% 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/Hoare/prob_337__3253366_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:13:50.411

% Could-be-implicit typings (17)
thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J_J, type,
    set_op1790085995_state : $tType).
thf(ty_n_t__Option__Ooption_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J, type,
    option1481361675_state : $tType).
thf(ty_n_t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J, type,
    set_Ho840737317_state : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Com__Opname_Mt__Com__Opname_J_J, type,
    set_Pr15211605_pname : $tType).
thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_It__Com__Opname_Mt__Com__Opname_J_J, type,
    set_Su1011432617_pname : $tType).
thf(ty_n_t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
    hoare_958474565_state : $tType).
thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Com__Opname_J_J, type,
    set_option_pname : $tType).
thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Com__Ocom_J_J, type,
    set_option_com : $tType).
thf(ty_n_t__Set__Oset_It__Set__Oset_It__Com__Opname_J_J, type,
    set_set_pname : $tType).
thf(ty_n_t__Option__Ooption_It__Com__Opname_J, type,
    option_pname : $tType).
thf(ty_n_t__Filter__Ofilter_It__Com__Opname_J, type,
    filter_pname : $tType).
thf(ty_n_t__Option__Ooption_It__Com__Ocom_J, type,
    option_com : $tType).
thf(ty_n_t__Set__Oset_It__Com__Opname_J, type,
    set_pname : $tType).
thf(ty_n_t__Set__Oset_It__Com__Ocom_J, type,
    set_com : $tType).
thf(ty_n_t__Com__Ostate, type,
    state : $tType).
thf(ty_n_t__Com__Opname, type,
    pname : $tType).
thf(ty_n_t__Com__Ocom, type,
    com : $tType).

% Explicit typings (66)
thf(sy_c_Com_OWT, type,
    wt : com > $o).
thf(sy_c_Com_OWT__bodies, type,
    wT_bodies : $o).
thf(sy_c_Com_Obody, type,
    body : pname > option_com).
thf(sy_c_Com_Ocom_OBODY, type,
    body2 : pname > com).
thf(sy_c_Com_Ocom_OSKIP, type,
    skip : com).
thf(sy_c_Com_Ocom_OSemi, type,
    semi : com > com > com).
thf(sy_c_Filter_Ocofinite_001t__Com__Opname, type,
    cofinite_pname : filter_pname).
thf(sy_c_Finite__Set_Ofinite_001t__Com__Ocom, type,
    finite_finite_com : set_com > $o).
thf(sy_c_Finite__Set_Ofinite_001t__Com__Opname, type,
    finite_finite_pname : set_pname > $o).
thf(sy_c_Finite__Set_Ofinite_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
    finite1986656878_state : set_Ho840737317_state > $o).
thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Com__Ocom_J, type,
    finite596631031on_com : set_option_com > $o).
thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Com__Opname_J, type,
    finite1292484209_pname : set_option_pname > $o).
thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Com__Opname_Mt__Com__Opname_J, type,
    finite1490780830_pname : set_Pr15211605_pname > $o).
thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Com__Opname_J, type,
    finite505202775_pname : set_set_pname > $o).
thf(sy_c_Finite__Set_Ofinite_001t__Sum____Type__Osum_It__Com__Opname_Mt__Com__Opname_J, type,
    finite1993869834_pname : set_Su1011432617_pname > $o).
thf(sy_c_Hoare__Mirabelle__raqjowkjvm_OMGT, type,
    hoare_Mirabelle_MGT : com > hoare_958474565_state).
thf(sy_c_Hoare__Mirabelle__raqjowkjvm_Ohoare__derivs_001t__Com__Ostate, type,
    hoare_604442164_state : set_Ho840737317_state > set_Ho840737317_state > $o).
thf(sy_c_Hoare__Mirabelle__raqjowkjvm_Ohoare__valids_001t__Com__Ostate, type,
    hoare_318887606_state : set_Ho840737317_state > set_Ho840737317_state > $o).
thf(sy_c_Hoare__Mirabelle__raqjowkjvm_Ostate__not__singleton, type,
    hoare_405891322gleton : $o).
thf(sy_c_Hoare__Mirabelle__raqjowkjvm_Otriple_Otriple_001t__Com__Ostate, type,
    hoare_1659279548_state : (state > state > $o) > com > (state > state > $o) > hoare_958474565_state).
thf(sy_c_Map_Odom_001t__Com__Opname_001t__Com__Ocom, type,
    dom_pname_com : (pname > option_com) > set_pname).
thf(sy_c_Map_Odom_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_001t__Com__Ocom, type,
    dom_Ho256784515te_com : (hoare_958474565_state > option_com) > set_Ho840737317_state).
thf(sy_c_Option_Ooption_ONone_001t__Com__Ocom, type,
    none_com : option_com).
thf(sy_c_Option_Ooption_ONone_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
    none_H2001963430_state : option1481361675_state).
thf(sy_c_Option_Ooption_OSome_001t__Com__Ocom, type,
    some_com : com > option_com).
thf(sy_c_Option_Ooption_OSome_001t__Com__Opname, type,
    some_pname : pname > option_pname).
thf(sy_c_Option_Ooption_OSome_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
    some_H1327573290_state : hoare_958474565_state > option1481361675_state).
thf(sy_c_Option_Ooption_Othe_001t__Com__Ocom, type,
    the_com : option_com > com).
thf(sy_c_Option_Othese_001t__Com__Ocom, type,
    these_com : set_option_com > set_com).
thf(sy_c_Option_Othese_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
    these_1282564994_state : set_op1790085995_state > set_Ho840737317_state).
thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_M_Eo_J, type,
    bot_bo1428770700tate_o : hoare_958474565_state > $o).
thf(sy_c_Orderings_Obot__class_Obot_001t__Filter__Ofilter_It__Com__Opname_J, type,
    bot_bot_filter_pname : filter_pname).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Com__Ocom_J, type,
    bot_bot_set_com : set_com).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Com__Opname_J, type,
    bot_bot_set_pname : set_pname).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J, type,
    bot_bo105666705_state : set_Ho840737317_state).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_It__Com__Ocom_J_J, type,
    bot_bo697186986on_com : set_option_com).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J_J, type,
    bot_bo472264663_state : set_op1790085995_state).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_M_Eo_J, type,
    top_to1619606952tate_o : hoare_958474565_state > $o).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Com__Ocom_J, type,
    top_top_set_com : set_com).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Com__Opname_J, type,
    top_top_set_pname : set_pname).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J, type,
    top_to519946101_state : set_Ho840737317_state).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Com__Ocom_J_J, type,
    top_to182305990on_com : set_option_com).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Com__Opname_J_J, type,
    top_to1034942016_pname : set_option_pname).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Com__Opname_Mt__Com__Opname_J_J, type,
    top_to2104644005_pname : set_Pr15211605_pname).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_It__Com__Opname_J_J, type,
    top_to1806476070_pname : set_set_pname).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Sum____Type__Osum_It__Com__Opname_Mt__Com__Opname_J_J, type,
    top_to380724057_pname : set_Su1011432617_pname).
