% 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_234__5229902_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:23:57.791

% Could-be-implicit typings (10)
thf(ty_n_t__Set__Oset_It__List__Olist_It__Event__Oevent_J_J, type,
    set_list_event : $tType).
thf(ty_n_t__Set__Oset_It__Message__Oagent_J, type,
    set_agent : $tType).
thf(ty_n_t__List__Olist_It__Event__Oevent_J, type,
    list_event : $tType).
thf(ty_n_t__Set__Oset_It__Message__Omsg_J, type,
    set_msg : $tType).
thf(ty_n_t__Set__Oset_It__Event__Oevent_J, type,
    set_event : $tType).
thf(ty_n_t__Set__Oset_It__Nat__Onat_J, type,
    set_nat : $tType).
thf(ty_n_t__Message__Oagent, type,
    agent : $tType).
thf(ty_n_t__Message__Omsg, type,
    msg : $tType).
thf(ty_n_t__Event__Oevent, type,
    event : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (50)
thf(sy_c_Event_Obad, type,
    bad : set_agent).
thf(sy_c_Event_Oevent_OSays, type,
    says : agent > agent > msg > event).
thf(sy_c_Event_Oknows, type,
    knows : agent > list_event > set_msg).
thf(sy_c_Event_Oused, type,
    used : list_event > set_msg).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Message__Oagent_J, type,
    uminus1992895513_agent : set_agent > set_agent).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Message__Omsg_J, type,
    uminus676873109et_msg : set_msg > set_msg).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Nat__Onat_J, type,
    uminus814679503et_nat : set_nat > set_nat).
thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat, type,
    sup_sup_nat : nat > nat > nat).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Message__Oagent_J, type,
    sup_sup_set_agent : set_agent > set_agent > set_agent).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Message__Omsg_J, type,
    sup_sup_set_msg : set_msg > set_msg > set_msg).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J, type,
    sup_sup_set_nat : set_nat > set_nat > set_nat).
thf(sy_c_List_Olist_Oset_001t__Event__Oevent, type,
    set_event2 : list_event > set_event).
thf(sy_c_Message_Oagent_OServer, type,
    server : agent).
thf(sy_c_Message_Oagent_OSpy, type,
    spy : agent).
thf(sy_c_Message_Oanalz, type,
    analz : set_msg > set_msg).
thf(sy_c_Message_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_OsymKeys, type,
    symKeys : set_nat).
thf(sy_c_NS__Shared__Mirabelle__xwdrtqxrux_Ons__shared, type,
    nS_Sha1061662329shared : set_list_event).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat, type,
    ord_less_eq_nat : nat > nat > $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_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J, type,
    ord_less_eq_set_nat : set_nat > set_nat > $o).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Message__Oagent_J, type,
    top_top_set_agent : set_agent).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Message__Omsg_J, type,
    top_top_set_msg : set_msg).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J, type,
    top_top_set_nat : set_nat).
thf(sy_c_Public_OshrK, type,
    shrK : agent > nat).
thf(sy_c_Set_OCollect_001t__Event__Oevent, type,
    collect_event : (event > $o) > set_event).
thf(sy_c_Set_OCollect_001t__List__Olist_It__Event__Oevent_J, type,
    collect_list_event : (list_event > $o) > set_list_event).
thf(sy_c_Set_OCollect_001t__Message__Oagent, type,
    collect_agent : (agent > $o) > set_agent).
thf(sy_c_Set_OCollect_001t__Message__Omsg, type,
    collect_msg : (msg > $o) > set_msg).
thf(sy_c_Set_OCollect_001t__Nat__Onat, type,
    collect_nat : (nat > $o) > set_nat).
thf(sy_c_Set_Oimage_001t__Message__Oagent_001t__Nat__Onat, type,
    image_agent_nat : (agent > nat) > set_agent > set_nat).
thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Message__Omsg, type,
    image_nat_msg : (nat > msg) > set_nat > set_msg).
thf(sy_c_member_001t__Event__Oevent, type,
    member_event : event > set_event > $o).
thf(sy_c_member_001t__List__Olist_It__Event__Oevent_J, type,
    member_list_event : list_event > set_list_event > $o).
thf(sy_c_member_001t__Message__Oagent, type,
    member_agent : agent > set_agent > $o).
thf(sy_c_member_001t__Message__Omsg, type,
    member_msg : msg > set_msg > $o).
thf(sy_c_member_001t__Nat__Onat, type,
    member_nat : nat > set_nat > $o).
thf(sy_v_A, type,
    a : agent).
thf(sy_v_A_H, type,
    a2 : agent).
thf(sy_v_B, type,
    b : agent).
thf(sy_v_K, type,
    k : nat).
thf(sy_v_KAB, type,
    kab : nat).
thf(sy_v_KK, type,
    kk : set_nat).
thf(sy_v_NA, type,
    na : nat).
thf(sy_v_evs2, type,
    evs2 : list_event).

% Relevant facts (249)
thf(fact_0_shrK__in__used, axiom,
    ((![A : agent, Evs : list_event]: (member_msg @ (key @ (shrK @ A)) @ (used @ Evs))))). % shrK_in_used
thf(fact_1_analz__image__Key, axiom,
    ((![N : set_nat]: ((analz @ (image_nat_msg @ key @ N)) = (image_nat_msg @ key @ N))))). % analz_image_Key
thf(fact_2_shrK__in__knows, axiom,
    ((![A : agent, Evs : list_event]: (member_msg @ (key @ (shrK @ A)) @ (knows @ A @ Evs))))). % shrK_in_knows
thf(fact_3_compl__sup__top, axiom,
    ((![X : set_msg]: ((sup_sup_set_msg @ (uminus676873109et_msg @ X) @ X) = top_top_set_msg)))). % compl_sup_top
thf(fact_4_compl__sup__top, axiom,
    ((![X : set_agent]: ((sup_sup_set_agent @ (uminus1992895513_agent @ X) @ X) = top_top_set_agent)))). % compl_sup_top
thf(fact_5_compl__sup__top, axiom,
    ((![X : set_nat]: ((sup_sup_set_nat @ (uminus814679503et_nat @ X) @ X) = top_top_set_nat)))). % compl_sup_top
thf(fact_6_sup__compl__top, axiom,
    ((![X : set_msg]: ((sup_sup_set_msg @ X @ (uminus676873109et_msg @ X)) = top_top_set_msg)))). % sup_compl_top
thf(fact_7_sup__compl__top, axiom,
    ((![X : set_agent]: ((sup_sup_set_agent @ X @ (uminus1992895513_agent @ X)) = top_top_set_agent)))). % sup_compl_top
thf(fact_8_sup__compl__top, axiom,
    ((![X : set_nat]: ((sup_sup_set_nat @ X @ (uminus814679503et_nat @ X)) = top_top_set_nat)))). % sup_compl_top
thf(fact_9_sup__compl__top__left1, axiom,
    ((![X : set_msg, Y : set_msg]: ((sup_sup_set_msg @ (uminus676873109et_msg @ X) @ (sup_sup_set_msg @ X @ Y)) = top_top_set_msg)))). % sup_compl_top_left1
thf(fact_10_sup__compl__top__left1, axiom,
    ((![X : set_agent, Y : set_agent]: ((sup_sup_set_agent @ (uminus1992895513_agent @ X) @ (sup_sup_set_agent @ X @ Y)) = top_top_set_agent)))). % sup_compl_top_left1
thf(fact_11_sup__compl__top__left1, axiom,
    ((![X : set_nat, Y : set_nat]: ((sup_sup_set_nat @ (uminus814679503et_nat @ X) @ (sup_sup_set_nat @ X @ Y)) = top_top_set_nat)))). % sup_compl_top_left1
thf(fact_12_sup__compl__top__left2, axiom,
