% 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_217__3251576_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:12:49.467

% Could-be-implicit typings (3)
thf(ty_n_t__Set__Oset_It__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_Itf__a_J_J_J, type,
    set_se152467259iple_a : $tType).
thf(ty_n_t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_Itf__a_J_J, type,
    set_Ho137910533iple_a : $tType).
thf(ty_n_t__Hoare____Mirabelle____raqjowkjvm__Otriple_Itf__a_J, type,
    hoare_1678595023iple_a : $tType).

% Explicit typings (19)
thf(sy_c_Hoare__Mirabelle__raqjowkjvm_Ohoare__derivs_001tf__a, type,
    hoare_129598474rivs_a : set_Ho137910533iple_a > set_Ho137910533iple_a > $o).
thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_Itf__a_J_J, type,
    inf_in1336607127iple_a : set_Ho137910533iple_a > set_Ho137910533iple_a > set_Ho137910533iple_a).
thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_Itf__a_J_J, type,
    ord_le1356158809iple_a : set_Ho137910533iple_a > set_Ho137910533iple_a > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_Itf__a_J_J_J, type,
    ord_le1048771374iple_a : ($o > set_Ho137910533iple_a) > ($o > set_Ho137910533iple_a) > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_Itf__a_J_J, type,
    ord_le1221261669iple_a : set_Ho137910533iple_a > set_Ho137910533iple_a > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_Itf__a_J_J_J, type,
    ord_le1677170587iple_a : set_se152467259iple_a > set_se152467259iple_a > $o).
thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_Itf__a_J_J, type,
    order_929906668iple_a : (set_Ho137910533iple_a > $o) > set_Ho137910533iple_a).
thf(sy_c_Orderings_Oorder__class_Oantimono_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_Itf__a_J_J_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_Itf__a_J_J, type,
    order_1710851741iple_a : (set_Ho137910533iple_a > set_Ho137910533iple_a) > $o).
thf(sy_c_Set_OCollect_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_Itf__a_J, type,
    collec1600235172iple_a : (hoare_1678595023iple_a > $o) > set_Ho137910533iple_a).
thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_Itf__a_J_J, type,
    set_or1668187408iple_a : set_Ho137910533iple_a > set_Ho137910533iple_a > set_se152467259iple_a).
thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_Itf__a_J_J, type,
    set_or439502900iple_a : set_Ho137910533iple_a > set_Ho137910533iple_a > set_se152467259iple_a).
thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_Itf__a_J_J, type,
    set_or1109361786iple_a : set_Ho137910533iple_a > set_se152467259iple_a).
thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_Itf__a_J_J, type,
    set_or1587679614iple_a : set_Ho137910533iple_a > set_se152467259iple_a).
thf(sy_c_member_001t__Hoare____Mirabelle____raqjowkjvm__Otriple_Itf__a_J, type,
    member1332298086iple_a : hoare_1678595023iple_a > set_Ho137910533iple_a > $o).
thf(sy_c_member_001t__Set__Oset_It__Hoare____Mirabelle____raqjowkjvm__Otriple_Itf__a_J_J, type,
    member521824924iple_a : set_Ho137910533iple_a > set_se152467259iple_a > $o).
thf(sy_v_G, type,
    g : set_Ho137910533iple_a).
thf(sy_v_Ga, type,
    ga : set_Ho137910533iple_a).
thf(sy_v_ts_H, type,
    ts : set_Ho137910533iple_a).
thf(sy_v_tsa, type,
    tsa : set_Ho137910533iple_a).

% Relevant facts (100)
thf(fact_0_asm, axiom,
    ((![Ts : set_Ho137910533iple_a, G : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ Ts @ G) => (hoare_129598474rivs_a @ G @ Ts))))). % asm
thf(fact_1_cut, axiom,
    ((![G2 : set_Ho137910533iple_a, Ts : set_Ho137910533iple_a, G : set_Ho137910533iple_a]: ((hoare_129598474rivs_a @ G2 @ Ts) => ((hoare_129598474rivs_a @ G @ G2) => (hoare_129598474rivs_a @ G @ Ts)))))). % cut
