% 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_329__3253238_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:13:49.365

% Could-be-implicit typings (4)
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__Com__Ostate, type,
    state : $tType).
thf(ty_n_t__Com__Ocom, type,
    com : $tType).

% Explicit typings (20)
thf(sy_c_Com_Ocom_OSKIP, type,
    skip : com).
thf(sy_c_Com_Ocom_OSemi, type,
    semi : com > com > com).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J, type,
    minus_1628593292_state : set_Ho840737317_state > set_Ho840737317_state > set_Ho840737317_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_Otriple_Otriple_001t__Com__Ostate, type,
    hoare_1659279548_state : (state > state > $o) > com > (state > state > $o) > hoare_958474565_state).
thf(sy_c_Natural_Oevalc, type,
    evalc : com > state > state > $o).
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__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__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__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_Opairwise_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
    pairwi17519280_state : (hoare_958474565_state > hoare_958474565_state > $o) > 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__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J, type,
    member109514606_state : hoare_958474565_state > set_Ho840737317_state > $o).
thf(sy_v_P, type,
    p : state > state > $o).
thf(sy_v_Q, type,
    q : state > state > $o).
thf(sy_v_c, type,
    c : com).

% Relevant facts (100)
thf(fact_0_triple_Oinject, axiom,
    ((![X1 : state > state > $o, X2 : com, X3 : state > state > $o, Y1 : state > state > $o, Y2 : com, Y3 : state > state > $o]: (((hoare_1659279548_state @ X1 @ X2 @ X3) = (hoare_1659279548_state @ Y1 @ Y2 @ Y3)) = (((X1 = Y1)) & ((((X2 = Y2)) & ((X3 = Y3))))))))). % triple.inject
thf(fact_1_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_2_triple_Oexhaust, axiom,
    ((![Y : hoare_958474565_state]: (~ ((![X12 : state > state > $o, X22 : com, X32 : state > state > $o]: (~ ((Y = (hoare_1659279548_state @ X12 @ X22 @ X32)))))))))). % triple.exhaust
thf(fact_3_singletonI, axiom,
    ((![A : hoare_958474565_state]: (member109514606_state @ A @ (insert776267541_state @ A @ bot_bo105666705_state))))). % singletonI
thf(fact_4_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_5_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_6_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_7_empty__iff, axiom,
    ((![C : hoare_958474565_state]: (~ ((member109514606_state @ C @ bot_bo105666705_state)))))). % empty_iff
thf(fact_8_all__not__in__conv, axiom,
    ((![A2 : set_Ho840737317_state]: ((![X4 : hoare_958474565_state]: (~ ((member109514606_state @ X4 @ A2)))) = (A2 = bot_bo105666705_state))))). % all_not_in_conv
thf(fact_9_Collect__empty__eq, axiom,
    ((![P : hoare_958474565_state > $o]: (((collec305460656_state @ P) = bot_bo105666705_state) = (![X4 : hoare_958474565_state]: (~ ((P @ X4)))))))). % Collect_empty_eq
thf(fact_10_empty__Collect__eq, axiom,
    ((![P : hoare_958474565_state > $o]: ((bot_bo105666705_state = (collec305460656_state @ P)) = (![X4 : hoare_958474565_state]: (~ ((P @ X4)))))))). % empty_Collect_eq
thf(fact_11_singletonD, axiom,
    ((![B2 : hoare_958474565_state, A : hoare_958474565_state]: ((member109514606_state @ B2 @ (insert776267541_state @ A @ bot_bo105666705_state)) => (B2 = A))))). % singletonD