thf(sy_c_Set_OCollect_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
    collec305460656_state : (hoare_958474565_state > $o) > set_Ho840737317_state).
thf(sy_c_Set_Oimage_001t__Com__Ocom_001t__Option__Ooption_It__Com__Ocom_J, type,
    image_com_option_com : (com > option_com) > set_com > set_option_com).
thf(sy_c_Set_Oimage_001t__Com__Opname_001t__Com__Opname, type,
    image_pname_pname : (pname > pname) > set_pname > set_pname).
thf(sy_c_Set_Oimage_001t__Com__Opname_001t__Option__Ooption_It__Com__Opname_J, type,
    image_1833247979_pname : (pname > option_pname) > set_pname > set_option_pname).
thf(sy_c_Set_Oimage_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
    image_1849792670_state : (hoare_958474565_state > hoare_958474565_state) > set_Ho840737317_state > set_Ho840737317_state).
thf(sy_c_Set_Oinsert_001t__Com__Ocom, type,
    insert_com : com > set_com > set_com).
thf(sy_c_Set_Oinsert_001t__Com__Opname, type,
    insert_pname : pname > set_pname > set_pname).
thf(sy_c_Set_Oinsert_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
    insert776267541_state : hoare_958474565_state > set_Ho840737317_state > set_Ho840737317_state).
thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Com__Ocom_J, type,
    insert_option_com : option_com > set_option_com > set_option_com).
thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J, type,
    insert677809883_state : option1481361675_state > set_op1790085995_state > set_op1790085995_state).
thf(sy_c_Set_Ois__empty_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
    is_emp266830871_state : set_Ho840737317_state > $o).
thf(sy_c_Set_Ois__singleton_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
    is_sin536631353_state : set_Ho840737317_state > $o).
thf(sy_c_Set_Othe__elem_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
    the_el1300254266_state : set_Ho840737317_state > hoare_958474565_state).
thf(sy_c_member_001t__Com__Ocom, type,
    member_com : com > set_com > $o).
thf(sy_c_member_001t__Com__Opname, type,
    member_pname : pname > set_pname > $o).
thf(sy_c_member_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
    member109514606_state : hoare_958474565_state > set_Ho840737317_state > $o).
thf(sy_c_member_001t__Option__Ooption_It__Com__Ocom_J, type,
    member_option_com : option_com > set_option_com > $o).
thf(sy_c_member_001t__Option__Ooption_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J, type,
    member1754906036_state : option1481361675_state > set_op1790085995_state > $o).
thf(sy_v_G, type,
    g : set_Ho840737317_state).
thf(sy_v_c, type,
    c : com).

% Relevant facts (146)
thf(fact_0_single__stateE, axiom,
    ((hoare_405891322gleton => (![T : state]: (~ ((![S : state]: (S = T)))))))). % single_stateE
thf(fact_1_derivs__insertD, axiom,
    ((![G : set_Ho840737317_state, T2 : hoare_958474565_state, Ts : set_Ho840737317_state]: ((hoare_604442164_state @ G @ (insert776267541_state @ T2 @ Ts)) => ((hoare_604442164_state @ G @ (insert776267541_state @ T2 @ bot_bo105666705_state)) & (hoare_604442164_state @ G @ Ts)))))). % derivs_insertD
thf(fact_2_cut, axiom,
    ((![G2 : set_Ho840737317_state, Ts : set_Ho840737317_state, G : set_Ho840737317_state]: ((hoare_604442164_state @ G2 @ Ts) => ((hoare_604442164_state @ G @ G2) => (hoare_604442164_state @ G @ Ts)))))). % cut
thf(fact_3_empty, axiom,
    ((![G : set_Ho840737317_state]: (hoare_604442164_state @ G @ bot_bo105666705_state)))). % empty
thf(fact_4_hoare__derivs_Oinsert, axiom,
    ((![G : set_Ho840737317_state, T2 : hoare_958474565_state, Ts : set_Ho840737317_state]: ((hoare_604442164_state @ G @ (insert776267541_state @ T2 @ bot_bo105666705_state)) => ((hoare_604442164_state @ G @ Ts) => (hoare_604442164_state @ G @ (insert776267541_state @ T2 @ Ts))))))). % hoare_derivs.insert
thf(fact_5_state__not__singleton__def, axiom,
    ((hoare_405891322gleton = (?[S2 : state]: (?[T3 : state]: (~ ((S2 = T3)))))))). % state_not_singleton_def
thf(fact_6_singletonI, axiom,
    ((![A : hoare_958474565_state]: (member109514606_state @ A @ (insert776267541_state @ A @ bot_bo105666705_state))))). % singletonI
thf(fact_7_com_Oinject_I6_J, axiom,
    ((![X7 : pname, Y7 : pname]: (((body2 @ X7) = (body2 @ Y7)) = (X7 = Y7))))). % com.inject(6)
thf(fact_8_insertCI, axiom,
    ((![A : hoare_958474565_state, B : set_Ho840737317_state, B2 : hoare_958474565_state]: (((~ ((member109514606_state @ A @ B))) => (A = B2)) => (member109514606_state @ A @ (insert776267541_state @ B2 @ B)))))). % insertCI
thf(fact_9_insert__iff, axiom,
    ((![A : hoare_958474565_state, B2 : hoare_958474565_state, A2 : set_Ho840737317_state]: ((member109514606_state @ A @ (insert776267541_state @ B2 @ A2)) = (((A = B2)) | ((member109514606_state @ A @ A2))))))). % insert_iff
thf(fact_10_insert__absorb2, axiom,
    ((![X : hoare_958474565_state, A2 : set_Ho840737317_state]: ((insert776267541_state @ X @ (insert776267541_state @ X @ A2)) = (insert776267541_state @ X @ A2))))). % insert_absorb2
thf(fact_11_empty__iff, axiom,
    ((![C : hoare_958474565_state]: (~ ((member109514606_state @ C @ bot_bo105666705_state)))))). % empty_iff
thf(fact_12_all__not__in__conv, axiom,