thf(fact_2_weaken, axiom,
    ((![G : set_Ho137910533iple_a, Ts2 : set_Ho137910533iple_a, Ts : set_Ho137910533iple_a]: ((hoare_129598474rivs_a @ G @ Ts2) => ((ord_le1221261669iple_a @ Ts @ Ts2) => (hoare_129598474rivs_a @ G @ Ts)))))). % weaken
thf(fact_3_subsetI, axiom,
    ((![A : set_Ho137910533iple_a, B : set_Ho137910533iple_a]: ((![X : hoare_1678595023iple_a]: ((member1332298086iple_a @ X @ A) => (member1332298086iple_a @ X @ B))) => (ord_le1221261669iple_a @ A @ B))))). % subsetI
thf(fact_4_subset__antisym, axiom,
    ((![A : set_Ho137910533iple_a, B : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ A @ B) => ((ord_le1221261669iple_a @ B @ A) => (A = B)))))). % subset_antisym
thf(fact_5_order__refl, axiom,
    ((![X2 : set_Ho137910533iple_a]: (ord_le1221261669iple_a @ X2 @ X2)))). % order_refl
thf(fact_6_in__mono, axiom,
    ((![A : set_Ho137910533iple_a, B : set_Ho137910533iple_a, X2 : hoare_1678595023iple_a]: ((ord_le1221261669iple_a @ A @ B) => ((member1332298086iple_a @ X2 @ A) => (member1332298086iple_a @ X2 @ B)))))). % in_mono
thf(fact_7_subsetD, axiom,
    ((![A : set_Ho137910533iple_a, B : set_Ho137910533iple_a, C : hoare_1678595023iple_a]: ((ord_le1221261669iple_a @ A @ B) => ((member1332298086iple_a @ C @ A) => (member1332298086iple_a @ C @ B)))))). % subsetD
thf(fact_8_equalityE, axiom,
    ((![A : set_Ho137910533iple_a, B : set_Ho137910533iple_a]: ((A = B) => (~ (((ord_le1221261669iple_a @ A @ B) => (~ ((ord_le1221261669iple_a @ B @ A)))))))))). % equalityE
thf(fact_9_subset__eq, axiom,
    ((ord_le1221261669iple_a = (^[A2 : set_Ho137910533iple_a]: (^[B2 : set_Ho137910533iple_a]: (![X3 : hoare_1678595023iple_a]: (((member1332298086iple_a @ X3 @ A2)) => ((member1332298086iple_a @ X3 @ B2))))))))). % subset_eq
thf(fact_10_equalityD1, axiom,
    ((![A : set_Ho137910533iple_a, B : set_Ho137910533iple_a]: ((A = B) => (ord_le1221261669iple_a @ A @ B))))). % equalityD1
thf(fact_11_equalityD2, axiom,
    ((![A : set_Ho137910533iple_a, B : set_Ho137910533iple_a]: ((A = B) => (ord_le1221261669iple_a @ B @ A))))). % equalityD2
thf(fact_12_subset__iff, axiom,
    ((ord_le1221261669iple_a = (^[A2 : set_Ho137910533iple_a]: (^[B2 : set_Ho137910533iple_a]: (![T : hoare_1678595023iple_a]: (((member1332298086iple_a @ T @ A2)) => ((member1332298086iple_a @ T @ B2))))))))). % subset_iff
thf(fact_13_subset__refl, axiom,
    ((![A : set_Ho137910533iple_a]: (ord_le1221261669iple_a @ A @ A)))). % subset_refl
thf(fact_14_Collect__mono, axiom,
    ((![P : hoare_1678595023iple_a > $o, Q : hoare_1678595023iple_a > $o]: ((![X : hoare_1678595023iple_a]: ((P @ X) => (Q @ X))) => (ord_le1221261669iple_a @ (collec1600235172iple_a @ P) @ (collec1600235172iple_a @ Q)))))). % Collect_mono
thf(fact_15_dual__order_Oantisym, axiom,
    ((![B3 : set_Ho137910533iple_a, A3 : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ B3 @ A3) => ((ord_le1221261669iple_a @ A3 @ B3) => (A3 = B3)))))). % dual_order.antisym
thf(fact_16_dual__order_Oeq__iff, axiom,
    (((^[Y : set_Ho137910533iple_a]: (^[Z : set_Ho137910533iple_a]: (Y = Z))) = (^[A4 : set_Ho137910533iple_a]: (^[B4 : set_Ho137910533iple_a]: (((ord_le1221261669iple_a @ B4 @ A4)) & ((ord_le1221261669iple_a @ A4 @ B4)))))))). % dual_order.eq_iff
thf(fact_17_dual__order_Otrans, axiom,
    ((![B3 : set_Ho137910533iple_a, A3 : set_Ho137910533iple_a, C : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ B3 @ A3) => ((ord_le1221261669iple_a @ C @ B3) => (ord_le1221261669iple_a @ C @ A3)))))). % dual_order.trans
thf(fact_18_dual__order_Orefl, axiom,
    ((![A3 : set_Ho137910533iple_a]: (ord_le1221261669iple_a @ A3 @ A3)))). % dual_order.refl
thf(fact_19_order__trans, axiom,