thf(fact_12_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_13_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_14_bot__set__def, axiom,
    ((bot_bo105666705_state = (collec305460656_state @ bot_bo1428770700tate_o)))). % bot_set_def
thf(fact_15_ex__in__conv, axiom,
    ((![A2 : set_Ho840737317_state]: ((?[X4 : hoare_958474565_state]: (member109514606_state @ X4 @ A2)) = (~ ((A2 = bot_bo105666705_state))))))). % ex_in_conv
thf(fact_16_equals0I, axiom,
    ((![A2 : set_Ho840737317_state]: ((![Y4 : hoare_958474565_state]: (~ ((member109514606_state @ Y4 @ A2)))) => (A2 = bot_bo105666705_state))))). % equals0I
thf(fact_17_equals0D, axiom,
    ((![A2 : set_Ho840737317_state, A : hoare_958474565_state]: ((A2 = bot_bo105666705_state) => (~ ((member109514606_state @ A @ A2))))))). % equals0D
thf(fact_18_emptyE, axiom,
    ((![A : hoare_958474565_state]: (~ ((member109514606_state @ A @ bot_bo105666705_state)))))). % emptyE
thf(fact_19_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_20_insert__commute, axiom,
    ((![X : hoare_958474565_state, Y : hoare_958474565_state, A2 : set_Ho840737317_state]: ((insert776267541_state @ X @ (insert776267541_state @ Y @ A2)) = (insert776267541_state @ Y @ (insert776267541_state @ X @ A2)))))). % insert_commute
thf(fact_21_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_22_insert__absorb, axiom,
    ((![A : hoare_958474565_state, A2 : set_Ho840737317_state]: ((member109514606_state @ A @ A2) => ((insert776267541_state @ A @ A2) = A2))))). % insert_absorb
thf(fact_23_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_24_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_25_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_26_insertI1, axiom,
    ((![A : hoare_958474565_state, B : set_Ho840737317_state]: (member109514606_state @ A @ (insert776267541_state @ A @ B))))). % insertI1
thf(fact_27_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_28_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_29_insert__not__empty, axiom,
    ((![A : hoare_958474565_state, A2 : set_Ho840737317_state]: (~ (((insert776267541_state @ A @ A2) = bot_bo105666705_state)))))). % insert_not_empty
thf(fact_30_the__elem__eq, axiom,
    ((![X : hoare_958474565_state]: ((the_el1300254266_state @ (insert776267541_state @ X @ bot_bo105666705_state)) = X)))). % the_elem_eq
thf(fact_31_is__singletonI, axiom,
    ((![X : hoare_958474565_state]: (is_sin536631353_state @ (insert776267541_state @ X @ bot_bo105666705_state))))). % is_singletonI
thf(fact_32_Set_Ois__empty__def, axiom,
    ((is_emp266830871_state = (^[A3 : set_Ho840737317_state]: (A3 = bot_bo105666705_state))))). % Set.is_empty_def
thf(fact_33_is__singleton__def, axiom,
    ((is_sin536631353_state = (^[A3 : set_Ho840737317_state]: (?[X4 : hoare_958474565_state]: (A3 = (insert776267541_state @ X4 @ bot_bo105666705_state))))))). % is_singleton_def
thf(fact_34_is__singletonE, axiom,
    ((![A2 : set_Ho840737317_state]: ((is_sin536631353_state @ A2) => (~ ((![X5 : hoare_958474565_state]: (~ ((A2 = (insert776267541_state @ X5 @ bot_bo105666705_state))))))))))). % is_singletonE
thf(fact_35_com__det, axiom,
    ((![C : com, S : state, T : state, U : state]: ((evalc @ C @ S @ T) => ((evalc @ C @ S @ U) => (U = T)))))). % com_det
thf(fact_36_conseq, axiom,
