% 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/Arrow_Order/prob_42__5184536_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:15:47.003

% Could-be-implicit typings (6)
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_Pr448479039le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc1556433673le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    set_Pr367596371le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc16571293le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    set_Ar1665529862le_alt : $tType).
thf(ty_n_t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    arrow_1857593510le_alt : $tType).

% Explicit typings (28)
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    ord_le1885758387le_alt : set_Pr367596371le_alt > set_Pr367596371le_alt > $o).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_M_Eo_J, type,
    top_to1074038850_alt_o : produc16571293le_alt > $o).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    top_to224369155le_alt : set_Pr367596371le_alt).
thf(sy_c_Product__Type_OPair_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1494124311le_alt : arrow_1857593510le_alt > arrow_1857593510le_alt > produc16571293le_alt).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc41061307le_alt : produc16571293le_alt > produc16571293le_alt > produc1556433673le_alt).
thf(sy_c_Product__Type_Oapfst_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1245692284le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt) > produc16571293le_alt > produc16571293le_alt).
thf(sy_c_Product__Type_Oapsnd_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1710313402le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt) > produc16571293le_alt > produc16571293le_alt).
thf(sy_c_Product__Type_Ocurry_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001_Eo, type,
    produc392997491_alt_o : (produc16571293le_alt > $o) > arrow_1857593510le_alt > arrow_1857593510le_alt > $o).
thf(sy_c_Product__Type_Omap__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1074667658le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt) > (arrow_1857593510le_alt > arrow_1857593510le_alt) > produc16571293le_alt > produc16571293le_alt).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001_Eo, type,
    produc624247124_alt_o : (arrow_1857593510le_alt > arrow_1857593510le_alt > $o) > produc16571293le_alt > $o).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc860300173le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt) > produc16571293le_alt > set_Pr367596371le_alt).
thf(sy_c_Product__Type_Oprod_Ofst_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc2071652395le_alt : produc16571293le_alt > arrow_1857593510le_alt).
thf(sy_c_Product__Type_Oprod_Osnd_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1272650601le_alt : produc16571293le_alt > arrow_1857593510le_alt).
thf(sy_c_Product__Type_Oprod_Oswap_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1794822519le_alt : produc16571293le_alt > produc16571293le_alt).
thf(sy_c_Relation_OId__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    id_on_426682691le_alt : set_Ar1665529862le_alt > set_Pr367596371le_alt).
thf(sy_c_Relation_OId__on_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    id_on_714194496le_alt : set_Pr367596371le_alt > set_Pr448479039le_alt).
thf(sy_c_Relation_Oasym_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    asym_A231202199le_alt : set_Pr367596371le_alt > $o).
thf(sy_c_Relation_Oinv__image_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    inv_im155136540le_alt : set_Pr367596371le_alt > (arrow_1857593510le_alt > arrow_1857593510le_alt) > set_Pr367596371le_alt).
thf(sy_c_Relation_Osingle__valued_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    single1846972971le_alt : set_Pr367596371le_alt > $o).
thf(sy_c_Relation_Otrans_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    trans_1364318725le_alt : set_Pr367596371le_alt > $o).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    collec531981554le_alt : (produc16571293le_alt > $o) > set_Pr367596371le_alt).
thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    image_1873259469le_alt : (produc16571293le_alt > produc16571293le_alt) > set_Pr367596371le_alt > set_Pr367596371le_alt).
thf(sy_c_member_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    member519365071le_alt : arrow_1857593510le_alt > set_Ar1665529862le_alt > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    member2048039092le_alt : produc16571293le_alt > set_Pr367596371le_alt > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member2146260128le_alt : produc1556433673le_alt > set_Pr448479039le_alt > $o).
thf(sy_v_L, type,
    l : set_Pr367596371le_alt).
thf(sy_v_x, type,
    x : arrow_1857593510le_alt).
thf(sy_v_y, type,
    y : arrow_1857593510le_alt).

