% 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_404__3254488_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:14:31.357

% Could-be-implicit typings (5)
thf(ty_n_t__Set__Oset_It__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J_J, type,
    set_se421025541_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__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 (22)
thf(sy_c_Com_OWT, type,
    wt : com > $o).
thf(sy_c_Com_OWT__bodies, type,
    wT_bodies : $o).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J, type,
    uminus1561791772_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_Ostate__not__singleton, type,
    hoare_405891322gleton : $o).
thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J, type,
    ord_le229826769_state : set_Ho840737317_state > set_Ho840737317_state > $o).
thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J_J, type,
    ord_le1174267313_state : set_se421025541_state > set_se421025541_state > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J_J, type,
    ord_le1366095314_state : ($o > set_Ho840737317_state) > ($o > set_Ho840737317_state) > $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_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J_J, type,
    ord_le1363676837_state : set_se421025541_state > set_se421025541_state > $o).
thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J, type,
    order_800490238_state : (set_Ho840737317_state > $o) > set_Ho840737317_state).
thf(sy_c_Orderings_Oorder__class_Oantimono_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J, type,
    order_1585167943_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__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J, type,
    set_or411291354_state : set_Ho840737317_state > set_Ho840737317_state > set_se421025541_state).
thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J, type,
    set_or524090864_state : set_Ho840737317_state > set_se421025541_state).
thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J, type,
    set_or898808300_state : set_Ho840737317_state > set_se421025541_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_c_member_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_It__Com__Ostate_J_J, type,
    member1959617614_state : set_Ho840737317_state > set_se421025541_state > $o).
thf(sy_v_G, type,
    g : set_Ho840737317_state).
thf(sy_v_c, type,
    c : com).
thf(sy_v_ts, type,
    ts : set_Ho840737317_state).

% Relevant facts (96)
thf(fact_0_thin, axiom,
    ((![G : set_Ho840737317_state, Ts : set_Ho840737317_state, G2 : set_Ho840737317_state]: ((hoare_604442164_state @ G @ Ts) => ((ord_le1945819589_state @ G @ G2) => (hoare_604442164_state @ G2 @ Ts)))))). % thin
thf(fact_1_single__stateE, axiom,
    ((hoare_405891322gleton => (![T : state]: (~ ((![S : state]: (S = T)))))))). % single_stateE
thf(fact_2_asm, axiom,
    ((![Ts : set_Ho840737317_state, G2 : set_Ho840737317_state]: ((ord_le1945819589_state @ Ts @ G2) => (hoare_604442164_state @ G2 @ Ts))))). % asm
thf(fact_3_cut, axiom,
    ((![G : set_Ho840737317_state, Ts : set_Ho840737317_state, G2 : set_Ho840737317_state]: ((hoare_604442164_state @ G @ Ts) => ((hoare_604442164_state @ G2 @ G) => (hoare_604442164_state @ G2 @ Ts)))))). % cut
thf(fact_4_weaken, axiom,
    ((![G2 : set_Ho840737317_state, Ts2 : set_Ho840737317_state, Ts : set_Ho840737317_state]: ((hoare_604442164_state @ G2 @ Ts2) => ((ord_le1945819589_state @ Ts @ Ts2) => (hoare_604442164_state @ G2 @ Ts)))))). % weaken
