% 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_341__3253408_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:13:54.212

% Could-be-implicit typings (7)
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__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
    hoare_958474565_state : $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__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 (27)
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_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_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_Option_Ooption_Othe_001t__Com__Ocom, type,
    the_com : option_com > com).
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__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_Oord__class_Oless__eq_001t__Set__Oset_It__Com__Opname_J, type,
    ord_le865024672_pname : set_pname > set_pname > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J, type,
    ord_le1945819589_state : set_Ho840737317_state > set_Ho840737317_state > $o).
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_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_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__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_v_G, type,
    g : set_Ho840737317_state).

% Relevant facts (112)
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_com_Odistinct_I11_J, axiom,
    ((![X7 : pname]: (~ ((skip = (body2 @ X7))))))). % com.distinct(11)
thf(fact_16_singletonD, axiom,
    ((![B2 : hoare_958474565_state, A : hoare_958474565_state]: ((member109514606_state @ B2 @ (insert776267541_state @ A @ bot_bo105666705_state)) => (B2 = A))))). % singletonD
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_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_35_the__elem__eq, axiom,
    ((![X : hoare_958474565_state]: ((the_el1300254266_state @ (insert776267541_state @ X @ bot_bo105666705_state)) = X)))). % the_elem_eq
thf(fact_36_is__singletonI, axiom,
    ((![X : hoare_958474565_state]: (is_sin536631353_state @ (insert776267541_state @ X @ bot_bo105666705_state))))). % is_singletonI
thf(fact_37_Set_Ois__empty__def, axiom,
    ((is_emp266830871_state = (^[A3 : set_Ho840737317_state]: (A3 = bot_bo105666705_state))))). % Set.is_empty_def
thf(fact_38_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_39_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_40_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_41_finite__dom__body, axiom,
    ((finite_finite_pname @ (dom_pname_com @ body)))). % finite_dom_body
thf(fact_42_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_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_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_46_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_47_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_48_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_49_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_50_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_51_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_52_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_53_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_54_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_55_finite__insert, axiom,
    ((![A : hoare_958474565_state, A2 : set_Ho840737317_state]: ((finite1986656878_state @ (insert776267541_state @ A @ A2)) = (finite1986656878_state @ A2))))). % finite_insert
thf(fact_56_finite__insert, axiom,
    ((![A : pname, A2 : set_pname]: ((finite_finite_pname @ (insert_pname @ A @ A2)) = (finite_finite_pname @ A2))))). % finite_insert
thf(fact_57_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_58_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_59_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_60_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_61_finite__induct, axiom,
