%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : ITP093^1 : TPTP v7.5.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% DateTime : Sun Mar 21 13:24:09 EDT 2021

% Result   : Unknown 0.90s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ITP093^1 : TPTP v7.5.0. Released v7.5.0.
% 0.07/0.12  % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.33  % Computer : n013.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit : 300
% 0.14/0.33  % DateTime : Fri Mar 19 05:41:17 EDT 2021
% 0.14/0.33  % CPUTime  : 
% 0.14/0.34  ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.14/0.35  Python 2.7.5
% 0.38/0.61  Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.38/0.61  FOF formula (<kernel.Constant object at 0xf6f2d8>, <kernel.Type object at 0xf6f098>) of role type named ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring set_Pr1295299783od_a_a:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0xf6af38>, <kernel.Type object at 0xf6f6c8>) of role type named ty_n_t__Pair____Digraph__Opair____pre____digraph__Opair____pre____digraph____ext_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J_Mt__Product____Type__Ounit_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring pair_p1593840546t_unit:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0xf6f638>, <kernel.Type object at 0xf6f758>) of role type named ty_n_t__Pair____Digraph__Opair____pre____digraph__Opair____pre____digraph____ext_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Ounit_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring pair_p2041852168t_unit:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0xf6f098>, <kernel.Type object at 0xf6f128>) of role type named ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring set_Pr1490359111at_nat:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0xf6f6c8>, <kernel.Type object at 0xf6f758>) of role type named ty_n_t__Pair____Digraph__Opair____pre____digraph__Opair____pre____digraph____ext_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Ounit_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring pair_p1765063010t_unit:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0xf6fd88>, <kernel.Type object at 0x2b74e81c7878>) of role type named ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring set_se958357159od_a_a:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0xf6f128>, <kernel.Type object at 0x2b74e81c7878>) of role type named ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring set_Pr1948701895od_a_a:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0xf6f758>, <kernel.Type object at 0x2b74e81c76c8>) of role type named ty_n_t__Pair____Digraph__Opair____pre____digraph__Opair____pre____digraph____ext_It__Nat__Onat_Mt__Product____Type__Ounit_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring pair_p1914262621t_unit:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0xf6f248>, <kernel.Type object at 0x2b74e81c7e60>) of role type named ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring set_Pr1746169692at_nat:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0xf6f758>, <kernel.Type object at 0x2b74e81c7e18>) of role type named ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring produc1572603623od_a_a:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0xf6f128>, <kernel.Type object at 0x2b74e81c7ea8>) of role type named ty_n_t__Pair____Digraph__Opair____pre____digraph__Opair____pre____digraph____ext_Itf__a_Mt__Product____Type__Ounit_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring pair_p125712459t_unit:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0xf6f758>, <kernel.Type object at 0x2b74e81c7b90>) of role type named ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring set_Pr7688842at_nat:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0xf6f758>, <kernel.Type object at 0x2b74e81c7c20>) of role type named ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Nat__Onat_J_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring set_Pr894832732_a_nat:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0x2b74e81c7ea8>, <kernel.Type object at 0x2b74e81c72d8>) of role type named ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring set_Pr339609346od_a_a:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0x2b74e81c7b90>, <kernel.Type object at 0x2b74e81c7998>) of role type named ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring set_Pr681306928od_a_a:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0x2b74e81c7c20>, <kernel.Type object at 0x2b74e81c7758>) of role type named ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mtf__a_J_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring set_Pr1689873822_a_a_a:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0x2b74e81c72d8>, <kernel.Type object at 0x2b74e81c7998>) of role type named ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring set_se1612935105at_nat:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0x2b74e81c7e18>, <kernel.Type object at 0x10d2fc8>) of role type named ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring set_se1596668135od_a_a:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0x2b74e81c7758>, <kernel.Type object at 0x10d2fc8>) of role type named ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring set_Pr1986765409at_nat:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0x2b74e81c7998>, <kernel.Type object at 0x10d2f80>) of role type named ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mt__Nat__Onat_J_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring set_Pr548851891_a_nat:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0x2b74e81c7200>, <kernel.Type object at 0x10d2f38>) of role type named ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mtf__a_J_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring set_Pr967348953_nat_a:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0x2b74e81c7998>, <kernel.Type object at 0x10d2e60>) of role type named ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring set_Product_prod_a_a:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0x2b74e81c7758>, <kernel.Type object at 0x10d2ea8>) of role type named ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring product_prod_nat_nat:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0x2b74e81c7998>, <kernel.Type object at 0x10d2dd0>) of role type named ty_n_t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring set_set_nat:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0x2b74e81c7998>, <kernel.Type object at 0x10d2e18>) of role type named ty_n_t__Product____Type__Oprod_Itf__a_Mtf__a_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring product_prod_a_a:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0x10d2ea8>, <kernel.Type object at 0x10d2d40>) of role type named ty_n_t__Set__Oset_It__Set__Oset_Itf__a_J_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring set_set_a:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0x10d2f80>, <kernel.Type object at 0x10d2e18>) of role type named ty_n_t__Set__Oset_It__Nat__Onat_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring set_nat:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0x10d2dd0>, <kernel.Type object at 0x10d2c20>) of role type named ty_n_t__Product____Type__Ounit
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring product_unit:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0x10d2d40>, <kernel.Type object at 0x10d2f80>) of role type named ty_n_t__Set__Oset_Itf__a_J
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring set_a:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0x10d2b90>, <kernel.Type object at 0x10d2bd8>) of role type named ty_n_t__Nat__Onat
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring nat:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0x10d2c20>, <kernel.Type object at 0x10d2e18>) of role type named ty_n_tf__a
% 0.38/0.61  Using role type
% 0.38/0.61  Declaring a:Type
% 0.38/0.61  FOF formula (<kernel.Constant object at 0x10d2c68>, <kernel.DependentProduct object at 0x10d2a28>) of role type named sy_c_Finite__Set_OFpow_001t__Nat__Onat
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite_Fpow_nat:(set_nat->set_set_nat)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d2a70>, <kernel.DependentProduct object at 0x10d2950>) of role type named sy_c_Finite__Set_OFpow_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite361944167at_nat:(set_Pr1986765409at_nat->set_se1612935105at_nat)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d2b00>, <kernel.DependentProduct object at 0x10d2998>) of role type named sy_c_Finite__Set_OFpow_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite702915405od_a_a:(set_Pr1948701895od_a_a->set_se958357159od_a_a)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d2a28>, <kernel.DependentProduct object at 0x10d28c0>) of role type named sy_c_Finite__Set_OFpow_001t__Product____Type__Oprod_Itf__a_Mtf__a_J
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite351630733od_a_a:(set_Product_prod_a_a->set_se1596668135od_a_a)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d2e60>, <kernel.DependentProduct object at 0x10d2830>) of role type named sy_c_Finite__Set_OFpow_001tf__a
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite_Fpow_a:(set_a->set_set_a)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d2950>, <kernel.DependentProduct object at 0x10d2878>) of role type named sy_c_Finite__Set_Ocard_001tf__a
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite_card_a:(set_a->nat)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d2b00>, <kernel.DependentProduct object at 0x10d2a28>) of role type named sy_c_Finite__Set_Ofinite_001t__Nat__Onat
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite_finite_nat:(set_nat->Prop)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d2e60>, <kernel.DependentProduct object at 0x10d2998>) of role type named sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite772653738at_nat:(set_Pr1986765409at_nat->Prop)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d2950>, <kernel.DependentProduct object at 0x10d2710>) of role type named sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite277291581at_nat:(set_Pr1746169692at_nat->Prop)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d2a28>, <kernel.DependentProduct object at 0x10d2758>) of role type named sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite1297454819od_a_a:(set_Pr339609346od_a_a->Prop)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d2998>, <kernel.DependentProduct object at 0x10d2680>) of role type named sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Nat__Onat_Mtf__a_J
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite1808550458_nat_a:(set_Pr967348953_nat_a->Prop)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d2710>, <kernel.DependentProduct object at 0x10d26c8>) of role type named sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite48957584at_nat:(set_Pr1490359111at_nat->Prop)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d2758>, <kernel.DependentProduct object at 0x10d25f0>) of role type named sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J_Mt__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite256329232od_a_a:(set_Pr1295299783od_a_a->Prop)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d2680>, <kernel.DependentProduct object at 0x10d2638>) of role type named sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Nat__Onat_J
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite1837575485_a_nat:(set_Pr894832732_a_nat->Prop)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d26c8>, <kernel.DependentProduct object at 0x10d2560>) of role type named sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite1664988688od_a_a:(set_Pr1948701895od_a_a->Prop)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d25f0>, <kernel.DependentProduct object at 0x10d25a8>) of role type named sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mtf__a_J
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite1919032935_a_a_a:(set_Pr1689873822_a_a_a->Prop)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d2638>, <kernel.DependentProduct object at 0x10d24d0>) of role type named sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_Itf__a_Mt__Nat__Onat_J
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite1743148308_a_nat:(set_Pr548851891_a_nat->Prop)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d2560>, <kernel.DependentProduct object at 0x10d2518>) of role type named sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite942416723at_nat:(set_Pr7688842at_nat->Prop)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d25a8>, <kernel.DependentProduct object at 0x10d2440>) of role type named sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite676513017od_a_a:(set_Pr681306928od_a_a->Prop)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d24d0>, <kernel.DependentProduct object at 0x10d2488>) of role type named sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_Itf__a_Mtf__a_J
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite179568208od_a_a:(set_Product_prod_a_a->Prop)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d2518>, <kernel.DependentProduct object at 0x10d23b0>) of role type named sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Nat__Onat_J
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite2012248349et_nat:(set_set_nat->Prop)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d2440>, <kernel.DependentProduct object at 0x10d23f8>) of role type named sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite1457549322at_nat:(set_se1612935105at_nat->Prop)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d2488>, <kernel.DependentProduct object at 0x10d2320>) of role type named sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite323969008od_a_a:(set_se958357159od_a_a->Prop)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d23b0>, <kernel.DependentProduct object at 0x10d2368>) of role type named sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite1145471536od_a_a:(set_se1596668135od_a_a->Prop)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d23f8>, <kernel.DependentProduct object at 0x10d2290>) of role type named sy_c_Finite__Set_Ofinite_001t__Set__Oset_Itf__a_J
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite_finite_set_a:(set_set_a->Prop)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d2b90>, <kernel.DependentProduct object at 0x10d2200>) of role type named sy_c_Finite__Set_Ofinite_001tf__a
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring finite_finite_a:(set_a->Prop)
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d2830>, <kernel.Constant object at 0x10d2b90>) of role type named sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring bot_bot_set_nat:set_nat
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d2200>, <kernel.Constant object at 0x10d2b90>) of role type named sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J
% 0.38/0.62  Using role type
% 0.38/0.62  Declaring bot_bo2130386637at_nat:set_Pr1986765409at_nat
% 0.38/0.62  FOF formula (<kernel.Constant object at 0x10d23f8>, <kernel.Constant object at 0x10d2b90>) of role type named sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J
% 0.38/0.62  Using role type
% 0.47/0.62  Declaring bot_bo2131659635od_a_a:set_Product_prod_a_a
% 0.47/0.62  FOF formula (<kernel.Constant object at 0x10d2830>, <kernel.Constant object at 0x10d2b90>) of role type named sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J