    ((![X : set_msg, Y : set_msg]: ((sup_sup_set_msg @ X @ (sup_sup_set_msg @ (uminus676873109et_msg @ X) @ Y)) = top_top_set_msg)))). % sup_compl_top_left2
thf(fact_13_sup__compl__top__left2, axiom,
    ((![X : set_agent, Y : set_agent]: ((sup_sup_set_agent @ X @ (sup_sup_set_agent @ (uminus1992895513_agent @ X) @ Y)) = top_top_set_agent)))). % sup_compl_top_left2
thf(fact_14_sup__compl__top__left2, axiom,
    ((![X : set_nat, Y : set_nat]: ((sup_sup_set_nat @ X @ (sup_sup_set_nat @ (uminus814679503et_nat @ X) @ Y)) = top_top_set_nat)))). % sup_compl_top_left2
thf(fact_15_sym__shrK, axiom,
    ((![X2 : agent]: (member_nat @ (shrK @ X2) @ symKeys)))). % sym_shrK
thf(fact_16_shrK__image__eq, axiom,
    ((![X : agent, AA : set_agent]: ((member_nat @ (shrK @ X) @ (image_agent_nat @ shrK @ AA)) = (member_agent @ X @ AA))))). % shrK_image_eq
thf(fact_17_Key__not__used, axiom,
    ((![K : nat, Evs : list_event]: ((~ ((member_msg @ (key @ K) @ (used @ Evs)))) => (~ ((member_nat @ K @ (image_agent_nat @ shrK @ top_top_set_agent)))))))). % Key_not_used
thf(fact_18_Key__image__eq, axiom,
    ((![X : nat, A : set_nat]: ((member_msg @ (key @ X) @ (image_nat_msg @ key @ A)) = (member_nat @ X @ A))))). % Key_image_eq
thf(fact_19_Says__imp__analz__Spy, axiom,
    ((![A : agent, B : agent, X2 : msg, Evs : list_event]: ((member_event @ (says @ A @ B @ X2) @ (set_event2 @ Evs)) => (member_msg @ X2 @ (analz @ (knows @ spy @ Evs))))))). % Says_imp_analz_Spy
thf(fact_20_compl__eq__compl__iff, axiom,
    ((![X : set_nat, Y : set_nat]: (((uminus814679503et_nat @ X) = (uminus814679503et_nat @ Y)) = (X = Y))))). % compl_eq_compl_iff
thf(fact_21_compl__eq__compl__iff, axiom,
    ((![X : set_agent, Y : set_agent]: (((uminus1992895513_agent @ X) = (uminus1992895513_agent @ Y)) = (X = Y))))). % compl_eq_compl_iff
thf(fact_22_compl__eq__compl__iff, axiom,
    ((![X : set_msg, Y : set_msg]: (((uminus676873109et_msg @ X) = (uminus676873109et_msg @ Y)) = (X = Y))))). % compl_eq_compl_iff
thf(fact_23_double__compl, axiom,
    ((![X : set_nat]: ((uminus814679503et_nat @ (uminus814679503et_nat @ X)) = X)))). % double_compl
thf(fact_24_double__compl, axiom,
    ((![X : set_agent]: ((uminus1992895513_agent @ (uminus1992895513_agent @ X)) = X)))). % double_compl
thf(fact_25_double__compl, axiom,
    ((![X : set_msg]: ((uminus676873109et_msg @ (uminus676873109et_msg @ X)) = X)))). % double_compl
thf(fact_26_sup_Oright__idem, axiom,
    ((![A2 : set_msg, B2 : set_msg]: ((sup_sup_set_msg @ (sup_sup_set_msg @ A2 @ B2) @ B2) = (sup_sup_set_msg @ A2 @ B2))))). % sup.right_idem
thf(fact_27_sup_Oright__idem, axiom,
    ((![A2 : set_nat, B2 : set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ A2 @ B2) @ B2) = (sup_sup_set_nat @ A2 @ B2))))). % sup.right_idem
thf(fact_28_sup_Oright__idem, axiom,
    ((![A2 : set_agent, B2 : set_agent]: ((sup_sup_set_agent @ (sup_sup_set_agent @ A2 @ B2) @ B2) = (sup_sup_set_agent @ A2 @ B2))))). % sup.right_idem
thf(fact_29_sup__left__idem, axiom,
    ((![X : set_msg, Y : set_msg]: ((sup_sup_set_msg @ X @ (sup_sup_set_msg @ X @ Y)) = (sup_sup_set_msg @ X @ Y))))). % sup_left_idem
thf(fact_30_sup__left__idem, axiom,
    ((![X : set_nat, Y : set_nat]: ((sup_sup_set_nat @ X @ (sup_sup_set_nat @ X @ Y)) = (sup_sup_set_nat @ X @ Y))))). % sup_left_idem
thf(fact_31_sup__left__idem, axiom,
    ((![X : set_agent, Y : set_agent]: ((sup_sup_set_agent @ X @ (sup_sup_set_agent @ X @ Y)) = (sup_sup_set_agent @ X @ Y))))). % sup_left_idem
thf(fact_32_sup_Oleft__idem, axiom,
    ((![A2 : set_msg, B2 : set_msg]: ((sup_sup_set_msg @ A2 @ (sup_sup_set_msg @ A2 @ B2)) = (sup_sup_set_msg @ A2 @ B2))))). % sup.left_idem
thf(fact_33_sup_Oleft__idem, axiom,
    ((![A2 : set_nat, B2 : set_nat]: ((sup_sup_set_nat @ A2 @ (sup_sup_set_nat @ A2 @ B2)) = (sup_sup_set_nat @ A2 @ B2))))). % sup.left_idem
thf(fact_34_sup_Oleft__idem, axiom,
    ((![A2 : set_agent, B2 : set_agent]: ((sup_sup_set_agent @ A2 @ (sup_sup_set_agent @ A2 @ B2)) = (sup_sup_set_agent @ A2 @ B2))))). % sup.left_idem
thf(fact_35_sup__idem, axiom,
    ((![X : set_msg]: ((sup_sup_set_msg @ X @ X) = X)))). % sup_idem
thf(fact_36_sup__idem, axiom,
    ((![X : set_nat]: ((sup_sup_set_nat @ X @ X) = X)))). % sup_idem
thf(fact_37_sup__idem, axiom,
    ((![X : set_agent]: ((sup_sup_set_agent @ X @ X) = X)))). % sup_idem
thf(fact_38_sup_Oidem, axiom,
    ((![A2 : set_msg]: ((sup_sup_set_msg @ A2 @ A2) = A2)))). % sup.idem
thf(fact_39_sup_Oidem, axiom,
    ((![A2 : set_nat]: ((sup_sup_set_nat @ A2 @ A2) = A2)))). % sup.idem
thf(fact_40_sup_Oidem, axiom,
    ((![A2 : set_agent]: ((sup_sup_set_agent @ A2 @ A2) = A2)))). % sup.idem
thf(fact_41_analz__idem, axiom,
    ((![H : set_msg]: ((analz @ (analz @ H)) = (analz @ H))))). % analz_idem
thf(fact_42_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_43_msg_Oinject_I4_J, axiom,
    ((![X4 : nat, Y4 : nat]: (((key @ X4) = (key @ Y4)) = (X4 = Y4))))). % msg.inject(4)
thf(fact_44_msg_Oinject_I3_J, axiom,
    ((![X3 : nat, Y3 : nat]: (((nonce @ X3) = (nonce @ Y3)) = (X3 = Y3))))). % msg.inject(3)
thf(fact_45_msg_Oinject_I1_J, axiom,
    ((![X1 : agent, Y1 : agent]: (((agent2 @ X1) = (agent2 @ Y1)) = (X1 = Y1))))). % msg.inject(1)
thf(fact_46_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_47_shrK__injective, axiom,
    ((![X : agent, Y : agent]: (((shrK @ X) = (shrK @ Y)) = (X = Y))))). % shrK_injective
thf(fact_48_compl__le__compl__iff, axiom,
    ((![X : set_agent, Y : set_agent]: ((ord_le722097072_agent @ (uminus1992895513_agent @ X) @ (uminus1992895513_agent @ Y)) = (ord_le722097072_agent @ Y @ X))))). % compl_le_compl_iff
thf(fact_49_compl__le__compl__iff, axiom,
    ((![X : set_nat, Y : set_nat]: ((ord_less_eq_set_nat @ (uminus814679503et_nat @ X) @ (uminus814679503et_nat @ Y)) = (ord_less_eq_set_nat @ Y @ X))))). % compl_le_compl_iff
thf(fact_50_compl__le__compl__iff, axiom,
    ((![X : set_msg, Y : set_msg]: ((ord_less_eq_set_msg @ (uminus676873109et_msg @ X) @ (uminus676873109et_msg @ Y)) = (ord_less_eq_set_msg @ Y @ X))))). % compl_le_compl_iff
thf(fact_51_sup_Obounded__iff, axiom,
    ((![B2 : set_agent, C : set_agent, A2 : set_agent]: ((ord_le722097072_agent @ (sup_sup_set_agent @ B2 @ C) @ A2) = (((ord_le722097072_agent @ B2 @ A2)) & ((ord_le722097072_agent @ C @ A2))))))). % sup.bounded_iff
thf(fact_52_sup_Obounded__iff, axiom,
    ((![B2 : set_nat, C : set_nat, A2 : set_nat]: ((ord_less_eq_set_nat @ (sup_sup_set_nat @ B2 @ C) @ A2) = (((ord_less_eq_set_nat @ B2 @ A2)) & ((ord_less_eq_set_nat @ C @ A2))))))). % sup.bounded_iff
thf(fact_53_sup_Obounded__iff, axiom,