thf(fact_5_state__not__singleton__def, axiom,
    ((hoare_405891322gleton = (?[S2 : state]: (?[T2 : state]: (~ ((S2 = T2)))))))). % state_not_singleton_def
thf(fact_6_subsetI, axiom,
    ((![A : set_Ho840737317_state, B : set_Ho840737317_state]: ((![X : hoare_958474565_state]: ((member109514606_state @ X @ A) => (member109514606_state @ X @ B))) => (ord_le1945819589_state @ A @ B))))). % subsetI
thf(fact_7_subset__antisym, axiom,
    ((![A : set_Ho840737317_state, B : set_Ho840737317_state]: ((ord_le1945819589_state @ A @ B) => ((ord_le1945819589_state @ B @ A) => (A = B)))))). % subset_antisym
thf(fact_8_order__refl, axiom,
    ((![X2 : set_Ho840737317_state]: (ord_le1945819589_state @ X2 @ X2)))). % order_refl
thf(fact_9_in__mono, axiom,
    ((![A : set_Ho840737317_state, B : set_Ho840737317_state, X2 : hoare_958474565_state]: ((ord_le1945819589_state @ A @ B) => ((member109514606_state @ X2 @ A) => (member109514606_state @ X2 @ B)))))). % in_mono
thf(fact_10_subsetD, axiom,
    ((![A : set_Ho840737317_state, B : set_Ho840737317_state, C : hoare_958474565_state]: ((ord_le1945819589_state @ A @ B) => ((member109514606_state @ C @ A) => (member109514606_state @ C @ B)))))). % subsetD
thf(fact_11_equalityE, axiom,
    ((![A : set_Ho840737317_state, B : set_Ho840737317_state]: ((A = B) => (~ (((ord_le1945819589_state @ A @ B) => (~ ((ord_le1945819589_state @ B @ A)))))))))). % equalityE
thf(fact_12_subset__eq, axiom,
    ((ord_le1945819589_state = (^[A2 : set_Ho840737317_state]: (^[B2 : set_Ho840737317_state]: (![X3 : hoare_958474565_state]: (((member109514606_state @ X3 @ A2)) => ((member109514606_state @ X3 @ B2))))))))). % subset_eq
thf(fact_13_equalityD1, axiom,
    ((![A : set_Ho840737317_state, B : set_Ho840737317_state]: ((A = B) => (ord_le1945819589_state @ A @ B))))). % equalityD1
thf(fact_14_equalityD2, axiom,
    ((![A : set_Ho840737317_state, B : set_Ho840737317_state]: ((A = B) => (ord_le1945819589_state @ B @ A))))). % equalityD2
thf(fact_15_subset__iff, axiom,
    ((ord_le1945819589_state = (^[A2 : set_Ho840737317_state]: (^[B2 : set_Ho840737317_state]: (![T2 : hoare_958474565_state]: (((member109514606_state @ T2 @ A2)) => ((member109514606_state @ T2 @ B2))))))))). % subset_iff
thf(fact_16_subset__refl, axiom,
    ((![A : set_Ho840737317_state]: (ord_le1945819589_state @ A @ A)))). % subset_refl
thf(fact_17_Collect__mono, axiom,
    ((![P : hoare_958474565_state > $o, Q : hoare_958474565_state > $o]: ((![X : hoare_958474565_state]: ((P @ X) => (Q @ X))) => (ord_le1945819589_state @ (collec305460656_state @ P) @ (collec305460656_state @ Q)))))). % Collect_mono
thf(fact_18_dual__order_Oantisym, axiom,
    ((![B3 : set_Ho840737317_state, A3 : set_Ho840737317_state]: ((ord_le1945819589_state @ B3 @ A3) => ((ord_le1945819589_state @ A3 @ B3) => (A3 = B3)))))). % dual_order.antisym
thf(fact_19_dual__order_Oeq__iff, axiom,
    (((^[Y : set_Ho840737317_state]: (^[Z : set_Ho840737317_state]: (Y = Z))) = (^[A4 : set_Ho840737317_state]: (^[B4 : set_Ho840737317_state]: (((ord_le1945819589_state @ B4 @ A4)) & ((ord_le1945819589_state @ A4 @ B4)))))))). % dual_order.eq_iff
thf(fact_20_dual__order_Otrans, axiom,
    ((![B3 : set_Ho840737317_state, A3 : set_Ho840737317_state, C : set_Ho840737317_state]: ((ord_le1945819589_state @ B3 @ A3) => ((ord_le1945819589_state @ C @ B3) => (ord_le1945819589_state @ C @ A3)))))). % dual_order.trans