% 0.47/0.62  Using role type
% 0.47/0.62  Declaring bot_bot_set_a:set_a
% 0.47/0.62  FOF formula (<kernel.Constant object at 0x10d2200>, <kernel.DependentProduct object at 0x10d20e0>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Nat__Onat_M_Eo_J
% 0.47/0.62  Using role type
% 0.47/0.62  Declaring ord_less_eq_nat_o:((nat->Prop)->((nat->Prop)->Prop))
% 0.47/0.62  FOF formula (<kernel.Constant object at 0x10d2170>, <kernel.DependentProduct object at 0x10d2128>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Product____Type__Oprod_Itf__a_Mtf__a_J_M_Eo_J
% 0.47/0.62  Using role type
% 0.47/0.62  Declaring ord_le1347718902_a_a_o:((product_prod_a_a->Prop)->((product_prod_a_a->Prop)->Prop))
% 0.47/0.62  FOF formula (<kernel.Constant object at 0x10d2050>, <kernel.DependentProduct object at 0x10d20e0>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001_062_Itf__a_M_Eo_J
% 0.47/0.62  Using role type
% 0.47/0.62  Declaring ord_less_eq_a_o:((a->Prop)->((a->Prop)->Prop))
% 0.47/0.62  FOF formula (<kernel.Constant object at 0x10d23f8>, <kernel.DependentProduct object at 0x10d2128>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat
% 0.47/0.62  Using role type
% 0.47/0.62  Declaring ord_less_eq_nat:(nat->(nat->Prop))
% 0.47/0.62  FOF formula (<kernel.Constant object at 0x10d2248>, <kernel.DependentProduct object at 0x2b74e81e4098>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J
% 0.47/0.62  Using role type
% 0.47/0.62  Declaring ord_less_eq_set_nat:(set_nat->(set_nat->Prop))
% 0.47/0.62  FOF formula (<kernel.Constant object at 0x10d20e0>, <kernel.DependentProduct object at 0x2b74e81e4d88>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J
% 0.47/0.62  Using role type
% 0.47/0.62  Declaring ord_le841296385at_nat:(set_Pr1986765409at_nat->(set_Pr1986765409at_nat->Prop))
% 0.47/0.62  FOF formula (<kernel.Constant object at 0x10d2050>, <kernel.DependentProduct object at 0x2b74e81e4248>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J
% 0.47/0.62  Using role type
% 0.47/0.62  Declaring ord_le2084554594od_a_a:(set_Pr339609346od_a_a->(set_Pr339609346od_a_a->Prop))
% 0.47/0.62  FOF formula (<kernel.Constant object at 0x10d2248>, <kernel.DependentProduct object at 0x2b74e81e4f80>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mtf__a_J_J
% 0.47/0.62  Using role type
% 0.47/0.62  Declaring ord_le344568633_nat_a:(set_Pr967348953_nat_a->(set_Pr967348953_nat_a->Prop))
% 0.47/0.62  FOF formula (<kernel.Constant object at 0x10d20e0>, <kernel.DependentProduct object at 0x2b74e81e45a8>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Nat__Onat_J_J
% 0.47/0.62  Using role type
% 0.47/0.62  Declaring ord_le492294332_a_nat:(set_Pr894832732_a_nat->(set_Pr894832732_a_nat->Prop))
% 0.47/0.62  FOF formula (<kernel.Constant object at 0x10d2248>, <kernel.DependentProduct object at 0x10d2050>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J
% 0.47/0.62  Using role type
% 0.47/0.62  Declaring ord_le456379495od_a_a:(set_Pr1948701895od_a_a->(set_Pr1948701895od_a_a->Prop))
% 0.47/0.62  FOF formula (<kernel.Constant object at 0x10d20e0>, <kernel.DependentProduct object at 0x1206b48>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mtf__a_J_J
% 0.47/0.62  Using role type
% 0.47/0.62  Declaring ord_le677315902_a_a_a:(set_Pr1689873822_a_a_a->(set_Pr1689873822_a_a_a->Prop))
% 0.47/0.62  FOF formula (<kernel.Constant object at 0x10d2050>, <kernel.DependentProduct object at 0x1206ab8>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mt__Nat__Onat_J_J
% 0.47/0.62  Using role type
% 0.47/0.62  Declaring ord_le2073555219_a_nat:(set_Pr548851891_a_nat->(set_Pr548851891_a_nat->Prop))
% 0.47/0.63  FOF formula (<kernel.Constant object at 0x10d2050>, <kernel.DependentProduct object at 0x1206d40>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring ord_le1816232656od_a_a:(set_Pr681306928od_a_a->(set_Pr681306928od_a_a->Prop))
% 0.47/0.63  FOF formula (<kernel.Constant object at 0x2b74e81e45a8>, <kernel.DependentProduct object at 0x1206b00>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring ord_le1824328871od_a_a:(set_Product_prod_a_a->(set_Product_prod_a_a->Prop))
% 0.47/0.63  FOF formula (<kernel.Constant object at 0x2b74e81e4d88>, <kernel.DependentProduct object at 0x12069e0>) of role type named sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring ord_less_eq_set_a:(set_a->(set_a->Prop))
% 0.47/0.63  FOF formula (<kernel.Constant object at 0x2b74e81e45a8>, <kernel.DependentProduct object at 0x1206fc8>) of role type named sy_c_Pair__Digraph_Opair__fin__digraph_001t__Nat__Onat
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring pair_p128415500ph_nat:(pair_p1914262621t_unit->Prop)
% 0.47/0.63  FOF formula (<kernel.Constant object at 0x2b74e81e4d88>, <kernel.DependentProduct object at 0xf72cf8>) of role type named sy_c_Pair__Digraph_Opair__fin__digraph_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring pair_p752841413at_nat:(pair_p2041852168t_unit->Prop)
% 0.47/0.63  FOF formula (<kernel.Constant object at 0x2b74e81e45a8>, <kernel.DependentProduct object at 0xf72518>) of role type named sy_c_Pair__Digraph_Opair__fin__digraph_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring pair_p159207083od_a_a:(pair_p1593840546t_unit->Prop)
% 0.47/0.63  FOF formula (<kernel.Constant object at 0x2b74e81e45a8>, <kernel.DependentProduct object at 0xf72440>) of role type named sy_c_Pair__Digraph_Opair__fin__digraph_001t__Product____Type__Oprod_Itf__a_Mtf__a_J
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring pair_p374947051od_a_a:(pair_p1765063010t_unit->Prop)
% 0.47/0.63  FOF formula (<kernel.Constant object at 0x12069e0>, <kernel.DependentProduct object at 0xf72758>) of role type named sy_c_Pair__Digraph_Opair__fin__digraph_001tf__a
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring pair_p1802376898raph_a:(pair_p125712459t_unit->Prop)
% 0.47/0.63  FOF formula (<kernel.Constant object at 0x1206d40>, <kernel.DependentProduct object at 0xf72680>) of role type named sy_c_Pair__Digraph_Opair__fin__digraph__axioms_001t__Nat__Onat
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring pair_p1027063983ms_nat:(pair_p1914262621t_unit->Prop)
% 0.47/0.63  FOF formula (<kernel.Constant object at 0x1206b00>, <kernel.DependentProduct object at 0xf72b48>) of role type named sy_c_Pair__Digraph_Opair__fin__digraph__axioms_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring pair_p56914274at_nat:(pair_p2041852168t_unit->Prop)
% 0.47/0.63  FOF formula (<kernel.Constant object at 0x1206d40>, <kernel.DependentProduct object at 0xf725f0>) of role type named sy_c_Pair__Digraph_Opair__fin__digraph__axioms_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring pair_p1906342088od_a_a:(pair_p1593840546t_unit->Prop)
% 0.47/0.63  FOF formula (<kernel.Constant object at 0x1206b00>, <kernel.DependentProduct object at 0xf72560>) of role type named sy_c_Pair__Digraph_Opair__fin__digraph__axioms_001t__Product____Type__Oprod_Itf__a_Mtf__a_J
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring pair_p504738056od_a_a:(pair_p1765063010t_unit->Prop)
% 0.47/0.63  FOF formula (<kernel.Constant object at 0x1206b00>, <kernel.DependentProduct object at 0xf725a8>) of role type named sy_c_Pair__Digraph_Opair__fin__digraph__axioms_001tf__a
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring pair_p1864019935ioms_a:(pair_p125712459t_unit->Prop)
% 0.47/0.63  FOF formula (<kernel.Constant object at 0xf725f0>, <kernel.DependentProduct object at 0x10db290>) of role type named sy_c_Pair__Digraph_Opair__pre__digraph_Omore_001t__Nat__Onat_001t__Product____Type__Ounit
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring pair_p69470259t_unit:(pair_p1914262621t_unit->product_unit)
% 0.47/0.63  FOF formula (<kernel.Constant object at 0xf72560>, <kernel.DependentProduct object at 0x10db2d8>) of role type named sy_c_Pair__Digraph_Opair__pre__digraph_Omore_001t__Product____Type__Oprod_Itf__a_Mtf__a_J_001t__Product____Type__Ounit
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring pair_p1984658862t_unit:(pair_p1765063010t_unit->product_unit)
% 0.47/0.63  FOF formula (<kernel.Constant object at 0xf724d0>, <kernel.DependentProduct object at 0x10db200>) of role type named sy_c_Pair__Digraph_Opair__pre__digraph_Omore_001tf__a_001t__Product____Type__Ounit
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring pair_p1896222615t_unit:(pair_p125712459t_unit->product_unit)
% 0.47/0.63  FOF formula (<kernel.Constant object at 0xf72518>, <kernel.DependentProduct object at 0x10db290>) of role type named sy_c_Pair__Digraph_Opair__pre__digraph_Opair__pre__digraph__ext_001t__Nat__Onat_001t__Product____Type__Ounit
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring pair_p1167410509t_unit:(set_nat->(set_Pr1986765409at_nat->(product_unit->pair_p1914262621t_unit)))
% 0.47/0.63  FOF formula (<kernel.Constant object at 0xf72560>, <kernel.DependentProduct object at 0x10db170>) of role type named sy_c_Pair__Digraph_Opair__pre__digraph_Opair__pre__digraph__ext_001t__Product____Type__Oprod_Itf__a_Mtf__a_J_001t__Product____Type__Ounit
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring pair_p398687508t_unit:(set_Product_prod_a_a->(set_Pr1948701895od_a_a->(product_unit->pair_p1765063010t_unit)))
% 0.47/0.63  FOF formula (<kernel.Constant object at 0xf724d0>, <kernel.DependentProduct object at 0x10db290>) of role type named sy_c_Pair__Digraph_Opair__pre__digraph_Opair__pre__digraph__ext_001tf__a_001t__Product____Type__Ounit
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring pair_p1621517565t_unit:(set_a->(set_Product_prod_a_a->(product_unit->pair_p125712459t_unit)))
% 0.47/0.63  FOF formula (<kernel.Constant object at 0xf72560>, <kernel.DependentProduct object at 0x10db248>) of role type named sy_c_Pair__Digraph_Opair__pre__digraph_Oparcs_001t__Nat__Onat_001t__Product____Type__Ounit
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring pair_p715279805t_unit:(pair_p1914262621t_unit->set_Pr1986765409at_nat)
% 0.47/0.63  FOF formula (<kernel.Constant object at 0xf72518>, <kernel.DependentProduct object at 0x10db098>) of role type named sy_c_Pair__Digraph_Opair__pre__digraph_Oparcs_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Ounit
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring pair_p806300874t_unit:(pair_p2041852168t_unit->set_Pr1490359111at_nat)
% 0.47/0.63  FOF formula (<kernel.Constant object at 0xf72560>, <kernel.DependentProduct object at 0x10db1b8>) of role type named sy_c_Pair__Digraph_Opair__pre__digraph_Oparcs_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J_001t__Product____Type__Ounit
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring pair_p1559300324t_unit:(pair_p1593840546t_unit->set_Pr1295299783od_a_a)
% 0.47/0.63  FOF formula (<kernel.Constant object at 0xf72560>, <kernel.DependentProduct object at 0x10db0e0>) of role type named sy_c_Pair__Digraph_Opair__pre__digraph_Oparcs_001t__Product____Type__Oprod_Itf__a_Mtf__a_J_001t__Product____Type__Ounit
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring pair_p1783210148t_unit:(pair_p1765063010t_unit->set_Pr1948701895od_a_a)
% 0.47/0.63  FOF formula (<kernel.Constant object at 0x10db098>, <kernel.DependentProduct object at 0x10db368>) of role type named sy_c_Pair__Digraph_Opair__pre__digraph_Oparcs_001tf__a_001t__Product____Type__Ounit
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring pair_p133601421t_unit:(pair_p125712459t_unit->set_Product_prod_a_a)
% 0.47/0.63  FOF formula (<kernel.Constant object at 0x10db1b8>, <kernel.DependentProduct object at 0x10db3b0>) of role type named sy_c_Pair__Digraph_Opair__pre__digraph_Opverts_001t__Nat__Onat_001t__Product____Type__Ounit
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring pair_p1677060310t_unit:(pair_p1914262621t_unit->set_nat)
% 0.47/0.63  FOF formula (<kernel.Constant object at 0x10db0e0>, <kernel.DependentProduct object at 0x10db3f8>) of role type named sy_c_Pair__Digraph_Opair__pre__digraph_Opverts_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Ounit
% 0.47/0.63  Using role type
% 0.47/0.63  Declaring pair_p210955889t_unit:(pair_p2041852168t_unit->set_Pr1986765409at_nat)
% 0.47/0.63  FOF formula (<kernel.Constant object at 0x10db368>, <kernel.DependentProduct object at 0x10db440>) of role type named sy_c_Pair__Digraph_Opair__pre__digraph_Opverts_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J_001t__Product____Type__Ounit
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring pair_p1652294923t_unit:(pair_p1593840546t_unit->set_Pr1948701895od_a_a)
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db3b0>, <kernel.DependentProduct object at 0x10db488>) of role type named sy_c_Pair__Digraph_Opair__pre__digraph_Opverts_001t__Product____Type__Oprod_Itf__a_Mtf__a_J_001t__Product____Type__Ounit
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring pair_p447552203t_unit:(pair_p1765063010t_unit->set_Product_prod_a_a)
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db3f8>, <kernel.DependentProduct object at 0x10db4d0>) of role type named sy_c_Pair__Digraph_Opair__pre__digraph_Opverts_001tf__a_001t__Product____Type__Ounit
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring pair_p1047056820t_unit:(pair_p125712459t_unit->set_a)
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db440>, <kernel.DependentProduct object at 0x10db0e0>) of role type named sy_c_Pair__Digraph_Opair__wf__digraph_001t__Nat__Onat
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring pair_p1515597646ph_nat:(pair_p1914262621t_unit->Prop)
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db488>, <kernel.DependentProduct object at 0x10db518>) of role type named sy_c_Pair__Digraph_Opair__wf__digraph_001t__Product____Type__Oprod_Itf__a_Mtf__a_J
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring pair_p646030121od_a_a:(pair_p1765063010t_unit->Prop)
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db4d0>, <kernel.DependentProduct object at 0x10db560>) of role type named sy_c_Pair__Digraph_Opair__wf__digraph_001tf__a
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring pair_p68905728raph_a:(pair_p125712459t_unit->Prop)
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db0e0>, <kernel.DependentProduct object at 0x10db368>) of role type named sy_c_Product__Type_OPair_001tf__a_001tf__a
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring product_Pair_a_a:(a->(a->product_prod_a_a))
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db518>, <kernel.DependentProduct object at 0x10db6c8>) of role type named sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Nat__Onat
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring produc45129834at_nat:(set_nat->((nat->set_nat)->set_Pr1986765409at_nat))
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db560>, <kernel.DependentProduct object at 0x10db710>) of role type named sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring produc894163943at_nat:(set_nat->((nat->set_Pr1986765409at_nat)->set_Pr1746169692at_nat))
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db368>, <kernel.DependentProduct object at 0x10db758>) of role type named sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Product____Type__Oprod_Itf__a_Mtf__a_J
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring produc1182842125od_a_a:(set_nat->((nat->set_Product_prod_a_a)->set_Pr339609346od_a_a))
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db6c8>, <kernel.DependentProduct object at 0x10db7a0>) of role type named sy_c_Product__Type_OSigma_001t__Nat__Onat_001tf__a