    ((![A2 : set_Ho840737317_state]: ((![X2 : hoare_958474565_state]: (~ ((member109514606_state @ X2 @ A2)))) = (A2 = bot_bo105666705_state))))). % all_not_in_conv
thf(fact_13_Collect__empty__eq, axiom,
    ((![P : hoare_958474565_state > $o]: (((collec305460656_state @ P) = bot_bo105666705_state) = (![X2 : hoare_958474565_state]: (~ ((P @ X2)))))))). % Collect_empty_eq
thf(fact_14_empty__Collect__eq, axiom,
    ((![P : hoare_958474565_state > $o]: ((bot_bo105666705_state = (collec305460656_state @ P)) = (![X2 : hoare_958474565_state]: (~ ((P @ X2)))))))). % empty_Collect_eq
thf(fact_15_singletonD, axiom,
    ((![B2 : hoare_958474565_state, A : hoare_958474565_state]: ((member109514606_state @ B2 @ (insert776267541_state @ A @ bot_bo105666705_state)) => (B2 = A))))). % singletonD
thf(fact_16_singleton__iff, axiom,
    ((![B2 : hoare_958474565_state, A : hoare_958474565_state]: ((member109514606_state @ B2 @ (insert776267541_state @ A @ bot_bo105666705_state)) = (B2 = A))))). % singleton_iff
thf(fact_17_bot__set__def, axiom,
    ((bot_bo105666705_state = (collec305460656_state @ bot_bo1428770700tate_o)))). % bot_set_def
thf(fact_18_ex__in__conv, axiom,
    ((![A2 : set_Ho840737317_state]: ((?[X2 : hoare_958474565_state]: (member109514606_state @ X2 @ A2)) = (~ ((A2 = bot_bo105666705_state))))))). % ex_in_conv
thf(fact_19_equals0I, axiom,
    ((![A2 : set_Ho840737317_state]: ((![Y : hoare_958474565_state]: (~ ((member109514606_state @ Y @ A2)))) => (A2 = bot_bo105666705_state))))). % equals0I
thf(fact_20_equals0D, axiom,
    ((![A2 : set_Ho840737317_state, A : hoare_958474565_state]: ((A2 = bot_bo105666705_state) => (~ ((member109514606_state @ A @ A2))))))). % equals0D
thf(fact_21_emptyE, axiom,
    ((![A : hoare_958474565_state]: (~ ((member109514606_state @ A @ bot_bo105666705_state)))))). % emptyE
thf(fact_22_mk__disjoint__insert, axiom,
    ((![A : hoare_958474565_state, A2 : set_Ho840737317_state]: ((member109514606_state @ A @ A2) => (?[B3 : set_Ho840737317_state]: ((A2 = (insert776267541_state @ A @ B3)) & (~ ((member109514606_state @ A @ B3))))))))). % mk_disjoint_insert
thf(fact_23_insert__commute, axiom,
    ((![X : hoare_958474565_state, Y2 : hoare_958474565_state, A2 : set_Ho840737317_state]: ((insert776267541_state @ X @ (insert776267541_state @ Y2 @ A2)) = (insert776267541_state @ Y2 @ (insert776267541_state @ X @ A2)))))). % insert_commute
thf(fact_24_insert__eq__iff, axiom,
    ((![A : hoare_958474565_state, A2 : set_Ho840737317_state, B2 : hoare_958474565_state, B : set_Ho840737317_state]: ((~ ((member109514606_state @ A @ A2))) => ((~ ((member109514606_state @ B2 @ B))) => (((insert776267541_state @ A @ A2) = (insert776267541_state @ B2 @ B)) = (((((A = B2)) => ((A2 = B)))) & ((((~ ((A = B2)))) => ((?[C2 : set_Ho840737317_state]: (((A2 = (insert776267541_state @ B2 @ C2))) & ((((~ ((member109514606_state @ B2 @ C2)))) & ((((B = (insert776267541_state @ A @ C2))) & ((~ ((member109514606_state @ A @ C2)))))))))))))))))))). % insert_eq_iff
thf(fact_25_insert__absorb, axiom,
    ((![A : hoare_958474565_state, A2 : set_Ho840737317_state]: ((member109514606_state @ A @ A2) => ((insert776267541_state @ A @ A2) = A2))))). % insert_absorb
thf(fact_26_insert__ident, axiom,
    ((![X : hoare_958474565_state, A2 : set_Ho840737317_state, B : set_Ho840737317_state]: ((~ ((member109514606_state @ X @ A2))) => ((~ ((member109514606_state @ X @ B))) => (((insert776267541_state @ X @ A2) = (insert776267541_state @ X @ B)) = (A2 = B))))))). % insert_ident
thf(fact_27_Set_Oset__insert, axiom,
    ((![X : hoare_958474565_state, A2 : set_Ho840737317_state]: ((member109514606_state @ X @ A2) => (~ ((![B3 : set_Ho840737317_state]: ((A2 = (insert776267541_state @ X @ B3)) => (member109514606_state @ X @ B3))))))))). % Set.set_insert
thf(fact_28_insertI2, axiom,
    ((![A : hoare_958474565_state, B : set_Ho840737317_state, B2 : hoare_958474565_state]: ((member109514606_state @ A @ B) => (member109514606_state @ A @ (insert776267541_state @ B2 @ B)))))). % insertI2
thf(fact_29_insertI1, axiom,
    ((![A : hoare_958474565_state, B : set_Ho840737317_state]: (member109514606_state @ A @ (insert776267541_state @ A @ B))))). % insertI1
thf(fact_30_insertE, axiom,
    ((![A : hoare_958474565_state, B2 : hoare_958474565_state, A2 : set_Ho840737317_state]: ((member109514606_state @ A @ (insert776267541_state @ B2 @ A2)) => ((~ ((A = B2))) => (member109514606_state @ A @ A2)))))). % insertE
thf(fact_31_singleton__inject, axiom,
    ((![A : hoare_958474565_state, B2 : hoare_958474565_state]: (((insert776267541_state @ A @ bot_bo105666705_state) = (insert776267541_state @ B2 @ bot_bo105666705_state)) => (A = B2))))). % singleton_inject
thf(fact_32_insert__not__empty, axiom,
    ((![A : hoare_958474565_state, A2 : set_Ho840737317_state]: (~ (((insert776267541_state @ A @ A2) = bot_bo105666705_state)))))). % insert_not_empty
thf(fact_33_doubleton__eq__iff, axiom,
    ((![A : hoare_958474565_state, B2 : hoare_958474565_state, C : hoare_958474565_state, D : hoare_958474565_state]: (((insert776267541_state @ A @ (insert776267541_state @ B2 @ bot_bo105666705_state)) = (insert776267541_state @ C @ (insert776267541_state @ D @ bot_bo105666705_state))) = (((((A = C)) & ((B2 = D)))) | ((((A = D)) & ((B2 = C))))))))). % doubleton_eq_iff
thf(fact_34_the__elem__eq, axiom,
