% 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_442__5232558_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:24:55.462

% 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 (53)
thf(sy_c_Event_Obad, type,
    bad : set_agent).
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_List_Oappend_001t__Event__Oevent, type,
    append_event : list_event > list_event > list_event).
thf(sy_c_List_Oappend_001t__List__Olist_It__Event__Oevent_J, type,
    append_list_event : list_list_event > list_list_event > list_list_event).
thf(sy_c_List_Oappend_001t__Message__Oagent, type,
    append_agent : list_agent > list_agent > list_agent).
thf(sy_c_List_Oappend_001t__Message__Omsg, type,
    append_msg : list_msg > list_msg > list_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_ONil_001t__Event__Oevent, type,
    nil_event : list_event).
thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Event__Oevent_J, type,
    nil_list_event : list_list_event).
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_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_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_NS__Shared__Mirabelle__xwdrtqxrux_Ons__shared, type,
    nS_Sha1061662329shared : set_list_event).
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_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_Aa, type,
    aa : agent).
thf(sy_v_B, type,
    b : agent).
thf(sy_v_Ba, type,
    ba : agent).
thf(sy_v_K, type,
    k : nat).
thf(sy_v_Ka, type,
    ka : nat).
thf(sy_v_NA, type,
    na : nat).
thf(sy_v_Nb, type,
    nb : nat).
thf(sy_v_S, type,
    s : agent).
thf(sy_v_X, type,
    x : msg).
thf(sy_v_evs3, type,
    evs3 : list_event).

% Relevant facts (194)
thf(fact_0_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_1_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_2_A__trusts__NS2, axiom,
    ((![A : agent, NA : msg, B : agent, K : nat, X : msg, Evs : list_event]: ((member_msg @ (crypt @ (shrK @ A) @ (mPair @ NA @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X)))) @ (parts @ (knows @ spy @ Evs))) => ((~ ((member_agent @ A @ bad))) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => (member_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ NA @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (set_event2 @ Evs)))))))). % A_trusts_NS2
thf(fact_3_B__trusts__NS3, axiom,
    ((![B : agent, K : nat, A : agent, Evs : list_event]: ((member_msg @ (crypt @ (shrK @ B) @ (mPair @ (key @ K) @ (agent2 @ A))) @ (parts @ (knows @ spy @ Evs))) => ((~ ((member_agent @ B @ bad))) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => (?[NA2 : msg]: (member_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ NA2 @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ (crypt @ (shrK @ B) @ (mPair @ (key @ K) @ (agent2 @ A)))))))) @ (set_event2 @ Evs))))))))). % B_trusts_NS3
thf(fact_4_ns__shared_ONS3, axiom,
    ((![Evs3 : list_event, A : agent, S : agent, NA : nat, B : agent, K : nat, X : msg]: ((member_list_event @ Evs3 @ nS_Sha1061662329shared) => ((~ ((A = server))) => ((member_event @ (says @ S @ A @ (crypt @ (shrK @ A) @ (mPair @ (nonce @ NA) @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (set_event2 @ Evs3)) => ((member_event @ (says @ A @ server @ (mPair @ (agent2 @ A) @ (mPair @ (agent2 @ B) @ (nonce @ NA)))) @ (set_event2 @ Evs3)) => (member_list_event @ (cons_event @ (says @ A @ B @ X) @ Evs3) @ nS_Sha1061662329shared)))))))). % ns_shared.NS3
thf(fact_5_ns__shared_ONil, axiom,
    ((member_list_event @ nil_event @ nS_Sha1061662329shared))). % ns_shared.Nil
thf(fact_6_spies__evs__rev, axiom,
    ((![Evs : list_event]: ((knows @ spy @ Evs) = (knows @ spy @ (rev_event @ Evs)))))). % spies_evs_rev
thf(fact_7_NS4__implies__NS3, axiom,
    ((![Evs : list_event, K : nat, A : agent, NA : msg, B : agent, X : msg, NB : nat]: ((member_list_event @ Evs @ nS_Sha1061662329shared) => ((~ ((member_msg @ (key @ K) @ (analz @ (knows @ spy @ Evs))))) => ((member_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ NA @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (set_event2 @ Evs)) => ((member_msg @ (crypt @ K @ (nonce @ NB)) @ (parts @ (knows @ spy @ Evs))) => (?[A2 : agent]: (member_event @ (says @ A2 @ B @ X) @ (set_event2 @ Evs)))))))))). % NS4_implies_NS3
thf(fact_8_Oops__parts__spies, axiom,
    ((![A : agent, NA : msg, B : msg, K : msg, X : msg, Evs : list_event]: ((member_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ NA @ (mPair @ B @ (mPair @ K @ X))))) @ (set_event2 @ Evs)) => (member_msg @ K @ (parts @ (knows @ spy @ Evs))))))). % Oops_parts_spies
thf(fact_9_A__trusts__NS4__lemma, axiom,
    ((![Evs : list_event, K : nat, A : agent, NA : msg, B : agent, X : msg, NB : nat]: ((member_list_event @ Evs @ nS_Sha1061662329shared) => ((~ ((member_msg @ (key @ K) @ (analz @ (knows @ spy @ Evs))))) => ((member_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ NA @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (set_event2 @ Evs)) => ((member_msg @ (crypt @ K @ (nonce @ NB)) @ (parts @ (knows @ spy @ Evs))) => (member_event @ (says @ B @ A @ (crypt @ K @ (nonce @ NB))) @ (set_event2 @ Evs))))))))). % A_trusts_NS4_lemma
thf(fact_10_B__trusts__NS5__lemma, axiom,
    ((![B : agent, Evs : list_event, K : nat, A : agent, NA : msg, NB : nat]: ((~ ((member_agent @ B @ bad))) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => ((~ ((member_msg @ (key @ K) @ (analz @ (knows @ spy @ Evs))))) => ((member_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ NA @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ (crypt @ (shrK @ B) @ (mPair @ (key @ K) @ (agent2 @ A)))))))) @ (set_event2 @ Evs)) => ((member_msg @ (crypt @ K @ (mPair @ (nonce @ NB) @ (nonce @ NB))) @ (parts @ (knows @ spy @ Evs))) => (member_event @ (says @ A @ B @ (crypt @ K @ (mPair @ (nonce @ NB) @ (nonce @ NB)))) @ (set_event2 @ Evs)))))))))). % B_trusts_NS5_lemma
thf(fact_11_unique__session__keys, axiom,
    ((![A : agent, NA : msg, B : agent, K : nat, X : msg, Evs : list_event, A3 : agent, NA3 : msg, B2 : agent, X2 : msg]: ((member_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ NA @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (set_event2 @ Evs)) => ((member_event @ (says @ server @ A3 @ (crypt @ (shrK @ A3) @ (mPair @ NA3 @ (mPair @ (agent2 @ B2) @ (mPair @ (key @ K) @ X2))))) @ (set_event2 @ Evs)) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => ((A = A3) & ((NA = NA3) & ((B = B2) & (X = X2)))))))))). % unique_session_keys