    ((![P : state > state > $o, G : set_Ho840737317_state, C : com, Q : state > state > $o]: ((![Z : state, S2 : state]: ((P @ Z @ S2) => (?[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 @ S2) => (Q2 @ Z2 @ S3))) => (Q @ Z @ S3))))))) => (hoare_604442164_state @ G @ (insert776267541_state @ (hoare_1659279548_state @ P @ C @ Q) @ bot_bo105666705_state)))))). % conseq
thf(fact_37_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, S2 : state]: ((P @ Z @ S2) => (![S3 : state]: ((![Z2 : state]: ((P3 @ Z2 @ S2) => (Q3 @ Z2 @ S3))) => (Q @ Z @ S3))))) => (hoare_604442164_state @ G @ (insert776267541_state @ (hoare_1659279548_state @ P @ C @ Q) @ bot_bo105666705_state))))))). % conseq12
thf(fact_38_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, S2 : state]: ((Q3 @ Z @ S2) => (Q @ Z @ S2))) => (hoare_604442164_state @ G @ (insert776267541_state @ (hoare_1659279548_state @ P @ C @ Q) @ bot_bo105666705_state))))))). % conseq2
thf(fact_39_empty, axiom,
    ((![G : set_Ho840737317_state]: (hoare_604442164_state @ G @ bot_bo105666705_state)))). % empty
thf(fact_40_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_41_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_42_Collect__mem__eq, axiom,
    ((![A2 : set_Ho840737317_state]: ((collec305460656_state @ (^[X4 : hoare_958474565_state]: (member109514606_state @ X4 @ A2))) = A2)))). % Collect_mem_eq
thf(fact_43_Collect__cong, axiom,
    ((![P : hoare_958474565_state > $o, Q : hoare_958474565_state > $o]: ((![X5 : hoare_958474565_state]: ((P @ X5) = (Q @ X5))) => ((collec305460656_state @ P) = (collec305460656_state @ Q)))))). % Collect_cong
thf(fact_44_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_45_derivs__insertD, axiom,
    ((![G : set_Ho840737317_state, T : hoare_958474565_state, Ts : set_Ho840737317_state]: ((hoare_604442164_state @ G @ (insert776267541_state @ T @ Ts)) => ((hoare_604442164_state @ G @ (insert776267541_state @ T @ bot_bo105666705_state)) & (hoare_604442164_state @ G @ Ts)))))). % derivs_insertD
thf(fact_46_hoare__derivs_Oinsert, axiom,
    ((![G : set_Ho840737317_state, T : hoare_958474565_state, Ts : set_Ho840737317_state]: ((hoare_604442164_state @ G @ (insert776267541_state @ T @ bot_bo105666705_state)) => ((hoare_604442164_state @ G @ Ts) => (hoare_604442164_state @ G @ (insert776267541_state @ T @ Ts))))))). % hoare_derivs.insert
thf(fact_47_is__singletonI_H, axiom,
    ((![A2 : set_Ho840737317_state]: ((~ ((A2 = bot_bo105666705_state))) => ((![X5 : hoare_958474565_state, Y4 : hoare_958474565_state]: ((member109514606_state @ X5 @ A2) => ((member109514606_state @ Y4 @ A2) => (X5 = Y4)))) => (is_sin536631353_state @ A2)))))). % is_singletonI'
thf(fact_48_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, S2 : state]: ((P @ Z @ S2) => (P3 @ Z @ S2))) => (hoare_604442164_state @ G @ (insert776267541_state @ (hoare_1659279548_state @ P @ C @ Q) @ bot_bo105666705_state))))))). % conseq1
thf(fact_49_bot__empty__eq, axiom,
    ((bot_bo1428770700tate_o = (^[X4 : hoare_958474565_state]: (member109514606_state @ X4 @ bot_bo105666705_state))))). % bot_empty_eq
thf(fact_50_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_51_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_52_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_53_pairwise__singleton, axiom,
    ((![P : hoare_958474565_state > hoare_958474565_state > $o, A2 : hoare_958474565_state]: (pairwi17519280_state @ P @ (insert776267541_state @ A2 @ bot_bo105666705_state))))). % pairwise_singleton