    ((![X : hoare_958474565_state]: ((the_el1300254266_state @ (insert776267541_state @ X @ bot_bo105666705_state)) = X)))). % the_elem_eq
thf(fact_35_is__singletonI, axiom,
    ((![X : hoare_958474565_state]: (is_sin536631353_state @ (insert776267541_state @ X @ bot_bo105666705_state))))). % is_singletonI
thf(fact_36_Set_Ois__empty__def, axiom,
    ((is_emp266830871_state = (^[A3 : set_Ho840737317_state]: (A3 = bot_bo105666705_state))))). % Set.is_empty_def
thf(fact_37_is__singleton__def, axiom,
    ((is_sin536631353_state = (^[A3 : set_Ho840737317_state]: (?[X2 : hoare_958474565_state]: (A3 = (insert776267541_state @ X2 @ bot_bo105666705_state))))))). % is_singleton_def
thf(fact_38_is__singletonE, axiom,
    ((![A2 : set_Ho840737317_state]: ((is_sin536631353_state @ A2) => (~ ((![X3 : hoare_958474565_state]: (~ ((A2 = (insert776267541_state @ X3 @ bot_bo105666705_state))))))))))). % is_singletonE
thf(fact_39_finite__dom__body, axiom,
    ((finite_finite_pname @ (dom_pname_com @ body)))). % finite_dom_body
thf(fact_40_MGF__complete, axiom,
    ((![C : com, P : state > state > $o, Q : state > state > $o]: ((hoare_604442164_state @ bot_bo105666705_state @ (insert776267541_state @ (hoare_Mirabelle_MGT @ C) @ bot_bo105666705_state)) => ((hoare_318887606_state @ bot_bo105666705_state @ (insert776267541_state @ (hoare_1659279548_state @ P @ C @ Q) @ bot_bo105666705_state)) => (hoare_604442164_state @ bot_bo105666705_state @ (insert776267541_state @ (hoare_1659279548_state @ P @ C @ Q) @ bot_bo105666705_state))))))). % MGF_complete
thf(fact_41_WT_OBody, axiom,
    ((![Pn : pname]: ((~ (((body @ Pn) = none_com))) => (wt @ (body2 @ Pn)))))). % WT.Body
thf(fact_42_conseq, axiom,
    ((![P : state > state > $o, G : set_Ho840737317_state, C : com, Q : state > state > $o]: ((![Z : state, S : state]: ((P @ Z @ S) => (?[P2 : state > state > $o, Q2 : state > state > $o]: ((hoare_604442164_state @ G @ (insert776267541_state @ (hoare_1659279548_state @ P2 @ C @ Q2) @ bot_bo105666705_state)) & (![S3 : state]: ((![Z2 : state]: ((P2 @ Z2 @ S) => (Q2 @ Z2 @ S3))) => (Q @ Z @ S3))))))) => (hoare_604442164_state @ G @ (insert776267541_state @ (hoare_1659279548_state @ P @ C @ Q) @ bot_bo105666705_state)))))). % conseq
thf(fact_43_mem__Collect__eq, axiom,
    ((![A : hoare_958474565_state, P : hoare_958474565_state > $o]: ((member109514606_state @ A @ (collec305460656_state @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_44_Collect__mem__eq, axiom,
    ((![A2 : set_Ho840737317_state]: ((collec305460656_state @ (^[X2 : hoare_958474565_state]: (member109514606_state @ X2 @ A2))) = A2)))). % Collect_mem_eq
thf(fact_45_triple_Oinject, axiom,
    ((![X1 : state > state > $o, X22 : com, X32 : state > state > $o, Y1 : state > state > $o, Y22 : com, Y3 : state > state > $o]: (((hoare_1659279548_state @ X1 @ X22 @ X32) = (hoare_1659279548_state @ Y1 @ Y22 @ Y3)) = (((X1 = Y1)) & ((((X22 = Y22)) & ((X32 = Y3))))))))). % triple.inject
thf(fact_46_triple_Oexhaust, axiom,
    ((![Y2 : hoare_958474565_state]: (~ ((![X12 : state > state > $o, X23 : com, X33 : state > state > $o]: (~ ((Y2 = (hoare_1659279548_state @ X12 @ X23 @ X33)))))))))). % triple.exhaust
thf(fact_47_triple_Oinduct, axiom,
    ((![P : hoare_958474565_state > $o, Triple : hoare_958474565_state]: ((![X1a : state > state > $o, X2a : com, X3a : state > state > $o]: (P @ (hoare_1659279548_state @ X1a @ X2a @ X3a))) => (P @ Triple))))). % triple.induct
thf(fact_48_is__singleton__the__elem, axiom,
    ((is_sin536631353_state = (^[A3 : set_Ho840737317_state]: (A3 = (insert776267541_state @ (the_el1300254266_state @ A3) @ bot_bo105666705_state)))))). % is_singleton_the_elem
thf(fact_49_is__singletonI_H, axiom,
    ((![A2 : set_Ho840737317_state]: ((~ ((A2 = bot_bo105666705_state))) => ((![X3 : hoare_958474565_state, Y : hoare_958474565_state]: ((member109514606_state @ X3 @ A2) => ((member109514606_state @ Y @ A2) => (X3 = Y)))) => (is_sin536631353_state @ A2)))))). % is_singletonI'
thf(fact_50_hoare__sound, axiom,
    ((![G : set_Ho840737317_state, Ts : set_Ho840737317_state]: ((hoare_604442164_state @ G @ Ts) => (hoare_318887606_state @ G @ Ts))))). % hoare_sound
thf(fact_51_conseq1, axiom,
    ((![G : set_Ho840737317_state, P3 : state > state > $o, C : com, Q : state > state > $o, P : state > state > $o]: ((hoare_604442164_state @ G @ (insert776267541_state @ (hoare_1659279548_state @ P3 @ C @ Q) @ bot_bo105666705_state)) => ((![Z : state, S : state]: ((P @ Z @ S) => (P3 @ Z @ S))) => (hoare_604442164_state @ G @ (insert776267541_state @ (hoare_1659279548_state @ P @ C @ Q) @ bot_bo105666705_state))))))). % conseq1
thf(fact_52_conseq2, axiom,
    ((![G : set_Ho840737317_state, P : state > state > $o, C : com, Q3 : state > state > $o, Q : state > state > $o]: ((hoare_604442164_state @ G @ (insert776267541_state @ (hoare_1659279548_state @ P @ C @ Q3) @ bot_bo105666705_state)) => ((![Z : state, S : state]: ((Q3 @ Z @ S) => (Q @ Z @ S))) => (hoare_604442164_state @ G @ (insert776267541_state @ (hoare_1659279548_state @ P @ C @ Q) @ bot_bo105666705_state))))))). % conseq2
thf(fact_53_conseq12, axiom,