thf(fact_12_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_13_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_14_rev__eq__Cons__iff, axiom,
    ((![Xs : list_event, Y : event, Ys : list_event]: (((rev_event @ Xs) = (cons_event @ Y @ Ys)) = (Xs = (append_event @ (rev_event @ Ys) @ (cons_event @ Y @ nil_event))))))). % rev_eq_Cons_iff
thf(fact_15_shrK__in__knows, axiom,
    ((![A : agent, Evs : list_event]: (member_msg @ (key @ (shrK @ A)) @ (knows @ A @ Evs))))). % shrK_in_knows
thf(fact_16_takeWhile__append1, axiom,
    ((![X3 : agent, Xs : list_agent, P : agent > $o, Ys : list_agent]: ((member_agent @ X3 @ (set_agent2 @ Xs)) => ((~ ((P @ X3))) => ((takeWhile_agent @ P @ (append_agent @ Xs @ Ys)) = (takeWhile_agent @ P @ Xs))))))). % takeWhile_append1
thf(fact_17_takeWhile__append1, axiom,
    ((![X3 : list_event, Xs : list_list_event, P : list_event > $o, Ys : list_list_event]: ((member_list_event @ X3 @ (set_list_event2 @ Xs)) => ((~ ((P @ X3))) => ((takeWhile_list_event @ P @ (append_list_event @ Xs @ Ys)) = (takeWhile_list_event @ P @ Xs))))))). % takeWhile_append1
thf(fact_18_takeWhile__append1, axiom,
    ((![X3 : msg, Xs : list_msg, P : msg > $o, Ys : list_msg]: ((member_msg @ X3 @ (set_msg2 @ Xs)) => ((~ ((P @ X3))) => ((takeWhile_msg @ P @ (append_msg @ Xs @ Ys)) = (takeWhile_msg @ P @ Xs))))))). % takeWhile_append1
thf(fact_19_takeWhile__append1, axiom,
    ((![X3 : event, Xs : list_event, P : event > $o, Ys : list_event]: ((member_event @ X3 @ (set_event2 @ Xs)) => ((~ ((P @ X3))) => ((takeWhile_event @ P @ (append_event @ Xs @ Ys)) = (takeWhile_event @ P @ Xs))))))). % takeWhile_append1
thf(fact_20_takeWhile__append2, axiom,
    ((![Xs : list_agent, P : agent > $o, Ys : list_agent]: ((![X4 : agent]: ((member_agent @ X4 @ (set_agent2 @ Xs)) => (P @ X4))) => ((takeWhile_agent @ P @ (append_agent @ Xs @ Ys)) = (append_agent @ Xs @ (takeWhile_agent @ P @ Ys))))))). % takeWhile_append2
thf(fact_21_takeWhile__append2, axiom,
    ((![Xs : list_list_event, P : list_event > $o, Ys : list_list_event]: ((![X4 : list_event]: ((member_list_event @ X4 @ (set_list_event2 @ Xs)) => (P @ X4))) => ((takeWhile_list_event @ P @ (append_list_event @ Xs @ Ys)) = (append_list_event @ Xs @ (takeWhile_list_event @ P @ Ys))))))). % takeWhile_append2
thf(fact_22_takeWhile__append2, axiom,
    ((![Xs : list_msg, P : msg > $o, Ys : list_msg]: ((![X4 : msg]: ((member_msg @ X4 @ (set_msg2 @ Xs)) => (P @ X4))) => ((takeWhile_msg @ P @ (append_msg @ Xs @ Ys)) = (append_msg @ Xs @ (takeWhile_msg @ P @ Ys))))))). % takeWhile_append2
thf(fact_23_takeWhile__append2, axiom,
    ((![Xs : list_event, P : event > $o, Ys : list_event]: ((![X4 : event]: ((member_event @ X4 @ (set_event2 @ Xs)) => (P @ X4))) => ((takeWhile_event @ P @ (append_event @ Xs @ Ys)) = (append_event @ Xs @ (takeWhile_event @ P @ Ys))))))). % takeWhile_append2
thf(fact_24_rev__singleton__conv, axiom,
    ((![Xs : list_event, X3 : event]: (((rev_event @ Xs) = (cons_event @ X3 @ nil_event)) = (Xs = (cons_event @ X3 @ nil_event)))))). % rev_singleton_conv
thf(fact_25_singleton__rev__conv, axiom,
    ((![X3 : event, Xs : list_event]: (((cons_event @ X3 @ nil_event) = (rev_event @ Xs)) = (Xs = (cons_event @ X3 @ nil_event)))))). % singleton_rev_conv
thf(fact_26_append1__eq__conv, axiom,
    ((![Xs : list_event, X3 : event, Ys : list_event, Y : event]: (((append_event @ Xs @ (cons_event @ X3 @ nil_event)) = (append_event @ Ys @ (cons_event @ Y @ nil_event))) = (((Xs = Ys)) & ((X3 = Y))))))). % append1_eq_conv
thf(fact_27_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_28_Spy__in__bad, axiom,
    ((member_agent @ spy @ bad))). % Spy_in_bad
thf(fact_29_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_30_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_31_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_32_same__append__eq, axiom,
    ((![Xs : list_event, Ys : list_event, Zs : list_event]: (((append_event @ Xs @ Ys) = (append_event @ Xs @ Zs)) = (Ys = Zs))))). % same_append_eq
thf(fact_33_append__same__eq, axiom,
    ((![Ys : list_event, Xs : list_event, Zs : list_event]: (((append_event @ Ys @ Xs) = (append_event @ Zs @ Xs)) = (Ys = Zs))))). % append_same_eq
thf(fact_34_append__assoc, axiom,
    ((![Xs : list_event, Ys : list_event, Zs : list_event]: ((append_event @ (append_event @ Xs @ Ys) @ Zs) = (append_event @ Xs @ (append_event @ Ys @ Zs)))))). % append_assoc
thf(fact_35_append_Oassoc, axiom,
    ((![A4 : list_event, B3 : list_event, C : list_event]: ((append_event @ (append_event @ A4 @ B3) @ C) = (append_event @ A4 @ (append_event @ B3 @ C)))))). % append.assoc
thf(fact_36_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_37_rev__rev__ident, axiom,
    ((![Xs : list_event]: ((rev_event @ (rev_event @ Xs)) = Xs)))). % rev_rev_ident
thf(fact_38_shrK__injective, axiom,
    ((![X3 : agent, Y : agent]: (((shrK @ X3) = (shrK @ Y)) = (X3 = Y))))). % shrK_injective
thf(fact_39_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_40_takeWhile__idem, axiom,
    ((![P : event > $o, Xs : list_event]: ((takeWhile_event @ P @ (takeWhile_event @ P @ Xs)) = (takeWhile_event @ P @ Xs))))). % takeWhile_idem
thf(fact_41_append_Oright__neutral, axiom,
    ((![A4 : list_event]: ((append_event @ A4 @ nil_event) = A4)))). % append.right_neutral
thf(fact_42_append__is__Nil__conv, axiom,
    ((![Xs : list_event, Ys : list_event]: (((append_event @ Xs @ Ys) = nil_event) = (((Xs = nil_event)) & ((Ys = nil_event))))))). % append_is_Nil_conv
thf(fact_43_Nil__is__append__conv, axiom,
    ((![Xs : list_event, Ys : list_event]: ((nil_event = (append_event @ Xs @ Ys)) = (((Xs = nil_event)) & ((Ys = nil_event))))))). % Nil_is_append_conv
thf(fact_44_self__append__conv2, axiom,
    ((![Ys : list_event, Xs : list_event]: ((Ys = (append_event @ Xs @ Ys)) = (Xs = nil_event))))). % self_append_conv2
thf(fact_45_append__self__conv2, axiom,
