TSTP Solution File: SCT105+1 by nanoCoP---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : SCT105+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:51:34 EDT 2023
% Result : Theorem 1.67s 2.41s
% Output : Proof 1.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SCT105+1 : TPTP v8.1.2. Released v5.2.0.
% 0.06/0.13 % Command : nanocop.sh %s %d
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu May 18 15:26:17 EDT 2023
% 0.12/0.34 % CPUTime :
% 1.67/2.41
% 1.67/2.41 /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 1.67/2.41 Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.67/2.41 %-----------------------------------------------------
% 1.67/2.41 ncf(matrix, plain, [(5932 ^ _63126) ^ [] : [5933 ^ _63126 : [(5934 ^ _63126) ^ [] : [-(c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt, v_L))], (5936 ^ _63126) ^ [_272907] : [c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, _272907, _272907), v_L)], (5938 ^ _63126) ^ [_273000, _273002] : [-(_273002 = _273000), -(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, _273000, _273002), v_L)), -(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, _273002, _273000), v_L))], (5948 ^ _63126) ^ [] : [c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt, v_L), -(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, 5953 ^ [], 5953 ^ []), v_L)), 5958 ^ _63126 : [(5959 ^ _63126) ^ [] : [5956 ^ [] = 5957 ^ []], (5961 ^ _63126) ^ [] : [c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, 5956 ^ [], 5957 ^ []), v_L)], (5963 ^ _63126) ^ [] : [c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, 5957 ^ [], 5956 ^ []), v_L)]]]], 5964 ^ _63126 : [(5965 ^ _63126) ^ [] : [-(c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt, v_L))], (5967 ^ _63126) ^ [_273830] : [c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, _273830, _273830), v_L)], (5969 ^ _63126) ^ [_273923, _273925] : [-(_273925 = _273923), -(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, _273925, _273923), v_L)), -(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, _273923, _273925), v_L))], (5979 ^ _63126) ^ [] : [c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt, v_L), -(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, 5984 ^ [], 5984 ^ []), v_L)), 5989 ^ _63126 : [(5990 ^ _63126) ^ [] : [5987 ^ [] = 5988 ^ []], (5992 ^ _63126) ^ [] : [c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, 5988 ^ [], 5987 ^ []), v_L)], (5994 ^ _63126) ^ [] : [c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, 5987 ^ [], 5988 ^ []), v_L)]]]]], (538 ^ _63126) ^ [_70990, _70992, _70994, _70996, _70998, _71000, _71002, _71004, _71006, _71008] : [-(c_Product__Type_Oprod_Oprod__rec(_71008, _71004, _71000, _70996, _70992) = c_Product__Type_Oprod_Oprod__rec(_71006, _71002, _70998, _70994, _70990)), _71008 = _71006, _71004 = _71002, _71000 = _70998, _70996 = _70994, _70992 = _70990], (560 ^ _63126) ^ [_71379, _71381, _71383, _71385, _71387, _71389, _71391, _71393, _71395, _71397] : [-(c_Product__Type_Ointernal__split(_71397, _71393, _71389, _71385, _71381) = c_Product__Type_Ointernal__split(_71395, _71391, _71387, _71383, _71379)), _71397 = _71395, _71393 = _71391, _71389 = _71387, _71385 = _71383, _71381 = _71379], (582 ^ _63126) ^ [_71768, _71770, _71772, _71774, _71776, _71778, _71780, _71782, _71784, _71786, _71788, _71790] : [-(c_Product__Type_Ocurry(_71790, _71786, _71782, _71778, _71774, _71770) = c_Product__Type_Ocurry(_71788, _71784, _71780, _71776, _71772, _71768)), _71790 = _71788, _71786 = _71784, _71782 = _71780, _71778 = _71776, _71774 = _71772, _71770 = _71768], (608 ^ _63126) ^ [_72253, _72255, _72257, _72259, _72261, _72263, _72265, _72267, _72269, _72271] : [-(c_Nitpick_Owf__wfrec_H(_72271, _72267, _72263, _72259, _72255) = c_Nitpick_Owf__wfrec_H(_72269, _72265, _72261, _72257, _72253)), _72271 = _72269, _72267 = _72265, _72263 = _72261, _72259 = _72257, _72255 = _72253], (630 ^ _63126) ^ [_72642, _72644, _72646, _72648, _72650, _72652, _72654, _72656] : [-(c_Nitpick_Owf__wfrec(_72656, _72652, _72648, _72644) = c_Nitpick_Owf__wfrec(_72654, _72650, _72646, _72642)), _72656 = _72654, _72652 = _72650, _72648 = _72646, _72644 = _72642], (648 ^ _63126) ^ [_72943, _72945, _72947, _72949, _72951, _72953, _72955, _72957, _72959, _72961] : [-(c_Recdef_Ocut(_72961, _72957, _72953, _72949, _72945) = c_Recdef_Ocut(_72959, _72955, _72951, _72947, _72943)), _72961 = _72959, _72957 = _72955, _72953 = _72951, _72949 = _72947, _72945 = _72943], (670 ^ _63126) ^ [_73332, _73334, _73336, _73338, _73340, _73342, _73344, _73346] : [-(c_Recdef_Owfrec(_73346, _73342, _73338, _73334) = c_Recdef_Owfrec(_73344, _73340, _73336, _73332)), _73346 = _73344, _73342 = _73340, _73338 = _73336, _73334 = _73332], (688 ^ _63126) ^ [_73633, _73635, _73637, _73639, _73641, _73643, _73645, _73647] : [-(c_Recdef_Osame__fst(_73647, _73643, _73639, _73635) = c_Recdef_Osame__fst(_73645, _73641, _73637, _73633)), _73647 = _73645, _73643 = _73641, _73639 = _73637, _73635 = _73633], (706 ^ _63126) ^ [_73934, _73936, _73938, _73940, _73942, _73944] : [-(c_FunDef_Oin__rel(_73944, _73940, _73936) = c_FunDef_Oin__rel(_73942, _73938, _73934)), _73944 = _73942, _73940 = _73938, _73936 = _73934], (720 ^ _63126) ^ [_74155, _74157] : [_74157 = _74155, -(c_Wellfounded_Omeasure(_74157) = c_Wellfounded_Omeasure(_74155))], (726 ^ _63126) ^ [_74240, _74242, _74244, _74246, _74248, _74250] : [-(c_Relation_Oinv__image(_74250, _74246, _74242) = c_Relation_Oinv__image(_74248, _74244, _74240)), _74250 = _74248, _74246 = _74244, _74242 = _74240], (740 ^ _63126) ^ [_74461, _74463, _74465, _74467] : [-(c_Wellfounded_Oacc(_74467, _74463) = c_Wellfounded_Oacc(_74465, _74461)), _74467 = _74465, _74463 = _74461], (750 ^ _63126) ^ [_74610, _74612, _74614, _74616, _74618, _74620] : [-(c_Wellfounded_Omlex__prod(_74620, _74616, _74612) = c_Wellfounded_Omlex__prod(_74618, _74614, _74610)), _74620 = _74618, _74616 = _74614, _74612 = _74610], (764 ^ _63126) ^ [_74831, _74833, _74835, _74837] : [-(c_Relation_OId__on(_74837, _74833) = c_Relation_OId__on(_74835, _74831)), _74837 = _74835, _74833 = _74831], (774 ^ _63126) ^ [_74980, _74982, _74984, _74986, _74988, _74990] : [-(c_Relation_ODomain(_74990, _74986, _74982) = c_Relation_ODomain(_74988, _74984, _74980)), _74990 = _74988, _74986 = _74984, _74982 = _74980], (788 ^ _63126) ^ [_75201, _75203, _75205, _75207, _75209, _75211] : [-(c_Relation_ORange(_75211, _75207, _75203) = c_Relation_ORange(_75209, _75205, _75201)), _75211 = _75209, _75207 = _75205, _75203 = _75201], (802 ^ _63126) ^ [_75422, _75424, _75426, _75428] : [-(c_Transitive__Closure_Otrancl(_75428, _75424) = c_Transitive__Closure_Otrancl(_75426, _75422)), _75428 = _75426, _75424 = _75422], (812 ^ _63126) ^ [_75571, _75573, _75575, _75577, _75579, _75581, _75583, _75585] : [-(c_Wellfounded_Olex__prod(_75585, _75581, _75577, _75573) = c_Wellfounded_Olex__prod(_75583, _75579, _75575, _75571)), _75585 = _75583, _75581 = _75579, _75577 = _75575, _75573 = _75571], (830 ^ _63126) ^ [_75872, _75874, _75876, _75878] : [-(c_Wellfounded_Omax__ext(_75878, _75874) = c_Wellfounded_Omax__ext(_75876, _75872)), _75878 = _75876, _75874 = _75872], (840 ^ _63126) ^ [_76021, _76023, _76025, _76027] : [-(c_Wellfounded_Omin__ext(_76027, _76023) = c_Wellfounded_Omin__ext(_76025, _76021)), _76027 = _76025, _76023 = _76021], (850 ^ _63126) ^ [_76170, _76172, _76174, _76176] : [-(c_Set_Othe__elem(_76176, _76172) = c_Set_Othe__elem(_76174, _76170)), _76176 = _76174, _76172 = _76170], (860 ^ _63126) ^ [_76319, _76321, _76323, _76325] : [-(c_Relation_OField(_76325, _76321) = c_Relation_OField(_76323, _76319)), _76325 = _76323, _76321 = _76319], (870 ^ _63126) ^ [_76468, _76470, _76472, _76474, _76476, _76478] : [-(c_Groups_Ominus__class_Ominus(_76478, _76474, _76470) = c_Groups_Ominus__class_Ominus(_76476, _76472, _76468)), _76478 = _76476, _76474 = _76472, _76470 = _76468], (884 ^ _63126) ^ [_76689, _76691, _76693, _76695, _76697, _76699, _76701, _76703] : [-(c_FunDef_Orp__inv__image(_76703, _76699, _76695, _76691) = c_FunDef_Orp__inv__image(_76701, _76697, _76693, _76689)), _76703 = _76701, _76699 = _76697, _76695 = _76693, _76691 = _76689], (902 ^ _63126) ^ [_76990, _76992] : [_76992 = _76990, -(c_Relation_OId(_76992) = c_Relation_OId(_76990))], (908 ^ _63126) ^ [_77075, _77077, _77079, _77081] : [-(c_Transitive__Closure_Ortrancl(_77081, _77077) = c_Transitive__Closure_Ortrancl(_77079, _77075)), _77081 = _77079, _77077 = _77075], (918 ^ _63126) ^ [_77224, _77226, _77228, _77230, _77232, _77234, _77236, _77238] : [-(c_Relation_OImage(_77238, _77234, _77230, _77226) = c_Relation_OImage(_77236, _77232, _77228, _77224)), _77238 = _77236, _77234 = _77232, _77230 = _77228, _77226 = _77224], (936 ^ _63126) ^ [_77525, _77527, _77529, _77531, _77533, _77535] : [-(c_Set_Oinsert(_77535, _77531, _77527) = c_Set_Oinsert(_77533, _77529, _77525)), _77535 = _77533, _77531 = _77529, _77527 = _77525], (950 ^ _63126) ^ [_77746, _77748, _77750, _77752, _77754, _77756, _77758, _77760, _77762, _77764] : [-(c_Relation_Orel__comp(_77764, _77760, _77756, _77752, _77748) = c_Relation_Orel__comp(_77762, _77758, _77754, _77750, _77746)), _77764 = _77762, _77760 = _77758, _77756 = _77754, _77752 = _77750, _77748 = _77746], (972 ^ _63126) ^ [_78135, _78137, _78139, _78141, _78143, _78145] : [-(c_Lattices_Osemilattice__sup__class_Osup(_78145, _78141, _78137) = c_Lattices_Osemilattice__sup__class_Osup(_78143, _78139, _78135)), _78145 = _78143, _78141 = _78139, _78137 = _78135], (986 ^ _63126) ^ [_78356, _78358] : [_78358 = _78356, -(c_Orderings_Obot__class_Obot(_78358) = c_Orderings_Obot__class_Obot(_78356))], (992 ^ _63126) ^ [_78441, _78443, _78445, _78447] : [-(tc_fun(_78447, _78443) = tc_fun(_78445, _78441)), _78447 = _78445, _78443 = _78441], (1002 ^ _63126) ^ [_78590, _78592, _78594, _78596] : [-(hAPP(_78596, _78592) = hAPP(_78594, _78590)), _78596 = _78594, _78592 = _78590], (1012 ^ _63126) ^ [_78739, _78741] : [_78741 = _78739, -(c_fequal(_78741) = c_fequal(_78739))], (1018 ^ _63126) ^ [_78824, _78826, _78828, _78830] : [-(tc_prod(_78830, _78826) = tc_prod(_78828, _78824)), _78830 = _78828, _78826 = _78824], (1028 ^ _63126) ^ [_78969, _78971, _78973, _78975, _78977, _78979, _78981, _78983] : [-(c_Product__Type_OPair(_78983, _78979, _78975, _78971) = c_Product__Type_OPair(_78981, _78977, _78973, _78969)), _78983 = _78981, _78979 = _78977, _78975 = _78973, _78971 = _78969], (2 ^ _63126) ^ [_63156] : [-(_63156 = _63156)], (4 ^ _63126) ^ [_63179, _63181] : [_63181 = _63179, -(_63179 = _63181)], (10 ^ _63126) ^ [_63252, _63254, _63256] : [-(_63256 = _63252), _63256 = _63254, _63254 = _63252], (20 ^ _63126) ^ [_63389, _63391, _63393, _63395] : [-(c_Nitpick_Orefl_H(_63393, _63389)), c_Nitpick_Orefl_H(_63395, _63391), _63395 = _63393, _63391 = _63389], (34 ^ _63126) ^ [_63582, _63584, _63586, _63588, _63590, _63592, _63594, _63596, _63598, _63600, _63602, _63604] : [-(c_Recdef_Owfrec__rel(_63602, _63598, _63594, _63590, _63586, _63582)), c_Recdef_Owfrec__rel(_63604, _63600, _63596, _63592, _63588, _63584), _63604 = _63602, _63600 = _63598, _63596 = _63594, _63592 = _63590, _63588 = _63586, _63584 = _63582], (64 ^ _63126) ^ [_64127, _64129, _64131, _64133, _64135, _64137] : [-(c_Order__Relation_Ostrict__linear__order__on(_64135, _64131, _64127)), c_Order__Relation_Ostrict__linear__order__on(_64137, _64133, _64129), _64137 = _64135, _64133 = _64131, _64129 = _64127], (82 ^ _63126) ^ [_64396, _64398, _64400, _64402] : [-(c_Relation_Oirrefl(_64400, _64396)), c_Relation_Oirrefl(_64402, _64398), _64402 = _64400, _64398 = _64396], (96 ^ _63126) ^ [_64589, _64591, _64593, _64595] : [-(c_Wellfounded_Oacyclic(_64593, _64589)), c_Wellfounded_Oacyclic(_64595, _64591), _64595 = _64593, _64591 = _64589], (110 ^ _63126) ^ [_64782, _64784, _64786, _64788, _64790, _64792] : [-(c_Relation_Osingle__valued(_64790, _64786, _64782)), c_Relation_Osingle__valued(_64792, _64788, _64784), _64792 = _64790, _64788 = _64786, _64784 = _64782], (128 ^ _63126) ^ [_65051, _65053, _65055, _65057] : [-(c_Wellfounded_OwfP(_65055, _65051)), c_Wellfounded_OwfP(_65057, _65053), _65057 = _65055, _65053 = _65051], (142 ^ _63126) ^ [_65244, _65246] : [-(class_Groups_Oab__group__add(_65244)), _65246 = _65244, class_Groups_Oab__group__add(_65246)], (152 ^ _63126) ^ [_65369, _65371] : [-(class_Groups_Oordered__ab__group__add(_65369)), _65371 = _65369, class_Groups_Oordered__ab__group__add(_65371)], (162 ^ _63126) ^ [_65494, _65496, _65498, _65500, _65502, _65504] : [-(c_Relation_Ototal__on(_65502, _65498, _65494)), c_Relation_Ototal__on(_65504, _65500, _65496), _65504 = _65502, _65500 = _65498, _65496 = _65494], (180 ^ _63126) ^ [_65763, _65765, _65767, _65769, _65771, _65773] : [-(c_Order__Relation_Olinear__order__on(_65771, _65767, _65763)), c_Order__Relation_Olinear__order__on(_65773, _65769, _65765), _65773 = _65771, _65769 = _65767, _65765 = _65763], (198 ^ _63126) ^ [_66032, _66034, _66036, _66038, _66040, _66042] : [-(c_Order__Relation_Owell__order__on(_66040, _66036, _66032)), c_Order__Relation_Owell__order__on(_66042, _66038, _66034), _66042 = _66040, _66038 = _66036, _66034 = _66032], (216 ^ _63126) ^ [_66301, _66303, _66305, _66307, _66309, _66311] : [-(c_Orderings_Oord__class_Oless(_66309, _66305, _66301)), c_Orderings_Oord__class_Oless(_66311, _66307, _66303), _66311 = _66309, _66307 = _66305, _66303 = _66301], (234 ^ _63126) ^ [_66570, _66572, _66574, _66576, _66578, _66580] : [-(c_Order__Relation_Opartial__order__on(_66578, _66574, _66570)), c_Order__Relation_Opartial__order__on(_66580, _66576, _66572), _66580 = _66578, _66576 = _66574, _66572 = _66570], (252 ^ _63126) ^ [_66839, _66841, _66843, _66845, _66847, _66849] : [-(c_Relation_Orefl__on(_66847, _66843, _66839)), c_Relation_Orefl__on(_66849, _66845, _66841), _66849 = _66847, _66845 = _66843, _66841 = _66839], (270 ^ _63126) ^ [_67108, _67110, _67112, _67114] : [-(c_Relation_Oantisym(_67112, _67108)), c_Relation_Oantisym(_67114, _67110), _67114 = _67112, _67110 = _67108], (284 ^ _63126) ^ [_67301, _67303, _67305, _67307, _67309, _67311] : [-(c_Order__Relation_Opreorder__on(_67309, _67305, _67301)), c_Order__Relation_Opreorder__on(_67311, _67307, _67303), _67311 = _67309, _67307 = _67305, _67303 = _67301], (302 ^ _63126) ^ [_67570, _67572, _67574, _67576, _67578, _67580, _67582, _67584, _67586, _67588, _67590, _67592] : [-(c_Nitpick_Ofold__graph_H(_67590, _67586, _67582, _67578, _67574, _67570)), c_Nitpick_Ofold__graph_H(_67592, _67588, _67584, _67580, _67576, _67572), _67592 = _67590, _67588 = _67586, _67584 = _67582, _67580 = _67578, _67576 = _67574, _67572 = _67570], (332 ^ _63126) ^ [_68115, _68117, _68119, _68121] : [-(c_Wellfounded_Owf(_68119, _68115)), c_Wellfounded_Owf(_68121, _68117), _68121 = _68119, _68117 = _68115], (346 ^ _63126) ^ [_68308, _68310, _68312, _68314] : [-(c_FunDef_Oreduction__pair(_68312, _68308)), c_FunDef_Oreduction__pair(_68314, _68310), _68314 = _68312, _68310 = _68308], (360 ^ _63126) ^ [_68501, _68503, _68505, _68507, _68509, _68511] : [-(c_Orderings_Oord__class_Oless__eq(_68509, _68505, _68501)), c_Orderings_Oord__class_Oless__eq(_68511, _68507, _68503), _68511 = _68509, _68507 = _68505, _68503 = _68501], (378 ^ _63126) ^ [_68770, _68772, _68774, _68776, _68778, _68780] : [-(c_Equiv__Relations_Oequiv(_68778, _68774, _68770)), c_Equiv__Relations_Oequiv(_68780, _68776, _68772), _68780 = _68778, _68776 = _68774, _68772 = _68770], (396 ^ _63126) ^ [_69039, _69041] : [-(class_Lattices_Obounded__lattice(_69039)), _69041 = _69039, class_Lattices_Obounded__lattice(_69041)], (406 ^ _63126) ^ [_69164, _69166] : [-(class_Orderings_Olinorder(_69164)), _69166 = _69164, class_Orderings_Olinorder(_69166)], (416 ^ _63126) ^ [_69289, _69291] : [-(class_Lattices_Obounded__lattice__bot(_69289)), _69291 = _69289, class_Lattices_Obounded__lattice__bot(_69291)], (426 ^ _63126) ^ [_69414, _69416] : [-(class_Lattices_Osemilattice__sup(_69414)), _69416 = _69414, class_Lattices_Osemilattice__sup(_69416)], (436 ^ _63126) ^ [_69539, _69541] : [-(class_Orderings_Opreorder(_69539)), _69541 = _69539, class_Orderings_Opreorder(_69541)], (446 ^ _63126) ^ [_69664, _69666] : [-(class_Lattices_Olattice(_69664)), _69666 = _69664, class_Lattices_Olattice(_69666)], (456 ^ _63126) ^ [_69789, _69791] : [-(class_Orderings_Oorder(_69789)), _69791 = _69789, class_Orderings_Oorder(_69791)], (466 ^ _63126) ^ [_69914, _69916] : [-(class_Orderings_Oord(_69914)), _69916 = _69914, class_Orderings_Oord(_69916)], (476 ^ _63126) ^ [_70039, _70041] : [-(class_Orderings_Obot(_70039)), _70041 = _70039, class_Orderings_Obot(_70041)], (486 ^ _63126) ^ [_70164, _70166] : [-(class_Groups_Ominus(_70164)), _70166 = _70164, class_Groups_Ominus(_70166)], (496 ^ _63126) ^ [_70289, _70291] : [-(hBOOL(_70289)), _70291 = _70289, hBOOL(_70291)], (506 ^ _63126) ^ [_70414, _70416, _70418, _70420] : [-(c_Relation_Otrans(_70418, _70414)), c_Relation_Otrans(_70420, _70416), _70420 = _70418, _70416 = _70414], (520 ^ _63126) ^ [_70603, _70605, _70607, _70609, _70611, _70613] : [-(c_member(_70611, _70607, _70603)), c_member(_70613, _70609, _70605), _70613 = _70611, _70609 = _70607, _70605 = _70603], (1046 ^ _63126) ^ [_79389, _79391] : [hAPP(_79389, 1047 ^ [_79389, _79391]) = hAPP(_79391, 1047 ^ [_79389, _79391]), -(_79389 = _79391)], (1067 ^ _63126) ^ [_79862, _79864] : [1070 ^ _63126 : [(1071 ^ _63126) ^ [] : [-(c_member(tc_prod(_79862, _79862), c_Product__Type_OPair(_79862, _79862, 1068 ^ [_79862, _79864], 1069 ^ [_79862, _79864]), _79864))], (1074 ^ _63126) ^ [] : [-(c_member(tc_prod(_79862, _79862), c_Product__Type_OPair(_79862, _79862, 1069 ^ [_79862, _79864], 1072 ^ [_79862, _79864]), _79864))], (1076 ^ _63126) ^ [] : [c_member(tc_prod(_79862, _79862), c_Product__Type_OPair(_79862, _79862, 1068 ^ [_79862, _79864], 1072 ^ [_79862, _79864]), _79864)]], -(c_Relation_Otrans(_79862, _79864))], (1053 ^ _63126) ^ [_79530, _79532] : [c_Relation_Otrans(_79530, _79532), 1056 ^ _63126 : [(1057 ^ _63126) ^ [_79636, _79638] : [c_member(tc_prod(_79530, _79530), c_Product__Type_OPair(_79530, _79530, _79638, _79636), _79532), 1060 ^ _63126 : [(1061 ^ _63126) ^ [_79739] : [c_member(tc_prod(_79530, _79530), c_Product__Type_OPair(_79530, _79530, _79636, _79739), _79532), -(c_member(tc_prod(_79530, _79530), c_Product__Type_OPair(_79530, _79530, _79638, _79739), _79532))]]]]], (1080 ^ _63126) ^ [_80192, _80194, _80196, _80198, _80200] : [c_Relation_Otrans(_80192, _80194), c_member(tc_prod(_80192, _80192), c_Product__Type_OPair(_80192, _80192, _80196, _80198), _80194), c_member(tc_prod(_80192, _80192), c_Product__Type_OPair(_80192, _80192, _80198, _80200), _80194), -(c_member(tc_prod(_80192, _80192), c_Product__Type_OPair(_80192, _80192, _80196, _80200), _80194))], (1094 ^ _63126) ^ [_80445, _80447, _80449, _80451] : [_80445 = _80447, 1099 ^ _63126 : [(1100 ^ _63126) ^ [] : [-(c_member(_80449, _80451, _80445))], (1102 ^ _63126) ^ [] : [-(c_member(_80449, _80451, _80447))]], 1103 ^ _63126 : [(1104 ^ _63126) ^ [] : [c_member(_80449, _80451, _80445)], (1106 ^ _63126) ^ [] : [c_member(_80449, _80451, _80447)]]], (1108 ^ _63126) ^ [_80684, _80686, _80688, _80690, _80692] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_80684, _80686, _80688), _80690), _80692)), -(c_member(tc_prod(_80684, _80686), c_Product__Type_OPair(_80684, _80686, _80690, _80692), _80688))], (1114 ^ _63126) ^ [_80799, _80801, _80803, _80805, _80807] : [c_member(tc_prod(_80799, _80801), c_Product__Type_OPair(_80799, _80801, _80805, _80807), _80803), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_80799, _80801, _80803), _80805), _80807)))], (1120 ^ _63126) ^ [_80920, _80922, _80924, _80926, _80928, _80930, _80932] : [hBOOL(hAPP(_80920, _80922)), c_member(tc_prod(_80924, _80924), c_Product__Type_OPair(_80924, _80924, _80926, _80928), hAPP(_80930, _80922)), -(c_member(tc_prod(tc_prod(_80932, _80924), tc_prod(_80932, _80924)), c_Product__Type_OPair(tc_prod(_80932, _80924), tc_prod(_80932, _80924), c_Product__Type_OPair(_80932, _80924, _80922, _80926), c_Product__Type_OPair(_80932, _80924, _80922, _80928)), c_Recdef_Osame__fst(_80932, _80924, _80920, _80930)))], (1130 ^ _63126) ^ [_81184, _81186] : [c_Nitpick_Orefl_H(_81184, _81186), 1133 ^ _63126 : [(1134 ^ _63126) ^ [_81252] : [-(c_member(tc_prod(_81184, _81184), c_Product__Type_OPair(_81184, _81184, _81252, _81252), _81186))]]], (1136 ^ _63126) ^ [_81284, _81286] : [c_member(tc_prod(_81284, _81284), c_Product__Type_OPair(_81284, _81284, 1137 ^ [_81284, _81286], 1137 ^ [_81284, _81286]), _81286), -(c_Nitpick_Orefl_H(_81284, _81286))], (1143 ^ _63126) ^ [_81421, _81423, _81425] : [c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), _81421, c_Arrow__Order__Mirabelle_OLin), -(_81423 = _81425), 1150 ^ _63126 : [(1151 ^ _63126) ^ [] : [-(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, _81423, _81425), _81421)), -(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, _81425, _81423), _81421))], (1157 ^ _63126) ^ [] : [c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, _81425, _81423), _81421), c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, _81423, _81425), _81421)]]], (1163 ^ _63126) ^ [_81703, _81705, _81707] : [hBOOL(hAPP(_81703, 1164 ^ [_81703, _81705, _81707])), 1167 ^ _63126 : [(1168 ^ _63126) ^ [_81810, _81812] : [-(hBOOL(hAPP(_81703, c_Product__Type_OPair(_81705, _81707, _81812, _81810))))]]], (1170 ^ _63126) ^ [_81842, _81844, _81846] : [hBOOL(hAPP(_81842, c_Product__Type_OPair(_81844, _81846, 1171 ^ [_81842, _81844, _81846], 1172 ^ [_81842, _81844, _81846]))), 1175 ^ _63126 : [(1176 ^ _63126) ^ [_81977] : [-(hBOOL(hAPP(_81842, _81977)))]]], (1178 ^ _63126) ^ [_82035, _82037, _82039, _82041, _82043, _82045] : [c_Product__Type_OPair(_82035, _82037, _82039, _82041) = c_Product__Type_OPair(_82035, _82037, _82043, _82045), 1181 ^ _63126 : [(1182 ^ _63126) ^ [] : [-(_82039 = _82043)], (1184 ^ _63126) ^ [] : [-(_82041 = _82045)]]], (1186 ^ _63126) ^ [_82162, _82164, _82166, _82168, _82170, _82172] : [-(c_Product__Type_OPair(_82162, _82164, _82166, _82168) = c_Product__Type_OPair(_82162, _82164, _82170, _82172)), _82166 = _82170, _82168 = _82172], (1196 ^ _63126) ^ [_82329, _82331, _82333, _82335, _82337, _82339] : [c_Product__Type_OPair(_82329, _82331, _82333, _82335) = c_Product__Type_OPair(_82329, _82331, _82337, _82339), 1199 ^ _63126 : [(1200 ^ _63126) ^ [] : [-(_82333 = _82337)], (1202 ^ _63126) ^ [] : [-(_82335 = _82339)]]], (1204 ^ _63126) ^ [_82482, _82484, _82486] : [c_member(_82482, _82484, _82486), -(hBOOL(hAPP(_82486, _82484)))], (1210 ^ _63126) ^ [_82563, _82565, _82567] : [hBOOL(hAPP(_82567, _82565)), -(c_member(_82563, _82565, _82567))], (1216 ^ _63126) ^ [_82650, _82652, _82654, _82656] : [_82650 = _82652, c_member(_82654, _82652, _82656), -(c_member(_82654, _82650, _82656))], (1226 ^ _63126) ^ [_82791, _82793, _82795, _82797] : [_82791 = _82793, 1229 ^ _63126 : [(1230 ^ _63126) ^ [] : [c_member(_82795, _82791, _82797), -(c_member(_82795, _82793, _82797))], (1236 ^ _63126) ^ [] : [c_member(_82795, _82793, _82797), -(c_member(_82795, _82791, _82797))]]], (1242 ^ _63126) ^ [_83016, _83018, _83020, _83022] : [_83016 = _83018, 1245 ^ _63126 : [(1246 ^ _63126) ^ [] : [c_member(_83020, _83022, _83016), -(c_member(_83020, _83022, _83018))], (1252 ^ _63126) ^ [] : [c_member(_83020, _83022, _83018), -(c_member(_83020, _83022, _83016))]]], (1258 ^ _63126) ^ [_83241, _83243, _83245, _83247, _83249, _83251] : [-(c_Product__Type_Oprod_Oprod__rec(_83241, _83243, _83245, _83247, c_Product__Type_OPair(_83241, _83243, _83249, _83251)) = hAPP(hAPP(_83247, _83249), _83251))], (1260 ^ _63126) ^ [_83306, _83308] : [c_Relation_Oirrefl(_83306, _83308), 1263 ^ _63126 : [(1264 ^ _63126) ^ [_83378] : [c_member(tc_prod(_83306, _83306), c_Product__Type_OPair(_83306, _83306, _83378, _83378), _83308)]]], (1266 ^ _63126) ^ [_83408, _83410] : [-(c_member(tc_prod(_83408, _83408), c_Product__Type_OPair(_83408, _83408, 1267 ^ [_83408, _83410], 1267 ^ [_83408, _83410]), _83410)), -(c_Relation_Oirrefl(_83408, _83410))], (1273 ^ _63126) ^ [_83502, _83504, _83506, _83508, _83510, _83512, _83514, _83516] : [c_member(tc_prod(tc_prod(_83502, _83504), tc_prod(_83502, _83504)), c_Product__Type_OPair(tc_prod(_83502, _83504), tc_prod(_83502, _83504), c_Product__Type_OPair(_83502, _83504, _83506, _83508), c_Product__Type_OPair(_83502, _83504, _83510, _83512)), c_Wellfounded_Olex__prod(_83502, _83504, _83514, _83516)), -(c_member(tc_prod(_83502, _83502), c_Product__Type_OPair(_83502, _83502, _83506, _83510), _83514)), 