thf(fact_21_dual__order_Orefl, axiom,
    ((![A3 : set_Ho840737317_state]: (ord_le1945819589_state @ A3 @ A3)))). % dual_order.refl
thf(fact_22_order__trans, axiom,
    ((![X2 : set_Ho840737317_state, Y2 : set_Ho840737317_state, Z2 : set_Ho840737317_state]: ((ord_le1945819589_state @ X2 @ Y2) => ((ord_le1945819589_state @ Y2 @ Z2) => (ord_le1945819589_state @ X2 @ Z2)))))). % order_trans
thf(fact_23_order__class_Oorder_Oantisym, axiom,
    ((![A3 : set_Ho840737317_state, B3 : set_Ho840737317_state]: ((ord_le1945819589_state @ A3 @ B3) => ((ord_le1945819589_state @ B3 @ A3) => (A3 = B3)))))). % order_class.order.antisym
thf(fact_24_ord__le__eq__trans, axiom,
    ((![A3 : set_Ho840737317_state, B3 : set_Ho840737317_state, C : set_Ho840737317_state]: ((ord_le1945819589_state @ A3 @ B3) => ((B3 = C) => (ord_le1945819589_state @ A3 @ C)))))). % ord_le_eq_trans
thf(fact_25_ord__eq__le__trans, axiom,
    ((![A3 : set_Ho840737317_state, B3 : set_Ho840737317_state, C : set_Ho840737317_state]: ((A3 = B3) => ((ord_le1945819589_state @ B3 @ C) => (ord_le1945819589_state @ A3 @ C)))))). % ord_eq_le_trans
thf(fact_26_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y : set_Ho840737317_state]: (^[Z : set_Ho840737317_state]: (Y = Z))) = (^[A4 : set_Ho840737317_state]: (^[B4 : set_Ho840737317_state]: (((ord_le1945819589_state @ A4 @ B4)) & ((ord_le1945819589_state @ B4 @ A4)))))))). % order_class.order.eq_iff
thf(fact_27_antisym__conv, axiom,
    ((![Y2 : set_Ho840737317_state, X2 : set_Ho840737317_state]: ((ord_le1945819589_state @ Y2 @ X2) => ((ord_le1945819589_state @ X2 @ Y2) = (X2 = Y2)))))). % antisym_conv
thf(fact_28_order_Otrans, axiom,
    ((![A3 : set_Ho840737317_state, B3 : set_Ho840737317_state, C : set_Ho840737317_state]: ((ord_le1945819589_state @ A3 @ B3) => ((ord_le1945819589_state @ B3 @ C) => (ord_le1945819589_state @ A3 @ C)))))). % order.trans
thf(fact_29_eq__refl, axiom,
    ((![X2 : set_Ho840737317_state, Y2 : set_Ho840737317_state]: ((X2 = Y2) => (ord_le1945819589_state @ X2 @ Y2))))). % eq_refl
thf(fact_30_antisym, axiom,
    ((![X2 : set_Ho840737317_state, Y2 : set_Ho840737317_state]: ((ord_le1945819589_state @ X2 @ Y2) => ((ord_le1945819589_state @ Y2 @ X2) => (X2 = Y2)))))). % antisym
thf(fact_31_eq__iff, axiom,
    (((^[Y : set_Ho840737317_state]: (^[Z : set_Ho840737317_state]: (Y = Z))) = (^[X3 : set_Ho840737317_state]: (^[Y3 : set_Ho840737317_state]: (((ord_le1945819589_state @ X3 @ Y3)) & ((ord_le1945819589_state @ Y3 @ X3)))))))). % eq_iff
thf(fact_32_ord__le__eq__subst, axiom,
    ((![A3 : set_Ho840737317_state, B3 : set_Ho840737317_state, F : set_Ho840737317_state > set_Ho840737317_state, C : set_Ho840737317_state]: ((ord_le1945819589_state @ A3 @ B3) => (((F @ B3) = C) => ((![X : set_Ho840737317_state, Y4 : set_Ho840737317_state]: ((ord_le1945819589_state @ X @ Y4) => (ord_le1945819589_state @ (F @ X) @ (F @ Y4)))) => (ord_le1945819589_state @ (F @ A3) @ C))))))). % ord_le_eq_subst
thf(fact_33_ord__eq__le__subst, axiom,
    ((![A3 : set_Ho840737317_state, F : set_Ho840737317_state > set_Ho840737317_state, B3 : set_Ho840737317_state, C : set_Ho840737317_state]: ((A3 = (F @ B3)) => ((ord_le1945819589_state @ B3 @ C) => ((![X : set_Ho840737317_state, Y4 : set_Ho840737317_state]: ((ord_le1945819589_state @ X @ Y4) => (ord_le1945819589_state @ (F @ X) @ (F @ Y4)))) => (ord_le1945819589_state @ A3 @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_34_order__subst2, axiom,
