% 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_388__5232018_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:24:33.427

% Could-be-implicit typings (6)
thf(ty_n_t__List__Olist_It__List__Olist_It__Event__Oevent_J_J, type,
    list_list_event : $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__Message__Oagent, type,
    agent : $tType).
thf(ty_n_t__Message__Omsg, type,
    msg : $tType).
thf(ty_n_t__Event__Oevent, type,
    event : $tType).

% Explicit typings (24)
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_List_Oappend_001t__Event__Oevent, type,
    append_event : list_event > list_event > list_event).
thf(sy_c_List_Obind_001t__Event__Oevent_001t__Event__Oevent, type,
    bind_event_event : list_event > (event > list_event) > list_event).
thf(sy_c_List_Obutlast_001t__Event__Oevent, type,
    butlast_event : list_event > list_event).
thf(sy_c_List_Oinsert_001t__Event__Oevent, type,
    insert_event : event > list_event > list_event).
thf(sy_c_List_Olast_001t__Event__Oevent, type,
    last_event : list_event > event).
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_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_Omaps_001t__Event__Oevent_001t__Event__Oevent, type,
    maps_event_event : (event > list_event) > list_event > list_event).
thf(sy_c_List_Oproduct__lists_001t__Event__Oevent, type,
    product_lists_event : list_list_event > list_list_event).
thf(sy_c_List_Orotate1_001t__Event__Oevent, type,
    rotate1_event : list_event > list_event).
thf(sy_c_Message_Oagent_OSpy, type,
    spy : agent).
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_Set_OCollect_001t__Message__Omsg, type,
    collect_msg : (msg > $o) > set_msg).
thf(sy_c_Set_Oinsert_001t__Message__Omsg, type,
    insert_msg : msg > set_msg > set_msg).
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_X, type,
    x : msg).

% Relevant facts (133)
thf(fact_0_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_1_append1__eq__conv, axiom,
    ((![Xs : list_event, X2 : event, Ys : list_event, Y : event]: (((append_event @ Xs @ (cons_event @ X2 @ nil_event)) = (append_event @ Ys @ (cons_event @ Y @ nil_event))) = (((Xs = Ys)) & ((X2 = Y))))))). % append1_eq_conv
thf(fact_2_append__Nil2, axiom,
    ((![Xs : list_event]: ((append_event @ Xs @ nil_event) = Xs)))). % append_Nil2
thf(fact_3_append__self__conv, axiom,
    ((![Xs : list_event, Ys : list_event]: (((append_event @ Xs @ Ys) = Xs) = (Ys = nil_event))))). % append_self_conv
thf(fact_4_self__append__conv, axiom,
    ((![Xs : list_event, Ys : list_event]: ((Xs = (append_event @ Xs @ Ys)) = (Ys = nil_event))))). % self_append_conv
thf(fact_5_append__self__conv2, axiom,
    ((![Xs : list_event, Ys : list_event]: (((append_event @ Xs @ Ys) = Ys) = (Xs = nil_event))))). % append_self_conv2
thf(fact_6_self__append__conv2, axiom,
    ((![Ys : list_event, Xs : list_event]: ((Ys = (append_event @ Xs @ Ys)) = (Xs = nil_event))))). % self_append_conv2
thf(fact_7_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_8_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_9_append_Oright__neutral, axiom,
    ((![A2 : list_event]: ((append_event @ A2 @ nil_event) = A2)))). % append.right_neutral
thf(fact_10_rev__induct, axiom,
    ((![P : list_event > $o, Xs : list_event]: ((P @ nil_event) => ((![X3 : event, Xs2 : list_event]: ((P @ Xs2) => (P @ (append_event @ Xs2 @ (cons_event @ X3 @ nil_event))))) => (P @ Xs)))))). % rev_induct