    ((![Xs : list_event, Ys : list_event]: (((append_event @ Xs @ Ys) = Ys) = (Xs = nil_event))))). % append_self_conv2
thf(fact_46_self__append__conv, axiom,
    ((![Xs : list_event, Ys : list_event]: ((Xs = (append_event @ Xs @ Ys)) = (Ys = nil_event))))). % self_append_conv
thf(fact_47_append__self__conv, axiom,
    ((![Xs : list_event, Ys : list_event]: (((append_event @ Xs @ Ys) = Xs) = (Ys = nil_event))))). % append_self_conv
thf(fact_48_append__Nil2, axiom,
    ((![Xs : list_event]: ((append_event @ Xs @ nil_event) = Xs)))). % append_Nil2
thf(fact_49_rev__is__Nil__conv, axiom,
    ((![Xs : list_event]: (((rev_event @ Xs) = nil_event) = (Xs = nil_event))))). % rev_is_Nil_conv
thf(fact_50_Nil__is__rev__conv, axiom,
    ((![Xs : list_event]: ((nil_event = (rev_event @ Xs)) = (Xs = nil_event))))). % Nil_is_rev_conv
thf(fact_51_mem__Collect__eq, axiom,
    ((![A4 : agent, P : agent > $o]: ((member_agent @ A4 @ (collect_agent @ P)) = (P @ A4))))). % mem_Collect_eq
thf(fact_52_mem__Collect__eq, axiom,
    ((![A4 : list_event, P : list_event > $o]: ((member_list_event @ A4 @ (collect_list_event @ P)) = (P @ A4))))). % mem_Collect_eq
thf(fact_53_mem__Collect__eq, axiom,
    ((![A4 : event, P : event > $o]: ((member_event @ A4 @ (collect_event @ P)) = (P @ A4))))). % mem_Collect_eq
thf(fact_54_mem__Collect__eq, axiom,
    ((![A4 : msg, P : msg > $o]: ((member_msg @ A4 @ (collect_msg @ P)) = (P @ A4))))). % mem_Collect_eq
thf(fact_55_Collect__mem__eq, axiom,
    ((![A : set_agent]: ((collect_agent @ (^[X5 : agent]: (member_agent @ X5 @ A))) = A)))). % Collect_mem_eq
thf(fact_56_Collect__mem__eq, axiom,
    ((![A : set_list_event]: ((collect_list_event @ (^[X5 : list_event]: (member_list_event @ X5 @ A))) = A)))). % Collect_mem_eq
thf(fact_57_Collect__mem__eq, axiom,
    ((![A : set_event]: ((collect_event @ (^[X5 : event]: (member_event @ X5 @ A))) = A)))). % Collect_mem_eq
thf(fact_58_Collect__mem__eq, axiom,
    ((![A : set_msg]: ((collect_msg @ (^[X5 : msg]: (member_msg @ X5 @ A))) = A)))). % Collect_mem_eq
thf(fact_59_set__rev, axiom,
    ((![Xs : list_event]: ((set_event2 @ (rev_event @ Xs)) = (set_event2 @ Xs))))). % set_rev
thf(fact_60_rev__append, axiom,
    ((![Xs : list_event, Ys : list_event]: ((rev_event @ (append_event @ Xs @ Ys)) = (append_event @ (rev_event @ Ys) @ (rev_event @ Xs)))))). % rev_append
thf(fact_61_takeWhile__eq__all__conv, axiom,
    ((![P : event > $o, Xs : list_event]: (((takeWhile_event @ P @ Xs) = Xs) = (![X5 : event]: (((member_event @ X5 @ (set_event2 @ Xs))) => ((P @ X5)))))))). % takeWhile_eq_all_conv
thf(fact_62_not__Cons__self2, axiom,
    ((![X3 : event, Xs : list_event]: (~ (((cons_event @ X3 @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_63_append__eq__append__conv2, axiom,
    ((![Xs : list_event, Ys : list_event, Zs : list_event, Ts : list_event]: (((append_event @ Xs @ Ys) = (append_event @ Zs @ Ts)) = (?[Us : list_event]: (((((Xs = (append_event @ Zs @ Us))) & (((append_event @ Us @ Ys) = Ts)))) | (((((append_event @ Xs @ Us) = Zs)) & ((Ys = (append_event @ Us @ Ts))))))))))). % append_eq_append_conv2
thf(fact_64_append__eq__appendI, axiom,
    ((![Xs : list_event, Xs1 : list_event, Zs : list_event, Ys : list_event, Us2 : list_event]: (((append_event @ Xs @ Xs1) = Zs) => ((Ys = (append_event @ Xs1 @ Us2)) => ((append_event @ Xs @ Ys) = (append_event @ Zs @ Us2))))))). % append_eq_appendI
thf(fact_65_rev__swap, axiom,
    ((![Xs : list_event, Ys : list_event]: (((rev_event @ Xs) = Ys) = (Xs = (rev_event @ Ys)))))). % rev_swap
thf(fact_66_map__tailrec__rev_Oinduct, axiom,
    ((![P : (event > event) > list_event > list_event > $o, A0 : event > event, A1 : list_event, A22 : list_event]: ((![F : event > event, X_1 : list_event]: (P @ F @ nil_event @ X_1)) => ((![F : event > event, A5 : event, As : list_event, Bs : list_event]: ((P @ F @ As @ (cons_event @ (F @ A5) @ Bs)) => (P @ F @ (cons_event @ A5 @ As) @ Bs))) => (P @ A0 @ A1 @ A22)))))). % map_tailrec_rev.induct
thf(fact_67_list__nonempty__induct, axiom,
    ((![Xs : list_event, P : list_event > $o]: ((~ ((Xs = nil_event))) => ((![X4 : event]: (P @ (cons_event @ X4 @ nil_event))) => ((![X4 : event, Xs2 : list_event]: ((~ ((Xs2 = nil_event))) => ((P @ Xs2) => (P @ (cons_event @ X4 @ Xs2))))) => (P @ Xs))))))). % list_nonempty_induct
thf(fact_68_successively_Oinduct, axiom,
    ((![P : (event > event > $o) > list_event > $o, A0 : event > event > $o, A1 : list_event]: ((![P2 : event > event > $o]: (P @ P2 @ nil_event)) => ((![P2 : event > event > $o, X4 : event]: (P @ P2 @ (cons_event @ X4 @ nil_event))) => ((![P2 : event > event > $o, X4 : event, Y2 : event, Xs2 : list_event]: ((P @ P2 @ (cons_event @ Y2 @ Xs2)) => (P @ P2 @ (cons_event @ X4 @ (cons_event @ Y2 @ Xs2))))) => (P @ A0 @ A1))))))). % successively.induct
thf(fact_69_remdups__adj_Oinduct, axiom,
    ((![P : list_event > $o, A0 : list_event]: ((P @ nil_event) => ((![X4 : event]: (P @ (cons_event @ X4 @ nil_event))) => ((![X4 : event, Y2 : event, Xs2 : list_event]: (((X4 = Y2) => (P @ (cons_event @ X4 @ Xs2))) => (((~ ((X4 = Y2))) => (P @ (cons_event @ Y2 @ Xs2))) => (P @ (cons_event @ X4 @ (cons_event @ Y2 @ Xs2)))))) => (P @ A0))))))). % remdups_adj.induct
thf(fact_70_sorted__wrt_Oinduct, axiom,
    ((![P : (event > event > $o) > list_event > $o, A0 : event > event > $o, A1 : list_event]: ((![P2 : event > event > $o]: (P @ P2 @ nil_event)) => ((![P2 : event > event > $o, X4 : event, Ys2 : list_event]: ((P @ P2 @ Ys2) => (P @ P2 @ (cons_event @ X4 @ Ys2)))) => (P @ A0 @ A1)))))). % sorted_wrt.induct
thf(fact_71_remdups__adj_Ocases, axiom,
    ((![X3 : list_event]: ((~ ((X3 = nil_event))) => ((![X4 : event]: (~ ((X3 = (cons_event @ X4 @ nil_event))))) => (~ ((![X4 : event, Y2 : event, Xs2 : list_event]: (~ ((X3 = (cons_event @ X4 @ (cons_event @ Y2 @ Xs2))))))))))))). % remdups_adj.cases
thf(fact_72_transpose_Ocases, axiom,
    ((![X3 : list_list_event]: ((~ ((X3 = nil_list_event))) => ((![Xss : list_list_event]: (~ ((X3 = (cons_list_event @ nil_event @ Xss))))) => (~ ((![X4 : event, Xs2 : list_event, Xss : list_list_event]: (~ ((X3 = (cons_list_event @ (cons_event @ X4 @ Xs2) @ Xss)))))))))))). % transpose.cases
thf(fact_73_shuffles_Oinduct, axiom,