    ((![A3 : set_Ho840737317_state, B3 : set_Ho840737317_state, F : set_Ho840737317_state > set_Ho840737317_state, C : set_Ho840737317_state]: ((ord_le1945819589_state @ A3 @ B3) => ((ord_le1945819589_state @ (F @ B3) @ C) => ((![X : set_Ho840737317_state, Y4 : set_Ho840737317_state]: ((ord_le1945819589_state @ X @ Y4) => (ord_le1945819589_state @ (F @ X) @ (F @ Y4)))) => (ord_le1945819589_state @ (F @ A3) @ C))))))). % order_subst2
thf(fact_35_order__subst1, axiom,
    ((![A3 : set_Ho840737317_state, F : set_Ho840737317_state > set_Ho840737317_state, B3 : set_Ho840737317_state, C : set_Ho840737317_state]: ((ord_le1945819589_state @ A3 @ (F @ B3)) => ((ord_le1945819589_state @ B3 @ C) => ((![X : set_Ho840737317_state, Y4 : set_Ho840737317_state]: ((ord_le1945819589_state @ X @ Y4) => (ord_le1945819589_state @ (F @ X) @ (F @ Y4)))) => (ord_le1945819589_state @ A3 @ (F @ C)))))))). % order_subst1
thf(fact_36_Collect__mono__iff, axiom,
    ((![P : hoare_958474565_state > $o, Q : hoare_958474565_state > $o]: ((ord_le1945819589_state @ (collec305460656_state @ P) @ (collec305460656_state @ Q)) = (![X3 : hoare_958474565_state]: (((P @ X3)) => ((Q @ X3)))))))). % Collect_mono_iff
thf(fact_37_mem__Collect__eq, axiom,
    ((![A3 : hoare_958474565_state, P : hoare_958474565_state > $o]: ((member109514606_state @ A3 @ (collec305460656_state @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_38_Collect__mem__eq, axiom,
    ((![A : set_Ho840737317_state]: ((collec305460656_state @ (^[X3 : hoare_958474565_state]: (member109514606_state @ X3 @ A))) = A)))). % Collect_mem_eq
thf(fact_39_set__eq__subset, axiom,
    (((^[Y : set_Ho840737317_state]: (^[Z : set_Ho840737317_state]: (Y = Z))) = (^[A2 : set_Ho840737317_state]: (^[B2 : set_Ho840737317_state]: (((ord_le1945819589_state @ A2 @ B2)) & ((ord_le1945819589_state @ B2 @ A2)))))))). % set_eq_subset
thf(fact_40_subset__trans, axiom,
    ((![A : set_Ho840737317_state, B : set_Ho840737317_state, C2 : set_Ho840737317_state]: ((ord_le1945819589_state @ A @ B) => ((ord_le1945819589_state @ B @ C2) => (ord_le1945819589_state @ A @ C2)))))). % subset_trans
thf(fact_41_Greatest__equality, axiom,
    ((![P : set_Ho840737317_state > $o, X2 : set_Ho840737317_state]: ((P @ X2) => ((![Y4 : set_Ho840737317_state]: ((P @ Y4) => (ord_le1945819589_state @ Y4 @ X2))) => ((order_800490238_state @ P) = X2)))))). % Greatest_equality
thf(fact_42_GreatestI2__order, axiom,
    ((![P : set_Ho840737317_state > $o, X2 : set_Ho840737317_state, Q : set_Ho840737317_state > $o]: ((P @ X2) => ((![Y4 : set_Ho840737317_state]: ((P @ Y4) => (ord_le1945819589_state @ Y4 @ X2))) => ((![X : set_Ho840737317_state]: ((P @ X) => ((![Y5 : set_Ho840737317_state]: ((P @ Y5) => (ord_le1945819589_state @ Y5 @ X))) => (Q @ X)))) => (Q @ (order_800490238_state @ P)))))))). % GreatestI2_order
thf(fact_43_le__rel__bool__arg__iff, axiom,
    ((ord_le1366095314_state = (^[X4 : $o > set_Ho840737317_state]: (^[Y6 : $o > set_Ho840737317_state]: (((ord_le1945819589_state @ (X4 @ $false) @ (Y6 @ $false))) & ((ord_le1945819589_state @ (X4 @ $true) @ (Y6 @ $true))))))))). % le_rel_bool_arg_iff
thf(fact_44_hoare__sound, axiom,
    ((![G2 : set_Ho840737317_state, Ts : set_Ho840737317_state]: ((hoare_604442164_state @ G2 @ Ts) => (hoare_318887606_state @ G2 @ Ts))))). % hoare_sound
thf(fact_45_antimono__def, axiom,