1280 ^ _63126 : [(1281 ^ _63126) ^ [] : [-(_83506 = _83510)], (1283 ^ _63126) ^ [] : [-(c_member(tc_prod(_83504, _83504), c_Product__Type_OPair(_83504, _83504, _83508, _83512), _83516))]]], (1285 ^ _63126) ^ [_83751, _83753, _83755, _83757, _83759, _83761, _83763, _83765] : [-(c_member(tc_prod(tc_prod(_83751, _83753), tc_prod(_83751, _83753)), c_Product__Type_OPair(tc_prod(_83751, _83753), tc_prod(_83751, _83753), c_Product__Type_OPair(_83751, _83753, _83755, _83757), c_Product__Type_OPair(_83751, _83753, _83759, _83761)), c_Wellfounded_Olex__prod(_83751, _83753, _83763, _83765))), 1286 ^ _63126 : [(1287 ^ _63126) ^ [] : [c_member(tc_prod(_83751, _83751), c_Product__Type_OPair(_83751, _83751, _83755, _83759), _83763)], (1289 ^ _63126) ^ [] : [_83755 = _83759, c_member(tc_prod(_83753, _83753), c_Product__Type_OPair(_83753, _83753, _83757, _83761), _83765)]]], (1297 ^ _63126) ^ [_84050, _84052, _84054, _84056, _84058, _84060] : [-(c_Product__Type_Ointernal__split(_84050, _84052, _84054, _84056, c_Product__Type_OPair(_84050, _84052, _84058, _84060)) = hAPP(hAPP(_84056, _84058), _84060))], (1299 ^ _63126) ^ [_84100, _84102, _84104, _84106, _84108] : [c_member(tc_prod(_84100, _84102), c_Product__Type_OPair(_84100, _84102, _84104, _84106), _84108), -(c_member(_84102, _84106, c_Relation_ORange(_84100, _84102, _84108)))], (1305 ^ _63126) ^ [_84232, _84234, _84236, _84238] : [c_member(tc_prod(_84232, _84232), c_Product__Type_OPair(_84232, _84232, _84234, _84236), c_Relation_OId__on(_84232, _84238)), 1308 ^ _63126 : [(1309 ^ _63126) ^ [] : [-(_84234 = _84236)], (1311 ^ _63126) ^ [] : [-(c_member(_84232, _84234, _84238))]]], (1313 ^ _63126) ^ [_84361, _84363, _84365, _84367] : [-(c_member(tc_prod(_84361, _84361), c_Product__Type_OPair(_84361, _84361, _84363, _84365), c_Relation_OId__on(_84361, _84367))), _84363 = _84365, c_member(_84361, _84363, _84367)], (1323 ^ _63126) ^ [_84526, _84528, _84530, _84532] : [_84526 = _84528, c_member(_84530, _84526, _84532), -(c_member(tc_prod(_84530, _84530), c_Product__Type_OPair(_84530, _84530, _84526, _84528), c_Relation_OId__on(_84530, _84532)))], (1333 ^ _63126) ^ [_84689, _84691, _84693, _84695, _84697] : [c_member(tc_prod(_84689, _84691), c_Product__Type_OPair(_84689, _84691, _84693, _84695), _84697), -(c_member(_84689, _84693, c_Relation_ODomain(_84689, _84691, _84697)))], (1339 ^ _63126) ^ [_84800, _84802] : [1342 ^ _63126 : [(1343 ^ _63126) ^ [] : [-(c_member(tc_prod(_84800, _84800), c_Product__Type_OPair(_84800, _84800, 1340 ^ [_84800, _84802], 1341 ^ [_84800, _84802]), _84802))], (1346 ^ _63126) ^ [] : [-(c_member(tc_prod(_84800, _84800), c_Product__Type_OPair(_84800, _84800, 1341 ^ [_84800, _84802], 1344 ^ [_84800, _84802]), _84802))], (1348 ^ _63126) ^ [] : [c_member(tc_prod(_84800, _84800), c_Product__Type_OPair(_84800, _84800, 1340 ^ [_84800, _84802], 1344 ^ [_84800, _84802]), _84802)]], -(c_Relation_Otrans(_84800, _84802))], (1374 ^ _63126) ^ [_85513, _85515, _85517] : [1376 ^ _63126 : [(1377 ^ _63126) ^ [] : [-(c_member(_85513, 1375 ^ [_85513, _85515, _85517], _85515))], (1380 ^ _63126) ^ [] : [-(c_member(_85513, 1378 ^ [_85513, _85515, _85517], _85515))], (1382 ^ _63126) ^ [] : [1375 ^ [_85513, _85515, _85517] = 1378 ^ [_85513, _85515, _85517]], (1384 ^ _63126) ^ [] : [c_member(tc_prod(_85513, _85513), c_Product__Type_OPair(_85513, _85513, 1375 ^ [_85513, _85515, _85517], 1378 ^ [_85513, _85515, _85517]), _85517)], (1386 ^ _63126) ^ [] : [c_member(tc_prod(_85513, _85513), c_Product__Type_OPair(_85513, _85513, 1378 ^ [_85513, _85515, _85517], 1375 ^ [_85513, _85515, _85517]), _85517)]], -(c_Relation_Ototal__on(_85513, _85515, _85517))], (1352 ^ _63126) ^ [_85146, _85148, _85150] : [c_Relation_Ototal__on(_85146, _85148, _85150), 1355 ^ _63126 : [(1356 ^ _63126) ^ [_85258] : [c_member(_85146, _85258, _85148), 1359 ^ _63126 : [(1360 ^ _63126) ^ [_85360] : [c_member(_85146, _85360, _85148), -(_85258 = _85360), -(c_member(tc_prod(_85146, _85146), c_Product__Type_OPair(_85146, _85146, _85258, _85360), _85150)), -(c_member(tc_prod(_85146, _85146), c_Product__Type_OPair(_85146, _85146, _85360, _85258), _85150))]]]]], (1390 ^ _63126) ^ [_86012, _86014, _86016, _86018, _86020, _86022] : [c_member(tc_prod(_86012, _86012), c_Product__Type_OPair(_86012, _86012, _86014, _86016), hAPP(c_Relation_Oinv__image(_86018, _86012, _86020), _86022)), -(c_member(tc_prod(_86018, _86018), c_Product__Type_OPair(_86018, _86018, hAPP(_86022, _86014), hAPP(_86022, _86016)), _86020))], (1396 ^ _63126) ^ [_86155, _86157, _86159, _86161, _86163, _86165] : [c_member(tc_prod(_86161, _86161), c_Product__Type_OPair(_86161, _86161, hAPP(_86165, _86157), hAPP(_86165, _86159)), _86163), -(c_member(tc_prod(_86155, _86155), c_Product__Type_OPair(_86155, _86155, _86157, _86159), hAPP(c_Relation_Oinv__image(_86161, _86155, _86163), _86165)))], (1402 ^ _63126) ^ [_86304, _86306, _86308, _86310] : [c_Relation_Otrans(_86304, _86306), c_Relation_Otrans(_86308, _86310), -(c_Relation_Otrans(tc_prod(_86304, _86308), c_Wellfounded_Olex__prod(_86304, _86308, _86306, _86310)))], (1412 ^ _63126) ^ [_86457, _86459] : [-(c_Relation_ORange(_86457, _86457, c_Relation_OId__on(_86457, _86459)) = _86459)], (1414 ^ _63126) ^ [_86489, _86491] : [-(c_Relation_ODomain(_86489, _86489, c_Relation_OId__on(_86489, _86491)) = _86491)], (1416 ^ _63126) ^ [_86521, _86523] : [-(c_Relation_Otrans(_86521, c_Relation_OId__on(_86521, _86523)))], (1418 ^ _63126) ^ [_86549, _86551, _86553, _86555] : [c_Relation_Otrans(_86549, _86551), -(c_Relation_Otrans(_86553, hAPP(c_Relation_Oinv__image(_86549, _86553, _86551), _86555)))], (1424 ^ _63126) ^ [_86782, _86784, _86786, _86788] : [c_member(_86782, _86784, c_Relation_ODomain(_86782, _86786, _86788)), -(c_member(tc_prod(_86782, _86786), c_Product__Type_OPair(_86782, _86786, _86784, 1427 ^ [_86782, _86784, _86786, _86788]), _86788))], (1431 ^ _63126) ^ [_87062, _87064, _87066, _87068] : [1432 ^ _63126 : [(1433 ^ _63126) ^ [_87150] : [c_member(tc_prod(_87062, _87066), c_Product__Type_OPair(_87062, _87066, _87064, _87150), _87068)]], -(c_member(_87062, _87064, c_Relation_ODomain(_87062, _87066, _87068)))], (1437 ^ _63126) ^ [_87393, _87395, _87397, _87399] : [c_member(_87393, _87395, c_Relation_ORange(_87397, _87393, _87399)), -(c_member(tc_prod(_87397, _87393), c_Product__Type_OPair(_87397, _87393, 1440 ^ [_87393, _87395, _87397, _87399], _87395), _87399))], (1444 ^ _63126) ^ [_87673, _87675, _87677, _87679] : [1445 ^ _63126 : [(1446 ^ _63126) ^ [_87761] : [c_member(tc_prod(_87677, _87673), c_Product__Type_OPair(_87677, _87673, _87761, _87675), _87679)]], -(c_member(_87673, _87675, c_Relation_ORange(_87677, _87673, _87679)))], (1450 ^ _63126) ^ [_87990, _87992, _87994] : [c_Order__Relation_Ostrict__linear__order__on(_87990, _87992, _87994), 1453 ^ _63126 : [(1454 ^ _63126) ^ [] : [-(c_Relation_Otrans(_87990, _87994))], (1456 ^ _63126) ^ [] : [-(c_Relation_Oirrefl(_87990, _87994))], (1458 ^ _63126) ^ [] : [-(c_Relation_Ototal__on(_87990, _87992, _87994))]]], (1460 ^ _63126) ^ [_88315, _88317, _88319] : [-(c_Order__Relation_Ostrict__linear__order__on(_88315, _88317, _88319)), c_Relation_Otrans(_88315, _88319), c_Relation_Oirrefl(_88315, _88319), c_Relation_Ototal__on(_88315, _88317, _88319)], (1474 ^ _63126) ^ [_88737, _88739, _88741] : [c_member(tc_prod(_88737, _88737), _88739, c_Relation_OId__on(_88737, _88741)), 1478 ^ _63126 : [(1479 ^ _63126) ^ [] : [-(c_member(_88737, 1477 ^ [_88737, _88739, _88741], _88741))], (1481 ^ _63126) ^ [] : [-(_88739 = c_Product__Type_OPair(_88737, _88737, 1477 ^ [_88737, _88739, _88741], 1477 ^ [_88737, _88739, _88741]))]]], (1483 ^ _63126) ^ [_89183, _89185, _89187, _89189] : [c_member(_89183, _89185, c_Relation_ORange(_89187, _89183, _89189)), -(c_member(tc_prod(_89187, _89183), c_Product__Type_OPair(_89187, _89183, 1486 ^ [_89183, _89185, _89187, _89189], _89185), _89189))], (1490 ^ _63126) ^ [_89545, _89547, _89549, _89551] : [c_member(_89545, _89547, c_Relation_ODomain(_89545, _89549, _89551)), -(c_member(tc_prod(_89545, _89549), c_Product__Type_OPair(_89545, _89549, _89547, 1493 ^ [_89545, _89547, _89549, _89551]), _89551))], (1507 ^ _63126) ^ [_90295, _90297, _90299] : [1509 ^ _63126 : [(1510 ^ _63126) ^ [] : [-(c_member(tc_prod(_90295, _90295), c_Product__Type_OPair(_90295, _90295, 1508 ^ [_90295, _90297, _90299], _90297), _90299))], (1512 ^ _63126) ^ [] : [c_member(_90295, 1508 ^ [_90295, _90297, _90299], c_Wellfounded_Oacc(_90295, _90299))]], -(c_member(_90295, _90297, c_Wellfounded_Oacc(_90295, _90299)))], (1497 ^ _63126) ^ [_89922, _89924, _89926] : [c_member(_89922, _89924, c_Wellfounded_Oacc(_89922, _89926)), 1500 ^ _63126 : [(1501 ^ _63126) ^ [_90084] : [c_member(tc_prod(_89922, _89922), c_Product__Type_OPair(_89922, _89922, _90084, _89924), _89926), -(c_member(_89922, _90084, c_Wellfounded_Oacc(_89922, _89926)))]]], (1516 ^ _63126) ^ [_90743, _90745, _90747, _90749] : [c_member(_90743, _90745, c_Wellfounded_Oacc(_90743, _90747)), c_member(tc_prod(_90743, _90743), c_Product__Type_OPair(_90743, _90743, _90749, _90745), _90747), -(c_member(_90743, _90749, c_Wellfounded_Oacc(_90743, _90747)))], (1526 ^ _63126) ^ [_91124, _91126, _91128, _91130] : [c_Relation_Orefl__on(_91124, _91126, _91128), c_member(_91124, _91130, _91126), -(c_member(tc_prod(_91124, _91124), c_Product__Type_OPair(_91124, _91124, _91130, _91130), _91128))], (1536 ^ _63126) ^ [_91507, _91509, _91511, _91513, _91515] : [c_Relation_Orefl__on(_91507, _91509, _91511), c_member(tc_prod(_91507, _91507), c_Product__Type_OPair(_91507, _91507, _91513, _91515), _91511), -(c_member(_91507, _91513, _91509))], (1546 ^ _63126) ^ [_91900, _91902, _91904, _91906, _91908] : [c_Relation_Orefl__on(_91900, _91902, _91904), c_member(tc_prod(_91900, _91900), c_Product__Type_OPair(_91900, _91900, _91906, _91908), _91904), -(c_member(_91900, _91908, _91902))], (1556 ^ _63126) ^ [_92336, _92338, _92340, _92342, _92344, _92346] : [c_Recdef_Owfrec__rel(_92336, _92338, _92340, _92342, _92344, hAPP(hAPP(_92342, _92346), _92344)), 1560 ^ _63126 : [(1561 ^ _63126) ^ [] : [-(hAPP(hAPP(_92342, _92346), _92344) = hAPP(hAPP(_92342, 1559 ^ [_92336, _92338, _92340, _92342, _92344, _92346]), _92344))], (1563 ^ _63126) ^ [_92755] : [c_member(tc_prod(_92336, _92336), c_Product__Type_OPair(_92336, _92336, _92755, _92344), _92340), -(c_Recdef_Owfrec__rel(_92336, _92338, _92340, _92342, _92755, hAPP(1559 ^ [_92336, _92338, _92340, _92342, _92344, _92346], _92755)))]]], (1569 ^ _63126) ^ [_93028, _93030, _93032, _93034, _93036, _93038] : [-(c_Recdef_Owfrec__rel(_93028, _93030, _93032, _93034, _93036, hAPP(hAPP(_93034, _93038), _93036))), 1570 ^ _63126 : [(1571 ^ _63126) ^ [_93177] : [hAPP(hAPP(_93034, _93038), _93036) = hAPP(hAPP(_93034, _93177), _93036), 1575 ^ _63126 : [(1576 ^ _63126) ^ [] : [-(c_member(tc_prod(_93028, _93028), c_Product__Type_OPair(_93028, _93028, 1574 ^ [_93028, _93030, _93032, _93034, _93036, _93038, _93177], _93036), _93032))], (1578 ^ _63126) ^ [] : [c_Recdef_Owfrec__rel(_93028, _93030, _93032, _93034, 1574 ^ [_93028, _93030, _93032, _93034, _93036, _93038, _93177], hAPP(_93177, 1574 ^ [_93028, _93030, _93032, _93034, _93036, _93038, _93177]))]]]]], (1582 ^ _63126) ^ [_93768, _93770] : [-(c_Relation_Orefl__on(_93768, _93770, c_Relation_OId__on(_93768, _93770)))], (1584 ^ _63126) ^ [_93924, _93926, _93928] : [c_Order__Relation_Opreorder__on(_93924, _93926, _93928), 1587 ^ _63126 : [(1588 ^ _63126) ^ [] : [-(c_Relation_Orefl__on(_93924, _93926, _93928))], (1590 ^ _63126) ^ [] : [-(c_Relation_Otrans(_93924, _93928))]]], (1592 ^ _63126) ^ [_94173, _94175, _94177] : [-(c_Order__Relation_Opreorder__on(_94173, _94175, _94177)), c_Relation_Orefl__on(_94173, _94175, _94177), c_Relation_Otrans(_94173, _94177)], (1602 ^ _63126) ^ [_94502, _94504, _94506] : [-(c_member(_94502, _94504, c_Wellfounded_Oacc(_94502, _94506))), 1606 ^ _63126 : [(1607 ^ _63126) ^ [] : [-(c_member(tc_prod(_94502, _94502), c_Product__Type_OPair(_94502, _94502, 1605 ^ [_94502, _94504, _94506], _94504), _94506))], (1609 ^ _63126) ^ [] : [c_member(_94502, 1605 ^ [_94502, _94504, _94506], c_Wellfounded_Oacc(_94502, _94506))]]], (1611 ^ _63126) ^ [_94938, _94940, _94942] : [1613 ^ _63126 : [(1614 ^ _63126) ^ [] : [-(c_member(tc_prod(_94938, _94938), c_Product__Type_OPair(_94938, _94938, 1612 ^ [_94938, _94940, _94942], _94940), _94942))], (1616 ^ _63126) ^ [] : [c_member(_94938, 1612 ^ [_94938, _94940, _94942], c_Wellfounded_Oacc(_94938, _94942))]], -(c_member(_94938, _94940, c_Wellfounded_Oacc(_94938, _94942)))], (1620 ^ _63126) ^ [_95412, _95414, _95416, _95418, _95420, _95422] : [1622 ^ _63126 : [(1623 ^ _63126) ^ [] : [-(c_member(tc_prod(_95412, _95412), c_Product__Type_OPair(_95412, _95412, 1621 ^ [_95412, _95414, _95416, _95418, _95420, _95422], _95414), _95416))], (1625 ^ _63126) ^ [] : [c_Recdef_Owfrec__rel(_95412, _95418, _95416, _95420, 1621 ^ [_95412, _95414, _95416, _95418, _95420, _95422], hAPP(_95422, 1621 ^ [_95412, _95414, _95416, _95418, _95420, _95422]))]], -(c_Recdef_Owfrec__rel(_95412, _95418, _95416, _95420, _95414, hAPP(hAPP(_95420, _95422), _95414)))], (1629 ^ _63126) ^ [_95999, _96001, _96003, _96005, _96007, _96009] : [c_Recdef_Owfrec__rel(_95999, _96001, _96003, _96005, _96007, _96009), 1633 ^ _63126 : [(1634 ^ _63126) ^ [] : [-(_96009 = hAPP(hAPP(_96005, 1632 ^ [_95999, _96001, _96003, _96005, _96007, _96009]), _96007))], (1636 ^ _63126) ^ [_96388] : [c_member(tc_prod(_95999, _95999), c_Product__Type_OPair(_95999, _95999, _96388, _96007), _96003), -(c_Recdef_Owfrec__rel(_95999, _96001, _96003, _96005, _96388, hAPP(1632 ^ [_95999, _96001, _96003, _96005, _96007, _96009], _96388)))]]], (1642 ^ _63126) ^ [_96661, _96663, _96665, _96667, _96669, _96671] : [-(c_Recdef_Owfrec__rel(_96661, _96663, _96665, _96667, _96669, _96671)), 1643 ^ _63126 : [(1644 ^ _63126) ^ [_96798] : [_96671 = hAPP(hAPP(_96667, _96798), _96669), 1648 ^ _63126 : [(1649 ^ _63126) ^ [] : [-(c_member(tc_prod(_96661, _96661), c_Product__Type_OPair(_96661, _96661, 1647 ^ [_96661, _96663, _96665, _96667, _96669, _96671, _96798], _96669), _96665))], (1651 ^ _63126) ^ [] : [c_Recdef_Owfrec__rel(_96661, _96663, _96665, _96667, 1647 ^ [_96661, _96663, _96665, _96667, _96669, _96671, _96798], hAPP(_96798, 1647 ^ [_96661, _96663, _96665, _96667, _96669, _96671, _96798]))]]]]], (1655 ^ _63126) ^ [_97414, _97416, _97418, _97420] : [c_member(tc_prod(_97414, _97414), c_Product__Type_OPair(_97414, _97414, _97416, _97418), c_Transitive__Closure_Ortrancl(_97414, _97420)), c_member(_97414, _97418, c_Wellfounded_Oacc(_97414, _97420)), -(c_member(_97414, _97416, c_Wellfounded_Oacc(_97414, _97420)))], (1665 ^ _63126) ^ [_97801, _97803, _97805, _97807] : [c_member(_97801, _97803, c_Wellfounded_Oacc(_97801, _97805)), c_member(tc_prod(_97801, _97801), c_Product__Type_OPair(_97801, _97801, _97807, _97803), c_Transitive__Closure_Ortrancl(_97801, _97805)), -(c_member(_97801, _97807, c_Wellfounded_Oacc(_97801, _97805)))], (1675 ^ _63126) ^ [_98202, _98204, _98206, _98208, _98210] : [hBOOL(hAPP(_98202, c_Product__Type_OPair(_98204, _98206, _98208, _98210))), -(hBOOL(c_Product__Type_Ocurry(_98204, _98206, tc_HOL_Obool, _98202, _98208, _98210)))], (1681 ^ _63126) ^ [_98512, _98514, _98516, _98518, _98520, _98522] : [c_Relation_Osingle__valued(_98512, _98514, _98516), c_member(tc_prod(_98512, _98514), c_Product__Type_OPair(_98512, _98514, _98518, _98520), _98516), c_member(tc_prod(_98512, _98514), c_Product__Type_OPair(_98512, _98514, _98518, _98522), _98516), -(_98520 = _98522)], (1709 ^ _63126) ^ [_99634, _99636, _99638] : [1712 ^ _63126 : [(1713 ^ _63126) ^ [] : [-(c_member(tc_prod(_99634, _99636), c_Product__Type_OPair(_99634, _99636, 1710 ^ [_99634, _99636, _99638], 1711 ^ [_99634, _99636, _99638]), _99638))], (1716 ^ _63126) ^ [] : [-(c_member(tc_prod(_99634, _99636), c_Product__Type_OPair(_99634, _99636, 1710 ^ [_99634, _99636, _99638], 1714 ^ [_99634, _99636, _99638]), _99638))], (1718 ^ _63126) ^ [] : [1711 ^ [_99634, _99636, _99638] = 1714 ^ [_99634, _99636, _99638]]], -(c_Relation_Osingle__valued(_99634, _99636, _99638))], (1695 ^ _63126) ^ [_99037, _99039, _99041] : [c_Relation_Osingle__valued(_99037, _99039, _99041), 1698 ^ _63126 : [(1699 ^ _63126) ^ [_99228, _99230] : [c_member(tc_prod(_99037, _99039), c_Product__Type_OPair(_99037, _99039, _99230, _99228), _99041), 1702 ^ _63126 : [(1703 ^ _63126) ^ [_99410] : [c_member(tc_prod(_99037, _99039), c_Product__Type_OPair(_99037, _99039, _99230, _99410), _99041), -(_99228 = _99410)]]]]], (1722 ^ _63126) ^ [_100427, _100429, _100431, _100433, _100435] : [hBOOL(c_Product__Type_Ocurry(_100427, _100429, tc_HOL_Obool, _100431, _100433, _100435)), -(hBOOL(hAPP(_100431, c_Product__Type_OPair(_100427, _100429, _100433, _100435))))], (1728 ^ _63126) ^ [_100723, _100725, _100727, _100729, _100731] : [hBOOL(c_Product__Type_Ocurry(_100723, _100725, tc_HOL_Obool, _100727, _100729, _100731)), -(hBOOL(hAPP(_100727, c_Product__Type_OPair(_100723, _100725, _100729, _100731))))], (1734 ^ _63126) ^ [_100962, _100964] : [-(c_Relation_Osingle__valued(_100962, _100962, c_Relation_OId__on(_100962, _100964)))], (1736 ^ _63126) ^ [_101116, _101118, _101120, _101122, _101124, _101126] : [-(c_Product__Type_Ocurry(_101116, _101118, _101120, _101122, _101124, _101126) = hAPP(_101122, c_Product__Type_OPair(_101116, _101118, _101124, _101126)))], (1738 ^ _63126) ^ [_101247, _101249, _101251] : [-(c_member(tc_prod(_101247, _101247), c_Product__Type_OPair(_101247, _101247, _101249, _101249), c_Transitive__Closure_Ortrancl(_101247, _101251)))], (1740 ^ _63126) ^ [_101384, _101386, _101388] : [c_member(tc_prod(_101384, _101384), _101386, _101388), -(c_member(tc_prod(_101384, _101384), _101386, c_Transitive__Closure_Ortrancl(_101384, _101388)))], (1746 ^ _63126) ^ [_101650, _101652, _101654, _101656] : [-(c_member(_101650, _101652, c_Relation_ODomain(_101650, _101650, _101654))), 1749 ^ _63126 : [(1750 ^ _63126) ^ [] : [c_member(tc_prod(_101650, _101650), c_Product__Type_OPair(_101650, _101650, _101652, _101656), c_Transitive__Closure_Ortrancl(_101650, _101654)), -(_101652 = _101656)], (1756 ^ _63126) ^ [] : [_101652 = _101656, -(c_member(tc_prod(_101650, _101650), c_Product__Type_OPair(_101650, _101650, _101652, _101656), c_Transitive__Closure_Ortrancl(_101650, _101654)))]]], (1762 ^ _63126) ^ [_102233, _102235, _102237, _102239, _102241] : [c_Relation_Osingle__valued(_102233, _102233, _102235), c_member(tc_prod(_102233, _102233), c_Product__Type_OPair(_102233, _102233, _102237, _102239), c_Transitive__Closure_Ortrancl(_102233, _102235)), c_member(tc_prod(_102233, _102233), c_Product__Type_OPair(_102233, _102233, _102237, _102241), c_Transitive__Closure_Ortrancl(_102233, _102235)), -(c_member(tc_prod(_102233, _102233), c_Product__Type_OPair(_102233, _102233, _102239, _102241), c_Transitive__Closure_Ortrancl(_102233, _102235))), -(c_member(tc_prod(_102233, _102233), c_Product__Type_OPair(_102233, _102233, _102241, _102239), c_Transitive__Closure_Ortrancl(_102233, _102235)))], (1780 ^ _63126) ^ [_102905, _102907, _102909, _102911, _102913] : [c_member(tc_prod(_102905, _102905), c_Product__Type_OPair(_102905, _102905, _102907, _102909), _102911), c_member(tc_prod(_102905, _102905), c_Product__Type_OPair(_102905, _102905, _102909, _102913), c_Transitive__Closure_Ortrancl(_102905, _102911)), -(c_member(tc_prod(_102905, _102905), c_Product__Type_OPair(_102905, _102905, _102907, _102913), c_Transitive__Closure_Ortrancl(_102905, _102911)))], (1790 ^ _63126) ^ [_103342, _103344, _103346, _103348, _103350] : [c_member(tc_prod(_103342, _103342), c_Product__Type_OPair(_103342, _103342, _103344, _103346), c_Transitive__Closure_Ortrancl(_103342, _103348)), c_member(tc_prod(_103342, _103342), c_Product__Type_OPair(_103342, _103342, _103346, _103350), _103348), -(c_member(tc_prod(_103342, _103342), c_Product__Type_OPair(_103342, _103342, _103344, _103350), c_Transitive__Closure_Ortrancl(_103342, _103348)))], (1800 ^ _63126) ^ [_103779, _103781, _103783, _103785, _103787] : [c_member(tc_prod(_103779, _103779), c_Product__Type_OPair(_103779, _103779, _103781, _103783), c_Transitive__Closure_Ortrancl(_103779, _103785)), c_member(tc_prod(_103779, _103779), c_Product__Type_OPair(_103779, _103779, _103783, _103787), c_Transitive__Closure_Ortrancl(_103779, _103785)), -(c_member(tc_prod(_103779, _103779), c_Product__Type_OPair(_103779, _103779, _103781, _103787), c_Transitive__Closure_Ortrancl(_103779, _103785)))], (1810 ^ _63126) ^ [_104165, _104167] : [-(c_Relation_Otrans(_104165, c_Transitive__Closure_Ortrancl(_104165, _104167)))], (1812 ^ _63126) ^ [_104291, _104293, _104295] : [1815 ^ _63126 : [(1816 ^ _63126) ^ [] : [-(c_member(tc_prod(_104291, _104293), c_Product__Type_OPair(_104291, _104293, 1813 ^ [_104291, _104293, _104295], 1814 ^ [_104291, _104293, _104295]), _104295))], (1819 ^ _63126) ^ [] : [-(c_member(tc_prod(_104291, _104293), c_Product__Type_OPair(_104291, _104293, 1813 ^ [_104291, _104293, _104295], 1817 ^ [_104291, _104293, _104295]), _104295))], (1821 ^ _63126) ^ [] : [1814 ^ [_104291, _104293, _104295] = 1817 ^ [_104291, _104293, _104295]]], -(c_Relation_Osingle__valued(_104291, _104293, _104295))], (1825 ^ _63126) ^ [_105025, _105027] : [-(c_Transitive__Closure_Ortrancl(_105025, c_Transitive__Closure_Ortrancl(_105025, _105027)) = c_Transitive__Closure_Ortrancl(_105025, _105027))], (1827 ^ _63126) ^ [_105227, _105229, _105231, _105233, _105235, _105237, _105239, _105241] : [c_member(tc_prod(tc_prod(_105227, _105229), tc_prod(_105227, _105229)), c_Product__Type_OPair(tc_prod(_105227, _105229), tc_prod(_105227, _105229), c_Product__Type_OPair(_105227, _105229, _105231, _105233), c_Product__Type_OPair(_105227, _105229, _105235, _105237)), c_Transitive__Closure_Ortrancl(tc_prod(_105227, _105229), _105239)), hBOOL(hAPP(hAPP(_105241, _105231), _105233)), 1838 ^ _63126 : [(1839 ^ _63126) ^ [] : [-(c_member(tc_prod(tc_prod(_105227, _105229), tc_prod(_105227, _105229)), c_Product__Type_OPair(tc_prod(_105227, _105229), tc_prod(_105227, _105229), c_Product__Type_OPair(_105227, _105229, _105231, _105233), c_Product__Type_OPair(_105227, _105229, 1836 ^ [_105227, _105229, _105231, _105233, _105235, _105237, _105239, _105241], 1837 ^ [_105227, _105229, _105231, _105233, _105235, _105237, _105239, _105241])), c_Transitive__Closure_Ortrancl(tc_prod(_105227, _105229), _105239)))], (1843 ^ _63126) ^ [] : [-(c_member(tc_prod(tc_prod(_105227, _105229), tc_prod(_105227, _105229)), c_Product__Type_OPair(tc_prod(_105227, _105229), tc_prod(_105227, _105229), c_Product__Type_OPair(_105227, _105229, 1836 ^ [_105227, _105229, _105231, _105233, _105235, _105237, _105239, _105241], 1837 ^ [_105227, _105229, _105231, _105233, _105235, _105237, _105239, _105241]), c_Product__Type_OPair(_105227, _105229, 1840 ^ [_105227, _105229, _105231, _105233, _105235, _105237, _105239, _105241], 1841 ^ [_105227, _105229, _105231, _105233, _105235, _105237, _105239, _105241])), _105239))], (1845 ^ _63126) ^ [] : [-(hBOOL(hAPP(hAPP(_105241, 1836 ^ [_105227, _105229, _105231, _105233, _105235, _105237, _105239, _105241]), 1837 ^ [_105227, _105229, _105231, _105233, _105235, _105237, _105239, _105241])))], (1847 ^ _63126) ^ [] : [hBOOL(hAPP(hAPP(_105241, 1840 ^ [_105227, _105229, _105231, _105233, _105235, _105237, _105239, _105241]), 1841 ^ [_105227, _105229, _105231, _105233, _105235, _105237, _105239, _105241]))]], -(hBOOL(hAPP(hAPP(_105241, _105235), _105237)))], (1851 ^ _63126) ^ [_107353, _107355, _107357, _107359, _107361, _107363, _107365, _107367] : [c_member(tc_prod(tc_prod(_107353, _107355), tc_prod(_107353, _107355)), c_Product__Type_OPair(tc_prod(_107353, _107355), tc_prod(_107353, _107355), c_Product__Type_OPair(_107353, _107355, _107357, _107359), c_Product__Type_OPair(_107353, _107355, _107361, _107363)), c_Transitive__Closure_Ortrancl(tc_prod(_107353, _107355), _107365)), hBOOL(hAPP(hAPP(_107367, _107361), _107363)), 1864 ^ _63126 : [(1865 ^ _63126) ^ [] : [-(c_member(tc_prod(tc_prod(_107353, _107355), tc_prod(_107353, _107355)), c_Product__Type_OPair(tc_prod(_107353, _107355), tc_prod(_107353, _107355), c_Product__Type_OPair(_107353, _107355, 1860 ^ [_107353, _107355, _107357, _107359, _107361, _107363, _107365, _107367], 1861 ^ [_107353, _107355, _107357, _107359, _107361, _107363, _107365, _107367]), c_Product__Type_OPair(_107353, _107355, 