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring product_Sigma_nat_a:(set_nat->((nat->set_a)->set_Pr967348953_nat_a))
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db710>, <kernel.DependentProduct object at 0x10db7e8>) of role type named sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_Itf__a_Mtf__a_J_001t__Nat__Onat
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring produc931712687_a_nat:(set_Product_prod_a_a->((product_prod_a_a->set_nat)->set_Pr894832732_a_nat))
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db758>, <kernel.DependentProduct object at 0x10db830>) of role type named sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_Itf__a_Mtf__a_J_001t__Product____Type__Oprod_Itf__a_Mtf__a_J
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring produc304751368od_a_a:(set_Product_prod_a_a->((product_prod_a_a->set_Product_prod_a_a)->set_Pr1948701895od_a_a))
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db7a0>, <kernel.DependentProduct object at 0x10db878>) of role type named sy_c_Product__Type_OSigma_001t__Product____Type__Oprod_Itf__a_Mtf__a_J_001tf__a
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring produc1282482655_a_a_a:(set_Product_prod_a_a->((product_prod_a_a->set_a)->set_Pr1689873822_a_a_a))
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db7e8>, <kernel.DependentProduct object at 0x10db8c0>) of role type named sy_c_Product__Type_OSigma_001tf__a_001t__Nat__Onat
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring product_Sigma_a_nat:(set_a->((a->set_nat)->set_Pr548851891_a_nat))
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db830>, <kernel.DependentProduct object at 0x10db908>) of role type named sy_c_Product__Type_OSigma_001tf__a_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring produc292491723at_nat:(set_a->((a->set_Pr1986765409at_nat)->set_Pr7688842at_nat))
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db878>, <kernel.DependentProduct object at 0x10db950>) of role type named sy_c_Product__Type_OSigma_001tf__a_001t__Product____Type__Oprod_Itf__a_Mtf__a_J
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring produc520147185od_a_a:(set_a->((a->set_Product_prod_a_a)->set_Pr681306928od_a_a))
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db8c0>, <kernel.DependentProduct object at 0x10db998>) of role type named sy_c_Product__Type_OSigma_001tf__a_001tf__a
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring product_Sigma_a_a:(set_a->((a->set_a)->set_Product_prod_a_a))
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db908>, <kernel.DependentProduct object at 0x10db488>) of role type named sy_c_Product__Type_Oprod_Ocase__prod_001tf__a_001tf__a_001_Eo
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring produc1833107820_a_a_o:((a->(a->Prop))->(product_prod_a_a->Prop))
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db7e8>, <kernel.DependentProduct object at 0x10db998>) of role type named sy_c_Product__Type_Oproduct_001tf__a_001tf__a
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring product_product_a_a:(set_a->(set_a->set_Product_prod_a_a))
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db170>, <kernel.DependentProduct object at 0x10db8c0>) of role type named sy_c_Set_OCollect_001t__Nat__Onat
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring collect_nat:((nat->Prop)->set_nat)
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db830>, <kernel.DependentProduct object at 0x10db7e8>) of role type named sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring collec7649004at_nat:((product_prod_nat_nat->Prop)->set_Pr1986765409at_nat)
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db998>, <kernel.DependentProduct object at 0x10dba70>) of role type named sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring collec1635618130od_a_a:((produc1572603623od_a_a->Prop)->set_Pr1948701895od_a_a)
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10dba28>, <kernel.DependentProduct object at 0x10dbab8>) of role type named sy_c_Set_OCollect_001t__Product____Type__Oprod_Itf__a_Mtf__a_J
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring collec645855634od_a_a:((product_prod_a_a->Prop)->set_Product_prod_a_a)
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db638>, <kernel.DependentProduct object at 0x10dbb00>) of role type named sy_c_Set_OCollect_001t__Set__Oset_It__Nat__Onat_J
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring collect_set_nat:((set_nat->Prop)->set_set_nat)
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db8c0>, <kernel.DependentProduct object at 0x10dbb48>) of role type named sy_c_Set_OCollect_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring collec1606769740at_nat:((set_Pr1986765409at_nat->Prop)->set_se1612935105at_nat)
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db1b8>, <kernel.DependentProduct object at 0x10dbb90>) of role type named sy_c_Set_OCollect_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_Itf__a_Mtf__a_J_Mt__Product____Type__Oprod_Itf__a_Mtf__a_J_J_J
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring collec453062450od_a_a:((set_Pr1948701895od_a_a->Prop)->set_se958357159od_a_a)
% 0.47/0.64  FOF formula (<kernel.Constant object at 0x10db830>, <kernel.DependentProduct object at 0x10dbbd8>) of role type named sy_c_Set_OCollect_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J
% 0.47/0.64  Using role type
% 0.47/0.64  Declaring collec183727474od_a_a:((set_Product_prod_a_a->Prop)->set_se1596668135od_a_a)
% 0.47/0.65  FOF formula (<kernel.Constant object at 0x10db998>, <kernel.DependentProduct object at 0x10dbc20>) of role type named sy_c_Set_OCollect_001t__Set__Oset_Itf__a_J
% 0.47/0.65  Using role type
% 0.47/0.65  Declaring collect_set_a:((set_a->Prop)->set_set_a)
% 0.47/0.65  FOF formula (<kernel.Constant object at 0x10dba28>, <kernel.DependentProduct object at 0x10dbc68>) of role type named sy_c_Set_OCollect_001tf__a
% 0.47/0.65  Using role type
% 0.47/0.65  Declaring collect_a:((a->Prop)->set_a)
% 0.47/0.65  FOF formula (<kernel.Constant object at 0x10db638>, <kernel.DependentProduct object at 0x10db830>) of role type named sy_c_member_001t__Nat__Onat
% 0.47/0.65  Using role type
% 0.47/0.65  Declaring member_nat:(nat->(set_nat->Prop))
% 0.47/0.65  FOF formula (<kernel.Constant object at 0x10db8c0>, <kernel.DependentProduct object at 0x10db9e0>) of role type named sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J
% 0.47/0.65  Using role type
% 0.47/0.65  Declaring member701585322at_nat:(product_prod_nat_nat->(set_Pr1986765409at_nat->Prop))
% 0.47/0.65  FOF formula (<kernel.Constant object at 0x10dbc68>, <kernel.DependentProduct object at 0x10db998>) of role type named sy_c_member_001t__Product____Type__Oprod_Itf__a_Mtf__a_J
% 0.47/0.65  Using role type
% 0.47/0.65  Declaring member449909584od_a_a:(product_prod_a_a->(set_Product_prod_a_a->Prop))
% 0.47/0.65  FOF formula (<kernel.Constant object at 0x10dbcf8>, <kernel.DependentProduct object at 0x10dba28>) of role type named sy_c_member_001t__Set__Oset_It__Nat__Onat_J
% 0.47/0.65  Using role type
% 0.47/0.65  Declaring member_set_nat:(set_nat->(set_set_nat->Prop))
% 0.47/0.65  FOF formula (<kernel.Constant object at 0x10dbd40>, <kernel.DependentProduct object at 0x10db638>) of role type named sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mtf__a_J_J
% 0.47/0.65  Using role type
% 0.47/0.65  Declaring member1838126896od_a_a:(set_Product_prod_a_a->(set_se1596668135od_a_a->Prop))
% 0.47/0.65  FOF formula (<kernel.Constant object at 0x10db998>, <kernel.DependentProduct object at 0x10db8c0>) of role type named sy_c_member_001t__Set__Oset_Itf__a_J
% 0.47/0.65  Using role type
% 0.47/0.65  Declaring member_set_a:(set_a->(set_set_a->Prop))
% 0.47/0.65  FOF formula (<kernel.Constant object at 0x10dbdd0>, <kernel.DependentProduct object at 0x10dbc68>) of role type named sy_c_member_001tf__a
% 0.47/0.65  Using role type
% 0.47/0.65  Declaring member_a:(a->(set_a->Prop))
% 0.47/0.65  FOF formula (<kernel.Constant object at 0x10db638>, <kernel.Constant object at 0x10dbc68>) of role type named sy_v_G
% 0.47/0.65  Using role type
% 0.47/0.65  Declaring g:pair_p125712459t_unit
% 0.47/0.65  FOF formula (<kernel.Constant object at 0x10db998>, <kernel.Constant object at 0x10dbc68>) of role type named sy_v_n
% 0.47/0.65  Using role type
% 0.47/0.65  Declaring n:nat
% 0.47/0.65  FOF formula (finite179568208od_a_a ((product_Sigma_a_a (pair_p1047056820t_unit g)) (fun (Uu:a)=> (pair_p1047056820t_unit g)))) of role axiom named fact_0__092_060open_062finite_A_Ipverts_AG_A_092_060times_062_Apverts_AG_J_092_060close_062
% 0.47/0.65  A new axiom: (finite179568208od_a_a ((product_Sigma_a_a (pair_p1047056820t_unit g)) (fun (Uu:a)=> (pair_p1047056820t_unit g))))
% 0.47/0.65  FOF formula ((ord_le1824328871od_a_a (pair_p133601421t_unit g)) ((product_Sigma_a_a (pair_p1047056820t_unit g)) (fun (Uu:a)=> (pair_p1047056820t_unit g)))) of role axiom named fact_1__092_060open_062parcs_AG_A_092_060subseteq_062_Apverts_AG_A_092_060times_062_Apverts_AG_092_060close_062
% 0.47/0.65  A new axiom: ((ord_le1824328871od_a_a (pair_p133601421t_unit g)) ((product_Sigma_a_a (pair_p1047056820t_unit g)) (fun (Uu:a)=> (pair_p1047056820t_unit g))))
% 0.47/0.65  FOF formula (((eq (pair_p2041852168t_unit->Prop)) pair_p56914274at_nat) (fun (G:pair_p2041852168t_unit)=> ((and (finite772653738at_nat (pair_p210955889t_unit G))) (finite48957584at_nat (pair_p806300874t_unit G))))) of role axiom named fact_2_pair__fin__digraph__axioms__def
% 0.47/0.65  A new axiom: (((eq (pair_p2041852168t_unit->Prop)) pair_p56914274at_nat) (fun (G:pair_p2041852168t_unit)=> ((and (finite772653738at_nat (pair_p210955889t_unit G))) (finite48957584at_nat (pair_p806300874t_unit G)))))
% 0.47/0.65  FOF formula (((eq (pair_p1593840546t_unit->Prop)) pair_p1906342088od_a_a) (fun (G:pair_p1593840546t_unit)=> ((and (finite1664988688od_a_a (pair_p1652294923t_unit G))) (finite256329232od_a_a (pair_p1559300324t_unit G))))) of role axiom named fact_3_pair__fin__digraph__axioms__def
% 0.47/0.65  A new axiom: (((eq (pair_p1593840546t_unit->Prop)) pair_p1906342088od_a_a) (fun (G:pair_p1593840546t_unit)=> ((and (finite1664988688od_a_a (pair_p1652294923t_unit G))) (finite256329232od_a_a (pair_p1559300324t_unit G)))))
% 0.47/0.65  FOF formula (((eq (pair_p1765063010t_unit->Prop)) pair_p504738056od_a_a) (fun (G:pair_p1765063010t_unit)=> ((and (finite179568208od_a_a (pair_p447552203t_unit G))) (finite1664988688od_a_a (pair_p1783210148t_unit G))))) of role axiom named fact_4_pair__fin__digraph__axioms__def
% 0.47/0.65  A new axiom: (((eq (pair_p1765063010t_unit->Prop)) pair_p504738056od_a_a) (fun (G:pair_p1765063010t_unit)=> ((and (finite179568208od_a_a (pair_p447552203t_unit G))) (finite1664988688od_a_a (pair_p1783210148t_unit G)))))
% 0.47/0.65  FOF formula (((eq (pair_p1914262621t_unit->Prop)) pair_p1027063983ms_nat) (fun (G:pair_p1914262621t_unit)=> ((and (finite_finite_nat (pair_p1677060310t_unit G))) (finite772653738at_nat (pair_p715279805t_unit G))))) of role axiom named fact_5_pair__fin__digraph__axioms__def
% 0.47/0.65  A new axiom: (((eq (pair_p1914262621t_unit->Prop)) pair_p1027063983ms_nat) (fun (G:pair_p1914262621t_unit)=> ((and (finite_finite_nat (pair_p1677060310t_unit G))) (finite772653738at_nat (pair_p715279805t_unit G)))))
% 0.47/0.65  FOF formula (((eq (pair_p125712459t_unit->Prop)) pair_p1864019935ioms_a) (fun (G:pair_p125712459t_unit)=> ((and (finite_finite_a (pair_p1047056820t_unit G))) (finite179568208od_a_a (pair_p133601421t_unit G))))) of role axiom named fact_6_pair__fin__digraph__axioms__def
% 0.47/0.65  A new axiom: (((eq (pair_p125712459t_unit->Prop)) pair_p1864019935ioms_a) (fun (G:pair_p125712459t_unit)=> ((and (finite_finite_a (pair_p1047056820t_unit G))) (finite179568208od_a_a (pair_p133601421t_unit G)))))
% 0.47/0.65  FOF formula (forall (G2:pair_p2041852168t_unit), ((finite772653738at_nat (pair_p210955889t_unit G2))->((finite48957584at_nat (pair_p806300874t_unit G2))->(pair_p56914274at_nat G2)))) of role axiom named fact_7_pair__fin__digraph__axioms_Ointro
% 0.47/0.65  A new axiom: (forall (G2:pair_p2041852168t_unit), ((finite772653738at_nat (pair_p210955889t_unit G2))->((finite48957584at_nat (pair_p806300874t_unit G2))->(pair_p56914274at_nat G2))))
% 0.47/0.65  FOF formula (forall (G2:pair_p1593840546t_unit), ((finite1664988688od_a_a (pair_p1652294923t_unit G2))->((finite256329232od_a_a (pair_p1559300324t_unit G2))->(pair_p1906342088od_a_a G2)))) of role axiom named fact_8_pair__fin__digraph__axioms_Ointro
% 0.47/0.65  A new axiom: (forall (G2:pair_p1593840546t_unit), ((finite1664988688od_a_a (pair_p1652294923t_unit G2))->((finite256329232od_a_a (pair_p1559300324t_unit G2))->(pair_p1906342088od_a_a G2))))
% 0.47/0.65  FOF formula (forall (G2:pair_p1765063010t_unit), ((finite179568208od_a_a (pair_p447552203t_unit G2))->((finite1664988688od_a_a (pair_p1783210148t_unit G2))->(pair_p504738056od_a_a G2)))) of role axiom named fact_9_pair__fin__digraph__axioms_Ointro
% 0.47/0.65  A new axiom: (forall (G2:pair_p1765063010t_unit), ((finite179568208od_a_a (pair_p447552203t_unit G2))->((finite1664988688od_a_a (pair_p1783210148t_unit G2))->(pair_p504738056od_a_a G2))))
% 0.47/0.65  FOF formula (forall (G2:pair_p1914262621t_unit), ((finite_finite_nat (pair_p1677060310t_unit G2))->((finite772653738at_nat (pair_p715279805t_unit G2))->(pair_p1027063983ms_nat G2)))) of role axiom named fact_10_pair__fin__digraph__axioms_Ointro
% 0.47/0.65  A new axiom: (forall (G2:pair_p1914262621t_unit), ((finite_finite_nat (pair_p1677060310t_unit G2))->((finite772653738at_nat (pair_p715279805t_unit G2))->(pair_p1027063983ms_nat G2))))
% 0.47/0.65  FOF formula (forall (G2:pair_p125712459t_unit), ((finite_finite_a (pair_p1047056820t_unit G2))->((finite179568208od_a_a (pair_p133601421t_unit G2))->(pair_p1864019935ioms_a G2)))) of role axiom named fact_11_pair__fin__digraph__axioms_Ointro
% 0.47/0.65  A new axiom: (forall (G2:pair_p125712459t_unit), ((finite_finite_a (pair_p1047056820t_unit G2))->((finite179568208od_a_a (pair_p133601421t_unit G2))->(pair_p1864019935ioms_a G2))))
% 0.47/0.65  FOF formula (forall (G2:pair_p1914262621t_unit), ((pair_p128415500ph_nat G2)->(finite772653738at_nat (pair_p715279805t_unit G2)))) of role axiom named fact_12_pair__fin__digraph_Opair__finite__arcs
% 0.47/0.65  A new axiom: (forall (G2:pair_p1914262621t_unit), ((pair_p128415500ph_nat G2)->(finite772653738at_nat (pair_p715279805t_unit G2))))
% 0.47/0.67  FOF formula (forall (G2:pair_p1765063010t_unit), ((pair_p374947051od_a_a G2)->(finite1664988688od_a_a (pair_p1783210148t_unit G2)))) of role axiom named fact_13_pair__fin__digraph_Opair__finite__arcs
% 0.47/0.67  A new axiom: (forall (G2:pair_p1765063010t_unit), ((pair_p374947051od_a_a G2)->(finite1664988688od_a_a (pair_p1783210148t_unit G2))))
% 0.47/0.67  FOF formula (forall (G2:pair_p125712459t_unit), ((pair_p1802376898raph_a G2)->(finite179568208od_a_a (pair_p133601421t_unit G2)))) of role axiom named fact_14_pair__fin__digraph_Opair__finite__arcs
% 0.47/0.67  A new axiom: (forall (G2:pair_p125712459t_unit), ((pair_p1802376898raph_a G2)->(finite179568208od_a_a (pair_p133601421t_unit G2))))
% 0.47/0.67  FOF formula (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), (((ord_le841296385at_nat A) B)->((finite772653738at_nat B)->(finite772653738at_nat A)))) of role axiom named fact_15_finite__subset
% 0.47/0.67  A new axiom: (forall (A:set_Pr1986765409at_nat) (B:set_Pr1986765409at_nat), (((ord_le841296385at_nat A) B)->((finite772653738at_nat B)->(finite772653738at_nat A))))