    ((![F : set_pname, P : set_pname > $o]: ((finite_finite_pname @ F) => ((P @ bot_bot_set_pname) => ((![X3 : pname, F2 : set_pname]: ((finite_finite_pname @ F2) => ((~ ((member_pname @ X3 @ F2))) => ((P @ F2) => (P @ (insert_pname @ X3 @ F2)))))) => (P @ F))))))). % finite_induct
thf(fact_62_finite__induct, axiom,
    ((![F : set_Ho840737317_state, P : set_Ho840737317_state > $o]: ((finite1986656878_state @ F) => ((P @ bot_bo105666705_state) => ((![X3 : hoare_958474565_state, F2 : set_Ho840737317_state]: ((finite1986656878_state @ F2) => ((~ ((member109514606_state @ X3 @ F2))) => ((P @ F2) => (P @ (insert776267541_state @ X3 @ F2)))))) => (P @ F))))))). % finite_induct
thf(fact_63_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_64_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_65_finite__ne__induct, axiom,
    ((![F : set_pname, P : set_pname > $o]: ((finite_finite_pname @ F) => ((~ ((F = bot_bot_set_pname))) => ((![X3 : pname]: (P @ (insert_pname @ X3 @ bot_bot_set_pname))) => ((![X3 : pname, F2 : set_pname]: ((finite_finite_pname @ F2) => ((~ ((F2 = bot_bot_set_pname))) => ((~ ((member_pname @ X3 @ F2))) => ((P @ F2) => (P @ (insert_pname @ X3 @ F2))))))) => (P @ F)))))))). % finite_ne_induct
thf(fact_66_finite__ne__induct, axiom,
    ((![F : set_Ho840737317_state, P : set_Ho840737317_state > $o]: ((finite1986656878_state @ F) => ((~ ((F = bot_bo105666705_state))) => ((![X3 : hoare_958474565_state]: (P @ (insert776267541_state @ X3 @ bot_bo105666705_state))) => ((![X3 : hoare_958474565_state, F2 : set_Ho840737317_state]: ((finite1986656878_state @ F2) => ((~ ((F2 = bot_bo105666705_state))) => ((~ ((member109514606_state @ X3 @ F2))) => ((P @ F2) => (P @ (insert776267541_state @ X3 @ F2))))))) => (P @ F)))))))). % finite_ne_induct
thf(fact_67_finite_OemptyI, axiom,
    ((finite_finite_pname @ bot_bot_set_pname))). % finite.emptyI
thf(fact_68_finite_OemptyI, axiom,
    ((finite1986656878_state @ bot_bo105666705_state))). % finite.emptyI
thf(fact_69_infinite__imp__nonempty, axiom,
    ((![S4 : set_pname]: ((~ ((finite_finite_pname @ S4))) => (~ ((S4 = bot_bot_set_pname))))))). % infinite_imp_nonempty
thf(fact_70_infinite__imp__nonempty, axiom,
    ((![S4 : set_Ho840737317_state]: ((~ ((finite1986656878_state @ S4))) => (~ ((S4 = bot_bo105666705_state))))))). % infinite_imp_nonempty
thf(fact_71_finite_OinsertI, axiom,
    ((![A2 : set_Ho840737317_state, A : hoare_958474565_state]: ((finite1986656878_state @ A2) => (finite1986656878_state @ (insert776267541_state @ A @ A2)))))). % finite.insertI
thf(fact_72_finite_OinsertI, axiom,
    ((![A2 : set_pname, A : pname]: ((finite_finite_pname @ A2) => (finite_finite_pname @ (insert_pname @ A @ A2)))))). % finite.insertI
thf(fact_73_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, F2 : set_pname]: ((finite_finite_pname @ F2) => ((~ ((member_pname @ X3 @ F2))) => ((P @ F2) => (P @ (insert_pname @ X3 @ F2)))))) => (P @ A2))))))). % infinite_finite_induct
thf(fact_74_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, F2 : set_Ho840737317_state]: ((finite1986656878_state @ F2) => ((~ ((member109514606_state @ X3 @ F2))) => ((P @ F2) => (P @ (insert776267541_state @ X3 @ F2)))))) => (P @ A2))))))). % infinite_finite_induct
thf(fact_75_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_76_bot__empty__eq, axiom,
    ((bot_bo1428770700tate_o = (^[X2 : hoare_958474565_state]: (member109514606_state @ X2 @ bot_bo105666705_state))))). % bot_empty_eq
thf(fact_77_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_78_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_79_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_80_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_81_com_Odistinct_I41_J, axiom,
    ((![X41 : com, X42 : com, X7 : pname]: (~ (((semi @ X41 @ X42) = (body2 @ X7))))))). % com.distinct(41)
thf(fact_82_com_Odistinct_I5_J, axiom,
    ((![X41 : com, X42 : com]: (~ ((skip = (semi @ X41 @ X42))))))). % com.distinct(5)
thf(fact_83_finite__subset__induct, axiom,