% Relevant facts (71)
thf(fact_0_prod_Oinject, axiom,
    ((![X1 : arrow_1857593510le_alt, X2 : arrow_1857593510le_alt, Y1 : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ X1 @ X2) = (produc1494124311le_alt @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_1_old_Oprod_Oinject, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A @ B) = (produc1494124311le_alt @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_2_transD, axiom,
    ((![R : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, Z : arrow_1857593510le_alt]: ((trans_1364318725le_alt @ R) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ R) => ((member2048039092le_alt @ (produc1494124311le_alt @ Y @ Z) @ R) => (member2048039092le_alt @ (produc1494124311le_alt @ X @ Z) @ R))))))). % transD
thf(fact_3_transE, axiom,
    ((![R : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, Z : arrow_1857593510le_alt]: ((trans_1364318725le_alt @ R) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ R) => ((member2048039092le_alt @ (produc1494124311le_alt @ Y @ Z) @ R) => (member2048039092le_alt @ (produc1494124311le_alt @ X @ Z) @ R))))))). % transE
thf(fact_4_transI, axiom,
    ((![R : set_Pr367596371le_alt]: ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt, Z2 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y3) @ R) => ((member2048039092le_alt @ (produc1494124311le_alt @ Y3 @ Z2) @ R) => (member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Z2) @ R)))) => (trans_1364318725le_alt @ R))))). % transI
thf(fact_5_trans__def, axiom,
    ((trans_1364318725le_alt = (^[R2 : set_Pr367596371le_alt]: (![X4 : arrow_1857593510le_alt]: (![Y4 : arrow_1857593510le_alt]: (![Z3 : arrow_1857593510le_alt]: (((member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y4) @ R2)) => ((((member2048039092le_alt @ (produc1494124311le_alt @ Y4 @ Z3) @ R2)) => ((member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Z3) @ R2)))))))))))). % trans_def
thf(fact_6_surj__pair, axiom,
    ((![P : produc16571293le_alt]: (?[X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: (P = (produc1494124311le_alt @ X3 @ Y3)))))). % surj_pair
thf(fact_7_prod__cases, axiom,
    ((![P2 : produc16571293le_alt > $o, P : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (P2 @ (produc1494124311le_alt @ A3 @ B3))) => (P2 @ P))))). % prod_cases
thf(fact_8_Pair__inject, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A @ B) = (produc1494124311le_alt @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_9_old_Oprod_Oinducts, axiom,
    ((![P2 : produc16571293le_alt > $o, Prod : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (P2 @ (produc1494124311le_alt @ A3 @ B3))) => (P2 @ Prod))))). % old.prod.inducts
thf(fact_10_old_Oprod_Oexhaust, axiom,
    ((![Y : produc16571293le_alt]: (~ ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (~ ((Y = (produc1494124311le_alt @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_11_ssubst__Pair__rhs, axiom,
    ((![R : arrow_1857593510le_alt, S : arrow_1857593510le_alt, R3 : set_Pr367596371le_alt, S2 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ R @ S) @ R3) => ((S2 = S) => (member2048039092le_alt @ (produc1494124311le_alt @ R @ S2) @ R3)))))). % ssubst_Pair_rhs
thf(fact_12_in__inv__image, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, R : set_Pr367596371le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (inv_im155136540le_alt @ R @ F)) = (member2048039092le_alt @ (produc1494124311le_alt @ (F @ X) @ (F @ Y)) @ R))))). % in_inv_image
thf(fact_13_curryI, axiom,
    ((![F : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((F @ (produc1494124311le_alt @ A @ B)) => (produc392997491_alt_o @ F @ A @ B))))). % curryI
