot_set_msg)) = (((A3 = B3)) & ((ord_less_eq_set_msg @ A @ (insert_msg @ B3 @ bot_bot_set_msg)))))))). % singleton_insert_inj_eq'
thf(fact_163_singleton__insert__inj__eq, axiom,
    ((![B3 : msg, A3 : msg, A : set_msg]: (((insert_msg @ B3 @ bot_bot_set_msg) = (insert_msg @ A3 @ A)) = (((A3 = B3)) & ((ord_less_eq_set_msg @ A @ (insert_msg @ B3 @ bot_bot_set_msg)))))))). % singleton_insert_inj_eq
thf(fact_164_Crypt__Spy__analz__bad, axiom,
    ((![A : agent, X : msg, Evs : list_event]: ((member_msg @ (crypt @ (shrK @ A) @ X) @ (analz @ (knows @ spy @ Evs))) => ((member_agent @ A @ bad) => (member_msg @ X @ (analz @ (knows @ spy @ Evs)))))))). % Crypt_Spy_analz_bad
thf(fact_165_empty__iff, axiom,
    ((![C : agent]: (~ ((member_agent @ C @ bot_bot_set_agent)))))). % empty_iff
thf(fact_166_empty__iff, axiom,
    ((![C : list_event]: (~ ((member_list_event @ C @ bot_bo1693714908_event)))))). % empty_iff
thf(fact_167_empty__iff, axiom,
    ((![C : event]: (~ ((member_event @ C @ bot_bot_set_event)))))). % empty_iff
thf(fact_168_empty__iff, axiom,
    ((![C : msg]: (~ ((member_msg @ C @ bot_bot_set_msg)))))). % empty_iff
thf(fact_169_all__not__in__conv, axiom,
    ((![A : set_agent]: ((![X2 : agent]: (~ ((member_agent @ X2 @ A)))) = (A = bot_bot_set_agent))))). % all_not_in_conv
thf(fact_170_all__not__in__conv, axiom,
    ((![A : set_list_event]: ((![X2 : list_event]: (~ ((member_list_event @ X2 @ A)))) = (A = bot_bo1693714908_event))))). % all_not_in_conv
thf(fact_171_all__not__in__conv, axiom,
    ((![A : set_event]: ((![X2 : event]: (~ ((member_event @ X2 @ A)))) = (A = bot_bot_set_event))))). % all_not_in_conv
thf(fact_172_all__not__in__conv, axiom,
    ((![A : set_msg]: ((![X2 : msg]: (~ ((member_msg @ X2 @ A)))) = (A = bot_bot_set_msg))))). % all_not_in_conv
thf(fact_173_Collect__empty__eq, axiom,
    ((![P : msg > $o]: (((collect_msg @ P) = bot_bot_set_msg) = (![X2 : msg]: (~ ((P @ X2)))))))). % Collect_empty_eq
thf(fact_174_empty__Collect__eq, axiom,
    ((![P : msg > $o]: ((bot_bot_set_msg = (collect_msg @ P)) = (![X2 : msg]: (~ ((P @ X2)))))))). % empty_Collect_eq
thf(fact_175_insertCI, axiom,
    ((![A3 : agent, B : set_agent, B3 : agent]: (((~ ((member_agent @ A3 @ B))) => (A3 = B3)) => (member_agent @ A3 @ (insert_agent @ B3 @ B)))))). % insertCI
thf(fact_176_insertCI, axiom,
    ((![A3 : list_event, B : set_list_event, B3 : list_event]: (((~ ((member_list_event @ A3 @ B))) => (A3 = B3)) => (member_list_event @ A3 @ (insert_list_event @ B3 @ B)))))). % insertCI
thf(fact_177_insertCI, axiom,
    ((![A3 : msg, B : set_msg, B3 : msg]: (((~ ((member_msg @ A3 @ B))) => (A3 = B3)) => (member_msg @ A3 @ (insert_msg @ B3 @ B)))))). % insertCI
thf(fact_178_insertCI, axiom,
    ((![A3 : event, B : set_event, B3 : event]: (((~ ((member_event @ A3 @ B))) => (A3 = B3)) => (member_event @ A3 @ (insert_event @ B3 @ B)))))). % insertCI
thf(fact_179_insert__iff, axiom,
    ((![A3 : agent, B3 : agent, A : set_agent]: ((member_agent @ A3 @ (insert_agent @ B3 @ A)) = (((A3 = B3)) | ((member_agent @ A3 @ A))))))). % insert_iff
thf(fact_180_insert__iff, axiom,