    ((order_1585167943_state = (^[F2 : set_Ho840737317_state > set_Ho840737317_state]: (![X3 : set_Ho840737317_state]: (![Y3 : set_Ho840737317_state]: (((ord_le1945819589_state @ X3 @ Y3)) => ((ord_le1945819589_state @ (F2 @ Y3) @ (F2 @ X3)))))))))). % antimono_def
thf(fact_46_antimonoI, axiom,
    ((![F : set_Ho840737317_state > set_Ho840737317_state]: ((![X : set_Ho840737317_state, Y4 : set_Ho840737317_state]: ((ord_le1945819589_state @ X @ Y4) => (ord_le1945819589_state @ (F @ Y4) @ (F @ X)))) => (order_1585167943_state @ F))))). % antimonoI
thf(fact_47_antimonoE, axiom,
    ((![F : set_Ho840737317_state > set_Ho840737317_state, X2 : set_Ho840737317_state, Y2 : set_Ho840737317_state]: ((order_1585167943_state @ F) => ((ord_le1945819589_state @ X2 @ Y2) => (ord_le1945819589_state @ (F @ Y2) @ (F @ X2))))))). % antimonoE
thf(fact_48_antimonoD, axiom,
    ((![F : set_Ho840737317_state > set_Ho840737317_state, X2 : set_Ho840737317_state, Y2 : set_Ho840737317_state]: ((order_1585167943_state @ F) => ((ord_le1945819589_state @ X2 @ Y2) => (ord_le1945819589_state @ (F @ Y2) @ (F @ X2))))))). % antimonoD
thf(fact_49_atLeast__subset__iff, axiom,
    ((![X2 : set_Ho840737317_state, Y2 : set_Ho840737317_state]: ((ord_le1363676837_state @ (set_or524090864_state @ X2) @ (set_or524090864_state @ Y2)) = (ord_le1945819589_state @ Y2 @ X2))))). % atLeast_subset_iff
thf(fact_50_atMost__subset__iff, axiom,
    ((![X2 : set_Ho840737317_state, Y2 : set_Ho840737317_state]: ((ord_le1363676837_state @ (set_or898808300_state @ X2) @ (set_or898808300_state @ Y2)) = (ord_le1945819589_state @ X2 @ Y2))))). % atMost_subset_iff
thf(fact_51_atMost__iff, axiom,
    ((![I : set_Ho840737317_state, K : set_Ho840737317_state]: ((member1959617614_state @ I @ (set_or898808300_state @ K)) = (ord_le1945819589_state @ I @ K))))). % atMost_iff
thf(fact_52_atLeast__iff, axiom,
    ((![I : set_Ho840737317_state, K : set_Ho840737317_state]: ((member1959617614_state @ I @ (set_or524090864_state @ K)) = (ord_le1945819589_state @ K @ I))))). % atLeast_iff
thf(fact_53_Icc__subset__Ici__iff, axiom,
    ((![L : set_Ho840737317_state, H : set_Ho840737317_state, L2 : set_Ho840737317_state]: ((ord_le1363676837_state @ (set_or411291354_state @ L @ H) @ (set_or524090864_state @ L2)) = (((~ ((ord_le1945819589_state @ L @ H)))) | ((ord_le1945819589_state @ L2 @ L))))))). % Icc_subset_Ici_iff
thf(fact_54_Icc__subset__Iic__iff, axiom,
    ((![L : set_Ho840737317_state, H : set_Ho840737317_state, H2 : set_Ho840737317_state]: ((ord_le1363676837_state @ (set_or411291354_state @ L @ H) @ (set_or898808300_state @ H2)) = (((~ ((ord_le1945819589_state @ L @ H)))) | ((ord_le1945819589_state @ H @ H2))))))). % Icc_subset_Iic_iff
thf(fact_55_psubsetI, axiom,
    ((![A : set_Ho840737317_state, B : set_Ho840737317_state]: ((ord_le1945819589_state @ A @ B) => ((~ ((A = B))) => (ord_le229826769_state @ A @ B)))))). % psubsetI
thf(fact_56_ComplI, axiom,
    ((![C : hoare_958474565_state, A : set_Ho840737317_state]: ((~ ((member109514606_state @ C @ A))) => (member109514606_state @ C @ (uminus1561791772_state @ A)))))). % ComplI
thf(fact_57_Compl__iff, axiom,
    ((![C : hoare_958474565_state, A : set_Ho840737317_state]: ((member109514606_state @ C @ (uminus1561791772_state @ A)) = (~ ((member109514606_state @ C @ A))))))). % Compl_iff
thf(fact_58_Icc__eq__Icc, axiom,