    ((![G : set_Ho840737317_state, P3 : state > state > $o, C : com, Q3 : state > state > $o, P : state > state > $o, Q : state > state > $o]: ((hoare_604442164_state @ G @ (insert776267541_state @ (hoare_1659279548_state @ P3 @ C @ Q3) @ bot_bo105666705_state)) => ((![Z : state, S : state]: ((P @ Z @ S) => (![S3 : state]: ((![Z2 : state]: ((P3 @ Z2 @ S) => (Q3 @ Z2 @ S3))) => (Q @ Z @ S3))))) => (hoare_604442164_state @ G @ (insert776267541_state @ (hoare_1659279548_state @ P @ C @ Q) @ bot_bo105666705_state))))))). % conseq12
thf(fact_54_dom__eq__empty__conv, axiom,
    ((![F : pname > option_com]: (((dom_pname_com @ F) = bot_bot_set_pname) = (F = (^[X2 : pname]: none_com)))))). % dom_eq_empty_conv
thf(fact_55_dom__eq__empty__conv, axiom,
    ((![F : hoare_958474565_state > option_com]: (((dom_Ho256784515te_com @ F) = bot_bo105666705_state) = (F = (^[X2 : hoare_958474565_state]: none_com)))))). % dom_eq_empty_conv
thf(fact_56_finite__insert, axiom,
    ((![A : hoare_958474565_state, A2 : set_Ho840737317_state]: ((finite1986656878_state @ (insert776267541_state @ A @ A2)) = (finite1986656878_state @ A2))))). % finite_insert
thf(fact_57_finite__insert, axiom,
    ((![A : pname, A2 : set_pname]: ((finite_finite_pname @ (insert_pname @ A @ A2)) = (finite_finite_pname @ A2))))). % finite_insert
thf(fact_58_finite_Ocases, axiom,
    ((![A : set_pname]: ((finite_finite_pname @ A) => ((~ ((A = bot_bot_set_pname))) => (~ ((![A4 : set_pname]: ((?[A5 : pname]: (A = (insert_pname @ A5 @ A4))) => (~ ((finite_finite_pname @ A4)))))))))))). % finite.cases
thf(fact_59_finite_Ocases, axiom,
    ((![A : set_Ho840737317_state]: ((finite1986656878_state @ A) => ((~ ((A = bot_bo105666705_state))) => (~ ((![A4 : set_Ho840737317_state]: ((?[A5 : hoare_958474565_state]: (A = (insert776267541_state @ A5 @ A4))) => (~ ((finite1986656878_state @ A4)))))))))))). % finite.cases
thf(fact_60_finite_Osimps, axiom,
    ((finite_finite_pname = (^[A6 : set_pname]: (((A6 = bot_bot_set_pname)) | ((?[A3 : set_pname]: (?[B4 : pname]: (((A6 = (insert_pname @ B4 @ A3))) & ((finite_finite_pname @ A3))))))))))). % finite.simps
thf(fact_61_finite_Osimps, axiom,
    ((finite1986656878_state = (^[A6 : set_Ho840737317_state]: (((A6 = bot_bo105666705_state)) | ((?[A3 : set_Ho840737317_state]: (?[B4 : hoare_958474565_state]: (((A6 = (insert776267541_state @ B4 @ A3))) & ((finite1986656878_state @ A3))))))))))). % finite.simps
thf(fact_62_finite__induct, axiom,
    ((![F2 : set_pname, P : set_pname > $o]: ((finite_finite_pname @ F2) => ((P @ bot_bot_set_pname) => ((![X3 : pname, F3 : set_pname]: ((finite_finite_pname @ F3) => ((~ ((member_pname @ X3 @ F3))) => ((P @ F3) => (P @ (insert_pname @ X3 @ F3)))))) => (P @ F2))))))). % finite_induct
thf(fact_63_finite__induct, axiom,
    ((![F2 : set_Ho840737317_state, P : set_Ho840737317_state > $o]: ((finite1986656878_state @ F2) => ((P @ bot_bo105666705_state) => ((![X3 : hoare_958474565_state, F3 : set_Ho840737317_state]: ((finite1986656878_state @ F3) => ((~ ((member109514606_state @ X3 @ F3))) => ((P @ F3) => (P @ (insert776267541_state @ X3 @ F3)))))) => (P @ F2))))))). % finite_induct
thf(fact_64_finite_Oinducts, axiom,
    ((![X : set_pname, P : set_pname > $o]: ((finite_finite_pname @ X) => ((P @ bot_bot_set_pname) => ((![A4 : set_pname, A5 : pname]: ((finite_finite_pname @ A4) => ((P @ A4) => (P @ (insert_pname @ A5 @ A4))))) => (P @ X))))))). % finite.inducts
thf(fact_65_finite_Oinducts, axiom,
    ((![X : set_Ho840737317_state, P : set_Ho840737317_state > $o]: ((finite1986656878_state @ X) => ((P @ bot_bo105666705_state) => ((![A4 : set_Ho840737317_state, A5 : hoare_958474565_state]: ((finite1986656878_state @ A4) => ((P @ A4) => (P @ (insert776267541_state @ A5 @ A4))))) => (P @ X))))))). % finite.inducts
thf(fact_66_finite_OemptyI, axiom,
    ((finite_finite_pname @ bot_bot_set_pname))). % finite.emptyI
thf(fact_67_finite_OemptyI, axiom,
    ((finite1986656878_state @ bot_bo105666705_state))). % finite.emptyI
thf(fact_68_infinite__imp__nonempty, axiom,
    ((![S4 : set_pname]: ((~ ((finite_finite_pname @ S4))) => (~ ((S4 = bot_bot_set_pname))))))). % infinite_imp_nonempty
thf(fact_69_infinite__imp__nonempty, axiom,
    ((![S4 : set_Ho840737317_state]: ((~ ((finite1986656878_state @ S4))) => (~ ((S4 = bot_bo105666705_state))))))). % infinite_imp_nonempty
thf(fact_70_finite_OinsertI, axiom,
    ((![A2 : set_Ho840737317_state, A : hoare_958474565_state]: ((finite1986656878_state @ A2) => (finite1986656878_state @ (insert776267541_state @ A @ A2)))))). % finite.insertI
thf(fact_71_finite_OinsertI, axiom,
    ((![A2 : set_pname, A : pname]: ((finite_finite_pname @ A2) => (finite_finite_pname @ (insert_pname @ A @ A2)))))). % finite.insertI
thf(fact_72_domIff, axiom,
    ((![A : pname, M : pname > option_com]: ((member_pname @ A @ (dom_pname_com @ M)) = (~ (((M @ A) = none_com))))))). % domIff
thf(fact_73_domIff, axiom,
    ((![A : hoare_958474565_state, M : hoare_958474565_state > option_com]: ((member109514606_state @ A @ (dom_Ho256784515te_com @ M)) = (~ (((M @ A) = none_com))))))). % domIff
thf(fact_74_infinite__finite__induct, axiom,
    ((![P : set_pname > $o, A2 : set_pname]: ((![A4 : set_pname]: ((~ ((finite_finite_pname @ A4))) => (P @ A4))) => ((P @ bot_bot_set_pname) => ((![X3 : pname, F3 : set_pname]: ((finite_finite_pname @ F3) => ((~ ((member_pname @ X3 @ F3))) => ((P @ F3) => (P @ (insert_pname @ X3 @ F3)))))) => (P @ A2))))))). % infinite_finite_induct