    ((![A3 : list_event, B3 : list_event, A : set_list_event]: ((member_list_event @ A3 @ (insert_list_event @ B3 @ A)) = (((A3 = B3)) | ((member_list_event @ A3 @ A))))))). % insert_iff
thf(fact_181_insert__iff, axiom,
    ((![A3 : msg, B3 : msg, A : set_msg]: ((member_msg @ A3 @ (insert_msg @ B3 @ A)) = (((A3 = B3)) | ((member_msg @ A3 @ A))))))). % insert_iff
thf(fact_182_insert__iff, axiom,
    ((![A3 : event, B3 : event, A : set_event]: ((member_event @ A3 @ (insert_event @ B3 @ A)) = (((A3 = B3)) | ((member_event @ A3 @ A))))))). % insert_iff
thf(fact_183_insert__absorb2, axiom,
    ((![X6 : msg, A : set_msg]: ((insert_msg @ X6 @ (insert_msg @ X6 @ A)) = (insert_msg @ X6 @ A))))). % insert_absorb2
thf(fact_184_subsetI, axiom,
    ((![A : set_agent, B : set_agent]: ((![X5 : agent]: ((member_agent @ X5 @ A) => (member_agent @ X5 @ B))) => (ord_le722097072_agent @ A @ B))))). % subsetI
thf(fact_185_subsetI, axiom,
    ((![A : set_list_event, B : set_list_event]: ((![X5 : list_event]: ((member_list_event @ X5 @ A) => (member_list_event @ X5 @ B))) => (ord_le119303592_event @ A @ B))))). % subsetI
thf(fact_186_subsetI, axiom,
    ((![A : set_event, B : set_event]: ((![X5 : event]: ((member_event @ X5 @ A) => (member_event @ X5 @ B))) => (ord_le152226328_event @ A @ B))))). % subsetI
thf(fact_187_subsetI, axiom,
    ((![A : set_msg, B : set_msg]: ((![X5 : msg]: ((member_msg @ X5 @ A) => (member_msg @ X5 @ B))) => (ord_less_eq_set_msg @ A @ B))))). % subsetI
thf(fact_188_subset__antisym, axiom,
    ((![A : set_msg, B : set_msg]: ((ord_less_eq_set_msg @ A @ B) => ((ord_less_eq_set_msg @ B @ A) => (A = B)))))). % subset_antisym
thf(fact_189_shrK__injective, axiom,
    ((![X6 : agent, Y5 : agent]: (((shrK @ X6) = (shrK @ Y5)) = (X6 = Y5))))). % shrK_injective
thf(fact_190_singletonI, axiom,
    ((![A3 : agent]: (member_agent @ A3 @ (insert_agent @ A3 @ bot_bot_set_agent))))). % singletonI
thf(fact_191_singletonI, axiom,
    ((![A3 : list_event]: (member_list_event @ A3 @ (insert_list_event @ A3 @ bot_bo1693714908_event))))). % singletonI
thf(fact_192_singletonI, axiom,
    ((![A3 : event]: (member_event @ A3 @ (insert_event @ A3 @ bot_bot_set_event))))). % singletonI
thf(fact_193_singletonI, axiom,
    ((![A3 : msg]: (member_msg @ A3 @ (insert_msg @ A3 @ bot_bot_set_msg))))). % singletonI
thf(fact_194_subset__empty, axiom,
    ((![A : set_msg]: ((ord_less_eq_set_msg @ A @ bot_bot_set_msg) = (A = bot_bot_set_msg))))). % subset_empty
thf(fact_195_empty__subsetI, axiom,
    ((![A : set_msg]: (ord_less_eq_set_msg @ bot_bot_set_msg @ A)))). % empty_subsetI

% Conjectures (4)
thf(conj_0, hypothesis,
    ((~ ((member_agent @ a @ bad))))).
thf(conj_1, hypothesis,
    ((~ ((member_agent @ b @ bad))))).
thf(conj_2, hypothesis,
    ((member_list_event @ evs @ nS_Sha1061662329shared))).
thf(conj_3, conjecture,
    (((member_msg @ (key @ k) @ (analz @ (knows @ spy @ evs))) | ((~ ((member_event @ (says @ b @ a @ (crypt @ k @ (nonce @ nb))) @ (set_event2 @ evs)))) | (~ ((member_msg @ (crypt @ k @ (nonce @ nb)) @ (parts @ (knows @ spy @ (takeWhile_event @ (^[Z : event]: (~ ((Z = (says @ b @ a @ (crypt @ k @ (nonce @ nb))))))) @ (rev_event @ evs))))))))))).