    ((![P : list_event > list_event > $o, A0 : list_event, A1 : list_event]: ((![X_1 : list_event]: (P @ nil_event @ X_1)) => ((![Xs2 : list_event]: (P @ Xs2 @ nil_event)) => ((![X4 : event, Xs2 : list_event, Y2 : event, Ys2 : list_event]: ((P @ Xs2 @ (cons_event @ Y2 @ Ys2)) => ((P @ (cons_event @ X4 @ Xs2) @ Ys2) => (P @ (cons_event @ X4 @ Xs2) @ (cons_event @ Y2 @ Ys2))))) => (P @ A0 @ A1))))))). % shuffles.induct
thf(fact_74_induct__list012, axiom,
    ((![P : list_event > $o, Xs : list_event]: ((P @ nil_event) => ((![X4 : event]: (P @ (cons_event @ X4 @ nil_event))) => ((![X4 : event, Y2 : event, Zs2 : list_event]: ((P @ Zs2) => ((P @ (cons_event @ Y2 @ Zs2)) => (P @ (cons_event @ X4 @ (cons_event @ Y2 @ Zs2)))))) => (P @ Xs))))))). % induct_list012
thf(fact_75_splice_Oinduct, axiom,
    ((![P : list_event > list_event > $o, A0 : list_event, A1 : list_event]: ((![X_1 : list_event]: (P @ nil_event @ X_1)) => ((![X4 : event, Xs2 : list_event, Ys2 : list_event]: ((P @ Ys2 @ Xs2) => (P @ (cons_event @ X4 @ Xs2) @ Ys2))) => (P @ A0 @ A1)))))). % splice.induct
thf(fact_76_list__induct2_H, axiom,
    ((![P : list_event > list_event > $o, Xs : list_event, Ys : list_event]: ((P @ nil_event @ nil_event) => ((![X4 : event, Xs2 : list_event]: (P @ (cons_event @ X4 @ Xs2) @ nil_event)) => ((![Y2 : event, Ys2 : list_event]: (P @ nil_event @ (cons_event @ Y2 @ Ys2))) => ((![X4 : event, Xs2 : list_event, Y2 : event, Ys2 : list_event]: ((P @ Xs2 @ Ys2) => (P @ (cons_event @ X4 @ Xs2) @ (cons_event @ Y2 @ Ys2)))) => (P @ Xs @ Ys)))))))). % list_induct2'
thf(fact_77_neq__Nil__conv, axiom,
    ((![Xs : list_event]: ((~ ((Xs = nil_event))) = (?[Y3 : event]: (?[Ys3 : list_event]: (Xs = (cons_event @ Y3 @ Ys3)))))))). % neq_Nil_conv
thf(fact_78_list_Oinducts, axiom,
    ((![P : list_event > $o, List : list_event]: ((P @ nil_event) => ((![X1 : event, X23 : list_event]: ((P @ X23) => (P @ (cons_event @ X1 @ X23)))) => (P @ List)))))). % list.inducts
thf(fact_79_list_Oexhaust, axiom,
    ((![Y : list_event]: ((~ ((Y = nil_event))) => (~ ((![X212 : event, X222 : list_event]: (~ ((Y = (cons_event @ X212 @ X222))))))))))). % list.exhaust
thf(fact_80_list_OdiscI, axiom,
    ((![List : list_event, X21 : event, X22 : list_event]: ((List = (cons_event @ X21 @ X22)) => (~ ((List = nil_event))))))). % list.discI
thf(fact_81_list_Odistinct_I1_J, axiom,
    ((![X21 : event, X22 : list_event]: (~ ((nil_event = (cons_event @ X21 @ X22))))))). % list.distinct(1)
thf(fact_82_list_Oset__cases, axiom,
    ((![E : agent, A4 : list_agent]: ((member_agent @ E @ (set_agent2 @ A4)) => ((![Z2 : list_agent]: (~ ((A4 = (cons_agent @ E @ Z2))))) => (~ ((![Z1 : agent, Z2 : list_agent]: ((A4 = (cons_agent @ Z1 @ Z2)) => (~ ((member_agent @ E @ (set_agent2 @ Z2))))))))))))). % list.set_cases
thf(fact_83_list_Oset__cases, axiom,
    ((![E : list_event, A4 : list_list_event]: ((member_list_event @ E @ (set_list_event2 @ A4)) => ((![Z2 : list_list_event]: (~ ((A4 = (cons_list_event @ E @ Z2))))) => (~ ((![Z1 : list_event, Z2 : list_list_event]: ((A4 = (cons_list_event @ Z1 @ Z2)) => (~ ((member_list_event @ E @ (set_list_event2 @ Z2))))))))))))). % list.set_cases
thf(fact_84_list_Oset__cases, axiom,
    ((![E : msg, A4 : list_msg]: ((member_msg @ E @ (set_msg2 @ A4)) => ((![Z2 : list_msg]: (~ ((A4 = (cons_msg @ E @ Z2))))) => (~ ((![Z1 : msg, Z2 : list_msg]: ((A4 = (cons_msg @ Z1 @ Z2)) => (~ ((member_msg @ E @ (set_msg2 @ Z2))))))))))))). % list.set_cases
thf(fact_85_list_Oset__cases, axiom,
    ((![E : event, A4 : list_event]: ((member_event @ E @ (set_event2 @ A4)) => ((![Z2 : list_event]: (~ ((A4 = (cons_event @ E @ Z2))))) => (~ ((![Z1 : event, Z2 : list_event]: ((A4 = (cons_event @ Z1 @ Z2)) => (~ ((member_event @ E @ (set_event2 @ Z2))))))))))))). % list.set_cases
thf(fact_86_set__ConsD, axiom,
    ((![Y : agent, X3 : agent, Xs : list_agent]: ((member_agent @ Y @ (set_agent2 @ (cons_agent @ X3 @ Xs))) => ((Y = X3) | (member_agent @ Y @ (set_agent2 @ Xs))))))). % set_ConsD
thf(fact_87_set__ConsD, axiom,
    ((![Y : list_event, X3 : list_event, Xs : list_list_event]: ((member_list_event @ Y @ (set_list_event2 @ (cons_list_event @ X3 @ Xs))) => ((Y = X3) | (member_list_event @ Y @ (set_list_event2 @ Xs))))))). % set_ConsD
thf(fact_88_set__ConsD, axiom,
    ((![Y : msg, X3 : msg, Xs : list_msg]: ((member_msg @ Y @ (set_msg2 @ (cons_msg @ X3 @ Xs))) => ((Y = X3) | (member_msg @ Y @ (set_msg2 @ Xs))))))). % set_ConsD
thf(fact_89_set__ConsD, axiom,
    ((![Y : event, X3 : event, Xs : list_event]: ((member_event @ Y @ (set_event2 @ (cons_event @ X3 @ Xs))) => ((Y = X3) | (member_event @ Y @ (set_event2 @ Xs))))))). % set_ConsD
thf(fact_90_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_91_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_92_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_93_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_94_list_Oset__intros_I2_J, axiom,
    ((![Y : agent, X22 : list_agent, X21 : agent]: ((member_agent @ Y @ (set_agent2 @ X22)) => (member_agent @ Y @ (set_agent2 @ (cons_agent @ X21 @ X22))))))). % list.set_intros(2)
thf(fact_95_list_Oset__intros_I2_J, axiom,
    ((![Y : list_event, X22 : list_list_event, X21 : list_event]: ((member_list_event @ Y @ (set_list_event2 @ X22)) => (member_list_event @ Y @ (set_list_event2 @ (cons_list_event @ X21 @ X22))))))). % list.set_intros(2)
thf(fact_96_list_Oset__intros_I2_J, axiom,
    ((![Y : msg, X22 : list_msg, X21 : msg]: ((member_msg @ Y @ (set_msg2 @ X22)) => (member_msg @ Y @ (set_msg2 @ (cons_msg @ X21 @ X22))))))). % list.set_intros(2)
thf(fact_97_list_Oset__intros_I2_J, axiom,
    ((![Y : event, X22 : list_event, X21 : event]: ((member_event @ Y @ (set_event2 @ X22)) => (member_event @ Y @ (set_event2 @ (cons_event @ X21 @ X22))))))). % list.set_intros(2)
thf(fact_98_append__Cons, axiom,
    ((![X3 : event, Xs : list_event, Ys : list_event]: ((append_event @ (cons_event @ X3 @ Xs) @ Ys) = (cons_event @ X3 @ (append_event @ Xs @ Ys)))))). % append_Cons
thf(fact_99_Cons__eq__appendI, axiom,
    ((![X3 : event, Xs1 : list_event, Ys : list_event, Xs : list_event, Zs : list_event]: (((cons_event @ X3 @ Xs1) = Ys) => ((Xs = (append_event @ Xs1 @ Zs)) => ((cons_event @ X3 @ Xs) = (append_event @ Ys @ Zs))))))). % Cons_eq_appendI