    ((![F : set_pname, A2 : set_pname, P : set_pname > $o]: ((finite_finite_pname @ F) => ((ord_le865024672_pname @ F @ A2) => ((P @ bot_bot_set_pname) => ((![A5 : pname, F2 : set_pname]: ((finite_finite_pname @ F2) => ((member_pname @ A5 @ A2) => ((~ ((member_pname @ A5 @ F2))) => ((P @ F2) => (P @ (insert_pname @ A5 @ F2))))))) => (P @ F)))))))). % finite_subset_induct
thf(fact_84_finite__subset__induct, axiom,
    ((![F : set_Ho840737317_state, A2 : set_Ho840737317_state, P : set_Ho840737317_state > $o]: ((finite1986656878_state @ F) => ((ord_le1945819589_state @ F @ A2) => ((P @ bot_bo105666705_state) => ((![A5 : hoare_958474565_state, F2 : set_Ho840737317_state]: ((finite1986656878_state @ F2) => ((member109514606_state @ A5 @ A2) => ((~ ((member109514606_state @ A5 @ F2))) => ((P @ F2) => (P @ (insert776267541_state @ A5 @ F2))))))) => (P @ F)))))))). % finite_subset_induct
thf(fact_85_finite__subset__induct_H, axiom,
    ((![F : set_pname, A2 : set_pname, P : set_pname > $o]: ((finite_finite_pname @ F) => ((ord_le865024672_pname @ F @ A2) => ((P @ bot_bot_set_pname) => ((![A5 : pname, F2 : set_pname]: ((finite_finite_pname @ F2) => ((member_pname @ A5 @ A2) => ((ord_le865024672_pname @ F2 @ A2) => ((~ ((member_pname @ A5 @ F2))) => ((P @ F2) => (P @ (insert_pname @ A5 @ F2)))))))) => (P @ F)))))))). % finite_subset_induct'
thf(fact_86_finite__subset__induct_H, axiom,
    ((![F : set_Ho840737317_state, A2 : set_Ho840737317_state, P : set_Ho840737317_state > $o]: ((finite1986656878_state @ F) => ((ord_le1945819589_state @ F @ A2) => ((P @ bot_bo105666705_state) => ((![A5 : hoare_958474565_state, F2 : set_Ho840737317_state]: ((finite1986656878_state @ F2) => ((member109514606_state @ A5 @ A2) => ((ord_le1945819589_state @ F2 @ A2) => ((~ ((member109514606_state @ A5 @ F2))) => ((P @ F2) => (P @ (insert776267541_state @ A5 @ F2)))))))) => (P @ F)))))))). % finite_subset_induct'
thf(fact_87_subsetI, axiom,
    ((![A2 : set_Ho840737317_state, B : set_Ho840737317_state]: ((![X3 : hoare_958474565_state]: ((member109514606_state @ X3 @ A2) => (member109514606_state @ X3 @ B))) => (ord_le1945819589_state @ A2 @ B))))). % subsetI
thf(fact_88_empty__subsetI, axiom,
    ((![A2 : set_Ho840737317_state]: (ord_le1945819589_state @ bot_bo105666705_state @ A2)))). % empty_subsetI
thf(fact_89_subset__empty, axiom,
    ((![A2 : set_Ho840737317_state]: ((ord_le1945819589_state @ A2 @ bot_bo105666705_state) = (A2 = bot_bo105666705_state))))). % subset_empty
thf(fact_90_insert__subset, axiom,
    ((![X : hoare_958474565_state, A2 : set_Ho840737317_state, B : set_Ho840737317_state]: ((ord_le1945819589_state @ (insert776267541_state @ X @ A2) @ B) = (((member109514606_state @ X @ B)) & ((ord_le1945819589_state @ A2 @ B))))))). % insert_subset
thf(fact_91_singleton__insert__inj__eq_H, axiom,
    ((![A : hoare_958474565_state, A2 : set_Ho840737317_state, B2 : hoare_958474565_state]: (((insert776267541_state @ A @ A2) = (insert776267541_state @ B2 @ bot_bo105666705_state)) = (((A = B2)) & ((ord_le1945819589_state @ A2 @ (insert776267541_state @ B2 @ bot_bo105666705_state)))))))). % singleton_insert_inj_eq'
thf(fact_92_singleton__insert__inj__eq, axiom,
    ((![B2 : hoare_958474565_state, A : hoare_958474565_state, A2 : set_Ho840737317_state]: (((insert776267541_state @ B2 @ bot_bo105666705_state) = (insert776267541_state @ A @ A2)) = (((A = B2)) & ((ord_le1945819589_state @ A2 @ (insert776267541_state @ B2 @ bot_bo105666705_state)))))))). % singleton_insert_inj_eq
thf(fact_93_thin, axiom,
    ((![G2 : set_Ho840737317_state, Ts : set_Ho840737317_state, G : set_Ho840737317_state]: ((hoare_604442164_state @ G2 @ Ts) => ((ord_le1945819589_state @ G2 @ G) => (hoare_604442164_state @ G @ Ts)))))). % thin
thf(fact_94_asm, axiom,
    ((![Ts : set_Ho840737317_state, G : set_Ho840737317_state]: ((ord_le1945819589_state @ Ts @ G) => (hoare_604442164_state @ G @ Ts))))). % asm
thf(fact_95_weaken, axiom,
    ((![G : set_Ho840737317_state, Ts2 : set_Ho840737317_state, Ts : set_Ho840737317_state]: ((hoare_604442164_state @ G @ Ts2) => ((ord_le1945819589_state @ Ts @ Ts2) => (hoare_604442164_state @ G @ Ts)))))). % weaken