thf(fact_14_swap__simp, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((produc1794822519le_alt @ (produc1494124311le_alt @ X @ Y)) = (produc1494124311le_alt @ Y @ X))))). % swap_simp
thf(fact_15_trans__inv__image, axiom,
    ((![R : set_Pr367596371le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((trans_1364318725le_alt @ R) => (trans_1364318725le_alt @ (inv_im155136540le_alt @ R @ F)))))). % trans_inv_image
thf(fact_16_Id__onI, axiom,
    ((![A : produc16571293le_alt, A4 : set_Pr367596371le_alt]: ((member2048039092le_alt @ A @ A4) => (member2146260128le_alt @ (produc41061307le_alt @ A @ A) @ (id_on_714194496le_alt @ A4)))))). % Id_onI
thf(fact_17_Id__onI, axiom,
    ((![A : arrow_1857593510le_alt, A4 : set_Ar1665529862le_alt]: ((member519365071le_alt @ A @ A4) => (member2048039092le_alt @ (produc1494124311le_alt @ A @ A) @ (id_on_426682691le_alt @ A4)))))). % Id_onI
thf(fact_18_Id__onE, axiom,
    ((![C : produc1556433673le_alt, A4 : set_Pr367596371le_alt]: ((member2146260128le_alt @ C @ (id_on_714194496le_alt @ A4)) => (~ ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A4) => (~ ((C = (produc41061307le_alt @ X3 @ X3)))))))))))). % Id_onE
thf(fact_19_Id__onE, axiom,
    ((![C : produc16571293le_alt, A4 : set_Ar1665529862le_alt]: ((member2048039092le_alt @ C @ (id_on_426682691le_alt @ A4)) => (~ ((![X3 : arrow_1857593510le_alt]: ((member519365071le_alt @ X3 @ A4) => (~ ((C = (produc1494124311le_alt @ X3 @ X3)))))))))))). % Id_onE
thf(fact_20_Id__on__eqI, axiom,
    ((![A : produc16571293le_alt, B : produc16571293le_alt, A4 : set_Pr367596371le_alt]: ((A = B) => ((member2048039092le_alt @ A @ A4) => (member2146260128le_alt @ (produc41061307le_alt @ A @ B) @ (id_on_714194496le_alt @ A4))))))). % Id_on_eqI
thf(fact_21_Id__on__eqI, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : set_Ar1665529862le_alt]: ((A = B) => ((member519365071le_alt @ A @ A4) => (member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (id_on_426682691le_alt @ A4))))))). % Id_on_eqI
thf(fact_22_Id__on__iff, axiom,
    ((![X : produc16571293le_alt, Y : produc16571293le_alt, A4 : set_Pr367596371le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ X @ Y) @ (id_on_714194496le_alt @ A4)) = (((X = Y)) & ((member2048039092le_alt @ X @ A4))))))). % Id_on_iff
thf(fact_23_Id__on__iff, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, A4 : set_Ar1665529862le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (id_on_426682691le_alt @ A4)) = (((X = Y)) & ((member519365071le_alt @ X @ A4))))))). % Id_on_iff
thf(fact_24_trans__Id__on, axiom,
    ((![A4 : set_Ar1665529862le_alt]: (trans_1364318725le_alt @ (id_on_426682691le_alt @ A4))))). % trans_Id_on
thf(fact_25_curryD, axiom,
    ((![F : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc392997491_alt_o @ F @ A @ B) => (F @ (produc1494124311le_alt @ A @ B)))))). % curryD
thf(fact_26_curryE, axiom,
    ((![F : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc392997491_alt_o @ F @ A @ B) => (F @ (produc1494124311le_alt @ A @ B)))))). % curryE
thf(fact_27_pair__in__swap__image, axiom,
    ((![Y : arrow_1857593510le_alt, X : arrow_1857593510le_alt, A4 : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ Y @ X) @ (image_1873259469le_alt @ produc1794822519le_alt @ A4)) = (member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ A4))))). % pair_in_swap_image
thf(fact_28_apsnd__conv, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((produc1710313402le_alt @ F @ (produc1494124311le_alt @ X @ Y)) = (produc1494124311le_alt @ X @ (F @ Y)))))). % apsnd_conv
thf(fact_29_mem__Collect__eq, axiom,
    ((![A : produc16571293le_alt, P2 : produc16571293le_alt > $o]: ((member2048039092le_alt @ A @ (collec531981554le_alt @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_30_Collect__mem__eq, axiom,