1862 ^ [_107353, _107355, _107357, _107359, _107361, _107363, _107365, _107367], 1863 ^ [_107353, _107355, _107357, _107359, _107361, _107363, _107365, _107367])), _107365))], (1867 ^ _63126) ^ [] : [-(c_member(tc_prod(tc_prod(_107353, _107355), tc_prod(_107353, _107355)), c_Product__Type_OPair(tc_prod(_107353, _107355), tc_prod(_107353, _107355), c_Product__Type_OPair(_107353, _107355, 1862 ^ [_107353, _107355, _107357, _107359, _107361, _107363, _107365, _107367], 1863 ^ [_107353, _107355, _107357, _107359, _107361, _107363, _107365, _107367]), c_Product__Type_OPair(_107353, _107355, _107361, _107363)), c_Transitive__Closure_Ortrancl(tc_prod(_107353, _107355), _107365)))], (1869 ^ _63126) ^ [] : [-(hBOOL(hAPP(hAPP(_107367, 1862 ^ [_107353, _107355, _107357, _107359, _107361, _107363, _107365, _107367]), 1863 ^ [_107353, _107355, _107357, _107359, _107361, _107363, _107365, _107367])))], (1871 ^ _63126) ^ [] : [hBOOL(hAPP(hAPP(_107367, 1860 ^ [_107353, _107355, _107357, _107359, _107361, _107363, _107365, _107367]), 1861 ^ [_107353, _107355, _107357, _107359, _107361, _107363, _107365, _107367]))]], -(hBOOL(hAPP(hAPP(_107367, _107357), _107359)))], (1875 ^ _63126) ^ [_109551, _109553, _109555, _109557, _109559, _109561, _109563] : [c_member(tc_prod(tc_prod(_109551, _109553), tc_prod(_109551, _109553)), c_Product__Type_OPair(tc_prod(_109551, _109553), tc_prod(_109551, _109553), c_Product__Type_OPair(_109551, _109553, _109555, _109557), c_Product__Type_OPair(_109551, _109553, _109559, _109561)), c_Transitive__Closure_Ortrancl(tc_prod(_109551, _109553), _109563)), -(c_Product__Type_OPair(_109551, _109553, _109555, _109557) = c_Product__Type_OPair(_109551, _109553, _109559, _109561)), 1884 ^ _63126 : [(1885 ^ _63126) ^ [] : [-(c_member(tc_prod(tc_prod(_109551, _109553), tc_prod(_109551, _109553)), c_Product__Type_OPair(tc_prod(_109551, _109553), tc_prod(_109551, _109553), c_Product__Type_OPair(_109551, _109553, _109555, _109557), c_Product__Type_OPair(_109551, _109553, 1882 ^ [_109551, _109553, _109555, _109557, _109559, _109561, _109563], 1883 ^ [_109551, _109553, _109555, _109557, _109559, _109561, _109563])), _109563))], (1887 ^ _63126) ^ [] : [-(c_member(tc_prod(tc_prod(_109551, _109553), tc_prod(_109551, _109553)), c_Product__Type_OPair(tc_prod(_109551, _109553), tc_prod(_109551, _109553), c_Product__Type_OPair(_109551, _109553, 1882 ^ [_109551, _109553, _109555, _109557, _109559, _109561, _109563], 1883 ^ [_109551, _109553, _109555, _109557, _109559, _109561, _109563]), c_Product__Type_OPair(_109551, _109553, _109559, _109561)), c_Transitive__Closure_Ortrancl(tc_prod(_109551, _109553), _109563)))]]], (1889 ^ _63126) ^ [_110649, _110651, _110653, _110655] : [c_member(tc_prod(_110649, _110649), c_Product__Type_OPair(_110649, _110649, _110651, _110653), c_Transitive__Closure_Ortrancl(_110649, _110655)), -(_110651 = _110653), 1897 ^ _63126 : [(1898 ^ _63126) ^ [] : [-(c_member(tc_prod(_110649, _110649), c_Product__Type_OPair(_110649, _110649, _110651, 1896 ^ [_110649, _110651, _110653, _110655]), c_Transitive__Closure_Ortrancl(_110649, _110655)))], (1900 ^ _63126) ^ [] : [-(c_member(tc_prod(_110649, _110649), c_Product__Type_OPair(_110649, _110649, 1896 ^ [_110649, _110651, _110653, _110655], _110653), _110655))]]], (1902 ^ _63126) ^ [_111257, _111259, _111261, _111263] : [c_member(tc_prod(_111257, _111257), c_Product__Type_OPair(_111257, _111257, _111259, _111261), c_Transitive__Closure_Ortrancl(_111257, _111263)), -(_111259 = _111261), 1910 ^ _63126 : [(1911 ^ _63126) ^ [] : [-(c_member(tc_prod(_111257, _111257), c_Product__Type_OPair(_111257, _111257, _111259, 1909 ^ [_111257, _111259, _111261, _111263]), _111263))], (1913 ^ _63126) ^ [] : [-(c_member(tc_prod(_111257, _111257), c_Product__Type_OPair(_111257, _111257, 1909 ^ [_111257, _111259, _111261, _111263], _111261), c_Transitive__Closure_Ortrancl(_111257, _111263)))]]], (1915 ^ _63126) ^ [_111879, _111881, _111883, _111885, _111887] : [c_member(tc_prod(_111879, _111879), c_Product__Type_OPair(_111879, _111879, _111881, _111883), c_Transitive__Closure_Ortrancl(_111879, _111885)), hBOOL(hAPP(_111887, _111883)), 1926 ^ _63126 : [(1927 ^ _63126) ^ [] : [-(c_member(tc_prod(_111879, _111879), c_Product__Type_OPair(_111879, _111879, 1924 ^ [_111879, _111881, _111883, _111885, _111887], 1925 ^ [_111879, _111881, _111883, _111885, _111887]), _111885))], (1929 ^ _63126) ^ [] : [-(c_member(tc_prod(_111879, _111879), c_Product__Type_OPair(_111879, _111879, 1925 ^ [_111879, _111881, _111883, _111885, _111887], _111883), c_Transitive__Closure_Ortrancl(_111879, _111885)))], (1931 ^ _63126) ^ [] : [-(hBOOL(hAPP(_111887, 1925 ^ [_111879, _111881, _111883, _111885, _111887])))], (1933 ^ _63126) ^ [] : [hBOOL(hAPP(_111887, 1924 ^ [_111879, _111881, _111883, _111885, _111887]))]], -(hBOOL(hAPP(_111887, _111881)))], (1937 ^ _63126) ^ [_112980, _112982, _112984, _112986, _112988] : [c_member(tc_prod(_112980, _112980), c_Product__Type_OPair(_112980, _112980, _112982, _112984), c_Transitive__Closure_Ortrancl(_112980, _112986)), hBOOL(hAPP(_112988, _112982)), 1947 ^ _63126 : [(1948 ^ _63126) ^ [] : [-(c_member(tc_prod(_112980, _112980), c_Product__Type_OPair(_112980, _112980, _112982, 1946 ^ [_112980, _112982, _112984, _112986, _112988]), c_Transitive__Closure_Ortrancl(_112980, _112986)))], (1951 ^ _63126) ^ [] : [-(c_member(tc_prod(_112980, _112980), c_Product__Type_OPair(_112980, _112980, 1946 ^ [_112980, _112982, _112984, _112986, _112988], 1949 ^ [_112980, _112982, _112984, _112986, _112988]), _112986))], (1953 ^ _63126) ^ [] : [-(hBOOL(hAPP(_112988, 1946 ^ [_112980, _112982, _112984, _112986, _112988])))], (1955 ^ _63126) ^ [] : [hBOOL(hAPP(_112988, 1949 ^ [_112980, _112982, _112984, _112986, _112988]))]], -(hBOOL(hAPP(_112988, _112984)))], (1959 ^ _63126) ^ [_114049, _114051, _114053, _114055] : [c_member(tc_prod(_114049, _114049), c_Product__Type_OPair(_114049, _114049, _114051, _114053), c_Transitive__Closure_Otrancl(_114049, _114055)), -(c_member(tc_prod(_114049, _114049), c_Product__Type_OPair(_114049, _114049, _114051, _114053), c_Transitive__Closure_Ortrancl(_114049, _114055)))], (1965 ^ _63126) ^ [_114375, _114377, _114379, _114381, _114383, _114385] : [c_member(tc_prod(_114375, _114375), c_Product__Type_OPair(_114375, _114375, _114377, _114379), _114381), -(hAPP(c_Recdef_Ocut(_114375, _114383, _114385, _114381, _114379), _114377) = hAPP(_114385, _114377))], (1971 ^ _63126) ^ [_114679, _114681, _114683, _114685] : [c_member(tc_prod(_114679, _114679), c_Product__Type_OPair(_114679, _114679, _114681, _114683), _114685), -(c_member(tc_prod(_114679, _114679), c_Product__Type_OPair(_114679, _114679, _114681, _114683), c_Transitive__Closure_Otrancl(_114679, _114685)))], (1977 ^ _63126) ^ [_114957, _114959, _114961] : [c_member(tc_prod(_114957, _114957), _114959, _114961), -(c_member(tc_prod(_114957, _114957), _114959, c_Transitive__Closure_Otrancl(_114957, _114961)))], (1983 ^ _63126) ^ [_115180, _115182] : [-(c_Transitive__Closure_Ortrancl(_115180, c_Transitive__Closure_Otrancl(_115180, _115182)) = c_Transitive__Closure_Ortrancl(_115180, _115182))], (1985 ^ _63126) ^ [_115283, _115285] : [-(c_Transitive__Closure_Otrancl(_115283, c_Transitive__Closure_Ortrancl(_115283, _115285)) = c_Transitive__Closure_Ortrancl(_115283, _115285))], (1987 ^ _63126) ^ [_115386, _115388] : [-(c_Relation_ODomain(_115386, _115386, c_Transitive__Closure_Otrancl(_115386, _115388)) = c_Relation_ODomain(_115386, _115386, _115388))], (1989 ^ _63126) ^ [_115491, _115493] : [-(c_Relation_Otrans(_115491, c_Transitive__Closure_Otrancl(_115491, _115493)))], (1991 ^ _63126) ^ [_115603, _115605] : [c_Relation_Otrans(_115603, _115605), -(c_Transitive__Closure_Otrancl(_115603, _115605) = _115605)], (1997 ^ _63126) ^ [_115804, _115806] : [-(c_Relation_ORange(_115804, _115804, c_Transitive__Closure_Otrancl(_115804, _115806)) = c_Relation_ORange(_115804, _115804, _115806))], (1999 ^ _63126) ^ [_115966, _115968, _115970, _115972, _115974] : [c_member(tc_prod(_115966, _115966), c_Product__Type_OPair(_115966, _115966, _115968, _115970), _115972), c_member(tc_prod(_115966, _115966), c_Product__Type_OPair(_115966, _115966, _115970, _115974), _115972), -(c_member(tc_prod(_115966, _115966), c_Product__Type_OPair(_115966, _115966, _115968, _115974), c_Transitive__Closure_Otrancl(_115966, _115972)))], (2009 ^ _63126) ^ [_116397, _116399, _116401, _116403, _116405] : [c_member(tc_prod(_116397, _116397), c_Product__Type_OPair(_116397, _116397, _116399, _116401), _116403), c_member(tc_prod(_116397, _116397), c_Product__Type_OPair(_116397, _116397, _116401, _116405), c_Transitive__Closure_Otrancl(_116397, _116403)), -(c_member(tc_prod(_116397, _116397), c_Product__Type_OPair(_116397, _116397, _116399, _116405), c_Transitive__Closure_Otrancl(_116397, _116403)))], (2019 ^ _63126) ^ [_116834, _116836, _116838, _116840, _116842] : [c_member(tc_prod(_116834, _116834), c_Product__Type_OPair(_116834, _116834, _116836, _116838), c_Transitive__Closure_Otrancl(_116834, _116840)), c_member(tc_prod(_116834, _116834), c_Product__Type_OPair(_116834, _116834, _116838, _116842), _116840), -(c_member(tc_prod(_116834, _116834), c_Product__Type_OPair(_116834, _116834, _116836, _116842), c_Transitive__Closure_Otrancl(_116834, _116840)))], (2029 ^ _63126) ^ [_117271, _117273, _117275, _117277, _117279] : [c_member(tc_prod(_117271, _117271), c_Product__Type_OPair(_117271, _117271, _117273, _117275), c_Transitive__Closure_Otrancl(_117271, _117277)), c_member(tc_prod(_117271, _117271), c_Product__Type_OPair(_117271, _117271, _117275, _117279), c_Transitive__Closure_Otrancl(_117271, _117277)), -(c_member(tc_prod(_117271, _117271), c_Product__Type_OPair(_117271, _117271, _117273, _117279), c_Transitive__Closure_Otrancl(_117271, _117277)))], (2039 ^ _63126) ^ [_117729, _117731, _117733, _117735] : [c_member(tc_prod(_117729, _117729), c_Product__Type_OPair(_117729, _117729, _117731, _117733), c_Transitive__Closure_Ortrancl(_117729, _117735)), -(_117731 = _117733), 2046 ^ _63126 : [(2047 ^ _63126) ^ [] : [_117731 = _117733], (2049 ^ _63126) ^ [] : [-(c_member(tc_prod(_117729, _117729), c_Product__Type_OPair(_117729, _117729, _117731, _117733), c_Transitive__Closure_Otrancl(_117729, _117735)))]]], (2051 ^ _63126) ^ [_118129, _118131, _118133, _118135] : [-(c_member(tc_prod(_118129, _118129), c_Product__Type_OPair(_118129, _118129, _118131, _118133), c_Transitive__Closure_Ortrancl(_118129, _118135))), 2052 ^ _63126 : [(2053 ^ _63126) ^ [] : [_118131 = _118133], (2055 ^ _63126) ^ [] : [-(_118131 = _118133), c_member(tc_prod(_118129, _118129), c_Product__Type_OPair(_118129, _118129, _118131, _118133), c_Transitive__Closure_Otrancl(_118129, _118135))]]], (2063 ^ _63126) ^ [_118621, _118623, _118625, _118627, _118629] : [c_member(tc_prod(_118621, _118621), c_Product__Type_OPair(_118621, _118621, _118623, _118625), _118627), c_member(tc_prod(_118621, _118621), c_Product__Type_OPair(_118621, _118621, _118625, _118629), c_Transitive__Closure_Ortrancl(_118621, _118627)), -(c_member(tc_prod(_118621, _118621), c_Product__Type_OPair(_118621, _118621, _118623, _118629), c_Transitive__Closure_Otrancl(_118621, _118627)))], (2073 ^ _63126) ^ [_119044, _119046, _119048, _119050] : [c_member(tc_prod(_119044, _119044), c_Product__Type_OPair(_119044, _119044, _119046, _119048), c_Transitive__Closure_Ortrancl(_119044, _119050)), -(_119046 = _119048), 2080 ^ _63126 : [(2081 ^ _63126) ^ [] : [_119046 = _119048], (2083 ^ _63126) ^ [] : [-(c_member(tc_prod(_119044, _119044), c_Product__Type_OPair(_119044, _119044, _119046, _119048), c_Transitive__Closure_Otrancl(_119044, _119050)))]]], (2085 ^ _63126) ^ [_119534, _119536, _119538, _119540, _119542] : [c_member(tc_prod(_119534, _119534), c_Product__Type_OPair(_119534, _119534, _119536, _119538), c_Transitive__Closure_Ortrancl(_119534, _119540)), c_member(tc_prod(_119534, _119534), c_Product__Type_OPair(_119534, _119534, _119538, _119542), _119540), -(c_member(tc_prod(_119534, _119534), c_Product__Type_OPair(_119534, _119534, _119536, _119542), c_Transitive__Closure_Otrancl(_119534, _119540)))], (2095 ^ _63126) ^ [_119971, _119973, _119975, _119977, _119979] : [c_member(tc_prod(_119971, _119971), c_Product__Type_OPair(_119971, _119971, _119973, _119975), c_Transitive__Closure_Otrancl(_119971, _119977)), c_member(tc_prod(_119971, _119971), c_Product__Type_OPair(_119971, _119971, _119975, _119979), c_Transitive__Closure_Ortrancl(_119971, _119977)), -(c_member(tc_prod(_119971, _119971), c_Product__Type_OPair(_119971, _119971, _119973, _119979), c_Transitive__Closure_Otrancl(_119971, _119977)))], (2105 ^ _63126) ^ [_120414, _120416, _120418, _120420, _120422] : [c_member(tc_prod(_120414, _120414), c_Product__Type_OPair(_120414, _120414, _120416, _120418), c_Transitive__Closure_Ortrancl(_120414, _120420)), c_member(tc_prod(_120414, _120414), c_Product__Type_OPair(_120414, _120414, _120418, _120422), c_Transitive__Closure_Otrancl(_120414, _120420)), -(c_member(tc_prod(_120414, _120414), c_Product__Type_OPair(_120414, _120414, _120416, _120422), c_Transitive__Closure_Otrancl(_120414, _120420)))], (2115 ^ _63126) ^ [_120871, _120873, _120875, _120877, _120879, _120881] : [c_member(tc_prod(_120875, _120875), c_Product__Type_OPair(_120875, _120875, _120877, _120879), _120871), -(hAPP(c_Recdef_Ocut(_120875, _120881, _120873, _120871, _120879), _120877) = hAPP(_120873, _120877))], (2131 ^ _63126) ^ [_121663, _121665, _121667, _121669, _121671, _121673] : [2133 ^ _63126 : [(2134 ^ _63126) ^ [] : [-(c_member(tc_prod(_121663, _121663), c_Product__Type_OPair(_121663, _121663, 2132 ^ [_121663, _121665, _121667, _121669, _121671, _121673], _121671), _121669))], (2136 ^ _63126) ^ [] : [hAPP(_121667, 2132 ^ [_121663, _121665, _121667, _121669, _121671, _121673]) = hAPP(_121673, 2132 ^ [_121663, _121665, _121667, _121669, _121671, _121673])]], -(c_Recdef_Ocut(_121663, _121665, _121667, _121669, _121671) = c_Recdef_Ocut(_121663, _121665, _121673, _121669, _121671))], (2121 ^ _63126) ^ [_121232, _121234, _121236, _121238, _121240, _121242] : [c_Recdef_Ocut(_121232, _121234, _121236, _121238, _121240) = c_Recdef_Ocut(_121232, _121234, _121242, _121238, _121240), 2124 ^ _63126 : [(2125 ^ _63126) ^ [_121424] : [c_member(tc_prod(_121232, _121232), c_Product__Type_OPair(_121232, _121232, _121424, _121240), _121238), -(hAPP(_121236, _121424) = hAPP(_121242, _121424))]]], (2140 ^ _63126) ^ [_122196, _122198, _122200, _122202] : [c_member(tc_prod(_122196, _122196), c_Product__Type_OPair(_122196, _122196, _122198, _122200), c_Transitive__Closure_Otrancl(_122196, _122202)), 2144 ^ _63126 : [(2145 ^ _63126) ^ [] : [-(c_member(tc_prod(_122196, _122196), c_Product__Type_OPair(_122196, _122196, _122198, 2143 ^ [_122196, _122198, _122200, _122202]), c_Transitive__Closure_Ortrancl(_122196, _122202)))], (2147 ^ _63126) ^ [] : [-(c_member(tc_prod(_122196, _122196), c_Product__Type_OPair(_122196, _122196, 2143 ^ [_122196, _122198, _122200, _122202], _122200), _122202))]]], (2149 ^ _63126) ^ [_122698, _122700, _122702, _122704] : [c_member(tc_prod(_122698, _122698), c_Product__Type_OPair(_122698, _122698, _122700, _122702), c_Transitive__Closure_Otrancl(_122698, _122704)), 2153 ^ _63126 : [(2154 ^ _63126) ^ [] : [-(c_member(tc_prod(_122698, _122698), c_Product__Type_OPair(_122698, _122698, _122700, 2152 ^ [_122698, _122700, _122702, _122704]), _122704))], (2156 ^ _63126) ^ [] : [-(c_member(tc_prod(_122698, _122698), c_Product__Type_OPair(_122698, _122698, 2152 ^ [_122698, _122700, _122702, _122704], _122702), c_Transitive__Closure_Ortrancl(_122698, _122704)))]]], (2158 ^ _63126) ^ [_123201, _123203] : [c_Wellfounded_Oacyclic(_123201, _123203), 2161 ^ _63126 : [(2162 ^ _63126) ^ [_123330] : [c_member(tc_prod(_123201, _123201), c_Product__Type_OPair(_123201, _123201, _123330, _123330), c_Transitive__Closure_Otrancl(_123201, _123203))]]], (2164 ^ _63126) ^ [_123410, _123412] : [-(c_member(tc_prod(_123410, _123410), c_Product__Type_OPair(_123410, _123410, 2165 ^ [_123410, _123412], 2165 ^ [_123410, _123412]), c_Transitive__Closure_Otrancl(_123410, _123412))), -(c_Wellfounded_Oacyclic(_123410, _123412))], (2171 ^ _63126) ^ [_123755, _123757, _123759, _123761] : [-(c_member(tc_prod(_123755, _123755), c_Product__Type_OPair(_123755, _123755, 2172 ^ [_123755, _123757, _123759, _123761], 2172 ^ [_123755, _123757, _123759, _123761]), c_Transitive__Closure_Otrancl(_123755, _123757))), c_member(tc_prod(_123755, _123755), c_Product__Type_OPair(_123755, _123755, _123759, _123761), _123757), _123759 = _123761], (2182 ^ _63126) ^ [_124242, _124244, _124246, _124248] : [c_member(tc_prod(_124242, _124242), c_Product__Type_OPair(_124242, _124242, _124244, _124246), c_Transitive__Closure_Otrancl(_124242, _124248)), -(c_member(tc_prod(_124242, _124242), c_Product__Type_OPair(_124242, _124242, _124244, _124246), _124248)), 2190 ^ _63126 : [(2191 ^ _63126) ^ [] : [-(c_member(tc_prod(_124242, _124242), c_Product__Type_OPair(_124242, _124242, _124244, 2189 ^ [_124242, _124244, _124246, _124248]), _124248))], (2193 ^ _63126) ^ [] : [-(c_member(tc_prod(_124242, _124242), c_Product__Type_OPair(_124242, _124242, 2189 ^ [_124242, _124244, _124246, _124248], _124246), c_Transitive__Closure_Otrancl(_124242, _124248)))]]], (2195 ^ _63126) ^ [_124868, _124870, _124872, _124874] : [c_member(tc_prod(_124868, _124868), c_Product__Type_OPair(_124868, _124868, _124870, _124872), c_Transitive__Closure_Otrancl(_124868, _124874)), -(c_member(tc_prod(_124868, _124868), c_Product__Type_OPair(_124868, _124868, _124870, _124872), _124874)), 2203 ^ _63126 : [(2204 ^ _63126) ^ [] : [-(c_member(tc_prod(_124868, _124868), c_Product__Type_OPair(_124868, _124868, _124870, 2202 ^ [_124868, _124870, _124872, _124874]), c_Transitive__Closure_Otrancl(_124868, _124874)))], (2206 ^ _63126) ^ [] : [-(c_member(tc_prod(_124868, _124868), c_Product__Type_OPair(_124868, _124868, 2202 ^ [_124868, _124870, _124872, _124874], _124872), _124874))]]], (2208 ^ _63126) ^ [_125493, _125495, _125497, _125499, _125501] : [-(c_Nitpick_Owf__wfrec_H(_125493, _125495, _125497, _125499, _125501) = hAPP(hAPP(_125499, c_Recdef_Ocut(_125493, _125495, c_Nitpick_Owf__wfrec(_125493, _125495, _125497, _125499), _125497, _125501)), _125501))], (2210 ^ _63126) ^ [_125616, _125618] : [-(c_member(tc_prod(_125616, _125616), c_Product__Type_OPair(_125616, _125616, _125618, _125618), c_Relation_OId(_125616)))], (2212 ^ _63126) ^ [_125707] : [-(c_Relation_Otrans(_125707, c_Relation_OId(_125707)))], (2214 ^ _63126) ^ [_125787] : [-(c_Relation_Osingle__valued(_125787, _125787, c_Relation_OId(_125787)))], (2216 ^ _63126) ^ [_125940, _125942, _125944] : [c_member(tc_prod(_125940, _125940), c_Product__Type_OPair(_125940, _125940, _125942, _125944), c_Relation_OId(_125940)), -(_125942 = _125944)], (2222 ^ _63126) ^ [_126130, _126132, _126134] : [_126132 = _126134, -(c_member(tc_prod(_126130, _126130), c_Product__Type_OPair(_126130, _126130, _126132, _126134), c_Relation_OId(_126130)))], (2228 ^ _63126) ^ [_126370, _126372] : [-(c_member(tc_prod(_126370, _126370), c_Product__Type_OPair(_126370, _126370, 2229 ^ [_126370, _126372], 2229 ^ [_126370, _126372]), c_Transitive__Closure_Otrancl(_126370, _126372))), -(c_Wellfounded_Oacyclic(_126370, _126372))], (2235 ^ _63126) ^ [_126685, _126687] : [c_member(tc_prod(_126685, _126685), _126687, c_Relation_OId(_126685)), -(_126687 = c_Product__Type_OPair(_126685, _126685, 2238 ^ [_126685, _126687], 2238 ^ [_126685, _126687]))], (2242 ^ _63126) ^ [_127049, _127051, _127053, _127055] : [c_Wellfounded_Oacyclic(_127049, c_Set_Oinsert(tc_prod(_127049, _127049), c_Product__Type_OPair(_127049, _127049, _127051, _127053), _127055)), 2245 ^ _63126 : [(2246 ^ _63126) ^ [] : [-(c_Wellfounded_Oacyclic(_127049, _127055))], (2248 ^ _63126) ^ [] : [c_member(tc_prod(_127049, _127049), c_Product__Type_OPair(_127049, _127049, _127053, _127051), c_Transitive__Closure_Ortrancl(_127049, _127055))]]], (2250 ^ _63126) ^ [_127351, _127353, _127355, _127357] : [-(c_Wellfounded_Oacyclic(_127351, c_Set_Oinsert(tc_prod(_127351, _127351), c_Product__Type_OPair(_127351, _127351, _127353, _127355), _127357))), c_Wellfounded_Oacyclic(_127351, _127357), -(c_member(tc_prod(_127351, _127351), c_Product__Type_OPair(_127351, _127351, _127355, _127353), c_Transitive__Closure_Ortrancl(_127351, _127357)))], (2260 ^ _63126) ^ [_127723, _127725] : [c_Wellfounded_Oacyclic(_127723, _127725), -(c_Relation_Oantisym(_127723, c_Transitive__Closure_Ortrancl(_127723, _127725)))], (2266 ^ _63126) ^ [_127924, _127926] : [-(c_Transitive__Closure_Otrancl(_127924, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_127924, _127924), tc_HOL_Obool), _127926, c_Relation_OId(_127924))) = c_Transitive__Closure_Ortrancl(_127924, _127926))], (2268 ^ _63126) ^ [_128036, _128038] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_128036, _128036), tc_HOL_Obool), c_Transitive__Closure_Otrancl(_128036, _128038), c_Relation_OId(_128036)) = c_Transitive__Closure_Ortrancl(_128036, _128038))], (2270 ^ _63126) ^ [_128191, _128193, _128195, _128197] : [c_Relation_Oantisym(_128191, _128193), c_member(tc_prod(_128191, _128191), c_Product__Type_OPair(_128191, _128191, _128195, _128197), _128193), c_member(tc_prod(_128191, _128191), c_Product__Type_OPair(_128191, _128191, _128197, _128195), _128193), -(_128195 = _128197)], (2284 ^ _63126) ^ [_128671, _128673, _128675, _128677] : [c_member(_128671, _128673, c_Set_Oinsert(_128671, _128675, _128677)), -(_128673 = _128675), -(c_member(_128671, _128673, _128677))], (2294 ^ _63126) ^ [_129033, _129035, _129037, _129039] : [2295 ^ _63126 : [(2296 ^ _63126) ^ [] : [c_member(_129033, _129035, _129037)], (2298 ^ _63126) ^ [] : [_129035 = _129039]], -(c_member(_129033, _129035, c_Set_Oinsert(_129033, _129039, _129037)))], (2302 ^ _63126) ^ [_129375, _129377, _129379, _129381] : [c_member(_129375, _129377, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_129375, tc_HOL_Obool), _129379, _129381)), -(c_member(_129375, _129377, _129379)), -(c_member(_129375, _129377, _129381))], (2312 ^ _63126) ^ [_129745, _129747, _129749, _129751] : [2313 ^ _63126 : [(2314 ^ _63126) ^ [] : [c_member(_129745, _129747, _129749)], (2316 ^ _63126) ^ [] : [c_member(_129745, _129747, _129751)]], -(c_member(_129745, _129747, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_129745, tc_HOL_Obool), _129751, _129749)))], (2320 ^ _63126) ^ [_130096, _130098] : [c_Relation_Oantisym(_130096, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_130096, _130096), tc_HOL_Obool), _130098, c_Relation_OId(_130096))), -(c_Relation_Oantisym(_130096, _130098))], (2326 ^ _63126) ^ [_130282, _130284] : [c_Relation_Oantisym(_130282, _130284), -(c_Relation_Oantisym(_130282, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_130282, _130282), tc_HOL_Obool), _130284, c_Relation_OId(_130282))))], (2332 ^ _63126) ^ [_130503, _130505] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_130503, tc_HOL_Obool), _130505, _130505) = _130505)], (2334 ^ _63126) ^ [_130618, _130620, _130622] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_130618, tc_HOL_Obool), _130620, _130622) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_130618, tc_HOL_Obool), _130622, _130620))], (2336 ^ _63126) ^ [_130742, _130744, _130746] : [-(c_Set_Oinsert(_130742, _130744, c_Set_Oinsert(_130742, _130744, _130746)) = c_Set_Oinsert(_130742, _130744, _130746))], (2338 ^ _63126) ^ [_130864, _130866, _130868] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_130864, tc_HOL_Obool), _130866, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_130864, tc_HOL_Obool), _130866, _130868)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_130864, tc_HOL_Obool), _130866, _130868))], (2340 ^ _63126) ^ [_131009, _131011, _131013, _131015] : [-(c_Set_Oinsert(_131009, _131011, c_Set_Oinsert(_131009, _131013, _131015)) = c_Set_Oinsert(_131009, _131013, c_Set_Oinsert(_131009, _131011, _131015)))], (2342 ^ _63126) ^ [_131151, _131153, _131155, _131157] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_131151, tc_HOL_Obool), _131153, c_Set_Oinsert(_131151, _131155, _131157)) = c_Set_Oinsert(_131151, _131155, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_131151, tc_HOL_Obool), _131153, _131157)))], (2344 ^ _63126) ^ [_131299, _131301, _131303, _131305] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_131299, tc_HOL_Obool), _131301, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_131299, tc_HOL_Obool), _131303, _131305)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_131299, tc_HOL_Obool), _131303, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_131299, tc_HOL_Obool), _131301, _131305)))], (2346 ^ _63126) ^ [_131453, _131455, _131457, _131459] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_131453, tc_HOL_Obool), c_Set_Oinsert(_131453, _131455, _131457), _131459) = c_Set_Oinsert(_131453, _131455, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_131453, tc_HOL_Obool), _131457, _131459)))], (2348 ^ _63126) ^ [_131601, _131603, _131605, _131607] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_131601, tc_HOL_Obool), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_131601, tc_HOL_Obool), _131603, _131605), _131607) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_131601, tc_HOL_Obool), _131603, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_131601, tc_HOL_Obool), _131605, _131607)))], (2350 ^ _63126) ^ [_131799, _131801, _131803, _131805] : [2351 ^ _63126 : [(2352 ^ _63126) ^ [_131939] : [c_member(_131799, _131939, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_131799, tc_HOL_Obool), _131801, _131803)), hBOOL(hAPP(_131805, _131939))]], 2360 ^ _63126 : [(2361 ^ _63126) ^ [] : [-(c_member(_131799, 2359 ^ [_131799, _131801, _131803, _131805], _131801))], (2363 ^ _63126) ^ [] : [-(hBOOL(hAPP(_131805, 2359 ^ [_131799, _131801, _131803, _131805])))]], 2365 ^ _63126 : [(2366 ^ _63126) ^ [] : [-(c_member(_131799, 2364 ^ [_131799, _131801, _131803, _131805], _131803))], (2368 ^ _63126) ^ [] : [-(hBOOL(hAPP(_131805, 2364 ^ [_131799, _131801, _131803, _131805])))]]], (2370 ^ _63126) ^ [_132613, _132615, _132617, _132619] : [2384 ^ _63126 : [(2385 ^ _63126) ^ [] : [-(c_member(_132613, 2383 ^ [_132613, _132615, _132617, _132619], c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_132613, tc_HOL_Obool), _132615, _132617)))], (2387 ^ _63126) ^ [] : [-(hBOOL(hAPP(_132619, 2383 ^ [_132613, _132615, _132617, _132619])))]], 2371 ^ _63126 : [(2372 ^ _63126) ^ [_132773] : [c_member(_132613, _132773, _132615), hBOOL(hAPP(_132619, _132773))], (2378 ^ _63126) ^ [_132980] : [c_member(_132613, _132980, _132617), hBOOL(hAPP(_132619, _132980))]]], (2408 ^ _63126) ^ [_134303, _134305, _134307, _134309] : [2412 ^ _63126 : [(2413 ^ _63126) ^ [] : [-(c_member(_134303, 2411 ^ [_134303, _134305, _134307, _134309], _134305))], (2415 ^ _63126) ^ [] : [hBOOL(hAPP(_134309, 2411 ^ [_134303, _134305, _134307, _134309]))]], 2417 ^ _63126 : [(2418 ^ _63126) ^ [] : [-(c_member(_134303, 2416 ^ [_134303, _134305, _134307, _134309], _134307))], (2420 ^ _63126) ^ [] : [hBOOL(hAPP(_134309, 2416 ^ [_134303, _134305, _134307, _134309]))]], 2421 ^ _63126 : [(2422 ^ _63126) ^ [_134903] : [c_member(_134303, _134903, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_134303, tc_HOL_Obool), _134305, _134307)), -(hBOOL(hAPP(_134309, _134903)))]]], (2389 ^ _63126) ^ [_133511, _133513, _133515, _133517] : [2391 ^ _63126 : [(2392 ^ _63126) ^ [] : [-(c_member(_133511, 2390 ^ [_133511, _133513, _133515, _133517], c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_133511, tc_HOL_Obool), _133513, _133515)))], (2394 ^ _63126) ^ [] : [hBOOL(hAPP(_133517, 2390 ^ [_133511, _133513, _133515, _133517]))]], 2395 ^ _63126 : [(2396 ^ _63126) ^ [_133893] : [c_member(_133511, _133893, _133513), -(hBOOL(hAPP(_133517, _133893)))], (2402 ^ _63126) ^ [_134101] : [c_member(_133511, _134101, _133515), -(hBOOL(hAPP(_133517, _134101)))]]], (2438 ^ _63126) ^ [_135513, _135515, _135517, _135519] : [2439 ^ _63126 : [(2440 ^ _63126) ^ [] : [_135515 = _135519], (2442 ^ _63126) ^ [] : [hBOOL(hAPP(_135517, _135519))]], -(hBOOL(hAPP(c_Set_Oinsert(_135513, _135515, _135517), _135519)))], (2428 ^ _63126) ^ [_135225, _135227, _135229, _135231] : [hBOOL(hAPP(c_Set_Oinsert(_135225, _135227, _135229), _135231)), -(_135227 = _135231), -(hBOOL(hAPP(_135229, _135231)))], (2446 ^ _63126) ^ [_135873, _135875, _135877, _135879, _135881] : [c_Relation_Orefl__on(_135873, _135875, _135877), c_Relation_Orefl__on(_135873, _135879, _135881), -(c_Relation_Orefl__on(_135873, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_135873, tc_HOL_Obool), _135875, _135879), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_135873, _135873), tc_HOL_Obool), _135877, _135881)))], (2456 ^ _63126) ^ [_136255, _136257, _136259, _136261] : [-(c_Relation_ORange(_136255, _136257, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_136255, _136257), tc_HOL_Obool), _136259, _136261)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_136257, tc_HOL_Obool), c_Relation_ORange(_136255, _136257, _136259), c_Relation_ORange(_136255, _136257, _136261)))], (2458 ^ _63126) ^ [_136410, _136412, _136414, _136416] : [-(c_Relation_ODomain(_136410, _136412, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_136410, _136412), tc_HOL_Obool), _136414, _136416)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_136410, tc_HOL_Obool), c_Relation_ODomain(_136410, _136412, _136414), c_Relation_ODomain(_136410, _136412, _136416)))], (2460 ^ _63126) ^ [_136579, _136581, _136583, _136585, _136587] : [-(c_Relation_ODomain(_136579, _136581, c_Set_Oinsert(tc_prod(_136579, _136581), c_Product__Type_OPair(_136579, _136581, _136583, _136585), _136587)) = c_Set_Oinsert(_136579, _136583, c_Relation_ODomain(_136579, _136581, _136587)))], (2462 ^ _63126) ^ [_136745, _136747, _136749, _136751, _136753] : [-(c_Relation_ORange(_136745, _136747, c_Set_Oinsert(tc_prod(_136745, _136747), c_Product__Type_OPair(_136745, _136747, _136749, _136751), _136753)) = c_Set_Oinsert(_136747, _136751, c_Relation_ORange(_136745, _136747, _136753)))], (2474 ^ _63126) ^ [_137233, _137235, _137237, _137239] : [2475 ^ _63126 : [(2476 ^ _63126) ^ [] : [c_member(_137233, _137235, _137237)], (2478 ^ _63126) ^ [] : [c_member(_137233, _137235, _137239)]], -(c_member(_137233, _137235, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_137233, tc_HOL_Obool), _137237, _137239)))], (2464 ^ _63126) ^ [_136941, _136943, _136945, _136947] : [c_member(_136941, _136943, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_136941, tc_HOL_Obool), _136945, _136947)), -(c_member(_136941, _136943, _136945)), -(c_member(_136941, _136943, _136947))], (2482 ^ _63126) ^ [_137583, _137585, _137587, _137589] : [c_member(_137583, _137585, _137587), -(c_member(_137583, _137585, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_137583, tc_HOL_Obool), _137587, _137589)))], (2488 ^ _63126) ^ [_137851, _137853, _137855, _137857] : [c_member(_137851, _137853, _137855), -(c_member(_137851, _137853, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_137851, tc_HOL_Obool), _137857, _137855)))], (2494 ^ _63126) ^ [_138090, _138092, _138094] : [-(c_member(_138090, _138092, c_Set_Oinsert(_138090, _138092, _138094)))], (2506 ^ _63126) ^ [_138547, _138549, _138551, _138553] : [2507 ^ _63126 : [(2508 ^ _63126) ^ [] : [_138549 = _138551], (2510 ^ _63126) ^ [] : [c_member(_138547, _138549, _138553)]], -(c_member(_138547, _138549, c_Set_Oinsert(_138547, _138551, _138553)))], (2496 ^ _63126) ^ [_138263, _138265, _138267, _138269] : [c_member(_138263, _138265, c_Set_Oinsert(_138263, _138267, _138269)), -(_138265 = _138267), -(c_member(_138263, _138265, _138269))], (2514 ^ _63126) ^ [_138889, _138891, _138893, _138895] : [-(c_member(_138889, _138891, _138893)), -(c_member(_138889, _138891, _138895)), 2521 ^ _63126 : [(2522 ^ _63126) ^ [] : [c_Set_Oinsert(_138889, _138891, _138893) = c_Set_Oinsert(_138889, _138891, _138895), -(_138893 = _138895)], (2528 ^ _63126) ^ [] : [_138893 = _138895, -(c_Set_Oinsert(_138889, _138891, _138893) = c_Set_Oinsert(_138889, _138891, _138895))]]], (2534 ^ _63126) ^ [_139540, _139542, _139544, _139546] : [c_member(_139540, _139542, _139544), -(c_member(_139540, _139542, c_Set_Oinsert(_139540, _139546, _139544)))], (2540 ^ _63126) ^ [_139788, _139790, _139792] : [c_member(_139788, _139790, _139792), -(c_Set_Oinsert(_139788, _139790, _139792) = _139792)], (2546 ^ _63126) ^ [_140013, _140015, _140017] : [-(c_Transitive__Closure_Ortrancl(_140013, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_140013, _140013), tc_HOL_Obool), c_Transitive__Closure_Ortrancl(_140013, _140015), c_Transitive__Closure_Ortrancl(_140013, _140017))) = c_Transitive__Closure_Ortrancl(_140013, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_140013, _140013), tc_HOL_Obool), _140015, _140017)))], (2548 ^ _63126) ^ [_140127] : [-(c_Relation_Oantisym(_140127, c_Relation_OId(_140127)))], (2550 ^ _63126) ^ [_140264, _140266, _140268, _140270] : [2551 ^ _63126 : [(2552 ^ _63126) ^ [] : [c_member(tc_prod(_140264, _140264), _140266, c_Transitive__Closure_Ortrancl(_140264, _140268))], (2554 ^ _63126) ^ [] : [c_member(tc_prod(_140264, _140264), _140266, c_Transitive__Closure_Ortrancl(_140264, _140270))]], -(c_member(tc_prod(_140264, _140264), _140266, c_Transitive__Closure_Ortrancl(_140264, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_140264, _140264), tc_HOL_Obool), _140268, _140270))))], (2558 ^ _63126) ^ [_140611, _140613] : [-(c_Relation_Oantisym(_140611, c_Relation_OId__on(_140611, _140613)))], (2560 ^ _63126) ^ [_140708, _140710] : [-(c_Transitive__Closure_Ortrancl(_140708, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_140708, _140708), tc_HOL_Obool), _140710, c_Relation_OId(_140708))) = c_Transitive__Closure_Ortrancl(_140708, _140710))], (2562 ^ _63126) ^ [_140820, _140822] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_140820, _140820), tc_HOL_Obool), c_Transitive__Closure_Ortrancl(_140820, _140822), c_Relation_OId(_140820)) = c_Transitive__Closure_Ortrancl(_140820, _140822))], (2564 ^ _63126) ^ [_140947, _140949] : [c_Relation_Otrans(_140947, _140949), -(c_Relation_Otrans(_140947, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_140947, _140947), tc_HOL_Obool), _140949, c_Relation_OId(_140947))))], (2584 ^ _63126) ^ [_141706, _141708] : [2587 ^ _63126 : [(2588 ^ _63126) ^ [] : [-(c_member(tc_prod(_141706, _141706), c_Product__Type_OPair(_141706, _141706, 2585 ^ [_141706, _141708], 2586 ^ [_141706, _141708]), _141708))], (2590 ^ _63126) ^ [] : [-(c_member(tc_prod(_141706, _141706), c_Product__Type_OPair(_141706, _141706, 2586 ^ [_141706, _141708], 2585 ^ [_141706, _141708]), _141708))], (2592 ^ _63126) ^ [] : [2585 ^ [_141706, _141708] = 2586 ^ [_141706, _141708]]], -(c_Relation_Oantisym(_141706, _141708))], (2570 ^ _63126) ^ [_141210, _141212] : [c_Relation_Oantisym(_141210, _141212), 2573 ^ _63126 : [(2574 ^ _63126) ^ [_141390, _141392] : [c_member(tc_prod(_141210, _141210), c_Product__Type_OPair(_141210, _141210, _141392, _141390), _141212), c_member(tc_prod(_141210, _141210), c_Product__Type_OPair(_141210, _141210, _141390, _141392), _141212), -(_141392 = _141390)]]], (2596 ^ _63126) ^ [_142359, _142361, _142363, _142365] : [2597 ^ _63126 : [(2598 ^ _63126) ^ [] : [hBOOL(hAPP(_142359, _142361))], (2600 ^ _63126) ^ [] : [hBOOL(hAPP(_142363, _142361))]], -(hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_142365, tc_HOL_Obool), _142363, _142359), _142361)))], (2604 ^ _63126) ^ [_142715, _142717, _142719, _142721] : [hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_142715, tc_HOL_Obool), _142717, _142719), _142721)), -(hBOOL(hAPP(_142717, _142721))), -(hBOOL(hAPP(_142719, _142721)))], (2614 ^ _63126) ^ [_143105, _143107, _143109, _143111, _143113] : [class_Lattices_Olattice(_143105), -(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_143107, _143105), _143109, _143111), _143113) = c_Lattices_Osemilattice__sup__class_Osup(_143105, hAPP(_143109, _143113), hAPP(_143111, _143113)))], (2620 ^ _63126) ^ [_143414, _143416, _143418] : [c_Order__Relation_Opartial__order__on(_143414, _143416, _143418), 2623 ^ _63126 : [(2624 ^ _63126) ^ [] : [-(c_Order__Relation_Opreorder__on(_143414, _143416, _143418))], (2626 ^ _63126) ^ [] : [-(c_Relation_Oantisym(_143414, _143418))]]], (2628 ^ _63126) ^ [_143663, _143665, _143667] : [-(c_Order__Relation_Opartial__order__on(_143663, _143665, _143667)), c_Order__Relation_Opreorder__on(_143663, _143665, _143667), c_Relation_Oantisym(_143663, _143667)], (2638 ^ _63126) ^ [_144020, _144022, _144024, _144026, _144028] : [c_member(tc_prod(_144020, _144020), c_Product__Type_OPair(_144020, _144020, _144022, _144024), c_Transitive__Closure_Ortrancl(_144020, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_144020, _144020), tc_HOL_Obool), _144026, _144028))), 2644 ^ _63126 : [(2645 ^ _63126) ^ [] : [-(c_member(tc_prod(_144020, _144020), c_Product__Type_OPair(_144020, _144020, 2643 ^ [_144020, _144022, _144024, _144026, _144028], _144024), c_Transitive__Closure_Ortrancl(_144020, _144026)))], (2648 ^ _63126) ^ [] : [-(c_member(tc_prod(_144020, _144020), c_Product__Type_OPair(_144020, _144020, 2646 ^ [_144020, _144022, _144024, _144026, _144028], 2643 ^ [_144020, _144022, _144024, _144026, _144028]), _144028))], (2650 ^ _63126) ^ [] : [2646 ^ [_144020, _144022, _144024, _144026, _144028] = 2643 ^ [_144020, _144022, _144024, _144026, _144028]]], -(c_member(tc_prod(_144020, _144020), c_Product__Type_OPair(_144020, _144020, _144022, _144024), c_Transitive__Closure_Ortrancl(_144020, _144026)))], (2654 ^ _63126) ^ [_144930, _144932, _144934, _144936, _144938] : [c_member(tc_prod(_144930, _144930), c_Product__Type_OPair(_144930, _144930, _144932, _144934), c_Transitive__Closure_Ortrancl(_144930, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_144930, _144930), tc_HOL_Obool), _144936, _144938))), 2660 ^ _63126 : [(2661 ^ _63126) ^ [] : [-(c_member(tc_prod(_144930, _144930), c_Product__Type_OPair(_144930, _144930, _144932, 2659 ^ [_144930, _144932, _144934, _144936, _144938]), c_Transitive__Closure_Ortrancl(_144930, _144936)))], (2664 ^ _63126) ^ [] : [-(c_member(tc_prod(_144930, _144930), c_Product__Type_OPair(_144930, _144930, 2659 ^ [_144930, _144932, _144934, _144936, _144938], 2662 ^ [_144930, _144932, _144934, _144936, _144938]), _144938))], (2666 ^ _63126) ^ [] : [2659 ^ [_144930, _144932, _144934, _144936, _144938] = 2662 ^ [_144930, _144932, _144934, _144936, _144938]]], -(c_member(tc_prod(_144930, _144930), c_Product__Type_OPair(_144930, _144930, _144932, _144934), c_Transitive__Closure_Ortrancl(_144930, _144936)))], (2670 ^ _63126) ^ [_145855, _145857, _145859, _145861] : [c_Wellfounded_Owf(_145855, c_Set_Oinsert(tc_prod(_145855, _145855), c_Product__Type_OPair(_145855, _145855, _145857, _145859), _145861)), 2673 ^ _63126 : [(2674 ^ _63126) ^ [] : [-(c_Wellfounded_Owf(_145855, _145861))], (2676 ^ _63126) ^ [] : [c_member(tc_prod(_145855, _145855), c_Product__Type_OPair(_145855, _145855, _145859, _145857), c_Transitive__Closure_Ortrancl(_145855, _145861))]]], (2678 ^ _63126) ^ [_146157, _146159, _146161, _146163] : [-(c_Wellfounded_Owf(_146157, c_Set_Oinsert(tc_prod(_146157, _146157), c_Product__Type_OPair(_146157, _146157, _146159, _146161), _146163))), c_Wellfounded_Owf(_146157, _146163), -(c_member(tc_prod(_146157, _146157), c_Product__Type_OPair(_146157, _146157, _146161, _146159), c_Transitive__Closure_Ortrancl(_146157, _146163)))], (2688 ^ _63126) ^ [_146557, _146559, _146561, _146563] : [c_Wellfounded_Owf(_146557, _146559), -(c_Wellfounded_Owf(_146561, hAPP(c_Relation_Oinv__image(_146557, _146561, _146559), _146563)))], (2694 ^ _63126) ^ [_146821, _146823, _146825, _146827] : [c_Wellfounded_Owf(_146821, _146823), c_Wellfounded_Owf(_146825, _146827), -(c_Wellfounded_Owf(tc_prod(_146821, _146825), c_Wellfounded_Olex__prod(_146821, _146825, _146823, _146827)))], (2704 ^ _63126) ^ [_147156, _147158] : [c_Wellfounded_Owf(_147156, _147158), -(c_Wellfounded_Owf(_147156, c_Transitive__Closure_Otrancl(_147156, _147158)))], (2710 ^ _63126) ^ [_147372, _147374] : [c_Wellfounded_Owf(_147372, _147374), -(c_Wellfounded_Oacyclic(_147372, _147374))], (2716 ^ _63126) ^ [_147596, _147598, _147600] : [c_Wellfounded_Owf(_147596, _147598), c_member(tc_prod(_147596, _147596), c_Product__Type_OPair(_147596, _147596, _147600, _147600), _147598)], (2722 ^ _63126) ^ [_147859, _147861, _147863, _147865] : [c_Wellfounded_Owf(_147859, _147861), c_member(tc_prod(_147859, _147859), c_Product__Type_OPair(_147859, _147859, _147863, _147865), _147861), c_member(tc_prod(_147859, _147859), c_Product__Type_OPair(_147859, _147859, _147865, _147863), _147861)], (2732 ^ _63126) ^ [_148243, _148245, _148247, _148249] : [c_Wellfounded_Owf(_148243, _148245), c_member(tc_prod(_148243, _148243), c_Product__Type_OPair(_148243, _148243, _148247, _148249), _148245), c_member(tc_prod(_148243, _148243), c_Product__Type_OPair(_148243, _148243, _148249, _148247), _148245)], (2742 ^ _63126) ^ [_148613, _148615, _148617] : [c_Wellfounded_Owf(_148613, _148615), c_member(tc_prod(_148613, _148613), c_Product__Type_OPair(_148613, _148613, _148617, _148617), _148615)], (2748 ^ _63126) ^ [_148862, _148864, _148866] : [c_Wellfounded_Owf(_148862, _148864), -(c_member(_148862, _148866, c_Wellfounded_Oacc(_148862, _148864)))], (2754 ^ _63126) ^ [_149115, _149117] : [c_Wellfounded_Owf(_149115, _149117), 2757 ^ _63126 : [(2758 ^ _63126) ^ [_149235] : [-(c_member(_149115, _149235, c_Wellfounded_Oacc(_149115, _149117)))]]], (2760 ^ _63126) ^ [_149307, _149309] : [c_member(_149307, 2761 ^ [_149307, _149309], c_Wellfounded_Oacc(_149307, _149309)), -(c_Wellfounded_Owf(_149307, _149309))], (2767 ^ _63126) ^ [_149631, _149633, _149635] : [c_member(_149631, _149633, c_fequal(_149635)), -(_149633 = _149635)], (2773 ^ _63126) ^ [_149805, _149807, _149809] : [_149807 = _149809, -(c_member(_149805, _149807, c_fequal(_149809)))], (2779 ^ _63126) ^ [_150029, _150031] : [class_Lattices_Osemilattice__sup(_150029), -(c_Lattices_Osemilattice__sup__class_Osup(_150029, _150031, _150031) = _150031)], (2785 ^ _63126) ^ [_150245, _150247] : [class_Lattices_Osemilattice__sup(_150245), -(c_Lattices_Osemilattice__sup__class_Osup(_150245, _150247, _150247) = _150247)], (2791 ^ _63126) ^ [_150475, _150477, _150479] : [class_Lattices_Osemilattice__sup(_150475), -(c_Lattices_Osemilattice__sup__class_Osup(_150475, _150477, _150479) = c_Lattices_Osemilattice__sup__class_Osup(_150475, _150479, _150477))], (2797 ^ _63126) ^ [_150719, _150721, _150723] : [class_Lattices_Olattice(_150719), -(c_Lattices_Osemilattice__sup__class_Osup(_150719, _150721, _150723) = c_Lattices_Osemilattice__sup__class_Osup(_150719, _150723, _150721))], (2803 ^ _63126) ^ [_150963, _150965, _150967] : [class_Lattices_Osemilattice__sup(_150963), -(c_Lattices_Osemilattice__sup__class_Osup(_150963, _150965, _150967) = c_Lattices_Osemilattice__sup__class_Osup(_150963, _150967, _150965))], (2809 ^ _63126) ^ [_151207, _151209, _151211] : [class_Lattices_Osemilattice__sup(_151207), -(c_Lattices_Osemilattice__sup__class_Osup(_151207, _151209, c_Lattices_Osemilattice__sup__class_Osup(_151207, _151209, _151211)) = c_Lattices_Osemilattice__sup__class_Osup(_151207, _151209, _151211))], (2815 ^ _63126) ^ [_151459, _151461, _151463] : [class_Lattices_Olattice(_151459), -(c_Lattices_Osemilattice__sup__class_Osup(_151459, _151461, c_Lattices_Osemilattice__sup__class_Osup(_151459, _151461, _151463)) = c_Lattices_Osemilattice__sup__class_Osup(_151459, _151461, _151463))], (2821 ^ _63126) ^ [_151711, _151713, _151715] : [class_Lattices_Osemilattice__sup(_151711), -(c_Lattices_Osemilattice__sup__class_Osup(_151711, _151713, c_Lattices_Osemilattice__sup__class_Osup(_151711, _151713, _151715)) = c_Lattices_Osemilattice__sup__class_Osup(_151711, _151713, _151715))], (2827 ^ _63126) ^ [_151977, _151979, _151981, _151983] : [class_Lattices_Osemilattice__sup(_151977), -(c_Lattices_Osemilattice__sup__class_Osup(_151977, _151979, c_Lattices_Osemilattice__sup__class_Osup(_151977, _151981, _151983)) = c_Lattices_Osemilattice__sup__class_Osup(_151977, _151981, c_Lattices_Osemilattice__sup__class_Osup(_151977, _151979, _151983)))], (2833 ^ _63126) ^ [_152257, _152259, _152261, _152263] : [class_Lattices_Olattice(_152257), -(c_Lattices_Osemilattice__sup__class_Osup(_152257, _152259, c_Lattices_Osemilattice__sup__class_Osup(_152257, _152261, _152263)) = c_Lattices_Osemilattice__sup__class_Osup(_152257, _152261, c_Lattices_Osemilattice__sup__class_Osup(_152257, _152259, _152263)))], (2839 ^ _63126) ^ [_152537, _152539, _152541, _152543] : [class_Lattices_Osemilattice__sup(_152537), -(c_Lattices_Osemilattice__sup__class_Osup(_152537, _152539, c_Lattices_Osemilattice__sup__class_Osup(_152537, _152541, _152543)) = c_Lattices_Osemilattice__sup__class_Osup(_152537, _152541, c_Lattices_Osemilattice__sup__class_Osup(_152537, _152539, _152543)))], (2845 ^ _63126) ^ [_152817, _152819, _152821, _152823] : [class_Lattices_Osemilattice__sup(_152817), -(c_Lattices_Osemilattice__sup__class_Osup(_152817, c_Lattices_Osemilattice__sup__class_Osup(_152817, _152819, _152821), _152823) = c_Lattices_Osemilattice__sup__class_Osup(_152817, _152819, c_Lattices_Osemilattice__sup__class_Osup(_152817, _152821, _152823)))], (2851 ^ _63126) ^ [_153097, _153099, _153101, _153103] : [class_Lattices_Olattice(_153097), -(c_Lattices_Osemilattice__sup__class_Osup(_153097, c_Lattices_Osemilattice__sup__class_Osup(_153097, _153099, _153101), _153103) = c_Lattices_Osemilattice__sup__class_Osup(_153097, _153099, c_Lattices_Osemilattice__sup__class_Osup(_153097, _153101, _153103)))], (2857 ^ _63126) ^ [_153377, _153379, _153381, _153383] : [class_Lattices_Osemilattice__sup(_153377), -(c_Lattices_Osemilattice__sup__class_Osup(_153377, c_Lattices_Osemilattice__sup__class_Osup(_153377, _153379, _153381), _153383) = c_Lattices_Osemilattice__sup__class_Osup(_153377, _153379, c_Lattices_Osemilattice__sup__class_Osup(_153377, _153381, _153383)))], (2863 ^ _63126) ^ [_153657, _153659, _153661, _153663] : [hBOOL(hAPP(_153657, _153659)), -(hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_153661, tc_HOL_Obool), _153657, _153663), _153659)))], (2869 ^ _63126) ^ [_153929, _153931, _153933, _153935] : [hBOOL(hAPP(_153929, _153931)), -(hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_153933, tc_HOL_Obool), _153935, _153929), _153931)))], (2875 ^ _63126) ^ [_154158, _154160] : [-(c_Wellfounded_Owf(_154158, hAPP(c_Wellfounded_Omeasure(_154158), _154160)))], (2877 ^ _63126) ^ [_154315, _154317, _154319] : [c_Order__Relation_Olinear__order__on(_154315, _154317, _154319), 2880 ^ _63126 : [(2881 ^ _63126) ^ [] : [-(c_Order__Relation_Opartial__order__on(_154315, _154317, _154319))], (2883 ^ _63126) ^ [] : [-(c_Relation_Ototal__on(_154315, _154317, _154319))]]], (2885 ^ _63126) ^ [_154566, _154568, _154570] : [-(c_Order__Relation_Olinear__order__on(_154566, _154568, _154570)), c_Order__Relation_Opartial__order__on(_154566, _154568, _154570), c_Relation_Ototal__on(_154566, _154568, _154570)], (2895 ^ _63126) ^ [_154939, _154941, _154943, _154945, _154947, _154949] : [_154939 = c_Recdef_Owfrec(_154941, _154943, _154945, _154947), c_Wellfounded_Owf(_154941, _154945), -(hAPP(_154939, _154949) = hAPP(hAPP(_154947, c_Recdef_Ocut(_154941, _154943, _154939, _154945, _154949)), _154949))], (2905 ^ _63126) ^ [_155360, _155362, _155364, _155366, _155368] : [c_Wellfounded_Owf(_155360, _155362), -(hAPP(c_Recdef_Owfrec(_155360, _155364, _155362, _155366), _155368) = hAPP(hAPP(_155366, c_Recdef_Ocut(_155360, _155364, c_Recdef_Owfrec(_155360, _155364, _155362, _155366), _155362, _155368)), _155368))], (2911 ^ _63126) ^ [_155666, _155668, _155670, _155672] : [c_Wellfounded_Owf(_155670, _155666), 2914 ^ _63126 : [(2915 ^ _63126) ^ [_155815] : [-(hAPP(c_Recdef_Owfrec(_155670, _155672, _155666, _155668), _155815) = hAPP(hAPP(_155668, c_Recdef_Ocut(_155670, _155672, c_Recdef_Owfrec(_155670, _155672, _155666, _155668), _155666, _155815)), _155815))]]], (2934 ^ _63126) ^ [_156748, _156750] : [-(c_Wellfounded_Owf(_156748, _156750)), 2937 ^ _63126 : [(2938 ^ _63126) ^ [] : [-(c_member(_156748, 2936 ^ [_156748, _156750], 2935 ^ [_156748, _156750]))], (2940 ^ _63126) ^ [_157107] : [c_member(_156748, _157107, 2935 ^ [_156748, _156750]), 2944 ^ _63126 : [(2945 ^ _63126) ^ [] : [-(c_member(tc_prod(_156748, _156748), c_Product__Type_OPair(_156748, _156748, 2943 ^ [_156748, _156750, _157107], _157107), _156750))], (2947 ^ _63126) ^ [] : [-(c_member(_156748, 2943 ^ [_156748, _156750, _157107], 2935 ^ [_156748, _156750]))]]]]], (2917 ^ _63126) ^ [_155989, _155991] : [c_Wellfounded_Owf(_155989, _155991), 2920 ^ _63126 : [(2921 ^ _63126) ^ [_156167] : [2922 ^ _63126 : [(2923 ^ _63126) ^ [_156279] : [c_member(_155989, _156279, _156167)]], 