thf(fact_54_pairwiseI, axiom,
    ((![S4 : set_Ho840737317_state, R : hoare_958474565_state > hoare_958474565_state > $o]: ((![X5 : hoare_958474565_state, Y4 : hoare_958474565_state]: ((member109514606_state @ X5 @ S4) => ((member109514606_state @ Y4 @ S4) => ((~ ((X5 = Y4))) => (R @ X5 @ Y4))))) => (pairwi17519280_state @ R @ S4))))). % pairwiseI
thf(fact_55_pairwiseD, axiom,
    ((![R : hoare_958474565_state > hoare_958474565_state > $o, S4 : set_Ho840737317_state, X : hoare_958474565_state, Y : hoare_958474565_state]: ((pairwi17519280_state @ R @ S4) => ((member109514606_state @ X @ S4) => ((member109514606_state @ Y @ S4) => ((~ ((X = Y))) => (R @ X @ Y)))))))). % pairwiseD
thf(fact_56_pairwise__empty, axiom,
    ((![P : hoare_958474565_state > hoare_958474565_state > $o]: (pairwi17519280_state @ P @ bot_bo105666705_state)))). % pairwise_empty
thf(fact_57_pairwise__insert, axiom,
    ((![R2 : hoare_958474565_state > hoare_958474565_state > $o, X : hoare_958474565_state, S : set_Ho840737317_state]: ((pairwi17519280_state @ R2 @ (insert776267541_state @ X @ S)) = (((![Y5 : hoare_958474565_state]: (((((member109514606_state @ Y5 @ S)) & ((~ ((Y5 = X)))))) => ((((R2 @ X @ Y5)) & ((R2 @ Y5 @ X))))))) & ((pairwi17519280_state @ R2 @ S))))))). % pairwise_insert
thf(fact_58_evalc_OSemi, axiom,
    ((![C0 : com, S0 : state, S1 : state, C1 : com, S22 : state]: ((evalc @ C0 @ S0 @ S1) => ((evalc @ C1 @ S1 @ S22) => (evalc @ (semi @ C0 @ C1) @ S0 @ S22)))))). % evalc.Semi
thf(fact_59_evalc__elim__cases_I4_J, axiom,
    ((![C1 : com, C22 : com, S : state, T : state]: ((evalc @ (semi @ C1 @ C22) @ S @ T) => (~ ((![S12 : state]: ((evalc @ C1 @ S @ S12) => (~ ((evalc @ C22 @ S12 @ T))))))))))). % evalc_elim_cases(4)
thf(fact_60_evalc_OSkip, axiom,
    ((![S : state]: (evalc @ skip @ S @ S)))). % evalc.Skip
thf(fact_61_evalc__elim__cases_I1_J, axiom,
    ((![S : state, T : state]: ((evalc @ skip @ S @ T) => (T = S))))). % evalc_elim_cases(1)
thf(fact_62_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_63_com_Odistinct_I5_J, axiom,
    ((![X41 : com, X42 : com]: (~ ((skip = (semi @ X41 @ X42))))))). % com.distinct(5)
thf(fact_64_pairwise__alt, axiom,
    ((pairwi17519280_state = (^[R3 : hoare_958474565_state > hoare_958474565_state > $o]: (^[S5 : set_Ho840737317_state]: (![X4 : hoare_958474565_state]: (((member109514606_state @ X4 @ S5)) => ((![Y5 : hoare_958474565_state]: (((member109514606_state @ Y5 @ (minus_1628593292_state @ S5 @ (insert776267541_state @ X4 @ bot_bo105666705_state)))) => ((R3 @ X4 @ Y5)))))))))))). % pairwise_alt
thf(fact_65_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_66_subsetI, axiom,
    ((![A2 : set_Ho840737317_state, B : set_Ho840737317_state]: ((![X5 : hoare_958474565_state]: ((member109514606_state @ X5 @ A2) => (member109514606_state @ X5 @ B))) => (ord_le1945819589_state @ A2 @ B))))). % subsetI
thf(fact_67_DiffI, axiom,
    ((![C : hoare_958474565_state, A2 : set_Ho840737317_state, B : set_Ho840737317_state]: ((member109514606_state @ C @ A2) => ((~ ((member109514606_state @ C @ B))) => (member109514606_state @ C @ (minus_1628593292_state @ A2 @ B))))))). % DiffI
thf(fact_68_Diff__iff, axiom,
    ((![C : hoare_958474565_state, A2 : set_Ho840737317_state, B : set_Ho840737317_state]: ((member109514606_state @ C @ (minus_1628593292_state @ A2 @ B)) = (((member109514606_state @ C @ A2)) & ((~ ((member109514606_state @ C @ B))))))))). % Diff_iff