    ((![X2 : set_Ho137910533iple_a, Y2 : set_Ho137910533iple_a, Z2 : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ X2 @ Y2) => ((ord_le1221261669iple_a @ Y2 @ Z2) => (ord_le1221261669iple_a @ X2 @ Z2)))))). % order_trans
thf(fact_20_order__class_Oorder_Oantisym, axiom,
    ((![A3 : set_Ho137910533iple_a, B3 : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ A3 @ B3) => ((ord_le1221261669iple_a @ B3 @ A3) => (A3 = B3)))))). % order_class.order.antisym
thf(fact_21_ord__le__eq__trans, axiom,
    ((![A3 : set_Ho137910533iple_a, B3 : set_Ho137910533iple_a, C : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ A3 @ B3) => ((B3 = C) => (ord_le1221261669iple_a @ A3 @ C)))))). % ord_le_eq_trans
thf(fact_22_ord__eq__le__trans, axiom,
    ((![A3 : set_Ho137910533iple_a, B3 : set_Ho137910533iple_a, C : set_Ho137910533iple_a]: ((A3 = B3) => ((ord_le1221261669iple_a @ B3 @ C) => (ord_le1221261669iple_a @ A3 @ C)))))). % ord_eq_le_trans
thf(fact_23_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y : set_Ho137910533iple_a]: (^[Z : set_Ho137910533iple_a]: (Y = Z))) = (^[A4 : set_Ho137910533iple_a]: (^[B4 : set_Ho137910533iple_a]: (((ord_le1221261669iple_a @ A4 @ B4)) & ((ord_le1221261669iple_a @ B4 @ A4)))))))). % order_class.order.eq_iff
thf(fact_24_antisym__conv, axiom,
    ((![Y2 : set_Ho137910533iple_a, X2 : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ Y2 @ X2) => ((ord_le1221261669iple_a @ X2 @ Y2) = (X2 = Y2)))))). % antisym_conv
thf(fact_25_order_Otrans, axiom,
    ((![A3 : set_Ho137910533iple_a, B3 : set_Ho137910533iple_a, C : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ A3 @ B3) => ((ord_le1221261669iple_a @ B3 @ C) => (ord_le1221261669iple_a @ A3 @ C)))))). % order.trans
thf(fact_26_eq__refl, axiom,
    ((![X2 : set_Ho137910533iple_a, Y2 : set_Ho137910533iple_a]: ((X2 = Y2) => (ord_le1221261669iple_a @ X2 @ Y2))))). % eq_refl
thf(fact_27_antisym, axiom,
    ((![X2 : set_Ho137910533iple_a, Y2 : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ X2 @ Y2) => ((ord_le1221261669iple_a @ Y2 @ X2) => (X2 = Y2)))))). % antisym
thf(fact_28_eq__iff, axiom,
    (((^[Y : set_Ho137910533iple_a]: (^[Z : set_Ho137910533iple_a]: (Y = Z))) = (^[X3 : set_Ho137910533iple_a]: (^[Y3 : set_Ho137910533iple_a]: (((ord_le1221261669iple_a @ X3 @ Y3)) & ((ord_le1221261669iple_a @ Y3 @ X3)))))))). % eq_iff
thf(fact_29_ord__le__eq__subst, axiom,
    ((![A3 : set_Ho137910533iple_a, B3 : set_Ho137910533iple_a, F : set_Ho137910533iple_a > set_Ho137910533iple_a, C : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ A3 @ B3) => (((F @ B3) = C) => ((![X : set_Ho137910533iple_a, Y4 : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ X @ Y4) => (ord_le1221261669iple_a @ (F @ X) @ (F @ Y4)))) => (ord_le1221261669iple_a @ (F @ A3) @ C))))))). % ord_le_eq_subst
thf(fact_30_ord__eq__le__subst, axiom,
    ((![A3 : set_Ho137910533iple_a, F : set_Ho137910533iple_a > set_Ho137910533iple_a, B3 : set_Ho137910533iple_a, C : set_Ho137910533iple_a]: ((A3 = (F @ B3)) => ((ord_le1221261669iple_a @ B3 @ C) => ((![X : set_Ho137910533iple_a, Y4 : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ X @ Y4) => (ord_le1221261669iple_a @ (F @ X) @ (F @ Y4)))) => (ord_le1221261669iple_a @ A3 @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_31_order__subst2, axiom,
    ((![A3 : set_Ho137910533iple_a, B3 : set_Ho137910533iple_a, F : set_Ho137910533iple_a > set_Ho137910533iple_a, C : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ A3 @ B3) => ((ord_le1221261669iple_a @ (F @ B3) @ C) => ((![X : set_Ho137910533iple_a, Y4 : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ X @ Y4) => (ord_le1221261669iple_a @ (F @ X) @ (F @ Y4)))) => (ord_le1221261669iple_a @ (F @ A3) @ C))))))). % order_subst2
thf(fact_32_order__subst1, axiom,