thf(fact_100_append_Oleft__neutral, axiom,
    ((![A4 : list_event]: ((append_event @ nil_event @ A4) = A4)))). % append.left_neutral
thf(fact_101_append__Nil, axiom,
    ((![Ys : list_event]: ((append_event @ nil_event @ Ys) = Ys)))). % append_Nil
thf(fact_102_eq__Nil__appendI, axiom,
    ((![Xs : list_event, Ys : list_event]: ((Xs = Ys) => (Xs = (append_event @ nil_event @ Ys)))))). % eq_Nil_appendI
thf(fact_103_rev_Osimps_I1_J, axiom,
    (((rev_event @ nil_event) = nil_event))). % rev.simps(1)
thf(fact_104_takeWhile_Osimps_I1_J, axiom,
    ((![P : event > $o]: ((takeWhile_event @ P @ nil_event) = nil_event)))). % takeWhile.simps(1)
thf(fact_105_takeWhile__cong, axiom,
    ((![L : list_agent, K2 : list_agent, P : agent > $o, Q : agent > $o]: ((L = K2) => ((![X4 : agent]: ((member_agent @ X4 @ (set_agent2 @ L)) => ((P @ X4) = (Q @ X4)))) => ((takeWhile_agent @ P @ L) = (takeWhile_agent @ Q @ K2))))))). % takeWhile_cong
thf(fact_106_takeWhile__cong, axiom,
    ((![L : list_list_event, K2 : list_list_event, P : list_event > $o, Q : list_event > $o]: ((L = K2) => ((![X4 : list_event]: ((member_list_event @ X4 @ (set_list_event2 @ L)) => ((P @ X4) = (Q @ X4)))) => ((takeWhile_list_event @ P @ L) = (takeWhile_list_event @ Q @ K2))))))). % takeWhile_cong
thf(fact_107_takeWhile__cong, axiom,
    ((![L : list_msg, K2 : list_msg, P : msg > $o, Q : msg > $o]: ((L = K2) => ((![X4 : msg]: ((member_msg @ X4 @ (set_msg2 @ L)) => ((P @ X4) = (Q @ X4)))) => ((takeWhile_msg @ P @ L) = (takeWhile_msg @ Q @ K2))))))). % takeWhile_cong
thf(fact_108_takeWhile__cong, axiom,
    ((![L : list_event, K2 : list_event, P : event > $o, Q : event > $o]: ((L = K2) => ((![X4 : event]: ((member_event @ X4 @ (set_event2 @ L)) => ((P @ X4) = (Q @ X4)))) => ((takeWhile_event @ P @ L) = (takeWhile_event @ Q @ K2))))))). % takeWhile_cong
thf(fact_109_set__takeWhileD, axiom,
    ((![X3 : agent, P : agent > $o, Xs : list_agent]: ((member_agent @ X3 @ (set_agent2 @ (takeWhile_agent @ P @ Xs))) => ((member_agent @ X3 @ (set_agent2 @ Xs)) & (P @ X3)))))). % set_takeWhileD
thf(fact_110_set__takeWhileD, axiom,
    ((![X3 : list_event, P : list_event > $o, Xs : list_list_event]: ((member_list_event @ X3 @ (set_list_event2 @ (takeWhile_list_event @ P @ Xs))) => ((member_list_event @ X3 @ (set_list_event2 @ Xs)) & (P @ X3)))))). % set_takeWhileD
thf(fact_111_set__takeWhileD, axiom,
    ((![X3 : msg, P : msg > $o, Xs : list_msg]: ((member_msg @ X3 @ (set_msg2 @ (takeWhile_msg @ P @ Xs))) => ((member_msg @ X3 @ (set_msg2 @ Xs)) & (P @ X3)))))). % set_takeWhileD
thf(fact_112_set__takeWhileD, axiom,
    ((![X3 : event, P : event > $o, Xs : list_event]: ((member_event @ X3 @ (set_event2 @ (takeWhile_event @ P @ Xs))) => ((member_event @ X3 @ (set_event2 @ Xs)) & (P @ X3)))))). % set_takeWhileD
thf(fact_113_Server__not__bad, axiom,
    ((~ ((member_agent @ server @ bad))))). % Server_not_bad
thf(fact_114_rev__nonempty__induct, axiom,
    ((![Xs : list_event, P : list_event > $o]: ((~ ((Xs = nil_event))) => ((![X4 : event]: (P @ (cons_event @ X4 @ nil_event))) => ((![X4 : event, Xs2 : list_event]: ((~ ((Xs2 = nil_event))) => ((P @ Xs2) => (P @ (append_event @ Xs2 @ (cons_event @ X4 @ nil_event)))))) => (P @ Xs))))))). % rev_nonempty_induct
thf(fact_115_append__eq__Cons__conv, axiom,
    ((![Ys : list_event, Zs : list_event, X3 : event, Xs : list_event]: (((append_event @ Ys @ Zs) = (cons_event @ X3 @ Xs)) = (((((Ys = nil_event)) & ((Zs = (cons_event @ X3 @ Xs))))) | ((?[Ys4 : list_event]: (((Ys = (cons_event @ X3 @ Ys4))) & (((append_event @ Ys4 @ Zs) = Xs)))))))))). % append_eq_Cons_conv
thf(fact_116_Cons__eq__append__conv, axiom,
    ((![X3 : event, Xs : list_event, Ys : list_event, Zs : list_event]: (((cons_event @ X3 @ Xs) = (append_event @ Ys @ Zs)) = (((((Ys = nil_event)) & (((cons_event @ X3 @ Xs) = Zs)))) | ((?[Ys4 : list_event]: ((((cons_event @ X3 @ Ys4) = Ys)) & ((Xs = (append_event @ Ys4 @ Zs))))))))))). % Cons_eq_append_conv
thf(fact_117_rev__exhaust, axiom,
    ((![Xs : list_event]: ((~ ((Xs = nil_event))) => (~ ((![Ys2 : list_event, Y2 : event]: (~ ((Xs = (append_event @ Ys2 @ (cons_event @ Y2 @ nil_event)))))))))))). % rev_exhaust
thf(fact_118_rev__induct, axiom,
    ((![P : list_event > $o, Xs : list_event]: ((P @ nil_event) => ((![X4 : event, Xs2 : list_event]: ((P @ Xs2) => (P @ (append_event @ Xs2 @ (cons_event @ X4 @ nil_event))))) => (P @ Xs)))))). % rev_induct
thf(fact_119_split__list__first__prop__iff, axiom,
    ((![Xs : list_event, P : event > $o]: ((?[X5 : event]: (((member_event @ X5 @ (set_event2 @ Xs))) & ((P @ X5)))) = (?[Ys3 : list_event]: (?[X5 : event]: (((?[Zs3 : list_event]: (Xs = (append_event @ Ys3 @ (cons_event @ X5 @ Zs3))))) & ((((P @ X5)) & ((![Y3 : event]: (((member_event @ Y3 @ (set_event2 @ Ys3))) => ((~ ((P @ Y3)))))))))))))))). % split_list_first_prop_iff
thf(fact_120_split__list__last__prop__iff, axiom,
    ((![Xs : list_event, P : event > $o]: ((?[X5 : event]: (((member_event @ X5 @ (set_event2 @ Xs))) & ((P @ X5)))) = (?[Ys3 : list_event]: (?[X5 : event]: (?[Zs3 : list_event]: (((Xs = (append_event @ Ys3 @ (cons_event @ X5 @ Zs3)))) & ((((P @ X5)) & ((![Y3 : event]: (((member_event @ Y3 @ (set_event2 @ Zs3))) => ((~ ((P @ Y3))))))))))))))))). % split_list_last_prop_iff
thf(fact_121_in__set__conv__decomp__first, axiom,
    ((![X3 : agent, Xs : list_agent]: ((member_agent @ X3 @ (set_agent2 @ Xs)) = (?[Ys3 : list_agent]: (?[Zs3 : list_agent]: (((Xs = (append_agent @ Ys3 @ (cons_agent @ X3 @ Zs3)))) & ((~ ((member_agent @ X3 @ (set_agent2 @ Ys3)))))))))))). % in_set_conv_decomp_first
thf(fact_122_in__set__conv__decomp__first, axiom,
    ((![X3 : list_event, Xs : list_list_event]: ((member_list_event @ X3 @ (set_list_event2 @ Xs)) = (?[Ys3 : list_list_event]: (?[Zs3 : list_list_event]: (((Xs = (append_list_event @ Ys3 @ (cons_list_event @ X3 @ Zs3)))) & ((~ ((member_list_event @ X3 @ (set_list_event2 @ Ys3)))))))))))). % in_set_conv_decomp_first
thf(fact_123_in__set__conv__decomp__first, axiom,
    ((![X3 : msg, Xs : list_msg]: ((member_msg @ X3 @ (set_msg2 @ Xs)) = (?[Ys3 : list_msg]: (?[Zs3 : list_msg]: (((Xs = (append_msg @ Ys3 @ (cons_msg @ X3 @ Zs3)))) & ((~ ((member_msg @ X3 @ (set_msg2 @ Ys3)))))))))))). % in_set_conv_decomp_first