thf(fact_69_subset__empty, axiom,
    ((![A2 : set_Ho840737317_state]: ((ord_le1945819589_state @ A2 @ bot_bo105666705_state) = (A2 = bot_bo105666705_state))))). % subset_empty
thf(fact_70_empty__subsetI, axiom,
    ((![A2 : set_Ho840737317_state]: (ord_le1945819589_state @ bot_bo105666705_state @ A2)))). % empty_subsetI
thf(fact_71_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_72_Diff__empty, axiom,
    ((![A2 : set_Ho840737317_state]: ((minus_1628593292_state @ A2 @ bot_bo105666705_state) = A2)))). % Diff_empty
thf(fact_73_empty__Diff, axiom,
    ((![A2 : set_Ho840737317_state]: ((minus_1628593292_state @ bot_bo105666705_state @ A2) = bot_bo105666705_state)))). % empty_Diff
thf(fact_74_Diff__cancel, axiom,
    ((![A2 : set_Ho840737317_state]: ((minus_1628593292_state @ A2 @ A2) = bot_bo105666705_state)))). % Diff_cancel
thf(fact_75_Diff__insert0, axiom,
    ((![X : hoare_958474565_state, A2 : set_Ho840737317_state, B : set_Ho840737317_state]: ((~ ((member109514606_state @ X @ A2))) => ((minus_1628593292_state @ A2 @ (insert776267541_state @ X @ B)) = (minus_1628593292_state @ A2 @ B)))))). % Diff_insert0
thf(fact_76_insert__Diff1, axiom,
    ((![X : hoare_958474565_state, B : set_Ho840737317_state, A2 : set_Ho840737317_state]: ((member109514606_state @ X @ B) => ((minus_1628593292_state @ (insert776267541_state @ X @ A2) @ B) = (minus_1628593292_state @ A2 @ B)))))). % insert_Diff1
thf(fact_77_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_78_Diff__eq__empty__iff, axiom,
    ((![A2 : set_Ho840737317_state, B : set_Ho840737317_state]: (((minus_1628593292_state @ A2 @ B) = bot_bo105666705_state) = (ord_le1945819589_state @ A2 @ B))))). % Diff_eq_empty_iff
thf(fact_79_insert__Diff__single, axiom,
    ((![A : hoare_958474565_state, A2 : set_Ho840737317_state]: ((insert776267541_state @ A @ (minus_1628593292_state @ A2 @ (insert776267541_state @ A @ bot_bo105666705_state))) = (insert776267541_state @ A @ A2))))). % insert_Diff_single
thf(fact_80_Diff__single__insert, axiom,
    ((![A2 : set_Ho840737317_state, X : hoare_958474565_state, B : set_Ho840737317_state]: ((ord_le1945819589_state @ (minus_1628593292_state @ A2 @ (insert776267541_state @ X @ bot_bo105666705_state)) @ B) => (ord_le1945819589_state @ A2 @ (insert776267541_state @ X @ B)))))). % Diff_single_insert
thf(fact_81_subset__insert__iff, axiom,
    ((![A2 : set_Ho840737317_state, X : hoare_958474565_state, B : set_Ho840737317_state]: ((ord_le1945819589_state @ A2 @ (insert776267541_state @ X @ B)) = (((((member109514606_state @ X @ A2)) => ((ord_le1945819589_state @ (minus_1628593292_state @ A2 @ (insert776267541_state @ X @ bot_bo105666705_state)) @ B)))) & ((((~ ((member109514606_state @ X @ A2)))) => ((ord_le1945819589_state @ A2 @ B))))))))). % subset_insert_iff
thf(fact_82_DiffE, axiom,
    ((![C : hoare_958474565_state, A2 : set_Ho840737317_state, B : set_Ho840737317_state]: ((member109514606_state @ C @ (minus_1628593292_state @ A2 @ B)) => (~ (((member109514606_state @ C @ A2) => (member109514606_state @ C @ B)))))))). % DiffE
thf(fact_83_DiffD1, axiom,
    ((![C : hoare_958474565_state, A2 : set_Ho840737317_state, B : set_Ho840737317_state]: ((member109514606_state @ C @ (minus_1628593292_state @ A2 @ B)) => (member109514606_state @ C @ A2))))). % DiffD1
thf(fact_84_DiffD2, axiom,