    ((![L : set_Ho840737317_state, H : set_Ho840737317_state, L2 : set_Ho840737317_state, H2 : set_Ho840737317_state]: (((set_or411291354_state @ L @ H) = (set_or411291354_state @ L2 @ H2)) = (((((L = L2)) & ((H = H2)))) | ((((~ ((ord_le1945819589_state @ L @ H)))) & ((~ ((ord_le1945819589_state @ L2 @ H2))))))))))). % Icc_eq_Icc
thf(fact_59_atLeastAtMost__iff, axiom,
    ((![I : set_Ho840737317_state, L : set_Ho840737317_state, U : set_Ho840737317_state]: ((member1959617614_state @ I @ (set_or411291354_state @ L @ U)) = (((ord_le1945819589_state @ L @ I)) & ((ord_le1945819589_state @ I @ U))))))). % atLeastAtMost_iff
thf(fact_60_Compl__anti__mono, axiom,
    ((![A : set_Ho840737317_state, B : set_Ho840737317_state]: ((ord_le1945819589_state @ A @ B) => (ord_le1945819589_state @ (uminus1561791772_state @ B) @ (uminus1561791772_state @ A)))))). % Compl_anti_mono
thf(fact_61_Compl__subset__Compl__iff, axiom,
    ((![A : set_Ho840737317_state, B : set_Ho840737317_state]: ((ord_le1945819589_state @ (uminus1561791772_state @ A) @ (uminus1561791772_state @ B)) = (ord_le1945819589_state @ B @ A))))). % Compl_subset_Compl_iff
thf(fact_62_atLeastatMost__subset__iff, axiom,
    ((![A3 : set_Ho840737317_state, B3 : set_Ho840737317_state, C : set_Ho840737317_state, D : set_Ho840737317_state]: ((ord_le1363676837_state @ (set_or411291354_state @ A3 @ B3) @ (set_or411291354_state @ C @ D)) = (((~ ((ord_le1945819589_state @ A3 @ B3)))) | ((((ord_le1945819589_state @ C @ A3)) & ((ord_le1945819589_state @ B3 @ D))))))))). % atLeastatMost_subset_iff
thf(fact_63_atLeastatMost__psubset__iff, axiom,
    ((![A3 : set_Ho840737317_state, B3 : set_Ho840737317_state, C : set_Ho840737317_state, D : set_Ho840737317_state]: ((ord_le1174267313_state @ (set_or411291354_state @ A3 @ B3) @ (set_or411291354_state @ C @ D)) = (((((~ ((ord_le1945819589_state @ A3 @ B3)))) | ((((ord_le1945819589_state @ C @ A3)) & ((((ord_le1945819589_state @ B3 @ D)) & ((((ord_le229826769_state @ C @ A3)) | ((ord_le229826769_state @ B3 @ D)))))))))) & ((ord_le1945819589_state @ C @ D))))))). % atLeastatMost_psubset_iff
thf(fact_64_order_Onot__eq__order__implies__strict, axiom,
    ((![A3 : set_Ho840737317_state, B3 : set_Ho840737317_state]: ((~ ((A3 = B3))) => ((ord_le1945819589_state @ A3 @ B3) => (ord_le229826769_state @ A3 @ B3)))))). % order.not_eq_order_implies_strict
thf(fact_65_dual__order_Ostrict__implies__order, axiom,
    ((![B3 : set_Ho840737317_state, A3 : set_Ho840737317_state]: ((ord_le229826769_state @ B3 @ A3) => (ord_le1945819589_state @ B3 @ A3))))). % dual_order.strict_implies_order
thf(fact_66_dual__order_Ostrict__iff__order, axiom,
    ((ord_le229826769_state = (^[B4 : set_Ho840737317_state]: (^[A4 : set_Ho840737317_state]: (((ord_le1945819589_state @ B4 @ A4)) & ((~ ((A4 = B4)))))))))). % dual_order.strict_iff_order
thf(fact_67_dual__order_Oorder__iff__strict, axiom,
    ((ord_le1945819589_state = (^[B4 : set_Ho840737317_state]: (^[A4 : set_Ho840737317_state]: (((ord_le229826769_state @ B4 @ A4)) | ((A4 = B4)))))))). % dual_order.order_iff_strict
thf(fact_68_order_Ostrict__implies__order, axiom,
    ((![A3 : set_Ho840737317_state, B3 : set_Ho840737317_state]: ((ord_le229826769_state @ A3 @ B3) => (ord_le1945819589_state @ A3 @ B3))))). % order.strict_implies_order
thf(fact_69_dual__order_Ostrict__trans2, axiom,
    ((![B3 : set_Ho840737317_state, A3 : set_Ho840737317_state, C : set_Ho840737317_state]: ((ord_le229826769_state @ B3 @ A3) => ((ord_le1945819589_state @ C @ B3) => (ord_le229826769_state @ C @ A3)))))). % dual_order.strict_trans2