    ((![A3 : set_Ho137910533iple_a, F : set_Ho137910533iple_a > set_Ho137910533iple_a, B3 : set_Ho137910533iple_a, C : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ A3 @ (F @ B3)) => ((ord_le1221261669iple_a @ B3 @ C) => ((![X : set_Ho137910533iple_a, Y4 : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ X @ Y4) => (ord_le1221261669iple_a @ (F @ X) @ (F @ Y4)))) => (ord_le1221261669iple_a @ A3 @ (F @ C)))))))). % order_subst1
thf(fact_33_Collect__mono__iff, axiom,
    ((![P : hoare_1678595023iple_a > $o, Q : hoare_1678595023iple_a > $o]: ((ord_le1221261669iple_a @ (collec1600235172iple_a @ P) @ (collec1600235172iple_a @ Q)) = (![X3 : hoare_1678595023iple_a]: (((P @ X3)) => ((Q @ X3)))))))). % Collect_mono_iff
thf(fact_34_set__eq__subset, axiom,
    (((^[Y : set_Ho137910533iple_a]: (^[Z : set_Ho137910533iple_a]: (Y = Z))) = (^[A2 : set_Ho137910533iple_a]: (^[B2 : set_Ho137910533iple_a]: (((ord_le1221261669iple_a @ A2 @ B2)) & ((ord_le1221261669iple_a @ B2 @ A2)))))))). % set_eq_subset
thf(fact_35_subset__trans, axiom,
    ((![A : set_Ho137910533iple_a, B : set_Ho137910533iple_a, C2 : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ A @ B) => ((ord_le1221261669iple_a @ B @ C2) => (ord_le1221261669iple_a @ A @ C2)))))). % subset_trans
thf(fact_36_Greatest__equality, axiom,
    ((![P : set_Ho137910533iple_a > $o, X2 : set_Ho137910533iple_a]: ((P @ X2) => ((![Y4 : set_Ho137910533iple_a]: ((P @ Y4) => (ord_le1221261669iple_a @ Y4 @ X2))) => ((order_929906668iple_a @ P) = X2)))))). % Greatest_equality
thf(fact_37_mem__Collect__eq, axiom,
    ((![A3 : hoare_1678595023iple_a, P : hoare_1678595023iple_a > $o]: ((member1332298086iple_a @ A3 @ (collec1600235172iple_a @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_38_Collect__mem__eq, axiom,
    ((![A : set_Ho137910533iple_a]: ((collec1600235172iple_a @ (^[X3 : hoare_1678595023iple_a]: (member1332298086iple_a @ X3 @ A))) = A)))). % Collect_mem_eq
thf(fact_39_GreatestI2__order, axiom,
    ((![P : set_Ho137910533iple_a > $o, X2 : set_Ho137910533iple_a, Q : set_Ho137910533iple_a > $o]: ((P @ X2) => ((![Y4 : set_Ho137910533iple_a]: ((P @ Y4) => (ord_le1221261669iple_a @ Y4 @ X2))) => ((![X : set_Ho137910533iple_a]: ((P @ X) => ((![Y5 : set_Ho137910533iple_a]: ((P @ Y5) => (ord_le1221261669iple_a @ Y5 @ X))) => (Q @ X)))) => (Q @ (order_929906668iple_a @ P)))))))). % GreatestI2_order
thf(fact_40_le__rel__bool__arg__iff, axiom,
    ((ord_le1048771374iple_a = (^[X4 : $o > set_Ho137910533iple_a]: (^[Y6 : $o > set_Ho137910533iple_a]: (((ord_le1221261669iple_a @ (X4 @ $false) @ (Y6 @ $false))) & ((ord_le1221261669iple_a @ (X4 @ $true) @ (Y6 @ $true))))))))). % le_rel_bool_arg_iff
thf(fact_41_antimono__def, axiom,
    ((order_1710851741iple_a = (^[F2 : set_Ho137910533iple_a > set_Ho137910533iple_a]: (![X3 : set_Ho137910533iple_a]: (![Y3 : set_Ho137910533iple_a]: (((ord_le1221261669iple_a @ X3 @ Y3)) => ((ord_le1221261669iple_a @ (F2 @ Y3) @ (F2 @ X3)))))))))). % antimono_def
thf(fact_42_antimonoI, axiom,
    ((![F : set_Ho137910533iple_a > set_Ho137910533iple_a]: ((![X : set_Ho137910533iple_a, Y4 : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ X @ Y4) => (ord_le1221261669iple_a @ (F @ Y4) @ (F @ X)))) => (order_1710851741iple_a @ F))))). % antimonoI
thf(fact_43_antimonoE, axiom,
    ((![F : set_Ho137910533iple_a > set_Ho137910533iple_a, X2 : set_Ho137910533iple_a, Y2 : set_Ho137910533iple_a]: ((order_1710851741iple_a @ F) => ((ord_le1221261669iple_a @ X2 @ Y2) => (ord_le1221261669iple_a @ (F @ Y2) @ (F @ X2))))))). % antimonoE
thf(fact_44_antimonoD, axiom,
    ((![F : set_Ho137910533iple_a > set_Ho137910533iple_a, X2 : set_Ho137910533iple_a, Y2 : set_Ho137910533iple_a]: ((order_1710851741iple_a @ F) => ((ord_le1221261669iple_a @ X2 @ Y2) => (ord_le1221261669iple_a @ (F @ Y2) @ (F @ X2))))))). % antimonoD