thf(fact_124_in__set__conv__decomp__first, axiom,
    ((![X3 : event, Xs : list_event]: ((member_event @ X3 @ (set_event2 @ Xs)) = (?[Ys3 : list_event]: (?[Zs3 : list_event]: (((Xs = (append_event @ Ys3 @ (cons_event @ X3 @ Zs3)))) & ((~ ((member_event @ X3 @ (set_event2 @ Ys3)))))))))))). % in_set_conv_decomp_first
thf(fact_125_in__set__conv__decomp__last, axiom,
    ((![X3 : agent, Xs : list_agent]: ((member_agent @ X3 @ (set_agent2 @ Xs)) = (?[Ys3 : list_agent]: (?[Zs3 : list_agent]: (((Xs = (append_agent @ Ys3 @ (cons_agent @ X3 @ Zs3)))) & ((~ ((member_agent @ X3 @ (set_agent2 @ Zs3)))))))))))). % in_set_conv_decomp_last
thf(fact_126_in__set__conv__decomp__last, axiom,
    ((![X3 : list_event, Xs : list_list_event]: ((member_list_event @ X3 @ (set_list_event2 @ Xs)) = (?[Ys3 : list_list_event]: (?[Zs3 : list_list_event]: (((Xs = (append_list_event @ Ys3 @ (cons_list_event @ X3 @ Zs3)))) & ((~ ((member_list_event @ X3 @ (set_list_event2 @ Zs3)))))))))))). % in_set_conv_decomp_last
thf(fact_127_in__set__conv__decomp__last, axiom,
    ((![X3 : msg, Xs : list_msg]: ((member_msg @ X3 @ (set_msg2 @ Xs)) = (?[Ys3 : list_msg]: (?[Zs3 : list_msg]: (((Xs = (append_msg @ Ys3 @ (cons_msg @ X3 @ Zs3)))) & ((~ ((member_msg @ X3 @ (set_msg2 @ Zs3)))))))))))). % in_set_conv_decomp_last
thf(fact_128_in__set__conv__decomp__last, axiom,
    ((![X3 : event, Xs : list_event]: ((member_event @ X3 @ (set_event2 @ Xs)) = (?[Ys3 : list_event]: (?[Zs3 : list_event]: (((Xs = (append_event @ Ys3 @ (cons_event @ X3 @ Zs3)))) & ((~ ((member_event @ X3 @ (set_event2 @ Zs3)))))))))))). % in_set_conv_decomp_last
thf(fact_129_split__list__first__propE, axiom,
    ((![Xs : list_event, P : event > $o]: ((?[X6 : event]: ((member_event @ X6 @ (set_event2 @ Xs)) & (P @ X6))) => (~ ((![Ys2 : list_event, X4 : event]: ((?[Zs2 : list_event]: (Xs = (append_event @ Ys2 @ (cons_event @ X4 @ Zs2)))) => ((P @ X4) => (~ ((![Xa : event]: ((member_event @ Xa @ (set_event2 @ Ys2)) => (~ ((P @ Xa)))))))))))))))). % split_list_first_propE
thf(fact_130_split__list__last__propE, axiom,
    ((![Xs : list_event, P : event > $o]: ((?[X6 : event]: ((member_event @ X6 @ (set_event2 @ Xs)) & (P @ X6))) => (~ ((![Ys2 : list_event, X4 : event, Zs2 : list_event]: ((Xs = (append_event @ Ys2 @ (cons_event @ X4 @ Zs2))) => ((P @ X4) => (~ ((![Xa : event]: ((member_event @ Xa @ (set_event2 @ Zs2)) => (~ ((P @ Xa)))))))))))))))). % split_list_last_propE
thf(fact_131_split__list__first__prop, axiom,
    ((![Xs : list_event, P : event > $o]: ((?[X6 : event]: ((member_event @ X6 @ (set_event2 @ Xs)) & (P @ X6))) => (?[Ys2 : list_event, X4 : event]: ((?[Zs2 : list_event]: (Xs = (append_event @ Ys2 @ (cons_event @ X4 @ Zs2)))) & ((P @ X4) & (![Xa : event]: ((member_event @ Xa @ (set_event2 @ Ys2)) => (~ ((P @ Xa)))))))))))). % split_list_first_prop
thf(fact_132_split__list__last__prop, axiom,
    ((![Xs : list_event, P : event > $o]: ((?[X6 : event]: ((member_event @ X6 @ (set_event2 @ Xs)) & (P @ X6))) => (?[Ys2 : list_event, X4 : event, Zs2 : list_event]: ((Xs = (append_event @ Ys2 @ (cons_event @ X4 @ Zs2))) & ((P @ X4) & (![Xa : event]: ((member_event @ Xa @ (set_event2 @ Zs2)) => (~ ((P @ Xa)))))))))))). % split_list_last_prop
thf(fact_133_in__set__conv__decomp, axiom,
    ((![X3 : agent, Xs : list_agent]: ((member_agent @ X3 @ (set_agent2 @ Xs)) = (?[Ys3 : list_agent]: (?[Zs3 : list_agent]: (Xs = (append_agent @ Ys3 @ (cons_agent @ X3 @ Zs3))))))))). % in_set_conv_decomp
thf(fact_134_in__set__conv__decomp, axiom,
    ((![X3 : list_event, Xs : list_list_event]: ((member_list_event @ X3 @ (set_list_event2 @ Xs)) = (?[Ys3 : list_list_event]: (?[Zs3 : list_list_event]: (Xs = (append_list_event @ Ys3 @ (cons_list_event @ X3 @ Zs3))))))))). % in_set_conv_decomp
thf(fact_135_in__set__conv__decomp, axiom,
    ((![X3 : msg, Xs : list_msg]: ((member_msg @ X3 @ (set_msg2 @ Xs)) = (?[Ys3 : list_msg]: (?[Zs3 : list_msg]: (Xs = (append_msg @ Ys3 @ (cons_msg @ X3 @ Zs3))))))))). % in_set_conv_decomp
thf(fact_136_in__set__conv__decomp, axiom,
    ((![X3 : event, Xs : list_event]: ((member_event @ X3 @ (set_event2 @ Xs)) = (?[Ys3 : list_event]: (?[Zs3 : list_event]: (Xs = (append_event @ Ys3 @ (cons_event @ X3 @ Zs3))))))))). % in_set_conv_decomp
thf(fact_137_append__Cons__eq__iff, axiom,
    ((![X3 : agent, Xs : list_agent, Ys : list_agent, Xs3 : list_agent, Ys5 : list_agent]: ((~ ((member_agent @ X3 @ (set_agent2 @ Xs)))) => ((~ ((member_agent @ X3 @ (set_agent2 @ Ys)))) => (((append_agent @ Xs @ (cons_agent @ X3 @ Ys)) = (append_agent @ Xs3 @ (cons_agent @ X3 @ Ys5))) = (((Xs = Xs3)) & ((Ys = Ys5))))))))). % append_Cons_eq_iff
thf(fact_138_append__Cons__eq__iff, axiom,
    ((![X3 : list_event, Xs : list_list_event, Ys : list_list_event, Xs3 : list_list_event, Ys5 : list_list_event]: ((~ ((member_list_event @ X3 @ (set_list_event2 @ Xs)))) => ((~ ((member_list_event @ X3 @ (set_list_event2 @ Ys)))) => (((append_list_event @ Xs @ (cons_list_event @ X3 @ Ys)) = (append_list_event @ Xs3 @ (cons_list_event @ X3 @ Ys5))) = (((Xs = Xs3)) & ((Ys = Ys5))))))))). % append_Cons_eq_iff
thf(fact_139_append__Cons__eq__iff, axiom,
    ((![X3 : msg, Xs : list_msg, Ys : list_msg, Xs3 : list_msg, Ys5 : list_msg]: ((~ ((member_msg @ X3 @ (set_msg2 @ Xs)))) => ((~ ((member_msg @ X3 @ (set_msg2 @ Ys)))) => (((append_msg @ Xs @ (cons_msg @ X3 @ Ys)) = (append_msg @ Xs3 @ (cons_msg @ X3 @ Ys5))) = (((Xs = Xs3)) & ((Ys = Ys5))))))))). % append_Cons_eq_iff
thf(fact_140_append__Cons__eq__iff, axiom,
    ((![X3 : event, Xs : list_event, Ys : list_event, Xs3 : list_event, Ys5 : list_event]: ((~ ((member_event @ X3 @ (set_event2 @ Xs)))) => ((~ ((member_event @ X3 @ (set_event2 @ Ys)))) => (((append_event @ Xs @ (cons_event @ X3 @ Ys)) = (append_event @ Xs3 @ (cons_event @ X3 @ Ys5))) = (((Xs = Xs3)) & ((Ys = Ys5))))))))). % append_Cons_eq_iff
thf(fact_141_split__list__propE, axiom,
    ((![Xs : list_event, P : event > $o]: ((?[X6 : event]: ((member_event @ X6 @ (set_event2 @ Xs)) & (P @ X6))) => (~ ((![Ys2 : list_event, X4 : event]: ((?[Zs2 : list_event]: (Xs = (append_event @ Ys2 @ (cons_event @ X4 @ Zs2)))) => (~ ((P @ X4))))))))))). % split_list_propE