    ((![B2 : set_msg, C : set_msg, A2 : set_msg]: ((ord_less_eq_set_msg @ (sup_sup_set_msg @ B2 @ C) @ A2) = (((ord_less_eq_set_msg @ B2 @ A2)) & ((ord_less_eq_set_msg @ C @ A2))))))). % sup.bounded_iff
thf(fact_54_sup_Obounded__iff, axiom,
    ((![B2 : nat, C : nat, A2 : nat]: ((ord_less_eq_nat @ (sup_sup_nat @ B2 @ C) @ A2) = (((ord_less_eq_nat @ B2 @ A2)) & ((ord_less_eq_nat @ C @ A2))))))). % sup.bounded_iff
thf(fact_55_le__sup__iff, axiom,
    ((![X : set_agent, Y : set_agent, Z : set_agent]: ((ord_le722097072_agent @ (sup_sup_set_agent @ X @ Y) @ Z) = (((ord_le722097072_agent @ X @ Z)) & ((ord_le722097072_agent @ Y @ Z))))))). % le_sup_iff
thf(fact_56_le__sup__iff, axiom,
    ((![X : set_nat, Y : set_nat, Z : set_nat]: ((ord_less_eq_set_nat @ (sup_sup_set_nat @ X @ Y) @ Z) = (((ord_less_eq_set_nat @ X @ Z)) & ((ord_less_eq_set_nat @ Y @ Z))))))). % le_sup_iff
thf(fact_57_le__sup__iff, axiom,
    ((![X : set_msg, Y : set_msg, Z : set_msg]: ((ord_less_eq_set_msg @ (sup_sup_set_msg @ X @ Y) @ Z) = (((ord_less_eq_set_msg @ X @ Z)) & ((ord_less_eq_set_msg @ Y @ Z))))))). % le_sup_iff
thf(fact_58_le__sup__iff, axiom,
    ((![X : nat, Y : nat, Z : nat]: ((ord_less_eq_nat @ (sup_sup_nat @ X @ Y) @ Z) = (((ord_less_eq_nat @ X @ Z)) & ((ord_less_eq_nat @ Y @ Z))))))). % le_sup_iff
thf(fact_59_sup__top__right, axiom,
    ((![X : set_agent]: ((sup_sup_set_agent @ X @ top_top_set_agent) = top_top_set_agent)))). % sup_top_right
thf(fact_60_sup__top__right, axiom,
    ((![X : set_nat]: ((sup_sup_set_nat @ X @ top_top_set_nat) = top_top_set_nat)))). % sup_top_right
thf(fact_61_sup__top__right, axiom,
    ((![X : set_msg]: ((sup_sup_set_msg @ X @ top_top_set_msg) = top_top_set_msg)))). % sup_top_right
thf(fact_62_sup__top__left, axiom,
    ((![X : set_agent]: ((sup_sup_set_agent @ top_top_set_agent @ X) = top_top_set_agent)))). % sup_top_left
thf(fact_63_sup__top__left, axiom,
    ((![X : set_nat]: ((sup_sup_set_nat @ top_top_set_nat @ X) = top_top_set_nat)))). % sup_top_left
thf(fact_64_sup__top__left, axiom,
    ((![X : set_msg]: ((sup_sup_set_msg @ top_top_set_msg @ X) = top_top_set_msg)))). % sup_top_left
thf(fact_65_analz__analz__Un, axiom,
    ((![G : set_msg, H : set_msg]: ((analz @ (sup_sup_set_msg @ (analz @ G) @ H)) = (analz @ (sup_sup_set_msg @ G @ H)))))). % analz_analz_Un
thf(fact_66_sup__left__commute, axiom,
    ((![X : set_msg, Y : set_msg, Z : set_msg]: ((sup_sup_set_msg @ X @ (sup_sup_set_msg @ Y @ Z)) = (sup_sup_set_msg @ Y @ (sup_sup_set_msg @ X @ Z)))))). % sup_left_commute
thf(fact_67_sup__left__commute, axiom,
    ((![X : set_nat, Y : set_nat, Z : set_nat]: ((sup_sup_set_nat @ X @ (sup_sup_set_nat @ Y @ Z)) = (sup_sup_set_nat @ Y @ (sup_sup_set_nat @ X @ Z)))))). % sup_left_commute
thf(fact_68_sup__left__commute, axiom,
    ((![X : set_agent, Y : set_agent, Z : set_agent]: ((sup_sup_set_agent @ X @ (sup_sup_set_agent @ Y @ Z)) = (sup_sup_set_agent @ Y @ (sup_sup_set_agent @ X @ Z)))))). % sup_left_commute
thf(fact_69_sup_Oleft__commute, axiom,
    ((![B2 : set_msg, A2 : set_msg, C : set_msg]: ((sup_sup_set_msg @ B2 @ (sup_sup_set_msg @ A2 @ C)) = (sup_sup_set_msg @ A2 @ (sup_sup_set_msg @ B2 @ C)))))). % sup.left_commute
thf(fact_70_sup_Oleft__commute, axiom,
    ((![B2 : set_nat, A2 : set_nat, C : set_nat]: ((sup_sup_set_nat @ B2 @ (sup_sup_set_nat @ A2 @ C)) = (sup_sup_set_nat @ A2 @ (sup_sup_set_nat @ B2 @ C)))))). % sup.left_commute
thf(fact_71_sup_Oleft__commute, axiom,
    ((![B2 : set_agent, A2 : set_agent, C : set_agent]: ((sup_sup_set_agent @ B2 @ (sup_sup_set_agent @ A2 @ C)) = (sup_sup_set_agent @ A2 @ (sup_sup_set_agent @ B2 @ C)))))). % sup.left_commute
thf(fact_72_sup__commute, axiom,
    ((sup_sup_set_msg = (^[X5 : set_msg]: (^[Y2 : set_msg]: (sup_sup_set_msg @ Y2 @ X5)))))). % sup_commute
thf(fact_73_sup__commute, axiom,
    ((sup_sup_set_nat = (^[X5 : set_nat]: (^[Y2 : set_nat]: (sup_sup_set_nat @ Y2 @ X5)))))). % sup_commute
thf(fact_74_sup__commute, axiom,
    ((sup_sup_set_agent = (^[X5 : set_agent]: (^[Y2 : set_agent]: (sup_sup_set_agent @ Y2 @ X5)))))). % sup_commute
thf(fact_75_sup_Ocommute, axiom,
    ((sup_sup_set_msg = (^[A3 : set_msg]: (^[B3 : set_msg]: (sup_sup_set_msg @ B3 @ A3)))))). % sup.commute
thf(fact_76_sup_Ocommute, axiom,
    ((sup_sup_set_nat = (^[A3 : set_nat]: (^[B3 : set_nat]: (sup_sup_set_nat @ B3 @ A3)))))). % sup.commute
thf(fact_77_sup_Ocommute, axiom,
    ((sup_sup_set_agent = (^[A3 : set_agent]: (^[B3 : set_agent]: (sup_sup_set_agent @ B3 @ A3)))))). % sup.commute
thf(fact_78_sup__assoc, axiom,
    ((![X : set_msg, Y : set_msg, Z : set_msg]: ((sup_sup_set_msg @ (sup_sup_set_msg @ X @ Y) @ Z) = (sup_sup_set_msg @ X @ (sup_sup_set_msg @ Y @ Z)))))). % sup_assoc
thf(fact_79_sup__assoc, axiom,
    ((![X : set_nat, Y : set_nat, Z : set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ X @ Y) @ Z) = (sup_sup_set_nat @ X @ (sup_sup_set_nat @ Y @ Z)))))). % sup_assoc
thf(fact_80_sup__assoc, axiom,
    ((![X : set_agent, Y : set_agent, Z : set_agent]: ((sup_sup_set_agent @ (sup_sup_set_agent @ X @ Y) @ Z) = (sup_sup_set_agent @ X @ (sup_sup_set_agent @ Y @ Z)))))). % sup_assoc
thf(fact_81_sup_Oassoc, axiom,
    ((![A2 : set_msg, B2 : set_msg, C : set_msg]: ((sup_sup_set_msg @ (sup_sup_set_msg @ A2 @ B2) @ C) = (sup_sup_set_msg @ A2 @ (sup_sup_set_msg @ B2 @ C)))))). % sup.assoc
thf(fact_82_sup_Oassoc, axiom,
    ((![A2 : set_nat, B2 : set_nat, C : set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ A2 @ B2) @ C) = (sup_sup_set_nat @ A2 @ (sup_sup_set_nat @ B2 @ C)))))). % sup.assoc
thf(fact_83_sup_Oassoc, axiom,
    ((![A2 : set_agent, B2 : set_agent, C : set_agent]: ((sup_sup_set_agent @ (sup_sup_set_agent @ A2 @ B2) @ C) = (sup_sup_set_agent @ A2 @ (sup_sup_set_agent @ B2 @ C)))))). % sup.assoc
thf(fact_84_boolean__algebra__cancel_Osup2, axiom,
    ((![B : set_msg, K2 : set_msg, B2 : set_msg, A2 : set_msg]: ((B = (sup_sup_set_msg @ K2 @ B2)) => ((sup_sup_set_msg @ A2 @ B) = (sup_sup_set_msg @ K2 @ (sup_sup_set_msg @ A2 @ B2))))))). % boolean_algebra_cancel.sup2
thf(fact_85_boolean__algebra__cancel_Osup2, axiom,
    ((![B : set_nat, K2 : set_nat, B2 : set_nat, A2 : set_nat]: ((B = (sup_sup_set_nat @ K2 @ B2)) => ((sup_sup_set_nat @ A2 @ B) = (sup_sup_set_nat @ K2 @ (sup_sup_set_nat @ A2 @ B2))))))). % boolean_algebra_cancel.sup2
thf(fact_86_boolean__algebra__cancel_Osup2, axiom,
    ((![B : set_agent, K2 : set_agent, B2 : set_agent, A2 : set_agent]: ((B = (sup_sup_set_agent @ K2 @ B2)) => ((sup_sup_set_agent @ A2 @ B) = (sup_sup_set_agent @ K2 @ (sup_sup_set_agent @ A2 @ B2))))))). % boolean_algebra_cancel.sup2
thf(fact_87_boolean__algebra__cancel_Osup1, axiom,