thf(fact_75_infinite__finite__induct, axiom,
    ((![P : set_Ho840737317_state > $o, A2 : set_Ho840737317_state]: ((![A4 : set_Ho840737317_state]: ((~ ((finite1986656878_state @ A4))) => (P @ A4))) => ((P @ bot_bo105666705_state) => ((![X3 : hoare_958474565_state, F3 : set_Ho840737317_state]: ((finite1986656878_state @ F3) => ((~ ((member109514606_state @ X3 @ F3))) => ((P @ F3) => (P @ (insert776267541_state @ X3 @ F3)))))) => (P @ A2))))))). % infinite_finite_induct
thf(fact_76_finite__ne__induct, axiom,
    ((![F2 : set_pname, P : set_pname > $o]: ((finite_finite_pname @ F2) => ((~ ((F2 = bot_bot_set_pname))) => ((![X3 : pname]: (P @ (insert_pname @ X3 @ bot_bot_set_pname))) => ((![X3 : pname, F3 : set_pname]: ((finite_finite_pname @ F3) => ((~ ((F3 = bot_bot_set_pname))) => ((~ ((member_pname @ X3 @ F3))) => ((P @ F3) => (P @ (insert_pname @ X3 @ F3))))))) => (P @ F2)))))))). % finite_ne_induct
thf(fact_77_finite__ne__induct, axiom,
    ((![F2 : set_Ho840737317_state, P : set_Ho840737317_state > $o]: ((finite1986656878_state @ F2) => ((~ ((F2 = bot_bo105666705_state))) => ((![X3 : hoare_958474565_state]: (P @ (insert776267541_state @ X3 @ bot_bo105666705_state))) => ((![X3 : hoare_958474565_state, F3 : set_Ho840737317_state]: ((finite1986656878_state @ F3) => ((~ ((F3 = bot_bo105666705_state))) => ((~ ((member109514606_state @ X3 @ F3))) => ((P @ F3) => (P @ (insert776267541_state @ X3 @ F3))))))) => (P @ F2)))))))). % finite_ne_induct
thf(fact_78_Collect__empty__eq__bot, axiom,
    ((![P : hoare_958474565_state > $o]: (((collec305460656_state @ P) = bot_bo105666705_state) = (P = bot_bo1428770700tate_o))))). % Collect_empty_eq_bot
thf(fact_79_bot__empty__eq, axiom,
    ((bot_bo1428770700tate_o = (^[X2 : hoare_958474565_state]: (member109514606_state @ X2 @ bot_bo105666705_state))))). % bot_empty_eq
thf(fact_80_weak__Body, axiom,
    ((![G : set_Ho840737317_state, P : state > state > $o, Pn : pname, Q : state > state > $o]: ((hoare_604442164_state @ G @ (insert776267541_state @ (hoare_1659279548_state @ P @ (the_com @ (body @ Pn)) @ Q) @ bot_bo105666705_state)) => (hoare_604442164_state @ G @ (insert776267541_state @ (hoare_1659279548_state @ P @ (body2 @ Pn) @ Q) @ bot_bo105666705_state)))))). % weak_Body
thf(fact_81_BodyN, axiom,
    ((![P : state > state > $o, Pn : pname, Q : state > state > $o, G : set_Ho840737317_state]: ((hoare_604442164_state @ (insert776267541_state @ (hoare_1659279548_state @ P @ (body2 @ Pn) @ Q) @ G) @ (insert776267541_state @ (hoare_1659279548_state @ P @ (the_com @ (body @ Pn)) @ Q) @ bot_bo105666705_state)) => (hoare_604442164_state @ G @ (insert776267541_state @ (hoare_1659279548_state @ P @ (body2 @ Pn) @ Q) @ bot_bo105666705_state)))))). % BodyN
thf(fact_82_hoare__derivs_OSkip, axiom,
    ((![G : set_Ho840737317_state, P : state > state > $o]: (hoare_604442164_state @ G @ (insert776267541_state @ (hoare_1659279548_state @ P @ skip @ P) @ bot_bo105666705_state))))). % hoare_derivs.Skip
thf(fact_83_WT_OSkip, axiom,
    ((wt @ skip))). % WT.Skip
thf(fact_84_com_Odistinct_I11_J, axiom,
    ((![X7 : pname]: (~ ((skip = (body2 @ X7))))))). % com.distinct(11)
thf(fact_85_option_Oexpand, axiom,
    ((![Option : option_com, Option2 : option_com]: (((Option = none_com) = (Option2 = none_com)) => (((~ ((Option = none_com))) => ((~ ((Option2 = none_com))) => ((the_com @ Option) = (the_com @ Option2)))) => (Option = Option2)))))). % option.expand
thf(fact_86_Comp, axiom,
    ((![G : set_Ho840737317_state, P : state > state > $o, C : com, Q : state > state > $o, D : com, R : state > state > $o]: ((hoare_604442164_state @ G @ (insert776267541_state @ (hoare_1659279548_state @ P @ C @ Q) @ bot_bo105666705_state)) => ((hoare_604442164_state @ G @ (insert776267541_state @ (hoare_1659279548_state @ Q @ D @ R) @ bot_bo105666705_state)) => (hoare_604442164_state @ G @ (insert776267541_state @ (hoare_1659279548_state @ P @ (semi @ C @ D) @ R) @ bot_bo105666705_state))))))). % Comp
thf(fact_87_com_Oinject_I3_J, axiom,
    ((![X41 : com, X42 : com, Y41 : com, Y42 : com]: (((semi @ X41 @ X42) = (semi @ Y41 @ Y42)) = (((X41 = Y41)) & ((X42 = Y42))))))). % com.inject(3)
thf(fact_88_WT_OSemi, axiom,
    ((![C0 : com, C1 : com]: ((wt @ C0) => ((wt @ C1) => (wt @ (semi @ C0 @ C1))))))). % WT.Semi
thf(fact_89_WTs__elim__cases_I4_J, axiom,
    ((![C1 : com, C22 : com]: ((wt @ (semi @ C1 @ C22)) => (~ (((wt @ C1) => (~ ((wt @ C22)))))))))). % WTs_elim_cases(4)
thf(fact_90_com_Odistinct_I41_J, axiom,
    ((![X41 : com, X42 : com, X7 : pname]: (~ (((semi @ X41 @ X42) = (body2 @ X7))))))). % com.distinct(41)
thf(fact_91_com_Odistinct_I5_J, axiom,
    ((![X41 : com, X42 : com]: (~ ((skip = (semi @ X41 @ X42))))))). % com.distinct(5)
thf(fact_92_these__not__empty__eq, axiom,
    ((![B : set_option_com]: ((~ (((these_com @ B) = bot_bot_set_com))) = (((~ ((B = bot_bo697186986on_com)))) & ((~ ((B = (insert_option_com @ none_com @ bot_bo697186986on_com)))))))))). % these_not_empty_eq
thf(fact_93_these__not__empty__eq, axiom,
    ((![B : set_op1790085995_state]: ((~ (((these_1282564994_state @ B) = bot_bo105666705_state))) = (((~ ((B = bot_bo472264663_state)))) & ((~ ((B = (insert677809883_state @ none_H2001963430_state @ bot_bo472264663_state)))))))))). % these_not_empty_eq
