%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : SWW474^1 : TPTP v6.1.0. Released v5.3.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n187.star.cs.uiowa.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz % Memory : 32286.75MB % OS : Linux 2.6.32-431.20.3.el6.x86_64 % CPULimit : 300s % DateTime : Thu Jul 17 13:37:24 EDT 2014 % Result : Timeout 300.00s % Output : None % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----NO SOLUTION OUTPUT BY SYSTEM %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % % Problem : SWW474^1 : TPTP v6.1.0. Released v5.3.0. % % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % % Computer : n187.star.cs.uiowa.edu % % Model : x86_64 x86_64 % % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz % % Memory : 32286.75MB % % OS : Linux 2.6.32-431.20.3.el6.x86_64 % % CPULimit : 300 % % DateTime : Thu Jul 17 09:21:36 CDT 2014 % % CPUTime : 300.00 % Python 2.7.5 % Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/'] % FOF formula (<kernel.Constant object at 0x214a6c8>, <kernel.Type object at 0x214ac20>) of role type named ty_ty_tc__Com__Ocom % Using role type % Declaring com:Type % FOF formula (<kernel.Constant object at 0x2328050>, <kernel.Type object at 0x214a5f0>) of role type named ty_ty_tc__Com__Opname % Using role type % Declaring pname:Type % FOF formula (<kernel.Constant object at 0x214ab90>, <kernel.Type object at 0x214a7e8>) of role type named ty_ty_tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostate_J % Using role type % Declaring hoare_1262092251_state:Type % FOF formula (<kernel.Constant object at 0x214ac20>, <kernel.Type object at 0x214a4d0>) of role type named ty_ty_tc__Option__Ooption_Itc__Com__Ocom_J % Using role type % Declaring option_com:Type % FOF formula (<kernel.Constant object at 0x214acb0>, <kernel.DependentProduct object at 0x214a440>) of role type named sy_c_Com_OWT % Using role type % Declaring wt:(com->Prop) % FOF formula (<kernel.Constant object at 0x214add0>, <kernel.Sort object at 0x23f8b48>) of role type named sy_c_Com_OWT__bodies % Using role type % Declaring wT_bodies:Prop % FOF formula (<kernel.Constant object at 0x214ac20>, <kernel.DependentProduct object at 0x214a7a0>) of role type named sy_c_Com_Obody % Using role type % Declaring body:(pname->option_com) % FOF formula (<kernel.Constant object at 0x214a488>, <kernel.DependentProduct object at 0x2030f80>) of role type named sy_c_Com_Ocom_OBODY % Using role type % Declaring body_1:(pname->com) % FOF formula (<kernel.Constant object at 0x214acb0>, <kernel.DependentProduct object at 0x2030f80>) of role type named sy_c_Finite__Set_Ofinite_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_M_Eo % Using role type % Declaring finite1648353812_o_o_o:(((((pname->Prop)->Prop)->Prop)->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x214ab90>, <kernel.DependentProduct object at 0x2030d40>) of role type named sy_c_Finite__Set_Ofinite_000_062_I_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbq % Using role type % Declaring finite734360985_o_o_o:(((((hoare_1262092251_state->Prop)->Prop)->Prop)->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x214a560>, <kernel.DependentProduct object at 0x2030098>) of role type named sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J % Using role type % Declaring finite1066544169me_o_o:((((pname->Prop)->Prop)->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x214acb0>, <kernel.DependentProduct object at 0x20303b0>) of role type named sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Ot % Using role type % Declaring finite1303896758te_o_o:((((hoare_1262092251_state->Prop)->Prop)->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x214ab90>, <kernel.DependentProduct object at 0x2030098>) of role type named sy_c_Finite__Set_Ofinite_000_062_Itc__Com__Opname_M_Eo_J % Using role type % Declaring finite297249702name_o:(((pname->Prop)->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x214add0>, <kernel.DependentProduct object at 0x2347368>) of role type named sy_c_Finite__Set_Ofinite_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_ % Using role type % Declaring finite1423311111tate_o:(((hoare_1262092251_state->Prop)->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x214ab90>, <kernel.DependentProduct object at 0x2347368>) of role type named sy_c_Finite__Set_Ofinite_000tc__Com__Opname % Using role type % Declaring finite_finite_pname:((pname->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x214add0>, <kernel.DependentProduct object at 0x2347440>) of role type named sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__C % Using role type % Declaring finite1178804552_state:((hoare_1262092251_state->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x214add0>, <kernel.DependentProduct object at 0x23473b0>) of role type named sy_c_Hoare__Mirabelle__ghhkfsbqqq_OMGT % Using role type % Declaring hoare_Mirabelle_MGT:(com->hoare_1262092251_state) % FOF formula (<kernel.Constant object at 0x2030098>, <kernel.DependentProduct object at 0x2347320>) of role type named sy_c_Hoare__Mirabelle__ghhkfsbqqq_Ohoare__derivs_000tc__Com__Ostate % Using role type % Declaring hoare_930741239_state:((hoare_1262092251_state->Prop)->((hoare_1262092251_state->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x2030908>, <kernel.Sort object at 0x23f8b48>) of role type named sy_c_Hoare__Mirabelle__ghhkfsbqqq_Ostate__not__singleton % Using role type % Declaring hoare_1821564147gleton:Prop % FOF formula (<kernel.Constant object at 0x2030d40>, <kernel.DependentProduct object at 0x23471b8>) of role type named sy_c_Map_Odom_000_062_Itc__Com__Opname_M_Eo_J_000tc__Com__Ocom % Using role type % Declaring dom_pname_o_com:(((pname->Prop)->option_com)->((pname->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x2030908>, <kernel.DependentProduct object at 0x2347e18>) of role type named sy_c_Map_Odom_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__O % Using role type % Declaring dom_Ho1489634536_o_com:(((hoare_1262092251_state->Prop)->option_com)->((hoare_1262092251_state->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x2030908>, <kernel.DependentProduct object at 0x23473f8>) of role type named sy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Ocom % Using role type % Declaring dom_pname_com:((pname->option_com)->(pname->Prop)) % FOF formula (<kernel.Constant object at 0x23472d8>, <kernel.DependentProduct object at 0x2347758>) of role type named sy_c_Option_Ooption_OSome_000tc__Com__Ocom % Using role type % Declaring some_com:(com->option_com) % FOF formula (<kernel.Constant object at 0x2347440>, <kernel.DependentProduct object at 0x2347ef0>) of role type named sy_c_Option_Othe_000tc__Com__Ocom % Using role type % Declaring the_com:(option_com->com) % FOF formula (<kernel.Constant object at 0x2347fc8>, <kernel.DependentProduct object at 0x2347440>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo % Using role type % Declaring bot_bot_pname_o_o_o:(((pname->Prop)->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x2347758>, <kernel.DependentProduct object at 0x2347440>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_I_062_I_062_Itc__Hoare____Mirabelle____g % Using role type % Declaring bot_bo388435036_o_o_o:(((hoare_1262092251_state->Prop)->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x2347e18>, <kernel.DependentProduct object at 0x23472d8>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J % Using role type % Declaring bot_bot_pname_o_o:((pname->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x2347f38>, <kernel.DependentProduct object at 0x2347440>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Hoare____Mirabelle____ghhkfsb % Using role type % Declaring bot_bo1962689075te_o_o:((hoare_1262092251_state->Prop)->Prop) % FOF formula (<kernel.Constant object at 0x2347488>, <kernel.DependentProduct object at 0x2347ea8>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_Itc__Com__Opname_M_Eo_J % Using role type % Declaring bot_bot_pname_o:(pname->Prop) % FOF formula (<kernel.Constant object at 0x23477a0>, <kernel.DependentProduct object at 0x2347680>) of role type named sy_c_Orderings_Obot__class_Obot_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__O % Using role type % Declaring bot_bo113204042tate_o:(hoare_1262092251_state->Prop) % FOF formula (<kernel.Constant object at 0x2347440>, <kernel.DependentProduct object at 0x23475f0>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J % Using role type % Declaring ord_le1828183645_o_o_o:((((pname->Prop)->Prop)->Prop)->((((pname->Prop)->Prop)->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x2347ea8>, <kernel.DependentProduct object at 0x2347320>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_I_062_Itc__Hoare____Mirabelle % Using role type % Declaring ord_le1891858320_o_o_o:((((hoare_1262092251_state->Prop)->Prop)->Prop)->((((hoare_1262092251_state->Prop)->Prop)->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x2347680>, <kernel.DependentProduct object at 0x2165fc8>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_ % Using role type % Declaring ord_le1205211808me_o_o:(((pname->Prop)->Prop)->(((pname->Prop)->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x2347440>, <kernel.DependentProduct object at 0x2165e60>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Hoare____Mirabelle____gh % Using role type % Declaring ord_le2012720639te_o_o:(((hoare_1262092251_state->Prop)->Prop)->(((hoare_1262092251_state->Prop)->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x23472d8>, <kernel.DependentProduct object at 0x2165d40>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Com__Opname_M_Eo_J % Using role type % Declaring ord_less_eq_pname_o:((pname->Prop)->((pname->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x2347680>, <kernel.DependentProduct object at 0x2165dd0>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Hoare____Mirabelle____ghhkfsbq % Using role type % Declaring ord_le870406270tate_o:((hoare_1262092251_state->Prop)->((hoare_1262092251_state->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x2347440>, <kernel.DependentProduct object at 0x2165d40>) of role type named sy_c_Set_OCollect_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_M_Eo_J % Using role type % Declaring collect_pname_o_o_o:(((((pname->Prop)->Prop)->Prop)->Prop)->((((pname->Prop)->Prop)->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x2347680>, <kernel.DependentProduct object at 0x2165dd0>) of role type named sy_c_Set_OCollect_000_062_I_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otr % Using role type % Declaring collec101077467_o_o_o:(((((hoare_1262092251_state->Prop)->Prop)->Prop)->Prop)->((((hoare_1262092251_state->Prop)->Prop)->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x2347440>, <kernel.DependentProduct object at 0x2165f80>) of role type named sy_c_Set_OCollect_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J % Using role type % Declaring collect_pname_o_o:((((pname->Prop)->Prop)->Prop)->(((pname->Prop)->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x23472d8>, <kernel.DependentProduct object at 0x2165b00>) of role type named sy_c_Set_OCollect_000_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_I % Using role type % Declaring collec341954548te_o_o:((((hoare_1262092251_state->Prop)->Prop)->Prop)->(((hoare_1262092251_state->Prop)->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x23472d8>, <kernel.DependentProduct object at 0x21659e0>) of role type named sy_c_Set_OCollect_000_062_Itc__Com__Opname_M_Eo_J % Using role type % Declaring collect_pname_o:(((pname->Prop)->Prop)->((pname->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x2165f80>, <kernel.DependentProduct object at 0x2165a70>) of role type named sy_c_Set_OCollect_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Co % Using role type % Declaring collec313158217tate_o:(((hoare_1262092251_state->Prop)->Prop)->((hoare_1262092251_state->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x2165fc8>, <kernel.DependentProduct object at 0x2165b90>) of role type named sy_c_Set_OCollect_000tc__Com__Opname % Using role type % Declaring collect_pname:((pname->Prop)->(pname->Prop)) % FOF formula (<kernel.Constant object at 0x2165d40>, <kernel.DependentProduct object at 0x2165a70>) of role type named sy_c_Set_OCollect_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ost % Using role type % Declaring collec1121927558_state:((hoare_1262092251_state->Prop)->(hoare_1262092251_state->Prop)) % FOF formula (<kernel.Constant object at 0x2165dd0>, <kernel.DependentProduct object at 0x2165fc8>) of role type named sy_c_Set_Oimage_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_000tc__Com__Opname % Using role type % Declaring image_471733107_pname:((((pname->Prop)->Prop)->pname)->((((pname->Prop)->Prop)->Prop)->(pname->Prop))) % FOF formula (<kernel.Constant object at 0x2165c20>, <kernel.DependentProduct object at 0x2165d40>) of role type named sy_c_Set_Oimage_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_000tc__Hoare____Mir % Using role type % Declaring image_1036078444_state:((((pname->Prop)->Prop)->hoare_1262092251_state)->((((pname->Prop)->Prop)->Prop)->(hoare_1262092251_state->Prop))) % FOF formula (<kernel.Constant object at 0x2165cb0>, <kernel.DependentProduct object at 0x2165dd0>) of role type named sy_c_Set_Oimage_000_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc % Using role type % Declaring image_893364936_pname:((((hoare_1262092251_state->Prop)->Prop)->pname)->((((hoare_1262092251_state->Prop)->Prop)->Prop)->(pname->Prop))) % FOF formula (<kernel.Constant object at 0x2165638>, <kernel.DependentProduct object at 0x2165c20>) of role type named sy_c_Set_Oimage_000_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc_001 % Using role type % Declaring image_165349207_state:((((hoare_1262092251_state->Prop)->Prop)->hoare_1262092251_state)->((((hoare_1262092251_state->Prop)->Prop)->Prop)->(hoare_1262092251_state->Prop))) % FOF formula (<kernel.Constant object at 0x2165b90>, <kernel.DependentProduct object at 0x2165440>) of role type named sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Com__Opname % Using role type % Declaring image_pname_o_pname:(((pname->Prop)->pname)->(((pname->Prop)->Prop)->(pname->Prop))) % FOF formula (<kernel.Constant object at 0x21655f0>, <kernel.DependentProduct object at 0x2165cb0>) of role type named sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Hoare____Mirabelle____ghh % Using role type % Declaring image_1476171975_state:(((pname->Prop)->hoare_1262092251_state)->(((pname->Prop)->Prop)->(hoare_1262092251_state->Prop))) % FOF formula (<kernel.Constant object at 0x2165560>, <kernel.DependentProduct object at 0x2165638>) of role type named sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com_ % Using role type % Declaring image_1820530197_pname:(((hoare_1262092251_state->Prop)->pname)->(((hoare_1262092251_state->Prop)->Prop)->(pname->Prop))) % FOF formula (<kernel.Constant object at 0x21653b0>, <kernel.DependentProduct object at 0x2165b90>) of role type named sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__002 % Using role type % Declaring image_234589002_state:(((hoare_1262092251_state->Prop)->hoare_1262092251_state)->(((hoare_1262092251_state->Prop)->Prop)->(hoare_1262092251_state->Prop))) % FOF formula (<kernel.Constant object at 0x2165c20>, <kernel.DependentProduct object at 0x21655f0>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J % Using role type % Declaring image_504089495me_o_o:((pname->((pname->Prop)->Prop))->((pname->Prop)->(((pname->Prop)->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0x2165710>, <kernel.DependentProduct object at 0x21655f0>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000_062_I_062_Itc__Hoare____Mirabelle____ghhk % Using role type % Declaring image_827868872te_o_o:((pname->((hoare_1262092251_state->Prop)->Prop))->((pname->Prop)->(((hoare_1262092251_state->Prop)->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0x2165830>, <kernel.DependentProduct object at 0x21655f0>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Com__Opname_M_Eo_J % Using role type % Declaring image_pname_pname_o:((pname->(pname->Prop))->((pname->Prop)->((pname->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0x2165cb0>, <kernel.DependentProduct object at 0x21655f0>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq % Using role type % Declaring image_518521461tate_o:((pname->(hoare_1262092251_state->Prop))->((pname->Prop)->((hoare_1262092251_state->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0x2165b90>, <kernel.DependentProduct object at 0x2165440>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname % Using role type % Declaring image_pname_pname:((pname->pname)->((pname->Prop)->(pname->Prop))) % FOF formula (<kernel.Constant object at 0x2165638>, <kernel.DependentProduct object at 0x23482d8>) of role type named sy_c_Set_Oimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otri % Using role type % Declaring image_669833818_state:((pname->hoare_1262092251_state)->((pname->Prop)->(hoare_1262092251_state->Prop))) % FOF formula (<kernel.Constant object at 0x2165440>, <kernel.DependentProduct object at 0x2348a70>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostat % Using role type % Declaring image_333245000me_o_o:((hoare_1262092251_state->((pname->Prop)->Prop))->((hoare_1262092251_state->Prop)->(((pname->Prop)->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0x2165b90>, <kernel.DependentProduct object at 0x2348248>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostat_003 % Using role type % Declaring image_1731108951te_o_o:((hoare_1262092251_state->((hoare_1262092251_state->Prop)->Prop))->((hoare_1262092251_state->Prop)->(((hoare_1262092251_state->Prop)->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0x21655f0>, <kernel.DependentProduct object at 0x23482d8>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostat_004 % Using role type % Declaring image_1320925383name_o:((hoare_1262092251_state->(pname->Prop))->((hoare_1262092251_state->Prop)->((pname->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0x2165b90>, <kernel.DependentProduct object at 0x2348680>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostat_005 % Using role type % Declaring image_1403668518tate_o:((hoare_1262092251_state->(hoare_1262092251_state->Prop))->((hoare_1262092251_state->Prop)->((hoare_1262092251_state->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0x21655f0>, <kernel.DependentProduct object at 0x2348a28>) of role type named sy_c_Set_Oimage_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostat_006 % Using role type % Declaring image_202231862_pname:((hoare_1262092251_state->pname)->((hoare_1262092251_state->Prop)->(pname->Prop))) % FOF formula (<kernel.Constant object at 0x21655f0>, <kernel.DependentProduct object at 0x2348248>) of role type named sy_c_Set_Oinsert_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J % Using role type % Declaring insert_pname_o_o:(((pname->Prop)->Prop)->((((pname->Prop)->Prop)->Prop)->(((pname->Prop)->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0x23482d8>, <kernel.DependentProduct object at 0x2348680>) of role type named sy_c_Set_Oinsert_000_062_I_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It % Using role type % Declaring insert1691644879te_o_o:(((hoare_1262092251_state->Prop)->Prop)->((((hoare_1262092251_state->Prop)->Prop)->Prop)->(((hoare_1262092251_state->Prop)->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0x2348200>, <kernel.DependentProduct object at 0x2348680>) of role type named sy_c_Set_Oinsert_000_062_Itc__Com__Opname_M_Eo_J % Using role type % Declaring insert_pname_o:((pname->Prop)->(((pname->Prop)->Prop)->((pname->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0x2348170>, <kernel.DependentProduct object at 0x2348680>) of role type named sy_c_Set_Oinsert_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com % Using role type % Declaring insert1042460334tate_o:((hoare_1262092251_state->Prop)->(((hoare_1262092251_state->Prop)->Prop)->((hoare_1262092251_state->Prop)->Prop))) % FOF formula (<kernel.Constant object at 0x2348050>, <kernel.DependentProduct object at 0x215b908>) of role type named sy_c_Set_Oinsert_000tc__Com__Opname % Using role type % Declaring insert_pname:(pname->((pname->Prop)->(pname->Prop))) % FOF formula (<kernel.Constant object at 0x2348200>, <kernel.DependentProduct object at 0x215b830>) of role type named sy_c_Set_Oinsert_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Osta % Using role type % Declaring insert81609953_state:(hoare_1262092251_state->((hoare_1262092251_state->Prop)->(hoare_1262092251_state->Prop))) % FOF formula (<kernel.Constant object at 0x2348680>, <kernel.DependentProduct object at 0x215b758>) of role type named sy_c_fequal_000_062_Itc__Com__Opname_M_Eo_J % Using role type % Declaring fequal_pname_o:((pname->Prop)->((pname->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x2348200>, <kernel.DependentProduct object at 0x215b7a0>) of role type named sy_c_fequal_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ost % Using role type % Declaring fequal1529404211tate_o:((hoare_1262092251_state->Prop)->((hoare_1262092251_state->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x2348200>, <kernel.DependentProduct object at 0x215b878>) of role type named sy_c_fequal_000tc__Com__Opname % Using role type % Declaring fequal_pname:(pname->(pname->Prop)) % FOF formula (<kernel.Constant object at 0x2348680>, <kernel.DependentProduct object at 0x215b758>) of role type named sy_c_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostate_J % Using role type % Declaring fequal1925511196_state:(hoare_1262092251_state->(hoare_1262092251_state->Prop)) % FOF formula (<kernel.Constant object at 0x2348680>, <kernel.DependentProduct object at 0x215b710>) of role type named sy_c_member_000_062_Itc__Com__Opname_M_Eo_J % Using role type % Declaring member_pname_o:((pname->Prop)->(((pname->Prop)->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x215b950>, <kernel.DependentProduct object at 0x215b638>) of role type named sy_c_member_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ost % Using role type % Declaring member907417095tate_o:((hoare_1262092251_state->Prop)->(((hoare_1262092251_state->Prop)->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x215b908>, <kernel.DependentProduct object at 0x215b5f0>) of role type named sy_c_member_000tc__Com__Opname % Using role type % Declaring member_pname:(pname->((pname->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x215b7a0>, <kernel.DependentProduct object at 0x215b950>) of role type named sy_c_member_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com__Ostate_J % Using role type % Declaring member5164104_state:(hoare_1262092251_state->((hoare_1262092251_state->Prop)->Prop)) % FOF formula (<kernel.Constant object at 0x215b638>, <kernel.DependentProduct object at 0x215b5a8>) of role type named sy_v_Fa % Using role type % Declaring fa:(hoare_1262092251_state->Prop) % FOF formula (<kernel.Constant object at 0x215b908>, <kernel.Constant object at 0x215b5a8>) of role type named sy_v_pn % Using role type % Declaring pn:pname % FOF formula (<kernel.Constant object at 0x215b7a0>, <kernel.Constant object at 0x215b5a8>) of role type named sy_v_y % Using role type % Declaring y:com % FOF formula (forall (G:(hoare_1262092251_state->Prop)), ((hoare_930741239_state G) bot_bo113204042tate_o)) of role axiom named fact_0_empty % A new axiom: (forall (G:(hoare_1262092251_state->Prop)), ((hoare_930741239_state G) bot_bo113204042tate_o)) % FOF formula (forall (Ts_6:(hoare_1262092251_state->Prop)) (G_8:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o Ts_6) G_8)->((hoare_930741239_state G_8) Ts_6))) of role axiom named fact_1_asm % A new axiom: (forall (Ts_6:(hoare_1262092251_state->Prop)) (G_8:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o Ts_6) G_8)->((hoare_930741239_state G_8) Ts_6))) % FOF formula (forall (Ts_5:(hoare_1262092251_state->Prop)) (G_7:(hoare_1262092251_state->Prop)) (Ts_4:(hoare_1262092251_state->Prop)), (((hoare_930741239_state G_7) Ts_4)->(((ord_le870406270tate_o Ts_5) Ts_4)->((hoare_930741239_state G_7) Ts_5)))) of role axiom named fact_2_weaken % A new axiom: (forall (Ts_5:(hoare_1262092251_state->Prop)) (G_7:(hoare_1262092251_state->Prop)) (Ts_4:(hoare_1262092251_state->Prop)), (((hoare_930741239_state G_7) Ts_4)->(((ord_le870406270tate_o Ts_5) Ts_4)->((hoare_930741239_state G_7) Ts_5)))) % FOF formula (forall (G_6:(hoare_1262092251_state->Prop)) (G_5:(hoare_1262092251_state->Prop)) (Ts_3:(hoare_1262092251_state->Prop)), (((hoare_930741239_state G_5) Ts_3)->(((ord_le870406270tate_o G_5) G_6)->((hoare_930741239_state G_6) Ts_3)))) of role axiom named fact_3_thin % A new axiom: (forall (G_6:(hoare_1262092251_state->Prop)) (G_5:(hoare_1262092251_state->Prop)) (Ts_3:(hoare_1262092251_state->Prop)), (((hoare_930741239_state G_5) Ts_3)->(((ord_le870406270tate_o G_5) G_6)->((hoare_930741239_state G_6) Ts_3)))) % FOF formula (forall (G_4:(hoare_1262092251_state->Prop)) (G_3:(hoare_1262092251_state->Prop)) (Ts_2:(hoare_1262092251_state->Prop)), (((hoare_930741239_state G_3) Ts_2)->(((hoare_930741239_state G_4) G_3)->((hoare_930741239_state G_4) Ts_2)))) of role axiom named fact_4_cut % A new axiom: (forall (G_4:(hoare_1262092251_state->Prop)) (G_3:(hoare_1262092251_state->Prop)) (Ts_2:(hoare_1262092251_state->Prop)), (((hoare_930741239_state G_3) Ts_2)->(((hoare_930741239_state G_4) G_3)->((hoare_930741239_state G_4) Ts_2)))) % FOF formula (forall (Ts_1:(hoare_1262092251_state->Prop)) (G_2:(hoare_1262092251_state->Prop)) (T_1:hoare_1262092251_state), (((hoare_930741239_state G_2) ((insert81609953_state T_1) bot_bo113204042tate_o))->(((hoare_930741239_state G_2) Ts_1)->((hoare_930741239_state G_2) ((insert81609953_state T_1) Ts_1))))) of role axiom named fact_5_hoare__derivs_Oinsert % A new axiom: (forall (Ts_1:(hoare_1262092251_state->Prop)) (G_2:(hoare_1262092251_state->Prop)) (T_1:hoare_1262092251_state), (((hoare_930741239_state G_2) ((insert81609953_state T_1) bot_bo113204042tate_o))->(((hoare_930741239_state G_2) Ts_1)->((hoare_930741239_state G_2) ((insert81609953_state T_1) Ts_1))))) % FOF formula (forall (G_1:(hoare_1262092251_state->Prop)) (T:hoare_1262092251_state) (Ts:(hoare_1262092251_state->Prop)), (((hoare_930741239_state G_1) ((insert81609953_state T) Ts))->((and ((hoare_930741239_state G_1) ((insert81609953_state T) bot_bo113204042tate_o))) ((hoare_930741239_state G_1) Ts)))) of role axiom named fact_6_derivs__insertD % A new axiom: (forall (G_1:(hoare_1262092251_state->Prop)) (T:hoare_1262092251_state) (Ts:(hoare_1262092251_state->Prop)), (((hoare_930741239_state G_1) ((insert81609953_state T) Ts))->((and ((hoare_930741239_state G_1) ((insert81609953_state T) bot_bo113204042tate_o))) ((hoare_930741239_state G_1) Ts)))) % FOF formula (forall (Pn_1:pname) (G:(hoare_1262092251_state->Prop)), (((hoare_930741239_state ((insert81609953_state (hoare_Mirabelle_MGT (body_1 Pn_1))) G)) ((insert81609953_state (hoare_Mirabelle_MGT (the_com (body Pn_1)))) bot_bo113204042tate_o))->((hoare_930741239_state G) ((insert81609953_state (hoare_Mirabelle_MGT (body_1 Pn_1))) bot_bo113204042tate_o)))) of role axiom named fact_7_MGT__BodyN % A new axiom: (forall (Pn_1:pname) (G:(hoare_1262092251_state->Prop)), (((hoare_930741239_state ((insert81609953_state (hoare_Mirabelle_MGT (body_1 Pn_1))) G)) ((insert81609953_state (hoare_Mirabelle_MGT (the_com (body Pn_1)))) bot_bo113204042tate_o))->((hoare_930741239_state G) ((insert81609953_state (hoare_Mirabelle_MGT (body_1 Pn_1))) bot_bo113204042tate_o)))) % FOF formula (forall (A_77:(pname->Prop)), ((finite_finite_pname A_77)->(finite297249702name_o (collect_pname_o (fun (B_41:(pname->Prop))=> ((ord_less_eq_pname_o B_41) A_77)))))) of role axiom named fact_8_finite__Collect__subsets % A new axiom: (forall (A_77:(pname->Prop)), ((finite_finite_pname A_77)->(finite297249702name_o (collect_pname_o (fun (B_41:(pname->Prop))=> ((ord_less_eq_pname_o B_41) A_77)))))) % FOF formula (forall (A_77:(hoare_1262092251_state->Prop)), ((finite1178804552_state A_77)->(finite1423311111tate_o (collec313158217tate_o (fun (B_41:(hoare_1262092251_state->Prop))=> ((ord_le870406270tate_o B_41) A_77)))))) of role axiom named fact_9_finite__Collect__subsets % A new axiom: (forall (A_77:(hoare_1262092251_state->Prop)), ((finite1178804552_state A_77)->(finite1423311111tate_o (collec313158217tate_o (fun (B_41:(hoare_1262092251_state->Prop))=> ((ord_le870406270tate_o B_41) A_77)))))) % FOF formula (forall (A_77:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o A_77)->(finite1648353812_o_o_o (collect_pname_o_o_o (fun (B_41:(((pname->Prop)->Prop)->Prop))=> ((ord_le1828183645_o_o_o B_41) A_77)))))) of role axiom named fact_10_finite__Collect__subsets % A new axiom: (forall (A_77:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o A_77)->(finite1648353812_o_o_o (collect_pname_o_o_o (fun (B_41:(((pname->Prop)->Prop)->Prop))=> ((ord_le1828183645_o_o_o B_41) A_77)))))) % FOF formula (forall (A_77:(((hoare_1262092251_state->Prop)->Prop)->Prop)), ((finite1303896758te_o_o A_77)->(finite734360985_o_o_o (collec101077467_o_o_o (fun (B_41:(((hoare_1262092251_state->Prop)->Prop)->Prop))=> ((ord_le1891858320_o_o_o B_41) A_77)))))) of role axiom named fact_11_finite__Collect__subsets % A new axiom: (forall (A_77:(((hoare_1262092251_state->Prop)->Prop)->Prop)), ((finite1303896758te_o_o A_77)->(finite734360985_o_o_o (collec101077467_o_o_o (fun (B_41:(((hoare_1262092251_state->Prop)->Prop)->Prop))=> ((ord_le1891858320_o_o_o B_41) A_77)))))) % FOF formula (forall (A_77:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o A_77)->(finite1303896758te_o_o (collec341954548te_o_o (fun (B_41:((hoare_1262092251_state->Prop)->Prop))=> ((ord_le2012720639te_o_o B_41) A_77)))))) of role axiom named fact_12_finite__Collect__subsets % A new axiom: (forall (A_77:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o A_77)->(finite1303896758te_o_o (collec341954548te_o_o (fun (B_41:((hoare_1262092251_state->Prop)->Prop))=> ((ord_le2012720639te_o_o B_41) A_77)))))) % FOF formula (forall (A_77:((pname->Prop)->Prop)), ((finite297249702name_o A_77)->(finite1066544169me_o_o (collect_pname_o_o (fun (B_41:((pname->Prop)->Prop))=> ((ord_le1205211808me_o_o B_41) A_77)))))) of role axiom named fact_13_finite__Collect__subsets % A new axiom: (forall (A_77:((pname->Prop)->Prop)), ((finite297249702name_o A_77)->(finite1066544169me_o_o (collect_pname_o_o (fun (B_41:((pname->Prop)->Prop))=> ((ord_le1205211808me_o_o B_41) A_77)))))) % FOF formula (forall (H:(pname->hoare_1262092251_state)) (F_17:(pname->Prop)), ((finite_finite_pname F_17)->(finite1178804552_state ((image_669833818_state H) F_17)))) of role axiom named fact_14_finite__imageI % A new axiom: (forall (H:(pname->hoare_1262092251_state)) (F_17:(pname->Prop)), ((finite_finite_pname F_17)->(finite1178804552_state ((image_669833818_state H) F_17)))) % FOF formula (forall (H:(((pname->Prop)->Prop)->pname)) (F_17:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o F_17)->(finite_finite_pname ((image_471733107_pname H) F_17)))) of role axiom named fact_15_finite__imageI % A new axiom: (forall (H:(((pname->Prop)->Prop)->pname)) (F_17:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o F_17)->(finite_finite_pname ((image_471733107_pname H) F_17)))) % FOF formula (forall (H:(((hoare_1262092251_state->Prop)->Prop)->pname)) (F_17:(((hoare_1262092251_state->Prop)->Prop)->Prop)), ((finite1303896758te_o_o F_17)->(finite_finite_pname ((image_893364936_pname H) F_17)))) of role axiom named fact_16_finite__imageI % A new axiom: (forall (H:(((hoare_1262092251_state->Prop)->Prop)->pname)) (F_17:(((hoare_1262092251_state->Prop)->Prop)->Prop)), ((finite1303896758te_o_o F_17)->(finite_finite_pname ((image_893364936_pname H) F_17)))) % FOF formula (forall (H:((hoare_1262092251_state->Prop)->pname)) (F_17:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o F_17)->(finite_finite_pname ((image_1820530197_pname H) F_17)))) of role axiom named fact_17_finite__imageI % A new axiom: (forall (H:((hoare_1262092251_state->Prop)->pname)) (F_17:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o F_17)->(finite_finite_pname ((image_1820530197_pname H) F_17)))) % FOF formula (forall (H:((pname->Prop)->pname)) (F_17:((pname->Prop)->Prop)), ((finite297249702name_o F_17)->(finite_finite_pname ((image_pname_o_pname H) F_17)))) of role axiom named fact_18_finite__imageI % A new axiom: (forall (H:((pname->Prop)->pname)) (F_17:((pname->Prop)->Prop)), ((finite297249702name_o F_17)->(finite_finite_pname ((image_pname_o_pname H) F_17)))) % FOF formula (forall (H:(((pname->Prop)->Prop)->hoare_1262092251_state)) (F_17:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o F_17)->(finite1178804552_state ((image_1036078444_state H) F_17)))) of role axiom named fact_19_finite__imageI % A new axiom: (forall (H:(((pname->Prop)->Prop)->hoare_1262092251_state)) (F_17:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o F_17)->(finite1178804552_state ((image_1036078444_state H) F_17)))) % FOF formula (forall (H:(((hoare_1262092251_state->Prop)->Prop)->hoare_1262092251_state)) (F_17:(((hoare_1262092251_state->Prop)->Prop)->Prop)), ((finite1303896758te_o_o F_17)->(finite1178804552_state ((image_165349207_state H) F_17)))) of role axiom named fact_20_finite__imageI % A new axiom: (forall (H:(((hoare_1262092251_state->Prop)->Prop)->hoare_1262092251_state)) (F_17:(((hoare_1262092251_state->Prop)->Prop)->Prop)), ((finite1303896758te_o_o F_17)->(finite1178804552_state ((image_165349207_state H) F_17)))) % FOF formula (forall (H:((hoare_1262092251_state->Prop)->hoare_1262092251_state)) (F_17:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o F_17)->(finite1178804552_state ((image_234589002_state H) F_17)))) of role axiom named fact_21_finite__imageI % A new axiom: (forall (H:((hoare_1262092251_state->Prop)->hoare_1262092251_state)) (F_17:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o F_17)->(finite1178804552_state ((image_234589002_state H) F_17)))) % FOF formula (forall (H:((pname->Prop)->hoare_1262092251_state)) (F_17:((pname->Prop)->Prop)), ((finite297249702name_o F_17)->(finite1178804552_state ((image_1476171975_state H) F_17)))) of role axiom named fact_22_finite__imageI % A new axiom: (forall (H:((pname->Prop)->hoare_1262092251_state)) (F_17:((pname->Prop)->Prop)), ((finite297249702name_o F_17)->(finite1178804552_state ((image_1476171975_state H) F_17)))) % FOF formula (forall (H:(pname->((pname->Prop)->Prop))) (F_17:(pname->Prop)), ((finite_finite_pname F_17)->(finite1066544169me_o_o ((image_504089495me_o_o H) F_17)))) of role axiom named fact_23_finite__imageI % A new axiom: (forall (H:(pname->((pname->Prop)->Prop))) (F_17:(pname->Prop)), ((finite_finite_pname F_17)->(finite1066544169me_o_o ((image_504089495me_o_o