thf(fact_11_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_12_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_13_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_14_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_15_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_16_append_Oassoc, axiom,
    ((![A2 : list_event, B2 : list_event, C : list_event]: ((append_event @ (append_event @ A2 @ B2) @ C) = (append_event @ A2 @ (append_event @ B2 @ C)))))). % append.assoc
thf(fact_17_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_18_not__Cons__self2, axiom,
    ((![X2 : event, Xs : list_event]: (~ (((cons_event @ X2 @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_19_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_20_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_21_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, A3 : event, As : list_event, Bs : list_event]: ((P @ F @ As @ (cons_event @ (F @ A3) @ Bs)) => (P @ F @ (cons_event @ A3 @ As) @ Bs))) => (P @ A0 @ A1 @ A22)))))). % map_tailrec_rev.induct
thf(fact_22_list__nonempty__induct, axiom,
    ((![Xs : list_event, P : list_event > $o]: ((~ ((Xs = nil_event))) => ((![X3 : event]: (P @ (cons_event @ X3 @ nil_event))) => ((![X3 : event, Xs2 : list_event]: ((~ ((Xs2 = nil_event))) => ((P @ Xs2) => (P @ (cons_event @ X3 @ Xs2))))) => (P @ Xs))))))). % list_nonempty_induct
thf(fact_23_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, X3 : event]: (P @ P2 @ (cons_event @ X3 @ nil_event))) => ((![P2 : event > event > $o, X3 : event, Y2 : event, Xs2 : list_event]: ((P @ P2 @ (cons_event @ Y2 @ Xs2)) => (P @ P2 @ (cons_event @ X3 @ (cons_event @ Y2 @ Xs2))))) => (P @ A0 @ A1))))))). % successively.induct
thf(fact_24_remdups__adj_Oinduct, axiom,
    ((![P : list_event > $o, A0 : list_event]: ((P @ nil_event) => ((![X3 : event]: (P @ (cons_event @ X3 @ nil_event))) => ((![X3 : event, Y2 : event, Xs2 : list_event]: (((X3 = Y2) => (P @ (cons_event @ X3 @ Xs2))) => (((~ ((X3 = Y2))) => (P @ (cons_event @ Y2 @ Xs2))) => (P @ (cons_event @ X3 @ (cons_event @ Y2 @ Xs2)))))) => (P @ A0))))))). % remdups_adj.induct
thf(fact_25_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, X3 : event, Ys2 : list_event]: ((P @ P2 @ Ys2) => (P @ P2 @ (cons_event @ X3 @ Ys2)))) => (P @ A0 @ A1)))))). % sorted_wrt.induct
thf(fact_26_remdups__adj_Ocases, axiom,
    ((![X2 : list_event]: ((~ ((X2 = nil_event))) => ((![X3 : event]: (~ ((X2 = (cons_event @ X3 @ nil_event))))) => (~ ((![X3 : event, Y2 : event, Xs2 : list_event]: (~ ((X2 = (cons_event @ X3 @ (cons_event @ Y2 @ Xs2))))))))))))). % remdups_adj.cases
thf(fact_27_transpose_Ocases, axiom,
    ((![X2 : list_list_event]: ((~ ((X2 = nil_list_event))) => ((![Xss : list_list_event]: (~ ((X2 = (cons_list_event @ nil_event @ Xss))))) => (~ ((![X3 : event, Xs2 : list_event, Xss : list_list_event]: (~ ((X2 = (cons_list_event @ (cons_event @ X3 @ Xs2) @ Xss)))))))))))). % transpose.cases
thf(fact_28_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)) => ((![X3 : event, Xs2 : list_event, Y2 : event, Ys2 : list_event]: ((P @ Xs2 @ (cons_event @ Y2 @ Ys2)) => ((P @ (cons_event @ X3 @ Xs2) @ Ys2) => (P @ (cons_event @ X3 @ Xs2) @ (cons_event @ Y2 @ Ys2))))) => (P @ A0 @ A1))))))). % shuffles.induct