thf(fact_142_split__list__first, axiom,
    ((![X3 : agent, Xs : list_agent]: ((member_agent @ X3 @ (set_agent2 @ Xs)) => (?[Ys2 : list_agent, Zs2 : list_agent]: ((Xs = (append_agent @ Ys2 @ (cons_agent @ X3 @ Zs2))) & (~ ((member_agent @ X3 @ (set_agent2 @ Ys2)))))))))). % split_list_first
thf(fact_143_split__list__first, axiom,
    ((![X3 : list_event, Xs : list_list_event]: ((member_list_event @ X3 @ (set_list_event2 @ Xs)) => (?[Ys2 : list_list_event, Zs2 : list_list_event]: ((Xs = (append_list_event @ Ys2 @ (cons_list_event @ X3 @ Zs2))) & (~ ((member_list_event @ X3 @ (set_list_event2 @ Ys2)))))))))). % split_list_first
thf(fact_144_split__list__first, axiom,
    ((![X3 : msg, Xs : list_msg]: ((member_msg @ X3 @ (set_msg2 @ Xs)) => (?[Ys2 : list_msg, Zs2 : list_msg]: ((Xs = (append_msg @ Ys2 @ (cons_msg @ X3 @ Zs2))) & (~ ((member_msg @ X3 @ (set_msg2 @ Ys2)))))))))). % split_list_first
thf(fact_145_split__list__first, axiom,
    ((![X3 : event, Xs : list_event]: ((member_event @ X3 @ (set_event2 @ Xs)) => (?[Ys2 : list_event, Zs2 : list_event]: ((Xs = (append_event @ Ys2 @ (cons_event @ X3 @ Zs2))) & (~ ((member_event @ X3 @ (set_event2 @ Ys2)))))))))). % split_list_first
thf(fact_146_split__list__prop, axiom,
    ((![Xs : list_event, P : event > $o]: ((?[X6 : event]: ((member_event @ X6 @ (set_event2 @ Xs)) & (P @ X6))) => (?[Ys2 : list_event, X4 : event]: ((?[Zs2 : list_event]: (Xs = (append_event @ Ys2 @ (cons_event @ X4 @ Zs2)))) & (P @ X4))))))). % split_list_prop
thf(fact_147_split__list__last, axiom,
    ((![X3 : agent, Xs : list_agent]: ((member_agent @ X3 @ (set_agent2 @ Xs)) => (?[Ys2 : list_agent, Zs2 : list_agent]: ((Xs = (append_agent @ Ys2 @ (cons_agent @ X3 @ Zs2))) & (~ ((member_agent @ X3 @ (set_agent2 @ Zs2)))))))))). % split_list_last
thf(fact_148_split__list__last, axiom,
    ((![X3 : list_event, Xs : list_list_event]: ((member_list_event @ X3 @ (set_list_event2 @ Xs)) => (?[Ys2 : list_list_event, Zs2 : list_list_event]: ((Xs = (append_list_event @ Ys2 @ (cons_list_event @ X3 @ Zs2))) & (~ ((member_list_event @ X3 @ (set_list_event2 @ Zs2)))))))))). % split_list_last
thf(fact_149_split__list__last, axiom,
    ((![X3 : msg, Xs : list_msg]: ((member_msg @ X3 @ (set_msg2 @ Xs)) => (?[Ys2 : list_msg, Zs2 : list_msg]: ((Xs = (append_msg @ Ys2 @ (cons_msg @ X3 @ Zs2))) & (~ ((member_msg @ X3 @ (set_msg2 @ Zs2)))))))))). % split_list_last
thf(fact_150_split__list__last, axiom,
    ((![X3 : event, Xs : list_event]: ((member_event @ X3 @ (set_event2 @ Xs)) => (?[Ys2 : list_event, Zs2 : list_event]: ((Xs = (append_event @ Ys2 @ (cons_event @ X3 @ Zs2))) & (~ ((member_event @ X3 @ (set_event2 @ Zs2)))))))))). % split_list_last
thf(fact_151_split__list, axiom,
    ((![X3 : agent, Xs : list_agent]: ((member_agent @ X3 @ (set_agent2 @ Xs)) => (?[Ys2 : list_agent, Zs2 : list_agent]: (Xs = (append_agent @ Ys2 @ (cons_agent @ X3 @ Zs2)))))))). % split_list
thf(fact_152_split__list, axiom,
    ((![X3 : list_event, Xs : list_list_event]: ((member_list_event @ X3 @ (set_list_event2 @ Xs)) => (?[Ys2 : list_list_event, Zs2 : list_list_event]: (Xs = (append_list_event @ Ys2 @ (cons_list_event @ X3 @ Zs2)))))))). % split_list
thf(fact_153_split__list, axiom,
    ((![X3 : msg, Xs : list_msg]: ((member_msg @ X3 @ (set_msg2 @ Xs)) => (?[Ys2 : list_msg, Zs2 : list_msg]: (Xs = (append_msg @ Ys2 @ (cons_msg @ X3 @ Zs2)))))))). % split_list
thf(fact_154_split__list, axiom,
    ((![X3 : event, Xs : list_event]: ((member_event @ X3 @ (set_event2 @ Xs)) => (?[Ys2 : list_event, Zs2 : list_event]: (Xs = (append_event @ Ys2 @ (cons_event @ X3 @ Zs2)))))))). % split_list
thf(fact_155_takeWhile_Osimps_I2_J, axiom,
    ((![P : event > $o, X3 : event, Xs : list_event]: (((P @ X3) => ((takeWhile_event @ P @ (cons_event @ X3 @ Xs)) = (cons_event @ X3 @ (takeWhile_event @ P @ Xs)))) & ((~ ((P @ X3))) => ((takeWhile_event @ P @ (cons_event @ X3 @ Xs)) = nil_event)))))). % takeWhile.simps(2)
thf(fact_156_takeWhile__tail, axiom,
    ((![P : event > $o, X3 : event, Xs : list_event, L : list_event]: ((~ ((P @ X3))) => ((takeWhile_event @ P @ (append_event @ Xs @ (cons_event @ X3 @ L))) = (takeWhile_event @ P @ Xs)))))). % takeWhile_tail
thf(fact_157_analz__impI, axiom,
    ((![Y4 : msg, Evs : list_event, Q : $o]: (((~ ((member_msg @ Y4 @ (analz @ (knows @ spy @ Evs))))) => Q) => ((~ ((member_msg @ Y4 @ (analz @ (knows @ spy @ Evs))))) => Q))))). % analz_impI
thf(fact_158_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_159_rev_Osimps_I2_J, axiom,
    ((![X3 : event, Xs : list_event]: ((rev_event @ (cons_event @ X3 @ Xs)) = (append_event @ (rev_event @ Xs) @ (cons_event @ X3 @ nil_event)))))). % rev.simps(2)
thf(fact_160_analz__shrK__Decrypt, axiom,
    ((![A : agent, X : msg, H : set_msg]: ((member_msg @ (crypt @ (shrK @ A) @ X) @ (analz @ H)) => ((member_msg @ (key @ (shrK @ A)) @ (analz @ H)) => (member_msg @ X @ (analz @ H))))))). % analz_shrK_Decrypt
thf(fact_161_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_162_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_163_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_164_parts__analz, axiom,
    ((![H : set_msg]: ((parts @ (analz @ H)) = (parts @ H))))). % parts_analz
thf(fact_165_analz__parts, axiom,
    ((![H : set_msg]: ((analz @ (parts @ H)) = (parts @ H))))). % analz_parts
thf(fact_166_secrecy__lemma, axiom,
    ((![A : agent, NA : msg, B : agent, K : nat, Evs : list_event]: ((member_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ NA @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ (crypt @ (shrK @ B) @ (mPair @ (key @ K) @ (agent2 @ A)))))))) @ (set_event2 @ Evs)) => ((~ ((member_agent @ A @ bad))) => ((~ ((member_agent @ B @ bad))) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => ((![NB2 : msg]: (~ ((member_event @ (notes @ spy @ (mPair @ NA @ (mPair @ NB2 @ (key @ K)))) @ (set_event2 @ Evs))))) => (~ ((member_msg @ (key @ K) @ (analz @ (knows @ spy @ Evs))))))))))))). % secrecy_lemma
thf(fact_167_B__trusts__NS5, axiom,