thf(fact_70_dual__order_Ostrict__trans1, axiom,
    ((![B3 : set_Ho840737317_state, A3 : set_Ho840737317_state, C : set_Ho840737317_state]: ((ord_le1945819589_state @ B3 @ A3) => ((ord_le229826769_state @ C @ B3) => (ord_le229826769_state @ C @ A3)))))). % dual_order.strict_trans1
thf(fact_71_order_Ostrict__iff__order, axiom,
    ((ord_le229826769_state = (^[A4 : set_Ho840737317_state]: (^[B4 : set_Ho840737317_state]: (((ord_le1945819589_state @ A4 @ B4)) & ((~ ((A4 = B4)))))))))). % order.strict_iff_order
thf(fact_72_order_Oorder__iff__strict, axiom,
    ((ord_le1945819589_state = (^[A4 : set_Ho840737317_state]: (^[B4 : set_Ho840737317_state]: (((ord_le229826769_state @ A4 @ B4)) | ((A4 = B4)))))))). % order.order_iff_strict
thf(fact_73_order_Ostrict__trans2, axiom,
    ((![A3 : set_Ho840737317_state, B3 : set_Ho840737317_state, C : set_Ho840737317_state]: ((ord_le229826769_state @ A3 @ B3) => ((ord_le1945819589_state @ B3 @ C) => (ord_le229826769_state @ A3 @ C)))))). % order.strict_trans2
thf(fact_74_order_Ostrict__trans1, axiom,
    ((![A3 : set_Ho840737317_state, B3 : set_Ho840737317_state, C : set_Ho840737317_state]: ((ord_le1945819589_state @ A3 @ B3) => ((ord_le229826769_state @ B3 @ C) => (ord_le229826769_state @ A3 @ C)))))). % order.strict_trans1
thf(fact_75_less__le__not__le, axiom,
    ((ord_le229826769_state = (^[X3 : set_Ho840737317_state]: (^[Y3 : set_Ho840737317_state]: (((ord_le1945819589_state @ X3 @ Y3)) & ((~ ((ord_le1945819589_state @ Y3 @ X3)))))))))). % less_le_not_le
thf(fact_76_le__imp__less__or__eq, axiom,
    ((![X2 : set_Ho840737317_state, Y2 : set_Ho840737317_state]: ((ord_le1945819589_state @ X2 @ Y2) => ((ord_le229826769_state @ X2 @ Y2) | (X2 = Y2)))))). % le_imp_less_or_eq
thf(fact_77_less__le__trans, axiom,
    ((![X2 : set_Ho840737317_state, Y2 : set_Ho840737317_state, Z2 : set_Ho840737317_state]: ((ord_le229826769_state @ X2 @ Y2) => ((ord_le1945819589_state @ Y2 @ Z2) => (ord_le229826769_state @ X2 @ Z2)))))). % less_le_trans
thf(fact_78_le__less__trans, axiom,
    ((![X2 : set_Ho840737317_state, Y2 : set_Ho840737317_state, Z2 : set_Ho840737317_state]: ((ord_le1945819589_state @ X2 @ Y2) => ((ord_le229826769_state @ Y2 @ Z2) => (ord_le229826769_state @ X2 @ Z2)))))). % le_less_trans
thf(fact_79_less__imp__le, axiom,
    ((![X2 : set_Ho840737317_state, Y2 : set_Ho840737317_state]: ((ord_le229826769_state @ X2 @ Y2) => (ord_le1945819589_state @ X2 @ Y2))))). % less_imp_le
thf(fact_80_antisym__conv2, axiom,
    ((![X2 : set_Ho840737317_state, Y2 : set_Ho840737317_state]: ((ord_le1945819589_state @ X2 @ Y2) => ((~ ((ord_le229826769_state @ X2 @ Y2))) = (X2 = Y2)))))). % antisym_conv2
thf(fact_81_antisym__conv1, axiom,
    ((![X2 : set_Ho840737317_state, Y2 : set_Ho840737317_state]: ((~ ((ord_le229826769_state @ X2 @ Y2))) => ((ord_le1945819589_state @ X2 @ Y2) = (X2 = Y2)))))). % antisym_conv1
thf(fact_82_le__neq__trans, axiom,
    ((![A3 : set_Ho840737317_state, B3 : set_Ho840737317_state]: ((ord_le1945819589_state @ A3 @ B3) => ((~ ((A3 = B3))) => (ord_le229826769_state @ A3 @ B3)))))). % le_neq_trans
thf(fact_83_order__less__le__subst1, axiom,