% 0.47/0.67  FOF formula (forall (A:set_Pr1948701895od_a_a) (B:set_Pr1948701895od_a_a), (((ord_le456379495od_a_a A) B)->((finite1664988688od_a_a B)->(finite1664988688od_a_a A)))) of role axiom named fact_16_finite__subset
% 0.47/0.67  A new axiom: (forall (A:set_Pr1948701895od_a_a) (B:set_Pr1948701895od_a_a), (((ord_le456379495od_a_a A) B)->((finite1664988688od_a_a B)->(finite1664988688od_a_a A))))
% 0.47/0.67  FOF formula (forall (A:set_a) (B:set_a), (((ord_less_eq_set_a A) B)->((finite_finite_a B)->(finite_finite_a A)))) of role axiom named fact_17_finite__subset
% 0.47/0.67  A new axiom: (forall (A:set_a) (B:set_a), (((ord_less_eq_set_a A) B)->((finite_finite_a B)->(finite_finite_a A))))
% 0.47/0.67  FOF formula (forall (A:set_nat) (B:set_nat), (((ord_less_eq_set_nat A) B)->((finite_finite_nat B)->(finite_finite_nat A)))) of role axiom named fact_18_finite__subset
% 0.47/0.67  A new axiom: (forall (A:set_nat) (B:set_nat), (((ord_less_eq_set_nat A) B)->((finite_finite_nat B)->(finite_finite_nat A))))
% 0.47/0.67  FOF formula (forall (A:set_Product_prod_a_a) (B:set_Product_prod_a_a), (((ord_le1824328871od_a_a A) B)->((finite179568208od_a_a B)->(finite179568208od_a_a A)))) of role axiom named fact_19_finite__subset
% 0.47/0.67  A new axiom: (forall (A:set_Product_prod_a_a) (B:set_Product_prod_a_a), (((ord_le1824328871od_a_a A) B)->((finite179568208od_a_a B)->(finite179568208od_a_a A))))
% 0.47/0.67  FOF formula (forall (S:set_Pr1986765409at_nat) (T:set_Pr1986765409at_nat), (((ord_le841296385at_nat S) T)->(((finite772653738at_nat S)->False)->((finite772653738at_nat T)->False)))) of role axiom named fact_20_infinite__super
% 0.47/0.67  A new axiom: (forall (S:set_Pr1986765409at_nat) (T:set_Pr1986765409at_nat), (((ord_le841296385at_nat S) T)->(((finite772653738at_nat S)->False)->((finite772653738at_nat T)->False))))
% 0.47/0.67  FOF formula (forall (S:set_Pr1948701895od_a_a) (T:set_Pr1948701895od_a_a), (((ord_le456379495od_a_a S) T)->(((finite1664988688od_a_a S)->False)->((finite1664988688od_a_a T)->False)))) of role axiom named fact_21_infinite__super
% 0.47/0.67  A new axiom: (forall (S:set_Pr1948701895od_a_a) (T:set_Pr1948701895od_a_a), (((ord_le456379495od_a_a S) T)->(((finite1664988688od_a_a S)->False)->((finite1664988688od_a_a T)->False))))
% 0.47/0.67  FOF formula (forall (S:set_a) (T:set_a), (((ord_less_eq_set_a S) T)->(((finite_finite_a S)->False)->((finite_finite_a T)->False)))) of role axiom named fact_22_infinite__super
% 0.47/0.67  A new axiom: (forall (S:set_a) (T:set_a), (((ord_less_eq_set_a S) T)->(((finite_finite_a S)->False)->((finite_finite_a T)->False))))
% 0.47/0.67  FOF formula (forall (S:set_nat) (T:set_nat), (((ord_less_eq_set_nat S) T)->(((finite_finite_nat S)->False)->((finite_finite_nat T)->False)))) of role axiom named fact_23_infinite__super
% 0.47/0.67  A new axiom: (forall (S:set_nat) (T:set_nat), (((ord_less_eq_set_nat S) T)->(((finite_finite_nat S)->False)->((finite_finite_nat T)->False))))
% 0.47/0.67  FOF formula (forall (S:set_Product_prod_a_a) (T:set_Product_prod_a_a), (((ord_le1824328871od_a_a S) T)->(((finite179568208od_a_a S)->False)->((finite179568208od_a_a T)->False)))) of role axiom named fact_24_infinite__super
% 0.47/0.68  A new axiom: (forall (S:set_Product_prod_a_a) (T:set_Product_prod_a_a), (((ord_le1824328871od_a_a S) T)->(((finite179568208od_a_a S)->False)->((finite179568208od_a_a T)->False))))
% 0.47/0.68  FOF formula (forall (B:set_Pr1986765409at_nat) (A:set_Pr1986765409at_nat), ((finite772653738at_nat B)->(((ord_le841296385at_nat A) B)->(finite772653738at_nat A)))) of role axiom named fact_25_rev__finite__subset
% 0.47/0.68  A new axiom: (forall (B:set_Pr1986765409at_nat) (A:set_Pr1986765409at_nat), ((finite772653738at_nat B)->(((ord_le841296385at_nat A) B)->(finite772653738at_nat A))))
% 0.47/0.68  FOF formula (forall (B:set_Pr1948701895od_a_a) (A:set_Pr1948701895od_a_a), ((finite1664988688od_a_a B)->(((ord_le456379495od_a_a A) B)->(finite1664988688od_a_a A)))) of role axiom named fact_26_rev__finite__subset
% 0.47/0.68  A new axiom: (forall (B:set_Pr1948701895od_a_a) (A:set_Pr1948701895od_a_a), ((finite1664988688od_a_a B)->(((ord_le456379495od_a_a A) B)->(finite1664988688od_a_a A))))
% 0.47/0.68  FOF formula (forall (B:set_Product_prod_a_a) (A:set_Product_prod_a_a), ((finite179568208od_a_a B)->(((ord_le1824328871od_a_a A) B)->(finite179568208od_a_a A)))) of role axiom named fact_27_rev__finite__subset
% 0.47/0.68  A new axiom: (forall (B:set_Product_prod_a_a) (A:set_Product_prod_a_a), ((finite179568208od_a_a B)->(((ord_le1824328871od_a_a A) B)->(finite179568208od_a_a A))))
% 0.47/0.68  FOF formula (forall (B:set_nat) (A:set_nat), ((finite_finite_nat B)->(((ord_less_eq_set_nat A) B)->(finite_finite_nat A)))) of role axiom named fact_28_rev__finite__subset
% 0.47/0.68  A new axiom: (forall (B:set_nat) (A:set_nat), ((finite_finite_nat B)->(((ord_less_eq_set_nat A) B)->(finite_finite_nat A))))
% 0.47/0.68  FOF formula (forall (B:set_a) (A:set_a), ((finite_finite_a B)->(((ord_less_eq_set_a A) B)->(finite_finite_a A)))) of role axiom named fact_29_rev__finite__subset
% 0.47/0.68  A new axiom: (forall (B:set_a) (A:set_a), ((finite_finite_a B)->(((ord_less_eq_set_a A) B)->(finite_finite_a A))))
% 0.47/0.68  FOF formula (forall (A:set_se1596668135od_a_a) (A2:set_Product_prod_a_a), ((finite1145471536od_a_a A)->(((member1838126896od_a_a A2) A)->((ex set_Product_prod_a_a) (fun (X:set_Product_prod_a_a)=> ((and ((and ((member1838126896od_a_a X) A)) ((ord_le1824328871od_a_a A2) X))) (forall (Xa:set_Product_prod_a_a), (((member1838126896od_a_a Xa) A)->(((ord_le1824328871od_a_a X) Xa)->(((eq set_Product_prod_a_a) X) Xa)))))))))) of role axiom named fact_30_finite__has__maximal2
% 0.47/0.68  A new axiom: (forall (A:set_se1596668135od_a_a) (A2:set_Product_prod_a_a), ((finite1145471536od_a_a A)->(((member1838126896od_a_a A2) A)->((ex set_Product_prod_a_a) (fun (X:set_Product_prod_a_a)=> ((and ((and ((member1838126896od_a_a X) A)) ((ord_le1824328871od_a_a A2) X))) (forall (Xa:set_Product_prod_a_a), (((member1838126896od_a_a Xa) A)->(((ord_le1824328871od_a_a X) Xa)->(((eq set_Product_prod_a_a) X) Xa))))))))))
% 0.47/0.68  FOF formula (forall (A:set_nat) (A2:nat), ((finite_finite_nat A)->(((member_nat A2) A)->((ex nat) (fun (X:nat)=> ((and ((and ((member_nat X) A)) ((ord_less_eq_nat A2) X))) (forall (Xa:nat), (((member_nat Xa) A)->(((ord_less_eq_nat X) Xa)->(((eq nat) X) Xa)))))))))) of role axiom named fact_31_finite__has__maximal2
% 0.47/0.68  A new axiom: (forall (A:set_nat) (A2:nat), ((finite_finite_nat A)->(((member_nat A2) A)->((ex nat) (fun (X:nat)=> ((and ((and ((member_nat X) A)) ((ord_less_eq_nat A2) X))) (forall (Xa:nat), (((member_nat Xa) A)->(((ord_less_eq_nat X) Xa)->(((eq nat) X) Xa))))))))))
% 0.47/0.68  FOF formula (forall (A:set_set_nat) (A2:set_nat), ((finite2012248349et_nat A)->(((member_set_nat A2) A)->((ex set_nat) (fun (X:set_nat)=> ((and ((and ((member_set_nat X) A)) ((ord_less_eq_set_nat A2) X))) (forall (Xa:set_nat), (((member_set_nat Xa) A)->(((ord_less_eq_set_nat X) Xa)->(((eq set_nat) X) Xa)))))))))) of role axiom named fact_32_finite__has__maximal2
% 0.47/0.68  A new axiom: (forall (A:set_set_nat) (A2:set_nat), ((finite2012248349et_nat A)->(((member_set_nat A2) A)->((ex set_nat) (fun (X:set_nat)=> ((and ((and ((member_set_nat X) A)) ((ord_less_eq_set_nat A2) X))) (forall (Xa:set_nat), (((member_set_nat Xa) A)->(((ord_less_eq_set_nat X) Xa)->(((eq set_nat) X) Xa))))))))))
% 0.47/0.68  FOF formula (forall (A:set_set_a) (A2:set_a), ((finite_finite_set_a A)->(((member_set_a A2) A)->((ex set_a) (fun (X:set_a)=> ((and ((and ((member_set_a X) A)) ((ord_less_eq_set_a A2) X))) (forall (Xa:set_a), (((member_set_a Xa) A)->(((ord_less_eq_set_a X) Xa)->(((eq set_a) X) Xa)))))))))) of role axiom named fact_33_finite__has__maximal2
% 0.53/0.69  A new axiom: (forall (A:set_set_a) (A2:set_a), ((finite_finite_set_a A)->(((member_set_a A2) A)->((ex set_a) (fun (X:set_a)=> ((and ((and ((member_set_a X) A)) ((ord_less_eq_set_a A2) X))) (forall (Xa:set_a), (((member_set_a Xa) A)->(((ord_less_eq_set_a X) Xa)->(((eq set_a) X) Xa))))))))))
% 0.53/0.69  FOF formula (forall (P:(product_prod_a_a->Prop)) (Q:(product_prod_a_a->Prop)), (((or (finite179568208od_a_a (collec645855634od_a_a P))) (finite179568208od_a_a (collec645855634od_a_a Q)))->(finite179568208od_a_a (collec645855634od_a_a (fun (X2:product_prod_a_a)=> ((and (P X2)) (Q X2))))))) of role axiom named fact_34_finite__Collect__conjI
% 0.53/0.69  A new axiom: (forall (P:(product_prod_a_a->Prop)) (Q:(product_prod_a_a->Prop)), (((or (finite179568208od_a_a (collec645855634od_a_a P))) (finite179568208od_a_a (collec645855634od_a_a Q)))->(finite179568208od_a_a (collec645855634od_a_a (fun (X2:product_prod_a_a)=> ((and (P X2)) (Q X2)))))))
% 0.53/0.69  FOF formula (forall (P:(a->Prop)) (Q:(a->Prop)), (((or (finite_finite_a (collect_a P))) (finite_finite_a (collect_a Q)))->(finite_finite_a (collect_a (fun (X2:a)=> ((and (P X2)) (Q X2))))))) of role axiom named fact_35_finite__Collect__conjI
% 0.53/0.69  A new axiom: (forall (P:(a->Prop)) (Q:(a->Prop)), (((or (finite_finite_a (collect_a P))) (finite_finite_a (collect_a Q)))->(finite_finite_a (collect_a (fun (X2:a)=> ((and (P X2)) (Q X2)))))))
% 0.53/0.69  FOF formula (forall (P:(nat->Prop)) (Q:(nat->Prop)), (((or (finite_finite_nat (collect_nat P))) (finite_finite_nat (collect_nat Q)))->(finite_finite_nat (collect_nat (fun (X2:nat)=> ((and (P X2)) (Q X2))))))) of role axiom named fact_36_finite__Collect__conjI
% 0.53/0.69  A new axiom: (forall (P:(nat->Prop)) (Q:(nat->Prop)), (((or (finite_finite_nat (collect_nat P))) (finite_finite_nat (collect_nat Q)))->(finite_finite_nat (collect_nat (fun (X2:nat)=> ((and (P X2)) (Q X2)))))))
% 0.53/0.69  FOF formula (forall (P:(product_prod_nat_nat->Prop)) (Q:(product_prod_nat_nat->Prop)), (((or (finite772653738at_nat (collec7649004at_nat P))) (finite772653738at_nat (collec7649004at_nat Q)))->(finite772653738at_nat (collec7649004at_nat (fun (X2:product_prod_nat_nat)=> ((and (P X2)) (Q X2))))))) of role axiom named fact_37_finite__Collect__conjI
% 0.53/0.69  A new axiom: (forall (P:(product_prod_nat_nat->Prop)) (Q:(product_prod_nat_nat->Prop)), (((or (finite772653738at_nat (collec7649004at_nat P))) (finite772653738at_nat (collec7649004at_nat Q)))->(finite772653738at_nat (collec7649004at_nat (fun (X2:product_prod_nat_nat)=> ((and (P X2)) (Q X2)))))))
% 0.53/0.69  FOF formula (forall (P:(produc1572603623od_a_a->Prop)) (Q:(produc1572603623od_a_a->Prop)), (((or (finite1664988688od_a_a (collec1635618130od_a_a P))) (finite1664988688od_a_a (collec1635618130od_a_a Q)))->(finite1664988688od_a_a (collec1635618130od_a_a (fun (X2:produc1572603623od_a_a)=> ((and (P X2)) (Q X2))))))) of role axiom named fact_38_finite__Collect__conjI
% 0.53/0.69  A new axiom: (forall (P:(produc1572603623od_a_a->Prop)) (Q:(produc1572603623od_a_a->Prop)), (((or (finite1664988688od_a_a (collec1635618130od_a_a P))) (finite1664988688od_a_a (collec1635618130od_a_a Q)))->(finite1664988688od_a_a (collec1635618130od_a_a (fun (X2:produc1572603623od_a_a)=> ((and (P X2)) (Q X2)))))))
% 0.53/0.69  FOF formula (forall (P:(product_prod_a_a->Prop)) (Q:(product_prod_a_a->Prop)), (((eq Prop) (finite179568208od_a_a (collec645855634od_a_a (fun (X2:product_prod_a_a)=> ((or (P X2)) (Q X2)))))) ((and (finite179568208od_a_a (collec645855634od_a_a P))) (finite179568208od_a_a (collec645855634od_a_a Q))))) of role axiom named fact_39_finite__Collect__disjI
% 0.53/0.69  A new axiom: (forall (P:(product_prod_a_a->Prop)) (Q:(product_prod_a_a->Prop)), (((eq Prop) (finite179568208od_a_a (collec645855634od_a_a (fun (X2:product_prod_a_a)=> ((or (P X2)) (Q X2)))))) ((and (finite179568208od_a_a (collec645855634od_a_a P))) (finite179568208od_a_a (collec645855634od_a_a Q)))))
% 0.53/0.70  FOF formula (forall (P:(a->Prop)) (Q:(a->Prop)), (((eq Prop) (finite_finite_a (collect_a (fun (X2:a)=> ((or (P X2)) (Q X2)))))) ((and (finite_finite_a (collect_a P))) (finite_finite_a (collect_a Q))))) of role axiom named fact_40_finite__Collect__disjI
% 0.53/0.70  A new axiom: (forall (P:(a->Prop)) (Q:(a->Prop)), (((eq Prop) (finite_finite_a (collect_a (fun (X2:a)=> ((or (P X2)) (Q X2)))))) ((and (finite_finite_a (collect_a P))) (finite_finite_a (collect_a Q)))))
% 0.53/0.70  FOF formula (forall (P:(nat->Prop)) (Q:(nat->Prop)), (((eq Prop) (finite_finite_nat (collect_nat (fun (X2:nat)=> ((or (P X2)) (Q X2)))))) ((and (finite_finite_nat (collect_nat P))) (finite_finite_nat (collect_nat Q))))) of role axiom named fact_41_finite__Collect__disjI
% 0.53/0.70  A new axiom: (forall (P:(nat->Prop)) (Q:(nat->Prop)), (((eq Prop) (finite_finite_nat (collect_nat (fun (X2:nat)=> ((or (P X2)) (Q X2)))))) ((and (finite_finite_nat (collect_nat P))) (finite_finite_nat (collect_nat Q)))))
% 0.53/0.70  FOF formula (forall (P:(product_prod_nat_nat->Prop)) (Q:(product_prod_nat_nat->Prop)), (((eq Prop) (finite772653738at_nat (collec7649004at_nat (fun (X2:product_prod_nat_nat)=> ((or (P X2)) (Q X2)))))) ((and (finite772653738at_nat (collec7649004at_nat P))) (finite772653738at_nat (collec7649004at_nat Q))))) of role axiom named fact_42_finite__Collect__disjI
% 0.53/0.70  A new axiom: (forall (P:(product_prod_nat_nat->Prop)) (Q:(product_prod_nat_nat->Prop)), (((eq Prop) (finite772653738at_nat (collec7649004at_nat (fun (X2:product_prod_nat_nat)=> ((or (P X2)) (Q X2)))))) ((and (finite772653738at_nat (collec7649004at_nat P))) (finite772653738at_nat (collec7649004at_nat Q)))))
% 0.53/0.70  FOF formula (forall (P:(produc1572603623od_a_a->Prop)) (Q:(produc1572603623od_a_a->Prop)), (((eq Prop) (finite1664988688od_a_a (collec1635618130od_a_a (fun (X2:produc1572603623od_a_a)=> ((or (P X2)) (Q X2)))))) ((and (finite1664988688od_a_a (collec1635618130od_a_a P))) (finite1664988688od_a_a (collec1635618130od_a_a Q))))) of role axiom named fact_43_finite__Collect__disjI
% 0.53/0.70  A new axiom: (forall (P:(produc1572603623od_a_a->Prop)) (Q:(produc1572603623od_a_a->Prop)), (((eq Prop) (finite1664988688od_a_a (collec1635618130od_a_a (fun (X2:produc1572603623od_a_a)=> ((or (P X2)) (Q X2)))))) ((and (finite1664988688od_a_a (collec1635618130od_a_a P))) (finite1664988688od_a_a (collec1635618130od_a_a Q)))))
% 0.53/0.70  FOF formula (forall (A:set_Pr1986765409at_nat), ((finite772653738at_nat A)->(finite1457549322at_nat (collec1606769740at_nat (fun (B2:set_Pr1986765409at_nat)=> ((ord_le841296385at_nat B2) A)))))) of role axiom named fact_44_finite__Collect__subsets
% 0.53/0.70  A new axiom: (forall (A:set_Pr1986765409at_nat), ((finite772653738at_nat A)->(finite1457549322at_nat (collec1606769740at_nat (fun (B2:set_Pr1986765409at_nat)=> ((ord_le841296385at_nat B2) A))))))
% 0.53/0.70  FOF formula (forall (A:set_Pr1948701895od_a_a), ((finite1664988688od_a_a A)->(finite323969008od_a_a (collec453062450od_a_a (fun (B2:set_Pr1948701895od_a_a)=> ((ord_le456379495od_a_a B2) A)))))) of role axiom named fact_45_finite__Collect__subsets
% 0.53/0.70  A new axiom: (forall (A:set_Pr1948701895od_a_a), ((finite1664988688od_a_a A)->(finite323969008od_a_a (collec453062450od_a_a (fun (B2:set_Pr1948701895od_a_a)=> ((ord_le456379495od_a_a B2) A))))))
% 0.53/0.70  FOF formula (forall (A:set_Product_prod_a_a), ((finite179568208od_a_a A)->(finite1145471536od_a_a (collec183727474od_a_a (fun (B2:set_Product_prod_a_a)=> ((ord_le1824328871od_a_a B2) A)))))) of role axiom named fact_46_finite__Collect__subsets
% 0.53/0.70  A new axiom: (forall (A:set_Product_prod_a_a), ((finite179568208od_a_a A)->(finite1145471536od_a_a (collec183727474od_a_a (fun (B2:set_Product_prod_a_a)=> ((ord_le1824328871od_a_a B2) A))))))