H) F_17)))) % FOF formula (forall (H:(pname->((hoare_1262092251_state->Prop)->Prop))) (F_17:(pname->Prop)), ((finite_finite_pname F_17)->(finite1303896758te_o_o ((image_827868872te_o_o H) F_17)))) of role axiom named fact_24_finite__imageI % A new axiom: (forall (H:(pname->((hoare_1262092251_state->Prop)->Prop))) (F_17:(pname->Prop)), ((finite_finite_pname F_17)->(finite1303896758te_o_o ((image_827868872te_o_o H) F_17)))) % FOF formula (forall (H:(pname->(hoare_1262092251_state->Prop))) (F_17:(pname->Prop)), ((finite_finite_pname F_17)->(finite1423311111tate_o ((image_518521461tate_o H) F_17)))) of role axiom named fact_25_finite__imageI % A new axiom: (forall (H:(pname->(hoare_1262092251_state->Prop))) (F_17:(pname->Prop)), ((finite_finite_pname F_17)->(finite1423311111tate_o ((image_518521461tate_o H) F_17)))) % FOF formula (forall (H:(pname->(pname->Prop))) (F_17:(pname->Prop)), ((finite_finite_pname F_17)->(finite297249702name_o ((image_pname_pname_o H) F_17)))) of role axiom named fact_26_finite__imageI % A new axiom: (forall (H:(pname->(pname->Prop))) (F_17:(pname->Prop)), ((finite_finite_pname F_17)->(finite297249702name_o ((image_pname_pname_o H) F_17)))) % FOF formula (forall (H:(hoare_1262092251_state->((pname->Prop)->Prop))) (F_17:(hoare_1262092251_state->Prop)), ((finite1178804552_state F_17)->(finite1066544169me_o_o ((image_333245000me_o_o H) F_17)))) of role axiom named fact_27_finite__imageI % A new axiom: (forall (H:(hoare_1262092251_state->((pname->Prop)->Prop))) (F_17:(hoare_1262092251_state->Prop)), ((finite1178804552_state F_17)->(finite1066544169me_o_o ((image_333245000me_o_o H) F_17)))) % FOF formula (forall (H:(hoare_1262092251_state->((hoare_1262092251_state->Prop)->Prop))) (F_17:(hoare_1262092251_state->Prop)), ((finite1178804552_state F_17)->(finite1303896758te_o_o ((image_1731108951te_o_o H) F_17)))) of role axiom named fact_28_finite__imageI % A new axiom: (forall (H:(hoare_1262092251_state->((hoare_1262092251_state->Prop)->Prop))) (F_17:(hoare_1262092251_state->Prop)), ((finite1178804552_state F_17)->(finite1303896758te_o_o ((image_1731108951te_o_o H) F_17)))) % FOF formula (forall (H:(hoare_1262092251_state->(hoare_1262092251_state->Prop))) (F_17:(hoare_1262092251_state->Prop)), ((finite1178804552_state F_17)->(finite1423311111tate_o ((image_1403668518tate_o H) F_17)))) of role axiom named fact_29_finite__imageI % A new axiom: (forall (H:(hoare_1262092251_state->(hoare_1262092251_state->Prop))) (F_17:(hoare_1262092251_state->Prop)), ((finite1178804552_state F_17)->(finite1423311111tate_o ((image_1403668518tate_o H) F_17)))) % FOF formula (forall (H:(hoare_1262092251_state->(pname->Prop))) (F_17:(hoare_1262092251_state->Prop)), ((finite1178804552_state F_17)->(finite297249702name_o ((image_1320925383name_o H) F_17)))) of role axiom named fact_30_finite__imageI % A new axiom: (forall (H:(hoare_1262092251_state->(pname->Prop))) (F_17:(hoare_1262092251_state->Prop)), ((finite1178804552_state F_17)->(finite297249702name_o ((image_1320925383name_o H) F_17)))) % FOF formula (forall (H:(hoare_1262092251_state->pname)) (F_17:(hoare_1262092251_state->Prop)), ((finite1178804552_state F_17)->(finite_finite_pname ((image_202231862_pname H) F_17)))) of role axiom named fact_31_finite__imageI % A new axiom: (forall (H:(hoare_1262092251_state->pname)) (F_17:(hoare_1262092251_state->Prop)), ((finite1178804552_state F_17)->(finite_finite_pname ((image_202231862_pname H) F_17)))) % FOF formula (forall (H:(pname->pname)) (F_17:(pname->Prop)), ((finite_finite_pname F_17)->(finite_finite_pname ((image_pname_pname H) F_17)))) of role axiom named fact_32_finite__imageI % A new axiom: (forall (H:(pname->pname)) (F_17:(pname->Prop)), ((finite_finite_pname F_17)->(finite_finite_pname ((image_pname_pname H) F_17)))) % FOF formula (forall (A_76:(hoare_1262092251_state->Prop)), ((ord_le870406270tate_o bot_bo113204042tate_o) A_76)) of role axiom named fact_33_empty__subsetI % A new axiom: (forall (A_76:(hoare_1262092251_state->Prop)), ((ord_le870406270tate_o bot_bo113204042tate_o) A_76)) % FOF formula (forall (A_76:((pname->Prop)->Prop)), ((ord_le1205211808me_o_o bot_bot_pname_o_o) A_76)) of role axiom named fact_34_empty__subsetI % A new axiom: (forall (A_76:((pname->Prop)->Prop)), ((ord_le1205211808me_o_o bot_bot_pname_o_o) A_76)) % FOF formula (forall (A_76:((hoare_1262092251_state->Prop)->Prop)), ((ord_le2012720639te_o_o bot_bo1962689075te_o_o) A_76)) of role axiom named fact_35_empty__subsetI % A new axiom: (forall (A_76:((hoare_1262092251_state->Prop)->Prop)), ((ord_le2012720639te_o_o bot_bo1962689075te_o_o) A_76)) % FOF formula (forall (A_76:(pname->Prop)), ((ord_less_eq_pname_o bot_bot_pname_o) A_76)) of role axiom named fact_36_empty__subsetI % A new axiom: (forall (A_76:(pname->Prop)), ((ord_less_eq_pname_o bot_bot_pname_o) A_76)) % FOF formula (forall (A_75:hoare_1262092251_state) (A_74:(hoare_1262092251_state->Prop)), ((finite1178804552_state A_74)->(finite1178804552_state ((insert81609953_state A_75) A_74)))) of role axiom named fact_37_finite_OinsertI % A new axiom: (forall (A_75:hoare_1262092251_state) (A_74:(hoare_1262092251_state->Prop)), ((finite1178804552_state A_74)->(finite1178804552_state ((insert81609953_state A_75) A_74)))) % FOF formula (forall (A_75:pname) (A_74:(pname->Prop)), ((finite_finite_pname A_74)->(finite_finite_pname ((insert_pname A_75) A_74)))) of role axiom named fact_38_finite_OinsertI % A new axiom: (forall (A_75:pname) (A_74:(pname->Prop)), ((finite_finite_pname A_74)->(finite_finite_pname ((insert_pname A_75) A_74)))) % FOF formula (forall (A_75:((pname->Prop)->Prop)) (A_74:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o A_74)->(finite1066544169me_o_o ((insert_pname_o_o A_75) A_74)))) of role axiom named fact_39_finite_OinsertI % A new axiom: (forall (A_75:((pname->Prop)->Prop)) (A_74:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o A_74)->(finite1066544169me_o_o ((insert_pname_o_o A_75) A_74)))) % FOF formula (forall (A_75:((hoare_1262092251_state->Prop)->Prop)) (A_74:(((hoare_1262092251_state->Prop)->Prop)->Prop)), ((finite1303896758te_o_o A_74)->(finite1303896758te_o_o ((insert1691644879te_o_o A_75) A_74)))) of role axiom named fact_40_finite_OinsertI % A new axiom: (forall (A_75:((hoare_1262092251_state->Prop)->Prop)) (A_74:(((hoare_1262092251_state->Prop)->Prop)->Prop)), ((finite1303896758te_o_o A_74)->(finite1303896758te_o_o ((insert1691644879te_o_o A_75) A_74)))) % FOF formula (forall (A_75:(hoare_1262092251_state->Prop)) (A_74:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o A_74)->(finite1423311111tate_o ((insert1042460334tate_o A_75) A_74)))) of role axiom named fact_41_finite_OinsertI % A new axiom: (forall (A_75:(hoare_1262092251_state->Prop)) (A_74:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o A_74)->(finite1423311111tate_o ((insert1042460334tate_o A_75) A_74)))) % FOF formula (forall (A_75:(pname->Prop)) (A_74:((pname->Prop)->Prop)), ((finite297249702name_o A_74)->(finite297249702name_o ((insert_pname_o A_75) A_74)))) of role axiom named fact_42_finite_OinsertI % A new axiom: (forall (A_75:(pname->Prop)) (A_74:((pname->Prop)->Prop)), ((finite297249702name_o A_74)->(finite297249702name_o ((insert_pname_o A_75) A_74)))) % FOF formula (finite_finite_pname bot_bot_pname_o) of role axiom named fact_43_finite_OemptyI % A new axiom: (finite_finite_pname bot_bot_pname_o) % FOF formula (finite1178804552_state bot_bo113204042tate_o) of role axiom named fact_44_finite_OemptyI % A new axiom: (finite1178804552_state bot_bo113204042tate_o) % FOF formula (finite1066544169me_o_o bot_bot_pname_o_o_o) of role axiom named fact_45_finite_OemptyI % A new axiom: (finite1066544169me_o_o bot_bot_pname_o_o_o) % FOF formula (finite1303896758te_o_o bot_bo388435036_o_o_o) of role axiom named fact_46_finite_OemptyI % A new axiom: (finite1303896758te_o_o bot_bo388435036_o_o_o) % FOF formula (finite1423311111tate_o bot_bo1962689075te_o_o) of role axiom named fact_47_finite_OemptyI % A new axiom: (finite1423311111tate_o bot_bo1962689075te_o_o) % FOF formula (finite297249702name_o bot_bot_pname_o_o) of role axiom named fact_48_finite_OemptyI % A new axiom: (finite297249702name_o bot_bot_pname_o_o) % FOF formula (forall (Q_1:(pname->Prop)) (P_9:(pname->Prop)), (((or (finite_finite_pname (collect_pname P_9))) (finite_finite_pname (collect_pname Q_1)))->(finite_finite_pname (collect_pname (fun (X_1:pname)=> ((and (P_9 X_1)) (Q_1 X_1))))))) of role axiom named fact_49_finite__Collect__conjI % A new axiom: (forall (Q_1:(pname->Prop)) (P_9:(pname->Prop)), (((or (finite_finite_pname (collect_pname P_9))) (finite_finite_pname (collect_pname Q_1)))->(finite_finite_pname (collect_pname (fun (X_1:pname)=> ((and (P_9 X_1)) (Q_1 X_1))))))) % FOF formula (forall (Q_1:(hoare_1262092251_state->Prop)) (P_9:(hoare_1262092251_state->Prop)), (((or (finite1178804552_state (collec1121927558_state P_9))) (finite1178804552_state (collec1121927558_state Q_1)))->(finite1178804552_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> ((and (P_9 X_1)) (Q_1 X_1))))))) of role axiom named fact_50_finite__Collect__conjI % A new axiom: (forall (Q_1:(hoare_1262092251_state->Prop)) (P_9:(hoare_1262092251_state->Prop)), (((or (finite1178804552_state (collec1121927558_state P_9))) (finite1178804552_state (collec1121927558_state Q_1)))->(finite1178804552_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> ((and (P_9 X_1)) (Q_1 X_1))))))) % FOF formula (forall (Q_1:(((pname->Prop)->Prop)->Prop)) (P_9:(((pname->Prop)->Prop)->Prop)), (((or (finite1066544169me_o_o (collect_pname_o_o P_9))) (finite1066544169me_o_o (collect_pname_o_o Q_1)))->(finite1066544169me_o_o (collect_pname_o_o (fun (X_1:((pname->Prop)->Prop))=> ((and (P_9 X_1)) (Q_1 X_1))))))) of role axiom named fact_51_finite__Collect__conjI % A new axiom: (forall (Q_1:(((pname->Prop)->Prop)->Prop)) (P_9:(((pname->Prop)->Prop)->Prop)), (((or (finite1066544169me_o_o (collect_pname_o_o P_9))) (finite1066544169me_o_o (collect_pname_o_o Q_1)))->(finite1066544169me_o_o (collect_pname_o_o (fun (X_1:((pname->Prop)->Prop))=> ((and (P_9 X_1)) (Q_1 X_1))))))) % FOF formula (forall (Q_1:(((hoare_1262092251_state->Prop)->Prop)->Prop)) (P_9:(((hoare_1262092251_state->Prop)->Prop)->Prop)), (((or (finite1303896758te_o_o (collec341954548te_o_o P_9))) (finite1303896758te_o_o (collec341954548te_o_o Q_1)))->(finite1303896758te_o_o (collec341954548te_o_o (fun (X_1:((hoare_1262092251_state->Prop)->Prop))=> ((and (P_9 X_1)) (Q_1 X_1))))))) of role axiom named fact_52_finite__Collect__conjI % A new axiom: (forall (Q_1:(((hoare_1262092251_state->Prop)->Prop)->Prop)) (P_9:(((hoare_1262092251_state->Prop)->Prop)->Prop)), (((or (finite1303896758te_o_o (collec341954548te_o_o P_9))) (finite1303896758te_o_o (collec341954548te_o_o Q_1)))->(finite1303896758te_o_o (collec341954548te_o_o (fun (X_1:((hoare_1262092251_state->Prop)->Prop))=> ((and (P_9 X_1)) (Q_1 X_1))))))) % FOF formula (forall (Q_1:((hoare_1262092251_state->Prop)->Prop)) (P_9:((hoare_1262092251_state->Prop)->Prop)), (((or (finite1423311111tate_o (collec313158217tate_o P_9))) (finite1423311111tate_o (collec313158217tate_o Q_1)))->(finite1423311111tate_o (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> ((and (P_9 X_1)) (Q_1 X_1))))))) of role axiom named fact_53_finite__Collect__conjI % A new axiom: (forall (Q_1:((hoare_1262092251_state->Prop)->Prop)) (P_9:((hoare_1262092251_state->Prop)->Prop)), (((or (finite1423311111tate_o (collec313158217tate_o P_9))) (finite1423311111tate_o (collec313158217tate_o Q_1)))->(finite1423311111tate_o (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> ((and (P_9 X_1)) (Q_1 X_1))))))) % FOF formula (forall (Q_1:((pname->Prop)->Prop)) (P_9:((pname->Prop)->Prop)), (((or (finite297249702name_o (collect_pname_o P_9))) (finite297249702name_o (collect_pname_o Q_1)))->(finite297249702name_o (collect_pname_o (fun (X_1:(pname->Prop))=> ((and (P_9 X_1)) (Q_1 X_1))))))) of role axiom named fact_54_finite__Collect__conjI % A new axiom: (forall (Q_1:((pname->Prop)->Prop)) (P_9:((pname->Prop)->Prop)), (((or (finite297249702name_o (collect_pname_o P_9))) (finite297249702name_o (collect_pname_o Q_1)))->(finite297249702name_o (collect_pname_o (fun (X_1:(pname->Prop))=> ((and (P_9 X_1)) (Q_1 X_1))))))) % FOF formula (forall (C_8:hoare_1262092251_state) (A_73:(pname->Prop)), ((and ((((eq (pname->Prop)) A_73) bot_bot_pname_o)->(((eq (hoare_1262092251_state->Prop)) ((image_669833818_state (fun (X_1:pname)=> C_8)) A_73)) bot_bo113204042tate_o))) ((not (((eq (pname->Prop)) A_73) bot_bot_pname_o))->(((eq (hoare_1262092251_state->Prop)) ((image_669833818_state (fun (X_1:pname)=> C_8)) A_73)) ((insert81609953_state C_8) bot_bo113204042tate_o))))) of role axiom named fact_55_image__constant__conv % A new axiom: (forall (C_8:hoare_1262092251_state) (A_73:(pname->Prop)), ((and ((((eq (pname->Prop)) A_73) bot_bot_pname_o)->(((eq (hoare_1262092251_state->Prop)) ((image_669833818_state (fun (X_1:pname)=> C_8)) A_73)) bot_bo113204042tate_o))) ((not (((eq (pname->Prop)) A_73) bot_bot_pname_o))->(((eq (hoare_1262092251_state->Prop)) ((image_669833818_state (fun (X_1:pname)=> C_8)) A_73)) ((insert81609953_state C_8) bot_bo113204042tate_o))))) % FOF formula (forall (C_8:pname) (A_73:(hoare_1262092251_state->Prop)), ((and ((((eq (hoare_1262092251_state->Prop)) A_73) bot_bo113204042tate_o)->(((eq (pname->Prop)) ((image_202231862_pname (fun (X_1:hoare_1262092251_state)=> C_8)) A_73)) bot_bot_pname_o))) ((not (((eq (hoare_1262092251_state->Prop)) A_73) bot_bo113204042tate_o))->(((eq (pname->Prop)) ((image_202231862_pname (fun (X_1:hoare_1262092251_state)=> C_8)) A_73)) ((insert_pname C_8) bot_bot_pname_o))))) of role axiom named fact_56_image__constant__conv % A new axiom: (forall (C_8:pname) (A_73:(hoare_1262092251_state->Prop)), ((and ((((eq (hoare_1262092251_state->Prop)) A_73) bot_bo113204042tate_o)->(((eq (pname->Prop)) ((image_202231862_pname (fun (X_1:hoare_1262092251_state)=> C_8)) A_73)) bot_bot_pname_o))) ((not (((eq (hoare_1262092251_state->Prop)) A_73) bot_bo113204042tate_o))->(((eq (pname->Prop)) ((image_202231862_pname (fun (X_1:hoare_1262092251_state)=> C_8)) A_73)) ((insert_pname C_8) bot_bot_pname_o))))) % FOF formula (forall (C_8:(pname->Prop)) (A_73:(hoare_1262092251_state->Prop)), ((and ((((eq (hoare_1262092251_state->Prop)) A_73) bot_bo113204042tate_o)->(((eq ((pname->Prop)->Prop)) ((image_1320925383name_o (fun (X_1:hoare_1262092251_state)=> C_8)) A_73)) bot_bot_pname_o_o))) ((not (((eq (hoare_1262092251_state->Prop)) A_73) bot_bo113204042tate_o))->(((eq ((pname->Prop)->Prop)) ((image_1320925383name_o (fun (X_1:hoare_1262092251_state)=> C_8)) A_73)) ((insert_pname_o C_8) bot_bot_pname_o_o))))) of role axiom named fact_57_image__constant__conv % A new axiom: (forall (C_8:(pname->Prop)) (A_73:(hoare_1262092251_state->Prop)), ((and ((((eq (hoare_1262092251_state->Prop)) A_73) bot_bo113204042tate_o)->(((eq ((pname->Prop)->Prop)) ((image_1320925383name_o (fun (X_1:hoare_1262092251_state)=> C_8)) A_73)) bot_bot_pname_o_o))) ((not (((eq (hoare_1262092251_state->Prop)) A_73) bot_bo113204042tate_o))->(((eq ((pname->Prop)->Prop)) ((image_1320925383name_o (fun (X_1:hoare_1262092251_state)=> C_8)) A_73)) ((insert_pname_o C_8) bot_bot_pname_o_o))))) % FOF formula (forall (C_8:(hoare_1262092251_state->Prop)) (A_73:(hoare_1262092251_state->Prop)), ((and ((((eq (hoare_1262092251_state->Prop)) A_73) bot_bo113204042tate_o)->(((eq ((hoare_1262092251_state->Prop)->Prop)) ((image_1403668518tate_o (fun (X_1:hoare_1262092251_state)=> C_8)) A_73)) bot_bo1962689075te_o_o))) ((not (((eq (hoare_1262092251_state->Prop)) A_73) bot_bo113204042tate_o))->(((eq ((hoare_1262092251_state->Prop)->Prop)) ((image_1403668518tate_o (fun (X_1:hoare_1262092251_state)=> C_8)) A_73)) ((insert1042460334tate_o C_8) bot_bo1962689075te_o_o))))) of role axiom named fact_58_image__constant__conv % A new axiom: (forall (C_8:(hoare_1262092251_state->Prop)) (A_73:(hoare_1262092251_state->Prop)), ((and ((((eq (hoare_1262092251_state->Prop)) A_73) bot_bo113204042tate_o)->(((eq ((hoare_1262092251_state->Prop)->Prop)) ((image_1403668518tate_o (fun (X_1:hoare_1262092251_state)=> C_8)) A_73)) bot_bo1962689075te_o_o))) ((not (((eq (hoare_1262092251_state->Prop)) A_73) bot_bo113204042tate_o))->(((eq ((hoare_1262092251_state->Prop)->Prop)) ((image_1403668518tate_o (fun (X_1:hoare_1262092251_state)=> C_8)) A_73)) ((insert1042460334tate_o C_8) bot_bo1962689075te_o_o))))) % FOF formula (forall (C_8:(pname->Prop)) (A_73:(pname->Prop)), ((and ((((eq (pname->Prop)) A_73) bot_bot_pname_o)->(((eq ((pname->Prop)->Prop)) ((image_pname_pname_o (fun (X_1:pname)=> C_8)) A_73)) bot_bot_pname_o_o))) ((not (((eq (pname->Prop)) A_73) bot_bot_pname_o))->(((eq ((pname->Prop)->Prop)) ((image_pname_pname_o (fun (X_1:pname)=> C_8)) A_73)) ((insert_pname_o C_8) bot_bot_pname_o_o))))) of role axiom named fact_59_image__constant__conv % A new axiom: (forall (C_8:(pname->Prop)) (A_73:(pname->Prop)), ((and ((((eq (pname->Prop)) A_73) bot_bot_pname_o)->(((eq ((pname->Prop)->Prop)) ((image_pname_pname_o (fun (X_1:pname)=> C_8)) A_73)) bot_bot_pname_o_o))) ((not (((eq (pname->Prop)) A_73) bot_bot_pname_o))->(((eq ((pname->Prop)->Prop)) ((image_pname_pname_o (fun (X_1:pname)=> C_8)) A_73)) ((insert_pname_o C_8) bot_bot_pname_o_o))))) % FOF formula (forall (C_8:(hoare_1262092251_state->Prop)) (A_73:(pname->Prop)), ((and ((((eq (pname->Prop)) A_73) bot_bot_pname_o)->(((eq ((hoare_1262092251_state->Prop)->Prop)) ((image_518521461tate_o (fun (X_1:pname)=> C_8)) A_73)) bot_bo1962689075te_o_o))) ((not (((eq (pname->Prop)) A_73) bot_bot_pname_o))->(((eq ((hoare_1262092251_state->Prop)->Prop)) ((image_518521461tate_o (fun (X_1:pname)=> C_8)) A_73)) ((insert1042460334tate_o C_8) bot_bo1962689075te_o_o))))) of role axiom named fact_60_image__constant__conv % A new axiom: (forall (C_8:(hoare_1262092251_state->Prop)) (A_73:(pname->Prop)), ((and ((((eq (pname->Prop)) A_73) bot_bot_pname_o)->(((eq ((hoare_1262092251_state->Prop)->Prop)) ((image_518521461tate_o (fun (X_1:pname)=> C_8)) A_73)) bot_bo1962689075te_o_o))) ((not (((eq (pname->Prop)) A_73) bot_bot_pname_o))->(((eq ((hoare_1262092251_state->Prop)->Prop)) ((image_518521461tate_o (fun (X_1:pname)=> C_8)) A_73)) ((insert1042460334tate_o C_8) bot_bo1962689075te_o_o))))) % FOF formula (forall (C_8:pname) (A_73:(pname->Prop)), ((and ((((eq (pname->Prop)) A_73) bot_bot_pname_o)->(((eq (pname->Prop)) ((image_pname_pname (fun (X_1:pname)=> C_8)) A_73)) bot_bot_pname_o))) ((not (((eq (pname->Prop)) A_73) bot_bot_pname_o))->(((eq (pname->Prop)) ((image_pname_pname (fun (X_1:pname)=> C_8)) A_73)) ((insert_pname C_8) bot_bot_pname_o))))) of role axiom named fact_61_image__constant__conv % A new axiom: (forall (C_8:pname) (A_73:(pname->Prop)), ((and ((((eq (pname->Prop)) A_73) bot_bot_pname_o)->(((eq (pname->Prop)) ((image_pname_pname (fun (X_1:pname)=> C_8)) A_73)) bot_bot_pname_o))) ((not (((eq (pname->Prop)) A_73) bot_bot_pname_o))->(((eq (pname->Prop)) ((image_pname_pname (fun (X_1:pname)=> C_8)) A_73)) ((insert_pname C_8) bot_bot_pname_o))))) % FOF formula (forall (C_8:hoare_1262092251_state) (A_73:((pname->Prop)->Prop)), ((and ((((eq ((pname->Prop)->Prop)) A_73) bot_bot_pname_o_o)->(((eq (hoare_1262092251_state->Prop)) ((image_1476171975_state (fun (X_1:(pname->Prop))=> C_8)) A_73)) bot_bo113204042tate_o))) ((not (((eq ((pname->Prop)->Prop)) A_73) bot_bot_pname_o_o))->(((eq (hoare_1262092251_state->Prop)) ((image_1476171975_state (fun (X_1:(pname->Prop))=> C_8)) A_73)) ((insert81609953_state C_8) bot_bo113204042tate_o))))) of role axiom named fact_62_image__constant__conv % A new axiom: (forall (C_8:hoare_1262092251_state) (A_73:((pname->Prop)->Prop)), ((and ((((eq ((pname->Prop)->Prop)) A_73) bot_bot_pname_o_o)->(((eq (hoare_1262092251_state->Prop)) ((image_1476171975_state (fun (X_1:(pname->Prop))=> C_8)) A_73)) bot_bo113204042tate_o))) ((not (((eq ((pname->Prop)->Prop)) A_73) bot_bot_pname_o_o))->(((eq (hoare_1262092251_state->Prop)) ((image_1476171975_state (fun (X_1:(pname->Prop))=> C_8)) A_73)) ((insert81609953_state C_8) bot_bo113204042tate_o))))) % FOF formula (forall (C_8:hoare_1262092251_state) (A_73:((hoare_1262092251_state->Prop)->Prop)), ((and ((((eq ((hoare_1262092251_state->Prop)->Prop)) A_73) bot_bo1962689075te_o_o)->(((eq (hoare_1262092251_state->Prop)) ((image_234589002_state (fun (X_1:(hoare_1262092251_state->Prop))=> C_8)) A_73)) bot_bo113204042tate_o))) ((not (((eq ((hoare_1262092251_state->Prop)->Prop)) A_73) bot_bo1962689075te_o_o))->(((eq (hoare_1262092251_state->Prop)) ((image_234589002_state (fun (X_1:(hoare_1262092251_state->Prop))=> C_8)) A_73)) ((insert81609953_state C_8) bot_bo113204042tate_o))))) of role axiom named fact_63_image__constant__conv % A new axiom: (forall (C_8:hoare_1262092251_state) (A_73:((hoare_1262092251_state->Prop)->Prop)), ((and ((((eq ((hoare_1262092251_state->Prop)->Prop)) A_73) bot_bo1962689075te_o_o)->(((eq (hoare_1262092251_state->Prop)) ((image_234589002_state (fun (X_1:(hoare_1262092251_state->Prop))=> C_8)) A_73)) bot_bo113204042tate_o))) ((not (((eq ((hoare_1262092251_state->Prop)->Prop)) A_73) bot_bo1962689075te_o_o))->(((eq (hoare_1262092251_state->Prop)) ((image_234589002_state (fun (X_1:(hoare_1262092251_state->Prop))=> C_8)) A_73)) ((insert81609953_state C_8) bot_bo113204042tate_o))))) % FOF formula (forall (C_8:pname) (A_73:((pname->Prop)->Prop)), ((and ((((eq ((pname->Prop)->Prop)) A_73) bot_bot_pname_o_o)->(((eq (pname->Prop)) ((image_pname_o_pname (fun (X_1:(pname->Prop))=> C_8)) A_73)) bot_bot_pname_o))) ((not (((eq ((pname->Prop)->Prop)) A_73) bot_bot_pname_o_o))->(((eq (pname->Prop)) ((image_pname_o_pname (fun (X_1:(pname->Prop))=> C_8)) A_73)) ((insert_pname C_8) bot_bot_pname_o))))) of role axiom named fact_64_image__constant__conv % A new axiom: (forall (C_8:pname) (A_73:((pname->Prop)->Prop)), ((and ((((eq ((pname->Prop)->Prop)) A_73) bot_bot_pname_o_o)->(((eq (pname->Prop)) ((image_pname_o_pname (fun (X_1:(pname->Prop))=> C_8)) A_73)) bot_bot_pname_o))) ((not (((eq ((pname->Prop)->Prop)) A_73) bot_bot_pname_o_o))->(((eq (pname->Prop)) ((image_pname_o_pname (fun (X_1:(pname->Prop))=> C_8)) A_73)) ((insert_pname C_8) bot_bot_pname_o))))) % FOF formula (forall (C_8:pname) (A_73:((hoare_1262092251_state->Prop)->Prop)), ((and ((((eq ((hoare_1262092251_state->Prop)->Prop)) A_73) bot_bo1962689075te_o_o)->(((eq (pname->Prop)) ((image_1820530197_pname (fun (X_1:(hoare_1262092251_state->Prop))=> C_8)) A_73)) bot_bot_pname_o))) ((not (((eq ((hoare_1262092251_state->Prop)->Prop)) A_73) bot_bo1962689075te_o_o))->(((eq (pname->Prop)) ((image_1820530197_pname (fun (X_1:(hoare_1262092251_state->Prop))=> C_8)) A_73)) ((insert_pname C_8) bot_bot_pname_o))))) of role axiom named fact_65_image__constant__conv % A new axiom: (forall (C_8:pname) (A_73:((hoare_1262092251_state->Prop)->Prop)), ((and ((((eq ((hoare_1262092251_state->Prop)->Prop)) A_73) bot_bo1962689075te_o_o)->(((eq (pname->Prop)) ((image_1820530197_pname (fun (X_1:(hoare_1262092251_state->Prop))=> C_8)) A_73)) bot_bot_pname_o))) ((not (((eq ((hoare_1262092251_state->Prop)->Prop)) A_73) bot_bo1962689075te_o_o))->(((eq (pname->Prop)) ((image_1820530197_pname (fun (X_1:(hoare_1262092251_state->Prop))=> C_8)) A_73)) ((insert_pname C_8) bot_bot_pname_o))))) % FOF formula (forall (C_7:hoare_1262092251_state) (X_18:pname) (A_72:(pname->Prop)), (((member_pname X_18) A_72)->(((eq (hoare_1262092251_state->Prop)) ((image_669833818_state (fun (X_1:pname)=> C_7)) A_72)) ((insert81609953_state C_7) bot_bo113204042tate_o)))) of role axiom named fact_66_image__constant % A new axiom: (forall (C_7:hoare_1262092251_state) (X_18:pname) (A_72:(pname->Prop)), (((member_pname X_18) A_72)->(((eq (hoare_1262092251_state->Prop)) ((image_669833818_state (fun (X_1:pname)=> C_7)) A_72)) ((insert81609953_state C_7) bot_bo113204042tate_o)))) % FOF formula (forall (C_7:pname) (X_18:hoare_1262092251_state) (A_72:(hoare_1262092251_state->Prop)), (((member5164104_state X_18) A_72)->(((eq (pname->Prop)) ((image_202231862_pname (fun (X_1:hoare_1262092251_state)=> C_7)) A_72)) ((insert_pname C_7) bot_bot_pname_o)))) of role axiom named fact_67_image__constant % A new axiom: (forall (C_7:pname) (X_18:hoare_1262092251_state) (A_72:(hoare_1262092251_state->Prop)), (((member5164104_state X_18) A_72)->(((eq (pname->Prop)) ((image_202231862_pname (fun (X_1:hoare_1262092251_state)=> C_7)) A_72)) ((insert_pname C_7) bot_bot_pname_o)))) % FOF formula (forall (C_7:(pname->Prop)) (X_18:hoare_1262092251_state) (A_72:(hoare_1262092251_state->Prop)), (((member5164104_state X_18) A_72)->(((eq ((pname->Prop)->Prop)) ((image_1320925383name_o (fun (X_1:hoare_1262092251_state)=> C_7)) A_72)) ((insert_pname_o C_7) bot_bot_pname_o_o)))) of role axiom named fact_68_image__constant % A new axiom: (forall (C_7:(pname->Prop)) (X_18:hoare_1262092251_state) (A_72:(hoare_1262092251_state->Prop)), (((member5164104_state X_18) A_72)->(((eq ((pname->Prop)->Prop)) ((image_1320925383name_o (fun (X_1:hoare_1262092251_state)=> C_7)) A_72)) ((insert_pname_o C_7) bot_bot_pname_o_o)))) % FOF formula (forall (C_7:(hoare_1262092251_state->Prop)) (X_18:hoare_1262092251_state) (A_72:(hoare_1262092251_state->Prop)), (((member5164104_state X_18) A_72)->(((eq ((hoare_1262092251_state->Prop)->Prop)) ((image_1403668518tate_o (fun (X_1:hoare_1262092251_state)=> C_7)) A_72)) ((insert1042460334tate_o C_7) bot_bo1962689075te_o_o)))) of role axiom named fact_69_image__constant % A new axiom: (forall (C_7:(hoare_1262092251_state->Prop)) (X_18:hoare_1262092251_state) (A_72:(hoare_1262092251_state->Prop)), (((member5164104_state X_18) A_72)->(((eq ((hoare_1262092251_state->Prop)->Prop)) ((image_1403668518tate_o (fun (X_1:hoare_1262092251_state)=> C_7)) A_72)) ((insert1042460334tate_o C_7) bot_bo1962689075te_o_o)))) % FOF formula (forall (C_7:(pname->Prop)) (X_18:pname) (A_72:(pname->Prop)), (((member_pname X_18) A_72)->(((eq ((pname->Prop)->Prop)) ((image_pname_pname_o (fun (X_1:pname)=> C_7)) A_72)) ((insert_pname_o C_7) bot_bot_pname_o_o)))) of role axiom named fact_70_image__constant % A new axiom: (forall (C_7:(pname->Prop)) (X_18:pname) (A_72:(pname->Prop)), (((member_pname X_18) A_72)->(((eq ((pname->Prop)->Prop)) ((image_pname_pname_o (fun (X_1:pname)=> C_7)) A_72)) ((insert_pname_o C_7) bot_bot_pname_o_o)))) % FOF formula (forall (C_7:(hoare_1262092251_state->Prop)) (X_18:pname) (A_72:(pname->Prop)), (((member_pname X_18) A_72)->(((eq ((hoare_1262092251_state->Prop)->Prop)) ((image_518521461tate_o (fun (X_1:pname)=> C_7)) A_72)) ((insert1042460334tate_o C_7) bot_bo1962689075te_o_o)))) of role axiom named fact_71_image__constant % A new axiom: (forall (C_7:(hoare_1262092251_state->Prop)) (X_18:pname) (A_72:(pname->Prop)), (((member_pname X_18) A_72)->(((eq ((hoare_1262092251_state->Prop)->Prop)) ((image_518521461tate_o (fun (X_1:pname)=> C_7)) A_72)) ((insert1042460334tate_o C_7) bot_bo1962689075te_o_o)))) % FOF formula (forall (C_7:pname) (X_18:pname) (A_72:(pname->Prop)), (((member_pname X_18) A_72)->(((eq (pname->Prop)) ((image_pname_pname (fun (X_1:pname)=> C_7)) A_72)) ((insert_pname C_7) bot_bot_pname_o)))) of role axiom named fact_72_image__constant % A new axiom: (forall (C_7:pname) (X_18:pname) (A_72:(pname->Prop)), (((member_pname X_18) A_72)->(((eq (pname->Prop)) ((image_pname_pname (fun (X_1:pname)=> C_7)) A_72)) ((insert_pname C_7) bot_bot_pname_o)))) % FOF formula (forall (C_7:hoare_1262092251_state) (X_18:(pname->Prop)) (A_72:((pname->Prop)->Prop)), (((member_pname_o X_18) A_72)->(((eq (hoare_1262092251_state->Prop)) ((image_1476171975_state (fun (X_1:(pname->Prop))=> C_7)) A_72)) ((insert81609953_state C_7) bot_bo113204042tate_o)))) of role axiom named fact_73_image__constant % A new axiom: (forall (C_7:hoare_1262092251_state) (X_18:(pname->Prop)) (A_72:((pname->Prop)->Prop)), (((member_pname_o X_18) A_72)->(((eq (hoare_1262092251_state->Prop)) ((image_1476171975_state (fun (X_1:(pname->Prop))=> C_7)) A_72)) ((insert81609953_state C_7) bot_bo113204042tate_o)))) % FOF formula (forall (C_7:hoare_1262092251_state) (X_18:(hoare_1262092251_state->Prop)) (A_72:((hoare_1262092251_state->Prop)->Prop)), (((member907417095tate_o X_18) A_72)->(((eq (hoare_1262092251_state->Prop)) ((image_234589002_state (fun (X_1:(hoare_1262092251_state->Prop))=> C_7)) A_72)) ((insert81609953_state C_7) bot_bo113204042tate_o)))) of role axiom named fact_74_image__constant % A new axiom: (forall (C_7:hoare_1262092251_state) (X_18:(hoare_1262092251_state->Prop)) (A_72:((hoare_1262092251_state->Prop)->Prop)), (((member907417095tate_o X_18) A_72)->(((eq (hoare_1262092251_state->Prop)) ((image_234589002_state (fun (X_1:(hoare_1262092251_state->Prop))=> C_7)) A_72)) ((insert81609953_state C_7) bot_bo113204042tate_o)))) % FOF formula (forall (C_7:pname) (X_18:(pname->Prop)) (A_72:((pname->Prop)->Prop)), (((member_pname_o X_18) A_72)->(((eq (pname->Prop)) ((image_pname_o_pname (fun (X_1:(pname->Prop))=> C_7)) A_72)) ((insert_pname C_7) bot_bot_pname_o)))) of role axiom named fact_75_image__constant % A new axiom: (forall (C_7:pname) (X_18:(pname->Prop)) (A_72:((pname->Prop)->Prop)), (((member_pname_o X_18) A_72)->(((eq (pname->Prop)) ((image_pname_o_pname (fun (X_1:(pname->Prop))=> C_7)) A_72)) ((insert_pname C_7) bot_bot_pname_o)))) % FOF formula (forall (C_7:pname) (X_18:(hoare_1262092251_state->Prop)) (A_72:((hoare_1262092251_state->Prop)->Prop)), (((member907417095tate_o X_18) A_72)->(((eq (pname->Prop)) ((image_1820530197_pname (fun (X_1:(hoare_1262092251_state->Prop))=> C_7)) A_72)) ((insert_pname C_7) bot_bot_pname_o)))) of role axiom named fact_76_image__constant % A new axiom: (forall (C_7:pname) (X_18:(hoare_1262092251_state->Prop)) (A_72:((hoare_1262092251_state->Prop)->Prop)), (((member907417095tate_o X_18) A_72)->(((eq (pname->Prop)) ((image_1820530197_pname (fun (X_1:(hoare_1262092251_state->Prop))=> C_7)) A_72)) ((insert_pname C_7) bot_bot_pname_o)))) % FOF formula (forall (F_16:(pname->option_com)) (X_17:pname) (Y_4:com), ((((eq option_com) (F_16 X_17)) (some_com Y_4))->(((eq (pname->Prop)) ((insert_pname X_17) (dom_pname_com F_16))) (dom_pname_com F_16)))) of role axiom named fact_77_insert__dom % A new axiom: (forall (F_16:(pname->option_com)) (X_17:pname) (Y_4:com), ((((eq option_com) (F_16 X_17)) (some_com Y_4))->(((eq (pname->Prop)) ((insert_pname X_17) (dom_pname_com F_16))) (dom_pname_com F_16)))) % FOF formula (forall (F_16:((pname->Prop)->option_com)) (X_17:(pname->Prop)) (Y_4:com), ((((eq option_com) (F_16 X_17)) (some_com Y_4))->(((eq ((pname->Prop)->Prop)) ((insert_pname_o X_17) (dom_pname_o_com F_16))) (dom_pname_o_com F_16)))) of role axiom named fact_78_insert__dom % A new axiom: (forall (F_16:((pname->Prop)->option_com)) (X_17:(pname->Prop)) (Y_4:com), ((((eq option_com) (F_16 X_17)) (some_com Y_4))->(((eq ((pname->Prop)->Prop)) ((insert_pname_o X_17) (dom_pname_o_com F_16))) (dom_pname_o_com F_16)))) % FOF formula (forall (F_16:((hoare_1262092251_state->Prop)->option_com)) (X_17:(hoare_1262092251_state->Prop)) (Y_4:com), ((((eq option_com) (F_16 X_17)) (some_com Y_4))->(((eq ((hoare_1262092251_state->Prop)->Prop)) ((insert1042460334tate_o X_17) (dom_Ho1489634536_o_com F_16))) (dom_Ho1489634536_o_com F_16)))) of role axiom named fact_79_insert__dom % A new axiom: (forall (F_16:((hoare_1262092251_state->Prop)->option_com)) (X_17:(hoare_1262092251_state->Prop)) (Y_4:com), ((((eq option_com) (F_16 X_17)) (some_com Y_4))->(((eq ((hoare_1262092251_state->Prop)->Prop)) ((insert1042460334tate_o X_17) (dom_Ho1489634536_o_com F_16))) (dom_Ho1489634536_o_com F_16)))) % FOF formula (forall (B_40:(hoare_1262092251_state->Prop)) (F_15:(pname->hoare_1262092251_state)) (A_71:(pname->Prop)), ((finite_finite_pname A_71)->(((ord_le870406270tate_o B_40) ((image_669833818_state F_15) A_71))->(finite1178804552_state B_40)))) of role axiom named fact_80_finite__surj % A new axiom: (forall (B_40:(hoare_1262092251_state->Prop)) (F_15:(pname->hoare_1262092251_state)) (A_71:(pname->Prop)), ((finite_finite_pname A_71)->(((ord_le870406270tate_o B_40) ((image_669833818_state F_15) A_71))->(finite1178804552_state B_40)))) % FOF formula (forall (B_40:(pname->Prop)) (F_15:(((pname->Prop)->Prop)->pname)) (A_71:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o A_71)->(((ord_less_eq_pname_o B_40) ((image_471733107_pname F_15) A_71))->(finite_finite_pname B_40)))) of role axiom named fact_81_finite__surj % A new axiom: (forall (B_40:(pname->Prop)) (F_15:(((pname->Prop)->Prop)->pname)) (A_71:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o A_71)->(((ord_less_eq_pname_o B_40) ((image_471733107_pname F_15) A_71))->(finite_finite_pname B_40)))) % FOF formula (forall (B_40:(pname->Prop)) (F_15:(((hoare_1262092251_state->Prop)->Prop)->pname)) (A_71:(((hoare_1262092251_state->Prop)->Prop)->Prop)), ((finite1303896758te_o_o A_71)->(((ord_less_eq_pname_o B_40) ((image_893364936_pname F_15) A_71))->(finite_finite_pname B_40)))) of role axiom named fact_82_finite__surj % A new axiom: (forall (B_40:(pname->Prop)) (F_15:(((hoare_1262092251_state->Prop)->Prop)->pname)) (A_71:(((hoare_1262092251_state->Prop)->Prop)->Prop)), ((finite1303896758te_o_o A_71)->(((ord_less_eq_pname_o B_40) ((image_893364936_pname F_15) A_71))->(finite_finite_pname B_40)))) % FOF formula (forall (B_40:(pname->Prop)) (F_15:((hoare_1262092251_state->Prop)->pname)) (A_71:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o A_71)->(((ord_less_eq_pname_o B_40) ((image_1820530197_pname F_15) A_71))->(finite_finite_pname B_40)))) of role axiom named fact_83_finite__surj % A new axiom: (forall (B_40:(pname->Prop)) (F_15:((hoare_1262092251_state->Prop)->pname)) (A_71:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o A_71)->(((ord_less_eq_pname_o B_40) ((image_1820530197_pname F_15) A_71))->(finite_finite_pname B_40)))) % FOF formula (forall (B_40:(pname->Prop)) (F_15:((pname->Prop)->pname)) (A_71:((pname->Prop)->Prop)), ((finite297249702name_o A_71)->(((ord_less_eq_pname_o B_40) ((image_pname_o_pname F_15) A_71))->(finite_finite_pname B_40)))) of role axiom named fact_84_finite__surj % A new axiom: (forall (B_40:(pname->Prop)) (F_15:((pname->Prop)->pname)) (A_71:((pname->Prop)->Prop)), ((finite297249702name_o A_71)->(((ord_less_eq_pname_o B_40) ((image_pname_o_pname F_15) A_71))->(finite_finite_pname B_40)))) % FOF formula (forall (B_40:(hoare_1262092251_state->Prop)) (F_15:(((pname->Prop)->Prop)->hoare_1262092251_state)) (A_71:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o A_71)->(((ord_le870406270tate_o B_40) ((image_1036078444_state F_15) A_71))->(finite1178804552_state B_40)))) of role axiom named fact_85_finite__surj % A new axiom: (forall (B_40:(hoare_1262092251_state->Prop)) (F_15:(((pname->Prop)->Prop)->hoare_1262092251_state)) (A_71:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o A_71)->(((ord_le870406270tate_o B_40) ((image_1036078444_state F_15) A_71))->(finite1178804552_state B_40)))) % FOF formula (forall (B_40:(hoare_1262092251_state->Prop)) (F_15:(((hoare_1262092251_state->Prop)->Prop)->hoare_1262092251_state)) (A_71:(((hoare_1262092251_state->Prop)->Prop)->Prop)), ((finite1303896758te_o_o A_71)->(((ord_le870406270tate_o B_40) ((image_165349207_state F_15) A_71))->(finite1178804552_state B_40)))) of role axiom named fact_86_finite__surj % A new axiom: (forall (B_40:(hoare_1262092251_state->Prop)) (F_15:(((hoare_1262092251_state->Prop)->Prop)->hoare_1262092251_state)) (A_71:(((hoare_1262092251_state->Prop)->Prop)->Prop)), ((finite1303896758te_o_o A_71)->(((ord_le870406270tate_o B_40) ((image_165349207_state F_15) A_71))->(finite1178804552_state B_40)))) % FOF formula (forall (B_40:(hoare_1262092251_state->Prop)) (F_15:((hoare_1262092251_state->Prop)->hoare_1262092251_state)) (A_71:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o A_71)->(((ord_le870406270tate_o B_40) ((image_234589002_state F_15) A_71))->(finite1178804552_state B_40)))) of role axiom named fact_87_finite__surj % A new axiom: (forall (B_40:(hoare_1262092251_state->Prop)) (F_15:((hoare_1262092251_state->Prop)->hoare_1262092251_state)) (A_71:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o A_71)->(((ord_le870406270tate_o B_40) ((image_234589002_state F_15) A_71))->(finite1178804552_state B_40)))) % FOF formula (forall (B_40:(hoare_1262092251_state->Prop)) (F_15:((pname->Prop)->hoare_1262092251_state)) (A_71:((pname->Prop)->Prop)), ((finite297249702name_o A_71)->(((ord_le870406270tate_o B_40) ((image_1476171975_state F_15) A_71))->(finite1178804552_state B_40)))) of role axiom named fact_88_finite__surj % A new axiom: (forall (B_40:(hoare_1262092251_state->Prop)) (F_15:((pname->Prop)->hoare_1262092251_state)) (A_71:((pname->Prop)->Prop)), ((finite297249702name_o A_71)->(((ord_le870406270tate_o B_40) ((image_1476171975_state F_15) A_71))->(finite1178804552_state B_40)))) % FOF formula (forall (B_40:(((pname->Prop)->Prop)->Prop)) (F_15:(pname->((pname->Prop)->Prop))) (A_71:(pname->Prop)), ((finite_finite_pname A_71)->(((ord_le1828183645_o_o_o B_40) ((image_504089495me_o_o F_15) A_71))->(finite1066544169me_o_o B_40)))) of role axiom named fact_89_finite__surj % A new axiom: (forall (B_40:(((pname->Prop)->Prop)->Prop)) (F_15:(pname->((pname->Prop)->Prop))) (A_71:(pname->Prop)), ((finite_finite_pname A_71)->(((ord_le1828183645_o_o_o B_40) ((image_504089495me_o_o F_15) A_71))->(finite1066544169me_o_o B_40)))) % FOF formula (forall (B_40:(((hoare_1262092251_state->Prop)->Prop)->Prop)) (F_15:(pname->((hoare_1262092251_state->Prop)->Prop))) (A_71:(pname->Prop)), ((finite_finite_pname A_71)->(((ord_le1891858320_o_o_o B_40) ((image_827868872te_o_o F_15) A_71))->(finite1303896758te_o_o B_40)))) of role axiom named fact_90_finite__surj % A new axiom: (forall (B_40:(((hoare_1262092251_state->Prop)->Prop)->Prop)) (F_15:(pname->((hoare_1262092251_state->Prop)->Prop))) (A_71:(pname->Prop)), ((finite_finite_pname A_71)->(((ord_le1891858320_o_o_o B_40) ((image_827868872te_o_o F_15) A_71))->(finite1303896758te_o_o B_40)))) % FOF formula (forall (B_40:(pname->Prop)) (F_15:(pname->pname)) (A_71:(pname->Prop)), ((finite_finite_pname A_71)->(((ord_less_eq_pname_o B_40) ((image_pname_pname F_15) A_71))->(finite_finite_pname B_40)))) of role axiom named fact_91_finite__surj % A new axiom: (forall (B_40:(pname->Prop)) (F_15:(pname->pname)) (A_71:(pname->Prop)), ((finite_finite_pname A_71)->(((ord_less_eq_pname_o B_40) ((image_pname_pname F_15) A_71))->(finite_finite_pname B_40)))) % FOF formula (forall (B_40:((hoare_1262092251_state->Prop)->Prop)) (F_15:(pname->(hoare_1262092251_state->Prop))) (A_71:(pname->Prop)), ((finite_finite_pname A_71)->(((ord_le2012720639te_o_o B_40) ((image_518521461tate_o F_15) A_71))->(finite1423311111tate_o B_40)))) of role axiom named fact_92_finite__surj % A new axiom: (forall (B_40:((hoare_1262092251_state->Prop)->Prop)) (F_15:(pname->(hoare_1262092251_state->Prop))) (A_71:(pname->Prop)), ((finite_finite_pname A_71)->(((ord_le2012720639te_o_o B_40) ((image_518521461tate_o F_15) A_71))->(finite1423311111tate_o B_40)))) % FOF formula (forall (B_40:((pname->Prop)->Prop)) (F_15:(pname->(pname->Prop))) (A_71:(pname->Prop)), ((finite_finite_pname A_71)->(((ord_le1205211808me_o_o B_40) ((image_pname_pname_o F_15) A_71))->(finite297249702name_o B_40)))) of role axiom named fact_93_finite__surj % A new axiom: (forall (B_40:((pname->Prop)->Prop)) (F_15:(pname->(pname->Prop))) (A_71:(pname->Prop)), ((finite_finite_pname A_71)->(((ord_le1205211808me_o_o B_40) ((image_pname_pname_o F_15) A_71))->(finite297249702name_o B_40)))) % FOF formula (forall (B_40:(((pname->Prop)->Prop)->Prop)) (F_15:(hoare_1262092251_state->((pname->Prop)->Prop))) (A_71:(hoare_1262092251_state->Prop)), ((finite1178804552_state A_71)->(((ord_le1828183645_o_o_o B_40) ((image_333245000me_o_o F_15) A_71))->(finite1066544169me_o_o B_40)))) of role axiom named fact_94_finite__surj % A new axiom: (forall (B_40:(((pname->Prop)->Prop)->Prop)) (F_15:(hoare_1262092251_state->((pname->Prop)->Prop))) (A_71:(hoare_1262092251_state->Prop)), ((finite1178804552_state A_71)->(((ord_le1828183645_o_o_o B_40) ((image_333245000me_o_o F_15) A_71))->(finite1066544169me_o_o B_40)))) % FOF formula (forall (B_40:(((hoare_1262092251_state->Prop)->Prop)->Prop)) (F_15:(hoare_1262092251_state->((hoare_1262092251_state->Prop)->Prop))) (A_71:(hoare_1262092251_state->Prop)), ((finite1178804552_state A_71)->(((ord_le1891858320_o_o_o B_40) ((image_1731108951te_o_o F_15) A_71))->(finite1303896758te_o_o B_40)))) of role axiom named fact_95_finite__surj % A new axiom: (forall (B_40:(((hoare_1262092251_state->Prop)->Prop)->Prop)) (F_15:(hoare_1262092251_state->((hoare_1262092251_state->Prop)->Prop))) (A_71:(hoare_1262092251_state->Prop)), ((finite1178804552_state A_71)->(((ord_le1891858320_o_o_o B_40) ((image_1731108951te_o_o F_15) A_71))->(finite1303896758te_o_o B_40)))) % FOF formula (forall (B_40:(pname->Prop)) (F_15:(hoare_1262092251_state->pname)) (A_71:(hoare_1262092251_state->Prop)), ((finite1178804552_state A_71)->(((ord_less_eq_pname_o B_40) ((image_202231862_pname F_15) A_71))->(finite_finite_pname B_40)))) of role axiom named fact_96_finite__surj % A new axiom: (forall (B_40:(pname->Prop)) (F_15:(hoare_1262092251_state->pname)) (A_71:(hoare_1262092251_state->Prop)), ((finite1178804552_state A_71)->(((ord_less_eq_pname_o B_40) ((image_202231862_pname F_15) A_71))->(finite_finite_pname B_40)))) % FOF formula (forall (B_40:((hoare_1262092251_state->Prop)->Prop)) (F_15:(hoare_1262092251_state->(hoare_1262092251_state->Prop))) (A_71:(hoare_1262092251_state->Prop)), ((finite1178804552_state A_71)->(((ord_le2012720639te_o_o B_40) ((image_1403668518tate_o F_15) A_71))->(finite1423311111tate_o B_40)))) of role axiom named fact_97_finite__surj % A new axiom: (forall (B_40:((hoare_1262092251_state->Prop)->Prop)) (F_15:(hoare_1262092251_state->(hoare_1262092251_state->Prop))) (A_71:(hoare_1262092251_state->Prop)), ((finite1178804552_state A_71)->(((ord_le2012720639te_o_o B_40) ((image_1403668518tate_o F_15) A_71))->(finite1423311111tate_o B_40)))) % FOF formula (forall (B_40:((pname->Prop)->Prop)) (F_15:(hoare_1262092251_state->(pname->Prop))) (A_71:(hoare_1262092251_state->Prop)), ((finite1178804552_state A_71)->(((ord_le1205211808me_o_o B_40) ((image_1320925383name_o F_15) A_71))->(finite297249702name_o B_40)))) of role axiom named fact_98_finite__surj % A new axiom: (forall (B_40:((pname->Prop)->Prop)) (F_15:(hoare_1262092251_state->(pname->Prop))) (A_71:(hoare_1262092251_state->Prop)), ((finite1178804552_state A_71)->(((ord_le1205211808me_o_o B_40) ((image_1320925383name_o F_15) A_71))->(finite297249702name_o B_40)))) % FOF formula (forall (A_70:(hoare_1262092251_state->Prop)) (X_16:hoare_1262092251_state), (((ord_le870406270tate_o A_70) ((insert81609953_state X_16) bot_bo113204042tate_o))->((or (((eq (hoare_1262092251_state->Prop)) A_70) bot_bo113204042tate_o)) (((eq (hoare_1262092251_state->Prop)) A_70) ((insert81609953_state X_16) bot_bo113204042tate_o))))) of role axiom named fact_99_subset__singletonD % A new axiom: (forall (A_70:(hoare_1262092251_state->Prop)) (X_16:hoare_1262092251_state), (((ord_le870406270tate_o A_70) ((insert81609953_state X_16) bot_bo113204042tate_o))->((or (((eq (hoare_1262092251_state->Prop)) A_70) bot_bo113204042tate_o)) (((eq (hoare_1262092251_state->Prop)) A_70) ((insert81609953_state X_16) bot_bo113204042tate_o))))) % FOF formula (forall (A_70:((pname->Prop)->Prop)) (X_16:(pname->Prop)), (((ord_le1205211808me_o_o A_70) ((insert_pname_o X_16) bot_bot_pname_o_o))->((or (((eq ((pname->Prop)->Prop)) A_70) bot_bot_pname_o_o)) (((eq ((pname->Prop)->Prop)) A_70) ((insert_pname_o X_16) bot_bot_pname_o_o))))) of role axiom named fact_100_subset__singletonD % A new axiom: (forall (A_70:((pname->Prop)->Prop)) (X_16:(pname->Prop)), (((ord_le1205211808me_o_o A_70) ((insert_pname_o X_16) bot_bot_pname_o_o))->((or (((eq ((pname->Prop)->Prop)) A_70) bot_bot_pname_o_o)) (((eq ((pname->Prop)->Prop)) A_70) ((insert_pname_o X_16) bot_bot_pname_o_o))))) % FOF formula (forall (A_70:((hoare_1262092251_state->Prop)->Prop)) (X_16:(hoare_1262092251_state->Prop)), (((ord_le2012720639te_o_o A_70) ((insert1042460334tate_o X_16) bot_bo1962689075te_o_o))->((or (((eq ((hoare_1262092251_state->Prop)->Prop)) A_70) bot_bo1962689075te_o_o)) (((eq ((hoare_1262092251_state->Prop)->Prop)) A_70) ((insert1042460334tate_o X_16) bot_bo1962689075te_o_o))))) of role axiom named fact_101_subset__singletonD % A new axiom: (forall (A_70:((hoare_1262092251_state->Prop)->Prop)) (X_16:(hoare_1262092251_state->Prop)), (((ord_le2012720639te_o_o A_70) ((insert1042460334tate_o X_16) bot_bo1962689075te_o_o))->((or (((eq ((hoare_1262092251_state->Prop)->Prop)) A_70) bot_bo1962689075te_o_o)) (((eq ((hoare_1262092251_state->Prop)->Prop)) A_70) ((insert1042460334tate_o X_16) bot_bo1962689075te_o_o))))) % FOF formula (forall (A_70:(pname->Prop)) (X_16:pname), (((ord_less_eq_pname_o A_70) ((insert_pname X_16) bot_bot_pname_o))->((or (((eq (pname->Prop)) A_70) bot_bot_pname_o)) (((eq (pname->Prop)) A_70) ((insert_pname X_16) bot_bot_pname_o))))) of role axiom named fact_102_subset__singletonD % A new axiom: (forall (A_70:(pname->Prop)) (X_16:pname), (((ord_less_eq_pname_o A_70) ((insert_pname X_16) bot_bot_pname_o))->((or (((eq (pname->Prop)) A_70) bot_bot_pname_o)) (((eq (pname->Prop)) A_70) ((insert_pname X_16) bot_bot_pname_o))))) % FOF formula (forall (C_1:com), (hoare_1821564147gleton->(wT_bodies->((wt C_1)->((hoare_930741239_state bot_bo113204042tate_o) ((insert81609953_state (hoare_Mirabelle_MGT C_1)) bot_bo113204042tate_o)))))) of role axiom named fact_103_MGF % A new axiom: (forall (C_1:com), (hoare_1821564147gleton->(wT_bodies->((wt C_1)->((hoare_930741239_state bot_bo113204042tate_o) ((insert81609953_state (hoare_Mirabelle_MGT C_1)) bot_bo113204042tate_o)))))) % FOF formula (forall (A_69:hoare_1262092251_state), (((member5164104_state A_69) bot_bo113204042tate_o)->False)) of role axiom named fact_104_emptyE % A new axiom: (forall (A_69:hoare_1262092251_state), (((member5164104_state A_69) bot_bo113204042tate_o)->False)) % FOF formula (forall (A_69:(pname->Prop)), (((member_pname_o A_69) bot_bot_pname_o_o)->False)) of role axiom named fact_105_emptyE % A new axiom: (forall (A_69:(pname->Prop)), (((member_pname_o A_69) bot_bot_pname_o_o)->False)) % FOF formula (forall (A_69:(hoare_1262092251_state->Prop)), (((member907417095tate_o A_69) bot_bo1962689075te_o_o)->False)) of role axiom named fact_106_emptyE % A new axiom: (forall (A_69:(hoare_1262092251_state->Prop)), (((member907417095tate_o A_69) bot_bo1962689075te_o_o)->False)) % FOF formula (forall (A_69:pname), (((member_pname A_69) bot_bot_pname_o)->False)) of role axiom named fact_107_emptyE % A new axiom: (forall (A_69:pname), (((member_pname A_69) bot_bot_pname_o)->False)) % FOF formula (forall (B_39:hoare_1262092251_state) (A_68:hoare_1262092251_state) (B_38:(hoare_1262092251_state->Prop)), (((((member5164104_state A_68) B_38)->False)->(((eq hoare_1262092251_state) A_68) B_39))->((member5164104_state A_68) ((insert81609953_state B_39) B_38)))) of role axiom named fact_108_insertCI % A new axiom: (forall (B_39:hoare_1262092251_state) (A_68:hoare_1262092251_state) (B_38:(hoare_1262092251_state->Prop)), (((((member5164104_state A_68) B_38)->False)->(((eq hoare_1262092251_state) A_68) B_39))->((member5164104_state A_68) ((insert81609953_state B_39) B_38)))) % FOF formula (forall (B_39:(pname->Prop)) (A_68:(pname->Prop)) (B_38:((pname->Prop)->Prop)), (((((member_pname_o A_68) B_38)->False)->(((eq (pname->Prop)) A_68) B_39))->((member_pname_o A_68) ((insert_pname_o B_39) B_38)))) of role axiom named fact_109_insertCI % A new axiom: (forall (B_39:(pname->Prop)) (A_68:(pname->Prop)) (B_38:((pname->Prop)->Prop)), (((((member_pname_o A_68) B_38)->False)->(((eq (pname->Prop)) A_68) B_39))->((member_pname_o A_68) ((insert_pname_o B_39) B_38)))) % FOF formula (forall (B_39:(hoare_1262092251_state->Prop)) (A_68:(hoare_1262092251_state->Prop)) (B_38:((hoare_1262092251_state->Prop)->Prop)), (((((member907417095tate_o A_68) B_38)->False)->(((eq (hoare_1262092251_state->Prop)) A_68) B_39))->((member907417095tate_o A_68) ((insert1042460334tate_o B_39) B_38)))) of role axiom named fact_110_insertCI % A new axiom: (forall (B_39:(hoare_1262092251_state->Prop)) (A_68:(hoare_1262092251_state->Prop)) (B_38:((hoare_1262092251_state->Prop)->Prop)), (((((member907417095tate_o A_68) B_38)->False)->(((eq (hoare_1262092251_state->Prop)) A_68) B_39))->((member907417095tate_o A_68) ((insert1042460334tate_o B_39) B_38)))) % FOF formula (forall (B_39:pname) (A_68:pname) (B_38:(pname->Prop)), (((((member_pname A_68) B_38)->False)->(((eq pname) A_68) B_39))->((member_pname A_68) ((insert_pname B_39) B_38)))) of role axiom named fact_111_insertCI % A new axiom: (forall (B_39:pname) (A_68:pname) (B_38:(pname->Prop)), (((((member_pname A_68) B_38)->False)->(((eq pname) A_68) B_39))->((member_pname A_68) ((insert_pname B_39) B_38)))) % FOF formula (forall (A_67:hoare_1262092251_state) (B_37:hoare_1262092251_state) (A_66:(hoare_1262092251_state->Prop)), (((member5164104_state A_67) ((insert81609953_state B_37) A_66))->((not (((eq hoare_1262092251_state) A_67) B_37))->((member5164104_state A_67) A_66)))) of role axiom named fact_112_insertE % A new axiom: (forall (A_67:hoare_1262092251_state) (B_37:hoare_1262092251_state) (A_66:(hoare_1262092251_state->Prop)), (((member5164104_state A_67) ((insert81609953_state B_37) A_66))->((not (((eq hoare_1262092251_state) A_67) B_37))->((member5164104_state A_67) A_66)))) % FOF formula (forall (A_67:(pname->Prop)) (B_37:(pname->Prop)) (A_66:((pname->Prop)->Prop)), (((member_pname_o A_67) ((insert_pname_o B_37) A_66))->((not (((eq (pname->Prop)) A_67) B_37))->((member_pname_o A_67) A_66)))) of role axiom named fact_113_insertE % A new axiom: (forall (A_67:(pname->Prop)) (B_37:(pname->Prop)) (A_66:((pname->Prop)->Prop)), (((member_pname_o A_67) ((insert_pname_o B_37) A_66))->((not (((eq (pname->Prop)) A_67) B_37))->((member_pname_o A_67) A_66)))) % FOF formula (forall (A_67:(hoare_1262092251_state->Prop)) (B_37:(hoare_1262092251_state->Prop)) (A_66:((hoare_1262092251_state->Prop)->Prop)), (((member907417095tate_o A_67) ((insert1042460334tate_o B_37) A_66))->((not (((eq (hoare_1262092251_state->Prop)) A_67) B_37))->((member907417095tate_o A_67) A_66)))) of role axiom named fact_114_insertE % A new axiom: (forall (A_67:(hoare_1262092251_state->Prop)) (B_37:(hoare_1262092251_state->Prop)) (A_66:((hoare_1262092251_state->Prop)->Prop)), (((member907417095tate_o A_67) ((insert1042460334tate_o B_37) A_66))->((not (((eq (hoare_1262092251_state->Prop)) A_67) B_37))->((member907417095tate_o A_67) A_66)))) % FOF formula (forall (A_67:pname) (B_37:pname) (A_66:(pname->Prop)), (((member_pname A_67) ((insert_pname B_37) A_66))->((not (((eq pname) A_67) B_37))->((member_pname A_67) A_66)))) of role axiom named fact_115_insertE % A new axiom: (forall (A_67:pname) (B_37:pname) (A_66:(pname->Prop)), (((member_pname A_67) ((insert_pname B_37) A_66))->((not (((eq pname) A_67) B_37))->((member_pname A_67) A_66)))) % FOF formula (forall (A_65:(hoare_1262092251_state->Prop)) (B_36:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o A_65) B_36)->(((ord_le870406270tate_o B_36) A_65)->(((eq (hoare_1262092251_state->Prop)) A_65) B_36)))) of role axiom named fact_116_equalityI % A new axiom: (forall (A_65:(hoare_1262092251_state->Prop)) (B_36:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o A_65) B_36)->(((ord_le870406270tate_o B_36) A_65)->(((eq (hoare_1262092251_state->Prop)) A_65) B_36)))) % FOF formula (forall (A_65:((pname->Prop)->Prop)) (B_36:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_65) B_36)->(((ord_le1205211808me_o_o B_36) A_65)->(((eq ((pname->Prop)->Prop)) A_65) B_36)))) of role axiom named fact_117_equalityI % A new axiom: (forall (A_65:((pname->Prop)->Prop)) (B_36:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_65) B_36)->(((ord_le1205211808me_o_o B_36) A_65)->(((eq ((pname->Prop)->Prop)) A_65) B_36)))) % FOF formula (forall (A_65:((hoare_1262092251_state->Prop)->Prop)) (B_36:((hoare_1262092251_state->Prop)->Prop)), (((ord_le2012720639te_o_o A_65) B_36)->(((ord_le2012720639te_o_o B_36) A_65)->(((eq ((hoare_1262092251_state->Prop)->Prop)) A_65) B_36)))) of role axiom named fact_118_equalityI % A new axiom: (forall (A_65:((hoare_1262092251_state->Prop)->Prop)) (B_36:((hoare_1262092251_state->Prop)->Prop)), (((ord_le2012720639te_o_o A_65) B_36)->(((ord_le2012720639te_o_o B_36) A_65)->(((eq ((hoare_1262092251_state->Prop)->Prop)) A_65) B_36)))) % FOF formula (forall (A_65:(pname->Prop)) (B_36:(pname->Prop)), (((ord_less_eq_pname_o A_65) B_36)->(((ord_less_eq_pname_o B_36) A_65)->(((eq (pname->Prop)) A_65) B_36)))) of role axiom named fact_119_equalityI % A new axiom: (forall (A_65:(pname->Prop)) (B_36:(pname->Prop)), (((ord_less_eq_pname_o A_65) B_36)->(((ord_less_eq_pname_o B_36) A_65)->(((eq (pname->Prop)) A_65) B_36)))) % FOF formula (forall (C_6:hoare_1262092251_state) (A_64:(hoare_1262092251_state->Prop)) (B_35:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o A_64) B_35)->(((member5164104_state C_6) A_64)->((member5164104_state C_6) B_35)))) of role axiom named fact_120_subsetD % A new axiom: (forall (C_6:hoare_1262092251_state) (A_64:(hoare_1262092251_state->Prop)) (B_35:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o A_64) B_35)->(((member5164104_state C_6) A_64)->((member5164104_state C_6) B_35)))) % FOF formula (forall (C_6:(pname->Prop)) (A_64:((pname->Prop)->Prop)) (B_35:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_64) B_35)->(((member_pname_o C_6) A_64)->((member_pname_o C_6) B_35)))) of role axiom named fact_121_subsetD % A new axiom: (forall (C_6:(pname->Prop)) (A_64:((pname->Prop)->Prop)) (B_35:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_64) B_35)->(((member_pname_o C_6) A_64)->((member_pname_o C_6) B_35)))) % FOF formula (forall (C_6:(hoare_1262092251_state->Prop)) (A_64:((hoare_1262092251_state->Prop)->Prop)) (B_35:((hoare_1262092251_state->Prop)->Prop)), (((ord_le2012720639te_o_o A_64) B_35)->(((member907417095tate_o C_6) A_64)->((member907417095tate_o C_6) B_35)))) of role axiom named fact_122_subsetD % A new axiom: (forall (C_6:(hoare_1262092251_state->Prop)) (A_64:((hoare_1262092251_state->Prop)->Prop)) (B_35:((hoare_1262092251_state->Prop)->Prop)), (((ord_le2012720639te_o_o A_64) B_35)->(((member907417095tate_o C_6) A_64)->((member907417095tate_o C_6) B_35)))) % FOF formula (forall (C_6:pname) (A_64:(pname->Prop)) (B_35:(pname->Prop)), (((ord_less_eq_pname_o A_64) B_35)->(((member_pname C_6) A_64)->((member_pname C_6) B_35)))) of role axiom named fact_123_subsetD % A new axiom: (forall (C_6:pname) (A_64:(pname->Prop)) (B_35:(pname->Prop)), (((ord_less_eq_pname_o A_64) B_35)->(((member_pname C_6) A_64)->((member_pname C_6) B_35)))) % FOF formula (forall (A_63:(hoare_1262092251_state->Prop)) (B_34:(pname->Prop)) (F_14:(hoare_1262092251_state->(pname->Prop))) (X_15:hoare_1262092251_state), ((((eq (pname->Prop)) B_34) (F_14 X_15))->(((member5164104_state X_15) A_63)->((member_pname_o B_34) ((image_1320925383name_o F_14) A_63))))) of role axiom named fact_124_image__eqI % A new axiom: (forall (A_63:(hoare_1262092251_state->Prop)) (B_34:(pname->Prop)) (F_14:(hoare_1262092251_state->(pname->Prop))) (X_15:hoare_1262092251_state), ((((eq (pname->Prop)) B_34) (F_14 X_15))->(((member5164104_state X_15) A_63)->((member_pname_o B_34) ((image_1320925383name_o F_14) A_63))))) % FOF formula (forall (A_63:(hoare_1262092251_state->Prop)) (B_34:(hoare_1262092251_state->Prop)) (F_14:(hoare_1262092251_state->(hoare_1262092251_state->Prop))) (X_15:hoare_1262092251_state), ((((eq (hoare_1262092251_state->Prop)) B_34) (F_14 X_15))->(((member5164104_state X_15) A_63)->((member907417095tate_o B_34) ((image_1403668518tate_o F_14) A_63))))) of role axiom named fact_125_image__eqI % A new axiom: (forall (A_63:(hoare_1262092251_state->Prop)) (B_34:(hoare_1262092251_state->Prop)) (F_14:(hoare_1262092251_state->(hoare_1262092251_state->Prop))) (X_15:hoare_1262092251_state), ((((eq (hoare_1262092251_state->Prop)) B_34) (F_14 X_15))->(((member5164104_state X_15) A_63)->((member907417095tate_o B_34) ((image_1403668518tate_o F_14) A_63))))) % FOF formula (forall (A_63:(pname->Prop)) (B_34:(pname->Prop)) (F_14:(pname->(pname->Prop))) (X_15:pname), ((((eq (pname->Prop)) B_34) (F_14 X_15))->(((member_pname X_15) A_63)->((member_pname_o B_34) ((image_pname_pname_o F_14) A_63))))) of role axiom named fact_126_image__eqI % A new axiom: (forall (A_63:(pname->Prop)) (B_34:(pname->Prop)) (F_14:(pname->(pname->Prop))) (X_15:pname), ((((eq (pname->Prop)) B_34) (F_14 X_15))->(((member_pname X_15) A_63)->((member_pname_o B_34) ((image_pname_pname_o F_14) A_63))))) % FOF formula (forall (A_63:(pname->Prop)) (B_34:(hoare_1262092251_state->Prop)) (F_14:(pname->(hoare_1262092251_state->Prop))) (X_15:pname), ((((eq (hoare_1262092251_state->Prop)) B_34) (F_14 X_15))->(((member_pname X_15) A_63)->((member907417095tate_o B_34) ((image_518521461tate_o F_14) A_63))))) of role axiom named fact_127_image__eqI % A new axiom: (forall (A_63:(pname->Prop)) (B_34:(hoare_1262092251_state->Prop)) (F_14:(pname->(hoare_1262092251_state->Prop))) (X_15:pname), ((((eq (hoare_1262092251_state->Prop)) B_34) (F_14 X_15))->(((member_pname X_15) A_63)->((member907417095tate_o B_34) ((image_518521461tate_o F_14) A_63))))) % FOF formula (forall (A_63:((pname->Prop)->Prop)) (B_34:hoare_1262092251_state) (F_14:((pname->Prop)->hoare_1262092251_state)) (X_15:(pname->Prop)), ((((eq hoare_1262092251_state) B_34) (F_14 X_15))->(((member_pname_o X_15) A_63)->((member5164104_state B_34) ((image_1476171975_state F_14) A_63))))) of role axiom named fact_128_image__eqI % A new axiom: (forall (A_63:((pname->Prop)->Prop)) (B_34:hoare_1262092251_state) (F_14:((pname->Prop)->hoare_1262092251_state)) (X_15:(pname->Prop)), ((((eq hoare_1262092251_state) B_34) (F_14 X_15))->(((member_pname_o X_15) A_63)->((member5164104_state B_34) ((image_1476171975_state F_14) A_63))))) % FOF formula (forall (A_63:((hoare_1262092251_state->Prop)->Prop)) (B_34:hoare_1262092251_state) (F_14:((hoare_1262092251_state->Prop)->hoare_1262092251_state)) (X_15:(hoare_1262092251_state->Prop)), ((((eq hoare_1262092251_state) B_34) (F_14 X_15))->(((member907417095tate_o X_15) A_63)->((member5164104_state B_34) ((image_234589002_state F_14) A_63))))) of role axiom named fact_129_image__eqI % A new axiom: (forall (A_63:((hoare_1262092251_state->Prop)->Prop)) (B_34:hoare_1262092251_state) (F_14:((hoare_1262092251_state->Prop)->hoare_1262092251_state)) (X_15:(hoare_1262092251_state->Prop)), ((((eq hoare_1262092251_state) B_34) (F_14 X_15))->(((member907417095tate_o X_15) A_63)->((member5164104_state B_34) ((image_234589002_state F_14) A_63))))) % FOF formula (forall (A_63:(hoare_1262092251_state->Prop)) (B_34:pname) (F_14:(hoare_1262092251_state->pname)) (X_15:hoare_1262092251_state), ((((eq pname) B_34) (F_14 X_15))->(((member5164104_state X_15) A_63)->((member_pname B_34) ((image_202231862_pname F_14) A_63))))) of role axiom named fact_130_image__eqI % A new axiom: (forall (A_63:(hoare_1262092251_state->Prop)) (B_34:pname) (F_14:(hoare_1262092251_state->pname)) (X_15:hoare_1262092251_state), ((((eq pname) B_34) (F_14 X_15))->(((member5164104_state X_15) A_63)->((member_pname B_34) ((image_202231862_pname F_14) A_63))))) % FOF formula (forall (A_63:(pname->Prop)) (B_34:pname) (F_14:(pname->pname)) (X_15:pname), ((((eq pname) B_34) (F_14 X_15))->(((member_pname X_15) A_63)->((member_pname B_34) ((image_pname_pname F_14) A_63))))) of role axiom named fact_131_image__eqI % A new axiom: (forall (A_63:(pname->Prop)) (B_34:pname) (F_14:(pname->pname)) (X_15:pname), ((((eq pname) B_34) (F_14 X_15))->(((member_pname X_15) A_63)->((member_pname B_34) ((image_pname_pname F_14) A_63))))) % FOF formula (forall (A_63:((pname->Prop)->Prop)) (B_34:pname) (F_14:((pname->Prop)->pname)) (X_15:(pname->Prop)), ((((eq pname) B_34) (F_14 X_15))->(((member_pname_o X_15) A_63)->((member_pname B_34) ((image_pname_o_pname F_14) A_63))))) of role axiom named fact_132_image__eqI % A new axiom: (forall (A_63:((pname->Prop)->Prop)) (B_34:pname) (F_14:((pname->Prop)->pname)) (X_15:(pname->Prop)), ((((eq pname) B_34) (F_14 X_15))->(((member_pname_o X_15) A_63)->((member_pname B_34) ((image_pname_o_pname F_14) A_63))))) % FOF formula (forall (A_63:((hoare_1262092251_state->Prop)->Prop)) (B_34:pname) (F_14:((hoare_1262092251_state->Prop)->pname)) (X_15:(hoare_1262092251_state->Prop)), ((((eq pname) B_34) (F_14 X_15))->(((member907417095tate_o X_15) A_63)->((member_pname B_34) ((image_1820530197_pname F_14) A_63))))) of role axiom named fact_133_image__eqI % A new axiom: (forall (A_63:((hoare_1262092251_state->Prop)->Prop)) (B_34:pname) (F_14:((hoare_1262092251_state->Prop)->pname)) (X_15:(hoare_1262092251_state->Prop)), ((((eq pname) B_34) (F_14 X_15))->(((member907417095tate_o X_15) A_63)->((member_pname B_34) ((image_1820530197_pname F_14) A_63))))) % FOF formula (forall (A_63:(pname->Prop)) (B_34:hoare_1262092251_state) (F_14:(pname->hoare_1262092251_state)) (X_15:pname), ((((eq hoare_1262092251_state) B_34) (F_14 X_15))->(((member_pname X_15) A_63)->((member5164104_state B_34) ((image_669833818_state F_14) A_63))))) of role axiom named fact_134_image__eqI % A new axiom: (forall (A_63:(pname->Prop)) (B_34:hoare_1262092251_state) (F_14:(pname->hoare_1262092251_state)) (X_15:pname), ((((eq hoare_1262092251_state) B_34) (F_14 X_15))->(((member_pname X_15) A_63)->((member5164104_state B_34) ((image_669833818_state F_14) A_63))))) % FOF formula (forall (A_62:(pname->Prop)) (A_61:((pname->Prop)->Prop)), ((((eq ((pname->Prop)->Prop)) A_61) bot_bot_pname_o_o)->(((member_pname_o A_62) A_61)->False))) of role axiom named fact_135_equals0D % A new axiom: (forall (A_62:(pname->Prop)) (A_61:((pname->Prop)->Prop)), ((((eq ((pname->Prop)->Prop)) A_61) bot_bot_pname_o_o)->(((member_pname_o A_62) A_61)->False))) % FOF formula (forall (A_62:(hoare_1262092251_state->Prop)) (A_61:((hoare_1262092251_state->Prop)->Prop)), ((((eq ((hoare_1262092251_state->Prop)->Prop)) A_61) bot_bo1962689075te_o_o)->(((member907417095tate_o A_62) A_61)->False))) of role axiom named fact_136_equals0D % A new axiom: (forall (A_62:(hoare_1262092251_state->Prop)) (A_61:((hoare_1262092251_state->Prop)->Prop)), ((((eq ((hoare_1262092251_state->Prop)->Prop)) A_61) bot_bo1962689075te_o_o)->(((member907417095tate_o A_62) A_61)->False))) % FOF formula (forall (A_62:hoare_1262092251_state) (A_61:(hoare_1262092251_state->Prop)), ((((eq (hoare_1262092251_state->Prop)) A_61) bot_bo113204042tate_o)->(((member5164104_state A_62) A_61)->False))) of role axiom named fact_137_equals0D % A new axiom: (forall (A_62:hoare_1262092251_state) (A_61:(hoare_1262092251_state->Prop)), ((((eq (hoare_1262092251_state->Prop)) A_61) bot_bo113204042tate_o)->(((member5164104_state A_62) A_61)->False))) % FOF formula (forall (A_62:pname) (A_61:(pname->Prop)), ((((eq (pname->Prop)) A_61) bot_bot_pname_o)->(((member_pname A_62) A_61)->False))) of role axiom named fact_138_equals0D % A new axiom: (forall (A_62:pname) (A_61:(pname->Prop)), ((((eq (pname->Prop)) A_61) bot_bot_pname_o)->(((member_pname A_62) A_61)->False))) % FOF formula (forall (P_8:(((pname->Prop)->Prop)->Prop)), ((iff (((eq (((pname->Prop)->Prop)->Prop)) (collect_pname_o_o P_8)) bot_bot_pname_o_o_o)) (forall (X_1:((pname->Prop)->Prop)), ((P_8 X_1)->False)))) of role axiom named fact_139_Collect__empty__eq % A new axiom: (forall (P_8:(((pname->Prop)->Prop)->Prop)), ((iff (((eq (((pname->Prop)->Prop)->Prop)) (collect_pname_o_o P_8)) bot_bot_pname_o_o_o)) (forall (X_1:((pname->Prop)->Prop)), ((P_8 X_1)->False)))) % FOF formula (forall (P_8:(((hoare_1262092251_state->Prop)->Prop)->Prop)), ((iff (((eq (((hoare_1262092251_state->Prop)->Prop)->Prop)) (collec341954548te_o_o P_8)) bot_bo388435036_o_o_o)) (forall (X_1:((hoare_1262092251_state->Prop)->Prop)), ((P_8 X_1)->False)))) of role axiom named fact_140_Collect__empty__eq % A new axiom: (forall (P_8:(((hoare_1262092251_state->Prop)->Prop)->Prop)), ((iff (((eq (((hoare_1262092251_state->Prop)->Prop)->Prop)) (collec341954548te_o_o P_8)) bot_bo388435036_o_o_o)) (forall (X_1:((hoare_1262092251_state->Prop)->Prop)), ((P_8 X_1)->False)))) % FOF formula (forall (P_8:((hoare_1262092251_state->Prop)->Prop)), ((iff (((eq ((hoare_1262092251_state->Prop)->Prop)) (collec313158217tate_o P_8)) bot_bo1962689075te_o_o)) (forall (X_1:(hoare_1262092251_state->Prop)), ((P_8 X_1)->False)))) of role axiom named fact_141_Collect__empty__eq % A new axiom: (forall (P_8:((hoare_1262092251_state->Prop)->Prop)), ((iff (((eq ((hoare_1262092251_state->Prop)->Prop)) (collec313158217tate_o P_8)) bot_bo1962689075te_o_o)) (forall (X_1:(hoare_1262092251_state->Prop)), ((P_8 X_1)->False)))) % FOF formula (forall (P_8:((pname->Prop)->Prop)), ((iff (((eq ((pname->Prop)->Prop)) (collect_pname_o P_8)) bot_bot_pname_o_o)) (forall (X_1:(pname->Prop)), ((P_8 X_1)->False)))) of role axiom named fact_142_Collect__empty__eq % A new axiom: (forall (P_8:((pname->Prop)->Prop)), ((iff (((eq ((pname->Prop)->Prop)) (collect_pname_o P_8)) bot_bot_pname_o_o)) (forall (X_1:(pname->Prop)), ((P_8 X_1)->False)))) % FOF formula (forall (P_8:(hoare_1262092251_state->Prop)), ((iff (((eq (hoare_1262092251_state->Prop)) (collec1121927558_state P_8)) bot_bo113204042tate_o)) (forall (X_1:hoare_1262092251_state), ((P_8 X_1)->False)))) of role axiom named fact_143_Collect__empty__eq % A new axiom: (forall (P_8:(hoare_1262092251_state->Prop)), ((iff (((eq (hoare_1262092251_state->Prop)) (collec1121927558_state P_8)) bot_bo113204042tate_o)) (forall (X_1:hoare_1262092251_state), ((P_8 X_1)->False)))) % FOF formula (forall (P_8:(pname->Prop)), ((iff (((eq (pname->Prop)) (collect_pname P_8)) bot_bot_pname_o)) (forall (X_1:pname), ((P_8 X_1)->False)))) of role axiom named fact_144_Collect__empty__eq % A new axiom: (forall (P_8:(pname->Prop)), ((iff (((eq (pname->Prop)) (collect_pname P_8)) bot_bot_pname_o)) (forall (X_1:pname), ((P_8 X_1)->False)))) % FOF formula (forall (C_5:(pname->Prop)), (((member_pname_o C_5) bot_bot_pname_o_o)->False)) of role axiom named fact_145_empty__iff % A new axiom: (forall (C_5:(pname->Prop)), (((member_pname_o C_5) bot_bot_pname_o_o)->False)) % FOF formula (forall (C_5:(hoare_1262092251_state->Prop)), (((member907417095tate_o C_5) bot_bo1962689075te_o_o)->False)) of role axiom named fact_146_empty__iff % A new axiom: (forall (C_5:(hoare_1262092251_state->Prop)), (((member907417095tate_o C_5) bot_bo1962689075te_o_o)->False)) % FOF formula (forall (C_5:hoare_1262092251_state), (((member5164104_state C_5) bot_bo113204042tate_o)->False)) of role axiom named fact_147_empty__iff % A new axiom: (forall (C_5:hoare_1262092251_state), (((member5164104_state C_5) bot_bo113204042tate_o)->False)) % FOF formula (forall (C_5:pname), (((member_pname C_5) bot_bot_pname_o)->False)) of role axiom named fact_148_empty__iff % A new axiom: (forall (C_5:pname), (((member_pname C_5) bot_bot_pname_o)->False)) % FOF formula (forall (P_7:(((pname->Prop)->Prop)->Prop)), ((iff (((eq (((pname->Prop)->Prop)->Prop)) bot_bot_pname_o_o_o) (collect_pname_o_o P_7))) (forall (X_1:((pname->Prop)->Prop)), ((P_7 X_1)->False)))) of role axiom named fact_149_empty__Collect__eq % A new axiom: (forall (P_7:(((pname->Prop)->Prop)->Prop)), ((iff (((eq (((pname->Prop)->Prop)->Prop)) bot_bot_pname_o_o_o) (collect_pname_o_o P_7))) (forall (X_1:((pname->Prop)->Prop)), ((P_7 X_1)->False)))) % FOF formula (forall (P_7:(((hoare_1262092251_state->Prop)->Prop)->Prop)), ((iff (((eq (((hoare_1262092251_state->Prop)->Prop)->Prop)) bot_bo388435036_o_o_o) (collec341954548te_o_o P_7))) (forall (X_1:((hoare_1262092251_state->Prop)->Prop)), ((P_7 X_1)->False)))) of role axiom named fact_150_empty__Collect__eq % A new axiom: (forall (P_7:(((hoare_1262092251_state->Prop)->Prop)->Prop)), ((iff (((eq (((hoare_1262092251_state->Prop)->Prop)->Prop)) bot_bo388435036_o_o_o) (collec341954548te_o_o P_7))) (forall (X_1:((hoare_1262092251_state->Prop)->Prop)), ((P_7 X_1)->False)))) % FOF formula (forall (P_7:((hoare_1262092251_state->Prop)->Prop)), ((iff (((eq ((hoare_1262092251_state->Prop)->Prop)) bot_bo1962689075te_o_o) (collec313158217tate_o P_7))) (forall (X_1:(hoare_1262092251_state->Prop)), ((P_7 X_1)->False)))) of role axiom named fact_151_empty__Collect__eq % A new axiom: (forall (P_7:((hoare_1262092251_state->Prop)->Prop)), ((iff (((eq ((hoare_1262092251_state->Prop)->Prop)) bot_bo1962689075te_o_o) (collec313158217tate_o P_7))) (forall (X_1:(hoare_1262092251_state->Prop)), ((P_7 X_1)->False)))) % FOF formula (forall (P_7:((pname->Prop)->Prop)), ((iff (((eq ((pname->Prop)->Prop)) bot_bot_pname_o_o) (collect_pname_o P_7))) (forall (X_1:(pname->Prop)), ((P_7 X_1)->False)))) of role axiom named fact_152_empty__Collect__eq % A new axiom: (forall (P_7:((pname->Prop)->Prop)), ((iff (((eq ((pname->Prop)->Prop)) bot_bot_pname_o_o) (collect_pname_o P_7))) (forall (X_1:(pname->Prop)), ((P_7 X_1)->False)))) % FOF formula (forall (P_7:(hoare_1262092251_state->Prop)), ((iff (((eq (hoare_1262092251_state->Prop)) bot_bo113204042tate_o) (collec1121927558_state P_7))) (forall (X_1:hoare_1262092251_state), ((P_7 X_1)->False)))) of role axiom named fact_153_empty__Collect__eq % A new axiom: (forall (P_7:(hoare_1262092251_state->Prop)), ((iff (((eq (hoare_1262092251_state->Prop)) bot_bo113204042tate_o) (collec1121927558_state P_7))) (forall (X_1:hoare_1262092251_state), ((P_7 X_1)->False)))) % FOF formula (forall (P_7:(pname->Prop)), ((iff (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname P_7))) (forall (X_1:pname), ((P_7 X_1)->False)))) of role axiom named fact_154_empty__Collect__eq % A new axiom: (forall (P_7:(pname->Prop)), ((iff (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname P_7))) (forall (X_1:pname), ((P_7 X_1)->False)))) % FOF formula (forall (A_60:((pname->Prop)->Prop)), ((iff ((ex (pname->Prop)) (fun (X_1:(pname->Prop))=> ((member_pname_o X_1) A_60)))) (not (((eq ((pname->Prop)->Prop)) A_60) bot_bot_pname_o_o)))) of role axiom named fact_155_ex__in__conv % A new axiom: (forall (A_60:((pname->Prop)->Prop)), ((iff ((ex (pname->Prop)) (fun (X_1:(pname->Prop))=> ((member_pname_o X_1) A_60)))) (not (((eq ((pname->Prop)->Prop)) A_60) bot_bot_pname_o_o)))) % FOF formula (forall (A_60:((hoare_1262092251_state->Prop)->Prop)), ((iff ((ex (hoare_1262092251_state->Prop)) (fun (X_1:(hoare_1262092251_state->Prop))=> ((member907417095tate_o X_1) A_60)))) (not (((eq ((hoare_1262092251_state->Prop)->Prop)) A_60) bot_bo1962689075te_o_o)))) of role axiom named fact_156_ex__in__conv % A new axiom: (forall (A_60:((hoare_1262092251_state->Prop)->Prop)), ((iff ((ex (hoare_1262092251_state->Prop)) (fun (X_1:(hoare_1262092251_state->Prop))=> ((member907417095tate_o X_1) A_60)))) (not (((eq ((hoare_1262092251_state->Prop)->Prop)) A_60) bot_bo1962689075te_o_o)))) % FOF formula (forall (A_60:(hoare_1262092251_state->Prop)), ((iff ((ex hoare_1262092251_state) (fun (X_1:hoare_1262092251_state)=> ((member5164104_state X_1) A_60)))) (not (((eq (hoare_1262092251_state->Prop)) A_60) bot_bo113204042tate_o)))) of role axiom named fact_157_ex__in__conv % A new axiom: (forall (A_60:(hoare_1262092251_state->Prop)), ((iff ((ex hoare_1262092251_state) (fun (X_1:hoare_1262092251_state)=> ((member5164104_state X_1) A_60)))) (not (((eq (hoare_1262092251_state->Prop)) A_60) bot_bo113204042tate_o)))) % FOF formula (forall (A_60:(pname->Prop)), ((iff ((ex pname) (fun (X_1:pname)=> ((member_pname X_1) A_60)))) (not (((eq (pname->Prop)) A_60) bot_bot_pname_o)))) of role axiom named fact_158_ex__in__conv % A new axiom: (forall (A_60:(pname->Prop)), ((iff ((ex pname) (fun (X_1:pname)=> ((member_pname X_1) A_60)))) (not (((eq (pname->Prop)) A_60) bot_bot_pname_o)))) % FOF formula (forall (A_59:((pname->Prop)->Prop)), ((iff (forall (X_1:(pname->Prop)), (((member_pname_o X_1) A_59)->False))) (((eq ((pname->Prop)->Prop)) A_59) bot_bot_pname_o_o))) of role axiom named fact_159_all__not__in__conv % A new axiom: (forall (A_59:((pname->Prop)->Prop)), ((iff (forall (X_1:(pname->Prop)), (((member_pname_o X_1) A_59)->False))) (((eq ((pname->Prop)->Prop)) A_59) bot_bot_pname_o_o))) % FOF formula (forall (A_59:((hoare_1262092251_state->Prop)->Prop)), ((iff (forall (X_1:(hoare_1262092251_state->Prop)), (((member907417095tate_o X_1) A_59)->False))) (((eq ((hoare_1262092251_state->Prop)->Prop)) A_59) bot_bo1962689075te_o_o))) of role axiom named fact_160_all__not__in__conv % A new axiom: (forall (A_59:((hoare_1262092251_state->Prop)->Prop)), ((iff (forall (X_1:(hoare_1262092251_state->Prop)), (((member907417095tate_o X_1) A_59)->False))) (((eq ((hoare_1262092251_state->Prop)->Prop)) A_59) bot_bo1962689075te_o_o))) % FOF formula (forall (A_59:(hoare_1262092251_state->Prop)), ((iff (forall (X_1:hoare_1262092251_state), (((member5164104_state X_1) A_59)->False))) (((eq (hoare_1262092251_state->Prop)) A_59) bot_bo113204042tate_o))) of role axiom named fact_161_all__not__in__conv % A new axiom: (forall (A_59:(hoare_1262092251_state->Prop)), ((iff (forall (X_1:hoare_1262092251_state), (((member5164104_state X_1) A_59)->False))) (((eq (hoare_1262092251_state->Prop)) A_59) bot_bo113204042tate_o))) % FOF formula (forall (A_59:(pname->Prop)), ((iff (forall (X_1:pname), (((member_pname X_1) A_59)->False))) (((eq (pname->Prop)) A_59) bot_bot_pname_o))) of role axiom named fact_162_all__not__in__conv % A new axiom: (forall (A_59:(pname->Prop)), ((iff (forall (X_1:pname), (((member_pname X_1) A_59)->False))) (((eq (pname->Prop)) A_59) bot_bot_pname_o))) % FOF formula (((eq (((hoare_1262092251_state->Prop)->Prop)->Prop)) bot_bo388435036_o_o_o) (collec341954548te_o_o (fun (X_1:((hoare_1262092251_state->Prop)->Prop))=> False))) of role axiom named fact_163_empty__def % A new axiom: (((eq (((hoare_1262092251_state->Prop)->Prop)->Prop)) bot_bo388435036_o_o_o) (collec341954548te_o_o (fun (X_1:((hoare_1262092251_state->Prop)->Prop))=> False))) % FOF formula (((eq ((hoare_1262092251_state->Prop)->Prop)) bot_bo1962689075te_o_o) (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> False))) of role axiom named fact_164_empty__def % A new axiom: (((eq ((hoare_1262092251_state->Prop)->Prop)) bot_bo1962689075te_o_o) (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> False))) % FOF formula (((eq ((pname->Prop)->Prop)) bot_bot_pname_o_o) (collect_pname_o (fun (X_1:(pname->Prop))=> False))) of role axiom named fact_165_empty__def % A new axiom: (((eq ((pname->Prop)->Prop)) bot_bot_pname_o_o) (collect_pname_o (fun (X_1:(pname->Prop))=> False))) % FOF formula (((eq (hoare_1262092251_state->Prop)) bot_bo113204042tate_o) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> False))) of role axiom named fact_166_empty__def % A new axiom: (((eq (hoare_1262092251_state->Prop)) bot_bo113204042tate_o) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> False))) % FOF formula (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname (fun (X_1:pname)=> False))) of role axiom named fact_167_empty__def % A new axiom: (((eq (pname->Prop)) bot_bot_pname_o) (collect_pname (fun (X_1:pname)=> False))) % FOF formula (forall (A_58:pname) (A_57:(pname->Prop)), (((member_pname A_58) A_57)->(((eq (pname->Prop)) ((insert_pname A_58) A_57)) A_57))) of role axiom named fact_168_insert__absorb % A new axiom: (forall (A_58:pname) (A_57:(pname->Prop)), (((member_pname A_58) A_57)->(((eq (pname->Prop)) ((insert_pname A_58) A_57)) A_57))) % FOF formula (forall (A_58:hoare_1262092251_state) (A_57:(hoare_1262092251_state->Prop)), (((member5164104_state A_58) A_57)->(((eq (hoare_1262092251_state->Prop)) ((insert81609953_state A_58) A_57)) A_57))) of role axiom named fact_169_insert__absorb % A new axiom: (forall (A_58:hoare_1262092251_state) (A_57:(hoare_1262092251_state->Prop)), (((member5164104_state A_58) A_57)->(((eq (hoare_1262092251_state->Prop)) ((insert81609953_state A_58) A_57)) A_57))) % FOF formula (forall (B_33:pname) (A_56:pname) (B_32:(pname->Prop)), (((member_pname A_56) B_32)->((member_pname A_56) ((insert_pname B_33) B_32)))) of role axiom named fact_170_insertI2 % A new axiom: (forall (B_33:pname) (A_56:pname) (B_32:(pname->Prop)), (((member_pname A_56) B_32)->((member_pname A_56) ((insert_pname B_33) B_32)))) % FOF formula (forall (B_33:hoare_1262092251_state) (A_56:hoare_1262092251_state) (B_32:(hoare_1262092251_state->Prop)), (((member5164104_state A_56) B_32)->((member5164104_state A_56) ((insert81609953_state B_33) B_32)))) of role axiom named fact_171_insertI2 % A new axiom: (forall (B_33:hoare_1262092251_state) (A_56:hoare_1262092251_state) (B_32:(hoare_1262092251_state->Prop)), (((member5164104_state A_56) B_32)->((member5164104_state A_56) ((insert81609953_state B_33) B_32)))) % FOF formula (forall (B_31:(pname->Prop)) (X_14:pname) (A_55:(pname->Prop)), ((((member_pname X_14) A_55)->False)->((((member_pname X_14) B_31)->False)->((iff (((eq (pname->Prop)) ((insert_pname X_14) A_55)) ((insert_pname X_14) B_31))) (((eq (pname->Prop)) A_55) B_31))))) of role axiom named fact_172_insert__ident % A new axiom: (forall (B_31:(pname->Prop)) (X_14:pname) (A_55:(pname->Prop)), ((((member_pname X_14) A_55)->False)->((((member_pname X_14) B_31)->False)->((iff (((eq (pname->Prop)) ((insert_pname X_14) A_55)) ((insert_pname X_14) B_31))) (((eq (pname->Prop)) A_55) B_31))))) % FOF formula (forall (B_31:(hoare_1262092251_state->Prop)) (X_14:hoare_1262092251_state) (A_55:(hoare_1262092251_state->Prop)), ((((member5164104_state X_14) A_55)->False)->((((member5164104_state X_14) B_31)->False)->((iff (((eq (hoare_1262092251_state->Prop)) ((insert81609953_state X_14) A_55)) ((insert81609953_state X_14) B_31))) (((eq (hoare_1262092251_state->Prop)) A_55) B_31))))) of role axiom named fact_173_insert__ident % A new axiom: (forall (B_31:(hoare_1262092251_state->Prop)) (X_14:hoare_1262092251_state) (A_55:(hoare_1262092251_state->Prop)), ((((member5164104_state X_14) A_55)->False)->((((member5164104_state X_14) B_31)->False)->((iff (((eq (hoare_1262092251_state->Prop)) ((insert81609953_state X_14) A_55)) ((insert81609953_state X_14) B_31))) (((eq (hoare_1262092251_state->Prop)) A_55) B_31))))) % FOF formula (forall (Y_3:pname) (A_54:(pname->Prop)) (X_13:pname), ((iff (((insert_pname Y_3) A_54) X_13)) ((or (((eq pname) Y_3) X_13)) (A_54 X_13)))) of role axiom named fact_174_insert__code % A new axiom: (forall (Y_3:pname) (A_54:(pname->Prop)) (X_13:pname), ((iff (((insert_pname Y_3) A_54) X_13)) ((or (((eq pname) Y_3) X_13)) (A_54 X_13)))) % FOF formula (forall (Y_3:hoare_1262092251_state) (A_54:(hoare_1262092251_state->Prop)) (X_13:hoare_1262092251_state), ((iff (((insert81609953_state Y_3) A_54) X_13)) ((or (((eq hoare_1262092251_state) Y_3) X_13)) (A_54 X_13)))) of role axiom named fact_175_insert__code % A new axiom: (forall (Y_3:hoare_1262092251_state) (A_54:(hoare_1262092251_state->Prop)) (X_13:hoare_1262092251_state), ((iff (((insert81609953_state Y_3) A_54) X_13)) ((or (((eq hoare_1262092251_state) Y_3) X_13)) (A_54 X_13)))) % FOF formula (forall (A_53:pname) (B_30:pname) (A_52:(pname->Prop)), ((iff ((member_pname A_53) ((insert_pname B_30) A_52))) ((or (((eq pname) A_53) B_30)) ((member_pname A_53) A_52)))) of role axiom named fact_176_insert__iff % A new axiom: (forall (A_53:pname) (B_30:pname) (A_52:(pname->Prop)), ((iff ((member_pname A_53) ((insert_pname B_30) A_52))) ((or (((eq pname) A_53) B_30)) ((member_pname A_53) A_52)))) % FOF formula (forall (A_53:hoare_1262092251_state) (B_30:hoare_1262092251_state) (A_52:(hoare_1262092251_state->Prop)), ((iff ((member5164104_state A_53) ((insert81609953_state B_30) A_52))) ((or (((eq hoare_1262092251_state) A_53) B_30)) ((member5164104_state A_53) A_52)))) of role axiom named fact_177_insert__iff % A new axiom: (forall (A_53:hoare_1262092251_state) (B_30:hoare_1262092251_state) (A_52:(hoare_1262092251_state->Prop)), ((iff ((member5164104_state A_53) ((insert81609953_state B_30) A_52))) ((or (((eq hoare_1262092251_state) A_53) B_30)) ((member5164104_state A_53) A_52)))) % FOF formula (forall (X_12:pname) (Y_2:pname) (A_51:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_12) ((insert_pname Y_2) A_51))) ((insert_pname Y_2) ((insert_pname X_12) A_51)))) of role axiom named fact_178_insert__commute % A new axiom: (forall (X_12:pname) (Y_2:pname) (A_51:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_12) ((insert_pname Y_2) A_51))) ((insert_pname Y_2) ((insert_pname X_12) A_51)))) % FOF formula (forall (X_12:hoare_1262092251_state) (Y_2:hoare_1262092251_state) (A_51:(hoare_1262092251_state->Prop)), (((eq (hoare_1262092251_state->Prop)) ((insert81609953_state X_12) ((insert81609953_state Y_2) A_51))) ((insert81609953_state Y_2) ((insert81609953_state X_12) A_51)))) of role axiom named fact_179_insert__commute % A new axiom: (forall (X_12:hoare_1262092251_state) (Y_2:hoare_1262092251_state) (A_51:(hoare_1262092251_state->Prop)), (((eq (hoare_1262092251_state->Prop)) ((insert81609953_state X_12) ((insert81609953_state Y_2) A_51))) ((insert81609953_state Y_2) ((insert81609953_state X_12) A_51)))) % FOF formula (forall (X_11:pname) (A_50:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_11) ((insert_pname X_11) A_50))) ((insert_pname X_11) A_50))) of role axiom named fact_180_insert__absorb2 % A new axiom: (forall (X_11:pname) (A_50:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_11) ((insert_pname X_11) A_50))) ((insert_pname X_11) A_50))) % FOF formula (forall (X_11:hoare_1262092251_state) (A_50:(hoare_1262092251_state->Prop)), (((eq (hoare_1262092251_state->Prop)) ((insert81609953_state X_11) ((insert81609953_state X_11) A_50))) ((insert81609953_state X_11) A_50))) of role axiom named fact_181_insert__absorb2 % A new axiom: (forall (X_11:hoare_1262092251_state) (A_50:(hoare_1262092251_state->Prop)), (((eq (hoare_1262092251_state->Prop)) ((insert81609953_state X_11) ((insert81609953_state X_11) A_50))) ((insert81609953_state X_11) A_50))) % FOF formula (forall (A_49:pname) (P_6:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_49) (collect_pname P_6))) (collect_pname (fun (U:pname)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq pname) U) A_49))) (P_6 U)))))) of role axiom named fact_182_insert__Collect % A new axiom: (forall (A_49:pname) (P_6:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_49) (collect_pname P_6))) (collect_pname (fun (U:pname)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq pname) U) A_49))) (P_6 U)))))) % FOF formula (forall (A_49:hoare_1262092251_state) (P_6:(hoare_1262092251_state->Prop)), (((eq (hoare_1262092251_state->Prop)) ((insert81609953_state A_49) (collec1121927558_state P_6))) (collec1121927558_state (fun (U:hoare_1262092251_state)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_1262092251_state) U) A_49))) (P_6 U)))))) of role axiom named fact_183_insert__Collect % A new axiom: (forall (A_49:hoare_1262092251_state) (P_6:(hoare_1262092251_state->Prop)), (((eq (hoare_1262092251_state->Prop)) ((insert81609953_state A_49) (collec1121927558_state P_6))) (collec1121927558_state (fun (U:hoare_1262092251_state)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_1262092251_state) U) A_49))) (P_6 U)))))) % FOF formula (forall (A_49:(pname->Prop)) (P_6:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_49) (collect_pname_o P_6))) (collect_pname_o (fun (U:(pname->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (pname->Prop)) U) A_49))) (P_6 U)))))) of role axiom named fact_184_insert__Collect % A new axiom: (forall (A_49:(pname->Prop)) (P_6:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_49) (collect_pname_o P_6))) (collect_pname_o (fun (U:(pname->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (pname->Prop)) U) A_49))) (P_6 U)))))) % FOF formula (forall (A_49:(hoare_1262092251_state->Prop)) (P_6:((hoare_1262092251_state->Prop)->Prop)), (((eq ((hoare_1262092251_state->Prop)->Prop)) ((insert1042460334tate_o A_49) (collec313158217tate_o P_6))) (collec313158217tate_o (fun (U:(hoare_1262092251_state->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (hoare_1262092251_state->Prop)) U) A_49))) (P_6 U)))))) of role axiom named fact_185_insert__Collect % A new axiom: (forall (A_49:(hoare_1262092251_state->Prop)) (P_6:((hoare_1262092251_state->Prop)->Prop)), (((eq ((hoare_1262092251_state->Prop)->Prop)) ((insert1042460334tate_o A_49) (collec313158217tate_o P_6))) (collec313158217tate_o (fun (U:(hoare_1262092251_state->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (hoare_1262092251_state->Prop)) U) A_49))) (P_6 U)))))) % FOF formula (forall (A_48:pname) (B_29:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_48) B_29)) (collect_pname (fun (X_1:pname)=> ((or (((eq pname) X_1) A_48)) ((member_pname X_1) B_29)))))) of role axiom named fact_186_insert__compr % A new axiom: (forall (A_48:pname) (B_29:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_48) B_29)) (collect_pname (fun (X_1:pname)=> ((or (((eq pname) X_1) A_48)) ((member_pname X_1) B_29)))))) % FOF formula (forall (A_48:hoare_1262092251_state) (B_29:(hoare_1262092251_state->Prop)), (((eq (hoare_1262092251_state->Prop)) ((insert81609953_state A_48) B_29)) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> ((or (((eq hoare_1262092251_state) X_1) A_48)) ((member5164104_state X_1) B_29)))))) of role axiom named fact_187_insert__compr % A new axiom: (forall (A_48:hoare_1262092251_state) (B_29:(hoare_1262092251_state->Prop)), (((eq (hoare_1262092251_state->Prop)) ((insert81609953_state A_48) B_29)) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> ((or (((eq hoare_1262092251_state) X_1) A_48)) ((member5164104_state X_1) B_29)))))) % FOF formula (forall (A_48:(pname->Prop)) (B_29:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_48) B_29)) (collect_pname_o (fun (X_1:(pname->Prop))=> ((or (((eq (pname->Prop)) X_1) A_48)) ((member_pname_o X_1) B_29)))))) of role axiom named fact_188_insert__compr % A new axiom: (forall (A_48:(pname->Prop)) (B_29:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_48) B_29)) (collect_pname_o (fun (X_1:(pname->Prop))=> ((or (((eq (pname->Prop)) X_1) A_48)) ((member_pname_o X_1) B_29)))))) % FOF formula (forall (A_48:(hoare_1262092251_state->Prop)) (B_29:((hoare_1262092251_state->Prop)->Prop)), (((eq ((hoare_1262092251_state->Prop)->Prop)) ((insert1042460334tate_o A_48) B_29)) (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> ((or (((eq (hoare_1262092251_state->Prop)) X_1) A_48)) ((member907417095tate_o X_1) B_29)))))) of role axiom named fact_189_insert__compr % A new axiom: (forall (A_48:(hoare_1262092251_state->Prop)) (B_29:((hoare_1262092251_state->Prop)->Prop)), (((eq ((hoare_1262092251_state->Prop)->Prop)) ((insert1042460334tate_o A_48) B_29)) (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> ((or (((eq (hoare_1262092251_state->Prop)) X_1) A_48)) ((member907417095tate_o X_1) B_29)))))) % FOF formula (forall (A_47:pname) (B_28:(pname->Prop)), ((member_pname A_47) ((insert_pname A_47) B_28))) of role axiom named fact_190_insertI1 % A new axiom: (forall (A_47:pname) (B_28:(pname->Prop)), ((member_pname A_47) ((insert_pname A_47) B_28))) % FOF formula (forall (A_47:hoare_1262092251_state) (B_28:(hoare_1262092251_state->Prop)), ((member5164104_state A_47) ((insert81609953_state A_47) B_28))) of role axiom named fact_191_insertI1 % A new axiom: (forall (A_47:hoare_1262092251_state) (B_28:(hoare_1262092251_state->Prop)), ((member5164104_state A_47) ((insert81609953_state A_47) B_28))) % FOF formula (forall (A_46:(pname->Prop)) (B_27:(pname->Prop)), ((((eq (pname->Prop)) A_46) B_27)->((((ord_less_eq_pname_o A_46) B_27)->(((ord_less_eq_pname_o B_27) A_46)->False))->False))) of role axiom named fact_192_equalityE % A new axiom: (forall (A_46:(pname->Prop)) (B_27:(pname->Prop)), ((((eq (pname->Prop)) A_46) B_27)->((((ord_less_eq_pname_o A_46) B_27)->(((ord_less_eq_pname_o B_27) A_46)->False))->False))) % FOF formula (forall (A_46:(hoare_1262092251_state->Prop)) (B_27:(hoare_1262092251_state->Prop)), ((((eq (hoare_1262092251_state->Prop)) A_46) B_27)->((((ord_le870406270tate_o A_46) B_27)->(((ord_le870406270tate_o B_27) A_46)->False))->False))) of role axiom named fact_193_equalityE % A new axiom: (forall (A_46:(hoare_1262092251_state->Prop)) (B_27:(hoare_1262092251_state->Prop)), ((((eq (hoare_1262092251_state->Prop)) A_46) B_27)->((((ord_le870406270tate_o A_46) B_27)->(((ord_le870406270tate_o B_27) A_46)->False))->False))) % FOF formula (forall (C_4:(pname->Prop)) (A_45:(pname->Prop)) (B_26:(pname->Prop)), (((ord_less_eq_pname_o A_45) B_26)->(((ord_less_eq_pname_o B_26) C_4)->((ord_less_eq_pname_o A_45) C_4)))) of role axiom named fact_194_subset__trans % A new axiom: (forall (C_4:(pname->Prop)) (A_45:(pname->Prop)) (B_26:(pname->Prop)), (((ord_less_eq_pname_o A_45) B_26)->(((ord_less_eq_pname_o B_26) C_4)->((ord_less_eq_pname_o A_45) C_4)))) % FOF formula (forall (C_4:(hoare_1262092251_state->Prop)) (A_45:(hoare_1262092251_state->Prop)) (B_26:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o A_45) B_26)->(((ord_le870406270tate_o B_26) C_4)->((ord_le870406270tate_o A_45) C_4)))) of role axiom named fact_195_subset__trans % A new axiom: (forall (C_4:(hoare_1262092251_state->Prop)) (A_45:(hoare_1262092251_state->Prop)) (B_26:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o A_45) B_26)->(((ord_le870406270tate_o B_26) C_4)->((ord_le870406270tate_o A_45) C_4)))) % FOF formula (forall (X_10:pname) (A_44:(pname->Prop)) (B_25:(pname->Prop)), (((ord_less_eq_pname_o A_44) B_25)->(((member_pname X_10) A_44)->((member_pname X_10) B_25)))) of role axiom named fact_196_set__mp % A new axiom: (forall (X_10:pname) (A_44:(pname->Prop)) (B_25:(pname->Prop)), (((ord_less_eq_pname_o A_44) B_25)->(((member_pname X_10) A_44)->((member_pname X_10) B_25)))) % FOF formula (forall (X_10:hoare_1262092251_state) (A_44:(hoare_1262092251_state->Prop)) (B_25:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o A_44) B_25)->(((member5164104_state X_10) A_44)->((member5164104_state X_10) B_25)))) of role axiom named fact_197_set__mp % A new axiom: (forall (X_10:hoare_1262092251_state) (A_44:(hoare_1262092251_state->Prop)) (B_25:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o A_44) B_25)->(((member5164104_state X_10) A_44)->((member5164104_state X_10) B_25)))) % FOF formula (forall (B_24:(pname->Prop)) (X_9:pname) (A_43:(pname->Prop)), (((member_pname X_9) A_43)->(((ord_less_eq_pname_o A_43) B_24)->((member_pname X_9) B_24)))) of role axiom named fact_198_set__rev__mp % A new axiom: (forall (B_24:(pname->Prop)) (X_9:pname) (A_43:(pname->Prop)), (((member_pname X_9) A_43)->(((ord_less_eq_pname_o A_43) B_24)->((member_pname X_9) B_24)))) % FOF formula (forall (B_24:(hoare_1262092251_state->Prop)) (X_9:hoare_1262092251_state) (A_43:(hoare_1262092251_state->Prop)), (((member5164104_state X_9) A_43)->(((ord_le870406270tate_o A_43) B_24)->((member5164104_state X_9) B_24)))) of role axiom named fact_199_set__rev__mp % A new axiom: (forall (B_24:(hoare_1262092251_state->Prop)) (X_9:hoare_1262092251_state) (A_43:(hoare_1262092251_state->Prop)), (((member5164104_state X_9) A_43)->(((ord_le870406270tate_o A_43) B_24)->((member5164104_state X_9) B_24)))) % FOF formula (forall (X_8:pname) (A_42:(pname->Prop)) (B_23:(pname->Prop)), (((ord_less_eq_pname_o A_42) B_23)->(((member_pname X_8) A_42)->((member_pname X_8) B_23)))) of role axiom named fact_200_in__mono % A new axiom: (forall (X_8:pname) (A_42:(pname->Prop)) (B_23:(pname->Prop)), (((ord_less_eq_pname_o A_42) B_23)->(((member_pname X_8) A_42)->((member_pname X_8) B_23)))) % FOF formula (forall (X_8:hoare_1262092251_state) (A_42:(hoare_1262092251_state->Prop)) (B_23:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o A_42) B_23)->(((member5164104_state X_8) A_42)->((member5164104_state X_8) B_23)))) of role axiom named fact_201_in__mono % A new axiom: (forall (X_8:hoare_1262092251_state) (A_42:(hoare_1262092251_state->Prop)) (B_23:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o A_42) B_23)->(((member5164104_state X_8) A_42)->((member5164104_state X_8) B_23)))) % FOF formula (forall (A_41:(pname->Prop)) (B_22:(pname->Prop)), ((((eq (pname->Prop)) A_41) B_22)->((ord_less_eq_pname_o B_22) A_41))) of role axiom named fact_202_equalityD2 % A new axiom: (forall (A_41:(pname->Prop)) (B_22:(pname->Prop)), ((((eq (pname->Prop)) A_41) B_22)->((ord_less_eq_pname_o B_22) A_41))) % FOF formula (forall (A_41:(hoare_1262092251_state->Prop)) (B_22:(hoare_1262092251_state->Prop)), ((((eq (hoare_1262092251_state->Prop)) A_41) B_22)->((ord_le870406270tate_o B_22) A_41))) of role axiom named fact_203_equalityD2 % A new axiom: (forall (A_41:(hoare_1262092251_state->Prop)) (B_22:(hoare_1262092251_state->Prop)), ((((eq (hoare_1262092251_state->Prop)) A_41) B_22)->((ord_le870406270tate_o B_22) A_41))) % FOF formula (forall (A_40:(pname->Prop)) (B_21:(pname->Prop)), ((((eq (pname->Prop)) A_40) B_21)->((ord_less_eq_pname_o A_40) B_21))) of role axiom named fact_204_equalityD1 % A new axiom: (forall (A_40:(pname->Prop)) (B_21:(pname->Prop)), ((((eq (pname->Prop)) A_40) B_21)->((ord_less_eq_pname_o A_40) B_21))) % FOF formula (forall (A_40:(hoare_1262092251_state->Prop)) (B_21:(hoare_1262092251_state->Prop)), ((((eq (hoare_1262092251_state->Prop)) A_40) B_21)->((ord_le870406270tate_o A_40) B_21))) of role axiom named fact_205_equalityD1 % A new axiom: (forall (A_40:(hoare_1262092251_state->Prop)) (B_21:(hoare_1262092251_state->Prop)), ((((eq (hoare_1262092251_state->Prop)) A_40) B_21)->((ord_le870406270tate_o A_40) B_21))) % FOF formula (forall (A_39:(pname->Prop)) (B_20:(pname->Prop)), ((iff (((eq (pname->Prop)) A_39) B_20)) ((and ((ord_less_eq_pname_o A_39) B_20)) ((ord_less_eq_pname_o B_20) A_39)))) of role axiom named fact_206_set__eq__subset % A new axiom: (forall (A_39:(pname->Prop)) (B_20:(pname->Prop)), ((iff (((eq (pname->Prop)) A_39) B_20)) ((and ((ord_less_eq_pname_o A_39) B_20)) ((ord_less_eq_pname_o B_20) A_39)))) % FOF formula (forall (A_39:(hoare_1262092251_state->Prop)) (B_20:(hoare_1262092251_state->Prop)), ((iff (((eq (hoare_1262092251_state->Prop)) A_39) B_20)) ((and ((ord_le870406270tate_o A_39) B_20)) ((ord_le870406270tate_o B_20) A_39)))) of role axiom named fact_207_set__eq__subset % A new axiom: (forall (A_39:(hoare_1262092251_state->Prop)) (B_20:(hoare_1262092251_state->Prop)), ((iff (((eq (hoare_1262092251_state->Prop)) A_39) B_20)) ((and ((ord_le870406270tate_o A_39) B_20)) ((ord_le870406270tate_o B_20) A_39)))) % FOF formula (forall (A_38:(pname->Prop)), ((ord_less_eq_pname_o A_38) A_38)) of role axiom named fact_208_subset__refl % A new axiom: (forall (A_38:(pname->Prop)), ((ord_less_eq_pname_o A_38) A_38)) % FOF formula (forall (A_38:(hoare_1262092251_state->Prop)), ((ord_le870406270tate_o A_38) A_38)) of role axiom named fact_209_subset__refl % A new axiom: (forall (A_38:(hoare_1262092251_state->Prop)), ((ord_le870406270tate_o A_38) A_38)) % FOF formula (forall (B_19:hoare_1262092251_state) (F_13:(pname->hoare_1262092251_state)) (X_7:pname) (A_37:(pname->Prop)), (((member_pname X_7) A_37)->((((eq hoare_1262092251_state) B_19) (F_13 X_7))->((member5164104_state B_19) ((image_669833818_state F_13) A_37))))) of role axiom named fact_210_rev__image__eqI % A new axiom: (forall (B_19:hoare_1262092251_state) (F_13:(pname->hoare_1262092251_state)) (X_7:pname) (A_37:(pname->Prop)), (((member_pname X_7) A_37)->((((eq hoare_1262092251_state) B_19) (F_13 X_7))->((member5164104_state B_19) ((image_669833818_state F_13) A_37))))) % FOF formula (forall (F_12:(pname->hoare_1262092251_state)) (X_6:pname) (A_36:(pname->Prop)), (((member_pname X_6) A_36)->((member5164104_state (F_12 X_6)) ((image_669833818_state F_12) A_36)))) of role axiom named fact_211_imageI % A new axiom: (forall (F_12:(pname->hoare_1262092251_state)) (X_6:pname) (A_36:(pname->Prop)), (((member_pname X_6) A_36)->((member5164104_state (F_12 X_6)) ((image_669833818_state F_12) A_36)))) % FOF formula (forall (Z:hoare_1262092251_state) (F_11:(pname->hoare_1262092251_state)) (A_35:(pname->Prop)), ((iff ((member5164104_state Z) ((image_669833818_state F_11) A_35))) ((ex pname) (fun (X_1:pname)=> ((and ((member_pname X_1) A_35)) (((eq hoare_1262092251_state) Z) (F_11 X_1))))))) of role axiom named fact_212_image__iff % A new axiom: (forall (Z:hoare_1262092251_state) (F_11:(pname->hoare_1262092251_state)) (A_35:(pname->Prop)), ((iff ((member5164104_state Z) ((image_669833818_state F_11) A_35))) ((ex pname) (fun (X_1:pname)=> ((and ((member_pname X_1) A_35)) (((eq hoare_1262092251_state) Z) (F_11 X_1))))))) % FOF formula (forall (P_5:(pname->Prop)) (Q:(pname->Prop)), ((iff (finite_finite_pname (collect_pname (fun (X_1:pname)=> ((or (P_5 X_1)) (Q X_1)))))) ((and (finite_finite_pname (collect_pname P_5))) (finite_finite_pname (collect_pname Q))))) of role axiom named fact_213_finite__Collect__disjI % A new axiom: (forall (P_5:(pname->Prop)) (Q:(pname->Prop)), ((iff (finite_finite_pname (collect_pname (fun (X_1:pname)=> ((or (P_5 X_1)) (Q X_1)))))) ((and (finite_finite_pname (collect_pname P_5))) (finite_finite_pname (collect_pname Q))))) % FOF formula (forall (P_5:(hoare_1262092251_state->Prop)) (Q:(hoare_1262092251_state->Prop)), ((iff (finite1178804552_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> ((or (P_5 X_1)) (Q X_1)))))) ((and (finite1178804552_state (collec1121927558_state P_5))) (finite1178804552_state (collec1121927558_state Q))))) of role axiom named fact_214_finite__Collect__disjI % A new axiom: (forall (P_5:(hoare_1262092251_state->Prop)) (Q:(hoare_1262092251_state->Prop)), ((iff (finite1178804552_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> ((or (P_5 X_1)) (Q X_1)))))) ((and (finite1178804552_state (collec1121927558_state P_5))) (finite1178804552_state (collec1121927558_state Q))))) % FOF formula (forall (P_5:((pname->Prop)->Prop)) (Q:((pname->Prop)->Prop)), ((iff (finite297249702name_o (collect_pname_o (fun (X_1:(pname->Prop))=> ((or (P_5 X_1)) (Q X_1)))))) ((and (finite297249702name_o (collect_pname_o P_5))) (finite297249702name_o (collect_pname_o Q))))) of role axiom named fact_215_finite__Collect__disjI % A new axiom: (forall (P_5:((pname->Prop)->Prop)) (Q:((pname->Prop)->Prop)), ((iff (finite297249702name_o (collect_pname_o (fun (X_1:(pname->Prop))=> ((or (P_5 X_1)) (Q X_1)))))) ((and (finite297249702name_o (collect_pname_o P_5))) (finite297249702name_o (collect_pname_o Q))))) % FOF formula (forall (P_5:((hoare_1262092251_state->Prop)->Prop)) (Q:((hoare_1262092251_state->Prop)->Prop)), ((iff (finite1423311111tate_o (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> ((or (P_5 X_1)) (Q X_1)))))) ((and (finite1423311111tate_o (collec313158217tate_o P_5))) (finite1423311111tate_o (collec313158217tate_o Q))))) of role axiom named fact_216_finite__Collect__disjI % A new axiom: (forall (P_5:((hoare_1262092251_state->Prop)->Prop)) (Q:((hoare_1262092251_state->Prop)->Prop)), ((iff (finite1423311111tate_o (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> ((or (P_5 X_1)) (Q X_1)))))) ((and (finite1423311111tate_o (collec313158217tate_o P_5))) (finite1423311111tate_o (collec313158217tate_o Q))))) % FOF formula (forall (X_1:pname) (Xa:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_1) Xa)) (collect_pname (fun (Y_1:pname)=> ((or (((eq pname) Y_1) X_1)) ((member_pname Y_1) Xa)))))) of role axiom named fact_217_insert__compr__raw % A new axiom: (forall (X_1:pname) (Xa:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_1) Xa)) (collect_pname (fun (Y_1:pname)=> ((or (((eq pname) Y_1) X_1)) ((member_pname Y_1) Xa)))))) % FOF formula (forall (X_1:hoare_1262092251_state) (Xa:(hoare_1262092251_state->Prop)), (((eq (hoare_1262092251_state->Prop)) ((insert81609953_state X_1) Xa)) (collec1121927558_state (fun (Y_1:hoare_1262092251_state)=> ((or (((eq hoare_1262092251_state) Y_1) X_1)) ((member5164104_state Y_1) Xa)))))) of role axiom named fact_218_insert__compr__raw % A new axiom: (forall (X_1:hoare_1262092251_state) (Xa:(hoare_1262092251_state->Prop)), (((eq (hoare_1262092251_state->Prop)) ((insert81609953_state X_1) Xa)) (collec1121927558_state (fun (Y_1:hoare_1262092251_state)=> ((or (((eq hoare_1262092251_state) Y_1) X_1)) ((member5164104_state Y_1) Xa)))))) % FOF formula (forall (X_1:(pname->Prop)) (Xa:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o X_1) Xa)) (collect_pname_o (fun (Y_1:(pname->Prop))=> ((or (((eq (pname->Prop)) Y_1) X_1)) ((member_pname_o Y_1) Xa)))))) of role axiom named fact_219_insert__compr__raw % A new axiom: (forall (X_1:(pname->Prop)) (Xa:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o X_1) Xa)) (collect_pname_o (fun (Y_1:(pname->Prop))=> ((or (((eq (pname->Prop)) Y_1) X_1)) ((member_pname_o Y_1) Xa)))))) % FOF formula (forall (X_1:(hoare_1262092251_state->Prop)) (Xa:((hoare_1262092251_state->Prop)->Prop)), (((eq ((hoare_1262092251_state->Prop)->Prop)) ((insert1042460334tate_o X_1) Xa)) (collec313158217tate_o (fun (Y_1:(hoare_1262092251_state->Prop))=> ((or (((eq (hoare_1262092251_state->Prop)) Y_1) X_1)) ((member907417095tate_o Y_1) Xa)))))) of role axiom named fact_220_insert__compr__raw % A new axiom: (forall (X_1:(hoare_1262092251_state->Prop)) (Xa:((hoare_1262092251_state->Prop)->Prop)), (((eq ((hoare_1262092251_state->Prop)->Prop)) ((insert1042460334tate_o X_1) Xa)) (collec313158217tate_o (fun (Y_1:(hoare_1262092251_state->Prop))=> ((or (((eq (hoare_1262092251_state->Prop)) Y_1) X_1)) ((member907417095tate_o Y_1) Xa)))))) % FOF formula (forall (A_34:pname) (B_18:pname), ((((eq (pname->Prop)) ((insert_pname A_34) bot_bot_pname_o)) ((insert_pname B_18) bot_bot_pname_o))->(((eq pname) A_34) B_18))) of role axiom named fact_221_singleton__inject % A new axiom: (forall (A_34:pname) (B_18:pname), ((((eq (pname->Prop)) ((insert_pname A_34) bot_bot_pname_o)) ((insert_pname B_18) bot_bot_pname_o))->(((eq pname) A_34) B_18))) % FOF formula (forall (A_34:hoare_1262092251_state) (B_18:hoare_1262092251_state), ((((eq (hoare_1262092251_state->Prop)) ((insert81609953_state A_34) bot_bo113204042tate_o)) ((insert81609953_state B_18) bot_bo113204042tate_o))->(((eq hoare_1262092251_state) A_34) B_18))) of role axiom named fact_222_singleton__inject % A new axiom: (forall (A_34:hoare_1262092251_state) (B_18:hoare_1262092251_state), ((((eq (hoare_1262092251_state->Prop)) ((insert81609953_state A_34) bot_bo113204042tate_o)) ((insert81609953_state B_18) bot_bo113204042tate_o))->(((eq hoare_1262092251_state) A_34) B_18))) % FOF formula (forall (B_17:pname) (A_33:pname), (((member_pname B_17) ((insert_pname A_33) bot_bot_pname_o))->(((eq pname) B_17) A_33))) of role axiom named fact_223_singletonE % A new axiom: (forall (B_17:pname) (A_33:pname), (((member_pname B_17) ((insert_pname A_33) bot_bot_pname_o))->(((eq pname) B_17) A_33))) % FOF formula (forall (B_17:hoare_1262092251_state) (A_33:hoare_1262092251_state), (((member5164104_state B_17) ((insert81609953_state A_33) bot_bo113204042tate_o))->(((eq hoare_1262092251_state) B_17) A_33))) of role axiom named fact_224_singletonE % A new axiom: (forall (B_17:hoare_1262092251_state) (A_33:hoare_1262092251_state), (((member5164104_state B_17) ((insert81609953_state A_33) bot_bo113204042tate_o))->(((eq hoare_1262092251_state) B_17) A_33))) % FOF formula (forall (A_32:pname) (B_16:pname) (C_3:pname) (D_1:pname), ((iff (((eq (pname->Prop)) ((insert_pname A_32) ((insert_pname B_16) bot_bot_pname_o))) ((insert_pname C_3) ((insert_pname D_1) bot_bot_pname_o)))) ((or ((and (((eq pname) A_32) C_3)) (((eq pname) B_16) D_1))) ((and (((eq pname) A_32) D_1)) (((eq pname) B_16) C_3))))) of role axiom named fact_225_doubleton__eq__iff % A new axiom: (forall (A_32:pname) (B_16:pname) (C_3:pname) (D_1:pname), ((iff (((eq (pname->Prop)) ((insert_pname A_32) ((insert_pname B_16) bot_bot_pname_o))) ((insert_pname C_3) ((insert_pname D_1) bot_bot_pname_o)))) ((or ((and (((eq pname) A_32) C_3)) (((eq pname) B_16) D_1))) ((and (((eq pname) A_32) D_1)) (((eq pname) B_16) C_3))))) % FOF formula (forall (A_32:hoare_1262092251_state) (B_16:hoare_1262092251_state) (C_3:hoare_1262092251_state) (D_1:hoare_1262092251_state), ((iff (((eq (hoare_1262092251_state->Prop)) ((insert81609953_state A_32) ((insert81609953_state B_16) bot_bo113204042tate_o))) ((insert81609953_state C_3) ((insert81609953_state D_1) bot_bo113204042tate_o)))) ((or ((and (((eq hoare_1262092251_state) A_32) C_3)) (((eq hoare_1262092251_state) B_16) D_1))) ((and (((eq hoare_1262092251_state) A_32) D_1)) (((eq hoare_1262092251_state) B_16) C_3))))) of role axiom named fact_226_doubleton__eq__iff % A new axiom: (forall (A_32:hoare_1262092251_state) (B_16:hoare_1262092251_state) (C_3:hoare_1262092251_state) (D_1:hoare_1262092251_state), ((iff (((eq (hoare_1262092251_state->Prop)) ((insert81609953_state A_32) ((insert81609953_state B_16) bot_bo113204042tate_o))) ((insert81609953_state C_3) ((insert81609953_state