    ((![A3 : set_Ho840737317_state, F : set_Ho840737317_state > set_Ho840737317_state, B3 : set_Ho840737317_state, C : set_Ho840737317_state]: ((ord_le229826769_state @ A3 @ (F @ B3)) => ((ord_le1945819589_state @ B3 @ C) => ((![X : set_Ho840737317_state, Y4 : set_Ho840737317_state]: ((ord_le1945819589_state @ X @ Y4) => (ord_le1945819589_state @ (F @ X) @ (F @ Y4)))) => (ord_le229826769_state @ A3 @ (F @ C)))))))). % order_less_le_subst1
thf(fact_84_order__le__less__subst2, axiom,
    ((![A3 : set_Ho840737317_state, B3 : set_Ho840737317_state, F : set_Ho840737317_state > set_Ho840737317_state, C : set_Ho840737317_state]: ((ord_le1945819589_state @ A3 @ B3) => ((ord_le229826769_state @ (F @ B3) @ C) => ((![X : set_Ho840737317_state, Y4 : set_Ho840737317_state]: ((ord_le1945819589_state @ X @ Y4) => (ord_le1945819589_state @ (F @ X) @ (F @ Y4)))) => (ord_le229826769_state @ (F @ A3) @ C))))))). % order_le_less_subst2
thf(fact_85_less__le, axiom,
    ((ord_le229826769_state = (^[X3 : set_Ho840737317_state]: (^[Y3 : set_Ho840737317_state]: (((ord_le1945819589_state @ X3 @ Y3)) & ((~ ((X3 = Y3)))))))))). % less_le
thf(fact_86_le__less, axiom,
    ((ord_le1945819589_state = (^[X3 : set_Ho840737317_state]: (^[Y3 : set_Ho840737317_state]: (((ord_le229826769_state @ X3 @ Y3)) | ((X3 = Y3)))))))). % le_less
thf(fact_87_leD, axiom,
    ((![Y2 : set_Ho840737317_state, X2 : set_Ho840737317_state]: ((ord_le1945819589_state @ Y2 @ X2) => (~ ((ord_le229826769_state @ X2 @ Y2))))))). % leD
thf(fact_88_subset__iff__psubset__eq, axiom,
    ((ord_le1945819589_state = (^[A2 : set_Ho840737317_state]: (^[B2 : set_Ho840737317_state]: (((ord_le229826769_state @ A2 @ B2)) | ((A2 = B2)))))))). % subset_iff_psubset_eq
thf(fact_89_subset__psubset__trans, axiom,
    ((![A : set_Ho840737317_state, B : set_Ho840737317_state, C2 : set_Ho840737317_state]: ((ord_le1945819589_state @ A @ B) => ((ord_le229826769_state @ B @ C2) => (ord_le229826769_state @ A @ C2)))))). % subset_psubset_trans
thf(fact_90_subset__not__subset__eq, axiom,
    ((ord_le229826769_state = (^[A2 : set_Ho840737317_state]: (^[B2 : set_Ho840737317_state]: (((ord_le1945819589_state @ A2 @ B2)) & ((~ ((ord_le1945819589_state @ B2 @ A2)))))))))). % subset_not_subset_eq
thf(fact_91_psubset__subset__trans, axiom,
    ((![A : set_Ho840737317_state, B : set_Ho840737317_state, C2 : set_Ho840737317_state]: ((ord_le229826769_state @ A @ B) => ((ord_le1945819589_state @ B @ C2) => (ord_le229826769_state @ A @ C2)))))). % psubset_subset_trans
thf(fact_92_psubset__imp__subset, axiom,
    ((![A : set_Ho840737317_state, B : set_Ho840737317_state]: ((ord_le229826769_state @ A @ B) => (ord_le1945819589_state @ A @ B))))). % psubset_imp_subset
thf(fact_93_psubset__eq, axiom,
    ((ord_le229826769_state = (^[A2 : set_Ho840737317_state]: (^[B2 : set_Ho840737317_state]: (((ord_le1945819589_state @ A2 @ B2)) & ((~ ((A2 = B2)))))))))). % psubset_eq
thf(fact_94_psubsetE, axiom,
    ((![A : set_Ho840737317_state, B : set_Ho840737317_state]: ((ord_le229826769_state @ A @ B) => (~ (((ord_le1945819589_state @ A @ B) => (ord_le1945819589_state @ B @ A)))))))). % psubsetE
thf(fact_95_ComplD, axiom,
    ((![C : hoare_958474565_state, A : set_Ho840737317_state]: ((member109514606_state @ C @ (uminus1561791772_state @ A)) => (~ ((member109514606_state @ C @ A))))))). % ComplD

% Conjectures (5)
thf(conj_0, hypothesis,
    (hoare_405891322gleton)).
thf(conj_1, hypothesis,
    (wT_bodies)).
thf(conj_2, hypothesis,
    ((wt @ c))).
thf(conj_3, hypothesis,
    ((ord_le1945819589_state @ ts @ g))).
thf(conj_4, conjecture,
    ((hoare_604442164_state @ g @ ts))).