    ((![A : set_msg, K2 : set_msg, A2 : set_msg, B2 : set_msg]: ((A = (sup_sup_set_msg @ K2 @ A2)) => ((sup_sup_set_msg @ A @ B2) = (sup_sup_set_msg @ K2 @ (sup_sup_set_msg @ A2 @ B2))))))). % boolean_algebra_cancel.sup1
thf(fact_88_boolean__algebra__cancel_Osup1, axiom,
    ((![A : set_nat, K2 : set_nat, A2 : set_nat, B2 : set_nat]: ((A = (sup_sup_set_nat @ K2 @ A2)) => ((sup_sup_set_nat @ A @ B2) = (sup_sup_set_nat @ K2 @ (sup_sup_set_nat @ A2 @ B2))))))). % boolean_algebra_cancel.sup1
thf(fact_89_boolean__algebra__cancel_Osup1, axiom,
    ((![A : set_agent, K2 : set_agent, A2 : set_agent, B2 : set_agent]: ((A = (sup_sup_set_agent @ K2 @ A2)) => ((sup_sup_set_agent @ A @ B2) = (sup_sup_set_agent @ K2 @ (sup_sup_set_agent @ A2 @ B2))))))). % boolean_algebra_cancel.sup1
thf(fact_90_inf__sup__aci_I5_J, axiom,
    ((sup_sup_set_msg = (^[X5 : set_msg]: (^[Y2 : set_msg]: (sup_sup_set_msg @ Y2 @ X5)))))). % inf_sup_aci(5)
thf(fact_91_inf__sup__aci_I5_J, axiom,
    ((sup_sup_set_nat = (^[X5 : set_nat]: (^[Y2 : set_nat]: (sup_sup_set_nat @ Y2 @ X5)))))). % inf_sup_aci(5)
thf(fact_92_inf__sup__aci_I5_J, axiom,
    ((sup_sup_set_agent = (^[X5 : set_agent]: (^[Y2 : set_agent]: (sup_sup_set_agent @ Y2 @ X5)))))). % inf_sup_aci(5)
thf(fact_93_mem__Collect__eq, axiom,
    ((![A2 : list_event, P : list_event > $o]: ((member_list_event @ A2 @ (collect_list_event @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_94_mem__Collect__eq, axiom,
    ((![A2 : msg, P : msg > $o]: ((member_msg @ A2 @ (collect_msg @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_95_mem__Collect__eq, axiom,
    ((![A2 : nat, P : nat > $o]: ((member_nat @ A2 @ (collect_nat @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_96_mem__Collect__eq, axiom,
    ((![A2 : event, P : event > $o]: ((member_event @ A2 @ (collect_event @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_97_mem__Collect__eq, axiom,
    ((![A2 : agent, P : agent > $o]: ((member_agent @ A2 @ (collect_agent @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_98_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_99_Collect__mem__eq, axiom,
    ((![A : set_msg]: ((collect_msg @ (^[X5 : msg]: (member_msg @ X5 @ A))) = A)))). % Collect_mem_eq
thf(fact_100_Collect__mem__eq, axiom,
    ((![A : set_nat]: ((collect_nat @ (^[X5 : nat]: (member_nat @ X5 @ A))) = A)))). % Collect_mem_eq
thf(fact_101_Collect__mem__eq, axiom,
    ((![A : set_event]: ((collect_event @ (^[X5 : event]: (member_event @ X5 @ A))) = A)))). % Collect_mem_eq
thf(fact_102_Collect__mem__eq, axiom,
    ((![A : set_agent]: ((collect_agent @ (^[X5 : agent]: (member_agent @ X5 @ A))) = A)))). % Collect_mem_eq
thf(fact_103_inf__sup__aci_I6_J, axiom,
    ((![X : set_msg, Y : set_msg, Z : set_msg]: ((sup_sup_set_msg @ (sup_sup_set_msg @ X @ Y) @ Z) = (sup_sup_set_msg @ X @ (sup_sup_set_msg @ Y @ Z)))))). % inf_sup_aci(6)
thf(fact_104_inf__sup__aci_I6_J, axiom,
    ((![X : set_nat, Y : set_nat, Z : set_nat]: ((sup_sup_set_nat @ (sup_sup_set_nat @ X @ Y) @ Z) = (sup_sup_set_nat @ X @ (sup_sup_set_nat @ Y @ Z)))))). % inf_sup_aci(6)
thf(fact_105_inf__sup__aci_I6_J, axiom,
    ((![X : set_agent, Y : set_agent, Z : set_agent]: ((sup_sup_set_agent @ (sup_sup_set_agent @ X @ Y) @ Z) = (sup_sup_set_agent @ X @ (sup_sup_set_agent @ Y @ Z)))))). % inf_sup_aci(6)
thf(fact_106_inf__sup__aci_I7_J, axiom,
    ((![X : set_msg, Y : set_msg, Z : set_msg]: ((sup_sup_set_msg @ X @ (sup_sup_set_msg @ Y @ Z)) = (sup_sup_set_msg @ Y @ (sup_sup_set_msg @ X @ Z)))))). % inf_sup_aci(7)
thf(fact_107_inf__sup__aci_I7_J, axiom,
    ((![X : set_nat, Y : set_nat, Z : set_nat]: ((sup_sup_set_nat @ X @ (sup_sup_set_nat @ Y @ Z)) = (sup_sup_set_nat @ Y @ (sup_sup_set_nat @ X @ Z)))))). % inf_sup_aci(7)
thf(fact_108_inf__sup__aci_I7_J, axiom,
    ((![X : set_agent, Y : set_agent, Z : set_agent]: ((sup_sup_set_agent @ X @ (sup_sup_set_agent @ Y @ Z)) = (sup_sup_set_agent @ Y @ (sup_sup_set_agent @ X @ Z)))))). % inf_sup_aci(7)
thf(fact_109_inf__sup__aci_I8_J, axiom,
    ((![X : set_msg, Y : set_msg]: ((sup_sup_set_msg @ X @ (sup_sup_set_msg @ X @ Y)) = (sup_sup_set_msg @ X @ Y))))). % inf_sup_aci(8)
thf(fact_110_inf__sup__aci_I8_J, axiom,
    ((![X : set_nat, Y : set_nat]: ((sup_sup_set_nat @ X @ (sup_sup_set_nat @ X @ Y)) = (sup_sup_set_nat @ X @ Y))))). % inf_sup_aci(8)
thf(fact_111_inf__sup__aci_I8_J, axiom,
    ((![X : set_agent, Y : set_agent]: ((sup_sup_set_agent @ X @ (sup_sup_set_agent @ X @ Y)) = (sup_sup_set_agent @ X @ Y))))). % inf_sup_aci(8)
thf(fact_112_analz__analzD, axiom,
    ((![X2 : msg, H : set_msg]: ((member_msg @ X2 @ (analz @ (analz @ H))) => (member_msg @ X2 @ (analz @ H)))))). % analz_analzD
thf(fact_113_analz_OInj, axiom,
    ((![X2 : msg, H : set_msg]: ((member_msg @ X2 @ H) => (member_msg @ X2 @ (analz @ H)))))). % analz.Inj
thf(fact_114_symKeys__neq__imp__neq, axiom,
    ((![K : nat, K3 : nat]: ((~ (((member_nat @ K @ symKeys) = (member_nat @ K3 @ symKeys)))) => (~ ((K = K3))))))). % symKeys_neq_imp_neq
thf(fact_115_compl__le__swap2, axiom,
    ((![Y : set_agent, X : set_agent]: ((ord_le722097072_agent @ (uminus1992895513_agent @ Y) @ X) => (ord_le722097072_agent @ (uminus1992895513_agent @ X) @ Y))))). % compl_le_swap2
thf(fact_116_compl__le__swap2, axiom,
    ((![Y : set_nat, X : set_nat]: ((ord_less_eq_set_nat @ (uminus814679503et_nat @ Y) @ X) => (ord_less_eq_set_nat @ (uminus814679503et_nat @ X) @ Y))))). % compl_le_swap2
thf(fact_117_compl__le__swap2, axiom,
    ((![Y : set_msg, X : set_msg]: ((ord_less_eq_set_msg @ (uminus676873109et_msg @ Y) @ X) => (ord_less_eq_set_msg @ (uminus676873109et_msg @ X) @ Y))))). % compl_le_swap2
thf(fact_118_compl__le__swap1, axiom,
    ((![Y : set_agent, X : set_agent]: ((ord_le722097072_agent @ Y @ (uminus1992895513_agent @ X)) => (ord_le722097072_agent @ X @ (uminus1992895513_agent @ Y)))))). % compl_le_swap1
thf(fact_119_compl__le__swap1, axiom,
    ((![Y : set_nat, X : set_nat]: ((ord_less_eq_set_nat @ Y @ (uminus814679503et_nat @ X)) => (ord_less_eq_set_nat @ X @ (uminus814679503et_nat @ Y)))))). % compl_le_swap1
thf(fact_120_compl__le__swap1, axiom,
    ((![Y : set_msg, X : set_msg]: ((ord_less_eq_set_msg @ Y @ (uminus676873109et_msg @ X)) => (ord_less_eq_set_msg @ X @ (uminus676873109et_msg @ Y)))))). % compl_le_swap1
thf(fact_121_compl__mono, axiom,
    ((![X : set_agent, Y : set_agent]: ((ord_le722097072_agent @ X @ Y) => (ord_le722097072_agent @ (uminus1992895513_agent @ Y) @ (uminus1992895513_agent @ X)))))). % compl_mono
thf(fact_122_compl__mono, axiom,
    ((![X : set_nat, Y : set_nat]: ((ord_less_eq_set_nat @ X @ Y) => (ord_less_eq_set_nat @ (uminus814679503et_nat @ Y) @ (uminus814679503et_nat @ X)))))). % compl_mono