    ((![A4 : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (member2048039092le_alt @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_31_mem__case__prodE, axiom,
    ((![Z : produc16571293le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt, P : produc16571293le_alt]: ((member2048039092le_alt @ Z @ (produc860300173le_alt @ C @ P)) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P = (produc1494124311le_alt @ X3 @ Y3)) => (~ ((member2048039092le_alt @ Z @ (C @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_32_single__valued__def, axiom,
    ((single1846972971le_alt = (^[R2 : set_Pr367596371le_alt]: (![X4 : arrow_1857593510le_alt]: (![Y4 : arrow_1857593510le_alt]: (((member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y4) @ R2)) => ((![Z3 : arrow_1857593510le_alt]: (((member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Z3) @ R2)) => ((Y4 = Z3)))))))))))). % single_valued_def
thf(fact_33_single__valuedI, axiom,
    ((![R : set_Pr367596371le_alt]: ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt, Z2 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y3) @ R) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Z2) @ R) => (Y3 = Z2)))) => (single1846972971le_alt @ R))))). % single_valuedI
thf(fact_34_single__valuedD, axiom,
    ((![R : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, Z : arrow_1857593510le_alt]: ((single1846972971le_alt @ R) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ R) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Z) @ R) => (Y = Z))))))). % single_valuedD
thf(fact_35_asym_Oinducts, axiom,
    ((![X : set_Pr367596371le_alt, P2 : set_Pr367596371le_alt > $o]: ((asym_A231202199le_alt @ X) => ((![R4 : set_Pr367596371le_alt]: ((![A5 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ R4) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ B4 @ A5) @ R4))))) => (P2 @ R4))) => (P2 @ X)))))). % asym.inducts
thf(fact_36_asym_Ointros, axiom,
    ((![R3 : set_Pr367596371le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ R3) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ B3 @ A3) @ R3))))) => (asym_A231202199le_alt @ R3))))). % asym.intros
thf(fact_37_asym_Osimps, axiom,
    ((asym_A231202199le_alt = (^[A6 : set_Pr367596371le_alt]: (?[R5 : set_Pr367596371le_alt]: (((A6 = R5)) & ((![X4 : arrow_1857593510le_alt]: (![Y4 : arrow_1857593510le_alt]: (((member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y4) @ R5)) => ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ Y4 @ X4) @ R5)))))))))))))). % asym.simps
thf(fact_38_asym_Ocases, axiom,
    ((![A : set_Pr367596371le_alt]: ((asym_A231202199le_alt @ A) => (![A5 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ A) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ B4 @ A5) @ A))))))))). % asym.cases
thf(fact_39_asym__iff, axiom,
    ((asym_A231202199le_alt = (^[R5 : set_Pr367596371le_alt]: (![X4 : arrow_1857593510le_alt]: (![Y4 : arrow_1857593510le_alt]: (((member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y4) @ R5)) => ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ Y4 @ X4) @ R5))))))))))). % asym_iff
thf(fact_40_asymD, axiom,
    ((![R3 : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((asym_A231202199le_alt @ R3) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ R3) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ Y @ X) @ R3)))))))). % asymD
thf(fact_41_image__eqI, axiom,
    ((![B : produc16571293le_alt, F : produc16571293le_alt > produc16571293le_alt, X : produc16571293le_alt, A4 : set_Pr367596371le_alt]: ((B = (F @ X)) => ((member2048039092le_alt @ X @ A4) => (member2048039092le_alt @ B @ (image_1873259469le_alt @ F @ A4))))))). % image_eqI
thf(fact_42_imageI, axiom,