% 0.53/0.70  FOF formula (forall (A:set_nat), ((finite_finite_nat A)->(finite2012248349et_nat (collect_set_nat (fun (B2:set_nat)=> ((ord_less_eq_set_nat B2) A)))))) of role axiom named fact_47_finite__Collect__subsets
% 0.53/0.70  A new axiom: (forall (A:set_nat), ((finite_finite_nat A)->(finite2012248349et_nat (collect_set_nat (fun (B2:set_nat)=> ((ord_less_eq_set_nat B2) A))))))
% 0.53/0.70  FOF formula (forall (A:set_a), ((finite_finite_a A)->(finite_finite_set_a (collect_set_a (fun (B2:set_a)=> ((ord_less_eq_set_a B2) A)))))) of role axiom named fact_48_finite__Collect__subsets
% 0.53/0.72  A new axiom: (forall (A:set_a), ((finite_finite_a A)->(finite_finite_set_a (collect_set_a (fun (B2:set_a)=> ((ord_less_eq_set_a B2) A))))))
% 0.53/0.72  FOF formula (forall (A:set_a) (B:(a->set_nat)), ((finite_finite_a A)->((forall (A3:a), (((member_a A3) A)->(finite_finite_nat (B A3))))->(finite1743148308_a_nat ((product_Sigma_a_nat A) B))))) of role axiom named fact_49_finite__SigmaI
% 0.53/0.72  A new axiom: (forall (A:set_a) (B:(a->set_nat)), ((finite_finite_a A)->((forall (A3:a), (((member_a A3) A)->(finite_finite_nat (B A3))))->(finite1743148308_a_nat ((product_Sigma_a_nat A) B)))))
% 0.53/0.72  FOF formula (forall (A:set_nat) (B:(nat->set_a)), ((finite_finite_nat A)->((forall (A3:nat), (((member_nat A3) A)->(finite_finite_a (B A3))))->(finite1808550458_nat_a ((product_Sigma_nat_a A) B))))) of role axiom named fact_50_finite__SigmaI
% 0.53/0.72  A new axiom: (forall (A:set_nat) (B:(nat->set_a)), ((finite_finite_nat A)->((forall (A3:nat), (((member_nat A3) A)->(finite_finite_a (B A3))))->(finite1808550458_nat_a ((product_Sigma_nat_a A) B)))))
% 0.53/0.72  FOF formula (forall (A:set_nat) (B:(nat->set_nat)), ((finite_finite_nat A)->((forall (A3:nat), (((member_nat A3) A)->(finite_finite_nat (B A3))))->(finite772653738at_nat ((produc45129834at_nat A) B))))) of role axiom named fact_51_finite__SigmaI
% 0.53/0.72  A new axiom: (forall (A:set_nat) (B:(nat->set_nat)), ((finite_finite_nat A)->((forall (A3:nat), (((member_nat A3) A)->(finite_finite_nat (B A3))))->(finite772653738at_nat ((produc45129834at_nat A) B)))))
% 0.53/0.72  FOF formula (forall (A:set_a) (B:(a->set_a)), ((finite_finite_a A)->((forall (A3:a), (((member_a A3) A)->(finite_finite_a (B A3))))->(finite179568208od_a_a ((product_Sigma_a_a A) B))))) of role axiom named fact_52_finite__SigmaI
% 0.53/0.72  A new axiom: (forall (A:set_a) (B:(a->set_a)), ((finite_finite_a A)->((forall (A3:a), (((member_a A3) A)->(finite_finite_a (B A3))))->(finite179568208od_a_a ((product_Sigma_a_a A) B)))))
% 0.53/0.72  FOF formula (forall (A:set_Product_prod_a_a) (B:(product_prod_a_a->set_a)), ((finite179568208od_a_a A)->((forall (A3:product_prod_a_a), (((member449909584od_a_a A3) A)->(finite_finite_a (B A3))))->(finite1919032935_a_a_a ((produc1282482655_a_a_a A) B))))) of role axiom named fact_53_finite__SigmaI
% 0.53/0.72  A new axiom: (forall (A:set_Product_prod_a_a) (B:(product_prod_a_a->set_a)), ((finite179568208od_a_a A)->((forall (A3:product_prod_a_a), (((member449909584od_a_a A3) A)->(finite_finite_a (B A3))))->(finite1919032935_a_a_a ((produc1282482655_a_a_a A) B)))))
% 0.53/0.72  FOF formula (forall (A:set_Product_prod_a_a) (B:(product_prod_a_a->set_nat)), ((finite179568208od_a_a A)->((forall (A3:product_prod_a_a), (((member449909584od_a_a A3) A)->(finite_finite_nat (B A3))))->(finite1837575485_a_nat ((produc931712687_a_nat A) B))))) of role axiom named fact_54_finite__SigmaI
% 0.53/0.72  A new axiom: (forall (A:set_Product_prod_a_a) (B:(product_prod_a_a->set_nat)), ((finite179568208od_a_a A)->((forall (A3:product_prod_a_a), (((member449909584od_a_a A3) A)->(finite_finite_nat (B A3))))->(finite1837575485_a_nat ((produc931712687_a_nat A) B)))))
% 0.53/0.72  FOF formula (forall (A:set_a) (B:(a->set_Product_prod_a_a)), ((finite_finite_a A)->((forall (A3:a), (((member_a A3) A)->(finite179568208od_a_a (B A3))))->(finite676513017od_a_a ((produc520147185od_a_a A) B))))) of role axiom named fact_55_finite__SigmaI
% 0.53/0.72  A new axiom: (forall (A:set_a) (B:(a->set_Product_prod_a_a)), ((finite_finite_a A)->((forall (A3:a), (((member_a A3) A)->(finite179568208od_a_a (B A3))))->(finite676513017od_a_a ((produc520147185od_a_a A) B)))))
% 0.53/0.72  FOF formula (forall (A:set_a) (B:(a->set_Pr1986765409at_nat)), ((finite_finite_a A)->((forall (A3:a), (((member_a A3) A)->(finite772653738at_nat (B A3))))->(finite942416723at_nat ((produc292491723at_nat A) B))))) of role axiom named fact_56_finite__SigmaI
% 0.53/0.72  A new axiom: (forall (A:set_a) (B:(a->set_Pr1986765409at_nat)), ((finite_finite_a A)->((forall (A3:a), (((member_a A3) A)->(finite772653738at_nat (B A3))))->(finite942416723at_nat ((produc292491723at_nat A) B)))))
% 0.53/0.72  FOF formula (forall (A:set_nat) (B:(nat->set_Product_prod_a_a)), ((finite_finite_nat A)->((forall (A3:nat), (((member_nat A3) A)->(finite179568208od_a_a (B A3))))->(finite1297454819od_a_a ((produc1182842125od_a_a A) B))))) of role axiom named fact_57_finite__SigmaI
% 0.53/0.73  A new axiom: (forall (A:set_nat) (B:(nat->set_Product_prod_a_a)), ((finite_finite_nat A)->((forall (A3:nat), (((member_nat A3) A)->(finite179568208od_a_a (B A3))))->(finite1297454819od_a_a ((produc1182842125od_a_a A) B)))))
% 0.53/0.73  FOF formula (forall (A:set_nat) (B:(nat->set_Pr1986765409at_nat)), ((finite_finite_nat A)->((forall (A3:nat), (((member_nat A3) A)->(finite772653738at_nat (B A3))))->(finite277291581at_nat ((produc894163943at_nat A) B))))) of role axiom named fact_58_finite__SigmaI
% 0.53/0.73  A new axiom: (forall (A:set_nat) (B:(nat->set_Pr1986765409at_nat)), ((finite_finite_nat A)->((forall (A3:nat), (((member_nat A3) A)->(finite772653738at_nat (B A3))))->(finite277291581at_nat ((produc894163943at_nat A) B)))))
% 0.53/0.73  FOF formula (forall (G2:pair_p125712459t_unit), ((pair_p1802376898raph_a G2)->(pair_p1864019935ioms_a G2))) of role axiom named fact_59_pair__fin__digraph_Oaxioms_I2_J
% 0.53/0.73  A new axiom: (forall (G2:pair_p125712459t_unit), ((pair_p1802376898raph_a G2)->(pair_p1864019935ioms_a G2)))
% 0.53/0.73  FOF formula (forall (G2:pair_p1914262621t_unit), ((pair_p128415500ph_nat G2)->(pair_p1027063983ms_nat G2))) of role axiom named fact_60_pair__fin__digraph_Oaxioms_I2_J
% 0.53/0.73  A new axiom: (forall (G2:pair_p1914262621t_unit), ((pair_p128415500ph_nat G2)->(pair_p1027063983ms_nat G2)))
% 0.53/0.73  FOF formula (forall (G2:pair_p1765063010t_unit), ((pair_p374947051od_a_a G2)->(pair_p504738056od_a_a G2))) of role axiom named fact_61_pair__fin__digraph_Oaxioms_I2_J
% 0.53/0.73  A new axiom: (forall (G2:pair_p1765063010t_unit), ((pair_p374947051od_a_a G2)->(pair_p504738056od_a_a G2)))
% 0.53/0.73  FOF formula (forall (P:(product_prod_a_a->Prop)), (((finite179568208od_a_a (collec645855634od_a_a P))->False)->((ex product_prod_a_a) (fun (X_1:product_prod_a_a)=> (P X_1))))) of role axiom named fact_62_not__finite__existsD
% 0.53/0.73  A new axiom: (forall (P:(product_prod_a_a->Prop)), (((finite179568208od_a_a (collec645855634od_a_a P))->False)->((ex product_prod_a_a) (fun (X_1:product_prod_a_a)=> (P X_1)))))
% 0.53/0.73  FOF formula (forall (P:(a->Prop)), (((finite_finite_a (collect_a P))->False)->((ex a) (fun (X_1:a)=> (P X_1))))) of role axiom named fact_63_not__finite__existsD
% 0.53/0.73  A new axiom: (forall (P:(a->Prop)), (((finite_finite_a (collect_a P))->False)->((ex a) (fun (X_1:a)=> (P X_1)))))
% 0.53/0.73  FOF formula (forall (P:(nat->Prop)), (((finite_finite_nat (collect_nat P))->False)->((ex nat) (fun (X_1:nat)=> (P X_1))))) of role axiom named fact_64_not__finite__existsD
% 0.53/0.73  A new axiom: (forall (P:(nat->Prop)), (((finite_finite_nat (collect_nat P))->False)->((ex nat) (fun (X_1:nat)=> (P X_1)))))
% 0.53/0.73  FOF formula (forall (P:(product_prod_nat_nat->Prop)), (((finite772653738at_nat (collec7649004at_nat P))->False)->((ex product_prod_nat_nat) (fun (X_1:product_prod_nat_nat)=> (P X_1))))) of role axiom named fact_65_not__finite__existsD
% 0.53/0.73  A new axiom: (forall (P:(product_prod_nat_nat->Prop)), (((finite772653738at_nat (collec7649004at_nat P))->False)->((ex product_prod_nat_nat) (fun (X_1:product_prod_nat_nat)=> (P X_1)))))
% 0.53/0.73  FOF formula (forall (P:(produc1572603623od_a_a->Prop)), (((finite1664988688od_a_a (collec1635618130od_a_a P))->False)->((ex produc1572603623od_a_a) (fun (X_1:produc1572603623od_a_a)=> (P X_1))))) of role axiom named fact_66_not__finite__existsD
% 0.53/0.73  A new axiom: (forall (P:(produc1572603623od_a_a->Prop)), (((finite1664988688od_a_a (collec1635618130od_a_a P))->False)->((ex produc1572603623od_a_a) (fun (X_1:produc1572603623od_a_a)=> (P X_1)))))
% 0.53/0.73  FOF formula (forall (A:set_a) (B:set_a) (R:(a->(a->Prop))), (((finite_finite_a A)->False)->((finite_finite_a B)->((forall (X:a), (((member_a X) A)->((ex a) (fun (Xa:a)=> ((and ((member_a Xa) B)) ((R X) Xa))))))->((ex a) (fun (X:a)=> ((and ((member_a X) B)) ((finite_finite_a (collect_a (fun (A4:a)=> ((and ((member_a A4) A)) ((R A4) X)))))->False)))))))) of role axiom named fact_67_pigeonhole__infinite__rel
% 0.53/0.73  A new axiom: (forall (A:set_a) (B:set_a) (R:(a->(a->Prop))), (((finite_finite_a A)->False)->((finite_finite_a B)->((forall (X:a), (((member_a X) A)->((ex a) (fun (Xa:a)=> ((and ((member_a Xa) B)) ((R X) Xa))))))->((ex a) (fun (X:a)=> ((and ((member_a X) B)) ((finite_finite_a (collect_a (fun (A4:a)=> ((and ((member_a A4) A)) ((R A4) X)))))->False))))))))
% 0.53/0.74  FOF formula (forall (A:set_a) (B:set_nat) (R:(a->(nat->Prop))), (((finite_finite_a A)->False)->((finite_finite_nat B)->((forall (X:a), (((member_a X) A)->((ex nat) (fun (Xa:nat)=> ((and ((member_nat Xa) B)) ((R X) Xa))))))->((ex nat) (fun (X:nat)=> ((and ((member_nat X) B)) ((finite_finite_a (collect_a (fun (A4:a)=> ((and ((member_a A4) A)) ((R A4) X)))))->False)))))))) of role axiom named fact_68_pigeonhole__infinite__rel
% 0.53/0.74  A new axiom: (forall (A:set_a) (B:set_nat) (R:(a->(nat->Prop))), (((finite_finite_a A)->False)->((finite_finite_nat B)->((forall (X:a), (((member_a X) A)->((ex nat) (fun (Xa:nat)=> ((and ((member_nat Xa) B)) ((R X) Xa))))))->((ex nat) (fun (X:nat)=> ((and ((member_nat X) B)) ((finite_finite_a (collect_a (fun (A4:a)=> ((and ((member_a A4) A)) ((R A4) X)))))->False))))))))
% 0.53/0.75  FOF formula (forall (A:set_nat) (B:set_a) (R:(nat->(a->Prop))), (((finite_finite_nat A)->False)->((finite_finite_a B)->((forall (X:nat), (((member_nat X) A)->((ex a) (fun (Xa:a)=> ((and ((member_a Xa) B)) ((R X) Xa))))))->((ex a) (fun (X:a)=> ((and ((member_a X) B)) ((finite_finite_nat (collect_nat (fun (A4:nat)=> ((and ((member_nat A4) A)) ((R A4) X)))))->False)))))))) of role axiom named fact_69_pigeonhole__infinite__rel
% 0.53/0.75  A new axiom: (forall (A:set_nat) (B:set_a) (R:(nat->(a->Prop))), (((finite_finite_nat A)->False)->((finite_finite_a B)->((forall (X:nat), (((member_nat X) A)->((ex a) (fun (Xa:a)=> ((and ((member_a Xa) B)) ((R X) Xa))))))->((ex a) (fun (X:a)=> ((and ((member_a X) B)) ((finite_finite_nat (collect_nat (fun (A4:nat)=> ((and ((member_nat A4) A)) ((R A4) X)))))->False))))))))
% 0.53/0.75  FOF formula (forall (A:set_nat) (B:set_nat) (R:(nat->(nat->Prop))), (((finite_finite_nat A)->False)->((finite_finite_nat B)->((forall (X:nat), (((member_nat X) A)->((ex nat) (fun (Xa:nat)=> ((and ((member_nat Xa) B)) ((R X) Xa))))))->((ex nat) (fun (X:nat)=> ((and ((member_nat X) B)) ((finite_finite_nat (collect_nat (fun (A4:nat)=> ((and ((member_nat A4) A)) ((R A4) X)))))->False)))))))) of role axiom named fact_70_pigeonhole__infinite__rel
% 0.53/0.75  A new axiom: (forall (A:set_nat) (B:set_nat) (R:(nat->(nat->Prop))), (((finite_finite_nat A)->False)->((finite_finite_nat B)->((forall (X:nat), (((member_nat X) A)->((ex nat) (fun (Xa:nat)=> ((and ((member_nat Xa) B)) ((R X) Xa))))))->((ex nat) (fun (X:nat)=> ((and ((member_nat X) B)) ((finite_finite_nat (collect_nat (fun (A4:nat)=> ((and ((member_nat A4) A)) ((R A4) X)))))->False))))))))
% 0.53/0.75  FOF formula (forall (A:set_Product_prod_a_a) (B:set_a) (R:(product_prod_a_a->(a->Prop))), (((finite179568208od_a_a A)->False)->((finite_finite_a B)->((forall (X:product_prod_a_a), (((member449909584od_a_a X) A)->((ex a) (fun (Xa:a)=> ((and ((member_a Xa) B)) ((R X) Xa))))))->((ex a) (fun (X:a)=> ((and ((member_a X) B)) ((finite179568208od_a_a (collec645855634od_a_a (fun (A4:product_prod_a_a)=> ((and ((member449909584od_a_a A4) A)) ((R A4) X)))))->False)))))))) of role axiom named fact_71_pigeonhole__infinite__rel
% 0.53/0.75  A new axiom: (forall (A:set_Product_prod_a_a) (B:set_a) (R:(product_prod_a_a->(a->Prop))), (((finite179568208od_a_a A)->False)->((finite_finite_a B)->((forall (X:product_prod_a_a), (((member449909584od_a_a X) A)->((ex a) (fun (Xa:a)=> ((and ((member_a Xa) B)) ((R X) Xa))))))->((ex a) (fun (X:a)=> ((and ((member_a X) B)) ((finite179568208od_a_a (collec645855634od_a_a (fun (A4:product_prod_a_a)=> ((and ((member449909584od_a_a A4) A)) ((R A4) X)))))->False))))))))
% 0.53/0.75  FOF formula (forall (A:set_Product_prod_a_a) (B:set_nat) (R:(product_prod_a_a->(nat->Prop))), (((finite179568208od_a_a A)->False)->((finite_finite_nat B)->((forall (X:product_prod_a_a), (((member449909584od_a_a X) A)->((ex nat) (fun (Xa:nat)=> ((and ((member_nat Xa) B)) ((R X) Xa))))))->((ex nat) (fun (X:nat)=> ((and ((member_nat X) B)) ((finite179568208od_a_a (collec645855634od_a_a (fun (A4:product_prod_a_a)=> ((and ((member449909584od_a_a A4) A)) ((R A4) X)))))->False)))))))) of role axiom named fact_72_pigeonhole__infinite__rel
% 0.60/0.76  A new axiom: (forall (A:set_Product_prod_a_a) (B:set_nat) (R:(product_prod_a_a->(nat->Prop))), (((finite179568208od_a_a A)->False)->((finite_finite_nat B)->((forall (X:product_prod_a_a), (((member449909584od_a_a X) A)->((ex nat) (fun (Xa:nat)=> ((and ((member_nat Xa) B)) ((R X) Xa))))))->((ex nat) (fun (X:nat)=> ((and ((member_nat X) B)) ((finite179568208od_a_a (collec645855634od_a_a (fun (A4:product_prod_a_a)=> ((and ((member449909584od_a_a A4) A)) ((R A4) X)))))->False))))))))
% 0.60/0.76  FOF formula (forall (A:set_a) (B:set_Product_prod_a_a) (R:(a->(product_prod_a_a->Prop))), (((finite_finite_a A)->False)->((finite179568208od_a_a B)->((forall (X:a), (((member_a X) A)->((ex product_prod_a_a) (fun (Xa:product_prod_a_a)=> ((and ((member449909584od_a_a Xa) B)) ((R X) Xa))))))->((ex product_prod_a_a) (fun (X:product_prod_a_a)=> ((and ((member449909584od_a_a X) B)) ((finite_finite_a (collect_a (fun (A4:a)=> ((and ((member_a A4) A)) ((R A4) X)))))->False)))))))) of role axiom named fact_73_pigeonhole__infinite__rel
% 0.60/0.76  A new axiom: (forall (A:set_a) (B:set_Product_prod_a_a) (R:(a->(product_prod_a_a->Prop))), (((finite_finite_a A)->False)->((finite179568208od_a_a B)->((forall (X:a), (((member_a X) A)->((ex product_prod_a_a) (fun (Xa:product_prod_a_a)=> ((and ((member449909584od_a_a Xa) B)) ((R X) Xa))))))->((ex product_prod_a_a) (fun (X:product_prod_a_a)=> ((and ((member449909584od_a_a X) B)) ((finite_finite_a (collect_a (fun (A4:a)=> ((and ((member_a A4) A)) ((R A4) X)))))->False))))))))
% 0.60/0.76  FOF formula (forall (A:set_a) (B:set_Pr1986765409at_nat) (R:(a->(product_prod_nat_nat->Prop))), (((finite_finite_a A)->False)->((finite772653738at_nat B)->((forall (X:a), (((member_a X) A)->((ex product_prod_nat_nat) (fun (Xa:product_prod_nat_nat)=> ((and ((member701585322at_nat Xa) B)) ((R X) Xa))))))->((ex product_prod_nat_nat) (fun (X:product_prod_nat_nat)=> ((and ((member701585322at_nat X) B)) ((finite_finite_a (collect_a (fun (A4:a)=> ((and ((member_a A4) A)) ((R A4) X)))))->False)))))))) of role axiom named fact_74_pigeonhole__infinite__rel