thf(fact_123_compl__mono, axiom,
    ((![X : set_msg, Y : set_msg]: ((ord_less_eq_set_msg @ X @ Y) => (ord_less_eq_set_msg @ (uminus676873109et_msg @ Y) @ (uminus676873109et_msg @ X)))))). % compl_mono
thf(fact_124_sup_OcoboundedI2, axiom,
    ((![C : set_agent, B2 : set_agent, A2 : set_agent]: ((ord_le722097072_agent @ C @ B2) => (ord_le722097072_agent @ C @ (sup_sup_set_agent @ A2 @ B2)))))). % sup.coboundedI2
thf(fact_125_sup_OcoboundedI2, axiom,
    ((![C : set_nat, B2 : set_nat, A2 : set_nat]: ((ord_less_eq_set_nat @ C @ B2) => (ord_less_eq_set_nat @ C @ (sup_sup_set_nat @ A2 @ B2)))))). % sup.coboundedI2
thf(fact_126_sup_OcoboundedI2, axiom,
    ((![C : set_msg, B2 : set_msg, A2 : set_msg]: ((ord_less_eq_set_msg @ C @ B2) => (ord_less_eq_set_msg @ C @ (sup_sup_set_msg @ A2 @ B2)))))). % sup.coboundedI2
thf(fact_127_sup_OcoboundedI2, axiom,
    ((![C : nat, B2 : nat, A2 : nat]: ((ord_less_eq_nat @ C @ B2) => (ord_less_eq_nat @ C @ (sup_sup_nat @ A2 @ B2)))))). % sup.coboundedI2
thf(fact_128_sup_OcoboundedI1, axiom,
    ((![C : set_agent, A2 : set_agent, B2 : set_agent]: ((ord_le722097072_agent @ C @ A2) => (ord_le722097072_agent @ C @ (sup_sup_set_agent @ A2 @ B2)))))). % sup.coboundedI1
thf(fact_129_sup_OcoboundedI1, axiom,
    ((![C : set_nat, A2 : set_nat, B2 : set_nat]: ((ord_less_eq_set_nat @ C @ A2) => (ord_less_eq_set_nat @ C @ (sup_sup_set_nat @ A2 @ B2)))))). % sup.coboundedI1
thf(fact_130_sup_OcoboundedI1, axiom,
    ((![C : set_msg, A2 : set_msg, B2 : set_msg]: ((ord_less_eq_set_msg @ C @ A2) => (ord_less_eq_set_msg @ C @ (sup_sup_set_msg @ A2 @ B2)))))). % sup.coboundedI1
thf(fact_131_sup_OcoboundedI1, axiom,
    ((![C : nat, A2 : nat, B2 : nat]: ((ord_less_eq_nat @ C @ A2) => (ord_less_eq_nat @ C @ (sup_sup_nat @ A2 @ B2)))))). % sup.coboundedI1
thf(fact_132_sup_Oabsorb__iff2, axiom,
    ((ord_le722097072_agent = (^[A3 : set_agent]: (^[B3 : set_agent]: ((sup_sup_set_agent @ A3 @ B3) = B3)))))). % sup.absorb_iff2
thf(fact_133_sup_Oabsorb__iff2, axiom,
    ((ord_less_eq_set_nat = (^[A3 : set_nat]: (^[B3 : set_nat]: ((sup_sup_set_nat @ A3 @ B3) = B3)))))). % sup.absorb_iff2
thf(fact_134_sup_Oabsorb__iff2, axiom,
    ((ord_less_eq_set_msg = (^[A3 : set_msg]: (^[B3 : set_msg]: ((sup_sup_set_msg @ A3 @ B3) = B3)))))). % sup.absorb_iff2
thf(fact_135_sup_Oabsorb__iff2, axiom,
    ((ord_less_eq_nat = (^[A3 : nat]: (^[B3 : nat]: ((sup_sup_nat @ A3 @ B3) = B3)))))). % sup.absorb_iff2
thf(fact_136_sup_Oabsorb__iff1, axiom,
    ((ord_le722097072_agent = (^[B3 : set_agent]: (^[A3 : set_agent]: ((sup_sup_set_agent @ A3 @ B3) = A3)))))). % sup.absorb_iff1
thf(fact_137_sup_Oabsorb__iff1, axiom,
    ((ord_less_eq_set_nat = (^[B3 : set_nat]: (^[A3 : set_nat]: ((sup_sup_set_nat @ A3 @ B3) = A3)))))). % sup.absorb_iff1
thf(fact_138_sup_Oabsorb__iff1, axiom,
    ((ord_less_eq_set_msg = (^[B3 : set_msg]: (^[A3 : set_msg]: ((sup_sup_set_msg @ A3 @ B3) = A3)))))). % sup.absorb_iff1
thf(fact_139_sup_Oabsorb__iff1, axiom,
    ((ord_less_eq_nat = (^[B3 : nat]: (^[A3 : nat]: ((sup_sup_nat @ A3 @ B3) = A3)))))). % sup.absorb_iff1
thf(fact_140_sup_Ocobounded2, axiom,
    ((![B2 : set_agent, A2 : set_agent]: (ord_le722097072_agent @ B2 @ (sup_sup_set_agent @ A2 @ B2))))). % sup.cobounded2
thf(fact_141_sup_Ocobounded2, axiom,
    ((![B2 : set_nat, A2 : set_nat]: (ord_less_eq_set_nat @ B2 @ (sup_sup_set_nat @ A2 @ B2))))). % sup.cobounded2
thf(fact_142_sup_Ocobounded2, axiom,
    ((![B2 : set_msg, A2 : set_msg]: (ord_less_eq_set_msg @ B2 @ (sup_sup_set_msg @ A2 @ B2))))). % sup.cobounded2
thf(fact_143_sup_Ocobounded2, axiom,
    ((![B2 : nat, A2 : nat]: (ord_less_eq_nat @ B2 @ (sup_sup_nat @ A2 @ B2))))). % sup.cobounded2
thf(fact_144_sup_Ocobounded1, axiom,
    ((![A2 : set_agent, B2 : set_agent]: (ord_le722097072_agent @ A2 @ (sup_sup_set_agent @ A2 @ B2))))). % sup.cobounded1
thf(fact_145_sup_Ocobounded1, axiom,
    ((![A2 : set_nat, B2 : set_nat]: (ord_less_eq_set_nat @ A2 @ (sup_sup_set_nat @ A2 @ B2))))). % sup.cobounded1
thf(fact_146_sup_Ocobounded1, axiom,
    ((![A2 : set_msg, B2 : set_msg]: (ord_less_eq_set_msg @ A2 @ (sup_sup_set_msg @ A2 @ B2))))). % sup.cobounded1
thf(fact_147_sup_Ocobounded1, axiom,
    ((![A2 : nat, B2 : nat]: (ord_less_eq_nat @ A2 @ (sup_sup_nat @ A2 @ B2))))). % sup.cobounded1
thf(fact_148_sup_Oorder__iff, axiom,
    ((ord_le722097072_agent = (^[B3 : set_agent]: (^[A3 : set_agent]: (A3 = (sup_sup_set_agent @ A3 @ B3))))))). % sup.order_iff
thf(fact_149_sup_Oorder__iff, axiom,
    ((ord_less_eq_set_nat = (^[B3 : set_nat]: (^[A3 : set_nat]: (A3 = (sup_sup_set_nat @ A3 @ B3))))))). % sup.order_iff
thf(fact_150_sup_Oorder__iff, axiom,
    ((ord_less_eq_set_msg = (^[B3 : set_msg]: (^[A3 : set_msg]: (A3 = (sup_sup_set_msg @ A3 @ B3))))))). % sup.order_iff
thf(fact_151_sup_Oorder__iff, axiom,
    ((ord_less_eq_nat = (^[B3 : nat]: (^[A3 : nat]: (A3 = (sup_sup_nat @ A3 @ B3))))))). % sup.order_iff
thf(fact_152_sup_OboundedI, axiom,
    ((![B2 : set_agent, A2 : set_agent, C : set_agent]: ((ord_le722097072_agent @ B2 @ A2) => ((ord_le722097072_agent @ C @ A2) => (ord_le722097072_agent @ (sup_sup_set_agent @ B2 @ C) @ A2)))))). % sup.boundedI
thf(fact_153_sup_OboundedI, axiom,
    ((![B2 : set_nat, A2 : set_nat, C : set_nat]: ((ord_less_eq_set_nat @ B2 @ A2) => ((ord_less_eq_set_nat @ C @ A2) => (ord_less_eq_set_nat @ (sup_sup_set_nat @ B2 @ C) @ A2)))))). % sup.boundedI
thf(fact_154_sup_OboundedI, axiom,
    ((![B2 : set_msg, A2 : set_msg, C : set_msg]: ((ord_less_eq_set_msg @ B2 @ A2) => ((ord_less_eq_set_msg @ C @ A2) => (ord_less_eq_set_msg @ (sup_sup_set_msg @ B2 @ C) @ A2)))))). % sup.boundedI
thf(fact_155_sup_OboundedI, axiom,
    ((![B2 : nat, A2 : nat, C : nat]: ((ord_less_eq_nat @ B2 @ A2) => ((ord_less_eq_nat @ C @ A2) => (ord_less_eq_nat @ (sup_sup_nat @ B2 @ C) @ A2)))))). % sup.boundedI
thf(fact_156_sup_OboundedE, axiom,
    ((![B2 : set_agent, C : set_agent, A2 : set_agent]: ((ord_le722097072_agent @ (sup_sup_set_agent @ B2 @ C) @ A2) => (~ (((ord_le722097072_agent @ B2 @ A2) => (~ ((ord_le722097072_agent @ C @ A2)))))))))). % sup.boundedE
thf(fact_157_sup_OboundedE, axiom,
    ((![B2 : set_nat, C : set_nat, A2 : set_nat]: ((ord_less_eq_set_nat @ (sup_sup_set_nat @ B2 @ C) @ A2) => (~ (((ord_less_eq_set_nat @ B2 @ A2) => (~ ((ord_less_eq_set_nat @ C @ A2)))))))))). % sup.boundedE
thf(fact_158_sup_OboundedE, axiom,
    ((![B2 : set_msg, C : set_msg, A2 : set_msg]: ((ord_less_eq_set_msg @ (sup_sup_set_msg @ B2 @ C) @ A2) => (~ (((ord_less_eq_set_msg @ B2 @ A2) => (~ ((ord_less_eq_set_msg @ C @ A2)))))))))). % sup.boundedE