    ((![X : produc16571293le_alt, A4 : set_Pr367596371le_alt, F : produc16571293le_alt > produc16571293le_alt]: ((member2048039092le_alt @ X @ A4) => (member2048039092le_alt @ (F @ X) @ (image_1873259469le_alt @ F @ A4)))))). % imageI
thf(fact_43_UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % UNIV_I
thf(fact_44_UNIV__witness, axiom,
    ((?[X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ top_to224369155le_alt)))). % UNIV_witness
thf(fact_45_UNIV__eq__I, axiom,
    ((![A4 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ A4)) => (top_to224369155le_alt = A4))))). % UNIV_eq_I
thf(fact_46_rev__image__eqI, axiom,
    ((![X : produc16571293le_alt, A4 : set_Pr367596371le_alt, B : produc16571293le_alt, F : produc16571293le_alt > produc16571293le_alt]: ((member2048039092le_alt @ X @ A4) => ((B = (F @ X)) => (member2048039092le_alt @ B @ (image_1873259469le_alt @ F @ A4))))))). % rev_image_eqI
thf(fact_47_iso__tuple__UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % iso_tuple_UNIV_I
thf(fact_48_top__empty__eq, axiom,
    ((top_to1074038850_alt_o = (^[X4 : produc16571293le_alt]: (member2048039092le_alt @ X4 @ top_to224369155le_alt))))). % top_empty_eq
thf(fact_49_map__prod__simp, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, G : arrow_1857593510le_alt > arrow_1857593510le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc1074667658le_alt @ F @ G @ (produc1494124311le_alt @ A @ B)) = (produc1494124311le_alt @ (F @ A) @ (G @ B)))))). % map_prod_simp
thf(fact_50_prod_Ocollapse, axiom,
    ((![Prod : produc16571293le_alt]: ((produc1494124311le_alt @ (produc2071652395le_alt @ Prod) @ (produc1272650601le_alt @ Prod)) = Prod)))). % prod.collapse
thf(fact_51_map__prod__imageI, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, R3 : set_Pr367596371le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt, G : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ R3) => (member2048039092le_alt @ (produc1494124311le_alt @ (F @ A) @ (G @ B)) @ (image_1873259469le_alt @ (produc1074667658le_alt @ F @ G) @ R3)))))). % map_prod_imageI
thf(fact_52_surjective__pairing, axiom,
    ((![T : produc16571293le_alt]: (T = (produc1494124311le_alt @ (produc2071652395le_alt @ T) @ (produc1272650601le_alt @ T)))))). % surjective_pairing
thf(fact_53_prod_Oexhaust__sel, axiom,
    ((![Prod : produc16571293le_alt]: (Prod = (produc1494124311le_alt @ (produc2071652395le_alt @ Prod) @ (produc1272650601le_alt @ Prod)))))). % prod.exhaust_sel
thf(fact_54_fst__conv, axiom,
    ((![X1 : arrow_1857593510le_alt, X2 : arrow_1857593510le_alt]: ((produc2071652395le_alt @ (produc1494124311le_alt @ X1 @ X2)) = X1)))). % fst_conv
thf(fact_55_fst__eqD, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, A : arrow_1857593510le_alt]: (((produc2071652395le_alt @ (produc1494124311le_alt @ X @ Y)) = A) => (X = A))))). % fst_eqD
thf(fact_56_snd__conv, axiom,
    ((![X1 : arrow_1857593510le_alt, X2 : arrow_1857593510le_alt]: ((produc1272650601le_alt @ (produc1494124311le_alt @ X1 @ X2)) = X2)))). % snd_conv
thf(fact_57_snd__eqD, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, A : arrow_1857593510le_alt]: (((produc1272650601le_alt @ (produc1494124311le_alt @ X @ Y)) = A) => (Y = A))))). % snd_eqD
thf(fact_58_prod_Oswap__def, axiom,
    ((produc1794822519le_alt = (^[P3 : produc16571293le_alt]: (produc1494124311le_alt @ (produc1272650601le_alt @ P3) @ (produc2071652395le_alt @ P3)))))). % prod.swap_def
thf(fact_59_Product__Type_OCollect__case__prodD, axiom,
    ((![X : produc16571293le_alt, A4 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: ((member2048039092le_alt @ X @ (collec531981554le_alt @ (produc624247124_alt_o @ A4))) => (A4 @ (produc2071652395le_alt @ X) @ (produc1272650601le_alt @ X)))))). % Product_Type.Collect_case_prodD
thf(fact_60_prod__fun__imageE, axiom,