% 0.60/0.76  A new axiom: (forall (A:set_a) (B:set_Pr1986765409at_nat) (R:(a->(product_prod_nat_nat->Prop))), (((finite_finite_a A)->False)->((finite772653738at_nat B)->((forall (X:a), (((member_a X) A)->((ex product_prod_nat_nat) (fun (Xa:product_prod_nat_nat)=> ((and ((member701585322at_nat Xa) B)) ((R X) Xa))))))->((ex product_prod_nat_nat) (fun (X:product_prod_nat_nat)=> ((and ((member701585322at_nat X) B)) ((finite_finite_a (collect_a (fun (A4:a)=> ((and ((member_a A4) A)) ((R A4) X)))))->False))))))))
% 0.60/0.76  FOF formula (forall (A:set_nat) (B:set_Product_prod_a_a) (R:(nat->(product_prod_a_a->Prop))), (((finite_finite_nat A)->False)->((finite179568208od_a_a B)->((forall (X:nat), (((member_nat X) A)->((ex product_prod_a_a) (fun (Xa:product_prod_a_a)=> ((and ((member449909584od_a_a Xa) B)) ((R X) Xa))))))->((ex product_prod_a_a) (fun (X:product_prod_a_a)=> ((and ((member449909584od_a_a X) B)) ((finite_finite_nat (collect_nat (fun (A4:nat)=> ((and ((member_nat A4) A)) ((R A4) X)))))->False)))))))) of role axiom named fact_75_pigeonhole__infinite__rel
% 0.60/0.76  A new axiom: (forall (A:set_nat) (B:set_Product_prod_a_a) (R:(nat->(product_prod_a_a->Prop))), (((finite_finite_nat A)->False)->((finite179568208od_a_a B)->((forall (X:nat), (((member_nat X) A)->((ex product_prod_a_a) (fun (Xa:product_prod_a_a)=> ((and ((member449909584od_a_a Xa) B)) ((R X) Xa))))))->((ex product_prod_a_a) (fun (X:product_prod_a_a)=> ((and ((member449909584od_a_a X) B)) ((finite_finite_nat (collect_nat (fun (A4:nat)=> ((and ((member_nat A4) A)) ((R A4) X)))))->False))))))))
% 0.60/0.76  FOF formula (forall (A:set_nat) (B:set_Pr1986765409at_nat) (R:(nat->(product_prod_nat_nat->Prop))), (((finite_finite_nat A)->False)->((finite772653738at_nat B)->((forall (X:nat), (((member_nat X) A)->((ex product_prod_nat_nat) (fun (Xa:product_prod_nat_nat)=> ((and ((member701585322at_nat Xa) B)) ((R X) Xa))))))->((ex product_prod_nat_nat) (fun (X:product_prod_nat_nat)=> ((and ((member701585322at_nat X) B)) ((finite_finite_nat (collect_nat (fun (A4:nat)=> ((and ((member_nat A4) A)) ((R A4) X)))))->False)))))))) of role axiom named fact_76_pigeonhole__infinite__rel
% 0.61/0.77  A new axiom: (forall (A:set_nat) (B:set_Pr1986765409at_nat) (R:(nat->(product_prod_nat_nat->Prop))), (((finite_finite_nat A)->False)->((finite772653738at_nat B)->((forall (X:nat), (((member_nat X) A)->((ex product_prod_nat_nat) (fun (Xa:product_prod_nat_nat)=> ((and ((member701585322at_nat Xa) B)) ((R X) Xa))))))->((ex product_prod_nat_nat) (fun (X:product_prod_nat_nat)=> ((and ((member701585322at_nat X) B)) ((finite_finite_nat (collect_nat (fun (A4:nat)=> ((and ((member_nat A4) A)) ((R A4) X)))))->False))))))))
% 0.61/0.77  FOF formula (forall (G2:pair_p125712459t_unit), ((pair_p1802376898raph_a G2)->(pair_p1802376898raph_a G2))) of role axiom named fact_77_pair__fin__digraph_Opair__fin__digraph
% 0.61/0.77  A new axiom: (forall (G2:pair_p125712459t_unit), ((pair_p1802376898raph_a G2)->(pair_p1802376898raph_a G2)))
% 0.61/0.77  FOF formula (forall (A:set_a) (B:set_nat), ((finite_finite_a A)->((finite_finite_nat B)->(finite1743148308_a_nat ((product_Sigma_a_nat A) (fun (Uu:a)=> B)))))) of role axiom named fact_78_finite__cartesian__product
% 0.61/0.77  A new axiom: (forall (A:set_a) (B:set_nat), ((finite_finite_a A)->((finite_finite_nat B)->(finite1743148308_a_nat ((product_Sigma_a_nat A) (fun (Uu:a)=> B))))))
% 0.61/0.77  FOF formula (forall (A:set_nat) (B:set_a), ((finite_finite_nat A)->((finite_finite_a B)->(finite1808550458_nat_a ((product_Sigma_nat_a A) (fun (Uu:nat)=> B)))))) of role axiom named fact_79_finite__cartesian__product
% 0.61/0.77  A new axiom: (forall (A:set_nat) (B:set_a), ((finite_finite_nat A)->((finite_finite_a B)->(finite1808550458_nat_a ((product_Sigma_nat_a A) (fun (Uu:nat)=> B))))))
% 0.61/0.77  FOF formula (forall (A:set_nat) (B:set_nat), ((finite_finite_nat A)->((finite_finite_nat B)->(finite772653738at_nat ((produc45129834at_nat A) (fun (Uu:nat)=> B)))))) of role axiom named fact_80_finite__cartesian__product
% 0.61/0.77  A new axiom: (forall (A:set_nat) (B:set_nat), ((finite_finite_nat A)->((finite_finite_nat B)->(finite772653738at_nat ((produc45129834at_nat A) (fun (Uu:nat)=> B))))))
% 0.61/0.77  FOF formula (forall (A:set_a) (B:set_a), ((finite_finite_a A)->((finite_finite_a B)->(finite179568208od_a_a ((product_Sigma_a_a A) (fun (Uu:a)=> B)))))) of role axiom named fact_81_finite__cartesian__product
% 0.61/0.77  A new axiom: (forall (A:set_a) (B:set_a), ((finite_finite_a A)->((finite_finite_a B)->(finite179568208od_a_a ((product_Sigma_a_a A) (fun (Uu:a)=> B))))))
% 0.61/0.77  FOF formula (forall (A:set_Product_prod_a_a) (B:set_a), ((finite179568208od_a_a A)->((finite_finite_a B)->(finite1919032935_a_a_a ((produc1282482655_a_a_a A) (fun (Uu:product_prod_a_a)=> B)))))) of role axiom named fact_82_finite__cartesian__product
% 0.61/0.77  A new axiom: (forall (A:set_Product_prod_a_a) (B:set_a), ((finite179568208od_a_a A)->((finite_finite_a B)->(finite1919032935_a_a_a ((produc1282482655_a_a_a A) (fun (Uu:product_prod_a_a)=> B))))))
% 0.61/0.77  FOF formula (forall (A:set_Product_prod_a_a) (B:set_nat), ((finite179568208od_a_a A)->((finite_finite_nat B)->(finite1837575485_a_nat ((produc931712687_a_nat A) (fun (Uu:product_prod_a_a)=> B)))))) of role axiom named fact_83_finite__cartesian__product
% 0.61/0.77  A new axiom: (forall (A:set_Product_prod_a_a) (B:set_nat), ((finite179568208od_a_a A)->((finite_finite_nat B)->(finite1837575485_a_nat ((produc931712687_a_nat A) (fun (Uu:product_prod_a_a)=> B))))))
% 0.61/0.77  FOF formula (forall (A:set_a) (B:set_Product_prod_a_a), ((finite_finite_a A)->((finite179568208od_a_a B)->(finite676513017od_a_a ((produc520147185od_a_a A) (fun (Uu:a)=> B)))))) of role axiom named fact_84_finite__cartesian__product
% 0.61/0.77  A new axiom: (forall (A:set_a) (B:set_Product_prod_a_a), ((finite_finite_a A)->((finite179568208od_a_a B)->(finite676513017od_a_a ((produc520147185od_a_a A) (fun (Uu:a)=> B))))))
% 0.61/0.77  FOF formula (forall (A:set_a) (B:set_Pr1986765409at_nat), ((finite_finite_a A)->((finite772653738at_nat B)->(finite942416723at_nat ((produc292491723at_nat A) (fun (Uu:a)=> B)))))) of role axiom named fact_85_finite__cartesian__product
% 0.61/0.77  A new axiom: (forall (A:set_a) (B:set_Pr1986765409at_nat), ((finite_finite_a A)->((finite772653738at_nat B)->(finite942416723at_nat ((produc292491723at_nat A) (fun (Uu:a)=> B))))))
% 0.61/0.78  FOF formula (forall (A:set_nat) (B:set_Product_prod_a_a), ((finite_finite_nat A)->((finite179568208od_a_a B)->(finite1297454819od_a_a ((produc1182842125od_a_a A) (fun (Uu:nat)=> B)))))) of role axiom named fact_86_finite__cartesian__product
% 0.61/0.78  A new axiom: (forall (A:set_nat) (B:set_Product_prod_a_a), ((finite_finite_nat A)->((finite179568208od_a_a B)->(finite1297454819od_a_a ((produc1182842125od_a_a A) (fun (Uu:nat)=> B))))))
% 0.61/0.78  FOF formula (forall (A:set_nat) (B:set_Pr1986765409at_nat), ((finite_finite_nat A)->((finite772653738at_nat B)->(finite277291581at_nat ((produc894163943at_nat A) (fun (Uu:nat)=> B)))))) of role axiom named fact_87_finite__cartesian__product
% 0.61/0.78  A new axiom: (forall (A:set_nat) (B:set_Pr1986765409at_nat), ((finite_finite_nat A)->((finite772653738at_nat B)->(finite277291581at_nat ((produc894163943at_nat A) (fun (Uu:nat)=> B))))))
% 0.61/0.78  FOF formula (forall (G2:pair_p2041852168t_unit), ((pair_p752841413at_nat G2)->(finite772653738at_nat (pair_p210955889t_unit G2)))) of role axiom named fact_88_pair__fin__digraph_Opair__finite__verts
% 0.61/0.78  A new axiom: (forall (G2:pair_p2041852168t_unit), ((pair_p752841413at_nat G2)->(finite772653738at_nat (pair_p210955889t_unit G2))))
% 0.61/0.78  FOF formula (forall (G2:pair_p1593840546t_unit), ((pair_p159207083od_a_a G2)->(finite1664988688od_a_a (pair_p1652294923t_unit G2)))) of role axiom named fact_89_pair__fin__digraph_Opair__finite__verts
% 0.61/0.78  A new axiom: (forall (G2:pair_p1593840546t_unit), ((pair_p159207083od_a_a G2)->(finite1664988688od_a_a (pair_p1652294923t_unit G2))))
% 0.61/0.78  FOF formula (forall (G2:pair_p125712459t_unit), ((pair_p1802376898raph_a G2)->(finite_finite_a (pair_p1047056820t_unit G2)))) of role axiom named fact_90_pair__fin__digraph_Opair__finite__verts
% 0.61/0.78  A new axiom: (forall (G2:pair_p125712459t_unit), ((pair_p1802376898raph_a G2)->(finite_finite_a (pair_p1047056820t_unit G2))))
% 0.61/0.78  FOF formula (forall (G2:pair_p1914262621t_unit), ((pair_p128415500ph_nat G2)->(finite_finite_nat (pair_p1677060310t_unit G2)))) of role axiom named fact_91_pair__fin__digraph_Opair__finite__verts
% 0.61/0.78  A new axiom: (forall (G2:pair_p1914262621t_unit), ((pair_p128415500ph_nat G2)->(finite_finite_nat (pair_p1677060310t_unit G2))))
% 0.61/0.78  FOF formula (forall (G2:pair_p1765063010t_unit), ((pair_p374947051od_a_a G2)->(finite179568208od_a_a (pair_p447552203t_unit G2)))) of role axiom named fact_92_pair__fin__digraph_Opair__finite__verts
% 0.61/0.78  A new axiom: (forall (G2:pair_p1765063010t_unit), ((pair_p374947051od_a_a G2)->(finite179568208od_a_a (pair_p447552203t_unit G2))))
% 0.61/0.78  FOF formula (forall (A:set_se1596668135od_a_a) (A2:set_Product_prod_a_a), ((finite1145471536od_a_a A)->(((member1838126896od_a_a A2) A)->((ex set_Product_prod_a_a) (fun (X:set_Product_prod_a_a)=> ((and ((and ((member1838126896od_a_a X) A)) ((ord_le1824328871od_a_a X) A2))) (forall (Xa:set_Product_prod_a_a), (((member1838126896od_a_a Xa) A)->(((ord_le1824328871od_a_a Xa) X)->(((eq set_Product_prod_a_a) X) Xa)))))))))) of role axiom named fact_93_finite__has__minimal2
% 0.61/0.78  A new axiom: (forall (A:set_se1596668135od_a_a) (A2:set_Product_prod_a_a), ((finite1145471536od_a_a A)->(((member1838126896od_a_a A2) A)->((ex set_Product_prod_a_a) (fun (X:set_Product_prod_a_a)=> ((and ((and ((member1838126896od_a_a X) A)) ((ord_le1824328871od_a_a X) A2))) (forall (Xa:set_Product_prod_a_a), (((member1838126896od_a_a Xa) A)->(((ord_le1824328871od_a_a Xa) X)->(((eq set_Product_prod_a_a) X) Xa))))))))))
% 0.61/0.78  FOF formula (forall (A:set_nat) (A2:nat), ((finite_finite_nat A)->(((member_nat A2) A)->((ex nat) (fun (X:nat)=> ((and ((and ((member_nat X) A)) ((ord_less_eq_nat X) A2))) (forall (Xa:nat), (((member_nat Xa) A)->(((ord_less_eq_nat Xa) X)->(((eq nat) X) Xa)))))))))) of role axiom named fact_94_finite__has__minimal2
% 0.61/0.78  A new axiom: (forall (A:set_nat) (A2:nat), ((finite_finite_nat A)->(((member_nat A2) A)->((ex nat) (fun (X:nat)=> ((and ((and ((member_nat X) A)) ((ord_less_eq_nat X) A2))) (forall (Xa:nat), (((member_nat Xa) A)->(((ord_less_eq_nat Xa) X)->(((eq nat) X) Xa))))))))))
% 0.61/0.78  FOF formula (forall (A:set_set_nat) (A2:set_nat), ((finite2012248349et_nat A)->(((member_set_nat A2) A)->((ex set_nat) (fun (X:set_nat)=> ((and ((and ((member_set_nat X) A)) ((ord_less_eq_set_nat X) A2))) (forall (Xa:set_nat), (((member_set_nat Xa) A)->(((ord_less_eq_set_nat Xa) X)->(((eq set_nat) X) Xa)))))))))) of role axiom named fact_95_finite__has__minimal2
% 0.61/0.79  A new axiom: (forall (A:set_set_nat) (A2:set_nat), ((finite2012248349et_nat A)->(((member_set_nat A2) A)->((ex set_nat) (fun (X:set_nat)=> ((and ((and ((member_set_nat X) A)) ((ord_less_eq_set_nat X) A2))) (forall (Xa:set_nat), (((member_set_nat Xa) A)->(((ord_less_eq_set_nat Xa) X)->(((eq set_nat) X) Xa))))))))))
% 0.61/0.79  FOF formula (forall (A:set_set_a) (A2:set_a), ((finite_finite_set_a A)->(((member_set_a A2) A)->((ex set_a) (fun (X:set_a)=> ((and ((and ((member_set_a X) A)) ((ord_less_eq_set_a X) A2))) (forall (Xa:set_a), (((member_set_a Xa) A)->(((ord_less_eq_set_a Xa) X)->(((eq set_a) X) Xa)))))))))) of role axiom named fact_96_finite__has__minimal2
% 0.61/0.79  A new axiom: (forall (A:set_set_a) (A2:set_a), ((finite_finite_set_a A)->(((member_set_a A2) A)->((ex set_a) (fun (X:set_a)=> ((and ((and ((member_set_a X) A)) ((ord_less_eq_set_a X) A2))) (forall (Xa:set_a), (((member_set_a Xa) A)->(((ord_less_eq_set_a Xa) X)->(((eq set_a) X) Xa))))))))))
% 0.61/0.79  FOF formula (forall (A:set_a) (B:set_nat), (((finite_finite_a A)->False)->(((finite_finite_nat B)->False)->((finite1743148308_a_nat ((product_Sigma_a_nat A) (fun (Uu:a)=> B)))->False)))) of role axiom named fact_97_infinite__cartesian__product
% 0.61/0.79  A new axiom: (forall (A:set_a) (B:set_nat), (((finite_finite_a A)->False)->(((finite_finite_nat B)->False)->((finite1743148308_a_nat ((product_Sigma_a_nat A) (fun (Uu:a)=> B)))->False))))
% 0.61/0.79  FOF formula (forall (A:set_nat) (B:set_a), (((finite_finite_nat A)->False)->(((finite_finite_a B)->False)->((finite1808550458_nat_a ((product_Sigma_nat_a A) (fun (Uu:nat)=> B)))->False)))) of role axiom named fact_98_infinite__cartesian__product
% 0.61/0.79  A new axiom: (forall (A:set_nat) (B:set_a), (((finite_finite_nat A)->False)->(((finite_finite_a B)->False)->((finite1808550458_nat_a ((product_Sigma_nat_a A) (fun (Uu:nat)=> B)))->False))))
% 0.61/0.79  FOF formula (forall (A:set_nat) (B:set_nat), (((finite_finite_nat A)->False)->(((finite_finite_nat B)->False)->((finite772653738at_nat ((produc45129834at_nat A) (fun (Uu:nat)=> B)))->False)))) of role axiom named fact_99_infinite__cartesian__product
% 0.61/0.79  A new axiom: (forall (A:set_nat) (B:set_nat), (((finite_finite_nat A)->False)->(((finite_finite_nat B)->False)->((finite772653738at_nat ((produc45129834at_nat A) (fun (Uu:nat)=> B)))->False))))
% 0.61/0.79  FOF formula (forall (A:set_a) (B:set_a), (((finite_finite_a A)->False)->(((finite_finite_a B)->False)->((finite179568208od_a_a ((product_Sigma_a_a A) (fun (Uu:a)=> B)))->False)))) of role axiom named fact_100_infinite__cartesian__product
% 0.61/0.79  A new axiom: (forall (A:set_a) (B:set_a), (((finite_finite_a A)->False)->(((finite_finite_a B)->False)->((finite179568208od_a_a ((product_Sigma_a_a A) (fun (Uu:a)=> B)))->False))))
% 0.61/0.79  FOF formula (forall (A:set_Product_prod_a_a) (B:set_a), (((finite179568208od_a_a A)->False)->(((finite_finite_a B)->False)->((finite1919032935_a_a_a ((produc1282482655_a_a_a A) (fun (Uu:product_prod_a_a)=> B)))->False)))) of role axiom named fact_101_infinite__cartesian__product
% 0.61/0.79  A new axiom: (forall (A:set_Product_prod_a_a) (B:set_a), (((finite179568208od_a_a A)->False)->(((finite_finite_a B)->False)->((finite1919032935_a_a_a ((produc1282482655_a_a_a A) (fun (Uu:product_prod_a_a)=> B)))->False))))
% 0.61/0.79  FOF formula (forall (A:set_Product_prod_a_a) (B:set_nat), (((finite179568208od_a_a A)->False)->(((finite_finite_nat B)->False)->((finite1837575485_a_nat ((produc931712687_a_nat A) (fun (Uu:product_prod_a_a)=> B)))->False)))) of role axiom named fact_102_infinite__cartesian__product
% 0.61/0.79  A new axiom: (forall (A:set_Product_prod_a_a) (B:set_nat), (((finite179568208od_a_a A)->False)->(((finite_finite_nat B)->False)->((finite1837575485_a_nat ((produc931712687_a_nat A) (fun (Uu:product_prod_a_a)=> B)))->False))))
% 0.61/0.79  FOF formula (forall (A:set_a) (B:set_Product_prod_a_a), (((finite_finite_a A)->False)->(((finite179568208od_a_a B)->False)->((finite676513017od_a_a ((produc520147185od_a_a A) (fun (Uu:a)=> B)))->False)))) of role axiom named fact_103_infinite__cartesian__product
% 0.61/0.80  A new axiom: (forall (A:set_a) (B:set_Product_prod_a_a), (((finite_finite_a A)->False)->(((finite179568208od_a_a B)->False)->((finite676513017od_a_a ((produc520147185od_a_a A) (fun (Uu:a)=> B)))->False))))