thf(fact_29_induct__list012, axiom,
    ((![P : list_event > $o, Xs : list_event]: ((P @ nil_event) => ((![X3 : event]: (P @ (cons_event @ X3 @ nil_event))) => ((![X3 : event, Y2 : event, Zs2 : list_event]: ((P @ Zs2) => ((P @ (cons_event @ Y2 @ Zs2)) => (P @ (cons_event @ X3 @ (cons_event @ Y2 @ Zs2)))))) => (P @ Xs))))))). % induct_list012
thf(fact_30_splice_Oinduct, axiom,
    ((![P : list_event > list_event > $o, A0 : list_event, A1 : list_event]: ((![X_1 : list_event]: (P @ nil_event @ X_1)) => ((![X3 : event, Xs2 : list_event, Ys2 : list_event]: ((P @ Ys2 @ Xs2) => (P @ (cons_event @ X3 @ Xs2) @ Ys2))) => (P @ A0 @ A1)))))). % splice.induct
thf(fact_31_list__induct2_H, axiom,
    ((![P : list_event > list_event > $o, Xs : list_event, Ys : list_event]: ((P @ nil_event @ nil_event) => ((![X3 : event, Xs2 : list_event]: (P @ (cons_event @ X3 @ Xs2) @ nil_event)) => ((![Y2 : event, Ys2 : list_event]: (P @ nil_event @ (cons_event @ Y2 @ Ys2))) => ((![X3 : event, Xs2 : list_event, Y2 : event, Ys2 : list_event]: ((P @ Xs2 @ Ys2) => (P @ (cons_event @ X3 @ Xs2) @ (cons_event @ Y2 @ Ys2)))) => (P @ Xs @ Ys)))))))). % list_induct2'
thf(fact_32_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_33_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_34_list_Oexhaust, axiom,
    ((![Y : list_event]: ((~ ((Y = nil_event))) => (~ ((![X212 : event, X222 : list_event]: (~ ((Y = (cons_event @ X212 @ X222))))))))))). % list.exhaust
thf(fact_35_list_OdiscI, axiom,
    ((![List : list_event, X21 : event, X22 : list_event]: ((List = (cons_event @ X21 @ X22)) => (~ ((List = nil_event))))))). % list.discI
thf(fact_36_list_Odistinct_I1_J, axiom,
    ((![X21 : event, X22 : list_event]: (~ ((nil_event = (cons_event @ X21 @ X22))))))). % list.distinct(1)
thf(fact_37_append__Cons, axiom,
    ((![X2 : event, Xs : list_event, Ys : list_event]: ((append_event @ (cons_event @ X2 @ Xs) @ Ys) = (cons_event @ X2 @ (append_event @ Xs @ Ys)))))). % append_Cons
thf(fact_38_Cons__eq__appendI, axiom,
    ((![X2 : event, Xs1 : list_event, Ys : list_event, Xs : list_event, Zs : list_event]: (((cons_event @ X2 @ Xs1) = Ys) => ((Xs = (append_event @ Xs1 @ Zs)) => ((cons_event @ X2 @ Xs) = (append_event @ Ys @ Zs))))))). % Cons_eq_appendI
thf(fact_39_append_Oleft__neutral, axiom,
    ((![A2 : list_event]: ((append_event @ nil_event @ A2) = A2)))). % append.left_neutral
thf(fact_40_append__Nil, axiom,
    ((![Ys : list_event]: ((append_event @ nil_event @ Ys) = Ys)))). % append_Nil
thf(fact_41_eq__Nil__appendI, axiom,
    ((![Xs : list_event, Ys : list_event]: ((Xs = Ys) => (Xs = (append_event @ nil_event @ Ys)))))). % eq_Nil_appendI
thf(fact_42_rev__nonempty__induct, axiom,
    ((![Xs : list_event, P : list_event > $o]: ((~ ((Xs = nil_event))) => ((![X3 : event]: (P @ (cons_event @ X3 @ nil_event))) => ((![X3 : event, Xs2 : list_event]: ((~ ((Xs2 = nil_event))) => ((P @ Xs2) => (P @ (append_event @ Xs2 @ (cons_event @ X3 @ nil_event)))))) => (P @ Xs))))))). % rev_nonempty_induct
thf(fact_43_append__eq__Cons__conv, axiom,
    ((![Ys : list_event, Zs : list_event, X2 : event, Xs : list_event]: (((append_event @ Ys @ Zs) = (cons_event @ X2 @ Xs)) = (((((Ys = nil_event)) & ((Zs = (cons_event @ X2 @ Xs))))) | ((?[Ys4 : list_event]: (((Ys = (cons_event @ X2 @ Ys4))) & (((append_event @ Ys4 @ Zs) = Xs)))))))))). % append_eq_Cons_conv