thf(fact_159_sup_OboundedE, axiom,
    ((![B2 : nat, C : nat, A2 : nat]: ((ord_less_eq_nat @ (sup_sup_nat @ B2 @ C) @ A2) => (~ (((ord_less_eq_nat @ B2 @ A2) => (~ ((ord_less_eq_nat @ C @ A2)))))))))). % sup.boundedE
thf(fact_160_sup__absorb2, axiom,
    ((![X : set_agent, Y : set_agent]: ((ord_le722097072_agent @ X @ Y) => ((sup_sup_set_agent @ X @ Y) = Y))))). % sup_absorb2
thf(fact_161_sup__absorb2, axiom,
    ((![X : set_nat, Y : set_nat]: ((ord_less_eq_set_nat @ X @ Y) => ((sup_sup_set_nat @ X @ Y) = Y))))). % sup_absorb2
thf(fact_162_sup__absorb2, axiom,
    ((![X : set_msg, Y : set_msg]: ((ord_less_eq_set_msg @ X @ Y) => ((sup_sup_set_msg @ X @ Y) = Y))))). % sup_absorb2
thf(fact_163_sup__absorb2, axiom,
    ((![X : nat, Y : nat]: ((ord_less_eq_nat @ X @ Y) => ((sup_sup_nat @ X @ Y) = Y))))). % sup_absorb2
thf(fact_164_sup__absorb1, axiom,
    ((![Y : set_agent, X : set_agent]: ((ord_le722097072_agent @ Y @ X) => ((sup_sup_set_agent @ X @ Y) = X))))). % sup_absorb1
thf(fact_165_sup__absorb1, axiom,
    ((![Y : set_nat, X : set_nat]: ((ord_less_eq_set_nat @ Y @ X) => ((sup_sup_set_nat @ X @ Y) = X))))). % sup_absorb1
thf(fact_166_sup__absorb1, axiom,
    ((![Y : set_msg, X : set_msg]: ((ord_less_eq_set_msg @ Y @ X) => ((sup_sup_set_msg @ X @ Y) = X))))). % sup_absorb1
thf(fact_167_sup__absorb1, axiom,
    ((![Y : nat, X : nat]: ((ord_less_eq_nat @ Y @ X) => ((sup_sup_nat @ X @ Y) = X))))). % sup_absorb1
thf(fact_168_sup_Oabsorb2, axiom,
    ((![A2 : set_agent, B2 : set_agent]: ((ord_le722097072_agent @ A2 @ B2) => ((sup_sup_set_agent @ A2 @ B2) = B2))))). % sup.absorb2
thf(fact_169_sup_Oabsorb2, axiom,
    ((![A2 : set_nat, B2 : set_nat]: ((ord_less_eq_set_nat @ A2 @ B2) => ((sup_sup_set_nat @ A2 @ B2) = B2))))). % sup.absorb2
thf(fact_170_sup_Oabsorb2, axiom,
    ((![A2 : set_msg, B2 : set_msg]: ((ord_less_eq_set_msg @ A2 @ B2) => ((sup_sup_set_msg @ A2 @ B2) = B2))))). % sup.absorb2
thf(fact_171_sup_Oabsorb2, axiom,
    ((![A2 : nat, B2 : nat]: ((ord_less_eq_nat @ A2 @ B2) => ((sup_sup_nat @ A2 @ B2) = B2))))). % sup.absorb2
thf(fact_172_sup_Oabsorb1, axiom,
    ((![B2 : set_agent, A2 : set_agent]: ((ord_le722097072_agent @ B2 @ A2) => ((sup_sup_set_agent @ A2 @ B2) = A2))))). % sup.absorb1
thf(fact_173_sup_Oabsorb1, axiom,
    ((![B2 : set_nat, A2 : set_nat]: ((ord_less_eq_set_nat @ B2 @ A2) => ((sup_sup_set_nat @ A2 @ B2) = A2))))). % sup.absorb1
thf(fact_174_sup_Oabsorb1, axiom,
    ((![B2 : set_msg, A2 : set_msg]: ((ord_less_eq_set_msg @ B2 @ A2) => ((sup_sup_set_msg @ A2 @ B2) = A2))))). % sup.absorb1
thf(fact_175_sup_Oabsorb1, axiom,
    ((![B2 : nat, A2 : nat]: ((ord_less_eq_nat @ B2 @ A2) => ((sup_sup_nat @ A2 @ B2) = A2))))). % sup.absorb1
thf(fact_176_sup__unique, axiom,
    ((![F : set_agent > set_agent > set_agent, X : set_agent, Y : set_agent]: ((![X6 : set_agent, Y5 : set_agent]: (ord_le722097072_agent @ X6 @ (F @ X6 @ Y5))) => ((![X6 : set_agent, Y5 : set_agent]: (ord_le722097072_agent @ Y5 @ (F @ X6 @ Y5))) => ((![X6 : set_agent, Y5 : set_agent, Z2 : set_agent]: ((ord_le722097072_agent @ Y5 @ X6) => ((ord_le722097072_agent @ Z2 @ X6) => (ord_le722097072_agent @ (F @ Y5 @ Z2) @ X6)))) => ((sup_sup_set_agent @ X @ Y) = (F @ X @ Y)))))))). % sup_unique
thf(fact_177_sup__unique, axiom,
    ((![F : set_nat > set_nat > set_nat, X : set_nat, Y : set_nat]: ((![X6 : set_nat, Y5 : set_nat]: (ord_less_eq_set_nat @ X6 @ (F @ X6 @ Y5))) => ((![X6 : set_nat, Y5 : set_nat]: (ord_less_eq_set_nat @ Y5 @ (F @ X6 @ Y5))) => ((![X6 : set_nat, Y5 : set_nat, Z2 : set_nat]: ((ord_less_eq_set_nat @ Y5 @ X6) => ((ord_less_eq_set_nat @ Z2 @ X6) => (ord_less_eq_set_nat @ (F @ Y5 @ Z2) @ X6)))) => ((sup_sup_set_nat @ X @ Y) = (F @ X @ Y)))))))). % sup_unique
thf(fact_178_sup__unique, axiom,
    ((![F : set_msg > set_msg > set_msg, X : set_msg, Y : set_msg]: ((![X6 : set_msg, Y5 : set_msg]: (ord_less_eq_set_msg @ X6 @ (F @ X6 @ Y5))) => ((![X6 : set_msg, Y5 : set_msg]: (ord_less_eq_set_msg @ Y5 @ (F @ X6 @ Y5))) => ((![X6 : set_msg, Y5 : set_msg, Z2 : set_msg]: ((ord_less_eq_set_msg @ Y5 @ X6) => ((ord_less_eq_set_msg @ Z2 @ X6) => (ord_less_eq_set_msg @ (F @ Y5 @ Z2) @ X6)))) => ((sup_sup_set_msg @ X @ Y) = (F @ X @ Y)))))))). % sup_unique
thf(fact_179_sup__unique, axiom,
    ((![F : nat > nat > nat, X : nat, Y : nat]: ((![X6 : nat, Y5 : nat]: (ord_less_eq_nat @ X6 @ (F @ X6 @ Y5))) => ((![X6 : nat, Y5 : nat]: (ord_less_eq_nat @ Y5 @ (F @ X6 @ Y5))) => ((![X6 : nat, Y5 : nat, Z2 : nat]: ((ord_less_eq_nat @ Y5 @ X6) => ((ord_less_eq_nat @ Z2 @ X6) => (ord_less_eq_nat @ (F @ Y5 @ Z2) @ X6)))) => ((sup_sup_nat @ X @ Y) = (F @ X @ Y)))))))). % sup_unique
thf(fact_180_sup_OorderI, axiom,
    ((![A2 : set_agent, B2 : set_agent]: ((A2 = (sup_sup_set_agent @ A2 @ B2)) => (ord_le722097072_agent @ B2 @ A2))))). % sup.orderI
thf(fact_181_sup_OorderI, axiom,
    ((![A2 : set_nat, B2 : set_nat]: ((A2 = (sup_sup_set_nat @ A2 @ B2)) => (ord_less_eq_set_nat @ B2 @ A2))))). % sup.orderI
thf(fact_182_sup_OorderI, axiom,
    ((![A2 : set_msg, B2 : set_msg]: ((A2 = (sup_sup_set_msg @ A2 @ B2)) => (ord_less_eq_set_msg @ B2 @ A2))))). % sup.orderI
thf(fact_183_sup_OorderI, axiom,
    ((![A2 : nat, B2 : nat]: ((A2 = (sup_sup_nat @ A2 @ B2)) => (ord_less_eq_nat @ B2 @ A2))))). % sup.orderI
thf(fact_184_sup_OorderE, axiom,
    ((![B2 : set_agent, A2 : set_agent]: ((ord_le722097072_agent @ B2 @ A2) => (A2 = (sup_sup_set_agent @ A2 @ B2)))))). % sup.orderE
thf(fact_185_sup_OorderE, axiom,
    ((![B2 : set_nat, A2 : set_nat]: ((ord_less_eq_set_nat @ B2 @ A2) => (A2 = (sup_sup_set_nat @ A2 @ B2)))))). % sup.orderE
thf(fact_186_sup_OorderE, axiom,
    ((![B2 : set_msg, A2 : set_msg]: ((ord_less_eq_set_msg @ B2 @ A2) => (A2 = (sup_sup_set_msg @ A2 @ B2)))))). % sup.orderE
thf(fact_187_sup_OorderE, axiom,
    ((![B2 : nat, A2 : nat]: ((ord_less_eq_nat @ B2 @ A2) => (A2 = (sup_sup_nat @ A2 @ B2)))))). % sup.orderE
thf(fact_188_le__iff__sup, axiom,
    ((ord_le722097072_agent = (^[X5 : set_agent]: (^[Y2 : set_agent]: ((sup_sup_set_agent @ X5 @ Y2) = Y2)))))). % le_iff_sup
thf(fact_189_le__iff__sup, axiom,
    ((ord_less_eq_set_nat = (^[X5 : set_nat]: (^[Y2 : set_nat]: ((sup_sup_set_nat @ X5 @ Y2) = Y2)))))). % le_iff_sup
thf(fact_190_le__iff__sup, axiom,
    ((ord_less_eq_set_msg = (^[X5 : set_msg]: (^[Y2 : set_msg]: ((sup_sup_set_msg @ X5 @ Y2) = Y2)))))). % le_iff_sup
thf(fact_191_le__iff__sup, axiom,
    ((ord_less_eq_nat = (^[X5 : nat]: (^[Y2 : nat]: ((sup_sup_nat @ X5 @ Y2) = Y2)))))). % le_iff_sup
thf(fact_192_sup__least, axiom,