thf(fact_45_atLeast__subset__iff, axiom,
    ((![X2 : set_Ho137910533iple_a, Y2 : set_Ho137910533iple_a]: ((ord_le1677170587iple_a @ (set_or1109361786iple_a @ X2) @ (set_or1109361786iple_a @ Y2)) = (ord_le1221261669iple_a @ Y2 @ X2))))). % atLeast_subset_iff
thf(fact_46_atMost__subset__iff, axiom,
    ((![X2 : set_Ho137910533iple_a, Y2 : set_Ho137910533iple_a]: ((ord_le1677170587iple_a @ (set_or1587679614iple_a @ X2) @ (set_or1587679614iple_a @ Y2)) = (ord_le1221261669iple_a @ X2 @ Y2))))). % atMost_subset_iff
thf(fact_47_atMost__iff, axiom,
    ((![I : set_Ho137910533iple_a, K : set_Ho137910533iple_a]: ((member521824924iple_a @ I @ (set_or1587679614iple_a @ K)) = (ord_le1221261669iple_a @ I @ K))))). % atMost_iff
thf(fact_48_atLeast__iff, axiom,
    ((![I : set_Ho137910533iple_a, K : set_Ho137910533iple_a]: ((member521824924iple_a @ I @ (set_or1109361786iple_a @ K)) = (ord_le1221261669iple_a @ K @ I))))). % atLeast_iff
thf(fact_49_Icc__subset__Ici__iff, axiom,
    ((![L : set_Ho137910533iple_a, H : set_Ho137910533iple_a, L2 : set_Ho137910533iple_a]: ((ord_le1677170587iple_a @ (set_or1668187408iple_a @ L @ H) @ (set_or1109361786iple_a @ L2)) = (((~ ((ord_le1221261669iple_a @ L @ H)))) | ((ord_le1221261669iple_a @ L2 @ L))))))). % Icc_subset_Ici_iff
thf(fact_50_Icc__subset__Iic__iff, axiom,
    ((![L : set_Ho137910533iple_a, H : set_Ho137910533iple_a, H2 : set_Ho137910533iple_a]: ((ord_le1677170587iple_a @ (set_or1668187408iple_a @ L @ H) @ (set_or1587679614iple_a @ H2)) = (((~ ((ord_le1221261669iple_a @ L @ H)))) | ((ord_le1221261669iple_a @ H @ H2))))))). % Icc_subset_Iic_iff
thf(fact_51_psubsetI, axiom,
    ((![A : set_Ho137910533iple_a, B : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ A @ B) => ((~ ((A = B))) => (ord_le1356158809iple_a @ A @ B)))))). % psubsetI
thf(fact_52_IntI, axiom,
    ((![C : hoare_1678595023iple_a, A : set_Ho137910533iple_a, B : set_Ho137910533iple_a]: ((member1332298086iple_a @ C @ A) => ((member1332298086iple_a @ C @ B) => (member1332298086iple_a @ C @ (inf_in1336607127iple_a @ A @ B))))))). % IntI
thf(fact_53_Int__iff, axiom,
    ((![C : hoare_1678595023iple_a, A : set_Ho137910533iple_a, B : set_Ho137910533iple_a]: ((member1332298086iple_a @ C @ (inf_in1336607127iple_a @ A @ B)) = (((member1332298086iple_a @ C @ A)) & ((member1332298086iple_a @ C @ B))))))). % Int_iff
thf(fact_54_atLeastAtMost__iff, axiom,
    ((![I : set_Ho137910533iple_a, L : set_Ho137910533iple_a, U : set_Ho137910533iple_a]: ((member521824924iple_a @ I @ (set_or1668187408iple_a @ L @ U)) = (((ord_le1221261669iple_a @ L @ I)) & ((ord_le1221261669iple_a @ I @ U))))))). % atLeastAtMost_iff
thf(fact_55_Icc__eq__Icc, axiom,
    ((![L : set_Ho137910533iple_a, H : set_Ho137910533iple_a, L2 : set_Ho137910533iple_a, H2 : set_Ho137910533iple_a]: (((set_or1668187408iple_a @ L @ H) = (set_or1668187408iple_a @ L2 @ H2)) = (((((L = L2)) & ((H = H2)))) | ((((~ ((ord_le1221261669iple_a @ L @ H)))) & ((~ ((ord_le1221261669iple_a @ L2 @ H2))))))))))). % Icc_eq_Icc
thf(fact_56_Int__subset__iff, axiom,
    ((![C2 : set_Ho137910533iple_a, A : set_Ho137910533iple_a, B : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ C2 @ (inf_in1336607127iple_a @ A @ B)) = (((ord_le1221261669iple_a @ C2 @ A)) & ((ord_le1221261669iple_a @ C2 @ B))))))). % Int_subset_iff
thf(fact_57_atLeastLessThan__iff, axiom,
    ((![I : set_Ho137910533iple_a, L : set_Ho137910533iple_a, U : set_Ho137910533iple_a]: ((member521824924iple_a @ I @ (set_or439502900iple_a @ L @ U)) = (((ord_le1221261669iple_a @ L @ I)) & ((ord_le1356158809iple_a @ I @ U))))))). % atLeastLessThan_iff