thf(fact_44_Cons__eq__append__conv, axiom,
    ((![X2 : event, Xs : list_event, Ys : list_event, Zs : list_event]: (((cons_event @ X2 @ Xs) = (append_event @ Ys @ Zs)) = (((((Ys = nil_event)) & (((cons_event @ X2 @ Xs) = Zs)))) | ((?[Ys4 : list_event]: ((((cons_event @ X2 @ Ys4) = Ys)) & ((Xs = (append_event @ Ys4 @ Zs))))))))))). % Cons_eq_append_conv
thf(fact_45_insert__absorb2, axiom,
    ((![X2 : msg, A : set_msg]: ((insert_msg @ X2 @ (insert_msg @ X2 @ A)) = (insert_msg @ X2 @ A))))). % insert_absorb2
thf(fact_46_insert__iff, axiom,
    ((![A2 : msg, B2 : msg, A : set_msg]: ((member_msg @ A2 @ (insert_msg @ B2 @ A)) = (((A2 = B2)) | ((member_msg @ A2 @ A))))))). % insert_iff
thf(fact_47_insertCI, axiom,
    ((![A2 : msg, B : set_msg, B2 : msg]: (((~ ((member_msg @ A2 @ B))) => (A2 = B2)) => (member_msg @ A2 @ (insert_msg @ B2 @ B)))))). % insertCI
thf(fact_48_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_49_bind__simps_I2_J, axiom,
    ((![X2 : event, Xs : list_event, F2 : event > list_event]: ((bind_event_event @ (cons_event @ X2 @ Xs) @ F2) = (append_event @ (F2 @ X2) @ (bind_event_event @ Xs @ F2)))))). % bind_simps(2)
thf(fact_50_maps__simps_I1_J, axiom,
    ((![F2 : event > list_event, X2 : event, Xs : list_event]: ((maps_event_event @ F2 @ (cons_event @ X2 @ Xs)) = (append_event @ (F2 @ X2) @ (maps_event_event @ F2 @ Xs)))))). % maps_simps(1)
thf(fact_51_insert__Nil, axiom,
    ((![X2 : event]: ((insert_event @ X2 @ nil_event) = (cons_event @ X2 @ nil_event))))). % insert_Nil
thf(fact_52_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_53_rotate1_Osimps_I2_J, axiom,
    ((![X2 : event, Xs : list_event]: ((rotate1_event @ (cons_event @ X2 @ Xs)) = (append_event @ Xs @ (cons_event @ X2 @ nil_event)))))). % rotate1.simps(2)
thf(fact_54_butlast__snoc, axiom,
    ((![Xs : list_event, X2 : event]: ((butlast_event @ (append_event @ Xs @ (cons_event @ X2 @ nil_event))) = Xs)))). % butlast_snoc
thf(fact_55_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_56_subsetI, axiom,
    ((![A : set_msg, B : set_msg]: ((![X3 : msg]: ((member_msg @ X3 @ A) => (member_msg @ X3 @ B))) => (ord_less_eq_set_msg @ A @ B))))). % subsetI
thf(fact_57_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_58_insert__subset, axiom,
    ((![X2 : msg, A : set_msg, B : set_msg]: ((ord_less_eq_set_msg @ (insert_msg @ X2 @ A) @ B) = (((member_msg @ X2 @ B)) & ((ord_less_eq_set_msg @ A @ B))))))). % insert_subset
thf(fact_59_rotate1__is__Nil__conv, axiom,
    ((![Xs : list_event]: (((rotate1_event @ Xs) = nil_event) = (Xs = nil_event))))). % rotate1_is_Nil_conv
thf(fact_60_bind__simps_I1_J, axiom,
    ((![F2 : event > list_event]: ((bind_event_event @ nil_event @ F2) = nil_event)))). % bind_simps(1)
thf(fact_61_Collect__mono__iff, axiom,
    ((![P : msg > $o, Q : msg > $o]: ((ord_less_eq_set_msg @ (collect_msg @ P) @ (collect_msg @ Q)) = (![X4 : msg]: (((P @ X4)) => ((Q @ X4)))))))). % Collect_mono_iff
thf(fact_62_set__eq__subset, axiom,
    (((^[Y4 : set_msg]: (^[Z : set_msg]: (Y4 = Z))) = (^[A4 : set_msg]: (^[B3 : set_msg]: (((ord_less_eq_set_msg @ A4 @ B3)) & ((ord_less_eq_set_msg @ B3 @ A4)))))))). % set_eq_subset
thf(fact_63_subset__trans, axiom,
    ((![A : set_msg, B : set_msg, C2 : set_msg]: ((ord_less_eq_set_msg @ A @ B) => ((ord_less_eq_set_msg @ B @ C2) => (ord_less_eq_set_msg @ A @ C2)))))). % subset_trans