thf(fact_96_subset__iff, axiom,
    ((ord_le1945819589_state = (^[A3 : set_Ho840737317_state]: (^[B5 : set_Ho840737317_state]: (![T3 : hoare_958474565_state]: (((member109514606_state @ T3 @ A3)) => ((member109514606_state @ T3 @ B5))))))))). % subset_iff
thf(fact_97_subset__eq, axiom,
    ((ord_le1945819589_state = (^[A3 : set_Ho840737317_state]: (^[B5 : set_Ho840737317_state]: (![X2 : hoare_958474565_state]: (((member109514606_state @ X2 @ A3)) => ((member109514606_state @ X2 @ B5))))))))). % subset_eq
thf(fact_98_subsetD, axiom,
    ((![A2 : set_Ho840737317_state, B : set_Ho840737317_state, C : hoare_958474565_state]: ((ord_le1945819589_state @ A2 @ B) => ((member109514606_state @ C @ A2) => (member109514606_state @ C @ B)))))). % subsetD
thf(fact_99_in__mono, axiom,
    ((![A2 : set_Ho840737317_state, B : set_Ho840737317_state, X : hoare_958474565_state]: ((ord_le1945819589_state @ A2 @ B) => ((member109514606_state @ X @ A2) => (member109514606_state @ X @ B)))))). % in_mono
thf(fact_100_insert__mono, axiom,
    ((![C3 : set_Ho840737317_state, D2 : set_Ho840737317_state, A : hoare_958474565_state]: ((ord_le1945819589_state @ C3 @ D2) => (ord_le1945819589_state @ (insert776267541_state @ A @ C3) @ (insert776267541_state @ A @ D2)))))). % insert_mono
thf(fact_101_subset__insert, axiom,
    ((![X : hoare_958474565_state, A2 : set_Ho840737317_state, B : set_Ho840737317_state]: ((~ ((member109514606_state @ X @ A2))) => ((ord_le1945819589_state @ A2 @ (insert776267541_state @ X @ B)) = (ord_le1945819589_state @ A2 @ B)))))). % subset_insert
thf(fact_102_subset__insertI, axiom,
    ((![B : set_Ho840737317_state, A : hoare_958474565_state]: (ord_le1945819589_state @ B @ (insert776267541_state @ A @ B))))). % subset_insertI
thf(fact_103_subset__insertI2, axiom,
    ((![A2 : set_Ho840737317_state, B : set_Ho840737317_state, B2 : hoare_958474565_state]: ((ord_le1945819589_state @ A2 @ B) => (ord_le1945819589_state @ A2 @ (insert776267541_state @ B2 @ B)))))). % subset_insertI2
thf(fact_104_bot_Oextremum, axiom,
    ((![A : set_Ho840737317_state]: (ord_le1945819589_state @ bot_bo105666705_state @ A)))). % bot.extremum
thf(fact_105_bot_Oextremum__unique, axiom,
    ((![A : set_Ho840737317_state]: ((ord_le1945819589_state @ A @ bot_bo105666705_state) = (A = bot_bo105666705_state))))). % bot.extremum_unique
thf(fact_106_bot_Oextremum__uniqueI, axiom,
    ((![A : set_Ho840737317_state]: ((ord_le1945819589_state @ A @ bot_bo105666705_state) => (A = bot_bo105666705_state))))). % bot.extremum_uniqueI
thf(fact_107_finite__subset, axiom,
    ((![A2 : set_pname, B : set_pname]: ((ord_le865024672_pname @ A2 @ B) => ((finite_finite_pname @ B) => (finite_finite_pname @ A2)))))). % finite_subset
thf(fact_108_infinite__super, axiom,
    ((![S4 : set_pname, T4 : set_pname]: ((ord_le865024672_pname @ S4 @ T4) => ((~ ((finite_finite_pname @ S4))) => (~ ((finite_finite_pname @ T4)))))))). % infinite_super
thf(fact_109_rev__finite__subset, axiom,
    ((![B : set_pname, A2 : set_pname]: ((finite_finite_pname @ B) => ((ord_le865024672_pname @ A2 @ B) => (finite_finite_pname @ A2)))))). % rev_finite_subset
thf(fact_110_subset__singleton__iff, axiom,
    ((![X4 : set_Ho840737317_state, A : hoare_958474565_state]: ((ord_le1945819589_state @ X4 @ (insert776267541_state @ A @ bot_bo105666705_state)) = (((X4 = bot_bo105666705_state)) | ((X4 = (insert776267541_state @ A @ bot_bo105666705_state)))))))). % subset_singleton_iff
thf(fact_111_subset__singletonD, axiom,
    ((![A2 : set_Ho840737317_state, X : hoare_958474565_state]: ((ord_le1945819589_state @ A2 @ (insert776267541_state @ X @ bot_bo105666705_state)) => ((A2 = bot_bo105666705_state) | (A2 = (insert776267541_state @ X @ bot_bo105666705_state))))))). % subset_singletonD

% 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,
    ((hoare_604442164_state @ g @ (insert776267541_state @ (hoare_Mirabelle_MGT @ skip) @ bot_bo105666705_state)))).