thf(fact_94_these__empty__eq, axiom,
    ((![B : set_option_com]: (((these_com @ B) = bot_bot_set_com) = (((B = bot_bo697186986on_com)) | ((B = (insert_option_com @ none_com @ bot_bo697186986on_com)))))))). % these_empty_eq
thf(fact_95_these__empty__eq, axiom,
    ((![B : set_op1790085995_state]: (((these_1282564994_state @ B) = bot_bo105666705_state) = (((B = bot_bo472264663_state)) | ((B = (insert677809883_state @ none_H2001963430_state @ bot_bo472264663_state)))))))). % these_empty_eq
thf(fact_96_finite__map__freshness, axiom,
    ((![F : pname > option_com]: ((finite_finite_pname @ (dom_pname_com @ F)) => ((~ ((finite_finite_pname @ top_top_set_pname))) => (?[X3 : pname]: ((F @ X3) = none_com))))))). % finite_map_freshness
thf(fact_97_WTs__elim__cases_I7_J, axiom,
    ((![P : pname]: ((wt @ (body2 @ P)) => (~ ((![Y : com]: (~ (((body @ P) = (some_com @ Y))))))))))). % WTs_elim_cases(7)
thf(fact_98_UNIV__I, axiom,
    ((![X : hoare_958474565_state]: (member109514606_state @ X @ top_to519946101_state)))). % UNIV_I
thf(fact_99_option_Oinject, axiom,
    ((![X22 : com, Y22 : com]: (((some_com @ X22) = (some_com @ Y22)) = (X22 = Y22))))). % option.inject
thf(fact_100_finite__option__UNIV, axiom,
    (((finite1292484209_pname @ top_to1034942016_pname) = (finite_finite_pname @ top_top_set_pname)))). % finite_option_UNIV
thf(fact_101_finite__Plus__UNIV__iff, axiom,
    (((finite1993869834_pname @ top_to380724057_pname) = (((finite_finite_pname @ top_top_set_pname)) & ((finite_finite_pname @ top_top_set_pname)))))). % finite_Plus_UNIV_iff
thf(fact_102_not__None__eq, axiom,
    ((![X : option_com]: ((~ ((X = none_com))) = (?[Y4 : com]: (X = (some_com @ Y4))))))). % not_None_eq
thf(fact_103_not__Some__eq, axiom,
    ((![X : option_com]: ((![Y4 : com]: (~ ((X = (some_com @ Y4))))) = (X = none_com))))). % not_Some_eq
thf(fact_104_option_Ocollapse, axiom,
    ((![Option : option_com]: ((~ ((Option = none_com))) => ((some_com @ (the_com @ Option)) = Option))))). % option.collapse
thf(fact_105_these__empty, axiom,
    (((these_1282564994_state @ bot_bo472264663_state) = bot_bo105666705_state))). % these_empty
thf(fact_106_these__insert__None, axiom,
    ((![A2 : set_option_com]: ((these_com @ (insert_option_com @ none_com @ A2)) = (these_com @ A2))))). % these_insert_None
thf(fact_107_these__insert__Some, axiom,
    ((![X : hoare_958474565_state, A2 : set_op1790085995_state]: ((these_1282564994_state @ (insert677809883_state @ (some_H1327573290_state @ X) @ A2)) = (insert776267541_state @ X @ (these_1282564994_state @ A2)))))). % these_insert_Some
thf(fact_108_these__insert__Some, axiom,
    ((![X : com, A2 : set_option_com]: ((these_com @ (insert_option_com @ (some_com @ X) @ A2)) = (insert_com @ X @ (these_com @ A2)))))). % these_insert_Some
thf(fact_109_option_Osel, axiom,
    ((![X22 : com]: ((the_com @ (some_com @ X22)) = X22)))). % option.sel
thf(fact_110_in__these__eq, axiom,
    ((![X : hoare_958474565_state, A2 : set_op1790085995_state]: ((member109514606_state @ X @ (these_1282564994_state @ A2)) = (member1754906036_state @ (some_H1327573290_state @ X) @ A2))))). % in_these_eq
thf(fact_111_in__these__eq, axiom,
    ((![X : com, A2 : set_option_com]: ((member_com @ X @ (these_com @ A2)) = (member_option_com @ (some_com @ X) @ A2))))). % in_these_eq
thf(fact_112_option_Odistinct_I1_J, axiom,
    ((![X22 : com]: (~ ((none_com = (some_com @ X22))))))). % option.distinct(1)
thf(fact_113_option_OdiscI, axiom,
    ((![Option : option_com, X22 : com]: ((Option = (some_com @ X22)) => (~ ((Option = none_com))))))). % option.discI
thf(fact_114_option_Oexhaust, axiom,
    ((![Y2 : option_com]: ((~ ((Y2 = none_com))) => (~ ((![X23 : com]: (~ ((Y2 = (some_com @ X23))))))))))). % option.exhaust
thf(fact_115_option_Oinducts, axiom,
    ((![P : option_com > $o, Option : option_com]: ((P @ none_com) => ((![X3 : com]: (P @ (some_com @ X3))) => (P @ Option)))))). % option.inducts
thf(fact_116_split__option__ex, axiom,
    (((^[P4 : option_com > $o]: (?[X4 : option_com]: (P4 @ X4))) = (^[P5 : option_com > $o]: (((P5 @ none_com)) | ((?[X2 : com]: (P5 @ (some_com @ X2))))))))). % split_option_ex
thf(fact_117_split__option__all, axiom,
    (((^[P4 : option_com > $o]: (![X4 : option_com]: (P4 @ X4))) = (^[P5 : option_com > $o]: (((P5 @ none_com)) & ((![X2 : com]: (P5 @ (some_com @ X2))))))))). % split_option_all
thf(fact_118_combine__options__cases, axiom,
    ((![X : option_com, P : option_com > option_com > $o, Y2 : option_com]: (((X = none_com) => (P @ X @ Y2)) => (((Y2 = none_com) => (P @ X @ Y2)) => ((![A5 : com, B5 : com]: ((X = (some_com @ A5)) => ((Y2 = (some_com @ B5)) => (P @ X @ Y2)))) => (P @ X @ Y2))))))). % combine_options_cases
thf(fact_119_finite__Prod__UNIV, axiom,
    (((finite_finite_pname @ top_top_set_pname) => ((finite_finite_pname @ top_top_set_pname) => (finite1490780830_pname @ top_to2104644005_pname))))). % finite_Prod_UNIV
thf(fact_120_finite__prod, axiom,
    (((finite1490780830_pname @ top_to2104644005_pname) = (((finite_finite_pname @ top_top_set_pname)) & ((finite_finite_pname @ top_top_set_pname)))))). % finite_prod
thf(fact_121_Finite__Set_Ofinite__set, axiom,