thf(fact_64_Collect__mono, axiom,
    ((![P : msg > $o, Q : msg > $o]: ((![X3 : msg]: ((P @ X3) => (Q @ X3))) => (ord_less_eq_set_msg @ (collect_msg @ P) @ (collect_msg @ Q)))))). % Collect_mono
thf(fact_65_subset__refl, axiom,
    ((![A : set_msg]: (ord_less_eq_set_msg @ A @ A)))). % subset_refl
thf(fact_66_subset__iff, axiom,
    ((ord_less_eq_set_msg = (^[A4 : set_msg]: (^[B3 : set_msg]: (![T : msg]: (((member_msg @ T @ A4)) => ((member_msg @ T @ B3))))))))). % subset_iff
thf(fact_67_equalityD2, axiom,
    ((![A : set_msg, B : set_msg]: ((A = B) => (ord_less_eq_set_msg @ B @ A))))). % equalityD2
thf(fact_68_equalityD1, axiom,
    ((![A : set_msg, B : set_msg]: ((A = B) => (ord_less_eq_set_msg @ A @ B))))). % equalityD1
thf(fact_69_subset__eq, axiom,
    ((ord_less_eq_set_msg = (^[A4 : set_msg]: (^[B3 : set_msg]: (![X4 : msg]: (((member_msg @ X4 @ A4)) => ((member_msg @ X4 @ B3))))))))). % subset_eq
thf(fact_70_equalityE, axiom,
    ((![A : set_msg, B : set_msg]: ((A = B) => (~ (((ord_less_eq_set_msg @ A @ B) => (~ ((ord_less_eq_set_msg @ B @ A)))))))))). % equalityE
thf(fact_71_subsetD, axiom,
    ((![A : set_msg, B : set_msg, C : msg]: ((ord_less_eq_set_msg @ A @ B) => ((member_msg @ C @ A) => (member_msg @ C @ B)))))). % subsetD
thf(fact_72_in__mono, axiom,
    ((![A : set_msg, B : set_msg, X2 : msg]: ((ord_less_eq_set_msg @ A @ B) => ((member_msg @ X2 @ A) => (member_msg @ X2 @ B)))))). % in_mono
thf(fact_73_insert__mono, axiom,
    ((![C2 : set_msg, D : set_msg, A2 : msg]: ((ord_less_eq_set_msg @ C2 @ D) => (ord_less_eq_set_msg @ (insert_msg @ A2 @ C2) @ (insert_msg @ A2 @ D)))))). % insert_mono
thf(fact_74_subset__insert, axiom,
    ((![X2 : msg, A : set_msg, B : set_msg]: ((~ ((member_msg @ X2 @ A))) => ((ord_less_eq_set_msg @ A @ (insert_msg @ X2 @ B)) = (ord_less_eq_set_msg @ A @ B)))))). % subset_insert
thf(fact_75_subset__insertI, axiom,
    ((![B : set_msg, A2 : msg]: (ord_less_eq_set_msg @ B @ (insert_msg @ A2 @ B))))). % subset_insertI
thf(fact_76_subset__insertI2, axiom,
    ((![A : set_msg, B : set_msg, B2 : msg]: ((ord_less_eq_set_msg @ A @ B) => (ord_less_eq_set_msg @ A @ (insert_msg @ B2 @ B)))))). % subset_insertI2
thf(fact_77_butlast_Osimps_I1_J, axiom,
    (((butlast_event @ nil_event) = nil_event))). % butlast.simps(1)
thf(fact_78_knows__subset__knows__Gets, axiom,
    ((![A : agent, Evs : list_event, A5 : agent, X : msg]: (ord_less_eq_set_msg @ (knows @ A @ Evs) @ (knows @ A @ (cons_event @ (gets @ A5 @ X) @ Evs)))))). % knows_subset_knows_Gets
thf(fact_79_rotate1_Osimps_I1_J, axiom,
    (((rotate1_event @ nil_event) = nil_event))). % rotate1.simps(1)
thf(fact_80_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_81_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_82_butlast_Osimps_I2_J, axiom,
    ((![Xs : list_event, X2 : event]: (((Xs = nil_event) => ((butlast_event @ (cons_event @ X2 @ Xs)) = nil_event)) & ((~ ((Xs = nil_event))) => ((butlast_event @ (cons_event @ X2 @ Xs)) = (cons_event @ X2 @ (butlast_event @ Xs)))))))). % butlast.simps(2)
thf(fact_83_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_84_butlast__append, axiom,
    ((![Ys : list_event, Xs : list_event]: (((Ys = nil_event) => ((butlast_event @ (append_event @ Xs @ Ys)) = (butlast_event @ Xs))) & ((~ ((Ys = nil_event))) => ((butlast_event @ (append_event @ Xs @ Ys)) = (append_event @ Xs @ (butlast_event @ Ys)))))))). % butlast_append