2925 ^ _63126 : [(2926 ^ _63126) ^ [] : [-(c_member(_155989, 2924 ^ [_155989, _155991, _156167], _156167))], (2928 ^ _63126) ^ [_156516] : [c_member(tc_prod(_155989, _155989), c_Product__Type_OPair(_155989, _155989, _156516, 2924 ^ [_155989, _155991, _156167]), _155991), c_member(_155989, _156516, _156167)]]]]], (2951 ^ _63126) ^ [_157636, _157638, _157640, _157642] : [2953 ^ _63126 : [(2954 ^ _63126) ^ [] : [-(hBOOL(hAPP(_157636, 2952 ^ [_157636, _157638, _157640, _157642])))], (2956 ^ _63126) ^ [] : [c_Wellfounded_Owf(_157638, hAPP(_157640, 2952 ^ [_157636, _157638, _157640, _157642]))]], -(c_Wellfounded_Owf(tc_prod(_157642, _157638), c_Recdef_Osame__fst(_157642, _157638, _157636, _157640)))], (2960 ^ _63126) ^ [_158054, _158056] : [c_Wellfounded_Owf(_158054, _158056), -(c_Wellfounded_OwfP(_158054, c_FunDef_Oin__rel(_158054, _158054, _158056)))], (2966 ^ _63126) ^ [_158286, _158288, _158290] : [c_Order__Relation_Olinear__order__on(_158286, _158288, _158290), -(c_Order__Relation_Ostrict__linear__order__on(_158286, _158288, c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_158286, _158286), tc_HOL_Obool), _158290, c_Relation_OId(_158286))))], (2972 ^ _63126) ^ [_158530, _158532] : [2975 ^ _63126 : [(2976 ^ _63126) ^ [] : [-(c_member(tc_prod(_158530, _158530), c_Product__Type_OPair(_158530, _158530, 2973 ^ [_158530, _158532], 2974 ^ [_158530, _158532]), _158532))], (2978 ^ _63126) ^ [] : [-(c_member(tc_prod(_158530, _158530), c_Product__Type_OPair(_158530, _158530, 2974 ^ [_158530, _158532], 2973 ^ [_158530, _158532]), _158532))], (2980 ^ _63126) ^ [] : [2973 ^ [_158530, _158532] = 2974 ^ [_158530, _158532]]], -(c_Relation_Oantisym(_158530, _158532))], (2984 ^ _63126) ^ [_159153, _159155] : [c_member(_159153, 2985 ^ [_159153, _159155], c_Wellfounded_Oacc(_159153, _159155)), -(c_Wellfounded_Owf(_159153, _159155))], (2991 ^ _63126) ^ [_159460, _159462, _159464, _159466] : [c_member(_159460, _159462, c_Groups_Ominus__class_Ominus(tc_fun(_159460, tc_HOL_Obool), _159464, _159466)), 2994 ^ _63126 : [(2995 ^ _63126) ^ [] : [-(c_member(_159460, _159462, _159464))], (2997 ^ _63126) ^ [] : [c_member(_159460, _159462, _159466)]]], (2999 ^ _63126) ^ [_159810, _159812, _159814, _159816] : [c_member(_159810, _159812, _159814), -(c_member(_159810, _159812, _159816)), -(c_member(_159810, _159812, c_Groups_Ominus__class_Ominus(tc_fun(_159810, tc_HOL_Obool), _159814, _159816)))], (3009 ^ _63126) ^ [_160209, _160211, _160213, _160215] : [c_member(_160209, _160211, c_Groups_Ominus__class_Ominus(tc_fun(_160209, tc_HOL_Obool), _160213, _160215)), 3012 ^ _63126 : [(3013 ^ _63126) ^ [] : [-(c_member(_160209, _160211, _160213))], (3015 ^ _63126) ^ [] : [c_member(_160209, _160211, _160215)]]], (3017 ^ _63126) ^ [_160483, _160485, _160487, _160489] : [-(c_member(_160483, _160485, c_Groups_Ominus__class_Ominus(tc_fun(_160483, tc_HOL_Obool), _160487, _160489))), c_member(_160483, _160485, _160487), -(c_member(_160483, _160485, _160489))], (3027 ^ _63126) ^ [_160855, _160857, _160859, _160861] : [c_member(_160855, _160857, c_Groups_Ominus__class_Ominus(tc_fun(_160855, tc_HOL_Obool), _160859, _160861)), -(c_member(_160855, _160857, _160859))], (3033 ^ _63126) ^ [_161123, _161125, _161127, _161129] : [c_member(_161123, _161125, c_Groups_Ominus__class_Ominus(tc_fun(_161123, tc_HOL_Obool), _161127, _161129)), c_member(_161123, _161125, _161129)], (3039 ^ _63126) ^ [_161363, _161365, _161367] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_161363, tc_HOL_Obool), _161365, c_Groups_Ominus__class_Ominus(tc_fun(_161363, tc_HOL_Obool), _161367, _161365)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_161363, tc_HOL_Obool), _161365, _161367))], (3041 ^ _63126) ^ [_161494, _161496, _161498] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_161494, tc_HOL_Obool), c_Groups_Ominus__class_Ominus(tc_fun(_161494, tc_HOL_Obool), _161496, _161498), _161498) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_161494, tc_HOL_Obool), _161496, _161498))], (3043 ^ _63126) ^ [_161639, _161641, _161643, _161645] : [-(c_Groups_Ominus__class_Ominus(tc_fun(_161639, tc_HOL_Obool), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_161639, tc_HOL_Obool), _161641, _161643), _161645) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_161639, tc_HOL_Obool), c_Groups_Ominus__class_Ominus(tc_fun(_161639, tc_HOL_Obool), _161641, _161645), c_Groups_Ominus__class_Ominus(tc_fun(_161639, tc_HOL_Obool), _161643, _161645)))], (3045 ^ _63126) ^ [_161786, _161788, _161790] : [-(c_Groups_Ominus__class_Ominus(tc_fun(_161786, tc_HOL_Obool), c_Groups_Ominus__class_Ominus(tc_fun(_161786, tc_HOL_Obool), _161788, _161790), _161790) = c_Groups_Ominus__class_Ominus(tc_fun(_161786, tc_HOL_Obool), _161788, _161790))], (3047 ^ _63126) ^ [_161960, _161962, _161964, _161966, _161968] : [class_Groups_Ominus(_161960), -(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_161962, _161960), _161964, _161966), _161968) = c_Groups_Ominus__class_Ominus(_161960, hAPP(_161964, _161968), hAPP(_161966, _161968)))], (3053 ^ _63126) ^ [_162254, _162256, _162258, _162260] : [c_member(_162254, _162256, _162258), -(c_Groups_Ominus__class_Ominus(tc_fun(_162254, tc_HOL_Obool), c_Set_Oinsert(_162254, _162256, _162260), _162258) = c_Groups_Ominus__class_Ominus(tc_fun(_162254, tc_HOL_Obool), _162260, _162258))], (3059 ^ _63126) ^ [_162562, _162564, _162566, _162568] : [c_member(_162562, _162564, _162566), -(c_Groups_Ominus__class_Ominus(tc_fun(_162562, tc_HOL_Obool), c_Set_Oinsert(_162562, _162564, _162568), _162566) = c_Groups_Ominus__class_Ominus(tc_fun(_162562, tc_HOL_Obool), _162568, _162566))], (3065 ^ _63126) ^ [_162774, _162776, _162778, _162780] : [-(c_member(_162774, _162776, _162778)), -(c_Groups_Ominus__class_Ominus(tc_fun(_162774, tc_HOL_Obool), c_Set_Oinsert(_162774, _162776, _162780), _162778) = c_Set_Oinsert(_162774, _162776, c_Groups_Ominus__class_Ominus(tc_fun(_162774, tc_HOL_Obool), _162780, _162778)))], (3071 ^ _63126) ^ [_163032, _163034] : [-(c_Transitive__Closure_Ortrancl(_163032, c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_163032, _163032), tc_HOL_Obool), _163034, c_Relation_OId(_163032))) = c_Transitive__Closure_Ortrancl(_163032, _163034))], (3073 ^ _63126) ^ [_163202, _163204, _163206] : [c_Relation_Ototal__on(_163202, _163204, c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_163202, _163202), tc_HOL_Obool), _163206, c_Relation_OId(_163202))), -(c_Relation_Ototal__on(_163202, _163204, _163206))], (3079 ^ _63126) ^ [_163398, _163400, _163402] : [c_Relation_Ototal__on(_163398, _163400, _163402), -(c_Relation_Ototal__on(_163398, _163400, c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_163398, _163398), tc_HOL_Obool), _163402, c_Relation_OId(_163398))))], (3085 ^ _63126) ^ [_163629, _163631] : [-(c_Relation_Oirrefl(_163629, c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_163629, _163629), tc_HOL_Obool), _163631, c_Relation_OId(_163629))))], (3087 ^ _63126) ^ [_163750, _163752] : [c_Relation_Otrans(_163750, _163752), c_Relation_Oantisym(_163750, _163752), -(c_Relation_Otrans(_163750, c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_163750, _163750), tc_HOL_Obool), _163752, c_Relation_OId(_163750))))], (3097 ^ _63126) ^ [_164116, _164118, _164120] : [c_Order__Relation_Owell__order__on(_164116, _164118, _164120), 3100 ^ _63126 : [(3101 ^ _63126) ^ [] : [-(c_Order__Relation_Olinear__order__on(_164116, _164118, _164120))], (3103 ^ _63126) ^ [] : [-(c_Wellfounded_Owf(_164116, c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_164116, _164116), tc_HOL_Obool), _164120, c_Relation_OId(_164116))))]]], (3105 ^ _63126) ^ [_164389, _164391, _164393] : [-(c_Order__Relation_Owell__order__on(_164389, _164391, _164393)), c_Order__Relation_Olinear__order__on(_164389, _164391, _164393), c_Wellfounded_Owf(_164389, c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_164389, _164389), tc_HOL_Obool), _164393, c_Relation_OId(_164389)))], (3115 ^ _63126) ^ [_164713, _164715] : [-(c_Relation_OField(_164713, _164715) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_164713, tc_HOL_Obool), c_Relation_ODomain(_164713, _164713, _164715), c_Relation_ORange(_164713, _164713, _164715)))], (3117 ^ _63126) ^ [_164897, _164899, _164901, _164903] : [c_member(tc_prod(_164897, _164897), c_Product__Type_OPair(_164897, _164897, _164899, _164901), hAPP(c_Wellfounded_Omeasure(_164897), _164903)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(_164903, _164899), hAPP(_164903, _164901)))], (3123 ^ _63126) ^ [_165113, _165115, _165117, _165119] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(_165119, _165115), hAPP(_165119, _165117)), -(c_member(tc_prod(_165113, _165113), c_Product__Type_OPair(_165113, _165113, _165115, _165117), hAPP(c_Wellfounded_Omeasure(_165113), _165119)))], (3129 ^ _63126) ^ [_165350] : [-(c_Wellfounded_Omeasure(_165350) = c_Relation_Oinv__image(tc_Nat_Onat, _165350, c_Wellfounded_Oless__than))], (3131 ^ _63126) ^ [_165476, _165478, _165480, _165482] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_165476, tc_HOL_Obool), c_Groups_Ominus__class_Ominus(tc_fun(_165476, tc_HOL_Obool), c_Relation_ORange(_165478, _165476, _165480), c_Relation_ORange(_165478, _165476, _165482)), c_Relation_ORange(_165478, _165476, c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_165478, _165476), tc_HOL_Obool), _165480, _165482))))], (3133 ^ _63126) ^ [_165636, _165638, _165640] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_165636, tc_HOL_Obool), _165638, _165640), c_Orderings_Oord__class_Oless__eq(tc_fun(_165636, tc_HOL_Obool), _165640, _165638), -(_165638 = _165640)], (3143 ^ _63126) ^ [] : [-(c_Relation_Otrans(tc_Nat_Onat, c_Wellfounded_Oless__than))], (3145 ^ _63126) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (3147 ^ _63126) ^ [_166095, _166097, _166099, _166101] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_166095, tc_HOL_Obool), _166097, _166099), c_member(_166095, _166101, _166097), -(c_member(_166095, _166101, _166099))], (3157 ^ _63126) ^ [_166468, _166470, _166472, _166474, _166476] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_166468, tc_HOL_Obool), _166470, _166472), c_Orderings_Oord__class_Oless__eq(tc_fun(_166468, tc_HOL_Obool), _166474, _166476), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_166468, tc_HOL_Obool), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_166468, tc_HOL_Obool), _166470, _166474), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_166468, tc_HOL_Obool), _166472, _166476)))], (3167 ^ _63126) ^ [_166877, _166879, _166881, _166883] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_166877, tc_HOL_Obool), _166879, _166881), c_Orderings_Oord__class_Oless__eq(tc_fun(_166877, tc_HOL_Obool), _166883, _166881), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_166877, tc_HOL_Obool), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_166877, tc_HOL_Obool), _166879, _166883), _166881))], (3177 ^ _63126) ^ [_167248, _167250, _167252] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_167248, tc_HOL_Obool), _167250, _167252), -(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_167248, tc_HOL_Obool), _167252, _167250) = _167252)], (3183 ^ _63126) ^ [_167500, _167502, _167504] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_167500, tc_HOL_Obool), _167502, _167504), -(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_167500, tc_HOL_Obool), _167502, _167504) = _167504)], (3189 ^ _63126) ^ [_167781, _167783, _167785] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_167781, tc_HOL_Obool), _167783, _167785), -(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_167781, tc_HOL_Obool), _167783, _167785) = _167785)], (3195 ^ _63126) ^ [_167971, _167973, _167975] : [c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_167971, tc_HOL_Obool), _167973, _167975) = _167975, -(c_Orderings_Oord__class_Oless__eq(tc_fun(_167971, tc_HOL_Obool), _167973, _167975))], (3201 ^ _63126) ^ [_168210, _168212, _168214] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_168210, tc_HOL_Obool), _168212, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_168210, tc_HOL_Obool), _168214, _168212)))], (3203 ^ _63126) ^ [_168331, _168333, _168335] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_168331, tc_HOL_Obool), _168333, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_168331, tc_HOL_Obool), _168333, _168335)))], (3205 ^ _63126) ^ [_168481, _168483, _168485, _168487] : [hBOOL(hAPP(_168481, _168483)), c_Orderings_Oord__class_Oless__eq(tc_fun(_168485, tc_HOL_Obool), _168481, _168487), -(hBOOL(hAPP(_168487, _168483)))], (3215 ^ _63126) ^ [_168844, _168846, _168848, _168850] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_168844, tc_HOL_Obool), _168846, _168848), hBOOL(hAPP(_168846, _168850)), -(hBOOL(hAPP(_168848, _168850)))], (3225 ^ _63126) ^ [_169207, _169209, _169211, _169213] : [c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_169207, _169209), tc_HOL_Obool), _169211, _169213), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_169207, tc_HOL_Obool), c_Relation_ODomain(_169207, _169209, _169211), c_Relation_ODomain(_169207, _169209, _169213)))], (3231 ^ _63126) ^ [_169481, _169483, _169485] : [c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_169481, _169481), tc_HOL_Obool), _169483, _169485), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_169481, tc_HOL_Obool), c_Wellfounded_Oacc(_169481, _169485), c_Wellfounded_Oacc(_169481, _169483)))], (3237 ^ _63126) ^ [_169716, _169718] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_169716, tc_HOL_Obool), _169718, _169718))], (3239 ^ _63126) ^ [_169872, _169874, _169876] : [_169872 = _169874, 3242 ^ _63126 : [(3243 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_169876, tc_HOL_Obool), _169872, _169874))], (3245 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_169876, tc_HOL_Obool), _169874, _169872))]]], (3247 ^ _63126) ^ [_170133, _170135, _170137] : [-(_170133 = _170135), c_Orderings_Oord__class_Oless__eq(tc_fun(_170137, tc_HOL_Obool), _170133, _170135), c_Orderings_Oord__class_Oless__eq(tc_fun(_170137, tc_HOL_Obool), _170135, _170133)], (3257 ^ _63126) ^ [_170474, _170476, _170478] : [_170474 = _170476, -(c_Orderings_Oord__class_Oless__eq(tc_fun(_170478, tc_HOL_Obool), _170474, _170476))], (3263 ^ _63126) ^ [_170712, _170714, _170716] : [_170712 = _170714, -(c_Orderings_Oord__class_Oless__eq(tc_fun(_170716, tc_HOL_Obool), _170714, _170712))], (3269 ^ _63126) ^ [_170950, _170952, _170954] : [c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_170950, _170950), tc_HOL_Obool), _170952, _170954), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_170950, tc_HOL_Obool), c_Relation_OField(_170950, _170952), c_Relation_OField(_170950, _170954)))], (3275 ^ _63126) ^ [_171228, _171230, _171232, _171234] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_171228, tc_HOL_Obool), _171230, _171232), c_Orderings_Oord__class_Oless__eq(tc_fun(_171228, tc_HOL_Obool), _171232, _171234), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_171228, tc_HOL_Obool), _171230, _171234))], (3285 ^ _63126) ^ [_171585, _171587, _171589] : [_171585 = _171587, 3288 ^ _63126 : [(3289 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_171589, tc_HOL_Obool), _171585, _171587))], (3291 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_171589, tc_HOL_Obool), _171587, _171585))]]], (3293 ^ _63126) ^ [_171927, _171929] : [c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat, _171927, _171929), c_Wellfounded_Oless__than), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _171927, _171929))], (3299 ^ _63126) ^ [_172103, _172105] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _172103, _172105), -(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat, _172103, _172105), c_Wellfounded_Oless__than))], (3305 ^ _63126) ^ [_172357, _172359, _172361, _172363] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_172357, tc_HOL_Obool), _172359, _172361), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_172357, tc_HOL_Obool), c_Set_Oinsert(_172357, _172363, _172359), c_Set_Oinsert(_172357, _172363, _172361)))], (3311 ^ _63126) ^ [_172639, _172641, _172643, _172645] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_172639, tc_HOL_Obool), _172641, _172643), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_172639, tc_HOL_Obool), _172641, c_Set_Oinsert(_172639, _172645, _172643)))], (3317 ^ _63126) ^ [_172884, _172886, _172888] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_172884, tc_HOL_Obool), _172886, c_Set_Oinsert(_172884, _172888, _172886)))], (3319 ^ _63126) ^ [_173031, _173033, _173035, _173037] : [class_Lattices_Osemilattice__sup(_173031), c_Orderings_Oord__class_Oless__eq(_173031, c_Lattices_Osemilattice__sup__class_Osup(_173031, _173033, _173035), _173037), 3326 ^ _63126 : [(3327 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_173031, _173033, _173037))], (3329 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_173031, _173035, _173037))]]], (3331 ^ _63126) ^ [_173487, _173489, _173491, _173493, _173495] : [class_Lattices_Osemilattice__sup(_173487), c_Orderings_Oord__class_Oless__eq(_173487, _173489, _173491), c_Orderings_Oord__class_Oless__eq(_173487, _173493, _173495), -(c_Orderings_Oord__class_Oless__eq(_173487, c_Lattices_Osemilattice__sup__class_Osup(_173487, _173489, _173493), c_Lattices_Osemilattice__sup__class_Osup(_173487, _173491, _173495)))], (3345 ^ _63126) ^ [_173965, _173967, _173969, _173971] : [class_Lattices_Osemilattice__sup(_173965), c_Orderings_Oord__class_Oless__eq(_173965, _173967, _173969), c_Orderings_Oord__class_Oless__eq(_173965, _173971, _173969), -(c_Orderings_Oord__class_Oless__eq(_173965, c_Lattices_Osemilattice__sup__class_Osup(_173965, _173967, _173971), _173969))], (3359 ^ _63126) ^ [_174421, _174423, _174425, _174427] : [class_Lattices_Osemilattice__sup(_174421), c_Orderings_Oord__class_Oless__eq(_174421, _174423, _174425), c_Orderings_Oord__class_Oless__eq(_174421, _174427, _174425), -(c_Orderings_Oord__class_Oless__eq(_174421, c_Lattices_Osemilattice__sup__class_Osup(_174421, _174423, _174427), _174425))], (3373 ^ _63126) ^ [_174863, _174865, _174867] : [class_Lattices_Osemilattice__sup(_174863), c_Orderings_Oord__class_Oless__eq(_174863, _174865, _174867), -(c_Lattices_Osemilattice__sup__class_Osup(_174863, _174867, _174865) = _174867)], (3383 ^ _63126) ^ [_175194, _175196, _175198] : [class_Lattices_Osemilattice__sup(_175194), c_Orderings_Oord__class_Oless__eq(_175194, _175196, _175198), -(c_Lattices_Osemilattice__sup__class_Osup(_175194, _175196, _175198) = _175198)], (3393 ^ _63126) ^ [_175539, _175541, _175543, _175545] : [class_Lattices_Osemilattice__sup(_175539), c_Orderings_Oord__class_Oless__eq(_175539, _175541, _175543), -(c_Orderings_Oord__class_Oless__eq(_175539, _175541, c_Lattices_Osemilattice__sup__class_Osup(_175539, _175545, _175543)))], (3403 ^ _63126) ^ [_175896, _175898, _175900, _175902] : [class_Lattices_Osemilattice__sup(_175896), c_Orderings_Oord__class_Oless__eq(_175896, _175898, _175900), -(c_Orderings_Oord__class_Oless__eq(_175896, _175898, c_Lattices_Osemilattice__sup__class_Osup(_175896, _175900, _175902)))], (3413 ^ _63126) ^ [_176253, _176255, _176257, _176259] : [class_Lattices_Osemilattice__sup(_176253), 3416 ^ _63126 : [(3417 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless__eq(_176253, c_Lattices_Osemilattice__sup__class_Osup(_176253, _176255, _176257), _176259), 3420 ^ _63126 : [(3421 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_176253, _176255, _176259))], (3423 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_176253, _176257, _176259))]]], (3425 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_176253, c_Lattices_Osemilattice__sup__class_Osup(_176253, _176255, _176257), _176259)), c_Orderings_Oord__class_Oless__eq(_176253, _176255, _176259), c_Orderings_Oord__class_Oless__eq(_176253, _176257, _176259)]]], (3435 ^ _63126) ^ [_176948, _176950, _176952] : [class_Lattices_Osemilattice__sup(_176948), 3438 ^ _63126 : [(3439 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless__eq(_176948, _176950, _176952), -(c_Lattices_Osemilattice__sup__class_Osup(_176948, _176950, _176952) = _176952)], (3445 ^ _63126) ^ [] : [c_Lattices_Osemilattice__sup__class_Osup(_176948, _176950, _176952) = _176952, -(c_Orderings_Oord__class_Oless__eq(_176948, _176950, _176952))]]], (3451 ^ _63126) ^ [_177451, _177453, _177455] : [class_Lattices_Osemilattice__sup(_177451), -(c_Orderings_Oord__class_Oless__eq(_177451, _177453, c_Lattices_Osemilattice__sup__class_Osup(_177451, _177455, _177453)))], (3457 ^ _63126) ^ [_177689, _177691, _177693] : [class_Lattices_Olattice(_177689), -(c_Orderings_Oord__class_Oless__eq(_177689, _177691, c_Lattices_Osemilattice__sup__class_Osup(_177689, _177693, _177691)))], (3463 ^ _63126) ^ [_177927, _177929, _177931] : [class_Lattices_Osemilattice__sup(_177927), -(c_Orderings_Oord__class_Oless__eq(_177927, _177929, c_Lattices_Osemilattice__sup__class_Osup(_177927, _177929, _177931)))], (3469 ^ _63126) ^ [_178165, _178167, _178169] : [class_Lattices_Olattice(_178165), -(c_Orderings_Oord__class_Oless__eq(_178165, _178167, c_Lattices_Osemilattice__sup__class_Osup(_178165, _178167, _178169)))], (3475 ^ _63126) ^ [_178417, _178419, _178421, _178423] : [class_Lattices_Osemilattice__sup(_178417), c_Orderings_Oord__class_Oless(_178417, _178419, _178421), -(c_Orderings_Oord__class_Oless(_178417, _178419, c_Lattices_Osemilattice__sup__class_Osup(_178417, _178423, _178421)))], (3485 ^ _63126) ^ [_178774, _178776, _178778, _178780] : [class_Lattices_Osemilattice__sup(_178774), c_Orderings_Oord__class_Oless(_178774, _178776, _178778), -(c_Orderings_Oord__class_Oless(_178774, _178776, c_Lattices_Osemilattice__sup__class_Osup(_178774, _178778, _178780)))], (3495 ^ _63126) ^ [_179131, _179133, _179135, _179137] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_179131, tc_HOL_Obool), _179133, _179135), c_member(_179131, _179137, _179133), -(c_member(_179131, _179137, _179135))], (3505 ^ _63126) ^ [_179490, _179492, _179494, _179496] : [c_member(_179490, _179492, _179494), c_Orderings_Oord__class_Oless__eq(tc_fun(_179490, tc_HOL_Obool), _179494, _179496), -(c_member(_179490, _179492, _179496))], (3515 ^ _63126) ^ [_179849, _179851, _179853, _179855] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_179849, tc_HOL_Obool), _179851, _179853), c_member(_179849, _179855, _179851), -(c_member(_179849, _179855, _179853))], (3525 ^ _63126) ^ [_180179, _180181, _180183] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_180179, tc_HOL_Obool), c_Groups_Ominus__class_Ominus(tc_fun(_180179, tc_HOL_Obool), _180181, _180183), _180181))], (3527 ^ _63126) ^ [_180343, _180345, _180347, _180349, _180351] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_180343, tc_HOL_Obool), _180345, _180347), c_Orderings_Oord__class_Oless__eq(tc_fun(_180343, tc_HOL_Obool), _180349, _180351), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_180343, tc_HOL_Obool), c_Groups_Ominus__class_Ominus(tc_fun(_180343, tc_HOL_Obool), _180345, _180351), c_Groups_Ominus__class_Ominus(tc_fun(_180343, tc_HOL_Obool), _180347, _180349)))], (3537 ^ _63126) ^ [_180752, _180754, _180756, _180758] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_180752, tc_HOL_Obool), _180754, _180756), c_Orderings_Oord__class_Oless__eq(tc_fun(_180752, tc_HOL_Obool), _180756, _180758), -(c_Groups_Ominus__class_Ominus(tc_fun(_180752, tc_HOL_Obool), _180756, c_Groups_Ominus__class_Ominus(tc_fun(_180752, tc_HOL_Obool), _180758, _180754)) = _180754)], (3547 ^ _63126) ^ [_181129, _181131, _181133] : [c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_181129, _181129), tc_HOL_Obool), _181131, c_Transitive__Closure_Ortrancl(_181129, _181133)), -(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_181129, _181129), tc_HOL_Obool), c_Transitive__Closure_Ortrancl(_181129, _181131), c_Transitive__Closure_Ortrancl(_181129, _181133)))], (3553 ^ _63126) ^ [_181405, _181407, _181409] : [c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_181405, _181405), tc_HOL_Obool), _181407, _181409), c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_181405, _181405), tc_HOL_Obool), _181409, c_Transitive__Closure_Ortrancl(_181405, _181407)), -(c_Transitive__Closure_Ortrancl(_181405, _181409) = c_Transitive__Closure_Ortrancl(_181405, _181407))], (3563 ^ _63126) ^ [_181774, _181776, _181778] : [c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_181774, _181774), tc_HOL_Obool), _181776, _181778), -(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_181774, _181774), tc_HOL_Obool), c_Transitive__Closure_Ortrancl(_181774, _181776), c_Transitive__Closure_Ortrancl(_181774, _181778)))], (3569 ^ _63126) ^ [_182044, _182046, _182048] : [c_Wellfounded_Owf(_182044, _182046), c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_182044, _182044), tc_HOL_Obool), _182048, _182046), -(c_Wellfounded_Owf(_182044, _182048))], (3579 ^ _63126) ^ [_182381, _182383, _182385] : [c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_182381, _182381), tc_HOL_Obool), _182383, _182385), c_Relation_Oantisym(_182381, _182385), -(c_Relation_Oantisym(_182381, _182383))], (3589 ^ _63126) ^ [_182718, _182720, _182722] : [c_Wellfounded_Oacyclic(_182718, _182720), c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_182718, _182718), tc_HOL_Obool), _182722, _182720), -(c_Wellfounded_Oacyclic(_182718, _182722))], (3599 ^ _63126) ^ [_183069, _183071, _183073, _183075] : [c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_183069, _183071), tc_HOL_Obool), _183073, _183075), c_Relation_Osingle__valued(_183069, _183071, _183075), -(c_Relation_Osingle__valued(_183069, _183071, _183073))], (3609 ^ _63126) ^ [_183463, _183465, _183467, _183469] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_183463, tc_HOL_Obool), c_Set_Oinsert(_183463, _183465, _183467), _183469), 3612 ^ _63126 : [(3613 ^ _63126) ^ [] : [-(c_member(_183463, _183465, _183469))], (3615 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_183463, tc_HOL_Obool), _183467, _183469))]]], (3617 ^ _63126) ^ [_183742, _183744, _183746, _183748] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_183742, tc_HOL_Obool), c_Set_Oinsert(_183742, _183744, _183746), _183748)), c_member(_183742, _183744, _183748), c_Orderings_Oord__class_Oless__eq(tc_fun(_183742, tc_HOL_Obool), _183746, _183748)], (3627 ^ _63126) ^ [_184117, _184119, _184121, _184123] : [-(c_member(_184117, _184119, _184121)), 3630 ^ _63126 : [(3631 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_184117, tc_HOL_Obool), _184121, c_Set_Oinsert(_184117, _184119, _184123)), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_184117, tc_HOL_Obool), _184121, _184123))], (3637 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_184117, tc_HOL_Obool), _184121, _184123), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_184117, tc_HOL_Obool), _184121, c_Set_Oinsert(_184117, _184119, _184123)))]]], (3643 ^ _63126) ^ [_184707, _184709, _184711, _184713] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_184707, tc_HOL_Obool), c_Groups_Ominus__class_Ominus(tc_fun(_184707, tc_HOL_Obool), _184709, _184711), _184713), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_184707, tc_HOL_Obool), _184709, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_184707, tc_HOL_Obool), _184711, _184713)))], (3649 ^ _63126) ^ [_184925, _184927, _184929, _184931] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_184925, tc_HOL_Obool), _184927, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_184925, tc_HOL_Obool), _184929, _184931)), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_184925, tc_HOL_Obool), c_Groups_Ominus__class_Ominus(tc_fun(_184925, tc_HOL_Obool), _184927, _184929), _184931))], (3655 ^ _63126) ^ [_185207, _185209, _185211] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_185207, tc_HOL_Obool), _185209, _185211), -(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_185207, tc_HOL_Obool), _185209, c_Groups_Ominus__class_Ominus(tc_fun(_185207, tc_HOL_Obool), _185211, _185209)) = _185211)], (3661 ^ _63126) ^ [_185487, _185489, _185491, _185493] : [c_member(tc_prod(_185487, _185487), _185489, c_Transitive__Closure_Otrancl(_185487, _185491)), c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_185487, _185487), tc_HOL_Obool), _185491, _185493), -(c_member(tc_prod(_185487, _185487), _185489, c_Transitive__Closure_Otrancl(_185487, _185493)))], (3671 ^ _63126) ^ [_185847, _185849, _185851] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_185847, _185847), tc_HOL_Obool), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_185847, _185847), tc_HOL_Obool), c_Transitive__Closure_Ortrancl(_185847, _185849), c_Transitive__Closure_Ortrancl(_185847, _185851)), c_Transitive__Closure_Ortrancl(_185847, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_185847, _185847), tc_HOL_Obool), _185849, _185851))))], (3673 ^ _63126) ^ [_185993, _185995, _185997] : [-(c_Relation_OField(_185993, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_185993, _185993), tc_HOL_Obool), _185995, _185997)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_185993, tc_HOL_Obool), c_Relation_OField(_185993, _185995), c_Relation_OField(_185993, _185997)))], (3675 ^ _63126) ^ [_186143, _186145, _186147, _186149] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_186143, tc_HOL_Obool), c_Groups_Ominus__class_Ominus(tc_fun(_186143, tc_HOL_Obool), c_Relation_ODomain(_186143, _186145, _186147), c_Relation_ODomain(_186143, _186145, _186149)), c_Relation_ODomain(_186143, _186145, c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_186143, _186145), tc_HOL_Obool), _186147, _186149))))], (3677 ^ _63126) ^ [_186289, _186291] : [class_Orderings_Opreorder(_186289), -(c_Orderings_Oord__class_Oless__eq(_186289, _186291, _186291))], (3683 ^ _63126) ^ [_186541, _186543, _186545, _186547, _186549] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(_186541, _186543), hAPP(_186541, _186545)), -(c_member(tc_prod(_186547, _186547), c_Product__Type_OPair(_186547, _186547, _186543, _186545), c_Wellfounded_Omlex__prod(_186547, _186541, _186549)))], (3689 ^ _63126) ^ [_186851, _186853, _186855, _186857, _186859] : [class_Orderings_Oord(_186851), c_Orderings_Oord__class_Oless__eq(tc_fun(_186853, _186851), _186855, _186857), -(c_Orderings_Oord__class_Oless__eq(_186851, hAPP(_186855, _186859), hAPP(_186857, _186859)))], (3699 ^ _63126) ^ [_187242, _187244, _187246, _187248, _187250] : [class_Orderings_Oord(_187242), c_Orderings_Oord__class_Oless__eq(tc_fun(_187244, _187242), _187246, _187248), -(c_Orderings_Oord__class_Oless__eq(_187242, hAPP(_187246, _187250), hAPP(_187248, _187250)))], (3709 ^ _63126) ^ [_187634, _187636, _187638] : [c_Orderings_Oord__class_Oless(tc_fun(_187634, tc_HOL_Obool), _187636, _187638), 3712 ^ _63126 : [(3713 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_187634, tc_HOL_Obool), _187636, _187638))], (3715 ^ _63126) ^ [] : [_187636 = _187638]]], (3717 ^ _63126) ^ [_187896, _187898, _187900] : [-(c_Orderings_Oord__class_Oless(tc_fun(_187896, tc_HOL_Obool), _187898, _187900)), c_Orderings_Oord__class_Oless__eq(tc_fun(_187896, tc_HOL_Obool), _187898, _187900), -(_187898 = _187900)], (3737 ^ _63126) ^ [_188547, _188549, _188551] : [3738 ^ _63126 : [(3739 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless(tc_fun(_188547, tc_HOL_Obool), _188549, _188551)], (3741 ^ _63126) ^ [] : [_188549 = _188551]], -(c_Orderings_Oord__class_Oless__eq(tc_fun(_188547, tc_HOL_Obool), _188549, _188551))], (3727 ^ _63126) ^ [_188269, _188271, _188273] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_188269, tc_HOL_Obool), _188271, _188273), -(c_Orderings_Oord__class_Oless(tc_fun(_188269, tc_HOL_Obool), _188271, _188273)), -(_188271 = _188273)], (3745 ^ _63126) ^ [_188871, _188873, _188875] : [c_Orderings_Oord__class_Oless(tc_fun(_188871, tc_HOL_Obool), _188873, _188875), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_188871, tc_HOL_Obool), _188873, _188875))], (3751 ^ _63126) ^ [_189103, _189105] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _189103, _189105), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _189103, _189105))], (3757 ^ _63126) ^ [_189345, _189347, _189349, _189351] : [c_Orderings_Oord__class_Oless(tc_fun(_189345, tc_HOL_Obool), _189347, _189349), c_Orderings_Oord__class_Oless__eq(tc_fun(_189345, tc_HOL_Obool), _189349, _189351), -(c_Orderings_Oord__class_Oless(tc_fun(_189345, tc_HOL_Obool), _189347, _189351))], (3767 ^ _63126) ^ [_189716, _189718, _189720, _189722] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_189716, tc_HOL_Obool), _189718, _189720), c_Orderings_Oord__class_Oless(tc_fun(_189716, tc_HOL_Obool), _189720, _189722), -(c_Orderings_Oord__class_Oless(tc_fun(_189716, tc_HOL_Obool), _189718, _189722))], (3777 ^ _63126) ^ [_190087, _190089, _190091, _190093] : [class_Orderings_Oord(_190087), 3780 ^ _63126 : [(3781 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless(tc_fun(_190089, _190087), _190091, _190093), 3784 ^ _63126 : [(3785 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_190089, _190087), _190091, _190093))], (3787 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_190089, _190087), _190093, _190091)]]], (3789 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_fun(_190089, _190087), _190091, _190093)), c_Orderings_Oord__class_Oless__eq(tc_fun(_190089, _190087), _190091, _190093), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_190089, _190087), _190093, _190091))]]], (3799 ^ _63126) ^ [_190813, _190815, _190817, _190819] : [c_Orderings_Oord__class_Oless(tc_fun(_190813, tc_HOL_Obool), _190815, _190817), c_member(_190813, _190819, _190815), -(c_member(_190813, _190819, _190817))], (3809 ^ _63126) ^ [_191158, _191160, _191162] : [c_Wellfounded_OwfP(_191158, _191160), c_Orderings_Oord__class_Oless__eq(tc_fun(_191158, tc_fun(_191158, tc_HOL_Obool)), _191162, _191160), -(c_Wellfounded_OwfP(_191158, _191162))], (3819 ^ _63126) ^ [_191523, _191525, _191527, _191529, _191531] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(_191523, _191525), hAPP(_191523, _191527)), c_member(tc_prod(_191529, _191529), c_Product__Type_OPair(_191529, _191529, _191525, _191527), _191531), -(c_member(tc_prod(_191529, _191529), c_Product__Type_OPair(_191529, _191529, _191525, _191527), c_Wellfounded_Omlex__prod(_191529, _191523, _191531)))], (3829 ^ _63126) ^ [_191924, _191926, _191928] : [class_Orderings_Olinorder(_191924), -(c_Orderings_Oord__class_Oless__eq(_191924, _191926, _191928)), -(c_Orderings_Oord__class_Oless__eq(_191924, _191928, _191926))], (3839 ^ _63126) ^ [_192250, _192252, _192254] : [class_Orderings_Oorder(_192250), 3842 ^ _63126 : [(3843 ^ _63126) ^ [] : [_192252 = _192254, 3846 ^ _63126 : [(3847 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_192250, _192252, _192254))], (3849 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_192250, _192254, _192252))]]], (3851 ^ _63126) ^ [] : [-(_192252 = _192254), c_Orderings_Oord__class_Oless__eq(_192250, _192252, _192254), c_Orderings_Oord__class_Oless__eq(_192250, _192254, _192252)]]], (3861 ^ _63126) ^ [_192908, _192910, _192912] : [class_Orderings_Opreorder(_192908), _192910 = _192912, -(c_Orderings_Oord__class_Oless__eq(_192908, _192910, _192912))], (3871 ^ _63126) ^ [_193231, _193233, _193235] : [class_Orderings_Oorder(_193231), c_Orderings_Oord__class_Oless__eq(_193231, _193233, _193235), 3878 ^ _63126 : [(3879 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless__eq(_193231, _193235, _193233), -(_193235 = _193233)], (3885 ^ _63126) ^ [] : [_193235 = _193233, -(c_Orderings_Oord__class_Oless__eq(_193231, _193235, _193233))]]], (3891 ^ _63126) ^ [_193831, _193833, _193835, _193837] : [class_Orderings_Oord(_193831), _193833 = _193835, c_Orderings_Oord__class_Oless__eq(_193831, _193835, _193837), -(c_Orderings_Oord__class_Oless__eq(_193831, _193833, _193837))], (3905 ^ _63126) ^ [_194277, _194279, _194281, _194283] : [class_Orderings_Oorder(_194277), _194279 = _194281, c_Orderings_Oord__class_Oless__eq(_194277, _194283, _194281), -(c_Orderings_Oord__class_Oless__eq(_194277, _194283, _194279))], (3919 ^ _63126) ^ [_194723, _194725, _194727, _194729] : [class_Orderings_Oord(_194723), c_Orderings_Oord__class_Oless__eq(_194723, _194725, _194727), _194727 = _194729, -(c_Orderings_Oord__class_Oless__eq(_194723, _194725, _194729))], (3933 ^ _63126) ^ [_195169, _195171, _195173, _195175] : [class_Orderings_Oorder(_195169), c_Orderings_Oord__class_Oless__eq(_195169, _195171, _195173), _195171 = _195175, -(c_Orderings_Oord__class_Oless__eq(_195169, _195175, _195173))], (3947 ^ _63126) ^ [_195601, _195603, _195605] : [class_Orderings_Oorder(_195601), c_Orderings_Oord__class_Oless__eq(_195601, _195603, _195605), c_Orderings_Oord__class_Oless__eq(_195601, _195605, _195603), -(_195603 = _195605)], (3961 ^ _63126) ^ [_196033, _196035, _196037, _196039] : [class_Orderings_Opreorder(_196033), c_Orderings_Oord__class_Oless__eq(_196033, _196035, _196037), c_Orderings_Oord__class_Oless__eq(_196033, _196037, _196039), -(c_Orderings_Oord__class_Oless__eq(_196033, _196035, _196039))], (3975 ^ _63126) ^ [_196467, _196469, _196471] : [class_Orderings_Oorder(_196467), c_Orderings_Oord__class_Oless__eq(_196467, _196469, _196471), c_Orderings_Oord__class_Oless__eq(_196467, _196471, _196469), -(_196471 = _196469)], (3989 ^ _63126) ^ [_196899, _196901, _196903, _196905] : [class_Orderings_Oorder(_196899), c_Orderings_Oord__class_Oless__eq(_196899, _196901, _196903), c_Orderings_Oord__class_Oless__eq(_196899, _196905, _196901), -(c_Orderings_Oord__class_Oless__eq(_196899, _196905, _196903))], (4003 ^ _63126) ^ [_197333, _197335, _197337] : [class_Orderings_Olinorder(_197333), -(c_Orderings_Oord__class_Oless__eq(_197333, _197335, _197337)), -(c_Orderings_Oord__class_Oless__eq(_197333, _197337, _197335))], (4013 ^ _63126) ^ [_197647, _197649] : [class_Orderings_Opreorder(_197647), c_Orderings_Oord__class_Oless(_197647, _197649, _197649)], (4019 ^ _63126) ^ [_197872, _197874, _197876] : [class_Orderings_Olinorder(_197872), 4022 ^ _63126 : [(4033 ^ _63126) ^ [] : [4034 ^ _63126 : [(4035 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless(_197872, _197874, _197876)], (4037 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless(_197872, _197876, _197874)]], _197874 = _197876], (4023 ^ _63126) ^ [] : [-(_197874 = _197876), -(c_Orderings_Oord__class_Oless(_197872, _197874, _197876)), -(c_Orderings_Oord__class_Oless(_197872, _197876, _197874))]]], (4041 ^ _63126) ^ [_198532, _198534, _198536] : [class_Orderings_Olinorder(_198532), 4044 ^ _63126 : [(4055 ^ _63126) ^ [] : [4056 ^ _63126 : [(4057 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless(_198532, _198536, _198534)], (4059 ^ _63126) ^ [] : [_198534 = _198536]], c_Orderings_Oord__class_Oless(_198532, _198534, _198536)], (4045 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless(_198532, _198534, _198536)), -(c_Orderings_Oord__class_Oless(_198532, _198536, _198534)), -(_198534 = _198536)]]], (4063 ^ _63126) ^ [_199192, _199194, _199196] : [class_Orderings_Olinorder(_199192), -(c_Orderings_Oord__class_Oless(_199192, _199194, _199196)), -(_199194 = _199196), -(c_Orderings_Oord__class_Oless(_199192, _199196, _199194))], (4077 ^ _63126) ^ [_199612, _199614, _199616] : [class_Orderings_Olinorder(_199612), -(c_Orderings_Oord__class_Oless(_199612, _199614, _199616)), 4084 ^ _63126 : [(4085 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless(_199612, _199616, _199614)), -(_199616 = _199614)], (4091 ^ _63126) ^ [] : [_199616 = _199614, c_Orderings_Oord__class_Oless(_199612, _199616, _199614)]]], (4097 ^ _63126) ^ [_200203, _200205, _200207] : [class_Orderings_Olinorder(_200203), -(_200205 = _200207), -(c_Orderings_Oord__class_Oless(_200203, _200205, _200207)), -(c_Orderings_Oord__class_Oless(_200203, _200207, _200205))], (4111 ^ _63126) ^ [_200627, _200629, _200631] : [class_Orderings_Oorder(_200627), c_Orderings_Oord__class_Oless(_200627, _200629, _200631), _200629 = _200631], (4121 ^ _63126) ^ [_200951, _200953, _200955] : [class_Orderings_Opreorder(_200951), c_Orderings_Oord__class_Oless(_200951, _200953, _200955), c_Orderings_Oord__class_Oless(_200951, _200955, _200953)], (4131 ^ _63126) ^ [_201277, _201279, _201281] : [class_Orderings_Opreorder(_201277), c_Orderings_Oord__class_Oless(_201277, _201279, _201281), c_Orderings_Oord__class_Oless(_201277, _201281, _201279)], (4141 ^ _63126) ^ [_201603, _201605, _201607] : [class_Orderings_Oorder(_201603), c_Orderings_Oord__class_Oless(_201603, _201605, _201607), _201605 = _201607], (4151 ^ _63126) ^ [_201927, _201929, _201931] : [class_Orderings_Oorder(_201927), c_Orderings_Oord__class_Oless(_201927, _201929, _201931), _201931 = _201929], (4161 ^ _63126) ^ [_202251, _202253, _202255] : [class_Orderings_Opreorder(_202251), c_Orderings_Oord__class_Oless(_202251, _202253, _202255), c_Orderings_Oord__class_Oless(_202251, _202255, _202253)], (4171 ^ _63126) ^ [_202577, _202579, _202581] : [class_Orderings_Oorder(_202577), c_Orderings_Oord__class_Oless(_202577, _202579, _202581), c_Orderings_Oord__class_Oless(_202577, _202581, _202579)], (4181 ^ _63126) ^ [_202917, _202919, _202921, _202923] : [class_Orderings_Oord(_202917), _202919 = _202921, c_Orderings_Oord__class_Oless(_202917, _202921, _202923), -(c_Orderings_Oord__class_Oless(_202917, _202919, _202923))], (4195 ^ _63126) ^ [_203363, _203365, _203367, _203369] : [class_Orderings_Oorder(_203363), _203365 = _203367, c_Orderings_Oord__class_Oless(_203363, _203369, _203367), -(c_Orderings_Oord__class_Oless(_203363, _203369, _203365))], (4209 ^ _63126) ^ [_203809, _203811, _203813, _203815] : [class_Orderings_Oord(_203809), c_Orderings_Oord__class_Oless(_203809, _203811, _203813), _203813 = _203815, -(c_Orderings_Oord__class_Oless(_203809, _203811, _203815))], (4223 ^ _63126) ^ [_204255, _204257, _204259, _204261] : [class_Orderings_Oorder(_204255), c_Orderings_Oord__class_Oless(_204255, _204257, _204259), _204257 = _204261, -(c_Orderings_Oord__class_Oless(_204255, _204261, _204259))], (4237 ^ _63126) ^ [_204701, _204703, _204705, _204707] : [class_Orderings_Opreorder(_204701), c_Orderings_Oord__class_Oless(_204701, _204703, _204705), c_Orderings_Oord__class_Oless(_204701, _204705, _204707), -(c_Orderings_Oord__class_Oless(_204701, _204703, _204707))], (4251 ^ _63126) ^ [_205149, _205151, _205153, _205155] : [class_Orderings_Oorder(_205149), c_Orderings_Oord__class_Oless(_205149, _205151, _205153), c_Orderings_Oord__class_Oless(_205149, _205155, _205151), -(c_Orderings_Oord__class_Oless(_205149, _205155, _205153))], (4265 ^ _63126) ^ [_205583, _205585, _205587] : [class_Orderings_Opreorder(_205583), c_Orderings_Oord__class_Oless(_205583, _205585, _205587), c_Orderings_Oord__class_Oless(_205583, _205587, _205585)], (4275 ^ _63126) ^ [_205909, _205911, _205913] : [class_Orderings_Olinorder(_205909), -(c_Orderings_Oord__class_Oless(_205909, _205911, _205913)), -(_205911 = _205913), -(c_Orderings_Oord__class_Oless(_205909, _205913, _205911))], (4289 ^ _63126) ^ [_206333, _206335, _206337] : [c_Wellfounded_Owf(_206333, _206335), -(c_Wellfounded_Owf(_206333, c_Wellfounded_Omlex__prod(_206333, _206337, _206335)))], (4295 ^ _63126) ^ [_206571, _206573, _206575] : [class_Orderings_Olinorder(_206571), 4298 ^ _63126 : [(4299 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless(_206571, _206573, _206575)), -(c_Orderings_Oord__class_Oless__eq(_206571, _206575, _206573))], (4305 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless__eq(_206571, _206575, _206573), c_Orderings_Oord__class_Oless(_206571, _206573, _206575)]]], (4311 ^ _63126) ^ [_207067, _207069, _207071] : [class_Orderings_Olinorder(_207067), 4314 ^ _63126 : [(4315 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_207067, _207069, _207071)), -(c_Orderings_Oord__class_Oless(_207067, _207071, _207069))], (4321 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless(_207067, _207071, _207069), c_Orderings_Oord__class_Oless__eq(_207067, _207069, _207071)]]], (4327 ^ _63126) ^ [_207563, _207565, _207567] : [class_Orderings_Olinorder(_207563), -(c_Orderings_Oord__class_Oless__eq(_207563, _207565, _207567)), -(c_Orderings_Oord__class_Oless(_207563, _207567, _207565))], (4337 ^ _63126) ^ [_207889, _207891, _207893] : [class_Orderings_Oorder(_207889), 4340 ^ _63126 : [(4341 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless(_207889, _207891, _207893), 4344 ^ _63126 : [(4345 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_207889, _207891, _207893))], (4347 ^ _63126) ^ [] : [_207891 = _207893]]], (4349 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless(_207889, _207891, _207893)), c_Orderings_Oord__class_Oless__eq(_207889, _207891, _207893), -(_207891 = _207893)]]], (4359 ^ _63126) ^ [_208549, _208551, _208553] : [class_Orderings_Opreorder(_208549), 4362 ^ _63126 : [(4363 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless(_208549, _208551, _208553), 4366 ^ _63126 : [(4367 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_208549, _208551, _208553))], (4369 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless__eq(_208549, _208553, _208551)]]], (4371 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless(_208549, _208551, _208553)), c_Orderings_Oord__class_Oless__eq(_208549, _208551, _208553), -(c_Orderings_Oord__class_Oless__eq(_208549, _208553, _208551))]]], (4381 ^ _63126) ^ [_209212, _209214, _209216] : [class_Orderings_Oorder(_209212), 4384 ^ _63126 : [(4395 ^ _63126) ^ [] : [4396 ^ _63126 : [(4397 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless(_209212, _209214, _209216)], (4399 ^ _63126) ^ [] : [_209214 = _209216]], -(c_Orderings_Oord__class_Oless__eq(_209212, _209214, _209216))], (4385 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless__eq(_209212, _209214, _209216), -(c_Orderings_Oord__class_Oless(_209212, _209214, _209216)), -(_209214 = _209216)]]], (4403 ^ _63126) ^ [_209870, _209872, _209874] : [class_Orderings_Olinorder(_209870), -(c_Orderings_Oord__class_Oless(_209870, _209872, _209874)), -(c_Orderings_Oord__class_Oless__eq(_209870, _209874, _209872))], (4413 ^ _63126) ^ [_210198, _210200, _210202] : [class_Orderings_Olinorder(_210198), -(c_Orderings_Oord__class_Oless__eq(_210198, _210200, _210202)), -(c_Orderings_Oord__class_Oless(_210198, _210202, _210200))], (4423 ^ _63126) ^ [_210526, _210528, _210530] : [class_Orderings_Olinorder(_210526), -(c_Orderings_Oord__class_Oless(_210526, _210528, _210530)), 4430 ^ _63126 : [(4431 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless__eq(_210526, _210528, _210530), -(_210528 = _210530)], (4437 ^ _63126) ^ [] : [_210528 = _210530, -(c_Orderings_Oord__class_Oless__eq(_210526, _210528, _210530))]]], (4443 ^ _63126) ^ [_211115, _211117, _211119] : [class_Orderings_Oorder(_211115), -(_211117 = _211119), c_Orderings_Oord__class_Oless__eq(_211115, _211117, _211119), -(c_Orderings_Oord__class_Oless(_211115, _211117, _211119))], (4457 ^ _63126) ^ [_211536, _211538, _211540] : [class_Orderings_Oorder(_211536), -(_211538 = _211540), c_Orderings_Oord__class_Oless__eq(_211536, _211540, _211538), -(c_Orderings_Oord__class_Oless(_211536, _211540, _211538))], (4471 ^ _63126) ^ [_211957, _211959, _211961] : [class_Orderings_Olinorder(_211957), c_Orderings_Oord__class_Oless__eq(_211957, _211959, _211961), c_Orderings_Oord__class_Oless(_211957, _211961, _211959)], (4481 ^ _63126) ^ [_212283, _212285, _212287] : [class_Orderings_Opreorder(_212283), c_Orderings_Oord__class_Oless(_212283, _212285, _212287), -(c_Orderings_Oord__class_Oless__eq(_212283, _212285, _212287))], (4491 ^ _63126) ^ [_212608, _212610, _212612] : [class_Orderings_Olinorder(_212608), c_Orderings_Oord__class_Oless__eq(_212608, _212610, _212612), 4498 ^ _63126 : [(4499 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless(_212608, _212610, _212612)), -(_212610 = _212612)], (4505 ^ _63126) ^ [] : [_212610 = _212612, c_Orderings_Oord__class_Oless(_212608, _212610, _212612)]]], (4511 ^ _63126) ^ [_213196, _213198, _213200] : [class_Orderings_Oorder(_213196), c_Orderings_Oord__class_Oless__eq(_213196, _213198, _213200), -(c_Orderings_Oord__class_Oless(_213196, _213198, _213200)), -(_213198 = _213200)], (4525 ^ _63126) ^ [_213615, _213617, _213619] : [class_Orderings_Oorder(_213615), c_Orderings_Oord__class_Oless__eq(_213615, _213617, _213619), -(_213617 = _213619), -(c_Orderings_Oord__class_Oless(_213615, _213617, _213619))], (4539 ^ _63126) ^ [_214036, _214038, _214040] : [class_Orderings_Oorder(_214036), c_Orderings_Oord__class_Oless__eq(_214036, _214038, _214040), -(_214040 = _214038), -(c_Orderings_Oord__class_Oless(_214036, _214038, _214040))], (4553 ^ _63126) ^ [_214471, _214473, _214475, _214477] : [class_Orderings_Opreorder(_214471), c_Orderings_Oord__class_Oless(_214471, _214473, _214475), c_Orderings_Oord__class_Oless__eq(_214471, _214475, _214477), -(c_Orderings_Oord__class_Oless(_214471, _214473, _214477))], (4567 ^ _63126) ^ [_214919, _214921, _214923, _214925] : [class_Orderings_Oorder(_214919), c_Orderings_Oord__class_Oless(_214919, _214921, _214923), c_Orderings_Oord__class_Oless__eq(_214919, _214925, _214921), -(c_Orderings_Oord__class_Oless(_214919, _214925, _214923))], (4581 ^ _63126) ^ [_215367, _215369, _215371, _215373] : [class_Orderings_Opreorder(_215367), c_Orderings_Oord__class_Oless__eq(_215367, _215369, _215371), c_Orderings_Oord__class_Oless(_215367, _215371, _215373), -(c_Orderings_Oord__class_Oless(_215367, _215369, _215373))], (4595 ^ _63126) ^ [_215815, _215817, _215819, _215821] : [class_Orderings_Oorder(_215815), c_Orderings_Oord__class_Oless__eq(_215815, _215817, _215819), c_Orderings_Oord__class_Oless(_215815, _215821, _215817), -(c_Orderings_Oord__class_Oless(_215815, _215821, _215819))], (4609 ^ _63126) ^ [_216263, _216265, _216267, _216269] : [class_Orderings_Oord(_216263), 4612 ^ _63126 : [(4613 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_216265, _216263), _216267, _216269), 4616 ^ _63126 : [(4617 ^ _63126) ^ [_216522] : [-(c_Orderings_Oord__class_Oless__eq(_216263, hAPP(_216267, _216522), hAPP(_216269, _216522)))]]], (4619 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless__eq(_216263, hAPP(_216267, 4620 ^ [_216263, _216265, _216267, _216269]), hAPP(_216269, 4620 ^ [_216263, _216265, _216267, _216269])), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_216265, _216263), _216267, _216269))]]], (4626 ^ _63126) ^ [_216919, _216921] : [c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat, _216919, _216921), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _216919, _216921))], (4632 ^ _63126) ^ [_217095, _217097] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _217095, _217097), -(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat, _217095, _217097), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat)))], (4638 ^ _63126) ^ [_217350, _217352] : [c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat, _217350, _217352), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _217350, _217352))], (4644 ^ _63126) ^ [_217526, _217528] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _217526, _217528), -(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat, _217526, _217528), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat)))], (4650 ^ _63126) ^ [_217794, _217796, _217798, _217800, _217802] : [class_Groups_Oordered__ab__group__add(_217794), c_Groups_Ominus__class_Ominus(_217794, _217796, _217798) = c_Groups_Ominus__class_Ominus(_217794, _217800, _217802), 4657 ^ _63126 : [(4658 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless(_217794, _217796, _217798), -(c_Orderings_Oord__class_Oless(_217794, _217800, _217802))], (4664 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless(_217794, _217800, _217802), -(c_Orderings_Oord__class_Oless(_217794, _217796, _217798))]]], (4670 ^ _63126) ^ [_218479, _218481, _218483, _218485, _218487, _218489] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_218479, tc_fun(_218481, tc_HOL_Obool)), _218483, _218485), hBOOL(hAPP(hAPP(_218483, _218487), _218489)), -(hBOOL(hAPP(hAPP(_218485, _218487), _218489)))], (4680 ^ _63126) ^ [_218908, _218910, _218912, _218914, _218916, _218918] : [hBOOL(hAPP(hAPP(_218908, _218910), _218912)), c_Orderings_Oord__class_Oless__eq(tc_fun(_218914, tc_fun(_218916, tc_HOL_Obool)), _218908, _218918), -(hBOOL(hAPP(hAPP(_218918, _218910), _218912)))], (4690 ^ _63126) ^ [_219309, _219311, _219313, _219315] : [c_Orderings_Oord__class_Oless(tc_fun(_219309, tc_HOL_Obool), _219311, _219313), c_Orderings_Oord__class_Oless(tc_fun(_219309, tc_HOL_Obool), _219313, _219315), -(c_Orderings_Oord__class_Oless(tc_fun(_219309, tc_HOL_Obool), _219311, _219315))], (4700 ^ _63126) ^ [_219694, _219696, _219698, _219700, _219702] : [class_Groups_Oab__group__add(_219694), c_Groups_Ominus__class_Ominus(_219694, _219696, _219698) = c_Groups_Ominus__class_Ominus(_219694, _219700, _219702), 4707 ^ _63126 : [(4708 ^ _63126) ^ [] : [_219696 = _219698, -(_219700 = _219702)], (4714 ^ _63126) ^ [] : [_219700 = _219702, -(_219696 = _219698)]]], (4720 ^ _63126) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (4722 ^ _63126) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (4724 ^ _63126) ^ [_220465, _220467, _220469, _220471, _220473] : [class_Groups_Oordered__ab__group__add(_220465), c_Groups_Ominus__class_Ominus(_220465, _220467, _220469) = c_Groups_Ominus__class_Ominus(_220465, _220471, _220473), 4731 ^ _63126 : [(4732 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless__eq(_220465, _220467, _220469), -(c_Orderings_Oord__class_Oless__eq(_220465, _220471, _220473))], (4738 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless__eq(_220465, _220471, _220473), -(c_Orderings_Oord__class_Oless__eq(_220465, _220467, _220469))]]], (4744 ^ _63126) ^ [_221123, _221125] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _221123, _221125), 4747 ^ _63126 : [(4748 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _221123, _221125))], (4750 ^ _63126) ^ [] : [_221123 = _221125]]], (4752 ^ _63126) ^ [_221365, _221367] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _221365, _221367)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _221365, _221367), -(_221365 = _221367)], (4772 ^ _63126) ^ [_221958, _221960] : [4773 ^ _63126 : [(4774 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _221958, _221960)], (4776 ^ _63126) ^ [] : [_221958 = _221960]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _221958, _221960))], (4762 ^ _63126) ^ [_221702, _221704] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _221702, _221704), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _221702, _221704)), -(_221702 = _221704)], (4780 ^ _63126) ^ [_222218] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _222218, _222218)], (4792 ^ _63126) ^ [_222614, _222616] : [4793 ^ _63126 : [(4794 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _222614, _222616)], (4796 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _222616, _222614)]], _222614 = _222616], (4782 ^ _63126) ^ [_222355, _222357] : [-(_222355 = _222357), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _222355, _222357)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _222357, _222355))], (4800 ^ _63126) ^ [_222905, _222907] : [-(_222905 = _222907), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _222905, _222907)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _222907, _222905))], (4810 ^ _63126) ^ [_223184] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _223184, _223184)], (4812 ^ _63126) ^ [_223292, _223294] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _223292, _223294), _223294 = _223292], (4818 ^ _63126) ^ [_223505, _223507] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _223505, _223507), _223505 = _223507], (4824 ^ _63126) ^ [_223732, _223734, _223736] : [4825 ^ _63126 : [(4826 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _223732, _223734))], (4828 ^ _63126) ^ [] : [hBOOL(hAPP(hAPP(_223736, _223734), _223732))]], 4831 ^ _63126 : [(4832 ^ _63126) ^ [] : [-(_223732 = _223734)], (4834 ^ _63126) ^ [] : [hBOOL(hAPP(hAPP(_223736, _223734), _223732))]], 4837 ^ _63126 : [(4838 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _223734, _223732))], (4840 ^ _63126) ^ [] : [hBOOL(hAPP(hAPP(_223736, _223734), _223732))]], -(hBOOL(hAPP(hAPP(_223736, _223734), _223732)))], (4844 ^ _63126) ^ [_224423, _224425, _224427] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _224423, _224425), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _224423, _224427), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _224427, _224425), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _224427, _224423)))], (4854 ^ _63126) ^ [_224768, _224770, _224772] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _224768, _224770), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _224768, _224772), _224770))], (4860 ^ _63126) ^ [_224967] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _224967, _224967))], (4862 ^ _63126) ^ [_225075, _225077] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _225075, _225077)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _225077, _225075))], (4868 ^ _63126) ^ [_225290, _225292] : [_225290 = _225292, -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _225290, _225292))], (4874 ^ _63126) ^ [_225516, _225518, _225520] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _225516, _225518), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _225518, _225520), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _225516, _225520))], (4884 ^ _63126) ^ [_225831, _225833] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _225831, _225833), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _225833, _225831), -(_225831 = _225833)], (4894 ^ _63126) ^ [_226148, _226150, _226152] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _226148, _226150), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _226148, _226152), 4901 ^ _63126 : [(4902 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _226150, _226148), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _226152, _226148)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _226150, _226152))], (4908 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _226150, _226152), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _226150, _226148), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _226152, _226148)))]]], (4914 ^ _63126) ^ [_226765, _226767, _226769] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _226765, _226767), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _226765, _226769), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _226767, _226765), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _226769, _226765)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _226767, _226769))], (4924 ^ _63126) ^ [_227124, _227126, _227128] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _227124, _227126), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _227124, _227128), 4931 ^ _63126 : [(4932 ^ _63126) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _227126, _227124) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _227128, _227124), -(_227126 = _227128)], (4938 ^ _63126) ^ [] : [_227126 = _227128, -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _227126, _227124) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _227128, _227124))]]], (4944 ^ _63126) ^ [_227721, _227723] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _227721, _227723), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _227723, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _227723, _227721)) = _227721)], (4950 ^ _63126) ^ [_227963, _227965, _227967] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _227963, _227965), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _227963, _227967), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _227965, _227967)))], (4956 ^ _63126) ^ [_228213, _228215, _228217] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _228213, _228215), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _228217, _228215), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _228217, _228213)))], (4962 ^ _63126) ^ [_228434, _228436] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _228434, _228436), _228434))], (4964 ^ _63126) ^ [_228562, _228564, _228566] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _228562, _228564), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _228566, _228562), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _228562, _228566), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _228564, _228566)))], (4974 ^ _63126) ^ [_228907, _228909, _228911] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _228907, _228909), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _228907, _228911), 4981 ^ _63126 : [(4982 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _228909, _228907), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _228911, _228907)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _228909, _228911))], (4988 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _228909, _228911), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _228909, _228907), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _228911, _228907)))]]], (4994 ^ _63126) ^ [_229510, _229512] : [4995 ^ _63126 : [(4996 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _229510, _229512)], (4998 ^ _63126) ^ [] : [_229510 = _229512]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _229510, _229512))], (5002 ^ _63126) ^ [_229798, _229800] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _229798, _229800), -(_229798 = _229800), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _229798, _229800))], (5012 ^ _63126) ^ [_230104, _230106] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _230104, _230106), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _230104, _230106))], (5018 ^ _63126) ^ [_230346, _230348, _230350, _230352] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _230346, _230348), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _230350, _230352), -(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat, _230346, _230350), c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat, _230348, _230352)), c_FunDef_Opair__less))], (5028 ^ _63126) ^ [_230714, _230716, _230718, _230720] : [-(c_Relation_OField(_230714, c_Set_Oinsert(tc_prod(_230714, _230714), c_Product__Type_OPair(_230714, _230714, _230716, _230718), _230720)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_230714, tc_HOL_Obool), c_Set_Oinsert(_230714, _230716, c_Set_Oinsert(_230714, _230718, c_Orderings_Obot__class_Obot(tc_fun(_230714, tc_HOL_Obool)))), c_Relation_OField(_230714, _230720)))], (5030 ^ _63126) ^ [_230836] : [-(c_Wellfounded_Owf(_230836, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_230836, _230836), tc_HOL_Obool))))], (5032 ^ _63126) ^ [_230935, _230937] : [c_member(_230935, _230937, c_Orderings_Obot__class_Obot(tc_fun(_230935, tc_HOL_Obool)))], (5034 ^ _63126) ^ [_231035, _231037] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_231035, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(_231035, tc_HOL_Obool)), _231037))], (5036 ^ _63126) ^ [_231152, _231154, _231156] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _231152, _231154), _231156) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _231152, _231156), _231154))], (5038 ^ _63126) ^ [_231278, _231280, _231282] : [-(c_Set_Oinsert(_231278, _231280, _231282) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_231278, tc_HOL_Obool), c_Set_Oinsert(_231278, _231280, c_Orderings_Obot__class_Obot(tc_fun(_231278, tc_HOL_Obool))), _231282))], (5040 ^ _63126) ^ [_231408, _231410, _231412] : [-(c_Set_Oinsert(_231408, _231410, c_Groups_Ominus__class_Ominus(tc_fun(_231408, tc_HOL_Obool), _231412, c_Set_Oinsert(_231408, _231410, c_Orderings_Obot__class_Obot(tc_fun(_231408, tc_HOL_Obool))))) = c_Set_Oinsert(_231408, _231410, _231412))], (5042 ^ _63126) ^ [_231556, _231558, _231560, _231562] : [-(c_Groups_Ominus__class_Ominus(tc_fun(_231556, tc_HOL_Obool), _231558, c_Set_Oinsert(_231556, _231560, _231562)) = c_Groups_Ominus__class_Ominus(tc_fun(_231556, tc_HOL_Obool), c_Groups_Ominus__class_Ominus(tc_fun(_231556, tc_HOL_Obool), _231558, c_Set_Oinsert(_231556, _231560, c_Orderings_Obot__class_Obot(tc_fun(_231556, tc_HOL_Obool)))), _231562))], (5044 ^ _63126) ^ [_231716, _231718, _231720, _231722] : [-(c_Groups_Ominus__class_Ominus(tc_fun(_231716, tc_HOL_Obool), _231718, c_Set_Oinsert(_231716, _231720, _231722)) = c_Groups_Ominus__class_Ominus(tc_fun(_231716, tc_HOL_Obool), c_Groups_Ominus__class_Ominus(tc_fun(_231716, tc_HOL_Obool), _231718, _231722), c_Set_Oinsert(_231716, _231720, c_Orderings_Obot__class_Obot(tc_fun(_231716, tc_HOL_Obool)))))], (5046 ^ _63126) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (5048 ^ _63126) ^ [_231945, _231947] : [-(c_member(_231945, 5049 ^ [_231945, _231947], _231947)), -(_231947 = c_Orderings_Obot__class_Obot(tc_fun(_231945, tc_HOL_Obool)))], (5055 ^ _63126) ^ [_232182, _232184] : [_232184 = c_Orderings_Obot__class_Obot(tc_fun(_232182, tc_HOL_Obool)), 5058 ^ _63126 : [(5059 ^ _63126) ^ [_232310] : [c_member(_232182, _232310, _232184)]]], (5061 ^ _63126) ^ [_232458, _232460] : [5062 ^ _63126 : [(5063 ^ _63126) ^ [_232536] : [c_member(_232458, _232536, _232460)]], _232460 = c_Orderings_Obot__class_Obot(tc_fun(_232458, tc_HOL_Obool))], (5067 ^ _63126) ^ [_232655, _232657] : [-(_232657 = c_Orderings_Obot__class_Obot(tc_fun(_232655, tc_HOL_Obool))), -(c_member(_232655, 5070 ^ [_232655, _232657], _232657))], (5074 ^ _63126) ^ [_232924, _232926] : [c_member(_232924, _232926, c_Orderings_Obot__class_Obot(tc_fun(_232924, tc_HOL_Obool)))], (5076 ^ _63126) ^ [_233053, _233055, _233057] : [_233053 = c_Orderings_Obot__class_Obot(tc_fun(_233055, tc_HOL_Obool)), c_member(_233055, _233057, _233053)], (5082 ^ _63126) ^ [_233296, _233298, _233300] : [class_Orderings_Obot(_233296), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_233298, _233296)), _233300) = c_Orderings_Obot__class_Obot(_233296))], (5088 ^ _63126) ^ [_233501] : [-(c_Relation_Oantisym(_233501, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_233501, _233501), tc_HOL_Obool))))], (5090 ^ _63126) ^ [_233601, _233603] : [-(c_Relation_Ototal__on(_233601, c_Orderings_Obot__class_Obot(tc_fun(_233601, tc_HOL_Obool)), _233603))], (5092 ^ _63126) ^ [_233730, _233732, _233734] : [class_Lattices_Obounded__lattice__bot(_233730), 5095 ^ _63126 : [(5096 ^ _63126) ^ [] : [c_Lattices_Osemilattice__sup__class_Osup(_233730, _233732, _233734) = c_Orderings_Obot__class_Obot(_233730), 5099 ^ _63126 : [(5100 ^ _63126) ^ [] : [-(_233732 = c_Orderings_Obot__class_Obot(_233730))], (5102 ^ _63126) ^ [] : [-(_233734 = c_Orderings_Obot__class_Obot(_233730))]]], (5104 ^ _63126) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(_233730, _233732, _233734) = c_Orderings_Obot__class_Obot(_233730)), _233732 = c_Orderings_Obot__class_Obot(_233730), _233734 = c_Orderings_Obot__class_Obot(_233730)]]], (5114 ^ _63126) ^ [_234398, _234400] : [class_Lattices_Obounded__lattice__bot(_234398), -(c_Lattices_Osemilattice__sup__class_Osup(_234398, _234400, c_Orderings_Obot__class_Obot(_234398)) = _234400)], (5120 ^ _63126) ^ [_234618, _234620] : [class_Lattices_Obounded__lattice__bot(_234618), -(c_Lattices_Osemilattice__sup__class_Osup(_234618, c_Orderings_Obot__class_Obot(_234618), _234620) = _234620)], (5126 ^ _63126) ^ [_234809] : [-(c_Order__Relation_Opartial__order__on(_234809, c_Orderings_Obot__class_Obot(tc_fun(_234809, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_234809, _234809), tc_HOL_Obool))))], (5128 ^ _63126) ^ [_234901] : [-(c_Relation_OId__on(_234901, c_Orderings_Obot__class_Obot(tc_fun(_234901, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_234901, _234901), tc_HOL_Obool)))], (5130 ^ _63126) ^ [_234995] : [-(c_Order__Relation_Opreorder__on(_234995, c_Orderings_Obot__class_Obot(tc_fun(_234995, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_234995, _234995), tc_HOL_Obool))))], (5132 ^ _63126) ^ [_235159, _235161, _235163] : [c_Relation_ODomain(_235159, _235161, _235163) = c_Orderings_Obot__class_Obot(tc_fun(_235159, tc_HOL_Obool)), -(_235163 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_235159, _235161), tc_HOL_Obool)))], (5138 ^ _63126) ^ [_235361, _235363, _235365] : [_235365 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_235361, _235363), tc_HOL_Obool)), -(c_Relation_ODomain(_235361, _235363, _235365) = c_Orderings_Obot__class_Obot(tc_fun(_235361, tc_HOL_Obool)))], (5144 ^ _63126) ^ [_235598, _235600] : [-(c_Relation_ODomain(_235598, _235600, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_235598, _235600), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_235598, tc_HOL_Obool)))], (5146 ^ _63126) ^ [_235767, _235769, _235771] : [c_Relation_ORange(_235767, _235769, _235771) = c_Orderings_Obot__class_Obot(tc_fun(_235769, tc_HOL_Obool)), -(_235771 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_235767, _235769), tc_HOL_Obool)))], (5152 ^ _63126) ^ [_235969, _235971, _235973] : [_235973 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_235969, _235971), tc_HOL_Obool)), -(c_Relation_ORange(_235969, _235971, _235973) = c_Orderings_Obot__class_Obot(tc_fun(_235971, tc_HOL_Obool)))], (5158 ^ _63126) ^ [_236206, _236208] : [-(c_Relation_ORange(_236206, _236208, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_236206, _236208), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_236208, tc_HOL_Obool)))], (5160 ^ _63126) ^ [_236303] : [-(c_Relation_Orefl__on(_236303, c_Orderings_Obot__class_Obot(tc_fun(_236303, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_236303, _236303), tc_HOL_Obool))))], (5162 ^ _63126) ^ [_236395] : [-(c_Order__Relation_Olinear__order__on(_236395, c_Orderings_Obot__class_Obot(tc_fun(_236395, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_236395, _236395), tc_HOL_Obool))))], (5164 ^ _63126) ^ [_236501, _236503] : [-(c_Groups_Ominus__class_Ominus(tc_fun(_236501, tc_HOL_Obool), _236503, _236503) = c_Orderings_Obot__class_Obot(tc_fun(_236501, tc_HOL_Obool)))], (5166 ^ _63126) ^ [_236607, _236609] : [-(c_Groups_Ominus__class_Ominus(tc_fun(_236607, tc_HOL_Obool), _236609, c_Orderings_Obot__class_Obot(tc_fun(_236607, tc_HOL_Obool))) = _236609)], (5168 ^ _63126) ^ [_236713, _236715] : [-(c_Groups_Ominus__class_Ominus(tc_fun(_236713, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(_236713, tc_HOL_Obool)), _236715) = c_Orderings_Obot__class_Obot(tc_fun(_236713, tc_HOL_Obool)))], (5170 ^ _63126) ^ [_236882, _236884, _236886] : [c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_236882, tc_HOL_Obool), _236884, _236886) = c_Orderings_Obot__class_Obot(tc_fun(_236882, tc_HOL_Obool)), 5173 ^ _63126 : [(5174 ^ _63126) ^ [] : [-(_236884 = c_Orderings_Obot__class_Obot(tc_fun(_236882, tc_HOL_Obool)))], (5176 ^ _63126) ^ [] : [-(_236886 = c_Orderings_Obot__class_Obot(tc_fun(_236882, tc_HOL_Obool)))]]], (5178 ^ _63126) ^ [_237171, _237173, _237175] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_237171, tc_HOL_Obool), _237173, _237175) = c_Orderings_Obot__class_Obot(tc_fun(_237171, tc_HOL_Obool))), _237173 = c_Orderings_Obot__class_Obot(tc_fun(_237171, tc_HOL_Obool)), _237175 = c_Orderings_Obot__class_Obot(tc_fun(_237171, tc_HOL_Obool))], (5188 ^ _63126) ^ [_237511, _237513] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_237511, tc_HOL_Obool), _237513, c_Orderings_Obot__class_Obot(tc_fun(_237511, tc_HOL_Obool))) = _237513)], (5190 ^ _63126) ^ [_237617, _237619] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_237617, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(_237617, tc_HOL_Obool)), _237619) = _237619)], (5192 ^ _63126) ^ [_237752, _237754, _237756] : [c_Set_Oinsert(_237752, _237754, c_Orderings_Obot__class_Obot(tc_fun(_237752, tc_HOL_Obool))) = c_Set_Oinsert(_237752, _237756, c_Orderings_Obot__class_Obot(tc_fun(_237752, tc_HOL_Obool))), -(_237754 = _237756)], (5198 ^ _63126) ^ [_238075, _238077, _238079, _238081, _238083] : [c_Set_Oinsert(_238075, _238077, c_Set_Oinsert(_238075, _238079, c_Orderings_Obot__class_Obot(tc_fun(_238075, tc_HOL_Obool)))) = c_Set_Oinsert(_238075, _238081, c_Set_Oinsert(_238075, _238083, c_Orderings_Obot__class_Obot(tc_fun(_238075, tc_HOL_Obool)))), 5203 ^ _63126 : [(5204 ^ _63126) ^ [] : [-(_238077 = _238081)], (5206 ^ _63126) ^ [] : [-(_238079 = _238083)]], 5207 ^ _63126 : [(5208 ^ _63126) ^ [] : [-(_238077 = _238083)], (5210 ^ _63126) ^ [] : [-(_238079 = _238081)]]], (5212 ^ _63126) ^ [_238571, _238573, _238575, _238577, _238579] : [-(c_Set_Oinsert(_238571, _238573, c_Set_Oinsert(_238571, _238575, c_Orderings_Obot__class_Obot(tc_fun(_238571, tc_HOL_Obool)))) = c_Set_Oinsert(_238571, _238577, c_Set_Oinsert(_238571, _238579, c_Orderings_Obot__class_Obot(tc_fun(_238571, tc_HOL_Obool))))), 5213 ^ _63126 : [(5214 ^ _63126) ^ [] : [_238573 = _238577, _238575 = _238579], (5220 ^ _63126) ^ [] : [_238573 = _238579, _238575 = _238577]]], (5228 ^ _63126) ^ [_239133, _239135, _239137] : [c_Set_Oinsert(_239133, _239135, _239137) = c_Orderings_Obot__class_Obot(tc_fun(_239133, tc_HOL_Obool))], (5230 ^ _63126) ^ [_239251, _239253, _239255] : [c_Orderings_Obot__class_Obot(tc_fun(_239251, tc_HOL_Obool)) = c_Set_Oinsert(_239251, _239253, _239255)], (5232 ^ _63126) ^ [_239342] : [-(c_Relation_OField(_239342, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_239342, _239342), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_239342, tc_HOL_Obool)))], (5234 ^ _63126) ^ [_239436] : [-(c_Order__Relation_Owell__order__on(_239436, c_Orderings_Obot__class_Obot(tc_fun(_239436, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_239436, _239436), tc_HOL_Obool))))], (5236 ^ _63126) ^ [_239571, _239573, _239575] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_239571, tc_HOL_Obool), _239573, c_Set_Oinsert(_239571, _239575, c_Orderings_Obot__class_Obot(tc_fun(_239571, tc_HOL_Obool)))), -(_239573 = c_Orderings_Obot__class_Obot(tc_fun(_239571, tc_HOL_Obool))), -(_239573 = c_Set_Oinsert(_239571, _239575, c_Orderings_Obot__class_Obot(tc_fun(_239571, tc_HOL_Obool))))], (5246 ^ _63126) ^ [_239949, _239951, _239953] : [c_member(_239949, _239951, c_Set_Oinsert(_239949, _239953, c_Orderings_Obot__class_Obot(tc_fun(_239949, tc_HOL_Obool)))), -(_239951 = _239953)], (5252 ^ _63126) ^ [_240228, _240230, _240232] : [c_member(_240228, _240230, c_Set_Oinsert(_240228, _240232, c_Orderings_Obot__class_Obot(tc_fun(_240228, tc_HOL_Obool)))), -(_240230 = _240232)], (5258 ^ _63126) ^ [_240416, _240418, _240420] : [_240418 = _240420, -(c_member(_240416, _240418, c_Set_Oinsert(_240416, _240420, c_Orderings_Obot__class_Obot(tc_fun(_240416, tc_HOL_Obool)))))], (5264 ^ _63126) ^ [_240625] : [-(c_Transitive__Closure_Otrancl(_240625, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_240625, _240625), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_240625, _240625), tc_HOL_Obool)))], (5266 ^ _63126) ^ [_240751, _240753] : [class_Orderings_Obot(_240751), -(c_Orderings_Oord__class_Oless__eq(_240751, c_Orderings_Obot__class_Obot(_240751), _240753))], (5272 ^ _63126) ^ [_240979, _240981, _240983] : [_240979 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_240981, _240981), tc_HOL_Obool)), -(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_240981, _240981), tc_HOL_Obool), _240979, _240983))], (5278 ^ _63126) ^ [_241254, _241256] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_241254, tc_HOL_Obool), _241256, c_Orderings_Obot__class_Obot(tc_fun(_241254, tc_HOL_Obool))), -(_241256 = c_Orderings_Obot__class_Obot(tc_fun(_241254, tc_HOL_Obool)))], (5284 ^ _63126) ^ [_241444, _241446] : [_241446 = c_Orderings_Obot__class_Obot(tc_fun(_241444, tc_HOL_Obool)), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_241444, tc_HOL_Obool), _241446, c_Orderings_Obot__class_Obot(tc_fun(_241444, tc_HOL_Obool))))], (5290 ^ _63126) ^ [_241668, _241670] : [c_Orderings_Oord__class_Oless(tc_fun(_241668, tc_HOL_Obool), _241670, c_Orderings_Obot__class_Obot(tc_fun(_241668, tc_HOL_Obool)))], (5292 ^ _63126) ^ [_241757] : [-(c_Transitive__Closure_Ortrancl(_241757, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_241757, _241757), tc_HOL_Obool))) = c_Relation_OId(_241757))], (5294 ^ _63126) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (5296 ^ _63126) ^ [_241944, _241946, _241948] : [c_member(_241944, _241946, _241948), -(c_Set_Oinsert(_241944, _241946, c_Groups_Ominus__class_Ominus(tc_fun(_241944, tc_HOL_Obool), _241948, c_Set_Oinsert(_241944, _241946, c_Orderings_Obot__class_Obot(tc_fun(_241944, tc_HOL_Obool))))) = _241948)], (5302 ^ _63126) ^ [_242216, _242218, _242220] : [-(c_member(_242216, _242218, _242220)), -(c_Groups_Ominus__class_Ominus(tc_fun(_242216, tc_HOL_Obool), c_Set_Oinsert(_242216, _242218, _242220), c_Set_Oinsert(_242216, _242218, c_Orderings_Obot__class_Obot(tc_fun(_242216, tc_HOL_Obool)))) = _242220)], (5324 ^ _63126) ^ [_243052, _243054, _243056, _243058] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_243052, tc_HOL_Obool), _243054, c_Set_Oinsert(_243052, _243056, _243058))), 5327 ^ _63126 : [(5328 ^ _63126) ^ [] : [-(c_member(_243052, _243056, _243054))], (5330 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_243052, tc_HOL_Obool), c_Groups_Ominus__class_Ominus(tc_fun(_243052, tc_HOL_Obool), _243054, c_Set_Oinsert(_243052, _243056, c_Orderings_Obot__class_Obot(tc_fun(_243052, tc_HOL_Obool)))), _243058)]], 5331 ^ _63126 : [(5332 ^ _63126) ^ [] : [c_member(_243052, _243056, _243054)], (5334 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_243052, tc_HOL_Obool), _243054, _243058)]]], (5308 ^ _63126) ^ [_242534, _242536, _242538, _242540] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_242534, tc_HOL_Obool), _242536, c_Set_Oinsert(_242534, _242538, _242540)), 5311 ^ _63126 : [(5312 ^ _63126) ^ [] : [c_member(_242534, _242538, _242536), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_242534, tc_HOL_Obool), c_Groups_Ominus__class_Ominus(tc_fun(_242534, tc_HOL_Obool), _242536, c_Set_Oinsert(_242534, _242538, c_Orderings_Obot__class_Obot(tc_fun(_242534, tc_HOL_Obool)))), _242540))], (5318 ^ _63126) ^ [] : [-(c_member(_242534, _242538, _242536)), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_242534, tc_HOL_Obool), _242536, _242540))]]], (5338 ^ _63126) ^ [_243628, _243630, _243632, _243634] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_243628, tc_HOL_Obool), c_Groups_Ominus__class_Ominus(tc_fun(_243628, tc_HOL_Obool), _243630, c_Set_Oinsert(_243628, _243632, c_Orderings_Obot__class_Obot(tc_fun(_243628, tc_HOL_Obool)))), _243634), c_member(_243628, _243632, _243630), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_243628, tc_HOL_Obool), _243630, c_Set_Oinsert(_243628, _243632, _243634)))], (5348 ^ _63126) ^ [_244033, _244035, _244037, _244039] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _244033, _244035), -(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat, _244033, _244037), c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat, _244035, _244039)), c_FunDef_Opair__less))], (5380 ^ _63126) ^ [_245152, _245154, _245156, _245158] : [-(c_Orderings_Oord__class_Oless(tc_fun(_245152, tc_HOL_Obool), _245154, c_Set_Oinsert(_245152, _245156, _245158))), 5383 ^ _63126 : [(5384 ^ _63126) ^ [] : [-(c_member(_245152, _245156, _245158))], (5386 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless(tc_fun(_245152, tc_HOL_Obool), _245154, _245158)]], 5387 ^ _63126 : [(5388 ^ _63126) ^ [] : [c_member(_245152, _245156, _245158)], (5390 ^ _63126) ^ [] : [5391 ^ _63126 : [(5392 ^ _63126) ^ [] : [-(c_member(_245152, _245156, _245154))], (5394 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless(tc_fun(_245152, tc_HOL_Obool), c_Groups_Ominus__class_Ominus(tc_fun(_245152, tc_HOL_Obool), _245154, c_Set_Oinsert(_245152, _245156, c_Orderings_Obot__class_Obot(tc_fun(_245152, tc_HOL_Obool)))), _245158)]], 5395 ^ _63126 : [(5396 ^ _63126) ^ [] : [c_member(_245152, _245156, _245154)], (5398 ^ 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[c_member(_252353, _252355, c_Relation_OImage(_252357, _252353, _252359, _252361)), 5570 ^ _63126 : [(5571 ^ _63126) ^ [] : [-(c_member(_252357, 5569 ^ [_252353, _252355, _252357, _252359, _252361], _252361))], (5573 ^ _63126) ^ [] : [-(c_member(tc_prod(_252357, _252353), c_Product__Type_OPair(_252357, _252353, 5569 ^ [_252353, _252355, _252357, _252359, _252361], _252355), _252359))]]], (5575 ^ _63126) ^ [_252750, _252752, _252754, _252756, _252758] : [-(c_member(_252750, _252752, c_Relation_OImage(_252754, _252750, _252756, _252758))), 5576 ^ _63126 : [(5577 ^ _63126) ^ [_252864] : [c_member(_252754, _252864, _252758), c_member(tc_prod(_252754, _252750), c_Product__Type_OPair(_252754, _252750, _252864, _252752), _252756)]]], (5585 ^ _63126) ^ [_253248, _253250, _253252, _253254, _253256, _253258] : [c_member(_253248, _253250, _253252), c_member(tc_prod(_253248, _253254), c_Product__Type_OPair(_253248, _253254, _253250, _253256), _253258), -(c_member(_253254, _253256, c_Relation_OImage(_253248, _253254, _253258, _253252)))], (5595 ^ _63126) ^ [_253604, _253606] : [-(c_Relation_OImage(_253604, _253604, c_Relation_OId(_253604), _253606) = _253606)], (5597 ^ _63126) ^ [_253776, _253778, _253780, _253782, _253784, _253786] : [c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_253776, _253778), tc_HOL_Obool), _253780, _253782), c_Orderings_Oord__class_Oless__eq(tc_fun(_253776, tc_HOL_Obool), _253784, _253786), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_253778, tc_HOL_Obool), c_Relation_OImage(_253776, _253778, _253780, _253784), c_Relation_OImage(_253776, _253778, _253782, _253786)))], (5607 ^ _63126) ^ [_254179, _254181, _254183] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_254179, tc_HOL_Obool), c_Relation_OImage(_254179, _254179, _254181, _254183), _254183), -(c_Relation_OImage(_254179, _254179, c_Transitive__Closure_Ortrancl(_254179, _254181), _254183) = _254183)], (5613 ^ _63126) ^ [_254428, _254430, _254432] : [-(c_Relation_OImage(_254428, _254430, _254432, c_Orderings_Obot__class_Obot(tc_fun(_254428, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_254430, tc_HOL_Obool)))], (5615 ^ _63126) ^ [_254581, _254583, _254585, _254587, _254589] : [-(c_Relation_OImage(_254581, _254583, _254585, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_254581, tc_HOL_Obool), _254587, _254589)) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_254583, tc_HOL_Obool), c_Relation_OImage(_254581, _254583, _254585, _254587), c_Relation_OImage(_254581, _254583, _254585, _254589)))], (5617 ^ _63126) ^ [_254752, _254754, _254756, _254758, _254760] : [-(c_Relation_OImage(_254752, _254754, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_254752, _254754), tc_HOL_Obool), _254756, _254758), _254760) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_254754, tc_HOL_Obool), c_Relation_OImage(_254752, _254754, _254756, _254760), c_Relation_OImage(_254752, _254754, _254758, _254760)))], (5619 ^ _63126) ^ [_254970, _254972, _254974, _254976, _254978] : [c_member(_254970, _254972, c_Relation_OImage(_254974, _254970, _254976, c_Set_Oinsert(_254974, _254978, c_Orderings_Obot__class_Obot(tc_fun(_254974, tc_HOL_Obool))))), -(c_member(tc_prod(_254974, _254970), c_Product__Type_OPair(_254974, _254970, _254978, _254972), _254976))], (5625 ^ _63126) ^ [_255198, _255200, _255202, _255204, _255206] : [c_member(tc_prod(_255202, _255198), c_Product__Type_OPair(_255202, _255198, _255206, _255200), _255204), -(c_member(_255198, _255200, c_Relation_OImage(_255202, _255198, _255204, c_Set_Oinsert(_255202, _255206, c_Orderings_Obot__class_Obot(tc_fun(_255202, tc_HOL_Obool))))))], (5631 ^ _63126) ^ [_255504, _255506, _255508, _255510] : [c_Order__Relation_Opartial__order__on(_255504, c_Relation_OField(_255504, _255506), _255506), c_member(_255504, _255508, c_Relation_OField(_255504, _255506)), c_member(_255504, _255510, c_Relation_OField(_255504, _255506)), 5642 ^ _63126 : [(5643 ^ _63126) ^ [] : [c_Relation_OImage(_255504, _255504, _255506, c_Set_Oinsert(_255504, _255508, c_Orderings_Obot__class_Obot(tc_fun(_255504, tc_HOL_Obool)))) = c_Relation_OImage(_255504, _255504, _255506, c_Set_Oinsert(_255504, _255510, c_Orderings_Obot__class_Obot(tc_fun(_255504, tc_HOL_Obool)))), -(_255508 = _255510)], (5649 ^ _63126) ^ [] : [_255508 = _255510, -(c_Relation_OImage(_255504, _255504, _255506, c_Set_Oinsert(_255504, _255508, c_Orderings_Obot__class_Obot(tc_fun(_255504, tc_HOL_Obool)))) = c_Relation_OImage(_255504, _255504, _255506, c_Set_Oinsert(_255504, _255510, c_Orderings_Obot__class_Obot(tc_fun(_255504, tc_HOL_Obool)))))]]], (5655 ^ _63126) ^ [_256326, _256328, _256330, _256332] : [c_Relation_Orefl__on(_256326, c_Relation_OField(_256326, _256328), _256328), c_Relation_Oantisym(_256326, _256328), c_member(_256326, _256330, c_Relation_OField(_256326, _256328)), c_member(_256326, _256332, c_Relation_OField(_256326, _256328)), 5670 ^ _63126 : [(5671 ^ _63126) ^ [] : [c_Relation_OImage(_256326, _256326, _256328, c_Set_Oinsert(_256326, _256330, c_Orderings_Obot__class_Obot(tc_fun(_256326, tc_HOL_Obool)))) = c_Relation_OImage(_256326, _256326, _256328, c_Set_Oinsert(_256326, _256332, c_Orderings_Obot__class_Obot(tc_fun(_256326, tc_HOL_Obool)))), -(_256330 = _256332)], (5677 ^ _63126) ^ [] : [_256330 = _256332, -(c_Relation_OImage(_256326, _256326, _256328, c_Set_Oinsert(_256326, _256330, c_Orderings_Obot__class_Obot(tc_fun(_256326, tc_HOL_Obool)))) = c_Relation_OImage(_256326, _256326, _256328, c_Set_Oinsert(_256326, _256332, c_Orderings_Obot__class_Obot(tc_fun(_256326, tc_HOL_Obool)))))]]], (5683 ^ _63126) ^ [] : [-(c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_HOL_Obool), tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_HOL_Obool), c_FunDef_Omin__strict, c_FunDef_Omin__weak)))], (5685 ^ _63126) ^ [_257298, _257300, _257302, _257304] : [c_Order__Relation_Opreorder__on(_257298, c_Relation_OField(_257298, _257300), _257300), c_Orderings_Oord__class_Oless__eq(tc_fun(_257298, tc_HOL_Obool), _257302, c_Relation_OField(_257298, _257300)), c_Orderings_Oord__class_Oless__eq(tc_fun(_257298, tc_HOL_Obool), _257304, c_Relation_OField(_257298, _257300)), 5696 ^ _63126 : [(5697 ^ _63126) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_257298, tc_HOL_Obool), c_Relation_OImage(_257298, _257298, _257300, _257302), c_Relation_OImage(_257298, _257298, _257300, _257304)), 5700 ^ _63126 : [(5701 ^ _63126) ^ [_257837] : [c_member(_257298, _257837, _257302), 5705 ^ _63126 : [(5706 ^ _63126) ^ [] : [-(c_member(_257298, 5704 ^ [_257298, _257300, _257302, _257304, _257837], _257304))], (5708 ^ _63126) ^ [] : [-(c_member(tc_prod(_257298, _257298), c_Product__Type_OPair(_257298, _257298, 5704 ^ [_257298, _257300, _257302, _257304, _257837], _257837), _257300))]]]]], (5710 ^ _63126) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_257298, tc_HOL_Obool), c_Relation_OImage(_257298, _257298, _257300, _257302), c_Relation_OImage(_257298, _257298, _257300, _257304))), 5712 ^ _63126 : [(5713 ^ _63126) ^ [] : [-(c_member(_257298, 5711 ^ [_257298, _257300, _257302, _257304], _257302))], (5715 ^ _63126) ^ [_258452] : [c_member(_257298, _258452, _257304), c_member(tc_prod(_257298, _257298), c_Product__Type_OPair(_257298, _257298, _258452, 5711 ^ [_257298, _257300, _257302, _257304]), _257300)]]]]], (5723 ^ _63126) ^ [_258914, _258916, _258918, _258920, _258922, _258924, _258926] : [c_Nitpick_Ofold__graph_H(_258914, _258916, _258918, _258920, _258922, hAPP(hAPP(_258918, _258924), _258926)), 5728 ^ _63126 : [(5729 ^ _63126) ^ [] : [-(_258922 = c_Orderings_Obot__class_Obot(tc_fun(_258914, tc_HOL_Obool)))], (5731 ^ _63126) ^ [] : [-(hAPP(hAPP(_258918, _258924), _258926) = _258920)]], 5734 ^ _63126 : [(5735 ^ _63126) ^ [] : [-(hAPP(hAPP(_258918, _258924), _258926) = hAPP(hAPP(_258918, 5732 ^ [_258914, _258916, _258918, _258920, _258922, _258924, _258926]), 5733 ^ [_258914, _258916, _258918, _258920, _258922, _258924, _258926]))], (5737 ^ _63126) ^ [] : [-(c_member(_258914, 5732 ^ [_258914, _258916, _258918, _258920, _258922, _258924, _258926], _258922))], (5739 ^ _63126) ^ [] : [-(c_Nitpick_Ofold__graph_H(_258914, _258916, _258918, _258920, c_Groups_Ominus__class_Ominus(tc_fun(_258914, tc_HOL_Obool), _258922, c_Set_Oinsert(_258914, 5732 ^ [_258914, _258916, _258918, _258920, _258922, _258924, _258926], c_Orderings_Obot__class_Obot(tc_fun(_258914, tc_HOL_Obool)))), 5733 ^ [_258914, _258916, _258918, _258920, _258922, _258924, _258926]))]]], (5741 ^ _63126) ^ [_259949, _259951, _259953, _259955, _259957, _259959, _259961] : [-(c_Nitpick_Ofold__graph_H(_259949, _259951, _259953, _259955, _259957, hAPP(hAPP(_259953, _259959), _259961))), 5742 ^ _63126 : [(5743 ^ _63126) ^ [] : [_259957 = c_Orderings_Obot__class_Obot(tc_fun(_259949, tc_HOL_Obool)), hAPP(hAPP(_259953, _259959), _259961) = _259955], (5749 ^ _63126) ^ [_260331, _260333] : [hAPP(hAPP(_259953, _259959), _259961) = hAPP(hAPP(_259953, _260333), _260331), c_member(_259949, _260333, _259957), c_Nitpick_Ofold__graph_H(_259949, _259951, _259953, _259955, c_Groups_Ominus__class_Ominus(tc_fun(_259949, tc_HOL_Obool), _259957, c_Set_Oinsert(_259949, _260333, c_Orderings_Obot__class_Obot(tc_fun(_259949, tc_HOL_Obool)))), _260331)]]], (5761 ^ _63126) ^ [_260882, _260884, _260886, _260888] : [c_FunDef_Oreduction__pair(_260882, _260884), -(c_FunDef_Oreduction__pair(_260886, c_FunDef_Orp__inv__image(_260882, _260886, _260884, _260888)))], (5767 ^ _63126) ^ [_261156, _261158, _261160, _261162, _261164] : [c_member(_261156, _261158, c_Relation_OImage(_261160, _261156, _261162, _261164)), 5771 ^ _63126 : [(5772 ^ _63126) ^ [] : [-(c_member(tc_prod(_261160, _261156), c_Product__Type_OPair(_261160, _261156, 5770 ^ [_261156, _261158, _261160, _261162, _261164], _261158), _261162))], (5774 ^ _63126) ^ [] : [-(c_member(_261160, 5770 ^ [_261156, _261158, _261160, _261162, _261164], _261164))]]], (5776 ^ _63126) ^ [_261621, _261623, _261625] : [c_Wellfounded_Owf(_261621, _261623), c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_261621, _261621), tc_HOL_Obool), c_Relation_Orel__comp(_261621, _261621, _261621, _261623, _261625), _261623), -(c_FunDef_Oreduction__pair(_261621, c_Product__Type_OPair(tc_fun(tc_prod(_261621, _261621), tc_HOL_Obool), tc_fun(tc_prod(_261621, _261621), tc_HOL_Obool), _261623, _261625)))], (5786 ^ _63126) ^ [_262032, _262034, _262036, _262038, _262040] : [c_Equiv__Relations_Oequiv(_262032, _262034, _262036), c_Orderings_Oord__class_Oless__eq(tc_fun(_262032, tc_HOL_Obool), c_Relation_OImage(_262032, _262032, _262036, c_Set_Oinsert(_262032, _262038, c_Orderings_Obot__class_Obot(tc_fun(_262032, tc_HOL_Obool)))), c_Relation_OImage(_262032, _262032, _262036, c_Set_Oinsert(_262032, _262040, c_Orderings_Obot__class_Obot(tc_fun(_262032, tc_HOL_Obool))))), c_member(_262032, _262038, _262034), -(c_member(tc_prod(_262032, _262032), c_Product__Type_OPair(_262032, _262032, _262040, _262038), _262036))], (5800 ^ _63126) ^ [_262632, _262634, _262636, _262638, _262640, _262642, _262644, _262646] : [c_member(tc_prod(_262632, _262634), c_Product__Type_OPair(_262632, _262634, _262636, _262638), _262640), c_member(tc_prod(_262634, _262642), c_Product__Type_OPair(_262634, _262642, _262638, _262644), _262646), -(c_member(tc_prod(_262632, _262642), c_Product__Type_OPair(_262632, _262642, _262636, _262644), c_Relation_Orel__comp(_262632, _262634, _262642, _262640, _262646)))], (5810 ^ _63126) ^ [_263042, _263044] : [-(c_Transitive__Closure_Ortrancl(_263042, _263044) = c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_263042, _263042), tc_HOL_Obool), c_Relation_OId(_263042), c_Relation_Orel__comp(_263042, _263042, _263042, c_Transitive__Closure_Ortrancl(_263042, _263044), _263044)))], (5812 ^ _63126) ^ [_263203, _263205, _263207, _263209] : [c_Equiv__Relations_Oequiv(_263203, _263205, _263207), c_member(_263203, _263209, _263205), -(c_member(_263203, _263209, c_Relation_OImage(_263203, _263203, _263207, c_Set_Oinsert(_263203, _263209, c_Orderings_Obot__class_Obot(tc_fun(_263203, tc_HOL_Obool))))))], (5822 ^ _63126) ^ [_263584, _263586, _263588, _263590] : [c_Relation_Orel__comp(_263584, _263584, _263584, _263586, _263588) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_263584, _263584), tc_HOL_Obool)), c_Relation_Orel__comp(_263584, _263584, _263584, _263586, _263590) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_263584, _263584), tc_HOL_Obool)), -(c_Relation_Orel__comp(_263584, _263584, _263584, _263586, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_263584, _263584), tc_HOL_Obool), _263588, _263590)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_263584, _263584), tc_HOL_Obool)))], (5832 ^ _63126) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (5834 ^ _63126) ^ [_264060, _264062] : [class_Lattices_Obounded__lattice(_264060), -(class_Lattices_Obounded__lattice(tc_fun(_264062, _264060)))], (5840 ^ _63126) ^ [_264272, _264274] : [class_Lattices_Obounded__lattice(_264272), -(class_Lattices_Obounded__lattice__bot(tc_fun(_264274, _264272)))], (5846 ^ _63126) ^ [_264484, _264486] : [class_Lattices_Olattice(_264484), -(class_Lattices_Osemilattice__sup(tc_fun(_264486, _264484)))], (5852 ^ _63126) ^ [_264696, _264698] : [class_Orderings_Opreorder(_264696), -(class_Orderings_Opreorder(tc_fun(_264698, _264696)))], (5858 ^ _63126) ^ [_264908, _264910] : [class_Lattices_Olattice(_264908), -(class_Lattices_Olattice(tc_fun(_264910, _264908)))], (5864 ^ _63126) ^ [_265120, _265122] : [class_Orderings_Oorder(_265120), -(class_Orderings_Oorder(tc_fun(_265122, _265120)))], (5870 ^ _63126) ^ [_265332, _265334] : [class_Orderings_Oord(_265332), -(class_Orderings_Oord(tc_fun(_265334, _265332)))], (5876 ^ _63126) ^ [_265544, _265546] : [class_Orderings_Obot(_265544), -(class_Orderings_Obot(tc_fun(_265546, _265544)))], (5882 ^ _63126) ^ [_265756, _265758] : [class_Groups_Ominus(_265756), -(class_Groups_Ominus(tc_fun(_265758, _265756)))], (5888 ^ _63126) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (5890 ^ _63126) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (5892 ^ _63126) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (5894 ^ _63126) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (5896 ^ _63126) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (5898 ^ _63126) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (5900 ^ _63126) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (5902 ^ _63126) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (5904 ^ _63126) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (5906 ^ _63126) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (5908 ^ _63126) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (5910 ^ _63126) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (5912 ^ _63126) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (5914 ^ _63126) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (5916 ^ _63126) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (5918 ^ _63126) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (5920 ^ _63126) ^ [_266816, _266818] : [hBOOL(hAPP(c_fequal(_266816), _266818)), -(_266816 = _266818)], (5926 ^ _63126) ^ [_267016, _267018] : [_267016 = _267018, -(hBOOL(hAPP(c_fequal(_267016), _267018)))]], input).
% 1.67/2.41 ncf('1',plain,[5936 : c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, 5953 ^ [], 5953 ^ []), v_L), 5967 : c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, 5984 ^ [], 5984 ^ []), v_L)],start(5932 ^ 0,bind([[_272907, _273830], [5953 ^ [], 5984 ^ []]]))).
% 1.67/2.41 ncf('1.1',plain,[-(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, 5953 ^ [], 5953 ^ []), v_L)), c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt, v_L), 5959 : 5956 ^ [] = 5957 ^ []],extension(5948 ^ 3)).
% 1.67/2.41 ncf('1.1.1',plain,[-(c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt, v_L))],extension(5934 ^ 4)).
% 1.67/2.41 ncf('1.1.2',plain,[-(5956 ^ [] = 5957 ^ []), -(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, 5957 ^ [], 5956 ^ []), v_L)), -(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, 5956 ^ [], 5957 ^ []), v_L))],extension(5938 ^ 6,bind([[_273000, _273002], [5957 ^ [], 5956 ^ []]]))).
% 1.67/2.41 ncf('1.1.2.1',plain,[c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, 5957 ^ [], 5956 ^ []), v_L)],extension(5963 ^ 7)).
% 1.67/2.41 ncf('1.1.2.2',plain,[c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, 5956 ^ [], 5957 ^ []), v_L)],extension(5961 ^ 7)).
% 1.67/2.41 ncf('1.2',plain,[-(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, 5984 ^ [], 5984 ^ []), v_L)), c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt, v_L), 5990 : 5987 ^ [] = 5988 ^ []],extension(5979 ^ 3)).
% 1.67/2.41 ncf('1.2.1',plain,[-(c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt, v_L))],extension(5965 ^ 4)).
% 1.67/2.41 ncf('1.2.2',plain,[-(5987 ^ [] = 5988 ^ []), -(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, 5987 ^ [], 5988 ^ []), v_L)), -(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, 5988 ^ [], 5987 ^ []), v_L))],extension(5969 ^ 6,bind([[_273923, _273925], [5988 ^ [], 5987 ^ []]]))).
% 1.67/2.41 ncf('1.2.2.1',plain,[c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, 5987 ^ [], 5988 ^ []), v_L)],extension(5994 ^ 7)).
% 1.67/2.41 ncf('1.2.2.2',plain,[c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt, 5988 ^ [], 5987 ^ []), v_L)],extension(5992 ^ 7)).
% 1.67/2.41 %-----------------------------------------------------
% 1.67/2.41 End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
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