    ((![K : nat, NB : nat, Evs : list_event, B : agent, A : agent]: ((member_msg @ (crypt @ K @ (mPair @ (nonce @ NB) @ (nonce @ NB))) @ (parts @ (knows @ spy @ Evs))) => ((member_msg @ (crypt @ (shrK @ B) @ (mPair @ (key @ K) @ (agent2 @ A))) @ (parts @ (knows @ spy @ Evs))) => ((![NA2 : msg, NB2 : msg]: (~ ((member_event @ (notes @ spy @ (mPair @ NA2 @ (mPair @ NB2 @ (key @ K)))) @ (set_event2 @ Evs))))) => ((~ ((member_agent @ A @ bad))) => ((~ ((member_agent @ B @ bad))) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => (member_event @ (says @ A @ B @ (crypt @ K @ (mPair @ (nonce @ NB) @ (nonce @ NB)))) @ (set_event2 @ Evs))))))))))). % B_trusts_NS5
thf(fact_168_A__trusts__NS4, axiom,
    ((![K : nat, NB : nat, Evs : list_event, A : agent, NA : msg, B : agent, X : msg]: ((member_msg @ (crypt @ K @ (nonce @ NB)) @ (parts @ (knows @ spy @ Evs))) => ((member_msg @ (crypt @ (shrK @ A) @ (mPair @ NA @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X)))) @ (parts @ (knows @ spy @ Evs))) => ((![NB2 : msg]: (~ ((member_event @ (notes @ spy @ (mPair @ NA @ (mPair @ NB2 @ (key @ K)))) @ (set_event2 @ Evs))))) => ((~ ((member_agent @ A @ bad))) => ((~ ((member_agent @ B @ bad))) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => (member_event @ (says @ B @ A @ (crypt @ K @ (nonce @ NB))) @ (set_event2 @ Evs))))))))))). % A_trusts_NS4
thf(fact_169_ns__shared_OOops, axiom,
    ((![Evso : list_event, B : agent, A : agent, K : nat, NB : nat, NA : nat, X : msg]: ((member_list_event @ Evso @ nS_Sha1061662329shared) => ((member_event @ (says @ B @ A @ (crypt @ K @ (nonce @ NB))) @ (set_event2 @ Evso)) => ((member_event @ (says @ server @ A @ (crypt @ (shrK @ A) @ (mPair @ (nonce @ NA) @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X))))) @ (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_170_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_171_analz__idem, axiom,
    ((![H : set_msg]: ((analz @ (analz @ H)) = (analz @ H))))). % analz_idem
thf(fact_172_msg_Oinject_I4_J, axiom,
    ((![X42 : nat, Y42 : nat]: (((key @ X42) = (key @ Y42)) = (X42 = Y42))))). % msg.inject(4)
thf(fact_173_parts__idem, axiom,
    ((![H : set_msg]: ((parts @ (parts @ H)) = (parts @ H))))). % parts_idem
thf(fact_174_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_175_msg_Oinject_I3_J, axiom,
    ((![X32 : nat, Y32 : nat]: (((nonce @ X32) = (nonce @ Y32)) = (X32 = Y32))))). % msg.inject(3)
thf(fact_176_msg_Oinject_I1_J, axiom,
    ((![X14 : agent, Y1 : agent]: (((agent2 @ X14) = (agent2 @ Y1)) = (X14 = Y1))))). % msg.inject(1)
thf(fact_177_event_Oinject_I3_J, axiom,
    ((![X31 : agent, X322 : msg, Y31 : agent, Y322 : msg]: (((notes @ X31 @ X322) = (notes @ Y31 @ Y322)) = (((X31 = Y31)) & ((X322 = Y322))))))). % event.inject(3)
thf(fact_178_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_179_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_180_analz_OInj, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ H) => (member_msg @ X @ (analz @ H)))))). % analz.Inj
thf(fact_181_analz__analzD, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (analz @ (analz @ H))) => (member_msg @ X @ (analz @ H)))))). % analz_analzD
thf(fact_182_parts_OInj, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ H) => (member_msg @ X @ (parts @ H)))))). % parts.Inj
thf(fact_183_parts__partsD, axiom,
    ((![X : msg, H : set_msg]: ((member_msg @ X @ (parts @ (parts @ H))) => (member_msg @ X @ (parts @ H)))))). % parts_partsD
thf(fact_184_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_185_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_186_analz_OFst, axiom,
    ((![X : msg, Y4 : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y4) @ (analz @ H)) => (member_msg @ X @ (analz @ H)))))). % analz.Fst
thf(fact_187_analz_OSnd, axiom,
    ((![X : msg, Y4 : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y4) @ (analz @ H)) => (member_msg @ Y4 @ (analz @ H)))))). % analz.Snd
thf(fact_188_MPair__analz, axiom,
    ((![X : msg, Y4 : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y4) @ (analz @ H)) => (~ (((member_msg @ X @ (analz @ H)) => (~ ((member_msg @ Y4 @ (analz @ H))))))))))). % MPair_analz
thf(fact_189_msg_Odistinct_I33_J, axiom,
    ((![X42 : nat, X61 : msg, X62 : msg]: (~ (((key @ X42) = (mPair @ X61 @ X62))))))). % msg.distinct(33)
thf(fact_190_parts_OFst, axiom,
    ((![X : msg, Y4 : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y4) @ (parts @ H)) => (member_msg @ X @ (parts @ H)))))). % parts.Fst
thf(fact_191_parts_OSnd, axiom,
    ((![X : msg, Y4 : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y4) @ (parts @ H)) => (member_msg @ Y4 @ (parts @ H)))))). % parts.Snd
thf(fact_192_MPair__parts, axiom,
    ((![X : msg, Y4 : msg, H : set_msg]: ((member_msg @ (mPair @ X @ Y4) @ (parts @ H)) => (~ (((member_msg @ X @ (parts @ H)) => (~ ((member_msg @ Y4 @ (parts @ H))))))))))). % MPair_parts
thf(fact_193_analz__into__parts, axiom,
    ((![C : msg, H : set_msg]: ((member_msg @ C @ (analz @ H)) => (member_msg @ C @ (parts @ H)))))). % analz_into_parts

% Conjectures (9)
thf(conj_0, hypothesis,
    ((~ ((member_agent @ a @ bad))))).
thf(conj_1, hypothesis,
    ((~ ((member_agent @ b @ bad))))).
thf(conj_2, hypothesis,
    ((member_list_event @ evs3 @ nS_Sha1061662329shared))).
thf(conj_3, hypothesis,
    ((~ ((aa = server))))).
thf(conj_4, hypothesis,
    ((member_event @ (says @ s @ aa @ (crypt @ (shrK @ aa) @ (mPair @ (nonce @ na) @ (mPair @ (agent2 @ ba) @ (mPair @ (key @ ka) @ x))))) @ (set_event2 @ evs3)))).
thf(conj_5, hypothesis,
    ((member_event @ (says @ aa @ server @ (mPair @ (agent2 @ aa) @ (mPair @ (agent2 @ ba) @ (nonce @ na)))) @ (set_event2 @ evs3)))).
thf(conj_6, hypothesis,
    ((~ ((member_msg @ (key @ k) @ (analz @ (knows @ spy @ evs3))))))).
thf(conj_7, hypothesis,
    (((member_event @ (says @ b @ a @ (crypt @ k @ (nonce @ nb))) @ (set_event2 @ evs3)) => (~ ((member_msg @ (crypt @ k @ (nonce @ nb)) @ (parts @ (knows @ spy @ (takeWhile_event @ (^[Z : event]: (~ ((Z = (says @ b @ a @ (crypt @ k @ (nonce @ nb))))))) @ (rev_event @ evs3)))))))))).
thf(conj_8, conjecture,
    ((((~ ((b = aa))) | ((~ ((a = ba))) | (~ (((crypt @ k @ (nonce @ nb)) = x))))) | (~ ((member_msg @ x @ (parts @ (knows @ spy @ (takeWhile_event @ (^[Z : event]: (~ ((Z = (says @ aa @ ba @ x))))) @ (append_event @ (rev_event @ evs3) @ (cons_event @ (says @ aa @ ba @ x) @ nil_event))))))))))).