thf(fact_85_maps__simps_I2_J, axiom,
    ((![F2 : event > list_event]: ((maps_event_event @ F2 @ nil_event) = nil_event)))). % maps_simps(2)
thf(fact_86_insertE, axiom,
    ((![A2 : msg, B2 : msg, A : set_msg]: ((member_msg @ A2 @ (insert_msg @ B2 @ A)) => ((~ ((A2 = B2))) => (member_msg @ A2 @ A)))))). % insertE
thf(fact_87_insertI1, axiom,
    ((![A2 : msg, B : set_msg]: (member_msg @ A2 @ (insert_msg @ A2 @ B))))). % insertI1
thf(fact_88_insertI2, axiom,
    ((![A2 : msg, B : set_msg, B2 : msg]: ((member_msg @ A2 @ B) => (member_msg @ A2 @ (insert_msg @ B2 @ B)))))). % insertI2
thf(fact_89_Set_Oset__insert, axiom,
    ((![X2 : msg, A : set_msg]: ((member_msg @ X2 @ A) => (~ ((![B4 : set_msg]: ((A = (insert_msg @ X2 @ B4)) => (member_msg @ X2 @ B4))))))))). % Set.set_insert
thf(fact_90_insert__ident, axiom,
    ((![X2 : msg, A : set_msg, B : set_msg]: ((~ ((member_msg @ X2 @ A))) => ((~ ((member_msg @ X2 @ B))) => (((insert_msg @ X2 @ A) = (insert_msg @ X2 @ B)) = (A = B))))))). % insert_ident
thf(fact_91_insert__absorb, axiom,
    ((![A2 : msg, A : set_msg]: ((member_msg @ A2 @ A) => ((insert_msg @ A2 @ A) = A))))). % insert_absorb
thf(fact_92_insert__eq__iff, axiom,
    ((![A2 : msg, A : set_msg, B2 : msg, B : set_msg]: ((~ ((member_msg @ A2 @ A))) => ((~ ((member_msg @ B2 @ B))) => (((insert_msg @ A2 @ A) = (insert_msg @ B2 @ B)) = (((((A2 = B2)) => ((A = B)))) & ((((~ ((A2 = B2)))) => ((?[C3 : set_msg]: (((A = (insert_msg @ B2 @ C3))) & ((((~ ((member_msg @ B2 @ C3)))) & ((((B = (insert_msg @ A2 @ C3))) & ((~ ((member_msg @ A2 @ C3)))))))))))))))))))). % insert_eq_iff
thf(fact_93_insert__commute, axiom,
    ((![X2 : msg, Y : msg, A : set_msg]: ((insert_msg @ X2 @ (insert_msg @ Y @ A)) = (insert_msg @ Y @ (insert_msg @ X2 @ A)))))). % insert_commute
thf(fact_94_mk__disjoint__insert, axiom,
    ((![A2 : msg, A : set_msg]: ((member_msg @ A2 @ A) => (?[B4 : set_msg]: ((A = (insert_msg @ A2 @ B4)) & (~ ((member_msg @ A2 @ B4))))))))). % mk_disjoint_insert
thf(fact_95_knows__subset__knows__Says, axiom,
    ((![A : agent, Evs : list_event, A5 : agent, B : agent, X : msg]: (ord_less_eq_set_msg @ (knows @ A @ Evs) @ (knows @ A @ (cons_event @ (says @ A5 @ B @ X) @ Evs)))))). % knows_subset_knows_Says
thf(fact_96_order__refl, axiom,
    ((![X2 : set_msg]: (ord_less_eq_set_msg @ X2 @ X2)))). % order_refl
thf(fact_97_insert__subsetI, axiom,
    ((![X2 : msg, A : set_msg, X : set_msg]: ((member_msg @ X2 @ A) => ((ord_less_eq_set_msg @ X @ A) => (ord_less_eq_set_msg @ (insert_msg @ X2 @ X) @ A)))))). % insert_subsetI
thf(fact_98_product__lists_Osimps_I1_J, axiom,
    (((product_lists_event @ nil_list_event) = (cons_list_event @ nil_event @ nil_list_event)))). % product_lists.simps(1)
thf(fact_99_append__butlast__last__id, axiom,
    ((![Xs : list_event]: ((~ ((Xs = nil_event))) => ((append_event @ (butlast_event @ Xs) @ (cons_event @ (last_event @ Xs) @ nil_event)) = Xs))))). % append_butlast_last_id
thf(fact_100_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_101_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_102_last__appendR, axiom,
    ((![Ys : list_event, Xs : list_event]: ((~ ((Ys = nil_event))) => ((last_event @ (append_event @ Xs @ Ys)) = (last_event @ Ys)))))). % last_appendR