    ((![C : produc16571293le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt, G : arrow_1857593510le_alt > arrow_1857593510le_alt, R3 : set_Pr367596371le_alt]: ((member2048039092le_alt @ C @ (image_1873259469le_alt @ (produc1074667658le_alt @ F @ G) @ R3)) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((C = (produc1494124311le_alt @ (F @ X3) @ (G @ Y3))) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y3) @ R3))))))))))). % prod_fun_imageE
thf(fact_61_BNF__Greatest__Fixpoint_Osubst__Pair, axiom,
    ((![P2 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, A : produc16571293le_alt]: ((P2 @ X @ Y) => ((A = (produc1494124311le_alt @ X @ Y)) => (P2 @ (produc2071652395le_alt @ A) @ (produc1272650601le_alt @ A))))))). % BNF_Greatest_Fixpoint.subst_Pair
thf(fact_62_conjI__realizer, axiom,
    ((![P2 : arrow_1857593510le_alt > $o, P : arrow_1857593510le_alt, Q : arrow_1857593510le_alt > $o, Q2 : arrow_1857593510le_alt]: ((P2 @ P) => ((Q @ Q2) => ((P2 @ (produc2071652395le_alt @ (produc1494124311le_alt @ P @ Q2))) & (Q @ (produc1272650601le_alt @ (produc1494124311le_alt @ P @ Q2))))))))). % conjI_realizer
thf(fact_63_exI__realizer, axiom,
    ((![P2 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, Y : arrow_1857593510le_alt, X : arrow_1857593510le_alt]: ((P2 @ Y @ X) => (P2 @ (produc1272650601le_alt @ (produc1494124311le_alt @ X @ Y)) @ (produc2071652395le_alt @ (produc1494124311le_alt @ X @ Y))))))). % exI_realizer
thf(fact_64_apfst__conv, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((produc1245692284le_alt @ F @ (produc1494124311le_alt @ X @ Y)) = (produc1494124311le_alt @ (F @ X) @ Y))))). % apfst_conv
thf(fact_65_eq__snd__iff, axiom,
    ((![B : arrow_1857593510le_alt, P : produc16571293le_alt]: ((B = (produc1272650601le_alt @ P)) = (?[A6 : arrow_1857593510le_alt]: (P = (produc1494124311le_alt @ A6 @ B))))))). % eq_snd_iff
thf(fact_66_sndI, axiom,
    ((![X : produc16571293le_alt, Y : arrow_1857593510le_alt, Z : arrow_1857593510le_alt]: ((X = (produc1494124311le_alt @ Y @ Z)) => ((produc1272650601le_alt @ X) = Z))))). % sndI
thf(fact_67_fstI, axiom,
    ((![X : produc16571293le_alt, Y : arrow_1857593510le_alt, Z : arrow_1857593510le_alt]: ((X = (produc1494124311le_alt @ Y @ Z)) => ((produc2071652395le_alt @ X) = Y))))). % fstI
thf(fact_68_eq__fst__iff, axiom,
    ((![A : arrow_1857593510le_alt, P : produc16571293le_alt]: ((A = (produc2071652395le_alt @ P)) = (?[B5 : arrow_1857593510le_alt]: (P = (produc1494124311le_alt @ A @ B5))))))). % eq_fst_iff
thf(fact_69_subsetI, axiom,
    ((![A4 : set_Pr367596371le_alt, B6 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A4) => (member2048039092le_alt @ X3 @ B6))) => (ord_le1885758387le_alt @ A4 @ B6))))). % subsetI
thf(fact_70_image__subsetI, axiom,
    ((![A4 : set_Pr367596371le_alt, F : produc16571293le_alt > produc16571293le_alt, B6 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A4) => (member2048039092le_alt @ (F @ X3) @ B6))) => (ord_le1885758387le_alt @ (image_1873259469le_alt @ F @ A4) @ B6))))). % image_subsetI

% Conjectures (7)
thf(conj_0, hypothesis,
    ((~ ((x = y))))).
thf(conj_1, hypothesis,
    ((trans_1364318725le_alt @ l))).
thf(conj_2, hypothesis,
    ((![A5 : arrow_1857593510le_alt]: (~ ((member2048039092le_alt @ (produc1494124311le_alt @ A5 @ A5) @ l)))))).
thf(conj_3, hypothesis,
    ((![X5 : arrow_1857593510le_alt, Y5 : arrow_1857593510le_alt]: ((~ ((X5 = Y5))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X5 @ Y5) @ l) | (member2048039092le_alt @ (produc1494124311le_alt @ Y5 @ X5) @ l)))))).
thf(conj_4, hypothesis,
    ((member2048039092le_alt @ (produc1494124311le_alt @ y @ x) @ l))).
thf(conj_5, hypothesis,
    ((member2048039092le_alt @ (produc1494124311le_alt @ x @ y) @ l))).
thf(conj_6, conjecture,
    ($false)).