thf(fact_58_atLeastatMost__subset__iff, axiom,
    ((![A3 : set_Ho137910533iple_a, B3 : set_Ho137910533iple_a, C : set_Ho137910533iple_a, D : set_Ho137910533iple_a]: ((ord_le1677170587iple_a @ (set_or1668187408iple_a @ A3 @ B3) @ (set_or1668187408iple_a @ C @ D)) = (((~ ((ord_le1221261669iple_a @ A3 @ B3)))) | ((((ord_le1221261669iple_a @ C @ A3)) & ((ord_le1221261669iple_a @ B3 @ D))))))))). % atLeastatMost_subset_iff
thf(fact_59_order_Onot__eq__order__implies__strict, axiom,
    ((![A3 : set_Ho137910533iple_a, B3 : set_Ho137910533iple_a]: ((~ ((A3 = B3))) => ((ord_le1221261669iple_a @ A3 @ B3) => (ord_le1356158809iple_a @ A3 @ B3)))))). % order.not_eq_order_implies_strict
thf(fact_60_dual__order_Ostrict__implies__order, axiom,
    ((![B3 : set_Ho137910533iple_a, A3 : set_Ho137910533iple_a]: ((ord_le1356158809iple_a @ B3 @ A3) => (ord_le1221261669iple_a @ B3 @ A3))))). % dual_order.strict_implies_order
thf(fact_61_dual__order_Ostrict__iff__order, axiom,
    ((ord_le1356158809iple_a = (^[B4 : set_Ho137910533iple_a]: (^[A4 : set_Ho137910533iple_a]: (((ord_le1221261669iple_a @ B4 @ A4)) & ((~ ((A4 = B4)))))))))). % dual_order.strict_iff_order
thf(fact_62_dual__order_Oorder__iff__strict, axiom,
    ((ord_le1221261669iple_a = (^[B4 : set_Ho137910533iple_a]: (^[A4 : set_Ho137910533iple_a]: (((ord_le1356158809iple_a @ B4 @ A4)) | ((A4 = B4)))))))). % dual_order.order_iff_strict
thf(fact_63_order_Ostrict__implies__order, axiom,
    ((![A3 : set_Ho137910533iple_a, B3 : set_Ho137910533iple_a]: ((ord_le1356158809iple_a @ A3 @ B3) => (ord_le1221261669iple_a @ A3 @ B3))))). % order.strict_implies_order
thf(fact_64_dual__order_Ostrict__trans2, axiom,
    ((![B3 : set_Ho137910533iple_a, A3 : set_Ho137910533iple_a, C : set_Ho137910533iple_a]: ((ord_le1356158809iple_a @ B3 @ A3) => ((ord_le1221261669iple_a @ C @ B3) => (ord_le1356158809iple_a @ C @ A3)))))). % dual_order.strict_trans2
thf(fact_65_dual__order_Ostrict__trans1, axiom,
    ((![B3 : set_Ho137910533iple_a, A3 : set_Ho137910533iple_a, C : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ B3 @ A3) => ((ord_le1356158809iple_a @ C @ B3) => (ord_le1356158809iple_a @ C @ A3)))))). % dual_order.strict_trans1
thf(fact_66_order_Ostrict__iff__order, axiom,
    ((ord_le1356158809iple_a = (^[A4 : set_Ho137910533iple_a]: (^[B4 : set_Ho137910533iple_a]: (((ord_le1221261669iple_a @ A4 @ B4)) & ((~ ((A4 = B4)))))))))). % order.strict_iff_order
thf(fact_67_order_Oorder__iff__strict, axiom,
    ((ord_le1221261669iple_a = (^[A4 : set_Ho137910533iple_a]: (^[B4 : set_Ho137910533iple_a]: (((ord_le1356158809iple_a @ A4 @ B4)) | ((A4 = B4)))))))). % order.order_iff_strict
thf(fact_68_order_Ostrict__trans2, axiom,
    ((![A3 : set_Ho137910533iple_a, B3 : set_Ho137910533iple_a, C : set_Ho137910533iple_a]: ((ord_le1356158809iple_a @ A3 @ B3) => ((ord_le1221261669iple_a @ B3 @ C) => (ord_le1356158809iple_a @ A3 @ C)))))). % order.strict_trans2
thf(fact_69_order_Ostrict__trans1, axiom,
    ((![A3 : set_Ho137910533iple_a, B3 : set_Ho137910533iple_a, C : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ A3 @ B3) => ((ord_le1356158809iple_a @ B3 @ C) => (ord_le1356158809iple_a @ A3 @ C)))))). % order.strict_trans1
thf(fact_70_less__le__not__le, axiom,
    ((ord_le1356158809iple_a = (^[X3 : set_Ho137910533iple_a]: (^[Y3 : set_Ho137910533iple_a]: (((ord_le1221261669iple_a @ X3 @ Y3)) & ((~ ((ord_le1221261669iple_a @ Y3 @ X3)))))))))). % less_le_not_le
thf(fact_71_le__imp__less__or__eq, axiom,
    ((![X2 : set_Ho137910533iple_a, Y2 : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ X2 @ Y2) => ((ord_le1356158809iple_a @ X2 @ Y2) | (X2 = Y2)))))). % le_imp_less_or_eq
thf(fact_72_less__le__trans, axiom,