    ((![C : hoare_958474565_state, A2 : set_Ho840737317_state, B : set_Ho840737317_state]: ((member109514606_state @ C @ (minus_1628593292_state @ A2 @ B)) => (~ ((member109514606_state @ C @ B))))))). % DiffD2
thf(fact_85_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_86_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_87_subset__eq, axiom,
    ((ord_le1945819589_state = (^[A3 : set_Ho840737317_state]: (^[B4 : set_Ho840737317_state]: (![X4 : hoare_958474565_state]: (((member109514606_state @ X4 @ A3)) => ((member109514606_state @ X4 @ B4))))))))). % subset_eq
thf(fact_88_subset__iff, axiom,
    ((ord_le1945819589_state = (^[A3 : set_Ho840737317_state]: (^[B4 : set_Ho840737317_state]: (![T2 : hoare_958474565_state]: (((member109514606_state @ T2 @ A3)) => ((member109514606_state @ T2 @ B4))))))))). % subset_iff
thf(fact_89_Collect__mono, axiom,
    ((![P : hoare_958474565_state > $o, Q : hoare_958474565_state > $o]: ((![X5 : hoare_958474565_state]: ((P @ X5) => (Q @ X5))) => (ord_le1945819589_state @ (collec305460656_state @ P) @ (collec305460656_state @ Q)))))). % Collect_mono
thf(fact_90_Collect__mono__iff, axiom,
    ((![P : hoare_958474565_state > $o, Q : hoare_958474565_state > $o]: ((ord_le1945819589_state @ (collec305460656_state @ P) @ (collec305460656_state @ Q)) = (![X4 : hoare_958474565_state]: (((P @ X4)) => ((Q @ X4)))))))). % Collect_mono_iff
thf(fact_91_subset__Diff__insert, axiom,
    ((![A2 : set_Ho840737317_state, B : set_Ho840737317_state, X : hoare_958474565_state, C3 : set_Ho840737317_state]: ((ord_le1945819589_state @ A2 @ (minus_1628593292_state @ B @ (insert776267541_state @ X @ C3))) = (((ord_le1945819589_state @ A2 @ (minus_1628593292_state @ B @ C3))) & ((~ ((member109514606_state @ X @ A2))))))))). % subset_Diff_insert
thf(fact_92_insert__Diff__if, axiom,
    ((![X : hoare_958474565_state, B : set_Ho840737317_state, A2 : set_Ho840737317_state]: (((member109514606_state @ X @ B) => ((minus_1628593292_state @ (insert776267541_state @ X @ A2) @ B) = (minus_1628593292_state @ A2 @ B))) & ((~ ((member109514606_state @ X @ B))) => ((minus_1628593292_state @ (insert776267541_state @ X @ A2) @ B) = (insert776267541_state @ X @ (minus_1628593292_state @ A2 @ B)))))))). % insert_Diff_if
thf(fact_93_bot_Oextremum, axiom,
    ((![A : set_Ho840737317_state]: (ord_le1945819589_state @ bot_bo105666705_state @ A)))). % bot.extremum
thf(fact_94_bot_Oextremum__unique, axiom,
    ((![A : set_Ho840737317_state]: ((ord_le1945819589_state @ A @ bot_bo105666705_state) = (A = bot_bo105666705_state))))). % bot.extremum_unique
thf(fact_95_bot_Oextremum__uniqueI, axiom,
    ((![A : set_Ho840737317_state]: ((ord_le1945819589_state @ A @ bot_bo105666705_state) => (A = bot_bo105666705_state))))). % bot.extremum_uniqueI
thf(fact_96_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_97_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_98_subset__insertI, axiom,
    ((![B : set_Ho840737317_state, A : hoare_958474565_state]: (ord_le1945819589_state @ B @ (insert776267541_state @ A @ B))))). % subset_insertI
thf(fact_99_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

% Conjectures (2)
thf(conj_0, hypothesis,
    ((hoare_318887606_state @ bot_bo105666705_state @ (insert776267541_state @ (hoare_1659279548_state @ p @ c @ q) @ bot_bo105666705_state)))).
thf(conj_1, conjecture,
    ((![Z : state, S2 : state]: ((~ ((p @ Z @ S2))) | (![S3 : state]: ((?[Z2 : state]: ((Z2 = S2) & (~ ((evalc @ c @ Z2 @ S3))))) | (q @ Z @ S3))))))).