% 0.61/0.80  FOF formula (forall (A:set_a) (B:set_Pr1986765409at_nat), (((finite_finite_a A)->False)->(((finite772653738at_nat B)->False)->((finite942416723at_nat ((produc292491723at_nat A) (fun (Uu:a)=> B)))->False)))) of role axiom named fact_104_infinite__cartesian__product
% 0.61/0.80  A new axiom: (forall (A:set_a) (B:set_Pr1986765409at_nat), (((finite_finite_a A)->False)->(((finite772653738at_nat B)->False)->((finite942416723at_nat ((produc292491723at_nat A) (fun (Uu:a)=> B)))->False))))
% 0.61/0.80  FOF formula (forall (A:set_nat) (B:set_Product_prod_a_a), (((finite_finite_nat A)->False)->(((finite179568208od_a_a B)->False)->((finite1297454819od_a_a ((produc1182842125od_a_a A) (fun (Uu:nat)=> B)))->False)))) of role axiom named fact_105_infinite__cartesian__product
% 0.61/0.80  A new axiom: (forall (A:set_nat) (B:set_Product_prod_a_a), (((finite_finite_nat A)->False)->(((finite179568208od_a_a B)->False)->((finite1297454819od_a_a ((produc1182842125od_a_a A) (fun (Uu:nat)=> B)))->False))))
% 0.61/0.80  FOF formula (forall (A:set_nat) (B:set_Pr1986765409at_nat), (((finite_finite_nat A)->False)->(((finite772653738at_nat B)->False)->((finite277291581at_nat ((produc894163943at_nat A) (fun (Uu:nat)=> B)))->False)))) of role axiom named fact_106_infinite__cartesian__product
% 0.61/0.80  A new axiom: (forall (A:set_nat) (B:set_Pr1986765409at_nat), (((finite_finite_nat A)->False)->(((finite772653738at_nat B)->False)->((finite277291581at_nat ((produc894163943at_nat A) (fun (Uu:nat)=> B)))->False))))
% 0.61/0.80  FOF formula (forall (X3:product_prod_a_a) (C:set_Product_prod_a_a) (A:set_Product_prod_a_a) (B:set_Product_prod_a_a), (((member449909584od_a_a X3) C)->(((eq Prop) ((ord_le456379495od_a_a ((produc304751368od_a_a A) (fun (Uu:product_prod_a_a)=> C))) ((produc304751368od_a_a B) (fun (Uu:product_prod_a_a)=> C)))) ((ord_le1824328871od_a_a A) B)))) of role axiom named fact_107_Times__subset__cancel2
% 0.61/0.80  A new axiom: (forall (X3:product_prod_a_a) (C:set_Product_prod_a_a) (A:set_Product_prod_a_a) (B:set_Product_prod_a_a), (((member449909584od_a_a X3) C)->(((eq Prop) ((ord_le456379495od_a_a ((produc304751368od_a_a A) (fun (Uu:product_prod_a_a)=> C))) ((produc304751368od_a_a B) (fun (Uu:product_prod_a_a)=> C)))) ((ord_le1824328871od_a_a A) B))))
% 0.61/0.80  FOF formula (forall (X3:nat) (C:set_nat) (A:set_Product_prod_a_a) (B:set_Product_prod_a_a), (((member_nat X3) C)->(((eq Prop) ((ord_le492294332_a_nat ((produc931712687_a_nat A) (fun (Uu:product_prod_a_a)=> C))) ((produc931712687_a_nat B) (fun (Uu:product_prod_a_a)=> C)))) ((ord_le1824328871od_a_a A) B)))) of role axiom named fact_108_Times__subset__cancel2
% 0.61/0.80  A new axiom: (forall (X3:nat) (C:set_nat) (A:set_Product_prod_a_a) (B:set_Product_prod_a_a), (((member_nat X3) C)->(((eq Prop) ((ord_le492294332_a_nat ((produc931712687_a_nat A) (fun (Uu:product_prod_a_a)=> C))) ((produc931712687_a_nat B) (fun (Uu:product_prod_a_a)=> C)))) ((ord_le1824328871od_a_a A) B))))
% 0.61/0.80  FOF formula (forall (X3:product_prod_a_a) (C:set_Product_prod_a_a) (A:set_nat) (B:set_nat), (((member449909584od_a_a X3) C)->(((eq Prop) ((ord_le2084554594od_a_a ((produc1182842125od_a_a A) (fun (Uu:nat)=> C))) ((produc1182842125od_a_a B) (fun (Uu:nat)=> C)))) ((ord_less_eq_set_nat A) B)))) of role axiom named fact_109_Times__subset__cancel2
% 0.61/0.80  A new axiom: (forall (X3:product_prod_a_a) (C:set_Product_prod_a_a) (A:set_nat) (B:set_nat), (((member449909584od_a_a X3) C)->(((eq Prop) ((ord_le2084554594od_a_a ((produc1182842125od_a_a A) (fun (Uu:nat)=> C))) ((produc1182842125od_a_a B) (fun (Uu:nat)=> C)))) ((ord_less_eq_set_nat A) B))))
% 0.61/0.80  FOF formula (forall (X3:nat) (C:set_nat) (A:set_nat) (B:set_nat), (((member_nat X3) C)->(((eq Prop) ((ord_le841296385at_nat ((produc45129834at_nat A) (fun (Uu:nat)=> C))) ((produc45129834at_nat B) (fun (Uu:nat)=> C)))) ((ord_less_eq_set_nat A) B)))) of role axiom named fact_110_Times__subset__cancel2
% 0.65/0.81  A new axiom: (forall (X3:nat) (C:set_nat) (A:set_nat) (B:set_nat), (((member_nat X3) C)->(((eq Prop) ((ord_le841296385at_nat ((produc45129834at_nat A) (fun (Uu:nat)=> C))) ((produc45129834at_nat B) (fun (Uu:nat)=> C)))) ((ord_less_eq_set_nat A) B))))
% 0.65/0.81  FOF formula (forall (X3:product_prod_a_a) (C:set_Product_prod_a_a) (A:set_a) (B:set_a), (((member449909584od_a_a X3) C)->(((eq Prop) ((ord_le1816232656od_a_a ((produc520147185od_a_a A) (fun (Uu:a)=> C))) ((produc520147185od_a_a B) (fun (Uu:a)=> C)))) ((ord_less_eq_set_a A) B)))) of role axiom named fact_111_Times__subset__cancel2
% 0.65/0.81  A new axiom: (forall (X3:product_prod_a_a) (C:set_Product_prod_a_a) (A:set_a) (B:set_a), (((member449909584od_a_a X3) C)->(((eq Prop) ((ord_le1816232656od_a_a ((produc520147185od_a_a A) (fun (Uu:a)=> C))) ((produc520147185od_a_a B) (fun (Uu:a)=> C)))) ((ord_less_eq_set_a A) B))))
% 0.65/0.81  FOF formula (forall (X3:nat) (C:set_nat) (A:set_a) (B:set_a), (((member_nat X3) C)->(((eq Prop) ((ord_le2073555219_a_nat ((product_Sigma_a_nat A) (fun (Uu:a)=> C))) ((product_Sigma_a_nat B) (fun (Uu:a)=> C)))) ((ord_less_eq_set_a A) B)))) of role axiom named fact_112_Times__subset__cancel2
% 0.65/0.81  A new axiom: (forall (X3:nat) (C:set_nat) (A:set_a) (B:set_a), (((member_nat X3) C)->(((eq Prop) ((ord_le2073555219_a_nat ((product_Sigma_a_nat A) (fun (Uu:a)=> C))) ((product_Sigma_a_nat B) (fun (Uu:a)=> C)))) ((ord_less_eq_set_a A) B))))
% 0.65/0.81  FOF formula (forall (X3:a) (C:set_a) (A:set_a) (B:set_a), (((member_a X3) C)->(((eq Prop) ((ord_le1824328871od_a_a ((product_Sigma_a_a A) (fun (Uu:a)=> C))) ((product_Sigma_a_a B) (fun (Uu:a)=> C)))) ((ord_less_eq_set_a A) B)))) of role axiom named fact_113_Times__subset__cancel2
% 0.65/0.81  A new axiom: (forall (X3:a) (C:set_a) (A:set_a) (B:set_a), (((member_a X3) C)->(((eq Prop) ((ord_le1824328871od_a_a ((product_Sigma_a_a A) (fun (Uu:a)=> C))) ((product_Sigma_a_a B) (fun (Uu:a)=> C)))) ((ord_less_eq_set_a A) B))))
% 0.65/0.81  FOF formula (forall (A:set_Product_prod_a_a) (C:set_Product_prod_a_a) (B:(product_prod_a_a->set_Product_prod_a_a)) (D:(product_prod_a_a->set_Product_prod_a_a)), (((ord_le1824328871od_a_a A) C)->((forall (X:product_prod_a_a), (((member449909584od_a_a X) A)->((ord_le1824328871od_a_a (B X)) (D X))))->((ord_le456379495od_a_a ((produc304751368od_a_a A) B)) ((produc304751368od_a_a C) D))))) of role axiom named fact_114_Sigma__mono
% 0.65/0.81  A new axiom: (forall (A:set_Product_prod_a_a) (C:set_Product_prod_a_a) (B:(product_prod_a_a->set_Product_prod_a_a)) (D:(product_prod_a_a->set_Product_prod_a_a)), (((ord_le1824328871od_a_a A) C)->((forall (X:product_prod_a_a), (((member449909584od_a_a X) A)->((ord_le1824328871od_a_a (B X)) (D X))))->((ord_le456379495od_a_a ((produc304751368od_a_a A) B)) ((produc304751368od_a_a C) D)))))
% 0.65/0.81  FOF formula (forall (A:set_Product_prod_a_a) (C:set_Product_prod_a_a) (B:(product_prod_a_a->set_nat)) (D:(product_prod_a_a->set_nat)), (((ord_le1824328871od_a_a A) C)->((forall (X:product_prod_a_a), (((member449909584od_a_a X) A)->((ord_less_eq_set_nat (B X)) (D X))))->((ord_le492294332_a_nat ((produc931712687_a_nat A) B)) ((produc931712687_a_nat C) D))))) of role axiom named fact_115_Sigma__mono
% 0.65/0.81  A new axiom: (forall (A:set_Product_prod_a_a) (C:set_Product_prod_a_a) (B:(product_prod_a_a->set_nat)) (D:(product_prod_a_a->set_nat)), (((ord_le1824328871od_a_a A) C)->((forall (X:product_prod_a_a), (((member449909584od_a_a X) A)->((ord_less_eq_set_nat (B X)) (D X))))->((ord_le492294332_a_nat ((produc931712687_a_nat A) B)) ((produc931712687_a_nat C) D)))))
% 0.65/0.81  FOF formula (forall (A:set_Product_prod_a_a) (C:set_Product_prod_a_a) (B:(product_prod_a_a->set_a)) (D:(product_prod_a_a->set_a)), (((ord_le1824328871od_a_a A) C)->((forall (X:product_prod_a_a), (((member449909584od_a_a X) A)->((ord_less_eq_set_a (B X)) (D X))))->((ord_le677315902_a_a_a ((produc1282482655_a_a_a A) B)) ((produc1282482655_a_a_a C) D))))) of role axiom named fact_116_Sigma__mono
% 0.65/0.81  A new axiom: (forall (A:set_Product_prod_a_a) (C:set_Product_prod_a_a) (B:(product_prod_a_a->set_a)) (D:(product_prod_a_a->set_a)), (((ord_le1824328871od_a_a A) C)->((forall (X:product_prod_a_a), (((member449909584od_a_a X) A)->((ord_less_eq_set_a (B X)) (D X))))->((ord_le677315902_a_a_a ((produc1282482655_a_a_a A) B)) ((produc1282482655_a_a_a C) D)))))
% 0.65/0.82  FOF formula (forall (A:set_nat) (C:set_nat) (B:(nat->set_Product_prod_a_a)) (D:(nat->set_Product_prod_a_a)), (((ord_less_eq_set_nat A) C)->((forall (X:nat), (((member_nat X) A)->((ord_le1824328871od_a_a (B X)) (D X))))->((ord_le2084554594od_a_a ((produc1182842125od_a_a A) B)) ((produc1182842125od_a_a C) D))))) of role axiom named fact_117_Sigma__mono
% 0.65/0.82  A new axiom: (forall (A:set_nat) (C:set_nat) (B:(nat->set_Product_prod_a_a)) (D:(nat->set_Product_prod_a_a)), (((ord_less_eq_set_nat A) C)->((forall (X:nat), (((member_nat X) A)->((ord_le1824328871od_a_a (B X)) (D X))))->((ord_le2084554594od_a_a ((produc1182842125od_a_a A) B)) ((produc1182842125od_a_a C) D)))))
% 0.65/0.82  FOF formula (forall (A:set_nat) (C:set_nat) (B:(nat->set_nat)) (D:(nat->set_nat)), (((ord_less_eq_set_nat A) C)->((forall (X:nat), (((member_nat X) A)->((ord_less_eq_set_nat (B X)) (D X))))->((ord_le841296385at_nat ((produc45129834at_nat A) B)) ((produc45129834at_nat C) D))))) of role axiom named fact_118_Sigma__mono
% 0.65/0.82  A new axiom: (forall (A:set_nat) (C:set_nat) (B:(nat->set_nat)) (D:(nat->set_nat)), (((ord_less_eq_set_nat A) C)->((forall (X:nat), (((member_nat X) A)->((ord_less_eq_set_nat (B X)) (D X))))->((ord_le841296385at_nat ((produc45129834at_nat A) B)) ((produc45129834at_nat C) D)))))
% 0.65/0.82  FOF formula (forall (A:set_nat) (C:set_nat) (B:(nat->set_a)) (D:(nat->set_a)), (((ord_less_eq_set_nat A) C)->((forall (X:nat), (((member_nat X) A)->((ord_less_eq_set_a (B X)) (D X))))->((ord_le344568633_nat_a ((product_Sigma_nat_a A) B)) ((product_Sigma_nat_a C) D))))) of role axiom named fact_119_Sigma__mono
% 0.65/0.82  A new axiom: (forall (A:set_nat) (C:set_nat) (B:(nat->set_a)) (D:(nat->set_a)), (((ord_less_eq_set_nat A) C)->((forall (X:nat), (((member_nat X) A)->((ord_less_eq_set_a (B X)) (D X))))->((ord_le344568633_nat_a ((product_Sigma_nat_a A) B)) ((product_Sigma_nat_a C) D)))))
% 0.65/0.82  FOF formula (forall (A:set_a) (C:set_a) (B:(a->set_Product_prod_a_a)) (D:(a->set_Product_prod_a_a)), (((ord_less_eq_set_a A) C)->((forall (X:a), (((member_a X) A)->((ord_le1824328871od_a_a (B X)) (D X))))->((ord_le1816232656od_a_a ((produc520147185od_a_a A) B)) ((produc520147185od_a_a C) D))))) of role axiom named fact_120_Sigma__mono
% 0.65/0.82  A new axiom: (forall (A:set_a) (C:set_a) (B:(a->set_Product_prod_a_a)) (D:(a->set_Product_prod_a_a)), (((ord_less_eq_set_a A) C)->((forall (X:a), (((member_a X) A)->((ord_le1824328871od_a_a (B X)) (D X))))->((ord_le1816232656od_a_a ((produc520147185od_a_a A) B)) ((produc520147185od_a_a C) D)))))
% 0.65/0.82  FOF formula (forall (A:set_a) (C:set_a) (B:(a->set_nat)) (D:(a->set_nat)), (((ord_less_eq_set_a A) C)->((forall (X:a), (((member_a X) A)->((ord_less_eq_set_nat (B X)) (D X))))->((ord_le2073555219_a_nat ((product_Sigma_a_nat A) B)) ((product_Sigma_a_nat C) D))))) of role axiom named fact_121_Sigma__mono
% 0.65/0.82  A new axiom: (forall (A:set_a) (C:set_a) (B:(a->set_nat)) (D:(a->set_nat)), (((ord_less_eq_set_a A) C)->((forall (X:a), (((member_a X) A)->((ord_less_eq_set_nat (B X)) (D X))))->((ord_le2073555219_a_nat ((product_Sigma_a_nat A) B)) ((product_Sigma_a_nat C) D)))))
% 0.65/0.82  FOF formula (forall (A:set_a) (C:set_a) (B:(a->set_a)) (D:(a->set_a)), (((ord_less_eq_set_a A) C)->((forall (X:a), (((member_a X) A)->((ord_less_eq_set_a (B X)) (D X))))->((ord_le1824328871od_a_a ((product_Sigma_a_a A) B)) ((product_Sigma_a_a C) D))))) of role axiom named fact_122_Sigma__mono
% 0.65/0.82  A new axiom: (forall (A:set_a) (C:set_a) (B:(a->set_a)) (D:(a->set_a)), (((ord_less_eq_set_a A) C)->((forall (X:a), (((member_a X) A)->((ord_less_eq_set_a (B X)) (D X))))->((ord_le1824328871od_a_a ((product_Sigma_a_a A) B)) ((product_Sigma_a_a C) D)))))
% 0.65/0.82  FOF formula (forall (A:set_Product_prod_a_a) (B:set_Product_prod_a_a), ((forall (X:product_prod_a_a), (((member449909584od_a_a X) A)->((member449909584od_a_a X) B)))->((ord_le1824328871od_a_a A) B))) of role axiom named fact_123_subsetI
% 0.65/0.82  A new axiom: (forall (A:set_Product_prod_a_a) (B:set_Product_prod_a_a), ((forall (X:product_prod_a_a), (((member449909584od_a_a X) A)->((member449909584od_a_a X) B)))->((ord_le1824328871od_a_a A) B)))
% 0.65/0.83  FOF formula (forall (A:set_nat) (B:set_nat), ((forall (X:nat), (((member_nat X) A)->((member_nat X) B)))->((ord_less_eq_set_nat A) B))) of role axiom named fact_124_subsetI
% 0.65/0.83  A new axiom: (forall (A:set_nat) (B:set_nat), ((forall (X:nat), (((member_nat X) A)->((member_nat X) B)))->((ord_less_eq_set_nat A) B)))
% 0.65/0.83  FOF formula (forall (A:set_a) (B:set_a), ((forall (X:a), (((member_a X) A)->((member_a X) B)))->((ord_less_eq_set_a A) B))) of role axiom named fact_125_subsetI
% 0.65/0.83  A new axiom: (forall (A:set_a) (B:set_a), ((forall (X:a), (((member_a X) A)->((member_a X) B)))->((ord_less_eq_set_a A) B)))
% 0.65/0.83  FOF formula (forall (A:set_Product_prod_a_a) (B:set_Product_prod_a_a), (((ord_le1824328871od_a_a A) B)->(((ord_le1824328871od_a_a B) A)->(((eq set_Product_prod_a_a) A) B)))) of role axiom named fact_126_subset__antisym
% 0.65/0.83  A new axiom: (forall (A:set_Product_prod_a_a) (B:set_Product_prod_a_a), (((ord_le1824328871od_a_a A) B)->(((ord_le1824328871od_a_a B) A)->(((eq set_Product_prod_a_a) A) B))))
% 0.65/0.83  FOF formula (forall (A:set_nat) (B:set_nat), (((ord_less_eq_set_nat A) B)->(((ord_less_eq_set_nat B) A)->(((eq set_nat) A) B)))) of role axiom named fact_127_subset__antisym
% 0.65/0.83  A new axiom: (forall (A:set_nat) (B:set_nat), (((ord_less_eq_set_nat A) B)->(((ord_less_eq_set_nat B) A)->(((eq set_nat) A) B))))
% 0.65/0.83  FOF formula (forall (A:set_a) (B:set_a), (((ord_less_eq_set_a A) B)->(((ord_less_eq_set_a B) A)->(((eq set_a) A) B)))) of role axiom named fact_128_subset__antisym
% 0.65/0.83  A new axiom: (forall (A:set_a) (B:set_a), (((ord_less_eq_set_a A) B)->(((ord_less_eq_set_a B) A)->(((eq set_a) A) B))))
% 0.65/0.83  FOF formula (forall (X3:set_Product_prod_a_a), ((ord_le1824328871od_a_a X3) X3)) of role axiom named fact_129_order__refl
% 0.65/0.83  A new axiom: (forall (X3:set_Product_prod_a_a), ((ord_le1824328871od_a_a X3) X3))
% 0.65/0.83  FOF formula (forall (X3:nat), ((ord_less_eq_nat X3) X3)) of role axiom named fact_130_order__refl
% 0.65/0.83  A new axiom: (forall (X3:nat), ((ord_less_eq_nat X3) X3))
% 0.65/0.83  FOF formula (forall (X3:set_nat), ((ord_less_eq_set_nat X3) X3)) of role axiom named fact_131_order__refl
% 0.65/0.83  A new axiom: (forall (X3:set_nat), ((ord_less_eq_set_nat X3) X3))
% 0.65/0.83  FOF formula (forall (X3:set_a), ((ord_less_eq_set_a X3) X3)) of role axiom named fact_132_order__refl
% 0.65/0.83  A new axiom: (forall (X3:set_a), ((ord_less_eq_set_a X3) X3))
% 0.65/0.83  FOF formula (forall (R2:pair_p125712459t_unit) (R3:pair_p125712459t_unit), ((((eq set_a) (pair_p1047056820t_unit R2)) (pair_p1047056820t_unit R3))->((((eq set_Product_prod_a_a) (pair_p133601421t_unit R2)) (pair_p133601421t_unit R3))->((((eq product_unit) (pair_p1896222615t_unit R2)) (pair_p1896222615t_unit R3))->(((eq pair_p125712459t_unit) R2) R3))))) of role axiom named fact_133_pair__pre__digraph_Oequality