    ((![X2 : set_Ho137910533iple_a, Y2 : set_Ho137910533iple_a, Z2 : set_Ho137910533iple_a]: ((ord_le1356158809iple_a @ X2 @ Y2) => ((ord_le1221261669iple_a @ Y2 @ Z2) => (ord_le1356158809iple_a @ X2 @ Z2)))))). % less_le_trans
thf(fact_73_le__less__trans, axiom,
    ((![X2 : set_Ho137910533iple_a, Y2 : set_Ho137910533iple_a, Z2 : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ X2 @ Y2) => ((ord_le1356158809iple_a @ Y2 @ Z2) => (ord_le1356158809iple_a @ X2 @ Z2)))))). % le_less_trans
thf(fact_74_less__imp__le, axiom,
    ((![X2 : set_Ho137910533iple_a, Y2 : set_Ho137910533iple_a]: ((ord_le1356158809iple_a @ X2 @ Y2) => (ord_le1221261669iple_a @ X2 @ Y2))))). % less_imp_le
thf(fact_75_antisym__conv2, axiom,
    ((![X2 : set_Ho137910533iple_a, Y2 : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ X2 @ Y2) => ((~ ((ord_le1356158809iple_a @ X2 @ Y2))) = (X2 = Y2)))))). % antisym_conv2
thf(fact_76_antisym__conv1, axiom,
    ((![X2 : set_Ho137910533iple_a, Y2 : set_Ho137910533iple_a]: ((~ ((ord_le1356158809iple_a @ X2 @ Y2))) => ((ord_le1221261669iple_a @ X2 @ Y2) = (X2 = Y2)))))). % antisym_conv1
thf(fact_77_le__neq__trans, axiom,
    ((![A3 : set_Ho137910533iple_a, B3 : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ A3 @ B3) => ((~ ((A3 = B3))) => (ord_le1356158809iple_a @ A3 @ B3)))))). % le_neq_trans
thf(fact_78_order__less__le__subst1, axiom,
    ((![A3 : set_Ho137910533iple_a, F : set_Ho137910533iple_a > set_Ho137910533iple_a, B3 : set_Ho137910533iple_a, C : set_Ho137910533iple_a]: ((ord_le1356158809iple_a @ A3 @ (F @ B3)) => ((ord_le1221261669iple_a @ B3 @ C) => ((![X : set_Ho137910533iple_a, Y4 : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ X @ Y4) => (ord_le1221261669iple_a @ (F @ X) @ (F @ Y4)))) => (ord_le1356158809iple_a @ A3 @ (F @ C)))))))). % order_less_le_subst1
thf(fact_79_order__le__less__subst2, axiom,
    ((![A3 : set_Ho137910533iple_a, B3 : set_Ho137910533iple_a, F : set_Ho137910533iple_a > set_Ho137910533iple_a, C : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ A3 @ B3) => ((ord_le1356158809iple_a @ (F @ B3) @ C) => ((![X : set_Ho137910533iple_a, Y4 : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ X @ Y4) => (ord_le1221261669iple_a @ (F @ X) @ (F @ Y4)))) => (ord_le1356158809iple_a @ (F @ A3) @ C))))))). % order_le_less_subst2
thf(fact_80_less__le, axiom,
    ((ord_le1356158809iple_a = (^[X3 : set_Ho137910533iple_a]: (^[Y3 : set_Ho137910533iple_a]: (((ord_le1221261669iple_a @ X3 @ Y3)) & ((~ ((X3 = Y3)))))))))). % less_le
thf(fact_81_le__less, axiom,
    ((ord_le1221261669iple_a = (^[X3 : set_Ho137910533iple_a]: (^[Y3 : set_Ho137910533iple_a]: (((ord_le1356158809iple_a @ X3 @ Y3)) | ((X3 = Y3)))))))). % le_less
thf(fact_82_leD, axiom,
    ((![Y2 : set_Ho137910533iple_a, X2 : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ Y2 @ X2) => (~ ((ord_le1356158809iple_a @ X2 @ Y2))))))). % leD
thf(fact_83_Int__Collect__mono, axiom,
    ((![A : set_Ho137910533iple_a, B : set_Ho137910533iple_a, P : hoare_1678595023iple_a > $o, Q : hoare_1678595023iple_a > $o]: ((ord_le1221261669iple_a @ A @ B) => ((![X : hoare_1678595023iple_a]: ((member1332298086iple_a @ X @ A) => ((P @ X) => (Q @ X)))) => (ord_le1221261669iple_a @ (inf_in1336607127iple_a @ A @ (collec1600235172iple_a @ P)) @ (inf_in1336607127iple_a @ B @ (collec1600235172iple_a @ Q)))))))). % Int_Collect_mono
thf(fact_84_Int__greatest, axiom,
    ((![C2 : set_Ho137910533iple_a, A : set_Ho137910533iple_a, B : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ C2 @ A) => ((ord_le1221261669iple_a @ C2 @ B) => (ord_le1221261669iple_a @ C2 @ (inf_in1336607127iple_a @ A @ B))))))). % Int_greatest
thf(fact_85_Int__absorb2, axiom,