    (((finite505202775_pname @ top_to1806476070_pname) = (finite_finite_pname @ top_top_set_pname)))). % Finite_Set.finite_set
thf(fact_122_empty__not__UNIV, axiom,
    ((~ ((bot_bo105666705_state = top_to519946101_state))))). % empty_not_UNIV
thf(fact_123_UNIV__eq__I, axiom,
    ((![A2 : set_Ho840737317_state]: ((![X3 : hoare_958474565_state]: (member109514606_state @ X3 @ A2)) => (top_to519946101_state = A2))))). % UNIV_eq_I
thf(fact_124_UNIV__witness, axiom,
    ((?[X3 : hoare_958474565_state]: (member109514606_state @ X3 @ top_to519946101_state)))). % UNIV_witness
thf(fact_125_insert__UNIV, axiom,
    ((![X : hoare_958474565_state]: ((insert776267541_state @ X @ top_to519946101_state) = top_to519946101_state)))). % insert_UNIV
thf(fact_126_domD, axiom,
    ((![A : pname, M : pname > option_com]: ((member_pname @ A @ (dom_pname_com @ M)) => (?[B5 : com]: ((M @ A) = (some_com @ B5))))))). % domD
thf(fact_127_domD, axiom,
    ((![A : hoare_958474565_state, M : hoare_958474565_state > option_com]: ((member109514606_state @ A @ (dom_Ho256784515te_com @ M)) => (?[B5 : com]: ((M @ A) = (some_com @ B5))))))). % domD
thf(fact_128_domI, axiom,
    ((![M : pname > option_com, A : pname, B2 : com]: (((M @ A) = (some_com @ B2)) => (member_pname @ A @ (dom_pname_com @ M)))))). % domI
thf(fact_129_domI, axiom,
    ((![M : hoare_958474565_state > option_com, A : hoare_958474565_state, B2 : com]: (((M @ A) = (some_com @ B2)) => (member109514606_state @ A @ (dom_Ho256784515te_com @ M)))))). % domI
thf(fact_130_ex__new__if__finite, axiom,
    ((![A2 : set_Ho840737317_state]: ((~ ((finite1986656878_state @ top_to519946101_state))) => ((finite1986656878_state @ A2) => (?[A5 : hoare_958474565_state]: (~ ((member109514606_state @ A5 @ A2))))))))). % ex_new_if_finite
thf(fact_131_ex__new__if__finite, axiom,
    ((![A2 : set_pname]: ((~ ((finite_finite_pname @ top_top_set_pname))) => ((finite_finite_pname @ A2) => (?[A5 : pname]: (~ ((member_pname @ A5 @ A2))))))))). % ex_new_if_finite
thf(fact_132_insert__dom, axiom,
    ((![F : pname > option_com, X : pname, Y2 : com]: (((F @ X) = (some_com @ Y2)) => ((insert_pname @ X @ (dom_pname_com @ F)) = (dom_pname_com @ F)))))). % insert_dom
thf(fact_133_insert__dom, axiom,
    ((![F : hoare_958474565_state > option_com, X : hoare_958474565_state, Y2 : com]: (((F @ X) = (some_com @ Y2)) => ((insert776267541_state @ X @ (dom_Ho256784515te_com @ F)) = (dom_Ho256784515te_com @ F)))))). % insert_dom
thf(fact_134_option_Oexhaust__sel, axiom,
    ((![Option : option_com]: ((~ ((Option = none_com))) => (Option = (some_com @ (the_com @ Option))))))). % option.exhaust_sel
thf(fact_135_WT__bodiesD, axiom,
    ((![Pn : pname, B2 : com]: (wT_bodies => (((body @ Pn) = (some_com @ B2)) => (wt @ B2)))))). % WT_bodiesD
thf(fact_136_cofinite__bot, axiom,
    (((cofinite_pname = bot_bot_filter_pname) = (finite_finite_pname @ top_top_set_pname)))). % cofinite_bot
thf(fact_137_top__empty__eq, axiom,
    ((top_to1619606952tate_o = (^[X2 : hoare_958474565_state]: (member109514606_state @ X2 @ top_to519946101_state))))). % top_empty_eq
thf(fact_138_UNIV__option__conv, axiom,
    ((top_to182305990on_com = (insert_option_com @ none_com @ (image_com_option_com @ some_com @ top_top_set_com))))). % UNIV_option_conv
thf(fact_139_finite__range__Some, axiom,
    (((finite1292484209_pname @ (image_1833247979_pname @ some_pname @ top_top_set_pname)) = (finite_finite_pname @ top_top_set_pname)))). % finite_range_Some
thf(fact_140_finite__range__Some, axiom,
    (((finite596631031on_com @ (image_com_option_com @ some_com @ top_top_set_com)) = (finite_finite_com @ top_top_set_com)))). % finite_range_Some
thf(fact_141_image__eqI, axiom,
    ((![B2 : hoare_958474565_state, F : hoare_958474565_state > hoare_958474565_state, X : hoare_958474565_state, A2 : set_Ho840737317_state]: ((B2 = (F @ X)) => ((member109514606_state @ X @ A2) => (member109514606_state @ B2 @ (image_1849792670_state @ F @ A2))))))). % image_eqI
thf(fact_142_image__is__empty, axiom,
    ((![F : hoare_958474565_state > hoare_958474565_state, A2 : set_Ho840737317_state]: (((image_1849792670_state @ F @ A2) = bot_bo105666705_state) = (A2 = bot_bo105666705_state))))). % image_is_empty
thf(fact_143_empty__is__image, axiom,
    ((![F : hoare_958474565_state > hoare_958474565_state, A2 : set_Ho840737317_state]: ((bot_bo105666705_state = (image_1849792670_state @ F @ A2)) = (A2 = bot_bo105666705_state))))). % empty_is_image
thf(fact_144_image__empty, axiom,
    ((![F : hoare_958474565_state > hoare_958474565_state]: ((image_1849792670_state @ F @ bot_bo105666705_state) = bot_bo105666705_state)))). % image_empty
thf(fact_145_finite__imageI, axiom,
    ((![F2 : set_pname, H : pname > pname]: ((finite_finite_pname @ F2) => (finite_finite_pname @ (image_pname_pname @ H @ F2)))))). % finite_imageI

% Conjectures (3)
thf(conj_0, hypothesis,
    (hoare_405891322gleton)).
thf(conj_1, hypothesis,
    ((![X5 : pname]: ((member_pname @ X5 @ (dom_pname_com @ body)) => (hoare_604442164_state @ g @ (insert776267541_state @ (hoare_Mirabelle_MGT @ (body2 @ X5)) @ bot_bo105666705_state)))))).
thf(conj_2, conjecture,
    (((~ ((wt @ c))) | (hoare_604442164_state @ g @ (insert776267541_state @ (hoare_Mirabelle_MGT @ c) @ bot_bo105666705_state))))).