    ((![Y : set_agent, X : set_agent, Z : set_agent]: ((ord_le722097072_agent @ Y @ X) => ((ord_le722097072_agent @ Z @ X) => (ord_le722097072_agent @ (sup_sup_set_agent @ Y @ Z) @ X)))))). % sup_least
thf(fact_193_sup__least, axiom,
    ((![Y : set_nat, X : set_nat, Z : set_nat]: ((ord_less_eq_set_nat @ Y @ X) => ((ord_less_eq_set_nat @ Z @ X) => (ord_less_eq_set_nat @ (sup_sup_set_nat @ Y @ Z) @ X)))))). % sup_least
thf(fact_194_sup__least, axiom,
    ((![Y : set_msg, X : set_msg, Z : set_msg]: ((ord_less_eq_set_msg @ Y @ X) => ((ord_less_eq_set_msg @ Z @ X) => (ord_less_eq_set_msg @ (sup_sup_set_msg @ Y @ Z) @ X)))))). % sup_least
thf(fact_195_sup__least, axiom,
    ((![Y : nat, X : nat, Z : nat]: ((ord_less_eq_nat @ Y @ X) => ((ord_less_eq_nat @ Z @ X) => (ord_less_eq_nat @ (sup_sup_nat @ Y @ Z) @ X)))))). % sup_least
thf(fact_196_sup__mono, axiom,
    ((![A2 : set_agent, C : set_agent, B2 : set_agent, D : set_agent]: ((ord_le722097072_agent @ A2 @ C) => ((ord_le722097072_agent @ B2 @ D) => (ord_le722097072_agent @ (sup_sup_set_agent @ A2 @ B2) @ (sup_sup_set_agent @ C @ D))))))). % sup_mono
thf(fact_197_sup__mono, axiom,
    ((![A2 : set_nat, C : set_nat, B2 : set_nat, D : set_nat]: ((ord_less_eq_set_nat @ A2 @ C) => ((ord_less_eq_set_nat @ B2 @ D) => (ord_less_eq_set_nat @ (sup_sup_set_nat @ A2 @ B2) @ (sup_sup_set_nat @ C @ D))))))). % sup_mono
thf(fact_198_sup__mono, axiom,
    ((![A2 : set_msg, C : set_msg, B2 : set_msg, D : set_msg]: ((ord_less_eq_set_msg @ A2 @ C) => ((ord_less_eq_set_msg @ B2 @ D) => (ord_less_eq_set_msg @ (sup_sup_set_msg @ A2 @ B2) @ (sup_sup_set_msg @ C @ D))))))). % sup_mono
thf(fact_199_sup__mono, axiom,
    ((![A2 : nat, C : nat, B2 : nat, D : nat]: ((ord_less_eq_nat @ A2 @ C) => ((ord_less_eq_nat @ B2 @ D) => (ord_less_eq_nat @ (sup_sup_nat @ A2 @ B2) @ (sup_sup_nat @ C @ D))))))). % sup_mono
thf(fact_200_sup_Omono, axiom,
    ((![C : set_agent, A2 : set_agent, D : set_agent, B2 : set_agent]: ((ord_le722097072_agent @ C @ A2) => ((ord_le722097072_agent @ D @ B2) => (ord_le722097072_agent @ (sup_sup_set_agent @ C @ D) @ (sup_sup_set_agent @ A2 @ B2))))))). % sup.mono
thf(fact_201_sup_Omono, axiom,
    ((![C : set_nat, A2 : set_nat, D : set_nat, B2 : set_nat]: ((ord_less_eq_set_nat @ C @ A2) => ((ord_less_eq_set_nat @ D @ B2) => (ord_less_eq_set_nat @ (sup_sup_set_nat @ C @ D) @ (sup_sup_set_nat @ A2 @ B2))))))). % sup.mono
thf(fact_202_sup_Omono, axiom,
    ((![C : set_msg, A2 : set_msg, D : set_msg, B2 : set_msg]: ((ord_less_eq_set_msg @ C @ A2) => ((ord_less_eq_set_msg @ D @ B2) => (ord_less_eq_set_msg @ (sup_sup_set_msg @ C @ D) @ (sup_sup_set_msg @ A2 @ B2))))))). % sup.mono
thf(fact_203_sup_Omono, axiom,
    ((![C : nat, A2 : nat, D : nat, B2 : nat]: ((ord_less_eq_nat @ C @ A2) => ((ord_less_eq_nat @ D @ B2) => (ord_less_eq_nat @ (sup_sup_nat @ C @ D) @ (sup_sup_nat @ A2 @ B2))))))). % sup.mono
thf(fact_204_le__supI2, axiom,
    ((![X : set_nat, B2 : set_nat, A2 : set_nat]: ((ord_less_eq_set_nat @ X @ B2) => (ord_less_eq_set_nat @ X @ (sup_sup_set_nat @ A2 @ B2)))))). % le_supI2
thf(fact_205_le__supI2, axiom,
    ((![X : set_msg, B2 : set_msg, A2 : set_msg]: ((ord_less_eq_set_msg @ X @ B2) => (ord_less_eq_set_msg @ X @ (sup_sup_set_msg @ A2 @ B2)))))). % le_supI2
thf(fact_206_le__supI2, axiom,
    ((![X : nat, B2 : nat, A2 : nat]: ((ord_less_eq_nat @ X @ B2) => (ord_less_eq_nat @ X @ (sup_sup_nat @ A2 @ B2)))))). % le_supI2
thf(fact_207_MPair__analz, axiom,
    ((![X2 : msg, Y6 : msg, H : set_msg]: ((member_msg @ (mPair @ X2 @ Y6) @ (analz @ H)) => (~ (((member_msg @ X2 @ (analz @ H)) => (~ ((member_msg @ Y6 @ (analz @ H))))))))))). % MPair_analz
thf(fact_208_analz_OSnd, axiom,
    ((![X2 : msg, Y6 : msg, H : set_msg]: ((member_msg @ (mPair @ X2 @ Y6) @ (analz @ H)) => (member_msg @ Y6 @ (analz @ H)))))). % analz.Snd
thf(fact_209_analz_OFst, axiom,
    ((![X2 : msg, Y6 : msg, H : set_msg]: ((member_msg @ (mPair @ X2 @ Y6) @ (analz @ H)) => (member_msg @ X2 @ (analz @ H)))))). % analz.Fst
thf(fact_210_msg_Odistinct_I33_J, axiom,
    ((![X4 : nat, X61 : msg, X62 : msg]: (~ (((key @ X4) = (mPair @ X61 @ X62))))))). % msg.distinct(33)
thf(fact_211_msg_Odistinct_I27_J, axiom,
    ((![X3 : nat, X61 : msg, X62 : msg]: (~ (((nonce @ X3) = (mPair @ X61 @ X62))))))). % msg.distinct(27)
thf(fact_212_msg_Odistinct_I9_J, axiom,
    ((![X1 : agent, X61 : msg, X62 : msg]: (~ (((agent2 @ X1) = (mPair @ X61 @ X62))))))). % msg.distinct(9)
thf(fact_213_msg_Odistinct_I23_J, axiom,
    ((![X3 : nat, X4 : nat]: (~ (((nonce @ X3) = (key @ X4))))))). % msg.distinct(23)
thf(fact_214_analz__cong, axiom,
    ((![G : set_msg, G2 : set_msg, H : set_msg, H2 : set_msg]: (((analz @ G) = (analz @ G2)) => (((analz @ H) = (analz @ H2)) => ((analz @ (sup_sup_set_msg @ G @ H)) = (analz @ (sup_sup_set_msg @ G2 @ H2)))))))). % analz_cong
thf(fact_215_analz__image__freshK__simps_I63_J, axiom,
    ((![C : msg, G : set_msg, A : set_msg]: ((member_msg @ C @ (analz @ G)) => (member_msg @ C @ (analz @ (sup_sup_set_msg @ A @ G))))))). % analz_image_freshK_simps(63)
thf(fact_216_msg_Odistinct_I5_J, axiom,
    ((![X1 : agent, X4 : nat]: (~ (((agent2 @ X1) = (key @ X4))))))). % msg.distinct(5)
thf(fact_217_MPair__used__D, axiom,
    ((![X2 : msg, Y6 : msg, H : list_event]: ((member_msg @ (mPair @ X2 @ Y6) @ (used @ H)) => ((member_msg @ X2 @ (used @ H)) & (member_msg @ Y6 @ (used @ H))))))). % MPair_used_D
thf(fact_218_MPair__used, axiom,
    ((![X2 : msg, Y6 : msg, H : list_event]: ((member_msg @ (mPair @ X2 @ Y6) @ (used @ H)) => (~ (((member_msg @ X2 @ (used @ H)) => (~ ((member_msg @ Y6 @ (used @ H))))))))))). % MPair_used
thf(fact_219_msg_Odistinct_I3_J, axiom,
    ((![X1 : agent, X3 : nat]: (~ (((agent2 @ X1) = (nonce @ X3))))))). % msg.distinct(3)
thf(fact_220_Nonce__supply1, axiom,
    ((![Evs : list_event]: (?[N2 : nat]: (~ ((member_msg @ (nonce @ N2) @ (used @ Evs)))))))). % Nonce_supply1
thf(fact_221_agent_Odistinct_I3_J, axiom,
    ((~ ((server = spy))))). % agent.distinct(3)
thf(fact_222_analz__impI, axiom,
    ((![Y6 : msg, Evs : list_event, Q : $o]: (((~ ((member_msg @ Y6 @ (analz @ (knows @ spy @ Evs))))) => Q) => ((~ ((member_msg @ Y6 @ (analz @ (knows @ spy @ Evs))))) => Q))))). % analz_impI
thf(fact_223_shrK__neq, axiom,
    ((![K : nat, Evs : list_event, B : agent]: ((~ ((member_msg @ (key @ K) @ (used @ Evs)))) => (~ (((shrK @ B) = K))))))). % shrK_neq
thf(fact_224_neq__shrK, axiom,
    ((![S : nat, Evs : list_event, B : agent]: ((~ ((member_msg @ (key @ S) @ (used @ Evs)))) => (~ ((S = (shrK @ B)))))))). % neq_shrK
thf(fact_225_Nonce__Key__image__eq, axiom,
    ((![X : nat, A : set_nat]: (~ ((member_msg @ (nonce @ X) @ (image_nat_msg @ key @ A))))))). % Nonce_Key_image_eq