    ((![A : set_Ho137910533iple_a, B : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ A @ B) => ((inf_in1336607127iple_a @ A @ B) = A))))). % Int_absorb2
thf(fact_86_Int__absorb1, axiom,
    ((![B : set_Ho137910533iple_a, A : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ B @ A) => ((inf_in1336607127iple_a @ A @ B) = B))))). % Int_absorb1
thf(fact_87_Int__lower2, axiom,
    ((![A : set_Ho137910533iple_a, B : set_Ho137910533iple_a]: (ord_le1221261669iple_a @ (inf_in1336607127iple_a @ A @ B) @ B)))). % Int_lower2
thf(fact_88_Int__lower1, axiom,
    ((![A : set_Ho137910533iple_a, B : set_Ho137910533iple_a]: (ord_le1221261669iple_a @ (inf_in1336607127iple_a @ A @ B) @ A)))). % Int_lower1
thf(fact_89_Int__mono, axiom,
    ((![A : set_Ho137910533iple_a, C2 : set_Ho137910533iple_a, B : set_Ho137910533iple_a, D2 : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ A @ C2) => ((ord_le1221261669iple_a @ B @ D2) => (ord_le1221261669iple_a @ (inf_in1336607127iple_a @ A @ B) @ (inf_in1336607127iple_a @ C2 @ D2))))))). % Int_mono
thf(fact_90_subset__iff__psubset__eq, axiom,
    ((ord_le1221261669iple_a = (^[A2 : set_Ho137910533iple_a]: (^[B2 : set_Ho137910533iple_a]: (((ord_le1356158809iple_a @ A2 @ B2)) | ((A2 = B2)))))))). % subset_iff_psubset_eq
thf(fact_91_subset__psubset__trans, axiom,
    ((![A : set_Ho137910533iple_a, B : set_Ho137910533iple_a, C2 : set_Ho137910533iple_a]: ((ord_le1221261669iple_a @ A @ B) => ((ord_le1356158809iple_a @ B @ C2) => (ord_le1356158809iple_a @ A @ C2)))))). % subset_psubset_trans
thf(fact_92_subset__not__subset__eq, axiom,
    ((ord_le1356158809iple_a = (^[A2 : set_Ho137910533iple_a]: (^[B2 : set_Ho137910533iple_a]: (((ord_le1221261669iple_a @ A2 @ B2)) & ((~ ((ord_le1221261669iple_a @ B2 @ A2)))))))))). % subset_not_subset_eq
thf(fact_93_psubset__subset__trans, axiom,
    ((![A : set_Ho137910533iple_a, B : set_Ho137910533iple_a, C2 : set_Ho137910533iple_a]: ((ord_le1356158809iple_a @ A @ B) => ((ord_le1221261669iple_a @ B @ C2) => (ord_le1356158809iple_a @ A @ C2)))))). % psubset_subset_trans
thf(fact_94_psubset__imp__subset, axiom,
    ((![A : set_Ho137910533iple_a, B : set_Ho137910533iple_a]: ((ord_le1356158809iple_a @ A @ B) => (ord_le1221261669iple_a @ A @ B))))). % psubset_imp_subset
thf(fact_95_psubset__eq, axiom,
    ((ord_le1356158809iple_a = (^[A2 : set_Ho137910533iple_a]: (^[B2 : set_Ho137910533iple_a]: (((ord_le1221261669iple_a @ A2 @ B2)) & ((~ ((A2 = B2)))))))))). % psubset_eq
thf(fact_96_psubsetE, axiom,
    ((![A : set_Ho137910533iple_a, B : set_Ho137910533iple_a]: ((ord_le1356158809iple_a @ A @ B) => (~ (((ord_le1221261669iple_a @ A @ B) => (ord_le1221261669iple_a @ B @ A)))))))). % psubsetE
thf(fact_97_IntE, axiom,
    ((![C : hoare_1678595023iple_a, A : set_Ho137910533iple_a, B : set_Ho137910533iple_a]: ((member1332298086iple_a @ C @ (inf_in1336607127iple_a @ A @ B)) => (~ (((member1332298086iple_a @ C @ A) => (~ ((member1332298086iple_a @ C @ B)))))))))). % IntE
thf(fact_98_IntD1, axiom,
    ((![C : hoare_1678595023iple_a, A : set_Ho137910533iple_a, B : set_Ho137910533iple_a]: ((member1332298086iple_a @ C @ (inf_in1336607127iple_a @ A @ B)) => (member1332298086iple_a @ C @ A))))). % IntD1
thf(fact_99_IntD2, axiom,
    ((![C : hoare_1678595023iple_a, A : set_Ho137910533iple_a, B : set_Ho137910533iple_a]: ((member1332298086iple_a @ C @ (inf_in1336607127iple_a @ A @ B)) => (member1332298086iple_a @ C @ B))))). % IntD2

% Conjectures (5)
thf(conj_0, hypothesis,
    ((hoare_129598474rivs_a @ g @ ts))).
thf(conj_1, hypothesis,
    ((ord_le1221261669iple_a @ tsa @ ts))).
thf(conj_2, hypothesis,
    ((ord_le1221261669iple_a @ g @ ga))).
thf(conj_3, hypothesis,
    ((hoare_129598474rivs_a @ ga @ ts))).
thf(conj_4, conjecture,
    ((hoare_129598474rivs_a @ ga @ tsa))).