D_1) bot_bo113204042tate_o)))) ((or ((and (((eq hoare_1262092251_state) A_32) C_3)) (((eq hoare_1262092251_state) B_16) D_1))) ((and (((eq hoare_1262092251_state) A_32) D_1)) (((eq hoare_1262092251_state) B_16) C_3))))) % FOF formula (forall (B_15:pname) (A_31:pname), ((iff ((member_pname B_15) ((insert_pname A_31) bot_bot_pname_o))) (((eq pname) B_15) A_31))) of role axiom named fact_227_singleton__iff % A new axiom: (forall (B_15:pname) (A_31:pname), ((iff ((member_pname B_15) ((insert_pname A_31) bot_bot_pname_o))) (((eq pname) B_15) A_31))) % FOF formula (forall (B_15:hoare_1262092251_state) (A_31:hoare_1262092251_state), ((iff ((member5164104_state B_15) ((insert81609953_state A_31) bot_bo113204042tate_o))) (((eq hoare_1262092251_state) B_15) A_31))) of role axiom named fact_228_singleton__iff % A new axiom: (forall (B_15:hoare_1262092251_state) (A_31:hoare_1262092251_state), ((iff ((member5164104_state B_15) ((insert81609953_state A_31) bot_bo113204042tate_o))) (((eq hoare_1262092251_state) B_15) A_31))) % FOF formula (forall (A_30:pname) (A_29:(pname->Prop)), (not (((eq (pname->Prop)) ((insert_pname A_30) A_29)) bot_bot_pname_o))) of role axiom named fact_229_insert__not__empty % A new axiom: (forall (A_30:pname) (A_29:(pname->Prop)), (not (((eq (pname->Prop)) ((insert_pname A_30) A_29)) bot_bot_pname_o))) % FOF formula (forall (A_30:hoare_1262092251_state) (A_29:(hoare_1262092251_state->Prop)), (not (((eq (hoare_1262092251_state->Prop)) ((insert81609953_state A_30) A_29)) bot_bo113204042tate_o))) of role axiom named fact_230_insert__not__empty % A new axiom: (forall (A_30:hoare_1262092251_state) (A_29:(hoare_1262092251_state->Prop)), (not (((eq (hoare_1262092251_state->Prop)) ((insert81609953_state A_30) A_29)) bot_bo113204042tate_o))) % FOF formula (forall (A_28:pname) (A_27:(pname->Prop)), (not (((eq (pname->Prop)) bot_bot_pname_o) ((insert_pname A_28) A_27)))) of role axiom named fact_231_empty__not__insert % A new axiom: (forall (A_28:pname) (A_27:(pname->Prop)), (not (((eq (pname->Prop)) bot_bot_pname_o) ((insert_pname A_28) A_27)))) % FOF formula (forall (A_28:hoare_1262092251_state) (A_27:(hoare_1262092251_state->Prop)), (not (((eq (hoare_1262092251_state->Prop)) bot_bo113204042tate_o) ((insert81609953_state A_28) A_27)))) of role axiom named fact_232_empty__not__insert % A new axiom: (forall (A_28:hoare_1262092251_state) (A_27:(hoare_1262092251_state->Prop)), (not (((eq (hoare_1262092251_state->Prop)) bot_bo113204042tate_o) ((insert81609953_state A_28) A_27)))) % FOF formula (forall (A_26:pname) (A_25:(pname->Prop)), ((iff (finite_finite_pname ((insert_pname A_26) A_25))) (finite_finite_pname A_25))) of role axiom named fact_233_finite__insert % A new axiom: (forall (A_26:pname) (A_25:(pname->Prop)), ((iff (finite_finite_pname ((insert_pname A_26) A_25))) (finite_finite_pname A_25))) % FOF formula (forall (A_26:hoare_1262092251_state) (A_25:(hoare_1262092251_state->Prop)), ((iff (finite1178804552_state ((insert81609953_state A_26) A_25))) (finite1178804552_state A_25))) of role axiom named fact_234_finite__insert % A new axiom: (forall (A_26:hoare_1262092251_state) (A_25:(hoare_1262092251_state->Prop)), ((iff (finite1178804552_state ((insert81609953_state A_26) A_25))) (finite1178804552_state A_25))) % FOF formula (forall (A_26:(pname->Prop)) (A_25:((pname->Prop)->Prop)), ((iff (finite297249702name_o ((insert_pname_o A_26) A_25))) (finite297249702name_o A_25))) of role axiom named fact_235_finite__insert % A new axiom: (forall (A_26:(pname->Prop)) (A_25:((pname->Prop)->Prop)), ((iff (finite297249702name_o ((insert_pname_o A_26) A_25))) (finite297249702name_o A_25))) % FOF formula (forall (A_26:(hoare_1262092251_state->Prop)) (A_25:((hoare_1262092251_state->Prop)->Prop)), ((iff (finite1423311111tate_o ((insert1042460334tate_o A_26) A_25))) (finite1423311111tate_o A_25))) of role axiom named fact_236_finite__insert % A new axiom: (forall (A_26:(hoare_1262092251_state->Prop)) (A_25:((hoare_1262092251_state->Prop)->Prop)), ((iff (finite1423311111tate_o ((insert1042460334tate_o A_26) A_25))) (finite1423311111tate_o A_25))) % FOF formula (forall (A_24:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_24) bot_bot_pname_o)) (((eq (pname->Prop)) A_24) bot_bot_pname_o))) of role axiom named fact_237_subset__empty % A new axiom: (forall (A_24:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_24) bot_bot_pname_o)) (((eq (pname->Prop)) A_24) bot_bot_pname_o))) % FOF formula (forall (A_24:(hoare_1262092251_state->Prop)), ((iff ((ord_le870406270tate_o A_24) bot_bo113204042tate_o)) (((eq (hoare_1262092251_state->Prop)) A_24) bot_bo113204042tate_o))) of role axiom named fact_238_subset__empty % A new axiom: (forall (A_24:(hoare_1262092251_state->Prop)), ((iff ((ord_le870406270tate_o A_24) bot_bo113204042tate_o)) (((eq (hoare_1262092251_state->Prop)) A_24) bot_bo113204042tate_o))) % FOF formula (forall (F_10:(pname->hoare_1262092251_state)) (A_23:(pname->Prop)), ((iff (((eq (hoare_1262092251_state->Prop)) ((image_669833818_state F_10) A_23)) bot_bo113204042tate_o)) (((eq (pname->Prop)) A_23) bot_bot_pname_o))) of role axiom named fact_239_image__is__empty % A new axiom: (forall (F_10:(pname->hoare_1262092251_state)) (A_23:(pname->Prop)), ((iff (((eq (hoare_1262092251_state->Prop)) ((image_669833818_state F_10) A_23)) bot_bo113204042tate_o)) (((eq (pname->Prop)) A_23) bot_bot_pname_o))) % FOF formula (forall (F_9:(pname->hoare_1262092251_state)), (((eq (hoare_1262092251_state->Prop)) ((image_669833818_state F_9) bot_bot_pname_o)) bot_bo113204042tate_o)) of role axiom named fact_240_image__empty % A new axiom: (forall (F_9:(pname->hoare_1262092251_state)), (((eq (hoare_1262092251_state->Prop)) ((image_669833818_state F_9) bot_bot_pname_o)) bot_bo113204042tate_o)) % FOF formula (forall (F_8:(pname->hoare_1262092251_state)) (A_22:(pname->Prop)), ((iff (((eq (hoare_1262092251_state->Prop)) bot_bo113204042tate_o) ((image_669833818_state F_8) A_22))) (((eq (pname->Prop)) A_22) bot_bot_pname_o))) of role axiom named fact_241_empty__is__image % A new axiom: (forall (F_8:(pname->hoare_1262092251_state)) (A_22:(pname->Prop)), ((iff (((eq (hoare_1262092251_state->Prop)) bot_bo113204042tate_o) ((image_669833818_state F_8) A_22))) (((eq (pname->Prop)) A_22) bot_bot_pname_o))) % FOF formula (forall (A_21:((pname->Prop)->Prop)) (B_14:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_21) B_14)->((finite297249702name_o B_14)->(finite297249702name_o A_21)))) of role axiom named fact_242_finite__subset % A new axiom: (forall (A_21:((pname->Prop)->Prop)) (B_14:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_21) B_14)->((finite297249702name_o B_14)->(finite297249702name_o A_21)))) % FOF formula (forall (A_21:((hoare_1262092251_state->Prop)->Prop)) (B_14:((hoare_1262092251_state->Prop)->Prop)), (((ord_le2012720639te_o_o A_21) B_14)->((finite1423311111tate_o B_14)->(finite1423311111tate_o A_21)))) of role axiom named fact_243_finite__subset % A new axiom: (forall (A_21:((hoare_1262092251_state->Prop)->Prop)) (B_14:((hoare_1262092251_state->Prop)->Prop)), (((ord_le2012720639te_o_o A_21) B_14)->((finite1423311111tate_o B_14)->(finite1423311111tate_o A_21)))) % FOF formula (forall (A_21:(pname->Prop)) (B_14:(pname->Prop)), (((ord_less_eq_pname_o A_21) B_14)->((finite_finite_pname B_14)->(finite_finite_pname A_21)))) of role axiom named fact_244_finite__subset % A new axiom: (forall (A_21:(pname->Prop)) (B_14:(pname->Prop)), (((ord_less_eq_pname_o A_21) B_14)->((finite_finite_pname B_14)->(finite_finite_pname A_21)))) % FOF formula (forall (A_21:(hoare_1262092251_state->Prop)) (B_14:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o A_21) B_14)->((finite1178804552_state B_14)->(finite1178804552_state A_21)))) of role axiom named fact_245_finite__subset % A new axiom: (forall (A_21:(hoare_1262092251_state->Prop)) (B_14:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o A_21) B_14)->((finite1178804552_state B_14)->(finite1178804552_state A_21)))) % FOF formula (forall (A_20:((pname->Prop)->Prop)) (B_13:((pname->Prop)->Prop)), ((finite297249702name_o B_13)->(((ord_le1205211808me_o_o A_20) B_13)->(finite297249702name_o A_20)))) of role axiom named fact_246_rev__finite__subset % A new axiom: (forall (A_20:((pname->Prop)->Prop)) (B_13:((pname->Prop)->Prop)), ((finite297249702name_o B_13)->(((ord_le1205211808me_o_o A_20) B_13)->(finite297249702name_o A_20)))) % FOF formula (forall (A_20:((hoare_1262092251_state->Prop)->Prop)) (B_13:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o B_13)->(((ord_le2012720639te_o_o A_20) B_13)->(finite1423311111tate_o A_20)))) of role axiom named fact_247_rev__finite__subset % A new axiom: (forall (A_20:((hoare_1262092251_state->Prop)->Prop)) (B_13:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o B_13)->(((ord_le2012720639te_o_o A_20) B_13)->(finite1423311111tate_o A_20)))) % FOF formula (forall (A_20:(pname->Prop)) (B_13:(pname->Prop)), ((finite_finite_pname B_13)->(((ord_less_eq_pname_o A_20) B_13)->(finite_finite_pname A_20)))) of role axiom named fact_248_rev__finite__subset % A new axiom: (forall (A_20:(pname->Prop)) (B_13:(pname->Prop)), ((finite_finite_pname B_13)->(((ord_less_eq_pname_o A_20) B_13)->(finite_finite_pname A_20)))) % FOF formula (forall (A_20:(hoare_1262092251_state->Prop)) (B_13:(hoare_1262092251_state->Prop)), ((finite1178804552_state B_13)->(((ord_le870406270tate_o A_20) B_13)->(finite1178804552_state A_20)))) of role axiom named fact_249_rev__finite__subset % A new axiom: (forall (A_20:(hoare_1262092251_state->Prop)) (B_13:(hoare_1262092251_state->Prop)), ((finite1178804552_state B_13)->(((ord_le870406270tate_o A_20) B_13)->(finite1178804552_state A_20)))) % FOF formula (forall (A_19:pname) (C_2:(pname->Prop)) (D:(pname->Prop)), (((ord_less_eq_pname_o C_2) D)->((ord_less_eq_pname_o ((insert_pname A_19) C_2)) ((insert_pname A_19) D)))) of role axiom named fact_250_insert__mono % A new axiom: (forall (A_19:pname) (C_2:(pname->Prop)) (D:(pname->Prop)), (((ord_less_eq_pname_o C_2) D)->((ord_less_eq_pname_o ((insert_pname A_19) C_2)) ((insert_pname A_19) D)))) % FOF formula (forall (A_19:hoare_1262092251_state) (C_2:(hoare_1262092251_state->Prop)) (D:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o C_2) D)->((ord_le870406270tate_o ((insert81609953_state A_19) C_2)) ((insert81609953_state A_19) D)))) of role axiom named fact_251_insert__mono % A new axiom: (forall (A_19:hoare_1262092251_state) (C_2:(hoare_1262092251_state->Prop)) (D:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o C_2) D)->((ord_le870406270tate_o ((insert81609953_state A_19) C_2)) ((insert81609953_state A_19) D)))) % FOF formula (forall (X_5:pname) (A_18:(pname->Prop)), ((iff ((member_pname X_5) A_18)) (A_18 X_5))) of role axiom named fact_252_mem__def % A new axiom: (forall (X_5:pname) (A_18:(pname->Prop)), ((iff ((member_pname X_5) A_18)) (A_18 X_5))) % FOF formula (forall (X_5:hoare_1262092251_state) (A_18:(hoare_1262092251_state->Prop)), ((iff ((member5164104_state X_5) A_18)) (A_18 X_5))) of role axiom named fact_253_mem__def % A new axiom: (forall (X_5:hoare_1262092251_state) (A_18:(hoare_1262092251_state->Prop)), ((iff ((member5164104_state X_5) A_18)) (A_18 X_5))) % FOF formula (forall (P_4:(pname->Prop)), (((eq (pname->Prop)) (collect_pname P_4)) P_4)) of role axiom named fact_254_Collect__def % A new axiom: (forall (P_4:(pname->Prop)), (((eq (pname->Prop)) (collect_pname P_4)) P_4)) % FOF formula (forall (P_4:(hoare_1262092251_state->Prop)), (((eq (hoare_1262092251_state->Prop)) (collec1121927558_state P_4)) P_4)) of role axiom named fact_255_Collect__def % A new axiom: (forall (P_4:(hoare_1262092251_state->Prop)), (((eq (hoare_1262092251_state->Prop)) (collec1121927558_state P_4)) P_4)) % FOF formula (forall (P_4:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o P_4)) P_4)) of role axiom named fact_256_Collect__def % A new axiom: (forall (P_4:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o P_4)) P_4)) % FOF formula (forall (P_4:((hoare_1262092251_state->Prop)->Prop)), (((eq ((hoare_1262092251_state->Prop)->Prop)) (collec313158217tate_o P_4)) P_4)) of role axiom named fact_257_Collect__def % A new axiom: (forall (P_4:((hoare_1262092251_state->Prop)->Prop)), (((eq ((hoare_1262092251_state->Prop)->Prop)) (collec313158217tate_o P_4)) P_4)) % FOF formula (forall (B_12:pname) (A_17:(pname->Prop)) (B_11:(pname->Prop)), (((ord_less_eq_pname_o A_17) B_11)->((ord_less_eq_pname_o A_17) ((insert_pname B_12) B_11)))) of role axiom named fact_258_subset__insertI2 % A new axiom: (forall (B_12:pname) (A_17:(pname->Prop)) (B_11:(pname->Prop)), (((ord_less_eq_pname_o A_17) B_11)->((ord_less_eq_pname_o A_17) ((insert_pname B_12) B_11)))) % FOF formula (forall (B_12:hoare_1262092251_state) (A_17:(hoare_1262092251_state->Prop)) (B_11:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o A_17) B_11)->((ord_le870406270tate_o A_17) ((insert81609953_state B_12) B_11)))) of role axiom named fact_259_subset__insertI2 % A new axiom: (forall (B_12:hoare_1262092251_state) (A_17:(hoare_1262092251_state->Prop)) (B_11:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o A_17) B_11)->((ord_le870406270tate_o A_17) ((insert81609953_state B_12) B_11)))) % FOF formula (forall (B_10:(pname->Prop)) (X_4:pname) (A_16:(pname->Prop)), ((((member_pname X_4) A_16)->False)->((iff ((ord_less_eq_pname_o A_16) ((insert_pname X_4) B_10))) ((ord_less_eq_pname_o A_16) B_10)))) of role axiom named fact_260_subset__insert % A new axiom: (forall (B_10:(pname->Prop)) (X_4:pname) (A_16:(pname->Prop)), ((((member_pname X_4) A_16)->False)->((iff ((ord_less_eq_pname_o A_16) ((insert_pname X_4) B_10))) ((ord_less_eq_pname_o A_16) B_10)))) % FOF formula (forall (B_10:(hoare_1262092251_state->Prop)) (X_4:hoare_1262092251_state) (A_16:(hoare_1262092251_state->Prop)), ((((member5164104_state X_4) A_16)->False)->((iff ((ord_le870406270tate_o A_16) ((insert81609953_state X_4) B_10))) ((ord_le870406270tate_o A_16) B_10)))) of role axiom named fact_261_subset__insert % A new axiom: (forall (B_10:(hoare_1262092251_state->Prop)) (X_4:hoare_1262092251_state) (A_16:(hoare_1262092251_state->Prop)), ((((member5164104_state X_4) A_16)->False)->((iff ((ord_le870406270tate_o A_16) ((insert81609953_state X_4) B_10))) ((ord_le870406270tate_o A_16) B_10)))) % FOF formula (forall (X_3:pname) (A_15:(pname->Prop)) (B_9:(pname->Prop)), ((iff ((ord_less_eq_pname_o ((insert_pname X_3) A_15)) B_9)) ((and ((member_pname X_3) B_9)) ((ord_less_eq_pname_o A_15) B_9)))) of role axiom named fact_262_insert__subset % A new axiom: (forall (X_3:pname) (A_15:(pname->Prop)) (B_9:(pname->Prop)), ((iff ((ord_less_eq_pname_o ((insert_pname X_3) A_15)) B_9)) ((and ((member_pname X_3) B_9)) ((ord_less_eq_pname_o A_15) B_9)))) % FOF formula (forall (X_3:hoare_1262092251_state) (A_15:(hoare_1262092251_state->Prop)) (B_9:(hoare_1262092251_state->Prop)), ((iff ((ord_le870406270tate_o ((insert81609953_state X_3) A_15)) B_9)) ((and ((member5164104_state X_3) B_9)) ((ord_le870406270tate_o A_15) B_9)))) of role axiom named fact_263_insert__subset % A new axiom: (forall (X_3:hoare_1262092251_state) (A_15:(hoare_1262092251_state->Prop)) (B_9:(hoare_1262092251_state->Prop)), ((iff ((ord_le870406270tate_o ((insert81609953_state X_3) A_15)) B_9)) ((and ((member5164104_state X_3) B_9)) ((ord_le870406270tate_o A_15) B_9)))) % FOF formula (forall (B_8:(pname->Prop)) (A_14:pname), ((ord_less_eq_pname_o B_8) ((insert_pname A_14) B_8))) of role axiom named fact_264_subset__insertI % A new axiom: (forall (B_8:(pname->Prop)) (A_14:pname), ((ord_less_eq_pname_o B_8) ((insert_pname A_14) B_8))) % FOF formula (forall (B_8:(hoare_1262092251_state->Prop)) (A_14:hoare_1262092251_state), ((ord_le870406270tate_o B_8) ((insert81609953_state A_14) B_8))) of role axiom named fact_265_subset__insertI % A new axiom: (forall (B_8:(hoare_1262092251_state->Prop)) (A_14:hoare_1262092251_state), ((ord_le870406270tate_o B_8) ((insert81609953_state A_14) B_8))) % FOF formula (forall (F_7:(pname->hoare_1262092251_state)) (X_2:pname) (A_13:(pname->Prop)), (((member_pname X_2) A_13)->(((eq (hoare_1262092251_state->Prop)) ((insert81609953_state (F_7 X_2)) ((image_669833818_state F_7) A_13))) ((image_669833818_state F_7) A_13)))) of role axiom named fact_266_insert__image % A new axiom: (forall (F_7:(pname->hoare_1262092251_state)) (X_2:pname) (A_13:(pname->Prop)), (((member_pname X_2) A_13)->(((eq (hoare_1262092251_state->Prop)) ((insert81609953_state (F_7 X_2)) ((image_669833818_state F_7) A_13))) ((image_669833818_state F_7) A_13)))) % FOF formula (forall (F_6:(pname->hoare_1262092251_state)) (A_12:pname) (B_7:(pname->Prop)), (((eq (hoare_1262092251_state->Prop)) ((image_669833818_state F_6) ((insert_pname A_12) B_7))) ((insert81609953_state (F_6 A_12)) ((image_669833818_state F_6) B_7)))) of role axiom named fact_267_image__insert % A new axiom: (forall (F_6:(pname->hoare_1262092251_state)) (A_12:pname) (B_7:(pname->Prop)), (((eq (hoare_1262092251_state->Prop)) ((image_669833818_state F_6) ((insert_pname A_12) B_7))) ((insert81609953_state (F_6 A_12)) ((image_669833818_state F_6) B_7)))) % FOF formula (forall (F_5:(pname->hoare_1262092251_state)) (A_11:(pname->Prop)) (B_6:(pname->Prop)), (((ord_less_eq_pname_o A_11) B_6)->((ord_le870406270tate_o ((image_669833818_state F_5) A_11)) ((image_669833818_state F_5) B_6)))) of role axiom named fact_268_image__mono % A new axiom: (forall (F_5:(pname->hoare_1262092251_state)) (A_11:(pname->Prop)) (B_6:(pname->Prop)), (((ord_less_eq_pname_o A_11) B_6)->((ord_le870406270tate_o ((image_669833818_state F_5) A_11)) ((image_669833818_state F_5) B_6)))) % FOF formula (forall (B_5:(hoare_1262092251_state->Prop)) (F_4:(pname->hoare_1262092251_state)) (A_10:(pname->Prop)), ((iff ((ord_le870406270tate_o B_5) ((image_669833818_state F_4) A_10))) ((ex (pname->Prop)) (fun (AA:(pname->Prop))=> ((and ((ord_less_eq_pname_o AA) A_10)) (((eq (hoare_1262092251_state->Prop)) B_5) ((image_669833818_state F_4) AA))))))) of role axiom named fact_269_subset__image__iff % A new axiom: (forall (B_5:(hoare_1262092251_state->Prop)) (F_4:(pname->hoare_1262092251_state)) (A_10:(pname->Prop)), ((iff ((ord_le870406270tate_o B_5) ((image_669833818_state F_4) A_10))) ((ex (pname->Prop)) (fun (AA:(pname->Prop))=> ((and ((ord_less_eq_pname_o AA) A_10)) (((eq (hoare_1262092251_state->Prop)) B_5) ((image_669833818_state F_4) AA))))))) % FOF formula (forall (M:(pname->option_com)) (A_9:pname) (B_4:com), ((((eq option_com) (M A_9)) (some_com B_4))->((member_pname A_9) (dom_pname_com M)))) of role axiom named fact_270_domI % A new axiom: (forall (M:(pname->option_com)) (A_9:pname) (B_4:com), ((((eq option_com) (M A_9)) (some_com B_4))->((member_pname A_9) (dom_pname_com M)))) % FOF formula (forall (P_3:(pname->Prop)) (A_8:pname), ((and ((P_3 A_8)->(((eq (pname->Prop)) (collect_pname (fun (X_1:pname)=> ((and (((eq pname) X_1) A_8)) (P_3 X_1))))) ((insert_pname A_8) bot_bot_pname_o)))) (((P_3 A_8)->False)->(((eq (pname->Prop)) (collect_pname (fun (X_1:pname)=> ((and (((eq pname) X_1) A_8)) (P_3 X_1))))) bot_bot_pname_o)))) of role axiom named fact_271_Collect__conv__if % A new axiom: (forall (P_3:(pname->Prop)) (A_8:pname), ((and ((P_3 A_8)->(((eq (pname->Prop)) (collect_pname (fun (X_1:pname)=> ((and (((eq pname) X_1) A_8)) (P_3 X_1))))) ((insert_pname A_8) bot_bot_pname_o)))) (((P_3 A_8)->False)->(((eq (pname->Prop)) (collect_pname (fun (X_1:pname)=> ((and (((eq pname) X_1) A_8)) (P_3 X_1))))) bot_bot_pname_o)))) % FOF formula (forall (P_3:(hoare_1262092251_state->Prop)) (A_8:hoare_1262092251_state), ((and ((P_3 A_8)->(((eq (hoare_1262092251_state->Prop)) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> ((and (((eq hoare_1262092251_state) X_1) A_8)) (P_3 X_1))))) ((insert81609953_state A_8) bot_bo113204042tate_o)))) (((P_3 A_8)->False)->(((eq (hoare_1262092251_state->Prop)) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> ((and (((eq hoare_1262092251_state) X_1) A_8)) (P_3 X_1))))) bot_bo113204042tate_o)))) of role axiom named fact_272_Collect__conv__if % A new axiom: (forall (P_3:(hoare_1262092251_state->Prop)) (A_8:hoare_1262092251_state), ((and ((P_3 A_8)->(((eq (hoare_1262092251_state->Prop)) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> ((and (((eq hoare_1262092251_state) X_1) A_8)) (P_3 X_1))))) ((insert81609953_state A_8) bot_bo113204042tate_o)))) (((P_3 A_8)->False)->(((eq (hoare_1262092251_state->Prop)) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> ((and (((eq hoare_1262092251_state) X_1) A_8)) (P_3 X_1))))) bot_bo113204042tate_o)))) % FOF formula (forall (P_3:((pname->Prop)->Prop)) (A_8:(pname->Prop)), ((and ((P_3 A_8)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_1:(pname->Prop))=> ((and (((eq (pname->Prop)) X_1) A_8)) (P_3 X_1))))) ((insert_pname_o A_8) bot_bot_pname_o_o)))) (((P_3 A_8)->False)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_1:(pname->Prop))=> ((and (((eq (pname->Prop)) X_1) A_8)) (P_3 X_1))))) bot_bot_pname_o_o)))) of role axiom named fact_273_Collect__conv__if % A new axiom: (forall (P_3:((pname->Prop)->Prop)) (A_8:(pname->Prop)), ((and ((P_3 A_8)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_1:(pname->Prop))=> ((and (((eq (pname->Prop)) X_1) A_8)) (P_3 X_1))))) ((insert_pname_o A_8) bot_bot_pname_o_o)))) (((P_3 A_8)->False)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_1:(pname->Prop))=> ((and (((eq (pname->Prop)) X_1) A_8)) (P_3 X_1))))) bot_bot_pname_o_o)))) % FOF formula (forall (P_3:((hoare_1262092251_state->Prop)->Prop)) (A_8:(hoare_1262092251_state->Prop)), ((and ((P_3 A_8)->(((eq ((hoare_1262092251_state->Prop)->Prop)) (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> ((and (((eq (hoare_1262092251_state->Prop)) X_1) A_8)) (P_3 X_1))))) ((insert1042460334tate_o A_8) bot_bo1962689075te_o_o)))) (((P_3 A_8)->False)->(((eq ((hoare_1262092251_state->Prop)->Prop)) (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> ((and (((eq (hoare_1262092251_state->Prop)) X_1) A_8)) (P_3 X_1))))) bot_bo1962689075te_o_o)))) of role axiom named fact_274_Collect__conv__if % A new axiom: (forall (P_3:((hoare_1262092251_state->Prop)->Prop)) (A_8:(hoare_1262092251_state->Prop)), ((and ((P_3 A_8)->(((eq ((hoare_1262092251_state->Prop)->Prop)) (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> ((and (((eq (hoare_1262092251_state->Prop)) X_1) A_8)) (P_3 X_1))))) ((insert1042460334tate_o A_8) bot_bo1962689075te_o_o)))) (((P_3 A_8)->False)->(((eq ((hoare_1262092251_state->Prop)->Prop)) (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> ((and (((eq (hoare_1262092251_state->Prop)) X_1) A_8)) (P_3 X_1))))) bot_bo1962689075te_o_o)))) % FOF formula (forall (P_2:(pname->Prop)) (A_7:pname), ((and ((P_2 A_7)->(((eq (pname->Prop)) (collect_pname (fun (X_1:pname)=> ((and (((eq pname) A_7) X_1)) (P_2 X_1))))) ((insert_pname A_7) bot_bot_pname_o)))) (((P_2 A_7)->False)->(((eq (pname->Prop)) (collect_pname (fun (X_1:pname)=> ((and (((eq pname) A_7) X_1)) (P_2 X_1))))) bot_bot_pname_o)))) of role axiom named fact_275_Collect__conv__if2 % A new axiom: (forall (P_2:(pname->Prop)) (A_7:pname), ((and ((P_2 A_7)->(((eq (pname->Prop)) (collect_pname (fun (X_1:pname)=> ((and (((eq pname) A_7) X_1)) (P_2 X_1))))) ((insert_pname A_7) bot_bot_pname_o)))) (((P_2 A_7)->False)->(((eq (pname->Prop)) (collect_pname (fun (X_1:pname)=> ((and (((eq pname) A_7) X_1)) (P_2 X_1))))) bot_bot_pname_o)))) % FOF formula (forall (P_2:(hoare_1262092251_state->Prop)) (A_7:hoare_1262092251_state), ((and ((P_2 A_7)->(((eq (hoare_1262092251_state->Prop)) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> ((and (((eq hoare_1262092251_state) A_7) X_1)) (P_2 X_1))))) ((insert81609953_state A_7) bot_bo113204042tate_o)))) (((P_2 A_7)->False)->(((eq (hoare_1262092251_state->Prop)) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> ((and (((eq hoare_1262092251_state) A_7) X_1)) (P_2 X_1))))) bot_bo113204042tate_o)))) of role axiom named fact_276_Collect__conv__if2 % A new axiom: (forall (P_2:(hoare_1262092251_state->Prop)) (A_7:hoare_1262092251_state), ((and ((P_2 A_7)->(((eq (hoare_1262092251_state->Prop)) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> ((and (((eq hoare_1262092251_state) A_7) X_1)) (P_2 X_1))))) ((insert81609953_state A_7) bot_bo113204042tate_o)))) (((P_2 A_7)->False)->(((eq (hoare_1262092251_state->Prop)) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> ((and (((eq hoare_1262092251_state) A_7) X_1)) (P_2 X_1))))) bot_bo113204042tate_o)))) % FOF formula (forall (P_2:((pname->Prop)->Prop)) (A_7:(pname->Prop)), ((and ((P_2 A_7)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_1:(pname->Prop))=> ((and (((eq (pname->Prop)) A_7) X_1)) (P_2 X_1))))) ((insert_pname_o A_7) bot_bot_pname_o_o)))) (((P_2 A_7)->False)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_1:(pname->Prop))=> ((and (((eq (pname->Prop)) A_7) X_1)) (P_2 X_1))))) bot_bot_pname_o_o)))) of role axiom named fact_277_Collect__conv__if2 % A new axiom: (forall (P_2:((pname->Prop)->Prop)) (A_7:(pname->Prop)), ((and ((P_2 A_7)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_1:(pname->Prop))=> ((and (((eq (pname->Prop)) A_7) X_1)) (P_2 X_1))))) ((insert_pname_o A_7) bot_bot_pname_o_o)))) (((P_2 A_7)->False)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_1:(pname->Prop))=> ((and (((eq (pname->Prop)) A_7) X_1)) (P_2 X_1))))) bot_bot_pname_o_o)))) % FOF formula (forall (P_2:((hoare_1262092251_state->Prop)->Prop)) (A_7:(hoare_1262092251_state->Prop)), ((and ((P_2 A_7)->(((eq ((hoare_1262092251_state->Prop)->Prop)) (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> ((and (((eq (hoare_1262092251_state->Prop)) A_7) X_1)) (P_2 X_1))))) ((insert1042460334tate_o A_7) bot_bo1962689075te_o_o)))) (((P_2 A_7)->False)->(((eq ((hoare_1262092251_state->Prop)->Prop)) (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> ((and (((eq (hoare_1262092251_state->Prop)) A_7) X_1)) (P_2 X_1))))) bot_bo1962689075te_o_o)))) of role axiom named fact_278_Collect__conv__if2 % A new axiom: (forall (P_2:((hoare_1262092251_state->Prop)->Prop)) (A_7:(hoare_1262092251_state->Prop)), ((and ((P_2 A_7)->(((eq ((hoare_1262092251_state->Prop)->Prop)) (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> ((and (((eq (hoare_1262092251_state->Prop)) A_7) X_1)) (P_2 X_1))))) ((insert1042460334tate_o A_7) bot_bo1962689075te_o_o)))) (((P_2 A_7)->False)->(((eq ((hoare_1262092251_state->Prop)->Prop)) (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> ((and (((eq (hoare_1262092251_state->Prop)) A_7) X_1)) (P_2 X_1))))) bot_bo1962689075te_o_o)))) % FOF formula (forall (A_6:pname), (((eq (pname->Prop)) (collect_pname (fun (X_1:pname)=> (((eq pname) X_1) A_6)))) ((insert_pname A_6) bot_bot_pname_o))) of role axiom named fact_279_singleton__conv % A new axiom: (forall (A_6:pname), (((eq (pname->Prop)) (collect_pname (fun (X_1:pname)=> (((eq pname) X_1) A_6)))) ((insert_pname A_6) bot_bot_pname_o))) % FOF formula (forall (A_6:hoare_1262092251_state), (((eq (hoare_1262092251_state->Prop)) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) A_6)))) ((insert81609953_state A_6) bot_bo113204042tate_o))) of role axiom named fact_280_singleton__conv % A new axiom: (forall (A_6:hoare_1262092251_state), (((eq (hoare_1262092251_state->Prop)) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) A_6)))) ((insert81609953_state A_6) bot_bo113204042tate_o))) % FOF formula (forall (A_6:(pname->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_1:(pname->Prop))=> (((eq (pname->Prop)) X_1) A_6)))) ((insert_pname_o A_6) bot_bot_pname_o_o))) of role axiom named fact_281_singleton__conv % A new axiom: (forall (A_6:(pname->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_1:(pname->Prop))=> (((eq (pname->Prop)) X_1) A_6)))) ((insert_pname_o A_6) bot_bot_pname_o_o))) % FOF formula (forall (A_6:(hoare_1262092251_state->Prop)), (((eq ((hoare_1262092251_state->Prop)->Prop)) (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> (((eq (hoare_1262092251_state->Prop)) X_1) A_6)))) ((insert1042460334tate_o A_6) bot_bo1962689075te_o_o))) of role axiom named fact_282_singleton__conv % A new axiom: (forall (A_6:(hoare_1262092251_state->Prop)), (((eq ((hoare_1262092251_state->Prop)->Prop)) (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> (((eq (hoare_1262092251_state->Prop)) X_1) A_6)))) ((insert1042460334tate_o A_6) bot_bo1962689075te_o_o))) % FOF formula (forall (A_5:pname), (((eq (pname->Prop)) (collect_pname (fequal_pname A_5))) ((insert_pname A_5) bot_bot_pname_o))) of role axiom named fact_283_singleton__conv2 % A new axiom: (forall (A_5:pname), (((eq (pname->Prop)) (collect_pname (fequal_pname A_5))) ((insert_pname A_5) bot_bot_pname_o))) % FOF formula (forall (A_5:hoare_1262092251_state), (((eq (hoare_1262092251_state->Prop)) (collec1121927558_state (fequal1925511196_state A_5))) ((insert81609953_state A_5) bot_bo113204042tate_o))) of role axiom named fact_284_singleton__conv2 % A new axiom: (forall (A_5:hoare_1262092251_state), (((eq (hoare_1262092251_state->Prop)) (collec1121927558_state (fequal1925511196_state A_5))) ((insert81609953_state A_5) bot_bo113204042tate_o))) % FOF formula (forall (A_5:(pname->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fequal_pname_o A_5))) ((insert_pname_o A_5) bot_bot_pname_o_o))) of role axiom named fact_285_singleton__conv2 % A new axiom: (forall (A_5:(pname->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fequal_pname_o A_5))) ((insert_pname_o A_5) bot_bot_pname_o_o))) % FOF formula (forall (A_5:(hoare_1262092251_state->Prop)), (((eq ((hoare_1262092251_state->Prop)->Prop)) (collec313158217tate_o (fequal1529404211tate_o A_5))) ((insert1042460334tate_o A_5) bot_bo1962689075te_o_o))) of role axiom named fact_286_singleton__conv2 % A new axiom: (forall (A_5:(hoare_1262092251_state->Prop)), (((eq ((hoare_1262092251_state->Prop)->Prop)) (collec313158217tate_o (fequal1529404211tate_o A_5))) ((insert1042460334tate_o A_5) bot_bo1962689075te_o_o))) % FOF formula (forall (C_1:com) (G:(hoare_1262092251_state->Prop)), (hoare_1821564147gleton->((forall (X_1:pname), (((member_pname X_1) (dom_pname_com body))->((hoare_930741239_state G) ((insert81609953_state (hoare_Mirabelle_MGT (body_1 X_1))) bot_bo113204042tate_o))))->((wt C_1)->((hoare_930741239_state G) ((insert81609953_state (hoare_Mirabelle_MGT C_1)) bot_bo113204042tate_o)))))) of role axiom named fact_287_MGF__lemma1 % A new axiom: (forall (C_1:com) (G:(hoare_1262092251_state->Prop)), (hoare_1821564147gleton->((forall (X_1:pname), (((member_pname X_1) (dom_pname_com body))->((hoare_930741239_state G) ((insert81609953_state (hoare_Mirabelle_MGT (body_1 X_1))) bot_bo113204042tate_o))))->((wt C_1)->((hoare_930741239_state G) ((insert81609953_state (hoare_Mirabelle_MGT C_1)) bot_bo113204042tate_o)))))) % FOF formula (forall (Pn_1:pname) (B_3:com), (wT_bodies->((((eq option_com) (body Pn_1)) (some_com B_3))->(wt B_3)))) of role axiom named fact_288_WT__bodiesD % A new axiom: (forall (Pn_1:pname) (B_3:com), (wT_bodies->((((eq option_com) (body Pn_1)) (some_com B_3))->(wt B_3)))) % FOF formula (forall (B_2:hoare_1262092251_state) (F_3:(pname->hoare_1262092251_state)) (A_4:(pname->Prop)), (((member5164104_state B_2) ((image_669833818_state F_3) A_4))->((forall (X_1:pname), ((((eq hoare_1262092251_state) B_2) (F_3 X_1))->(((member_pname X_1) A_4)->False)))->False))) of role axiom named fact_289_imageE % A new axiom: (forall (B_2:hoare_1262092251_state) (F_3:(pname->hoare_1262092251_state)) (A_4:(pname->Prop)), (((member5164104_state B_2) ((image_669833818_state F_3) A_4))->((forall (X_1:pname), ((((eq hoare_1262092251_state) B_2) (F_3 X_1))->(((member_pname X_1) A_4)->False)))->False))) % FOF formula (forall (P_1:((pname->Prop)->Prop)) (A_2:(pname->Prop)) (F_1:(pname->Prop)), ((finite_finite_pname F_1)->(((ord_less_eq_pname_o F_1) A_2)->((P_1 bot_bot_pname_o)->((forall (A_3:pname) (F_2:(pname->Prop)), ((finite_finite_pname F_2)->(((member_pname A_3) A_2)->((((member_pname A_3) F_2)->False)->((P_1 F_2)->(P_1 ((insert_pname A_3) F_2)))))))->(P_1 F_1)))))) of role axiom named fact_290_finite__subset__induct % A new axiom: (forall (P_1:((pname->Prop)->Prop)) (A_2:(pname->Prop)) (F_1:(pname->Prop)), ((finite_finite_pname F_1)->(((ord_less_eq_pname_o F_1) A_2)->((P_1 bot_bot_pname_o)->((forall (A_3:pname) (F_2:(pname->Prop)), ((finite_finite_pname F_2)->(((member_pname A_3) A_2)->((((member_pname A_3) F_2)->False)->((P_1 F_2)->(P_1 ((insert_pname A_3) F_2)))))))->(P_1 F_1)))))) % FOF formula (forall (P_1:((hoare_1262092251_state->Prop)->Prop)) (A_2:(hoare_1262092251_state->Prop)) (F_1:(hoare_1262092251_state->Prop)), ((finite1178804552_state F_1)->(((ord_le870406270tate_o F_1) A_2)->((P_1 bot_bo113204042tate_o)->((forall (A_3:hoare_1262092251_state) (F_2:(hoare_1262092251_state->Prop)), ((finite1178804552_state F_2)->(((member5164104_state A_3) A_2)->((((member5164104_state A_3) F_2)->False)->((P_1 F_2)->(P_1 ((insert81609953_state A_3) F_2)))))))->(P_1 F_1)))))) of role axiom named fact_291_finite__subset__induct % A new axiom: (forall (P_1:((hoare_1262092251_state->Prop)->Prop)) (A_2:(hoare_1262092251_state->Prop)) (F_1:(hoare_1262092251_state->Prop)), ((finite1178804552_state F_1)->(((ord_le870406270tate_o F_1) A_2)->((P_1 bot_bo113204042tate_o)->((forall (A_3:hoare_1262092251_state) (F_2:(hoare_1262092251_state->Prop)), ((finite1178804552_state F_2)->(((member5164104_state A_3) A_2)->((((member5164104_state A_3) F_2)->False)->((P_1 F_2)->(P_1 ((insert81609953_state A_3) F_2)))))))->(P_1 F_1)))))) % FOF formula (forall (P_1:(((pname->Prop)->Prop)->Prop)) (A_2:((pname->Prop)->Prop)) (F_1:((pname->Prop)->Prop)), ((finite297249702name_o F_1)->(((ord_le1205211808me_o_o F_1) A_2)->((P_1 bot_bot_pname_o_o)->((forall (A_3:(pname->Prop)) (F_2:((pname->Prop)->Prop)), ((finite297249702name_o F_2)->(((member_pname_o A_3) A_2)->((((member_pname_o A_3) F_2)->False)->((P_1 F_2)->(P_1 ((insert_pname_o A_3) F_2)))))))->(P_1 F_1)))))) of role axiom named fact_292_finite__subset__induct % A new axiom: (forall (P_1:(((pname->Prop)->Prop)->Prop)) (A_2:((pname->Prop)->Prop)) (F_1:((pname->Prop)->Prop)), ((finite297249702name_o F_1)->(((ord_le1205211808me_o_o F_1) A_2)->((P_1 bot_bot_pname_o_o)->((forall (A_3:(pname->Prop)) (F_2:((pname->Prop)->Prop)), ((finite297249702name_o F_2)->(((member_pname_o A_3) A_2)->((((member_pname_o A_3) F_2)->False)->((P_1 F_2)->(P_1 ((insert_pname_o A_3) F_2)))))))->(P_1 F_1)))))) % FOF formula (forall (P_1:(((hoare_1262092251_state->Prop)->Prop)->Prop)) (A_2:((hoare_1262092251_state->Prop)->Prop)) (F_1:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o F_1)->(((ord_le2012720639te_o_o F_1) A_2)->((P_1 bot_bo1962689075te_o_o)->((forall (A_3:(hoare_1262092251_state->Prop)) (F_2:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o F_2)->(((member907417095tate_o A_3) A_2)->((((member907417095tate_o A_3) F_2)->False)->((P_1 F_2)->(P_1 ((insert1042460334tate_o A_3) F_2)))))))->(P_1 F_1)))))) of role axiom named fact_293_finite__subset__induct % A new axiom: (forall (P_1:(((hoare_1262092251_state->Prop)->Prop)->Prop)) (A_2:((hoare_1262092251_state->Prop)->Prop)) (F_1:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o F_1)->(((ord_le2012720639te_o_o F_1) A_2)->((P_1 bot_bo1962689075te_o_o)->((forall (A_3:(hoare_1262092251_state->Prop)) (F_2:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o F_2)->(((member907417095tate_o A_3) A_2)->((((member907417095tate_o A_3) F_2)->False)->((P_1 F_2)->(P_1 ((insert1042460334tate_o A_3) F_2)))))))->(P_1 F_1)))))) % FOF formula (forall (P:pname), ((wt (body_1 P))->((forall (Y_1:com), (not (((eq option_com) (body P)) (some_com Y_1))))->False))) of role axiom named fact_294_WTs__elim__cases_I7_J % A new axiom: (forall (P:pname), ((wt (body_1 P))->((forall (Y_1:com), (not (((eq option_com) (body P)) (some_com Y_1))))->False))) % FOF formula (forall (B_1:(pname->Prop)) (A_1:(pname->Prop)), ((forall (X_1:pname), (((member_pname X_1) A_1)->((member_pname X_1) B_1)))->((ord_less_eq_pname_o A_1) B_1))) of role axiom named fact_295_subsetI % A new axiom: (forall (B_1:(pname->Prop)) (A_1:(pname->Prop)), ((forall (X_1:pname), (((member_pname X_1) A_1)->((member_pname X_1) B_1)))->((ord_less_eq_pname_o A_1) B_1))) % FOF formula (forall (B_1:(hoare_1262092251_state->Prop)) (A_1:(hoare_1262092251_state->Prop)), ((forall (X_1:hoare_1262092251_state), (((member5164104_state X_1) A_1)->((member5164104_state X_1) B_1)))->((ord_le870406270tate_o A_1) B_1))) of role axiom named fact_296_subsetI % A new axiom: (forall (B_1:(hoare_1262092251_state->Prop)) (A_1:(hoare_1262092251_state->Prop)), ((forall (X_1:hoare_1262092251_state), (((member5164104_state X_1) A_1)->((member5164104_state X_1) B_1)))->((ord_le870406270tate_o A_1) B_1))) % FOF formula (forall (F:(pname->hoare_1262092251_state)) (A:(pname->Prop)) (B:(hoare_1262092251_state->Prop)), ((finite1178804552_state B)->(((ord_le870406270tate_o B) ((image_669833818_state F) A))->((ex (pname->Prop)) (fun (C:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C) A)) (finite_finite_pname C))) (((eq (hoare_1262092251_state->Prop)) B) ((image_669833818_state F) C)))))))) of role axiom named fact_297_finite__subset__image % A new axiom: (forall (F:(pname->hoare_1262092251_state)) (A:(pname->Prop)) (B:(hoare_1262092251_state->Prop)), ((finite1178804552_state B)->(((ord_le870406270tate_o B) ((image_669833818_state F) A))->((ex (pname->Prop)) (fun (C:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C) A)) (finite_finite_pname C))) (((eq (hoare_1262092251_state->Prop)) B) ((image_669833818_state F) C)))))))) % FOF formula (finite_finite_pname (dom_pname_com body)) of role axiom named fact_298_finite__dom__body % A new axiom: (finite_finite_pname (dom_pname_com body)) % FOF formula (forall (Pname_1:pname) (Pname:pname), ((iff (((eq com) (body_1 Pname_1)) (body_1 Pname))) (((eq pname) Pname_1) Pname))) of role axiom named fact_299_com_Osimps_I6_J % A new axiom: (forall (Pname_1:pname) (Pname:pname), ((iff (((eq com) (body_1 Pname_1)) (body_1 Pname))) (((eq pname) Pname_1) Pname))) % FOF formula (forall (X:pname) (Y:pname), ((or (((fequal_pname X) Y)->False)) (((eq pname) X) Y))) of role axiom named help_fequal_1_1_fequal_000tc__Com__Opname_T % A new axiom: (forall (X:pname) (Y:pname), ((or (((fequal_pname X) Y)->False)) (((eq pname) X) Y))) % FOF formula (forall (X:pname) (Y:pname), ((or (not (((eq pname) X) Y))) ((fequal_pname X) Y))) of role axiom named help_fequal_2_1_fequal_000tc__Com__Opname_T % A new axiom: (forall (X:pname) (Y:pname), ((or (not (((eq pname) X) Y))) ((fequal_pname X) Y))) % FOF formula (forall (X:(pname->Prop)) (Y:(pname->Prop)), ((or (((fequal_pname_o X) Y)->False)) (((eq (pname->Prop)) X) Y))) of role axiom named help_fequal_1_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T % A new axiom: (forall (X:(pname->Prop)) (Y:(pname->Prop)), ((or (((fequal_pname_o X) Y)->False)) (((eq (pname->Prop)) X) Y))) % FOF formula (forall (X:(pname->Prop)) (Y:(pname->Prop)), ((or (not (((eq (pname->Prop)) X) Y))) ((fequal_pname_o X) Y))) of role axiom named help_fequal_2_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T % A new axiom: (forall (X:(pname->Prop)) (Y:(pname->Prop)), ((or (not (((eq (pname->Prop)) X) Y))) ((fequal_pname_o X) Y))) % FOF formula (forall (X:hoare_1262092251_state) (Y:hoare_1262092251_state), ((or (((fequal1925511196_state X) Y)->False)) (((eq hoare_1262092251_state) X) Y))) of role axiom named help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com % A new axiom: (forall (X:hoare_1262092251_state) (Y:hoare_1262092251_state), ((or (((fequal1925511196_state X) Y)->False)) (((eq hoare_1262092251_state) X) Y))) % FOF formula (forall (X:hoare_1262092251_state) (Y:hoare_1262092251_state), ((or (not (((eq hoare_1262092251_state) X) Y))) ((fequal1925511196_state X) Y))) of role axiom named help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com % A new axiom: (forall (X:hoare_1262092251_state) (Y:hoare_1262092251_state), ((or (not (((eq hoare_1262092251_state) X) Y))) ((fequal1925511196_state X) Y))) % FOF formula (forall (X:(hoare_1262092251_state->Prop)) (Y:(hoare_1262092251_state->Prop)), ((or (((fequal1529404211tate_o X) Y)->False)) (((eq (hoare_1262092251_state->Prop)) X) Y))) of role axiom named help_fequal_1_1_fequal_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It % A new axiom: (forall (X:(hoare_1262092251_state->Prop)) (Y:(hoare_1262092251_state->Prop)), ((or (((fequal1529404211tate_o X) Y)->False)) (((eq (hoare_1262092251_state->Prop)) X) Y))) % FOF formula (forall (X:(hoare_1262092251_state->Prop)) (Y:(hoare_1262092251_state->Prop)), ((or (not (((eq (hoare_1262092251_state->Prop)) X) Y))) ((fequal1529404211tate_o X) Y))) of role axiom named help_fequal_2_1_fequal_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It % A new axiom: (forall (X:(hoare_1262092251_state->Prop)) (Y:(hoare_1262092251_state->Prop)), ((or (not (((eq (hoare_1262092251_state->Prop)) X) Y))) ((fequal1529404211tate_o X) Y))) % FOF formula hoare_1821564147gleton of role hypothesis named conj_0 % A new axiom: hoare_1821564147gleton % FOF formula wT_bodies of role hypothesis named conj_1 % A new axiom: wT_bodies % FOF formula (finite1178804552_state fa) of role hypothesis named conj_2 % A new axiom: (finite1178804552_state fa) % FOF formula (((member5164104_state (hoare_Mirabelle_MGT y)) fa)->False) of role hypothesis named conj_3 % A new axiom: (((member5164104_state (hoare_Mirabelle_MGT y)) fa)->False) % FOF formula ((ord_le870406270tate_o fa) ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (the_com (body Pn))))) (dom_pname_com body))) of role hypothesis named conj_4 % A new axiom: ((ord_le870406270tate_o fa) ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (the_com (body Pn))))) (dom_pname_com body))) % FOF formula (((eq option_com) (body pn)) (some_com y)) of role hypothesis named conj_5 % A new axiom: (((eq option_com) (body pn)) (some_com y)) % FOF formula ((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa) of role hypothesis named conj_6 % A new axiom: ((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa) % FOF formula ((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) of role conjecture named conj_7 % Conjecture to prove = ((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)):Prop % Parameter hoare_1262092251_state_DUMMY:hoare_1262092251_state. % Parameter option_com_DUMMY:option_com. % We need to prove ['((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o))'] % Parameter com:Type. % Parameter pname:Type. % Parameter hoare_1262092251_state:Type. % Parameter option_com:Type. % Parameter wt:(com->Prop). % Parameter wT_bodies:Prop. % Parameter body:(pname->option_com). % Parameter body_1:(pname->com). % Parameter finite1648353812_o_o_o:(((((pname->Prop)->Prop)->Prop)->Prop)->Prop). % Parameter finite734360985_o_o_o:(((((hoare_1262092251_state->Prop)->Prop)->Prop)->Prop)->Prop). % Parameter finite1066544169me_o_o:((((pname->Prop)->Prop)->Prop)->Prop). % Parameter finite1303896758te_o_o:((((hoare_1262092251_state->Prop)->Prop)->Prop)->Prop). % Parameter finite297249702name_o:(((pname->Prop)->Prop)->Prop). % Parameter finite1423311111tate_o:(((hoare_1262092251_state->Prop)->Prop)->Prop). % Parameter finite_finite_pname:((pname->Prop)->Prop). % Parameter finite1178804552_state:((hoare_1262092251_state->Prop)->Prop). % Parameter hoare_Mirabelle_MGT:(com->hoare_1262092251_state). % Parameter hoare_930741239_state:((hoare_1262092251_state->Prop)->((hoare_1262092251_state->Prop)->Prop)). % Parameter hoare_1821564147gleton:Prop. % Parameter dom_pname_o_com:(((pname->Prop)->option_com)->((pname->Prop)->Prop)). % Parameter dom_Ho1489634536_o_com:(((hoare_1262092251_state->Prop)->option_com)->((hoare_1262092251_state->Prop)->Prop)). % Parameter dom_pname_com:((pname->option_com)->(pname->Prop)). % Parameter some_com:(com->option_com). % Parameter the_com:(option_com->com). % Parameter bot_bot_pname_o_o_o:(((pname->Prop)->Prop)->Prop). % Parameter bot_bo388435036_o_o_o:(((hoare_1262092251_state->Prop)->Prop)->Prop). % Parameter bot_bot_pname_o_o:((pname->Prop)->Prop). % Parameter bot_bo1962689075te_o_o:((hoare_1262092251_state->Prop)->Prop). % Parameter bot_bot_pname_o:(pname->Prop). % Parameter bot_bo113204042tate_o:(hoare_1262092251_state->Prop). % Parameter ord_le1828183645_o_o_o:((((pname->Prop)->Prop)->Prop)->((((pname->Prop)->Prop)->Prop)->Prop)). % Parameter ord_le1891858320_o_o_o:((((hoare_1262092251_state->Prop)->Prop)->Prop)->((((hoare_1262092251_state->Prop)->Prop)->Prop)->Prop)). % Parameter ord_le1205211808me_o_o:(((pname->Prop)->Prop)->(((pname->Prop)->Prop)->Prop)). % Parameter ord_le2012720639te_o_o:(((hoare_1262092251_state->Prop)->Prop)->(((hoare_1262092251_state->Prop)->Prop)->Prop)). % Parameter ord_less_eq_pname_o:((pname->Prop)->((pname->Prop)->Prop)). % Parameter ord_le870406270tate_o:((hoare_1262092251_state->Prop)->((hoare_1262092251_state->Prop)->Prop)). % Parameter collect_pname_o_o_o:(((((pname->Prop)->Prop)->Prop)->Prop)->((((pname->Prop)->Prop)->Prop)->Prop)). % Parameter collec101077467_o_o_o:(((((hoare_1262092251_state->Prop)->Prop)->Prop)->Prop)->((((hoare_1262092251_state->Prop)->Prop)->Prop)->Prop)). % Parameter collect_pname_o_o:((((pname->Prop)->Prop)->Prop)->(((pname->Prop)->Prop)->Prop)). % Parameter collec341954548te_o_o:((((hoare_1262092251_state->Prop)->Prop)->Prop)->(((hoare_1262092251_state->Prop)->Prop)->Prop)). % Parameter collect_pname_o:(((pname->Prop)->Prop)->((pname->Prop)->Prop)). % Parameter collec313158217tate_o:(((hoare_1262092251_state->Prop)->Prop)->((hoare_1262092251_state->Prop)->Prop)). % Parameter collect_pname:((pname->Prop)->(pname->Prop)). % Parameter collec1121927558_state:((hoare_1262092251_state->Prop)->(hoare_1262092251_state->Prop)). % Parameter image_471733107_pname:((((pname->Prop)->Prop)->pname)->((((pname->Prop)->Prop)->Prop)->(pname->Prop))). % Parameter image_1036078444_state:((((pname->Prop)->Prop)->hoare_1262092251_state)->((((pname->Prop)->Prop)->Prop)->(hoare_1262092251_state->Prop))). % Parameter image_893364936_pname:((((hoare_1262092251_state->Prop)->Prop)->pname)->((((hoare_1262092251_state->Prop)->Prop)->Prop)->(pname->Prop))). % Parameter image_165349207_state:((((hoare_1262092251_state->Prop)->Prop)->hoare_1262092251_state)->((((hoare_1262092251_state->Prop)->Prop)->Prop)->(hoare_1262092251_state->Prop))). % Parameter image_pname_o_pname:(((pname->Prop)->pname)->(((pname->Prop)->Prop)->(pname->Prop))). % Parameter image_1476171975_state:(((pname->Prop)->hoare_1262092251_state)->(((pname->Prop)->Prop)->(hoare_1262092251_state->Prop))). % Parameter image_1820530197_pname:(((hoare_1262092251_state->Prop)->pname)->(((hoare_1262092251_state->Prop)->Prop)->(pname->Prop))). % Parameter image_234589002_state:(((hoare_1262092251_state->Prop)->hoare_1262092251_state)->(((hoare_1262092251_state->Prop)->Prop)->(hoare_1262092251_state->Prop))). % Parameter image_504089495me_o_o:((pname->((pname->Prop)->Prop))->((pname->Prop)->(((pname->Prop)->Prop)->Prop))). % Parameter image_827868872te_o_o:((pname->((hoare_1262092251_state->Prop)->Prop))->((pname->Prop)->(((hoare_1262092251_state->Prop)->Prop)->Prop))). % Parameter image_pname_pname_o:((pname->(pname->Prop))->((pname->Prop)->((pname->Prop)->Prop))). % Parameter image_518521461tate_o:((pname->(hoare_1262092251_state->Prop))->((pname->Prop)->((hoare_1262092251_state->Prop)->Prop))). % Parameter image_pname_pname:((pname->pname)->((pname->Prop)->(pname->Prop))). % Parameter image_669833818_state:((pname->hoare_1262092251_state)->((pname->Prop)->(hoare_1262092251_state->Prop))). % Parameter image_333245000me_o_o:((hoare_1262092251_state->((pname->Prop)->Prop))->((hoare_1262092251_state->Prop)->(((pname->Prop)->Prop)->Prop))). % Parameter image_1731108951te_o_o:((hoare_1262092251_state->((hoare_1262092251_state->Prop)->Prop))->((hoare_1262092251_state->Prop)->(((hoare_1262092251_state->Prop)->Prop)->Prop))). % Parameter image_1320925383name_o:((hoare_1262092251_state->(pname->Prop))->((hoare_1262092251_state->Prop)->((pname->Prop)->Prop))). % Parameter image_1403668518tate_o:((hoare_1262092251_state->(hoare_1262092251_state->Prop))->((hoare_1262092251_state->Prop)->((hoare_1262092251_state->Prop)->Prop))). % Parameter image_202231862_pname:((hoare_1262092251_state->pname)->((hoare_1262092251_state->Prop)->(pname->Prop))). % Parameter insert_pname_o_o:(((pname->Prop)->Prop)->((((pname->Prop)->Prop)->Prop)->(((pname->Prop)->Prop)->Prop))). % Parameter insert1691644879te_o_o:(((hoare_1262092251_state->Prop)->Prop)->((((hoare_1262092251_state->Prop)->Prop)->Prop)->(((hoare_1262092251_state->Prop)->Prop)->Prop))). % Parameter insert_pname_o:((pname->Prop)->(((pname->Prop)->Prop)->((pname->Prop)->Prop))). % Parameter insert1042460334tate_o:((hoare_1262092251_state->Prop)->(((hoare_1262092251_state->Prop)->Prop)->((hoare_1262092251_state->Prop)->Prop))). % Parameter insert_pname:(pname->((pname->Prop)->(pname->Prop))). % Parameter insert81609953_state:(hoare_1262092251_state->((hoare_1262092251_state->Prop)->(hoare_1262092251_state->Prop))). % Parameter fequal_pname_o:((pname->Prop)->((pname->Prop)->Prop)). % Parameter fequal1529404211tate_o:((hoare_1262092251_state->Prop)->((hoare_1262092251_state->Prop)->Prop)). % Parameter fequal_pname:(pname->(pname->Prop)). % Parameter fequal1925511196_state:(hoare_1262092251_state->(hoare_1262092251_state->Prop)). % Parameter member_pname_o:((pname->Prop)->(((pname->Prop)->Prop)->Prop)). % Parameter member907417095tate_o:((hoare_1262092251_state->Prop)->(((hoare_1262092251_state->Prop)->Prop)->Prop)). % Parameter member_pname:(pname->((pname->Prop)->Prop)). % Parameter member5164104_state:(hoare_1262092251_state->((hoare_1262092251_state->Prop)->Prop)). % Parameter fa:(hoare_1262092251_state->Prop). % Parameter pn:pname. % Parameter y:com. % Axiom fact_0_empty:(forall (G:(hoare_1262092251_state->Prop)), ((hoare_930741239_state G) bot_bo113204042tate_o)). % Axiom fact_1_asm:(forall (Ts_6:(hoare_1262092251_state->Prop)) (G_8:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o Ts_6) G_8)->((hoare_930741239_state G_8) Ts_6))). % Axiom fact_2_weaken:(forall (Ts_5:(hoare_1262092251_state->Prop)) (G_7:(hoare_1262092251_state->Prop)) (Ts_4:(hoare_1262092251_state->Prop)), (((hoare_930741239_state G_7) Ts_4)->(((ord_le870406270tate_o Ts_5) Ts_4)->((hoare_930741239_state G_7) Ts_5)))). % Axiom fact_3_thin:(forall (G_6:(hoare_1262092251_state->Prop)) (G_5:(hoare_1262092251_state->Prop)) (Ts_3:(hoare_1262092251_state->Prop)), (((hoare_930741239_state G_5) Ts_3)->(((ord_le870406270tate_o G_5) G_6)->((hoare_930741239_state G_6) Ts_3)))). % Axiom fact_4_cut:(forall (G_4:(hoare_1262092251_state->Prop)) (G_3:(hoare_1262092251_state->Prop)) (Ts_2:(hoare_1262092251_state->Prop)), (((hoare_930741239_state G_3) Ts_2)->(((hoare_930741239_state G_4) G_3)->((hoare_930741239_state G_4) Ts_2)))). % Axiom fact_5_hoare__derivs_Oinsert:(forall (Ts_1:(hoare_1262092251_state->Prop)) (G_2:(hoare_1262092251_state->Prop)) (T_1:hoare_1262092251_state), (((hoare_930741239_state G_2) ((insert81609953_state T_1) bot_bo113204042tate_o))->(((hoare_930741239_state G_2) Ts_1)->((hoare_930741239_state G_2) ((insert81609953_state T_1) Ts_1))))). % Axiom fact_6_derivs__insertD:(forall (G_1:(hoare_1262092251_state->Prop)) (T:hoare_1262092251_state) (Ts:(hoare_1262092251_state->Prop)), (((hoare_930741239_state G_1) ((insert81609953_state T) Ts))->((and ((hoare_930741239_state G_1) ((insert81609953_state T) bot_bo113204042tate_o))) ((hoare_930741239_state G_1) Ts)))). % Axiom fact_7_MGT__BodyN:(forall (Pn_1:pname) (G:(hoare_1262092251_state->Prop)), (((hoare_930741239_state ((insert81609953_state (hoare_Mirabelle_MGT (body_1 Pn_1))) G)) ((insert81609953_state (hoare_Mirabelle_MGT (the_com (body Pn_1)))) bot_bo113204042tate_o))->((hoare_930741239_state G) ((insert81609953_state (hoare_Mirabelle_MGT (body_1 Pn_1))) bot_bo113204042tate_o)))). % Axiom fact_8_finite__Collect__subsets:(forall (A_77:(pname->Prop)), ((finite_finite_pname A_77)->(finite297249702name_o (collect_pname_o (fun (B_41:(pname->Prop))=> ((ord_less_eq_pname_o B_41) A_77)))))). % Axiom fact_9_finite__Collect__subsets:(forall (A_77:(hoare_1262092251_state->Prop)), ((finite1178804552_state A_77)->(finite1423311111tate_o (collec313158217tate_o (fun (B_41:(hoare_1262092251_state->Prop))=> ((ord_le870406270tate_o B_41) A_77)))))). % Axiom fact_10_finite__Collect__subsets:(forall (A_77:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o A_77)->(finite1648353812_o_o_o (collect_pname_o_o_o (fun (B_41:(((pname->Prop)->Prop)->Prop))=> ((ord_le1828183645_o_o_o B_41) A_77)))))). % Axiom fact_11_finite__Collect__subsets:(forall (A_77:(((hoare_1262092251_state->Prop)->Prop)->Prop)), ((finite1303896758te_o_o A_77)->(finite734360985_o_o_o (collec101077467_o_o_o (fun (B_41:(((hoare_1262092251_state->Prop)->Prop)->Prop))=> ((ord_le1891858320_o_o_o B_41) A_77)))))). % Axiom fact_12_finite__Collect__subsets:(forall (A_77:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o A_77)->(finite1303896758te_o_o (collec341954548te_o_o (fun (B_41:((hoare_1262092251_state->Prop)->Prop))=> ((ord_le2012720639te_o_o B_41) A_77)))))). % Axiom fact_13_finite__Collect__subsets:(forall (A_77:((pname->Prop)->Prop)), ((finite297249702name_o A_77)->(finite1066544169me_o_o (collect_pname_o_o (fun (B_41:((pname->Prop)->Prop))=> ((ord_le1205211808me_o_o B_41) A_77)))))). % Axiom fact_14_finite__imageI:(forall (H:(pname->hoare_1262092251_state)) (F_17:(pname->Prop)), ((finite_finite_pname F_17)->(finite1178804552_state ((image_669833818_state H) F_17)))). % Axiom fact_15_finite__imageI:(forall (H:(((pname->Prop)->Prop)->pname)) (F_17:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o F_17)->(finite_finite_pname ((image_471733107_pname H) F_17)))). % Axiom fact_16_finite__imageI:(forall (H:(((hoare_1262092251_state->Prop)->Prop)->pname)) (F_17:(((hoare_1262092251_state->Prop)->Prop)->Prop)), ((finite1303896758te_o_o F_17)->(finite_finite_pname ((image_893364936_pname H) F_17)))). % Axiom fact_17_finite__imageI:(forall (H:((hoare_1262092251_state->Prop)->pname)) (F_17:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o F_17)->(finite_finite_pname ((image_1820530197_pname H) F_17)))). % Axiom fact_18_finite__imageI:(forall (H:((pname->Prop)->pname)) (F_17:((pname->Prop)->Prop)), ((finite297249702name_o F_17)->(finite_finite_pname ((image_pname_o_pname H) F_17)))). % Axiom fact_19_finite__imageI:(forall (H:(((pname->Prop)->Prop)->hoare_1262092251_state)) (F_17:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o F_17)->(finite1178804552_state ((image_1036078444_state H) F_17)))). % Axiom fact_20_finite__imageI:(forall (H:(((hoare_1262092251_state->Prop)->Prop)->hoare_1262092251_state)) (F_17:(((hoare_1262092251_state->Prop)->Prop)->Prop)), ((finite1303896758te_o_o F_17)->(finite1178804552_state ((image_165349207_state H) F_17)))). % Axiom fact_21_finite__imageI:(forall (H:((hoare_1262092251_state->Prop)->hoare_1262092251_state)) (F_17:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o F_17)->(finite1178804552_state ((image_234589002_state H) F_17)))). % Axiom fact_22_finite__imageI:(forall (H:((pname->Prop)->hoare_1262092251_state)) (F_17:((pname->Prop)->Prop)), ((finite297249702name_o F_17)->(finite1178804552_state ((image_1476171975_state H) F_17)))). % Axiom fact_23_finite__imageI:(forall (H:(pname->((pname->Prop)->Prop))) (F_17:(pname->Prop)), ((finite_finite_pname F_17)->(finite1066544169me_o_o ((image_504089495me_o_o H) F_17)))). % Axiom fact_24_finite__imageI:(forall (H:(pname->((hoare_1262092251_state->Prop)->Prop))) (F_17:(pname->Prop)), ((finite_finite_pname F_17)->(finite1303896758te_o_o ((image_827868872te_o_o H) F_17)))). % Axiom fact_25_finite__imageI:(forall (H:(pname->(hoare_1262092251_state->Prop))) (F_17:(pname->Prop)), ((finite_finite_pname F_17)->(finite1423311111tate_o ((image_518521461tate_o H) F_17)))). % Axiom fact_26_finite__imageI:(forall (H:(pname->(pname->Prop))) (F_17:(pname->Prop)), ((finite_finite_pname F_17)->(finite297249702name_o ((image_pname_pname_o H) F_17)))). % Axiom fact_27_finite__imageI:(forall (H:(hoare_1262092251_state->((pname->Prop)->Prop))) (F_17:(hoare_1262092251_state->Prop)), ((finite1178804552_state F_17)->(finite1066544169me_o_o ((image_333245000me_o_o H) F_17)))). % Axiom fact_28_finite__imageI:(forall (H:(hoare_1262092251_state->((hoare_1262092251_state->Prop)->Prop))) (F_17:(hoare_1262092251_state->Prop)), ((finite1178804552_state F_17)->(finite1303896758te_o_o ((image_1731108951te_o_o H) F_17)))). % Axiom fact_29_finite__imageI:(forall (H:(hoare_1262092251_state->(hoare_1262092251_state->Prop))) (F_17:(hoare_1262092251_state->Prop)), ((finite1178804552_state F_17)->(finite1423311111tate_o ((image_1403668518tate_o H) F_17)))). % Axiom fact_30_finite__imageI:(forall (H:(hoare_1262092251_state->(pname->Prop))) (F_17:(hoare_1262092251_state->Prop)), ((finite1178804552_state F_17)->(finite297249702name_o ((image_1320925383name_o H) F_17)))). % Axiom fact_31_finite__imageI:(forall (H:(hoare_1262092251_state->pname)) (F_17:(hoare_1262092251_state->Prop)), ((finite1178804552_state F_17)->(finite_finite_pname ((image_202231862_pname H) F_17)))). % Axiom fact_32_finite__imageI:(forall (H:(pname->pname)) (F_17:(pname->Prop)), ((finite_finite_pname F_17)->(finite_finite_pname ((image_pname_pname H) F_17)))). % Axiom fact_33_empty__subsetI:(forall (A_76:(hoare_1262092251_state->Prop)), ((ord_le870406270tate_o bot_bo113204042tate_o) A_76)). % Axiom fact_34_empty__subsetI:(forall (A_76:((pname->Prop)->Prop)), ((ord_le1205211808me_o_o bot_bot_pname_o_o) A_76)). % Axiom fact_35_empty__subsetI:(forall (A_76:((hoare_1262092251_state->Prop)->Prop)), ((ord_le2012720639te_o_o bot_bo1962689075te_o_o) A_76)). % Axiom fact_36_empty__subsetI:(forall (A_76:(pname->Prop)), ((ord_less_eq_pname_o bot_bot_pname_o) A_76)). % Axiom fact_37_finite_OinsertI:(forall (A_75:hoare_1262092251_state) (A_74:(hoare_1262092251_state->Prop)), ((finite1178804552_state A_74)->(finite1178804552_state ((insert81609953_state A_75) A_74)))). % Axiom fact_38_finite_OinsertI:(forall (A_75:pname) (A_74:(pname->Prop)), ((finite_finite_pname A_74)->(finite_finite_pname ((insert_pname A_75) A_74)))). % Axiom fact_39_finite_OinsertI:(forall (A_75:((pname->Prop)->Prop)) (A_74:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o A_74)->(finite1066544169me_o_o ((insert_pname_o_o A_75) A_74)))). % Axiom fact_40_finite_OinsertI:(forall (A_75:((hoare_1262092251_state->Prop)->Prop)) (A_74:(((hoare_1262092251_state->Prop)->Prop)->Prop)), ((finite1303896758te_o_o A_74)->(finite1303896758te_o_o ((insert1691644879te_o_o A_75) A_74)))). % Axiom fact_41_finite_OinsertI:(forall (A_75:(hoare_1262092251_state->Prop)) (A_74:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o A_74)->(finite1423311111tate_o ((insert1042460334tate_o A_75) A_74)))). % Axiom fact_42_finite_OinsertI:(forall (A_75:(pname->Prop)) (A_74:((pname->Prop)->Prop)), ((finite297249702name_o A_74)->(finite297249702name_o ((insert_pname_o A_75) A_74)))). % Axiom fact_43_finite_OemptyI:(finite_finite_pname bot_bot_pname_o). % Axiom fact_44_finite_OemptyI:(finite1178804552_state bot_bo113204042tate_o). % Axiom fact_45_finite_OemptyI:(finite1066544169me_o_o bot_bot_pname_o_o_o). % Axiom fact_46_finite_OemptyI:(finite1303896758te_o_o bot_bo388435036_o_o_o). % Axiom fact_47_finite_OemptyI:(finite1423311111tate_o bot_bo1962689075te_o_o). % Axiom fact_48_finite_OemptyI:(finite297249702name_o bot_bot_pname_o_o). % Axiom fact_49_finite__Collect__conjI:(forall (Q_1:(pname->Prop)) (P_9:(pname->Prop)), (((or (finite_finite_pname (collect_pname P_9))) (finite_finite_pname (collect_pname Q_1)))->(finite_finite_pname (collect_pname (fun (X_1:pname)=> ((and (P_9 X_1)) (Q_1 X_1))))))). % Axiom fact_50_finite__Collect__conjI:(forall (Q_1:(hoare_1262092251_state->Prop)) (P_9:(hoare_1262092251_state->Prop)), (((or (finite1178804552_state (collec1121927558_state P_9))) (finite1178804552_state (collec1121927558_state Q_1)))->(finite1178804552_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> ((and (P_9 X_1)) (Q_1 X_1))))))). % Axiom fact_51_finite__Collect__conjI:(forall (Q_1:(((pname->Prop)->Prop)->Prop)) (P_9:(((pname->Prop)->Prop)->Prop)), (((or (finite1066544169me_o_o (collect_pname_o_o P_9))) (finite1066544169me_o_o (collect_pname_o_o Q_1)))->(finite1066544169me_o_o (collect_pname_o_o (fun (X_1:((pname->Prop)->Prop))=> ((and (P_9 X_1)) (Q_1 X_1))))))). % Axiom fact_52_finite__Collect__conjI:(forall (Q_1:(((hoare_1262092251_state->Prop)->Prop)->Prop)) (P_9:(((hoare_1262092251_state->Prop)->Prop)->Prop)), (((or (finite1303896758te_o_o (collec341954548te_o_o P_9))) (finite1303896758te_o_o (collec341954548te_o_o Q_1)))->(finite1303896758te_o_o (collec341954548te_o_o (fun (X_1:((hoare_1262092251_state->Prop)->Prop))=> ((and (P_9 X_1)) (Q_1 X_1))))))). % Axiom fact_53_finite__Collect__conjI:(forall (Q_1:((hoare_1262092251_state->Prop)->Prop)) (P_9:((hoare_1262092251_state->Prop)->Prop)), (((or (finite1423311111tate_o (collec313158217tate_o P_9))) (finite1423311111tate_o (collec313158217tate_o Q_1)))->(finite1423311111tate_o (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> ((and (P_9 X_1)) (Q_1 X_1))))))). % Axiom fact_54_finite__Collect__conjI:(forall (Q_1:((pname->Prop)->Prop)) (P_9:((pname->Prop)->Prop)), (((or (finite297249702name_o (collect_pname_o P_9))) (finite297249702name_o (collect_pname_o Q_1)))->(finite297249702name_o (collect_pname_o (fun (X_1:(pname->Prop))=> ((and (P_9 X_1)) (Q_1 X_1))))))). % Axiom fact_55_image__constant__conv:(forall (C_8:hoare_1262092251_state) (A_73:(pname->Prop)), ((and ((((eq (pname->Prop)) A_73) bot_bot_pname_o)->(((eq (hoare_1262092251_state->Prop)) ((image_669833818_state (fun (X_1:pname)=> C_8)) A_73)) bot_bo113204042tate_o))) ((not (((eq (pname->Prop)) A_73) bot_bot_pname_o))->(((eq (hoare_1262092251_state->Prop)) ((image_669833818_state (fun (X_1:pname)=> C_8)) A_73)) ((insert81609953_state C_8) bot_bo113204042tate_o))))). % Axiom fact_56_image__constant__conv:(forall (C_8:pname) (A_73:(hoare_1262092251_state->Prop)), ((and ((((eq (hoare_1262092251_state->Prop)) A_73) bot_bo113204042tate_o)->(((eq (pname->Prop)) ((image_202231862_pname (fun (X_1:hoare_1262092251_state)=> C_8)) A_73)) bot_bot_pname_o))) ((not (((eq (hoare_1262092251_state->Prop)) A_73) bot_bo113204042tate_o))->(((eq (pname->Prop)) ((image_202231862_pname (fun (X_1:hoare_1262092251_state)=> C_8)) A_73)) ((insert_pname C_8) bot_bot_pname_o))))). % Axiom fact_57_image__constant__conv:(forall (C_8:(pname->Prop)) (A_73:(hoare_1262092251_state->Prop)), ((and ((((eq (hoare_1262092251_state->Prop)) A_73) bot_bo113204042tate_o)->(((eq ((pname->Prop)->Prop)) ((image_1320925383name_o (fun (X_1:hoare_1262092251_state)=> C_8)) A_73)) bot_bot_pname_o_o))) ((not (((eq (hoare_1262092251_state->Prop)) A_73) bot_bo113204042tate_o))->(((eq ((pname->Prop)->Prop)) ((image_1320925383name_o (fun (X_1:hoare_1262092251_state)=> C_8)) A_73)) ((insert_pname_o C_8) bot_bot_pname_o_o))))). % Axiom fact_58_image__constant__conv:(forall (C_8:(hoare_1262092251_state->Prop)) (A_73:(hoare_1262092251_state->Prop)), ((and ((((eq (hoare_1262092251_state->Prop)) A_73) bot_bo113204042tate_o)->(((eq ((hoare_1262092251_state->Prop)->Prop)) ((image_1403668518tate_o (fun (X_1:hoare_1262092251_state)=> C_8)) A_73)) bot_bo1962689075te_o_o))) ((not (((eq (hoare_1262092251_state->Prop)) A_73) bot_bo113204042tate_o))->(((eq ((hoare_1262092251_state->Prop)->Prop)) ((image_1403668518tate_o (fun (X_1:hoare_1262092251_state)=> C_8)) A_73)) ((insert1042460334tate_o C_8) bot_bo1962689075te_o_o))))). % Axiom fact_59_image__constant__conv:(forall (C_8:(pname->Prop)) (A_73:(pname->Prop)), ((and ((((eq (pname->Prop)) A_73) bot_bot_pname_o)->(((eq ((pname->Prop)->Prop)) ((image_pname_pname_o (fun (X_1:pname)=> C_8)) A_73)) bot_bot_pname_o_o))) ((not (((eq (pname->Prop)) A_73) bot_bot_pname_o))->(((eq ((pname->Prop)->Prop)) ((image_pname_pname_o (fun (X_1:pname)=> C_8)) A_73)) ((insert_pname_o C_8) bot_bot_pname_o_o))))). % Axiom fact_60_image__constant__conv:(forall (C_8:(hoare_1262092251_state->Prop)) (A_73:(pname->Prop)), ((and ((((eq (pname->Prop)) A_73) bot_bot_pname_o)->(((eq ((hoare_1262092251_state->Prop)->Prop)) ((image_518521461tate_o (fun (X_1:pname)=> C_8)) A_73)) bot_bo1962689075te_o_o))) ((not (((eq (pname->Prop)) A_73) bot_bot_pname_o))->(((eq ((hoare_1262092251_state->Prop)->Prop)) ((image_518521461tate_o (fun (X_1:pname)=> C_8)) A_73)) ((insert1042460334tate_o C_8) bot_bo1962689075te_o_o))))). % Axiom fact_61_image__constant__conv:(forall (C_8:pname) (A_73:(pname->Prop)), ((and ((((eq (pname->Prop)) A_73) bot_bot_pname_o)->(((eq (pname->Prop)) ((image_pname_pname (fun (X_1:pname)=> C_8)) A_73)) bot_bot_pname_o))) ((not (((eq (pname->Prop)) A_73) bot_bot_pname_o))->(((eq (pname->Prop)) ((image_pname_pname (fun (X_1:pname)=> C_8)) A_73)) ((insert_pname C_8) bot_bot_pname_o))))). % Axiom fact_62_image__constant__conv:(forall (C_8:hoare_1262092251_state) (A_73:((pname->Prop)->Prop)), ((and ((((eq ((pname->Prop)->Prop)) A_73) bot_bot_pname_o_o)->(((eq (hoare_1262092251_state->Prop)) ((image_1476171975_state (fun (X_1:(pname->Prop))=> C_8)) A_73)) bot_bo113204042tate_o))) ((not (((eq ((pname->Prop)->Prop)) A_73) bot_bot_pname_o_o))->(((eq (hoare_1262092251_state->Prop)) ((image_1476171975_state (fun (X_1:(pname->Prop))=> C_8)) A_73)) ((insert81609953_state C_8) bot_bo113204042tate_o))))). % Axiom fact_63_image__constant__conv:(forall (C_8:hoare_1262092251_state) (A_73:((hoare_1262092251_state->Prop)->Prop)), ((and ((((eq ((hoare_1262092251_state->Prop)->Prop)) A_73) bot_bo1962689075te_o_o)->(((eq (hoare_1262092251_state->Prop)) ((image_234589002_state (fun (X_1:(hoare_1262092251_state->Prop))=> C_8)) A_73)) bot_bo113204042tate_o))) ((not (((eq ((hoare_1262092251_state->Prop)->Prop)) A_73) bot_bo1962689075te_o_o))->(((eq (hoare_1262092251_state->Prop)) ((image_234589002_state (fun (X_1:(hoare_1262092251_state->Prop))=> C_8)) A_73)) ((insert81609953_state C_8) bot_bo113204042tate_o))))). % Axiom fact_64_image__constant__conv:(forall (C_8:pname) (A_73:((pname->Prop)->Prop)), ((and ((((eq ((pname->Prop)->Prop)) A_73) bot_bot_pname_o_o)->(((eq (pname->Prop)) ((image_pname_o_pname (fun (X_1:(pname->Prop))=> C_8)) A_73)) bot_bot_pname_o))) ((not (((eq ((pname->Prop)->Prop)) A_73) bot_bot_pname_o_o))->(((eq (pname->Prop)) ((image_pname_o_pname (fun (X_1:(pname->Prop))=> C_8)) A_73)) ((insert_pname C_8) bot_bot_pname_o))))). % Axiom fact_65_image__constant__conv:(forall (C_8:pname) (A_73:((hoare_1262092251_state->Prop)->Prop)), ((and ((((eq ((hoare_1262092251_state->Prop)->Prop)) A_73) bot_bo1962689075te_o_o)->(((eq (pname->Prop)) ((image_1820530197_pname (fun (X_1:(hoare_1262092251_state->Prop))=> C_8)) A_73)) bot_bot_pname_o))) ((not (((eq ((hoare_1262092251_state->Prop)->Prop)) A_73) bot_bo1962689075te_o_o))->(((eq (pname->Prop)) ((image_1820530197_pname (fun (X_1:(hoare_1262092251_state->Prop))=> C_8)) A_73)) ((insert_pname C_8) bot_bot_pname_o))))). % Axiom fact_66_image__constant:(forall (C_7:hoare_1262092251_state) (X_18:pname) (A_72:(pname->Prop)), (((member_pname X_18) A_72)->(((eq (hoare_1262092251_state->Prop)) ((image_669833818_state (fun (X_1:pname)=> C_7)) A_72)) ((insert81609953_state C_7) bot_bo113204042tate_o)))). % Axiom fact_67_image__constant:(forall (C_7:pname) (X_18:hoare_1262092251_state) (A_72:(hoare_1262092251_state->Prop)), (((member5164104_state X_18) A_72)->(((eq (pname->Prop)) ((image_202231862_pname (fun (X_1:hoare_1262092251_state)=> C_7)) A_72)) ((insert_pname C_7) bot_bot_pname_o)))). % Axiom fact_68_image__constant:(forall (C_7:(pname->Prop)) (X_18:hoare_1262092251_state) (A_72:(hoare_1262092251_state->Prop)), (((member5164104_state X_18) A_72)->(((eq ((pname->Prop)->Prop)) ((image_1320925383name_o (fun (X_1:hoare_1262092251_state)=> C_7)) A_72)) ((insert_pname_o C_7) bot_bot_pname_o_o)))). % Axiom fact_69_image__constant:(forall (C_7:(hoare_1262092251_state->Prop)) (X_18:hoare_1262092251_state) (A_72:(hoare_1262092251_state->Prop)), (((member5164104_state X_18) A_72)->(((eq ((hoare_1262092251_state->Prop)->Prop)) ((image_1403668518tate_o (fun (X_1:hoare_1262092251_state)=> C_7)) A_72)) ((insert1042460334tate_o C_7) bot_bo1962689075te_o_o)))). % Axiom fact_70_image__constant:(forall (C_7:(pname->Prop)) (X_18:pname) (A_72:(pname->Prop)), (((member_pname X_18) A_72)->(((eq ((pname->Prop)->Prop)) ((image_pname_pname_o (fun (X_1:pname)=> C_7)) A_72)) ((insert_pname_o C_7) bot_bot_pname_o_o)))). % Axiom fact_71_image__constant:(forall (C_7:(hoare_1262092251_state->Prop)) (X_18:pname) (A_72:(pname->Prop)), (((member_pname X_18) A_72)->(((eq ((hoare_1262092251_state->Prop)->Prop)) ((image_518521461tate_o (fun (X_1:pname)=> C_7)) A_72)) ((insert1042460334tate_o C_7) bot_bo1962689075te_o_o)))). % Axiom fact_72_image__constant:(forall (C_7:pname) (X_18:pname) (A_72:(pname->Prop)), (((member_pname X_18) A_72)->(((eq (pname->Prop)) ((image_pname_pname (fun (X_1:pname)=> C_7)) A_72)) ((insert_pname C_7) bot_bot_pname_o)))). % Axiom fact_73_image__constant:(forall (C_7:hoare_1262092251_state) (X_18:(pname->Prop)) (A_72:((pname->Prop)->Prop)), (((member_pname_o X_18) A_72)->(((eq (hoare_1262092251_state->Prop)) ((image_1476171975_state (fun (X_1:(pname->Prop))=> C_7)) A_72)) ((insert81609953_state C_7) bot_bo113204042tate_o)))). % Axiom fact_74_image__constant:(forall (C_7:hoare_1262092251_state) (X_18:(hoare_1262092251_state->Prop)) (A_72:((hoare_1262092251_state->Prop)->Prop)), (((member907417095tate_o X_18) A_72)->(((eq (hoare_1262092251_state->Prop)) ((image_234589002_state (fun (X_1:(hoare_1262092251_state->Prop))=> C_7)) A_72)) ((insert81609953_state C_7) bot_bo113204042tate_o)))). % Axiom fact_75_image__constant:(forall (C_7:pname) (X_18:(pname->Prop)) (A_72:((pname->Prop)->Prop)), (((member_pname_o X_18) A_72)->(((eq (pname->Prop)) ((image_pname_o_pname (fun (X_1:(pname->Prop))=> C_7)) A_72)) ((insert_pname C_7) bot_bot_pname_o)))). % Axiom fact_76_image__constant:(forall (C_7:pname) (X_18:(hoare_1262092251_state->Prop)) (A_72:((hoare_1262092251_state->Prop)->Prop)), (((member907417095tate_o X_18) A_72)->(((eq (pname->Prop)) ((image_1820530197_pname (fun (X_1:(hoare_1262092251_state->Prop))=> C_7)) A_72)) ((insert_pname C_7) bot_bot_pname_o)))). % Axiom fact_77_insert__dom:(forall (F_16:(pname->option_com)) (X_17:pname) (Y_4:com), ((((eq option_com) (F_16 X_17)) (some_com Y_4))->(((eq (pname->Prop)) ((insert_pname X_17) (dom_pname_com F_16))) (dom_pname_com F_16)))). % Axiom fact_78_insert__dom:(forall (F_16:((pname->Prop)->option_com)) (X_17:(pname->Prop)) (Y_4:com), ((((eq option_com) (F_16 X_17)) (some_com Y_4))->(((eq ((pname->Prop)->Prop)) ((insert_pname_o X_17) (dom_pname_o_com F_16))) (dom_pname_o_com F_16)))). % Axiom fact_79_insert__dom:(forall (F_16:((hoare_1262092251_state->Prop)->option_com)) (X_17:(hoare_1262092251_state->Prop)) (Y_4:com), ((((eq option_com) (F_16 X_17)) (some_com Y_4))->(((eq ((hoare_1262092251_state->Prop)->Prop)) ((insert1042460334tate_o X_17) (dom_Ho1489634536_o_com F_16))) (dom_Ho1489634536_o_com F_16)))). % Axiom fact_80_finite__surj:(forall (B_40:(hoare_1262092251_state->Prop)) (F_15:(pname->hoare_1262092251_state)) (A_71:(pname->Prop)), ((finite_finite_pname A_71)->(((ord_le870406270tate_o B_40) ((image_669833818_state F_15) A_71))->(finite1178804552_state B_40)))). % Axiom fact_81_finite__surj:(forall (B_40:(pname->Prop)) (F_15:(((pname->Prop)->Prop)->pname)) (A_71:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o A_71)->(((ord_less_eq_pname_o B_40) ((image_471733107_pname F_15) A_71))->(finite_finite_pname B_40)))). % Axiom fact_82_finite__surj:(forall (B_40:(pname->Prop)) (F_15:(((hoare_1262092251_state->Prop)->Prop)->pname)) (A_71:(((hoare_1262092251_state->Prop)->Prop)->Prop)), ((finite1303896758te_o_o A_71)->(((ord_less_eq_pname_o B_40) ((image_893364936_pname F_15) A_71))->(finite_finite_pname B_40)))). % Axiom fact_83_finite__surj:(forall (B_40:(pname->Prop)) (F_15:((hoare_1262092251_state->Prop)->pname)) (A_71:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o A_71)->(((ord_less_eq_pname_o B_40) ((image_1820530197_pname F_15) A_71))->(finite_finite_pname B_40)))). % Axiom fact_84_finite__surj:(forall (B_40:(pname->Prop)) (F_15:((pname->Prop)->pname)) (A_71:((pname->Prop)->Prop)), ((finite297249702name_o A_71)->(((ord_less_eq_pname_o B_40) ((image_pname_o_pname F_15) A_71))->(finite_finite_pname B_40)))). % Axiom fact_85_finite__surj:(forall (B_40:(hoare_1262092251_state->Prop)) (F_15:(((pname->Prop)->Prop)->hoare_1262092251_state)) (A_71:(((pname->Prop)->Prop)->Prop)), ((finite1066544169me_o_o A_71)->(((ord_le870406270tate_o B_40) ((image_1036078444_state F_15) A_71))->(finite1178804552_state B_40)))). % Axiom fact_86_finite__surj:(forall (B_40:(hoare_1262092251_state->Prop)) (F_15:(((hoare_1262092251_state->Prop)->Prop)->hoare_1262092251_state)) (A_71:(((hoare_1262092251_state->Prop)->Prop)->Prop)), ((finite1303896758te_o_o A_71)->(((ord_le870406270tate_o B_40) ((image_165349207_state F_15) A_71))->(finite1178804552_state B_40)))). % Axiom fact_87_finite__surj:(forall (B_40:(hoare_1262092251_state->Prop)) (F_15:((hoare_1262092251_state->Prop)->hoare_1262092251_state)) (A_71:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o A_71)->(((ord_le870406270tate_o B_40) ((image_234589002_state F_15) A_71))->(finite1178804552_state B_40)))). % Axiom fact_88_finite__surj:(forall (B_40:(hoare_1262092251_state->Prop)) (F_15:((pname->Prop)->hoare_1262092251_state)) (A_71:((pname->Prop)->Prop)), ((finite297249702name_o A_71)->(((ord_le870406270tate_o B_40) ((image_1476171975_state F_15) A_71))->(finite1178804552_state B_40)))). % Axiom fact_89_finite__surj:(forall (B_40:(((pname->Prop)->Prop)->Prop)) (F_15:(pname->((pname->Prop)->Prop))) (A_71:(pname->Prop)), ((finite_finite_pname A_71)->(((ord_le1828183645_o_o_o B_40) ((image_504089495me_o_o F_15) A_71))->(finite1066544169me_o_o B_40)))). % Axiom fact_90_finite__surj:(forall (B_40:(((hoare_1262092251_state->Prop)->Prop)->Prop)) (F_15:(pname->((hoare_1262092251_state->Prop)->Prop))) (A_71:(pname->Prop)), ((finite_finite_pname A_71)->(((ord_le1891858320_o_o_o B_40) ((image_827868872te_o_o F_15) A_71))->(finite1303896758te_o_o B_40)))). % Axiom fact_91_finite__surj:(forall (B_40:(pname->Prop)) (F_15:(pname->pname)) (A_71:(pname->Prop)), ((finite_finite_pname A_71)->(((ord_less_eq_pname_o B_40) ((image_pname_pname F_15) A_71))->(finite_finite_pname B_40)))). % Axiom fact_92_finite__surj:(forall (B_40:((hoare_1262092251_state->Prop)->Prop)) (F_15:(pname->(hoare_1262092251_state->Prop))) (A_71:(pname->Prop)), ((finite_finite_pname A_71)->(((ord_le2012720639te_o_o B_40) ((image_518521461tate_o F_15) A_71))->(finite1423311111tate_o B_40)))). % Axiom fact_93_finite__surj:(forall (B_40:((pname->Prop)->Prop)) (F_15:(pname->(pname->Prop))) (A_71:(pname->Prop)), ((finite_finite_pname A_71)->(((ord_le1205211808me_o_o B_40) ((image_pname_pname_o F_15) A_71))->(finite297249702name_o B_40)))). % Axiom fact_94_finite__surj:(forall (B_40:(((pname->Prop)->Prop)->Prop)) (F_15:(hoare_1262092251_state->((pname->Prop)->Prop))) (A_71:(hoare_1262092251_state->Prop)), ((finite1178804552_state A_71)->(((ord_le1828183645_o_o_o B_40) ((image_333245000me_o_o F_15) A_71))->(finite1066544169me_o_o B_40)))). % Axiom fact_95_finite__surj:(forall (B_40:(((hoare_1262092251_state->Prop)->Prop)->Prop)) (F_15:(hoare_1262092251_state->((hoare_1262092251_state->Prop)->Prop))) (A_71:(hoare_1262092251_state->Prop)), ((finite1178804552_state A_71)->(((ord_le1891858320_o_o_o B_40) ((image_1731108951te_o_o F_15) A_71))->(finite1303896758te_o_o B_40)))). % Axiom fact_96_finite__surj:(forall (B_40:(pname->Prop)) (F_15:(hoare_1262092251_state->pname)) (A_71:(hoare_1262092251_state->Prop)), ((finite1178804552_state A_71)->(((ord_less_eq_pname_o B_40) ((image_202231862_pname F_15) A_71))->(finite_finite_pname B_40)))). % Axiom fact_97_finite__surj:(forall (B_40:((hoare_1262092251_state->Prop)->Prop)) (F_15:(hoare_1262092251_state->(hoare_1262092251_state->Prop))) (A_71:(hoare_1262092251_state->Prop)), ((finite1178804552_state A_71)->(((ord_le2012720639te_o_o B_40) ((image_1403668518tate_o F_15) A_71))->(finite1423311111tate_o B_40)))). % Axiom fact_98_finite__surj:(forall (B_40:((pname->Prop)->Prop)) (F_15:(hoare_1262092251_state->(pname->Prop))) (A_71:(hoare_1262092251_state->Prop)), ((finite1178804552_state A_71)->(((ord_le1205211808me_o_o B_40) ((image_1320925383name_o F_15) A_71))->(finite297249702name_o B_40)))). % Axiom fact_99_subset__singletonD:(forall (A_70:(hoare_1262092251_state->Prop)) (X_16:hoare_1262092251_state), (((ord_le870406270tate_o A_70) ((insert81609953_state X_16) bot_bo113204042tate_o))->((or (((eq (hoare_1262092251_state->Prop)) A_70) bot_bo113204042tate_o)) (((eq (hoare_1262092251_state->Prop)) A_70) ((insert81609953_state X_16) bot_bo113204042tate_o))))). % Axiom fact_100_subset__singletonD:(forall (A_70:((pname->Prop)->Prop)) (X_16:(pname->Prop)), (((ord_le1205211808me_o_o A_70) ((insert_pname_o X_16) bot_bot_pname_o_o))->((or (((eq ((pname->Prop)->Prop)) A_70) bot_bot_pname_o_o)) (((eq ((pname->Prop)->Prop)) A_70) ((insert_pname_o X_16) bot_bot_pname_o_o))))). % Axiom fact_101_subset__singletonD:(forall (A_70:((hoare_1262092251_state->Prop)->Prop)) (X_16:(hoare_1262092251_state->Prop)), (((ord_le2012720639te_o_o A_70) ((insert1042460334tate_o X_16) bot_bo1962689075te_o_o))->((or (((eq ((hoare_1262092251_state->Prop)->Prop)) A_70) bot_bo1962689075te_o_o)) (((eq ((hoare_1262092251_state->Prop)->Prop)) A_70) ((insert1042460334tate_o X_16) bot_bo1962689075te_o_o))))). % Axiom fact_102_subset__singletonD:(forall (A_70:(pname->Prop)) (X_16:pname), (((ord_less_eq_pname_o A_70) ((insert_pname X_16) bot_bot_pname_o))->((or (((eq (pname->Prop)) A_70) bot_bot_pname_o)) (((eq (pname->Prop)) A_70) ((insert_pname X_16) bot_bot_pname_o))))). % Axiom fact_103_MGF:(forall (C_1:com), (hoare_1821564147gleton->(wT_bodies->((wt C_1)->((hoare_930741239_state bot_bo113204042tate_o) ((insert81609953_state (hoare_Mirabelle_MGT C_1)) bot_bo113204042tate_o)))))). % Axiom fact_104_emptyE:(forall (A_69:hoare_1262092251_state), (((member5164104_state A_69) bot_bo113204042tate_o)->False)). % Axiom fact_105_emptyE:(forall (A_69:(pname->Prop)), (((member_pname_o A_69) bot_bot_pname_o_o)->False)). % Axiom fact_106_emptyE:(forall (A_69:(hoare_1262092251_state->Prop)), (((member907417095tate_o A_69) bot_bo1962689075te_o_o)->False)). % Axiom fact_107_emptyE:(forall (A_69:pname), (((member_pname A_69) bot_bot_pname_o)->False)). % Axiom fact_108_insertCI:(forall (B_39:hoare_1262092251_state) (A_68:hoare_1262092251_state) (B_38:(hoare_1262092251_state->Prop)), (((((member5164104_state A_68) B_38)->False)->(((eq hoare_1262092251_state) A_68) B_39))->((member5164104_state A_68) ((insert81609953_state B_39) B_38)))). % Axiom fact_109_insertCI:(forall (B_39:(pname->Prop)) (A_68:(pname->Prop)) (B_38:((pname->Prop)->Prop)), (((((member_pname_o A_68) B_38)->False)->(((eq (pname->Prop)) A_68) B_39))->((member_pname_o A_68) ((insert_pname_o B_39) B_38)))). % Axiom fact_110_insertCI:(forall (B_39:(hoare_1262092251_state->Prop)) (A_68:(hoare_1262092251_state->Prop)) (B_38:((hoare_1262092251_state->Prop)->Prop)), (((((member907417095tate_o A_68) B_38)->False)->(((eq (hoare_1262092251_state->Prop)) A_68) B_39))->((member907417095tate_o A_68) ((insert1042460334tate_o B_39) B_38)))). % Axiom fact_111_insertCI:(forall (B_39:pname) (A_68:pname) (B_38:(pname->Prop)), (((((member_pname A_68) B_38)->False)->(((eq pname) A_68) B_39))->((member_pname A_68) ((insert_pname B_39) B_38)))). % Axiom fact_112_insertE:(forall (A_67:hoare_1262092251_state) (B_37:hoare_1262092251_state) (A_66:(hoare_1262092251_state->Prop)), (((member5164104_state A_67) ((insert81609953_state B_37) A_66))->((not (((eq hoare_1262092251_state) A_67) B_37))->((member5164104_state A_67) A_66)))). % Axiom fact_113_insertE:(forall (A_67:(pname->Prop)) (B_37:(pname->Prop)) (A_66:((pname->Prop)->Prop)), (((member_pname_o A_67) ((insert_pname_o B_37) A_66))->((not (((eq (pname->Prop)) A_67) B_37))->((member_pname_o A_67) A_66)))). % Axiom fact_114_insertE:(forall (A_67:(hoare_1262092251_state->Prop)) (B_37:(hoare_1262092251_state->Prop)) (A_66:((hoare_1262092251_state->Prop)->Prop)), (((member907417095tate_o A_67) ((insert1042460334tate_o B_37) A_66))->((not (((eq (hoare_1262092251_state->Prop)) A_67) B_37))->((member907417095tate_o A_67) A_66)))). % Axiom fact_115_insertE:(forall (A_67:pname) (B_37:pname) (A_66:(pname->Prop)), (((member_pname A_67) ((insert_pname B_37) A_66))->((not (((eq pname) A_67) B_37))->((member_pname A_67) A_66)))). % Axiom fact_116_equalityI:(forall (A_65:(hoare_1262092251_state->Prop)) (B_36:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o A_65) B_36)->(((ord_le870406270tate_o B_36) A_65)->(((eq (hoare_1262092251_state->Prop)) A_65) B_36)))). % Axiom fact_117_equalityI:(forall (A_65:((pname->Prop)->Prop)) (B_36:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_65) B_36)->(((ord_le1205211808me_o_o B_36) A_65)->(((eq ((pname->Prop)->Prop)) A_65) B_36)))). % Axiom fact_118_equalityI:(forall (A_65:((hoare_1262092251_state->Prop)->Prop)) (B_36:((hoare_1262092251_state->Prop)->Prop)), (((ord_le2012720639te_o_o A_65) B_36)->(((ord_le2012720639te_o_o B_36) A_65)->(((eq ((hoare_1262092251_state->Prop)->Prop)) A_65) B_36)))). % Axiom fact_119_equalityI:(forall (A_65:(pname->Prop)) (B_36:(pname->Prop)), (((ord_less_eq_pname_o A_65) B_36)->(((ord_less_eq_pname_o B_36) A_65)->(((eq (pname->Prop)) A_65) B_36)))). % Axiom fact_120_subsetD:(forall (C_6:hoare_1262092251_state) (A_64:(hoare_1262092251_state->Prop)) (B_35:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o A_64) B_35)->(((member5164104_state C_6) A_64)->((member5164104_state C_6) B_35)))). % Axiom fact_121_subsetD:(forall (C_6:(pname->Prop)) (A_64:((pname->Prop)->Prop)) (B_35:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_64) B_35)->(((member_pname_o C_6) A_64)->((member_pname_o C_6) B_35)))). % Axiom fact_122_subsetD:(forall (C_6:(hoare_1262092251_state->Prop)) (A_64:((hoare_1262092251_state->Prop)->Prop)) (B_35:((hoare_1262092251_state->Prop)->Prop)), (((ord_le2012720639te_o_o A_64) B_35)->(((member907417095tate_o C_6) A_64)->((member907417095tate_o C_6) B_35)))). % Axiom fact_123_subsetD:(forall (C_6:pname) (A_64:(pname->Prop)) (B_35:(pname->Prop)), (((ord_less_eq_pname_o A_64) B_35)->(((member_pname C_6) A_64)->((member_pname C_6) B_35)))). % Axiom fact_124_image__eqI:(forall (A_63:(hoare_1262092251_state->Prop)) (B_34:(pname->Prop)) (F_14:(hoare_1262092251_state->(pname->Prop))) (X_15:hoare_1262092251_state), ((((eq (pname->Prop)) B_34) (F_14 X_15))->(((member5164104_state X_15) A_63)->((member_pname_o B_34) ((image_1320925383name_o F_14) A_63))))). % Axiom fact_125_image__eqI:(forall (A_63:(hoare_1262092251_state->Prop)) (B_34:(hoare_1262092251_state->Prop)) (F_14:(hoare_1262092251_state->(hoare_1262092251_state->Prop))) (X_15:hoare_1262092251_state), ((((eq (hoare_1262092251_state->Prop)) B_34) (F_14 X_15))->(((member5164104_state X_15) A_63)->((member907417095tate_o B_34) ((image_1403668518tate_o F_14) A_63))))). % Axiom fact_126_image__eqI:(forall (A_63:(pname->Prop)) (B_34:(pname->Prop)) (F_14:(pname->(pname->Prop))) (X_15:pname), ((((eq (pname->Prop)) B_34) (F_14 X_15))->(((member_pname X_15) A_63)->((member_pname_o B_34) ((image_pname_pname_o F_14) A_63))))). % Axiom fact_127_image__eqI:(forall (A_63:(pname->Prop)) (B_34:(hoare_1262092251_state->Prop)) (F_14:(pname->(hoare_1262092251_state->Prop))) (X_15:pname), ((((eq (hoare_1262092251_state->Prop)) B_34) (F_14 X_15))->(((member_pname X_15) A_63)->((member907417095tate_o B_34) ((image_518521461tate_o F_14) A_63))))). % Axiom fact_128_image__eqI:(forall (A_63:((pname->Prop)->Prop)) (B_34:hoare_1262092251_state) (F_14:((pname->Prop)->hoare_1262092251_state)) (X_15:(pname->Prop)), ((((eq hoare_1262092251_state) B_34) (F_14 X_15))->(((member_pname_o X_15) A_63)->((member5164104_state B_34) ((image_1476171975_state F_14) A_63))))). % Axiom fact_129_image__eqI:(forall (A_63:((hoare_1262092251_state->Prop)->Prop)) (B_34:hoare_1262092251_state) (F_14:((hoare_1262092251_state->Prop)->hoare_1262092251_state)) (X_15:(hoare_1262092251_state->Prop)), ((((eq hoare_1262092251_state) B_34) (F_14 X_15))->(((member907417095tate_o X_15) A_63)->((member5164104_state B_34) ((image_234589002_state F_14) A_63))))). % Axiom fact_130_image__eqI:(forall (A_63:(hoare_1262092251_state->Prop)) (B_34:pname) (F_14:(hoare_1262092251_state->pname)) (X_15:hoare_1262092251_state), ((((eq pname) B_34) (F_14 X_15))->(((member5164104_state X_15) A_63)->((member_pname B_34) ((image_202231862_pname F_14) A_63))))). % Axiom fact_131_image__eqI:(forall (A_63:(pname->Prop)) (B_34:pname) (F_14:(pname->pname)) (X_15:pname), ((((eq pname) B_34) (F_14 X_15))->(((member_pname X_15) A_63)->((member_pname 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B_31)->False)->((iff (((eq (hoare_1262092251_state->Prop)) ((insert81609953_state X_14) A_55)) ((insert81609953_state X_14) B_31))) (((eq (hoare_1262092251_state->Prop)) A_55) B_31))))). % Axiom fact_174_insert__code:(forall (Y_3:pname) (A_54:(pname->Prop)) (X_13:pname), ((iff (((insert_pname Y_3) A_54) X_13)) ((or (((eq pname) Y_3) X_13)) (A_54 X_13)))). % Axiom fact_175_insert__code:(forall (Y_3:hoare_1262092251_state) (A_54:(hoare_1262092251_state->Prop)) (X_13:hoare_1262092251_state), ((iff (((insert81609953_state Y_3) A_54) X_13)) ((or (((eq hoare_1262092251_state) Y_3) X_13)) (A_54 X_13)))). % Axiom fact_176_insert__iff:(forall (A_53:pname) (B_30:pname) (A_52:(pname->Prop)), ((iff ((member_pname A_53) ((insert_pname B_30) A_52))) ((or (((eq pname) A_53) B_30)) ((member_pname A_53) A_52)))). % Axiom fact_177_insert__iff:(forall (A_53:hoare_1262092251_state) (B_30:hoare_1262092251_state) (A_52:(hoare_1262092251_state->Prop)), ((iff ((member5164104_state A_53) ((insert81609953_state B_30) A_52))) ((or (((eq hoare_1262092251_state) A_53) B_30)) ((member5164104_state A_53) A_52)))). % Axiom fact_178_insert__commute:(forall (X_12:pname) (Y_2:pname) (A_51:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_12) ((insert_pname Y_2) A_51))) ((insert_pname Y_2) ((insert_pname X_12) A_51)))). % Axiom fact_179_insert__commute:(forall (X_12:hoare_1262092251_state) (Y_2:hoare_1262092251_state) (A_51:(hoare_1262092251_state->Prop)), (((eq (hoare_1262092251_state->Prop)) ((insert81609953_state X_12) ((insert81609953_state Y_2) A_51))) ((insert81609953_state Y_2) ((insert81609953_state X_12) A_51)))). % Axiom fact_180_insert__absorb2:(forall (X_11:pname) (A_50:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_11) ((insert_pname X_11) A_50))) ((insert_pname X_11) A_50))). % Axiom fact_181_insert__absorb2:(forall (X_11:hoare_1262092251_state) (A_50:(hoare_1262092251_state->Prop)), (((eq (hoare_1262092251_state->Prop)) ((insert81609953_state X_11) ((insert81609953_state X_11) A_50))) ((insert81609953_state X_11) A_50))). % Axiom fact_182_insert__Collect:(forall (A_49:pname) (P_6:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_49) (collect_pname P_6))) (collect_pname (fun (U:pname)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq pname) U) A_49))) (P_6 U)))))). % Axiom fact_183_insert__Collect:(forall (A_49:hoare_1262092251_state) (P_6:(hoare_1262092251_state->Prop)), (((eq (hoare_1262092251_state->Prop)) ((insert81609953_state A_49) (collec1121927558_state P_6))) (collec1121927558_state (fun (U:hoare_1262092251_state)=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq hoare_1262092251_state) U) A_49))) (P_6 U)))))). % Axiom fact_184_insert__Collect:(forall (A_49:(pname->Prop)) (P_6:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_49) (collect_pname_o P_6))) (collect_pname_o (fun (U:(pname->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (pname->Prop)) U) A_49))) (P_6 U)))))). % Axiom fact_185_insert__Collect:(forall (A_49:(hoare_1262092251_state->Prop)) (P_6:((hoare_1262092251_state->Prop)->Prop)), (((eq ((hoare_1262092251_state->Prop)->Prop)) ((insert1042460334tate_o A_49) (collec313158217tate_o P_6))) (collec313158217tate_o (fun (U:(hoare_1262092251_state->Prop))=> (((fun (X:Prop) (Y:Prop)=> (X->Y)) (not (((eq (hoare_1262092251_state->Prop)) U) A_49))) (P_6 U)))))). % Axiom fact_186_insert__compr:(forall (A_48:pname) (B_29:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname A_48) B_29)) (collect_pname (fun (X_1:pname)=> ((or (((eq pname) X_1) A_48)) ((member_pname X_1) B_29)))))). % Axiom fact_187_insert__compr:(forall (A_48:hoare_1262092251_state) (B_29:(hoare_1262092251_state->Prop)), (((eq (hoare_1262092251_state->Prop)) ((insert81609953_state A_48) B_29)) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> ((or (((eq hoare_1262092251_state) X_1) A_48)) ((member5164104_state X_1) B_29)))))). % Axiom fact_188_insert__compr:(forall (A_48:(pname->Prop)) (B_29:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o A_48) B_29)) (collect_pname_o (fun (X_1:(pname->Prop))=> ((or (((eq (pname->Prop)) X_1) A_48)) ((member_pname_o X_1) B_29)))))). % Axiom fact_189_insert__compr:(forall (A_48:(hoare_1262092251_state->Prop)) (B_29:((hoare_1262092251_state->Prop)->Prop)), (((eq ((hoare_1262092251_state->Prop)->Prop)) ((insert1042460334tate_o A_48) B_29)) (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> ((or (((eq (hoare_1262092251_state->Prop)) X_1) A_48)) ((member907417095tate_o X_1) B_29)))))). % Axiom fact_190_insertI1:(forall (A_47:pname) (B_28:(pname->Prop)), ((member_pname A_47) ((insert_pname A_47) B_28))). % Axiom fact_191_insertI1:(forall (A_47:hoare_1262092251_state) (B_28:(hoare_1262092251_state->Prop)), ((member5164104_state A_47) ((insert81609953_state A_47) B_28))). % Axiom fact_192_equalityE:(forall (A_46:(pname->Prop)) (B_27:(pname->Prop)), ((((eq (pname->Prop)) A_46) B_27)->((((ord_less_eq_pname_o A_46) B_27)->(((ord_less_eq_pname_o B_27) A_46)->False))->False))). % Axiom fact_193_equalityE:(forall (A_46:(hoare_1262092251_state->Prop)) (B_27:(hoare_1262092251_state->Prop)), ((((eq (hoare_1262092251_state->Prop)) A_46) B_27)->((((ord_le870406270tate_o A_46) B_27)->(((ord_le870406270tate_o B_27) A_46)->False))->False))). % Axiom fact_194_subset__trans:(forall (C_4:(pname->Prop)) (A_45:(pname->Prop)) (B_26:(pname->Prop)), (((ord_less_eq_pname_o A_45) B_26)->(((ord_less_eq_pname_o B_26) C_4)->((ord_less_eq_pname_o A_45) C_4)))). % Axiom fact_195_subset__trans:(forall (C_4:(hoare_1262092251_state->Prop)) (A_45:(hoare_1262092251_state->Prop)) (B_26:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o A_45) B_26)->(((ord_le870406270tate_o B_26) C_4)->((ord_le870406270tate_o A_45) C_4)))). % Axiom fact_196_set__mp:(forall (X_10:pname) (A_44:(pname->Prop)) (B_25:(pname->Prop)), (((ord_less_eq_pname_o A_44) B_25)->(((member_pname X_10) A_44)->((member_pname X_10) B_25)))). % Axiom fact_197_set__mp:(forall (X_10:hoare_1262092251_state) (A_44:(hoare_1262092251_state->Prop)) (B_25:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o A_44) B_25)->(((member5164104_state X_10) A_44)->((member5164104_state X_10) B_25)))). % Axiom fact_198_set__rev__mp:(forall (B_24:(pname->Prop)) (X_9:pname) (A_43:(pname->Prop)), (((member_pname X_9) A_43)->(((ord_less_eq_pname_o A_43) B_24)->((member_pname X_9) B_24)))). % Axiom fact_199_set__rev__mp:(forall (B_24:(hoare_1262092251_state->Prop)) (X_9:hoare_1262092251_state) (A_43:(hoare_1262092251_state->Prop)), (((member5164104_state X_9) A_43)->(((ord_le870406270tate_o A_43) B_24)->((member5164104_state X_9) B_24)))). % Axiom fact_200_in__mono:(forall (X_8:pname) (A_42:(pname->Prop)) (B_23:(pname->Prop)), (((ord_less_eq_pname_o A_42) B_23)->(((member_pname X_8) A_42)->((member_pname X_8) B_23)))). % Axiom fact_201_in__mono:(forall (X_8:hoare_1262092251_state) (A_42:(hoare_1262092251_state->Prop)) (B_23:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o A_42) B_23)->(((member5164104_state X_8) A_42)->((member5164104_state X_8) B_23)))). % Axiom fact_202_equalityD2:(forall (A_41:(pname->Prop)) (B_22:(pname->Prop)), ((((eq (pname->Prop)) A_41) B_22)->((ord_less_eq_pname_o B_22) A_41))). % Axiom fact_203_equalityD2:(forall (A_41:(hoare_1262092251_state->Prop)) (B_22:(hoare_1262092251_state->Prop)), ((((eq (hoare_1262092251_state->Prop)) A_41) B_22)->((ord_le870406270tate_o B_22) A_41))). % Axiom fact_204_equalityD1:(forall (A_40:(pname->Prop)) (B_21:(pname->Prop)), ((((eq (pname->Prop)) A_40) B_21)->((ord_less_eq_pname_o A_40) B_21))). % Axiom fact_205_equalityD1:(forall (A_40:(hoare_1262092251_state->Prop)) (B_21:(hoare_1262092251_state->Prop)), ((((eq (hoare_1262092251_state->Prop)) A_40) B_21)->((ord_le870406270tate_o A_40) B_21))). % Axiom fact_206_set__eq__subset:(forall (A_39:(pname->Prop)) (B_20:(pname->Prop)), ((iff (((eq (pname->Prop)) A_39) B_20)) ((and ((ord_less_eq_pname_o A_39) B_20)) ((ord_less_eq_pname_o B_20) A_39)))). % Axiom fact_207_set__eq__subset:(forall (A_39:(hoare_1262092251_state->Prop)) (B_20:(hoare_1262092251_state->Prop)), ((iff (((eq (hoare_1262092251_state->Prop)) A_39) B_20)) ((and ((ord_le870406270tate_o A_39) B_20)) ((ord_le870406270tate_o B_20) A_39)))). % Axiom fact_208_subset__refl:(forall (A_38:(pname->Prop)), ((ord_less_eq_pname_o A_38) A_38)). % Axiom fact_209_subset__refl:(forall (A_38:(hoare_1262092251_state->Prop)), ((ord_le870406270tate_o A_38) A_38)). % Axiom fact_210_rev__image__eqI:(forall (B_19:hoare_1262092251_state) (F_13:(pname->hoare_1262092251_state)) (X_7:pname) (A_37:(pname->Prop)), (((member_pname X_7) A_37)->((((eq hoare_1262092251_state) B_19) (F_13 X_7))->((member5164104_state B_19) ((image_669833818_state F_13) A_37))))). % Axiom fact_211_imageI:(forall (F_12:(pname->hoare_1262092251_state)) (X_6:pname) (A_36:(pname->Prop)), (((member_pname X_6) A_36)->((member5164104_state (F_12 X_6)) ((image_669833818_state F_12) A_36)))). % Axiom fact_212_image__iff:(forall (Z:hoare_1262092251_state) (F_11:(pname->hoare_1262092251_state)) (A_35:(pname->Prop)), ((iff ((member5164104_state Z) ((image_669833818_state F_11) A_35))) ((ex pname) (fun (X_1:pname)=> ((and ((member_pname X_1) A_35)) (((eq hoare_1262092251_state) Z) (F_11 X_1))))))). % Axiom fact_213_finite__Collect__disjI:(forall (P_5:(pname->Prop)) (Q:(pname->Prop)), ((iff (finite_finite_pname (collect_pname (fun (X_1:pname)=> ((or (P_5 X_1)) (Q X_1)))))) ((and (finite_finite_pname (collect_pname P_5))) (finite_finite_pname (collect_pname Q))))). % Axiom fact_214_finite__Collect__disjI:(forall (P_5:(hoare_1262092251_state->Prop)) (Q:(hoare_1262092251_state->Prop)), ((iff (finite1178804552_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> ((or (P_5 X_1)) (Q X_1)))))) ((and (finite1178804552_state (collec1121927558_state P_5))) (finite1178804552_state (collec1121927558_state Q))))). % Axiom fact_215_finite__Collect__disjI:(forall (P_5:((pname->Prop)->Prop)) (Q:((pname->Prop)->Prop)), ((iff (finite297249702name_o (collect_pname_o (fun (X_1:(pname->Prop))=> ((or (P_5 X_1)) (Q X_1)))))) ((and (finite297249702name_o (collect_pname_o P_5))) (finite297249702name_o (collect_pname_o Q))))). % Axiom fact_216_finite__Collect__disjI:(forall (P_5:((hoare_1262092251_state->Prop)->Prop)) (Q:((hoare_1262092251_state->Prop)->Prop)), ((iff (finite1423311111tate_o (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> ((or (P_5 X_1)) (Q X_1)))))) ((and (finite1423311111tate_o (collec313158217tate_o P_5))) (finite1423311111tate_o (collec313158217tate_o Q))))). % Axiom fact_217_insert__compr__raw:(forall (X_1:pname) (Xa:(pname->Prop)), (((eq (pname->Prop)) ((insert_pname X_1) Xa)) (collect_pname (fun (Y_1:pname)=> ((or (((eq pname) Y_1) X_1)) ((member_pname Y_1) Xa)))))). % Axiom fact_218_insert__compr__raw:(forall (X_1:hoare_1262092251_state) (Xa:(hoare_1262092251_state->Prop)), (((eq (hoare_1262092251_state->Prop)) ((insert81609953_state X_1) Xa)) (collec1121927558_state (fun (Y_1:hoare_1262092251_state)=> ((or (((eq hoare_1262092251_state) Y_1) X_1)) ((member5164104_state Y_1) Xa)))))). % Axiom fact_219_insert__compr__raw:(forall (X_1:(pname->Prop)) (Xa:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) ((insert_pname_o X_1) Xa)) (collect_pname_o (fun (Y_1:(pname->Prop))=> ((or (((eq (pname->Prop)) Y_1) X_1)) ((member_pname_o Y_1) Xa)))))). % Axiom fact_220_insert__compr__raw:(forall (X_1:(hoare_1262092251_state->Prop)) (Xa:((hoare_1262092251_state->Prop)->Prop)), (((eq ((hoare_1262092251_state->Prop)->Prop)) ((insert1042460334tate_o X_1) Xa)) (collec313158217tate_o (fun (Y_1:(hoare_1262092251_state->Prop))=> ((or (((eq (hoare_1262092251_state->Prop)) Y_1) X_1)) ((member907417095tate_o Y_1) Xa)))))). % Axiom fact_221_singleton__inject:(forall (A_34:pname) (B_18:pname), ((((eq (pname->Prop)) ((insert_pname A_34) bot_bot_pname_o)) ((insert_pname B_18) bot_bot_pname_o))->(((eq pname) A_34) B_18))). % Axiom fact_222_singleton__inject:(forall (A_34:hoare_1262092251_state) (B_18:hoare_1262092251_state), ((((eq (hoare_1262092251_state->Prop)) ((insert81609953_state A_34) bot_bo113204042tate_o)) ((insert81609953_state B_18) bot_bo113204042tate_o))->(((eq hoare_1262092251_state) A_34) B_18))). % Axiom fact_223_singletonE:(forall (B_17:pname) (A_33:pname), (((member_pname B_17) ((insert_pname A_33) bot_bot_pname_o))->(((eq pname) B_17) A_33))). % Axiom fact_224_singletonE:(forall (B_17:hoare_1262092251_state) (A_33:hoare_1262092251_state), (((member5164104_state B_17) ((insert81609953_state A_33) bot_bo113204042tate_o))->(((eq hoare_1262092251_state) B_17) A_33))). % Axiom fact_225_doubleton__eq__iff:(forall (A_32:pname) (B_16:pname) (C_3:pname) (D_1:pname), ((iff (((eq (pname->Prop)) ((insert_pname A_32) ((insert_pname B_16) bot_bot_pname_o))) ((insert_pname C_3) ((insert_pname D_1) bot_bot_pname_o)))) ((or ((and (((eq pname) A_32) C_3)) (((eq pname) B_16) D_1))) ((and (((eq pname) A_32) D_1)) (((eq pname) B_16) C_3))))). % Axiom fact_226_doubleton__eq__iff:(forall (A_32:hoare_1262092251_state) (B_16:hoare_1262092251_state) (C_3:hoare_1262092251_state) (D_1:hoare_1262092251_state), ((iff (((eq (hoare_1262092251_state->Prop)) ((insert81609953_state A_32) ((insert81609953_state B_16) bot_bo113204042tate_o))) ((insert81609953_state C_3) ((insert81609953_state D_1) bot_bo113204042tate_o)))) ((or ((and (((eq hoare_1262092251_state) A_32) C_3)) (((eq hoare_1262092251_state) B_16) D_1))) ((and (((eq hoare_1262092251_state) A_32) D_1)) (((eq hoare_1262092251_state) B_16) C_3))))). % Axiom fact_227_singleton__iff:(forall (B_15:pname) (A_31:pname), ((iff ((member_pname B_15) ((insert_pname A_31) bot_bot_pname_o))) (((eq pname) B_15) A_31))). % Axiom fact_228_singleton__iff:(forall (B_15:hoare_1262092251_state) (A_31:hoare_1262092251_state), ((iff ((member5164104_state B_15) ((insert81609953_state A_31) bot_bo113204042tate_o))) (((eq hoare_1262092251_state) B_15) A_31))). % Axiom fact_229_insert__not__empty:(forall (A_30:pname) (A_29:(pname->Prop)), (not (((eq (pname->Prop)) ((insert_pname A_30) A_29)) bot_bot_pname_o))). % Axiom fact_230_insert__not__empty:(forall (A_30:hoare_1262092251_state) (A_29:(hoare_1262092251_state->Prop)), (not (((eq (hoare_1262092251_state->Prop)) ((insert81609953_state A_30) A_29)) bot_bo113204042tate_o))). % Axiom fact_231_empty__not__insert:(forall (A_28:pname) (A_27:(pname->Prop)), (not (((eq (pname->Prop)) bot_bot_pname_o) ((insert_pname A_28) A_27)))). % Axiom fact_232_empty__not__insert:(forall (A_28:hoare_1262092251_state) (A_27:(hoare_1262092251_state->Prop)), (not (((eq (hoare_1262092251_state->Prop)) bot_bo113204042tate_o) ((insert81609953_state A_28) A_27)))). % Axiom fact_233_finite__insert:(forall (A_26:pname) (A_25:(pname->Prop)), ((iff (finite_finite_pname ((insert_pname A_26) A_25))) (finite_finite_pname A_25))). % Axiom fact_234_finite__insert:(forall (A_26:hoare_1262092251_state) (A_25:(hoare_1262092251_state->Prop)), ((iff (finite1178804552_state ((insert81609953_state A_26) A_25))) (finite1178804552_state A_25))). % Axiom fact_235_finite__insert:(forall (A_26:(pname->Prop)) (A_25:((pname->Prop)->Prop)), ((iff (finite297249702name_o ((insert_pname_o A_26) A_25))) (finite297249702name_o A_25))). % Axiom fact_236_finite__insert:(forall (A_26:(hoare_1262092251_state->Prop)) (A_25:((hoare_1262092251_state->Prop)->Prop)), ((iff (finite1423311111tate_o ((insert1042460334tate_o A_26) A_25))) (finite1423311111tate_o A_25))). % Axiom fact_237_subset__empty:(forall (A_24:(pname->Prop)), ((iff ((ord_less_eq_pname_o A_24) bot_bot_pname_o)) (((eq (pname->Prop)) A_24) bot_bot_pname_o))). % Axiom fact_238_subset__empty:(forall (A_24:(hoare_1262092251_state->Prop)), ((iff ((ord_le870406270tate_o A_24) bot_bo113204042tate_o)) (((eq (hoare_1262092251_state->Prop)) A_24) bot_bo113204042tate_o))). % Axiom fact_239_image__is__empty:(forall (F_10:(pname->hoare_1262092251_state)) (A_23:(pname->Prop)), ((iff (((eq (hoare_1262092251_state->Prop)) ((image_669833818_state F_10) A_23)) bot_bo113204042tate_o)) (((eq (pname->Prop)) A_23) bot_bot_pname_o))). % Axiom fact_240_image__empty:(forall (F_9:(pname->hoare_1262092251_state)), (((eq (hoare_1262092251_state->Prop)) ((image_669833818_state F_9) bot_bot_pname_o)) bot_bo113204042tate_o)). % Axiom fact_241_empty__is__image:(forall (F_8:(pname->hoare_1262092251_state)) (A_22:(pname->Prop)), ((iff (((eq (hoare_1262092251_state->Prop)) bot_bo113204042tate_o) ((image_669833818_state F_8) A_22))) (((eq (pname->Prop)) A_22) bot_bot_pname_o))). % Axiom fact_242_finite__subset:(forall (A_21:((pname->Prop)->Prop)) (B_14:((pname->Prop)->Prop)), (((ord_le1205211808me_o_o A_21) B_14)->((finite297249702name_o B_14)->(finite297249702name_o A_21)))). % Axiom fact_243_finite__subset:(forall (A_21:((hoare_1262092251_state->Prop)->Prop)) (B_14:((hoare_1262092251_state->Prop)->Prop)), (((ord_le2012720639te_o_o A_21) B_14)->((finite1423311111tate_o B_14)->(finite1423311111tate_o A_21)))). % Axiom fact_244_finite__subset:(forall (A_21:(pname->Prop)) (B_14:(pname->Prop)), (((ord_less_eq_pname_o A_21) B_14)->((finite_finite_pname B_14)->(finite_finite_pname A_21)))). % Axiom fact_245_finite__subset:(forall (A_21:(hoare_1262092251_state->Prop)) (B_14:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o A_21) B_14)->((finite1178804552_state B_14)->(finite1178804552_state A_21)))). % Axiom fact_246_rev__finite__subset:(forall (A_20:((pname->Prop)->Prop)) (B_13:((pname->Prop)->Prop)), ((finite297249702name_o B_13)->(((ord_le1205211808me_o_o A_20) B_13)->(finite297249702name_o A_20)))). % Axiom fact_247_rev__finite__subset:(forall (A_20:((hoare_1262092251_state->Prop)->Prop)) (B_13:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o B_13)->(((ord_le2012720639te_o_o A_20) B_13)->(finite1423311111tate_o A_20)))). % Axiom fact_248_rev__finite__subset:(forall (A_20:(pname->Prop)) (B_13:(pname->Prop)), ((finite_finite_pname B_13)->(((ord_less_eq_pname_o A_20) B_13)->(finite_finite_pname A_20)))). % Axiom fact_249_rev__finite__subset:(forall (A_20:(hoare_1262092251_state->Prop)) (B_13:(hoare_1262092251_state->Prop)), ((finite1178804552_state B_13)->(((ord_le870406270tate_o A_20) B_13)->(finite1178804552_state A_20)))). % Axiom fact_250_insert__mono:(forall (A_19:pname) (C_2:(pname->Prop)) (D:(pname->Prop)), (((ord_less_eq_pname_o C_2) D)->((ord_less_eq_pname_o ((insert_pname A_19) C_2)) ((insert_pname A_19) D)))). % Axiom fact_251_insert__mono:(forall (A_19:hoare_1262092251_state) (C_2:(hoare_1262092251_state->Prop)) (D:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o C_2) D)->((ord_le870406270tate_o ((insert81609953_state A_19) C_2)) ((insert81609953_state A_19) D)))). % Axiom fact_252_mem__def:(forall (X_5:pname) (A_18:(pname->Prop)), ((iff ((member_pname X_5) A_18)) (A_18 X_5))). % Axiom fact_253_mem__def:(forall (X_5:hoare_1262092251_state) (A_18:(hoare_1262092251_state->Prop)), ((iff ((member5164104_state X_5) A_18)) (A_18 X_5))). % Axiom fact_254_Collect__def:(forall (P_4:(pname->Prop)), (((eq (pname->Prop)) (collect_pname P_4)) P_4)). % Axiom fact_255_Collect__def:(forall (P_4:(hoare_1262092251_state->Prop)), (((eq (hoare_1262092251_state->Prop)) (collec1121927558_state P_4)) P_4)). % Axiom fact_256_Collect__def:(forall (P_4:((pname->Prop)->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o P_4)) P_4)). % Axiom fact_257_Collect__def:(forall (P_4:((hoare_1262092251_state->Prop)->Prop)), (((eq ((hoare_1262092251_state->Prop)->Prop)) (collec313158217tate_o P_4)) P_4)). % Axiom fact_258_subset__insertI2:(forall (B_12:pname) (A_17:(pname->Prop)) (B_11:(pname->Prop)), (((ord_less_eq_pname_o A_17) B_11)->((ord_less_eq_pname_o A_17) ((insert_pname B_12) B_11)))). % Axiom fact_259_subset__insertI2:(forall (B_12:hoare_1262092251_state) (A_17:(hoare_1262092251_state->Prop)) (B_11:(hoare_1262092251_state->Prop)), (((ord_le870406270tate_o A_17) B_11)->((ord_le870406270tate_o A_17) ((insert81609953_state B_12) B_11)))). % Axiom fact_260_subset__insert:(forall (B_10:(pname->Prop)) (X_4:pname) (A_16:(pname->Prop)), ((((member_pname X_4) A_16)->False)->((iff ((ord_less_eq_pname_o A_16) ((insert_pname X_4) B_10))) ((ord_less_eq_pname_o A_16) B_10)))). % Axiom fact_261_subset__insert:(forall (B_10:(hoare_1262092251_state->Prop)) (X_4:hoare_1262092251_state) (A_16:(hoare_1262092251_state->Prop)), ((((member5164104_state X_4) A_16)->False)->((iff ((ord_le870406270tate_o A_16) ((insert81609953_state X_4) B_10))) ((ord_le870406270tate_o A_16) B_10)))). % Axiom fact_262_insert__subset:(forall (X_3:pname) (A_15:(pname->Prop)) (B_9:(pname->Prop)), ((iff ((ord_less_eq_pname_o ((insert_pname X_3) A_15)) B_9)) ((and ((member_pname X_3) B_9)) ((ord_less_eq_pname_o A_15) B_9)))). % Axiom fact_263_insert__subset:(forall (X_3:hoare_1262092251_state) (A_15:(hoare_1262092251_state->Prop)) (B_9:(hoare_1262092251_state->Prop)), ((iff ((ord_le870406270tate_o ((insert81609953_state X_3) A_15)) B_9)) ((and ((member5164104_state X_3) B_9)) ((ord_le870406270tate_o A_15) B_9)))). % Axiom fact_264_subset__insertI:(forall (B_8:(pname->Prop)) (A_14:pname), ((ord_less_eq_pname_o B_8) ((insert_pname A_14) B_8))). % Axiom fact_265_subset__insertI:(forall (B_8:(hoare_1262092251_state->Prop)) (A_14:hoare_1262092251_state), ((ord_le870406270tate_o B_8) ((insert81609953_state A_14) B_8))). % Axiom fact_266_insert__image:(forall (F_7:(pname->hoare_1262092251_state)) (X_2:pname) (A_13:(pname->Prop)), (((member_pname X_2) A_13)->(((eq (hoare_1262092251_state->Prop)) ((insert81609953_state (F_7 X_2)) ((image_669833818_state F_7) A_13))) ((image_669833818_state F_7) A_13)))). % Axiom fact_267_image__insert:(forall (F_6:(pname->hoare_1262092251_state)) (A_12:pname) (B_7:(pname->Prop)), (((eq (hoare_1262092251_state->Prop)) ((image_669833818_state F_6) ((insert_pname A_12) B_7))) ((insert81609953_state (F_6 A_12)) ((image_669833818_state F_6) B_7)))). % Axiom fact_268_image__mono:(forall (F_5:(pname->hoare_1262092251_state)) (A_11:(pname->Prop)) (B_6:(pname->Prop)), (((ord_less_eq_pname_o A_11) B_6)->((ord_le870406270tate_o ((image_669833818_state F_5) A_11)) ((image_669833818_state F_5) B_6)))). % Axiom fact_269_subset__image__iff:(forall (B_5:(hoare_1262092251_state->Prop)) (F_4:(pname->hoare_1262092251_state)) (A_10:(pname->Prop)), ((iff ((ord_le870406270tate_o B_5) ((image_669833818_state F_4) A_10))) ((ex (pname->Prop)) (fun (AA:(pname->Prop))=> ((and ((ord_less_eq_pname_o AA) A_10)) (((eq (hoare_1262092251_state->Prop)) B_5) ((image_669833818_state F_4) AA))))))). % Axiom fact_270_domI:(forall (M:(pname->option_com)) (A_9:pname) (B_4:com), ((((eq option_com) (M A_9)) (some_com B_4))->((member_pname A_9) (dom_pname_com M)))). % Axiom fact_271_Collect__conv__if:(forall (P_3:(pname->Prop)) (A_8:pname), ((and ((P_3 A_8)->(((eq (pname->Prop)) (collect_pname (fun (X_1:pname)=> ((and (((eq pname) X_1) A_8)) (P_3 X_1))))) ((insert_pname A_8) bot_bot_pname_o)))) (((P_3 A_8)->False)->(((eq (pname->Prop)) (collect_pname (fun (X_1:pname)=> ((and (((eq pname) X_1) A_8)) (P_3 X_1))))) bot_bot_pname_o)))). % Axiom fact_272_Collect__conv__if:(forall (P_3:(hoare_1262092251_state->Prop)) (A_8:hoare_1262092251_state), ((and ((P_3 A_8)->(((eq (hoare_1262092251_state->Prop)) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> ((and (((eq hoare_1262092251_state) X_1) A_8)) (P_3 X_1))))) ((insert81609953_state A_8) bot_bo113204042tate_o)))) (((P_3 A_8)->False)->(((eq (hoare_1262092251_state->Prop)) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> ((and (((eq hoare_1262092251_state) X_1) A_8)) (P_3 X_1))))) bot_bo113204042tate_o)))). % Axiom fact_273_Collect__conv__if:(forall (P_3:((pname->Prop)->Prop)) (A_8:(pname->Prop)), ((and ((P_3 A_8)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_1:(pname->Prop))=> ((and (((eq (pname->Prop)) X_1) A_8)) (P_3 X_1))))) ((insert_pname_o A_8) bot_bot_pname_o_o)))) (((P_3 A_8)->False)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_1:(pname->Prop))=> ((and (((eq (pname->Prop)) X_1) A_8)) (P_3 X_1))))) bot_bot_pname_o_o)))). % Axiom fact_274_Collect__conv__if:(forall (P_3:((hoare_1262092251_state->Prop)->Prop)) (A_8:(hoare_1262092251_state->Prop)), ((and ((P_3 A_8)->(((eq ((hoare_1262092251_state->Prop)->Prop)) (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> ((and (((eq (hoare_1262092251_state->Prop)) X_1) A_8)) (P_3 X_1))))) ((insert1042460334tate_o A_8) bot_bo1962689075te_o_o)))) (((P_3 A_8)->False)->(((eq ((hoare_1262092251_state->Prop)->Prop)) (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> ((and (((eq (hoare_1262092251_state->Prop)) X_1) A_8)) (P_3 X_1))))) bot_bo1962689075te_o_o)))). % Axiom fact_275_Collect__conv__if2:(forall (P_2:(pname->Prop)) (A_7:pname), ((and ((P_2 A_7)->(((eq (pname->Prop)) (collect_pname (fun (X_1:pname)=> ((and (((eq pname) A_7) X_1)) (P_2 X_1))))) ((insert_pname A_7) bot_bot_pname_o)))) (((P_2 A_7)->False)->(((eq (pname->Prop)) (collect_pname (fun (X_1:pname)=> ((and (((eq pname) A_7) X_1)) (P_2 X_1))))) bot_bot_pname_o)))). % Axiom fact_276_Collect__conv__if2:(forall (P_2:(hoare_1262092251_state->Prop)) (A_7:hoare_1262092251_state), ((and ((P_2 A_7)->(((eq (hoare_1262092251_state->Prop)) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> ((and (((eq hoare_1262092251_state) A_7) X_1)) (P_2 X_1))))) ((insert81609953_state A_7) bot_bo113204042tate_o)))) (((P_2 A_7)->False)->(((eq (hoare_1262092251_state->Prop)) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> ((and (((eq hoare_1262092251_state) A_7) X_1)) (P_2 X_1))))) bot_bo113204042tate_o)))). % Axiom fact_277_Collect__conv__if2:(forall (P_2:((pname->Prop)->Prop)) (A_7:(pname->Prop)), ((and ((P_2 A_7)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_1:(pname->Prop))=> ((and (((eq (pname->Prop)) A_7) X_1)) (P_2 X_1))))) ((insert_pname_o A_7) bot_bot_pname_o_o)))) (((P_2 A_7)->False)->(((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_1:(pname->Prop))=> ((and (((eq (pname->Prop)) A_7) X_1)) (P_2 X_1))))) bot_bot_pname_o_o)))). % Axiom fact_278_Collect__conv__if2:(forall (P_2:((hoare_1262092251_state->Prop)->Prop)) (A_7:(hoare_1262092251_state->Prop)), ((and ((P_2 A_7)->(((eq ((hoare_1262092251_state->Prop)->Prop)) (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> ((and (((eq (hoare_1262092251_state->Prop)) A_7) X_1)) (P_2 X_1))))) ((insert1042460334tate_o A_7) bot_bo1962689075te_o_o)))) (((P_2 A_7)->False)->(((eq ((hoare_1262092251_state->Prop)->Prop)) (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> ((and (((eq (hoare_1262092251_state->Prop)) A_7) X_1)) (P_2 X_1))))) bot_bo1962689075te_o_o)))). % Axiom fact_279_singleton__conv:(forall (A_6:pname), (((eq (pname->Prop)) (collect_pname (fun (X_1:pname)=> (((eq pname) X_1) A_6)))) ((insert_pname A_6) bot_bot_pname_o))). % Axiom fact_280_singleton__conv:(forall (A_6:hoare_1262092251_state), (((eq (hoare_1262092251_state->Prop)) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) A_6)))) ((insert81609953_state A_6) bot_bo113204042tate_o))). % Axiom fact_281_singleton__conv:(forall (A_6:(pname->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fun (X_1:(pname->Prop))=> (((eq (pname->Prop)) X_1) A_6)))) ((insert_pname_o A_6) bot_bot_pname_o_o))). % Axiom fact_282_singleton__conv:(forall (A_6:(hoare_1262092251_state->Prop)), (((eq ((hoare_1262092251_state->Prop)->Prop)) (collec313158217tate_o (fun (X_1:(hoare_1262092251_state->Prop))=> (((eq (hoare_1262092251_state->Prop)) X_1) A_6)))) ((insert1042460334tate_o A_6) bot_bo1962689075te_o_o))). % Axiom fact_283_singleton__conv2:(forall (A_5:pname), (((eq (pname->Prop)) (collect_pname (fequal_pname A_5))) ((insert_pname A_5) bot_bot_pname_o))). % Axiom fact_284_singleton__conv2:(forall (A_5:hoare_1262092251_state), (((eq (hoare_1262092251_state->Prop)) (collec1121927558_state (fequal1925511196_state A_5))) ((insert81609953_state A_5) bot_bo113204042tate_o))). % Axiom fact_285_singleton__conv2:(forall (A_5:(pname->Prop)), (((eq ((pname->Prop)->Prop)) (collect_pname_o (fequal_pname_o A_5))) ((insert_pname_o A_5) bot_bot_pname_o_o))). % Axiom fact_286_singleton__conv2:(forall (A_5:(hoare_1262092251_state->Prop)), (((eq ((hoare_1262092251_state->Prop)->Prop)) (collec313158217tate_o (fequal1529404211tate_o A_5))) ((insert1042460334tate_o A_5) bot_bo1962689075te_o_o))). % Axiom fact_287_MGF__lemma1:(forall (C_1:com) (G:(hoare_1262092251_state->Prop)), (hoare_1821564147gleton->((forall (X_1:pname), (((member_pname X_1) (dom_pname_com body))->((hoare_930741239_state G) ((insert81609953_state (hoare_Mirabelle_MGT (body_1 X_1))) bot_bo113204042tate_o))))->((wt C_1)->((hoare_930741239_state G) ((insert81609953_state (hoare_Mirabelle_MGT C_1)) bot_bo113204042tate_o)))))). % Axiom fact_288_WT__bodiesD:(forall (Pn_1:pname) (B_3:com), (wT_bodies->((((eq option_com) (body Pn_1)) (some_com B_3))->(wt B_3)))). % Axiom fact_289_imageE:(forall (B_2:hoare_1262092251_state) (F_3:(pname->hoare_1262092251_state)) (A_4:(pname->Prop)), (((member5164104_state B_2) ((image_669833818_state F_3) A_4))->((forall (X_1:pname), ((((eq hoare_1262092251_state) B_2) (F_3 X_1))->(((member_pname X_1) A_4)->False)))->False))). % Axiom fact_290_finite__subset__induct:(forall (P_1:((pname->Prop)->Prop)) (A_2:(pname->Prop)) (F_1:(pname->Prop)), ((finite_finite_pname F_1)->(((ord_less_eq_pname_o F_1) A_2)->((P_1 bot_bot_pname_o)->((forall (A_3:pname) (F_2:(pname->Prop)), ((finite_finite_pname F_2)->(((member_pname A_3) A_2)->((((member_pname A_3) F_2)->False)->((P_1 F_2)->(P_1 ((insert_pname A_3) F_2)))))))->(P_1 F_1)))))). % Axiom fact_291_finite__subset__induct:(forall (P_1:((hoare_1262092251_state->Prop)->Prop)) (A_2:(hoare_1262092251_state->Prop)) (F_1:(hoare_1262092251_state->Prop)), ((finite1178804552_state F_1)->(((ord_le870406270tate_o F_1) A_2)->((P_1 bot_bo113204042tate_o)->((forall (A_3:hoare_1262092251_state) (F_2:(hoare_1262092251_state->Prop)), ((finite1178804552_state F_2)->(((member5164104_state A_3) A_2)->((((member5164104_state A_3) F_2)->False)->((P_1 F_2)->(P_1 ((insert81609953_state A_3) F_2)))))))->(P_1 F_1)))))). % Axiom fact_292_finite__subset__induct:(forall (P_1:(((pname->Prop)->Prop)->Prop)) (A_2:((pname->Prop)->Prop)) (F_1:((pname->Prop)->Prop)), ((finite297249702name_o F_1)->(((ord_le1205211808me_o_o F_1) A_2)->((P_1 bot_bot_pname_o_o)->((forall (A_3:(pname->Prop)) (F_2:((pname->Prop)->Prop)), ((finite297249702name_o F_2)->(((member_pname_o A_3) A_2)->((((member_pname_o A_3) F_2)->False)->((P_1 F_2)->(P_1 ((insert_pname_o A_3) F_2)))))))->(P_1 F_1)))))). % Axiom fact_293_finite__subset__induct:(forall (P_1:(((hoare_1262092251_state->Prop)->Prop)->Prop)) (A_2:((hoare_1262092251_state->Prop)->Prop)) (F_1:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o F_1)->(((ord_le2012720639te_o_o F_1) A_2)->((P_1 bot_bo1962689075te_o_o)->((forall (A_3:(hoare_1262092251_state->Prop)) (F_2:((hoare_1262092251_state->Prop)->Prop)), ((finite1423311111tate_o F_2)->(((member907417095tate_o A_3) A_2)->((((member907417095tate_o A_3) F_2)->False)->((P_1 F_2)->(P_1 ((insert1042460334tate_o A_3) F_2)))))))->(P_1 F_1)))))). % Axiom fact_294_WTs__elim__cases_I7_J:(forall (P:pname), ((wt (body_1 P))->((forall (Y_1:com), (not (((eq option_com) (body P)) (some_com Y_1))))->False))). % Axiom fact_295_subsetI:(forall (B_1:(pname->Prop)) (A_1:(pname->Prop)), ((forall (X_1:pname), (((member_pname X_1) A_1)->((member_pname X_1) B_1)))->((ord_less_eq_pname_o A_1) B_1))). % Axiom fact_296_subsetI:(forall (B_1:(hoare_1262092251_state->Prop)) (A_1:(hoare_1262092251_state->Prop)), ((forall (X_1:hoare_1262092251_state), (((member5164104_state X_1) A_1)->((member5164104_state X_1) B_1)))->((ord_le870406270tate_o A_1) B_1))). % Axiom fact_297_finite__subset__image:(forall (F:(pname->hoare_1262092251_state)) (A:(pname->Prop)) (B:(hoare_1262092251_state->Prop)), ((finite1178804552_state B)->(((ord_le870406270tate_o B) ((image_669833818_state F) A))->((ex (pname->Prop)) (fun (C:(pname->Prop))=> ((and ((and ((ord_less_eq_pname_o C) A)) (finite_finite_pname C))) (((eq (hoare_1262092251_state->Prop)) B) ((image_669833818_state F) C)))))))). % Axiom fact_298_finite__dom__body:(finite_finite_pname (dom_pname_com body)). % Axiom fact_299_com_Osimps_I6_J:(forall (Pname_1:pname) (Pname:pname), ((iff (((eq com) (body_1 Pname_1)) (body_1 Pname))) (((eq pname) Pname_1) Pname))). % Axiom help_fequal_1_1_fequal_000tc__Com__Opname_T:(forall (X:pname) (Y:pname), ((or (((fequal_pname X) Y)->False)) (((eq pname) X) Y))). % Axiom help_fequal_2_1_fequal_000tc__Com__Opname_T:(forall (X:pname) (Y:pname), ((or (not (((eq pname) X) Y))) ((fequal_pname X) Y))). % Axiom help_fequal_1_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T:(forall (X:(pname->Prop)) (Y:(pname->Prop)), ((or (((fequal_pname_o X) Y)->False)) (((eq (pname->Prop)) X) Y))). % Axiom help_fequal_2_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T:(forall (X:(pname->Prop)) (Y:(pname->Prop)), ((or (not (((eq (pname->Prop)) X) Y))) ((fequal_pname_o X) Y))). % Axiom help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com:(forall (X:hoare_1262092251_state) (Y:hoare_1262092251_state), ((or (((fequal1925511196_state X) Y)->False)) (((eq hoare_1262092251_state) X) Y))). % Axiom help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_Itc__Com:(forall (X:hoare_1262092251_state) (Y:hoare_1262092251_state), ((or (not (((eq hoare_1262092251_state) X) Y))) ((fequal1925511196_state X) Y))). % Axiom help_fequal_1_1_fequal_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It:(forall (X:(hoare_1262092251_state->Prop)) (Y:(hoare_1262092251_state->Prop)), ((or (((fequal1529404211tate_o X) Y)->False)) (((eq (hoare_1262092251_state->Prop)) X) Y))). % Axiom help_fequal_2_1_fequal_000_062_Itc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It:(forall (X:(hoare_1262092251_state->Prop)) (Y:(hoare_1262092251_state->Prop)), ((or (not (((eq (hoare_1262092251_state->Prop)) X) Y))) ((fequal1529404211tate_o X) Y))). % Axiom conj_0:hoare_1821564147gleton. % Axiom conj_1:wT_bodies. % Axiom conj_2:(finite1178804552_state fa). % Axiom conj_3:(((member5164104_state (hoare_Mirabelle_MGT y)) fa)->False). % Axiom conj_4:((ord_le870406270tate_o fa) ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (the_com (body Pn))))) (dom_pname_com body))). % Axiom conj_5:(((eq option_com) (body pn)) (some_com y)). % Axiom conj_6:((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa). % Trying to prove ((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) % Found conj_0:hoare_1821564147gleton % Found conj_0 as proof of hoare_1821564147gleton % Found conj_6:((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa) % Instantiate: G_3:=fa:(hoare_1262092251_state->Prop) % Found conj_6 as proof of ((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) G_3) % Found conj_6:((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa) % Instantiate: G_3:=fa:(hoare_1262092251_state->Prop) % Found conj_6 as proof of ((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) G_3) % Found conj_6:((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa) % Instantiate: Ts_4:=fa:(hoare_1262092251_state->Prop) % Found conj_6 as proof of ((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) Ts_4) % Found fact_209_subset__refl0:=(fact_209_subset__refl ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)):((ord_le870406270tate_o ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) % Found (fact_209_subset__refl ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) as proof of ((ord_le870406270tate_o ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) Ts_4) % Found (fact_209_subset__refl ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) as proof of ((ord_le870406270tate_o ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) Ts_4) % Found (fact_209_subset__refl ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) as proof of ((ord_le870406270tate_o ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) Ts_4) % Found conj_1:wT_bodies % Found conj_1 as proof of wT_bodies % Found conj_1:wT_bodies % Found conj_1 as proof of wT_bodies % Found conj_1:wT_bodies % Found conj_1 as proof of wT_bodies % Found conj_0:hoare_1821564147gleton % Found conj_0 as proof of hoare_1821564147gleton % Found conj_1:wT_bodies % Found conj_1 as proof of wT_bodies % Found conj_6:((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa) % Instantiate: Ts_4:=fa:(hoare_1262092251_state->Prop) % Found conj_6 as proof of ((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) Ts_4) % Found fact_209_subset__refl0:=(fact_209_subset__refl G_5):((ord_le870406270tate_o G_5) G_5) % Found (fact_209_subset__refl G_5) as proof of ((ord_le870406270tate_o G_5) ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) % Found (fact_209_subset__refl G_5) as proof of ((ord_le870406270tate_o G_5) ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) % Found (fact_209_subset__refl G_5) as proof of ((ord_le870406270tate_o G_5) ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) % Found fact_209_subset__refl0:=(fact_209_subset__refl (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))):((ord_le870406270tate_o (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) % Found (fact_209_subset__refl (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) as proof of ((ord_le870406270tate_o (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) Ts_4) % Found (fact_209_subset__refl (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) as proof of ((ord_le870406270tate_o (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) Ts_4) % Found (fact_209_subset__refl (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) as proof of ((ord_le870406270tate_o (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) Ts_4) % Found fact_209_subset__refl0:=(fact_209_subset__refl G_5):((ord_le870406270tate_o G_5) G_5) % Found (fact_209_subset__refl G_5) as proof of ((ord_le870406270tate_o G_5) ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) % Found (fact_209_subset__refl G_5) as proof of ((ord_le870406270tate_o G_5) ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) % Found (fact_209_subset__refl G_5) as proof of ((ord_le870406270tate_o G_5) ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) % Found conj_6:((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa) % Instantiate: G_3:=fa:(hoare_1262092251_state->Prop) % Found conj_6 as proof of ((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) G_3) % Found conj_6:((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa) % Instantiate: G_3:=fa:(hoare_1262092251_state->Prop) % Found conj_6 as proof of ((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) G_3) % Found conj_6:((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa) % Instantiate: G_3:=fa:(hoare_1262092251_state->Prop) % Found conj_6 as proof of ((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) G_3) % Found conj_6:((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa) % Instantiate: G_3:=fa:(hoare_1262092251_state->Prop) % Found conj_6 as proof of ((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) G_3) % Found conj_6:((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa) % Instantiate: G_3:=fa:(hoare_1262092251_state->Prop) % Found conj_6 as proof of ((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) G_3) % Found conj_6:((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa) % Instantiate: Ts_4:=fa:(hoare_1262092251_state->Prop) % Found conj_6 as proof of ((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) Ts_4) % Found fact_209_subset__refl0:=(fact_209_subset__refl (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y)))))):((ord_le870406270tate_o (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y)))))) (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y)))))) % Found (fact_209_subset__refl (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y)))))) as proof of ((ord_le870406270tate_o (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y)))))) Ts_4) % Found (fact_209_subset__refl (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y)))))) as proof of ((ord_le870406270tate_o (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y)))))) Ts_4) % Found (fact_209_subset__refl (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y)))))) as proof of ((ord_le870406270tate_o (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y)))))) Ts_4) % Found fact_209_subset__refl0:=(fact_209_subset__refl (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))):((ord_le870406270tate_o (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) % Found (fact_209_subset__refl (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) as proof of ((ord_le870406270tate_o (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) G_3) % Found (fact_209_subset__refl (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) as proof of ((ord_le870406270tate_o (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) G_3) % Found (fact_209_subset__refl (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) as proof of ((ord_le870406270tate_o (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) G_3) % Found (fact_1_asm00 (fact_209_subset__refl (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y)))))) as proof of ((hoare_930741239_state G_3) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) % Found ((fact_1_asm0 G_3) (fact_209_subset__refl (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y)))))) as proof of ((hoare_930741239_state G_3) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) % Found (((fact_1_asm (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) G_3) (fact_209_subset__refl (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y)))))) as proof of ((hoare_930741239_state G_3) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) % Found (((fact_1_asm (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) G_3) (fact_209_subset__refl (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y)))))) as proof of ((hoare_930741239_state G_3) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) % Found conj_6:((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa) % Instantiate: G_3:=fa:(hoare_1262092251_state->Prop) % Found conj_6 as proof of ((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) G_3) % Found fact_33_empty__subsetI0:=(fact_33_empty__subsetI ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))):((ord_le870406270tate_o bot_bo113204042tate_o) ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) % Found (fact_33_empty__subsetI ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) as proof of ((ord_le870406270tate_o G_5) ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) % Found (fact_33_empty__subsetI ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) as proof of ((ord_le870406270tate_o G_5) ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) % Found (fact_33_empty__subsetI ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) as proof of ((ord_le870406270tate_o G_5) ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) % Found fact_209_subset__refl0:=(fact_209_subset__refl B_26):((ord_le870406270tate_o B_26) B_26) % Found (fact_209_subset__refl B_26) as proof of ((ord_le870406270tate_o B_26) ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) % Found (fact_209_subset__refl B_26) as proof of ((ord_le870406270tate_o B_26) ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) % Found (fact_209_subset__refl B_26) as proof of ((ord_le870406270tate_o B_26) ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) % Found fact_209_subset__refl0:=(fact_209_subset__refl (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))):((ord_le870406270tate_o (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) % Found (fact_209_subset__refl (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) as proof of ((ord_le870406270tate_o (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) B_26) % Found (fact_209_subset__refl (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) as proof of ((ord_le870406270tate_o (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) B_26) % Found (fact_209_subset__refl (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) as proof of ((ord_le870406270tate_o (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) B_26) % Found conj_6:((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa) % Instantiate: G_3:=fa:(hoare_1262092251_state->Prop) % Found conj_6 as proof of ((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) G_3) % Found fact_209_subset__refl0:=(fact_209_subset__refl ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)):((ord_le870406270tate_o ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) % Found (fact_209_subset__refl ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) as proof of ((ord_le870406270tate_o ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) G_3) % Found (fact_209_subset__refl ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) as proof of ((ord_le870406270tate_o ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) G_3) % Found (fact_209_subset__refl ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) as proof of ((ord_le870406270tate_o ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) G_3) % Found (fact_1_asm00 (fact_209_subset__refl ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o))) as proof of ((hoare_930741239_state G_3) ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) % Found ((fact_1_asm0 G_3) (fact_209_subset__refl ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o))) as proof of ((hoare_930741239_state G_3) ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) % Found (((fact_1_asm ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) G_3) (fact_209_subset__refl ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o))) as proof of ((hoare_930741239_state G_3) ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) % Found (((fact_1_asm ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) G_3) (fact_209_subset__refl ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o))) as proof of ((hoare_930741239_state G_3) ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) % Found fact_209_subset__refl0:=(fact_209_subset__refl (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))):((ord_le870406270tate_o (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) % Found (fact_209_subset__refl (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) as proof of ((ord_le870406270tate_o (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) G_5) % Found (fact_209_subset__refl (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) as proof of ((ord_le870406270tate_o (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) G_5) % Found (fact_209_subset__refl (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) as proof of ((ord_le870406270tate_o (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) G_5) % Found (fact_1_asm00 (fact_209_subset__refl (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y)))))) as proof of ((hoare_930741239_state G_5) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) % Found ((fact_1_asm0 G_5) (fact_209_subset__refl (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y)))))) as proof of ((hoare_930741239_state G_5) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) % Found (((fact_1_asm (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) G_5) (fact_209_subset__refl (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y)))))) as proof of ((hoare_930741239_state G_5) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) % Found (((fact_1_asm (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) G_5) (fact_209_subset__refl (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y)))))) as proof of ((hoare_930741239_state G_5) (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))) % Found conj_0:hoare_1821564147gleton % Found conj_0 as proof of hoare_1821564147gleton % Found conj_1:wT_bodies % Found conj_1 as proof of wT_bodies % Found conj_1:wT_bodies % Found conj_1 as proof of wT_bodies % Found conj_1:wT_bodies % Found conj_1 as proof of wT_bodies % Found conj_6:((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa) % Instantiate: G_3:=fa:(hoare_1262092251_state->Prop) % Found conj_6 as proof of ((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) G_3) % Found conj_0:hoare_1821564147gleton % Found conj_0 as proof of hoare_1821564147gleton % Found conj_0:hoare_1821564147gleton % Found conj_0 as proof of hoare_1821564147gleton % Found conj_0:hoare_1821564147gleton % Found conj_0 as proof of hoare_1821564147gleton % Found fact_0_empty0:=(fact_0_empty ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))):((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) bot_bo113204042tate_o) % Found (fact_0_empty ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) as proof of ((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) bot_bo113204042tate_o) % Found (fact_0_empty ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) as proof of ((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) bot_bo113204042tate_o) % Found fact_209_subset__refl0:=(fact_209_subset__refl ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)):((ord_le870406270tate_o ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) % Found (fact_209_subset__refl ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) as proof of ((ord_le870406270tate_o ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) A_2) % Found (fact_209_subset__refl ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) as proof of ((ord_le870406270tate_o ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) A_2) % Found (fact_209_subset__refl ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) as proof of ((ord_le870406270tate_o ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) A_2) % Found conj_6:((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa) % Instantiate: Ts_4:=fa:(hoare_1262092251_state->Prop) % Found conj_6 as proof of ((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) Ts_4) % Found conj_1:wT_bodies % Found conj_1 as proof of wT_bodies % Found conj_0:hoare_1821564147gleton % Found conj_0 as proof of hoare_1821564147gleton % Found conj_6:((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa) % Instantiate: G_3:=fa:(hoare_1262092251_state->Prop) % Found conj_6 as proof of ((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) G_3) % Found fact_209_subset__refl0:=(fact_209_subset__refl (collec1121927558_state (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))))):((ord_le870406270tate_o (collec1121927558_state (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))))) (collec1121927558_state (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))))) % Found (fact_209_subset__refl (collec1121927558_state (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))))) as proof of ((ord_le870406270tate_o (collec1121927558_state (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))))) Ts_4) % Found (fact_209_subset__refl (collec1121927558_state (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))))) as proof of ((ord_le870406270tate_o (collec1121927558_state (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))))) Ts_4) % Found (fact_209_subset__refl (collec1121927558_state (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))))) as proof of ((ord_le870406270tate_o (collec1121927558_state (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))))) Ts_4) % Found conj_6:((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) fa) % Instantiate: Ts_4:=fa:(hoare_1262092251_state->Prop) % Found conj_6 as proof of ((hoare_930741239_state ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) Ts_4) % Found fact_209_subset__refl0:=(fact_209_subset__refl ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)):((ord_le870406270tate_o ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) % Found (fact_209_subset__refl ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) as proof of ((ord_le870406270tate_o ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) B_26) % Found (fact_209_subset__refl ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) as proof of ((ord_le870406270tate_o ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) B_26) % Found (fact_209_subset__refl ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) as proof of ((ord_le870406270tate_o ((insert81609953_state (hoare_Mirabelle_MGT y)) bot_bo113204042tate_o)) B_26) % Found fact_209_subset__refl0:=(fact_209_subset__refl B_26):((ord_le870406270tate_o B_26) B_26) % Found (fact_209_subset__refl B_26) as proof of ((ord_le870406270tate_o B_26) ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) % Found (fact_209_subset__refl B_26) as proof of ((ord_le870406270tate_o B_26) ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) % Found (fact_209_subset__refl B_26) as proof of ((ord_le870406270tate_o B_26) ((image_669833818_state (fun (Pn:pname)=> (hoare_Mirabelle_MGT (body_1 Pn)))) (dom_pname_com body))) % Found fact_209_subset__refl0:=(fact_209_subset__refl (collec1121927558_state (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))))):((ord_le870406270tate_o (collec1121927558_state (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))))) (collec1121927558_state (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))))) % Found (fact_209_subset__refl (collec1121927558_state (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))))) as proof of ((ord_le870406270tate_o (collec1121927558_state (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))))) Ts_4) % Found (fact_209_subset__refl (collec1121927558_state (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))))) as proof of ((ord_le870406270tate_o (collec1121927558_state (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))))) Ts_4) % Found (fact_209_subset__refl (collec1121927558_state (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))))) as proof of ((ord_le870406270tate_o (collec1121927558_state (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y))))))) Ts_4) % Found fact_209_subset__refl0:=(fact_209_subset__refl (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y)))))):((ord_le870406270tate_o (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y)))))) (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y)))))) % Found (fact_209_subset__refl (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y)))))) as proof of ((ord_le870406270tate_o (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y)))))) G_3) % Found (fact_209_subset__refl (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y)))))) as proof of ((ord_le870406270tate_o (collec1121927558_state (collec1121927558_state (fun (X_1:hoare_1262092251_state)=> (((eq hoare_1262092251_state) X_1) (hoare_Mirabelle_MGT y)))))) G_3) % Found (fact_209_subset__refl (collec1121927558_state (collec1121927558_state (fun ( % EOF %------------------------------------------------------------------------------