thf(fact_103_last__appendL, axiom,
    ((![Ys : list_event, Xs : list_event]: ((Ys = nil_event) => ((last_event @ (append_event @ Xs @ Ys)) = (last_event @ Xs)))))). % last_appendL
thf(fact_104_last__snoc, axiom,
    ((![Xs : list_event, X2 : event]: ((last_event @ (append_event @ Xs @ (cons_event @ X2 @ nil_event))) = X2)))). % last_snoc
thf(fact_105_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_106_event_Odistinct_I5_J, axiom,
    ((![X21 : agent, X22 : msg, X31 : agent, X32 : msg]: (~ (((gets @ X21 @ X22) = (notes @ X31 @ X32))))))). % event.distinct(5)
thf(fact_107_last__ConsR, axiom,
    ((![Xs : list_event, X2 : event]: ((~ ((Xs = nil_event))) => ((last_event @ (cons_event @ X2 @ Xs)) = (last_event @ Xs)))))). % last_ConsR
thf(fact_108_last__ConsL, axiom,
    ((![Xs : list_event, X2 : event]: ((Xs = nil_event) => ((last_event @ (cons_event @ X2 @ Xs)) = X2))))). % last_ConsL
thf(fact_109_last_Osimps, axiom,
    ((![Xs : list_event, X2 : event]: (((Xs = nil_event) => ((last_event @ (cons_event @ X2 @ Xs)) = X2)) & ((~ ((Xs = nil_event))) => ((last_event @ (cons_event @ X2 @ Xs)) = (last_event @ Xs))))))). % last.simps
thf(fact_110_longest__common__suffix, axiom,
    ((![Xs : list_event, Ys : list_event]: (?[Ss : list_event, Xs3 : list_event, Ys5 : list_event]: ((Xs = (append_event @ Xs3 @ Ss)) & ((Ys = (append_event @ Ys5 @ Ss)) & ((Xs3 = nil_event) | ((Ys5 = nil_event) | (~ (((last_event @ Xs3) = (last_event @ Ys5)))))))))))). % longest_common_suffix
thf(fact_111_last__append, axiom,
    ((![Ys : list_event, Xs : list_event]: (((Ys = nil_event) => ((last_event @ (append_event @ Xs @ Ys)) = (last_event @ Xs))) & ((~ ((Ys = nil_event))) => ((last_event @ (append_event @ Xs @ Ys)) = (last_event @ Ys))))))). % last_append
thf(fact_112_order__subst1, axiom,
    ((![A2 : set_msg, F2 : set_msg > set_msg, B2 : set_msg, C : set_msg]: ((ord_less_eq_set_msg @ A2 @ (F2 @ B2)) => ((ord_less_eq_set_msg @ B2 @ C) => ((![X3 : set_msg, Y2 : set_msg]: ((ord_less_eq_set_msg @ X3 @ Y2) => (ord_less_eq_set_msg @ (F2 @ X3) @ (F2 @ Y2)))) => (ord_less_eq_set_msg @ A2 @ (F2 @ C)))))))). % order_subst1
thf(fact_113_order__subst2, axiom,
    ((![A2 : set_msg, B2 : set_msg, F2 : set_msg > set_msg, C : set_msg]: ((ord_less_eq_set_msg @ A2 @ B2) => ((ord_less_eq_set_msg @ (F2 @ B2) @ C) => ((![X3 : set_msg, Y2 : set_msg]: ((ord_less_eq_set_msg @ X3 @ Y2) => (ord_less_eq_set_msg @ (F2 @ X3) @ (F2 @ Y2)))) => (ord_less_eq_set_msg @ (F2 @ A2) @ C))))))). % order_subst2
thf(fact_114_ord__eq__le__subst, axiom,
    ((![A2 : set_msg, F2 : set_msg > set_msg, B2 : set_msg, C : set_msg]: ((A2 = (F2 @ B2)) => ((ord_less_eq_set_msg @ B2 @ C) => ((![X3 : set_msg, Y2 : set_msg]: ((ord_less_eq_set_msg @ X3 @ Y2) => (ord_less_eq_set_msg @ (F2 @ X3) @ (F2 @ Y2)))) => (ord_less_eq_set_msg @ A2 @ (F2 @ C)))))))). % ord_eq_le_subst
thf(fact_115_ord__le__eq__subst, axiom,
    ((![A2 : set_msg, B2 : set_msg, F2 : set_msg > set_msg, C : set_msg]: ((ord_less_eq_set_msg @ A2 @ B2) => (((F2 @ B2) = C) => ((![X3 : set_msg, Y2 : set_msg]: ((ord_less_eq_set_msg @ X3 @ Y2) => (ord_less_eq_set_msg @ (F2 @ X3) @ (F2 @ Y2)))) => (ord_less_eq_set_msg @ (F2 @ A2) @ C))))))). % ord_le_eq_subst
thf(fact_116_eq__iff, axiom,