thf(fact_226_Says__imp__knows, axiom,
    ((![A : agent, B : agent, X2 : msg, Evs : list_event]: ((member_event @ (says @ A @ B @ X2) @ (set_event2 @ Evs)) => (member_msg @ X2 @ (knows @ A @ Evs)))))). % Says_imp_knows
thf(fact_227_Says__imp__used, axiom,
    ((![A : agent, B : agent, X2 : msg, Evs : list_event]: ((member_event @ (says @ A @ B @ X2) @ (set_event2 @ Evs)) => (member_msg @ X2 @ (used @ Evs)))))). % Says_imp_used
thf(fact_228_analz__image__freshK__lemma, axiom,
    ((![K : nat, NE : set_nat, H : set_msg]: (((member_msg @ (key @ K) @ (analz @ (sup_sup_set_msg @ (image_nat_msg @ key @ NE) @ H))) => ((member_nat @ K @ NE) | (member_msg @ (key @ K) @ (analz @ H)))) => ((member_msg @ (key @ K) @ (analz @ (sup_sup_set_msg @ (image_nat_msg @ key @ NE) @ H))) = (((member_nat @ K @ NE)) | ((member_msg @ (key @ K) @ (analz @ H))))))))). % analz_image_freshK_lemma
thf(fact_229_Says__imp__knows__Spy, axiom,
    ((![A : agent, B : agent, X2 : msg, Evs : list_event]: ((member_event @ (says @ A @ B @ X2) @ (set_event2 @ Evs)) => (member_msg @ X2 @ (knows @ spy @ Evs)))))). % Says_imp_knows_Spy
thf(fact_230_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_231_Says__S__message__form, axiom,
    ((![S2 : agent, A : agent, NA : nat, B : agent, K : nat, X2 : msg, Evs : list_event]: ((member_event @ (says @ S2 @ A @ (crypt @ (shrK @ A) @ (mPair @ (nonce @ NA) @ (mPair @ (agent2 @ B) @ (mPair @ (key @ K) @ X2))))) @ (set_event2 @ Evs)) => ((member_list_event @ Evs @ nS_Sha1061662329shared) => (((~ ((member_nat @ K @ (image_agent_nat @ shrK @ top_top_set_agent)))) & (X2 = (crypt @ (shrK @ B) @ (mPair @ (key @ K) @ (agent2 @ A))))) | (member_msg @ X2 @ (analz @ (knows @ spy @ Evs))))))))). % Says_S_message_form
thf(fact_232_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_233_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_234_Spy__in__bad, axiom,
    ((member_agent @ spy @ bad))). % Spy_in_bad
thf(fact_235_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_236_msg_Odistinct_I41_J, axiom,
    ((![X61 : msg, X62 : msg, X71 : nat, X72 : msg]: (~ (((mPair @ X61 @ X62) = (crypt @ X71 @ X72))))))). % msg.distinct(41)
thf(fact_237_msg_Odistinct_I35_J, axiom,
    ((![X4 : nat, X71 : nat, X72 : msg]: (~ (((key @ X4) = (crypt @ X71 @ X72))))))). % msg.distinct(35)
thf(fact_238_msg_Odistinct_I29_J, axiom,
    ((![X3 : nat, X71 : nat, X72 : msg]: (~ (((nonce @ X3) = (crypt @ X71 @ X72))))))). % msg.distinct(29)
thf(fact_239_msg_Odistinct_I11_J, axiom,
    ((![X1 : agent, X71 : nat, X72 : msg]: (~ (((agent2 @ X1) = (crypt @ X71 @ X72))))))). % msg.distinct(11)
thf(fact_240_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_241_analz__trans, axiom,
    ((![X2 : msg, G : set_msg, H : set_msg]: ((member_msg @ X2 @ (analz @ G)) => ((ord_less_eq_set_msg @ G @ (analz @ H)) => (member_msg @ X2 @ (analz @ H))))))). % analz_trans
thf(fact_242_analz__increasing, axiom,
    ((![H : set_msg]: (ord_less_eq_set_msg @ H @ (analz @ H))))). % analz_increasing
thf(fact_243_analz__trivial, axiom,
    ((![H : set_msg]: ((![X7 : msg, Y7 : msg]: (~ ((member_msg @ (mPair @ X7 @ Y7) @ H)))) => ((![X7 : msg, K4 : nat]: (~ ((member_msg @ (crypt @ K4 @ X7) @ H)))) => ((analz @ H) = H)))))). % analz_trivial
thf(fact_244_Crypt__notin__image__Key, axiom,
    ((![K : nat, X2 : msg, A : set_nat]: (~ ((member_msg @ (crypt @ K @ X2) @ (image_nat_msg @ key @ A))))))). % Crypt_notin_image_Key
thf(fact_245_Server__not__bad, axiom,
    ((~ ((member_agent @ server @ bad))))). % Server_not_bad
thf(fact_246_analz__Un, axiom,
    ((![G : set_msg, H : set_msg]: (ord_less_eq_set_msg @ (sup_sup_set_msg @ (analz @ G) @ (analz @ H)) @ (analz @ (sup_sup_set_msg @ G @ H)))))). % analz_Un
thf(fact_247_analz__subset__cong, axiom,
    ((![G : set_msg, G2 : set_msg, H : set_msg, H2 : set_msg]: ((ord_less_eq_set_msg @ (analz @ G) @ (analz @ G2)) => ((ord_less_eq_set_msg @ (analz @ H) @ (analz @ H2)) => (ord_less_eq_set_msg @ (analz @ (sup_sup_set_msg @ G @ H)) @ (analz @ (sup_sup_set_msg @ G2 @ H2)))))))). % analz_subset_cong
thf(fact_248_Nonce__supply__lemma, axiom,
    ((![Evs : list_event]: (?[N2 : nat]: (![N3 : nat]: ((ord_less_eq_nat @ N2 @ N3) => (~ ((member_msg @ (nonce @ N3) @ (used @ Evs)))))))))). % Nonce_supply_lemma

% Conjectures (7)
thf(conj_0, hypothesis,
    ((member_list_event @ evs2 @ nS_Sha1061662329shared))).
thf(conj_1, hypothesis,
    ((![K5 : nat, KK : set_nat]: ((ord_less_eq_set_nat @ KK @ (uminus814679503et_nat @ (image_agent_nat @ shrK @ top_top_set_agent))) => ((member_msg @ (key @ K5) @ (analz @ (sup_sup_set_msg @ (image_nat_msg @ key @ KK) @ (knows @ spy @ evs2)))) = (((member_nat @ K5 @ KK)) | ((member_msg @ (key @ K5) @ (analz @ (knows @ spy @ evs2)))))))))).
thf(conj_2, hypothesis,
    ((~ ((member_msg @ (key @ kab) @ (used @ evs2)))))).
thf(conj_3, hypothesis,
    ((member_nat @ kab @ symKeys))).
thf(conj_4, hypothesis,
    ((member_event @ (says @ a2 @ server @ (mPair @ (agent2 @ a) @ (mPair @ (agent2 @ b) @ (nonce @ na)))) @ (set_event2 @ evs2)))).
thf(conj_5, hypothesis,
    ((ord_less_eq_set_nat @ kk @ (uminus814679503et_nat @ (image_agent_nat @ shrK @ top_top_set_agent))))).
thf(conj_6, conjecture,
    (((((~ (((shrK @ b) = kab))) & (~ ((member_msg @ (key @ (shrK @ b)) @ (analz @ (knows @ spy @ evs2)))))) | ((member_msg @ (key @ (shrK @ a)) @ (analz @ (knows @ spy @ evs2))) | ((((~ (((shrK @ b) = kab))) & ((~ ((member_nat @ (shrK @ b) @ kk))) & (~ ((member_msg @ (key @ (shrK @ b)) @ (analz @ (knows @ spy @ evs2))))))) | ((~ ((member_nat @ (shrK @ a) @ kk))) | (((~ ((k = kab))) & ((~ ((member_nat @ k @ kk))) & (~ ((member_msg @ (key @ k) @ (analz @ (knows @ spy @ evs2))))))) | ((member_nat @ k @ kk) | (member_msg @ (key @ k) @ (analz @ (knows @ spy @ evs2))))))) & ((((shrK @ b) = kab) | ((member_nat @ (shrK @ b) @ kk) | (member_msg @ (key @ (shrK @ b)) @ (analz @ (knows @ spy @ evs2))))) | ((~ ((member_nat @ (shrK @ a) @ kk))) | (((~ ((k = kab))) & ((~ ((member_nat @ k @ kk))) & (~ ((member_msg @ (key @ k) @ (analz @ (knows @ spy @ evs2))))))) | ((member_nat @ k @ kk) | (member_msg @ (key @ k) @ (analz @ (knows @ spy @ evs2)))))))))) & ((((shrK @ b) = kab) | (member_msg @ (key @ (shrK @ b)) @ (analz @ (knows @ spy @ evs2)))) | ((member_msg @ (key @ (shrK @ a)) @ (analz @ (knows @ spy @ evs2))) | ((~ ((member_nat @ (shrK @ a) @ kk))) | (((~ ((k = kab))) & ((~ ((member_nat @ k @ kk))) & (~ ((member_msg @ (key @ k) @ (analz @ (knows @ spy @ evs2))))))) | ((member_nat @ k @ kk) | (member_msg @ (key @ k) @ (analz @ (knows @ spy @ evs2))))))))))).