    (((^[Y4 : set_msg]: (^[Z : set_msg]: (Y4 = Z))) = (^[X4 : set_msg]: (^[Y3 : set_msg]: (((ord_less_eq_set_msg @ X4 @ Y3)) & ((ord_less_eq_set_msg @ Y3 @ X4)))))))). % eq_iff
thf(fact_117_antisym, axiom,
    ((![X2 : set_msg, Y : set_msg]: ((ord_less_eq_set_msg @ X2 @ Y) => ((ord_less_eq_set_msg @ Y @ X2) => (X2 = Y)))))). % antisym
thf(fact_118_eq__refl, axiom,
    ((![X2 : set_msg, Y : set_msg]: ((X2 = Y) => (ord_less_eq_set_msg @ X2 @ Y))))). % eq_refl
thf(fact_119_order_Otrans, axiom,
    ((![A2 : set_msg, B2 : set_msg, C : set_msg]: ((ord_less_eq_set_msg @ A2 @ B2) => ((ord_less_eq_set_msg @ B2 @ C) => (ord_less_eq_set_msg @ A2 @ C)))))). % order.trans
thf(fact_120_antisym__conv, axiom,
    ((![Y : set_msg, X2 : set_msg]: ((ord_less_eq_set_msg @ Y @ X2) => ((ord_less_eq_set_msg @ X2 @ Y) = (X2 = Y)))))). % antisym_conv
thf(fact_121_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y4 : set_msg]: (^[Z : set_msg]: (Y4 = Z))) = (^[A6 : set_msg]: (^[B5 : set_msg]: (((ord_less_eq_set_msg @ A6 @ B5)) & ((ord_less_eq_set_msg @ B5 @ A6)))))))). % order_class.order.eq_iff
thf(fact_122_ord__eq__le__trans, axiom,
    ((![A2 : set_msg, B2 : set_msg, C : set_msg]: ((A2 = B2) => ((ord_less_eq_set_msg @ B2 @ C) => (ord_less_eq_set_msg @ A2 @ C)))))). % ord_eq_le_trans
thf(fact_123_ord__le__eq__trans, axiom,
    ((![A2 : set_msg, B2 : set_msg, C : set_msg]: ((ord_less_eq_set_msg @ A2 @ B2) => ((B2 = C) => (ord_less_eq_set_msg @ A2 @ C)))))). % ord_le_eq_trans
thf(fact_124_order__class_Oorder_Oantisym, axiom,
    ((![A2 : set_msg, B2 : set_msg]: ((ord_less_eq_set_msg @ A2 @ B2) => ((ord_less_eq_set_msg @ B2 @ A2) => (A2 = B2)))))). % order_class.order.antisym
thf(fact_125_order__trans, axiom,
    ((![X2 : set_msg, Y : set_msg, Z2 : set_msg]: ((ord_less_eq_set_msg @ X2 @ Y) => ((ord_less_eq_set_msg @ Y @ Z2) => (ord_less_eq_set_msg @ X2 @ Z2)))))). % order_trans
thf(fact_126_dual__order_Orefl, axiom,
    ((![A2 : set_msg]: (ord_less_eq_set_msg @ A2 @ A2)))). % dual_order.refl
thf(fact_127_dual__order_Otrans, axiom,
    ((![B2 : set_msg, A2 : set_msg, C : set_msg]: ((ord_less_eq_set_msg @ B2 @ A2) => ((ord_less_eq_set_msg @ C @ B2) => (ord_less_eq_set_msg @ C @ A2)))))). % dual_order.trans
thf(fact_128_dual__order_Oeq__iff, axiom,
    (((^[Y4 : set_msg]: (^[Z : set_msg]: (Y4 = Z))) = (^[A6 : set_msg]: (^[B5 : set_msg]: (((ord_less_eq_set_msg @ B5 @ A6)) & ((ord_less_eq_set_msg @ A6 @ B5)))))))). % dual_order.eq_iff
thf(fact_129_dual__order_Oantisym, axiom,
    ((![B2 : set_msg, A2 : set_msg]: ((ord_less_eq_set_msg @ B2 @ A2) => ((ord_less_eq_set_msg @ A2 @ B2) => (A2 = B2)))))). % dual_order.antisym
thf(fact_130_event_Oexhaust, axiom,
    ((![Y : event]: ((![X112 : agent, X122 : agent, X132 : msg]: (~ ((Y = (says @ X112 @ X122 @ X132))))) => ((![X212 : agent, X222 : msg]: (~ ((Y = (gets @ X212 @ X222))))) => (~ ((![X312 : agent, X322 : msg]: (~ ((Y = (notes @ X312 @ X322)))))))))))). % event.exhaust
thf(fact_131_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_132_knows__subset__knows__Notes, axiom,
    ((![A : agent, Evs : list_event, A5 : agent, X : msg]: (ord_less_eq_set_msg @ (knows @ A @ Evs) @ (knows @ A @ (cons_event @ (notes @ A5 @ X) @ Evs)))))). % knows_subset_knows_Notes

% Conjectures (1)
thf(conj_0, conjecture,
    (((knows @ spy @ (append_event @ nil_event @ (cons_event @ (says @ a @ b @ x) @ nil_event))) = (insert_msg @ x @ (knows @ spy @ nil_event))))).