% 0.65/0.83  A new axiom: (forall (R2:pair_p125712459t_unit) (R3:pair_p125712459t_unit), ((((eq set_a) (pair_p1047056820t_unit R2)) (pair_p1047056820t_unit R3))->((((eq set_Product_prod_a_a) (pair_p133601421t_unit R2)) (pair_p133601421t_unit R3))->((((eq product_unit) (pair_p1896222615t_unit R2)) (pair_p1896222615t_unit R3))->(((eq pair_p125712459t_unit) R2) R3)))))
% 0.65/0.83  FOF formula (forall (R2:pair_p1914262621t_unit) (R3:pair_p1914262621t_unit), ((((eq set_nat) (pair_p1677060310t_unit R2)) (pair_p1677060310t_unit R3))->((((eq set_Pr1986765409at_nat) (pair_p715279805t_unit R2)) (pair_p715279805t_unit R3))->((((eq product_unit) (pair_p69470259t_unit R2)) (pair_p69470259t_unit R3))->(((eq pair_p1914262621t_unit) R2) R3))))) of role axiom named fact_134_pair__pre__digraph_Oequality
% 0.65/0.83  A new axiom: (forall (R2:pair_p1914262621t_unit) (R3:pair_p1914262621t_unit), ((((eq set_nat) (pair_p1677060310t_unit R2)) (pair_p1677060310t_unit R3))->((((eq set_Pr1986765409at_nat) (pair_p715279805t_unit R2)) (pair_p715279805t_unit R3))->((((eq product_unit) (pair_p69470259t_unit R2)) (pair_p69470259t_unit R3))->(((eq pair_p1914262621t_unit) R2) R3)))))
% 0.65/0.83  FOF formula (forall (R2:pair_p1765063010t_unit) (R3:pair_p1765063010t_unit), ((((eq set_Product_prod_a_a) (pair_p447552203t_unit R2)) (pair_p447552203t_unit R3))->((((eq set_Pr1948701895od_a_a) (pair_p1783210148t_unit R2)) (pair_p1783210148t_unit R3))->((((eq product_unit) (pair_p1984658862t_unit R2)) (pair_p1984658862t_unit R3))->(((eq pair_p1765063010t_unit) R2) R3))))) of role axiom named fact_135_pair__pre__digraph_Oequality
% 0.68/0.84  A new axiom: (forall (R2:pair_p1765063010t_unit) (R3:pair_p1765063010t_unit), ((((eq set_Product_prod_a_a) (pair_p447552203t_unit R2)) (pair_p447552203t_unit R3))->((((eq set_Pr1948701895od_a_a) (pair_p1783210148t_unit R2)) (pair_p1783210148t_unit R3))->((((eq product_unit) (pair_p1984658862t_unit R2)) (pair_p1984658862t_unit R3))->(((eq pair_p1765063010t_unit) R2) R3)))))
% 0.68/0.84  FOF formula (forall (A:set_a) (B:set_a) (C:(a->set_a)) (D:(a->set_a)), ((((eq set_a) A) B)->((forall (X:a), (((member_a X) B)->(((eq set_a) (C X)) (D X))))->(((eq set_Product_prod_a_a) ((product_Sigma_a_a A) C)) ((product_Sigma_a_a B) D))))) of role axiom named fact_136_Sigma__cong
% 0.68/0.84  A new axiom: (forall (A:set_a) (B:set_a) (C:(a->set_a)) (D:(a->set_a)), ((((eq set_a) A) B)->((forall (X:a), (((member_a X) B)->(((eq set_a) (C X)) (D X))))->(((eq set_Product_prod_a_a) ((product_Sigma_a_a A) C)) ((product_Sigma_a_a B) D)))))
% 0.68/0.84  FOF formula (forall (X3:a) (C:set_a) (A:set_a) (B:set_a), (((member_a X3) C)->(((eq Prop) (((eq set_Product_prod_a_a) ((product_Sigma_a_a A) (fun (Uu:a)=> C))) ((product_Sigma_a_a B) (fun (Uu:a)=> C)))) (((eq set_a) A) B)))) of role axiom named fact_137_Times__eq__cancel2
% 0.68/0.84  A new axiom: (forall (X3:a) (C:set_a) (A:set_a) (B:set_a), (((member_a X3) C)->(((eq Prop) (((eq set_Product_prod_a_a) ((product_Sigma_a_a A) (fun (Uu:a)=> C))) ((product_Sigma_a_a B) (fun (Uu:a)=> C)))) (((eq set_a) A) B))))
% 0.68/0.84  FOF formula (forall (A:set_Product_prod_a_a) (P:(product_prod_a_a->Prop)), ((ord_le1824328871od_a_a (collec645855634od_a_a (fun (X2:product_prod_a_a)=> ((and ((member449909584od_a_a X2) A)) (P X2))))) A)) of role axiom named fact_138_Collect__subset
% 0.68/0.84  A new axiom: (forall (A:set_Product_prod_a_a) (P:(product_prod_a_a->Prop)), ((ord_le1824328871od_a_a (collec645855634od_a_a (fun (X2:product_prod_a_a)=> ((and ((member449909584od_a_a X2) A)) (P X2))))) A))
% 0.68/0.84  FOF formula (forall (A:set_nat) (P:(nat->Prop)), ((ord_less_eq_set_nat (collect_nat (fun (X2:nat)=> ((and ((member_nat X2) A)) (P X2))))) A)) of role axiom named fact_139_Collect__subset
% 0.68/0.84  A new axiom: (forall (A:set_nat) (P:(nat->Prop)), ((ord_less_eq_set_nat (collect_nat (fun (X2:nat)=> ((and ((member_nat X2) A)) (P X2))))) A))
% 0.68/0.84  FOF formula (forall (A:set_a) (P:(a->Prop)), ((ord_less_eq_set_a (collect_a (fun (X2:a)=> ((and ((member_a X2) A)) (P X2))))) A)) of role axiom named fact_140_Collect__subset
% 0.68/0.84  A new axiom: (forall (A:set_a) (P:(a->Prop)), ((ord_less_eq_set_a (collect_a (fun (X2:a)=> ((and ((member_a X2) A)) (P X2))))) A))
% 0.68/0.84  FOF formula (((eq (set_Product_prod_a_a->(set_Product_prod_a_a->Prop))) ord_le1824328871od_a_a) (fun (A5:set_Product_prod_a_a) (B2:set_Product_prod_a_a)=> ((ord_le1347718902_a_a_o (fun (X2:product_prod_a_a)=> ((member449909584od_a_a X2) A5))) (fun (X2:product_prod_a_a)=> ((member449909584od_a_a X2) B2))))) of role axiom named fact_141_less__eq__set__def
% 0.68/0.84  A new axiom: (((eq (set_Product_prod_a_a->(set_Product_prod_a_a->Prop))) ord_le1824328871od_a_a) (fun (A5:set_Product_prod_a_a) (B2:set_Product_prod_a_a)=> ((ord_le1347718902_a_a_o (fun (X2:product_prod_a_a)=> ((member449909584od_a_a X2) A5))) (fun (X2:product_prod_a_a)=> ((member449909584od_a_a X2) B2)))))
% 0.68/0.84  FOF formula (((eq (set_nat->(set_nat->Prop))) ord_less_eq_set_nat) (fun (A5:set_nat) (B2:set_nat)=> ((ord_less_eq_nat_o (fun (X2:nat)=> ((member_nat X2) A5))) (fun (X2:nat)=> ((member_nat X2) B2))))) of role axiom named fact_142_less__eq__set__def
% 0.68/0.84  A new axiom: (((eq (set_nat->(set_nat->Prop))) ord_less_eq_set_nat) (fun (A5:set_nat) (B2:set_nat)=> ((ord_less_eq_nat_o (fun (X2:nat)=> ((member_nat X2) A5))) (fun (X2:nat)=> ((member_nat X2) B2)))))
% 0.68/0.84  FOF formula (((eq (set_a->(set_a->Prop))) ord_less_eq_set_a) (fun (A5:set_a) (B2:set_a)=> ((ord_less_eq_a_o (fun (X2:a)=> ((member_a X2) A5))) (fun (X2:a)=> ((member_a X2) B2))))) of role axiom named fact_143_less__eq__set__def
% 0.68/0.85  A new axiom: (((eq (set_a->(set_a->Prop))) ord_less_eq_set_a) (fun (A5:set_a) (B2:set_a)=> ((ord_less_eq_a_o (fun (X2:a)=> ((member_a X2) A5))) (fun (X2:a)=> ((member_a X2) B2)))))
% 0.68/0.85  FOF formula (forall (B3:set_Product_prod_a_a) (A2:set_Product_prod_a_a), (((ord_le1824328871od_a_a B3) A2)->(((ord_le1824328871od_a_a A2) B3)->(((eq set_Product_prod_a_a) A2) B3)))) of role axiom named fact_144_dual__order_Oantisym
% 0.68/0.85  A new axiom: (forall (B3:set_Product_prod_a_a) (A2:set_Product_prod_a_a), (((ord_le1824328871od_a_a B3) A2)->(((ord_le1824328871od_a_a A2) B3)->(((eq set_Product_prod_a_a) A2) B3))))
% 0.68/0.85  FOF formula (forall (B3:nat) (A2:nat), (((ord_less_eq_nat B3) A2)->(((ord_less_eq_nat A2) B3)->(((eq nat) A2) B3)))) of role axiom named fact_145_dual__order_Oantisym
% 0.68/0.85  A new axiom: (forall (B3:nat) (A2:nat), (((ord_less_eq_nat B3) A2)->(((ord_less_eq_nat A2) B3)->(((eq nat) A2) B3))))
% 0.68/0.85  FOF formula (forall (B3:set_nat) (A2:set_nat), (((ord_less_eq_set_nat B3) A2)->(((ord_less_eq_set_nat A2) B3)->(((eq set_nat) A2) B3)))) of role axiom named fact_146_dual__order_Oantisym
% 0.68/0.85  A new axiom: (forall (B3:set_nat) (A2:set_nat), (((ord_less_eq_set_nat B3) A2)->(((ord_less_eq_set_nat A2) B3)->(((eq set_nat) A2) B3))))
% 0.68/0.85  FOF formula (forall (B3:set_a) (A2:set_a), (((ord_less_eq_set_a B3) A2)->(((ord_less_eq_set_a A2) B3)->(((eq set_a) A2) B3)))) of role axiom named fact_147_dual__order_Oantisym
% 0.68/0.85  A new axiom: (forall (B3:set_a) (A2:set_a), (((ord_less_eq_set_a B3) A2)->(((ord_less_eq_set_a A2) B3)->(((eq set_a) A2) B3))))
% 0.68/0.85  FOF formula (((eq (set_Product_prod_a_a->(set_Product_prod_a_a->Prop))) (fun (Y:set_Product_prod_a_a) (Z:set_Product_prod_a_a)=> (((eq set_Product_prod_a_a) Y) Z))) (fun (A4:set_Product_prod_a_a) (B4:set_Product_prod_a_a)=> ((and ((ord_le1824328871od_a_a B4) A4)) ((ord_le1824328871od_a_a A4) B4)))) of role axiom named fact_148_dual__order_Oeq__iff
% 0.68/0.85  A new axiom: (((eq (set_Product_prod_a_a->(set_Product_prod_a_a->Prop))) (fun (Y:set_Product_prod_a_a) (Z:set_Product_prod_a_a)=> (((eq set_Product_prod_a_a) Y) Z))) (fun (A4:set_Product_prod_a_a) (B4:set_Product_prod_a_a)=> ((and ((ord_le1824328871od_a_a B4) A4)) ((ord_le1824328871od_a_a A4) B4))))
% 0.68/0.85  FOF formula (((eq (nat->(nat->Prop))) (fun (Y:nat) (Z:nat)=> (((eq nat) Y) Z))) (fun (A4:nat) (B4:nat)=> ((and ((ord_less_eq_nat B4) A4)) ((ord_less_eq_nat A4) B4)))) of role axiom named fact_149_dual__order_Oeq__iff
% 0.68/0.85  A new axiom: (((eq (nat->(nat->Prop))) (fun (Y:nat) (Z:nat)=> (((eq nat) Y) Z))) (fun (A4:nat) (B4:nat)=> ((and ((ord_less_eq_nat B4) A4)) ((ord_less_eq_nat A4) B4))))
% 0.68/0.85  FOF formula (((eq (set_nat->(set_nat->Prop))) (fun (Y:set_nat) (Z:set_nat)=> (((eq set_nat) Y) Z))) (fun (A4:set_nat) (B4:set_nat)=> ((and ((ord_less_eq_set_nat B4) A4)) ((ord_less_eq_set_nat A4) B4)))) of role axiom named fact_150_dual__order_Oeq__iff
% 0.68/0.85  A new axiom: (((eq (set_nat->(set_nat->Prop))) (fun (Y:set_nat) (Z:set_nat)=> (((eq set_nat) Y) Z))) (fun (A4:set_nat) (B4:set_nat)=> ((and ((ord_less_eq_set_nat B4) A4)) ((ord_less_eq_set_nat A4) B4))))
% 0.68/0.85  FOF formula (((eq (set_a->(set_a->Prop))) (fun (Y:set_a) (Z:set_a)=> (((eq set_a) Y) Z))) (fun (A4:set_a) (B4:set_a)=> ((and ((ord_less_eq_set_a B4) A4)) ((ord_less_eq_set_a A4) B4)))) of role axiom named fact_151_dual__order_Oeq__iff
% 0.68/0.85  A new axiom: (((eq (set_a->(set_a->Prop))) (fun (Y:set_a) (Z:set_a)=> (((eq set_a) Y) Z))) (fun (A4:set_a) (B4:set_a)=> ((and ((ord_less_eq_set_a B4) A4)) ((ord_less_eq_set_a A4) B4))))
% 0.68/0.85  FOF formula (forall (B3:set_Product_prod_a_a) (A2:set_Product_prod_a_a) (C2:set_Product_prod_a_a), (((ord_le1824328871od_a_a B3) A2)->(((ord_le1824328871od_a_a C2) B3)->((ord_le1824328871od_a_a C2) A2)))) of role axiom named fact_152_dual__order_Otrans
% 0.68/0.85  A new axiom: (forall (B3:set_Product_prod_a_a) (A2:set_Product_prod_a_a) (C2:set_Product_prod_a_a), (((ord_le1824328871od_a_a B3) A2)->(((ord_le1824328871od_a_a C2) B3)->((ord_le1824328871od_a_a C2) A2))))
% 0.68/0.85  FOF formula (forall (B3:nat) (A2:nat) (C2:nat), (((ord_less_eq_nat B3) A2)->(((ord_less_eq_nat C2) B3)->((ord_less_eq_nat C2) A2)))) of role axiom named fact_153_dual__order_Otrans
% 0.68/0.86  A new axiom: (forall (B3:nat) (A2:nat) (C2:nat), (((ord_less_eq_nat B3) A2)->(((ord_less_eq_nat C2) B3)->((ord_less_eq_nat C2) A2))))
% 0.68/0.86  FOF formula (forall (B3:set_nat) (A2:set_nat) (C2:set_nat), (((ord_less_eq_set_nat B3) A2)->(((ord_less_eq_set_nat C2) B3)->((ord_less_eq_set_nat C2) A2)))) of role axiom named fact_154_dual__order_Otrans
% 0.68/0.86  A new axiom: (forall (B3:set_nat) (A2:set_nat) (C2:set_nat), (((ord_less_eq_set_nat B3) A2)->(((ord_less_eq_set_nat C2) B3)->((ord_less_eq_set_nat C2) A2))))
% 0.68/0.86  FOF formula (forall (B3:set_a) (A2:set_a) (C2:set_a), (((ord_less_eq_set_a B3) A2)->(((ord_less_eq_set_a C2) B3)->((ord_less_eq_set_a C2) A2)))) of role axiom named fact_155_dual__order_Otrans
% 0.68/0.86  A new axiom: (forall (B3:set_a) (A2:set_a) (C2:set_a), (((ord_less_eq_set_a B3) A2)->(((ord_less_eq_set_a C2) B3)->((ord_less_eq_set_a C2) A2))))
% 0.68/0.86  FOF formula (forall (P:(nat->(nat->Prop))) (A2:nat) (B3:nat), ((forall (A3:nat) (B5:nat), (((ord_less_eq_nat A3) B5)->((P A3) B5)))->((forall (A3:nat) (B5:nat), (((P B5) A3)->((P A3) B5)))->((P A2) B3)))) of role axiom named fact_156_linorder__wlog
% 0.68/0.86  A new axiom: (forall (P:(nat->(nat->Prop))) (A2:nat) (B3:nat), ((forall (A3:nat) (B5:nat), (((ord_less_eq_nat A3) B5)->((P A3) B5)))->((forall (A3:nat) (B5:nat), (((P B5) A3)->((P A3) B5)))->((P A2) B3))))
% 0.68/0.86  FOF formula (forall (A2:set_Product_prod_a_a), ((ord_le1824328871od_a_a A2) A2)) of role axiom named fact_157_dual__order_Orefl
% 0.68/0.86  A new axiom: (forall (A2:set_Product_prod_a_a), ((ord_le1824328871od_a_a A2) A2))
% 0.68/0.86  FOF formula (forall (A2:nat), ((ord_less_eq_nat A2) A2)) of role axiom named fact_158_dual__order_Orefl
% 0.68/0.86  A new axiom: (forall (A2:nat), ((ord_less_eq_nat A2) A2))
% 0.68/0.86  FOF formula (forall (A2:set_nat), ((ord_less_eq_set_nat A2) A2)) of role axiom named fact_159_dual__order_Orefl
% 0.68/0.86  A new axiom: (forall (A2:set_nat), ((ord_less_eq_set_nat A2) A2))
% 0.68/0.86  FOF formula (forall (A2:set_a), ((ord_less_eq_set_a A2) A2)) of role axiom named fact_160_dual__order_Orefl
% 0.68/0.86  A new axiom: (forall (A2:set_a), ((ord_less_eq_set_a A2) A2))
% 0.68/0.86  FOF formula (forall (X3:set_Product_prod_a_a) (Y2:set_Product_prod_a_a) (Z2:set_Product_prod_a_a), (((ord_le1824328871od_a_a X3) Y2)->(((ord_le1824328871od_a_a Y2) Z2)->((ord_le1824328871od_a_a X3) Z2)))) of role axiom named fact_161_order__trans
% 0.68/0.86  A new axiom: (forall (X3:set_Product_prod_a_a) (Y2:set_Product_prod_a_a) (Z2:set_Product_prod_a_a), (((ord_le1824328871od_a_a X3) Y2)->(((ord_le1824328871od_a_a Y2) Z2)->((ord_le1824328871od_a_a X3) Z2))))
% 0.68/0.86  FOF formula (forall (X3:nat) (Y2:nat) (Z2:nat), (((ord_less_eq_nat X3) Y2)->(((ord_less_eq_nat Y2) Z2)->((ord_less_eq_nat X3) Z2)))) of role axiom named fact_162_order__trans
% 0.68/0.86  A new axiom: (forall (X3:nat) (Y2:nat) (Z2:nat), (((ord_less_eq_nat X3) Y2)->(((ord_less_eq_nat Y2) Z2)->((ord_less_eq_nat X3) Z2))))
% 0.68/0.86  FOF formula (forall (X3:set_nat) (Y2:set_nat) (Z2:set_nat), (((ord_less_eq_set_nat X3) Y2)->(((ord_less_eq_set_nat Y2) Z2)->((ord_less_eq_set_nat X3) Z2)))) of role axiom named fact_163_order__trans
% 0.68/0.86  A new axiom: (forall (X3:set_nat) (Y2:set_nat) (Z2:set_nat), (((ord_less_eq_set_nat X3) Y2)->(((ord_less_eq_set_nat Y2) Z2)->((ord_less_eq_set_nat X3) Z2))))
% 0.68/0.86  FOF formula (forall (X3:set_a) (Y2:set_a) (Z2:set_a), (((ord_less_eq_set_a X3) Y2)->(((ord_less_eq_set_a Y2) Z2)->((ord_less_eq_set_a X3) Z2)))) of role axiom named fact_164_order__trans
% 0.68/0.86  A new axiom: (forall (X3:set_a) (Y2:set_a) (Z2:set_a), (((ord_less_eq_set_a X3) Y2)->(((ord_less_eq_set_a Y2) Z2)->((ord_less_eq_set_a X3) Z2))))
% 0.68/0.86  FOF formula (forall (A2:set_Product_prod_a_a) (B3:set_Product_prod_a_a), (((ord_le1824328871od_a_a A2) B3)->(((ord_le1824328871od_a_a B3) A2)->(((eq set_Product_prod_a_a) A2) B3)))) of role axiom named fact_165_order__class_Oorder_Oantisym
% 0.68/0.86  A new axiom: (forall (A2:set_Product_prod_a_a) (B3:set_Product_prod_a_a), (((ord_le1824328871od_a_a A2) B3)->(((ord_le1824328871od_a_a B3) A2)->(((eq set_Product_prod_a_a) A2) B3))))
% 0.68/0.86  FOF formula (forall (A2:nat) (B3:nat), (((ord_less_eq_nat A2) B3)->(((ord_less_eq_nat B3) A2)->(((eq nat) A2) B3)))) of role axiom named fact_166_order__class_Oorder_Oantisym
% 0.68/0.87  A new axiom: (forall (A2:nat) (B3:nat), (((ord_less_eq_nat A2) B3)->(((ord_less_eq_nat B3) A2)->(((eq nat) A2) B3))))
% 0.68/0.87  FOF formula (forall (A2:set_nat) (B3:set_nat), (((ord_less_eq_set_nat A2) B3)->(((ord_less_eq_set_nat B3) A2)->(((eq set_nat) A2) B3)))) of role axiom named fact_167_order__class_Oorder_Oantisym
% 0.68/0.87  A new axiom: (forall (A2:set_nat) (B3:set_nat), (((ord_less_eq_set_nat A2) B3)->(((ord_less_eq_set_nat B3) A2)->(((eq set_nat) A2) B3))))
% 0.68/0.87  FOF formula (forall (A2:set_a) (B3:set_a), (((ord_less_eq_set_a A2) B3)->(((ord_less_eq_set_a B3) A2)->(((eq set_a) A2) B3)))) of role axiom named fact_168_order__class_Oorder_Oantisym
% 0.68/0.87  A new axiom: (forall (A2:set_a) (B3:set_a), (((ord_less_eq_set_a A2) B3)->(((ord_less_eq_set_a B3) A2)->(((eq set_a) A2) B3))))
% 0.68/0.87  FOF formula (forall (A2:set_Product_prod_a_a) (B3:set_Product_prod_a_a) (C2:set_Product_prod_a_a), (((ord_le1824328871od_a_a A2) B3)->((((eq set_Product_prod_a_a) B3) C2)->((ord_le1824328871od_a_a A2) C2)))) of role axiom named fact_169_ord__le__eq__trans
% 0.68/0.87  A new axiom: (forall (A2:set_Product_prod_a_a) (B3:set_Product_prod_a_a) (C2:set_Product_prod_a_a), (((ord_le1824328871od_a_a A2) B3)->((((eq set_Product_prod_a_a) B3) C2)->((ord_le1824328871od_a_a A2) C2))))
% 0.68/0.87  FOF formula (forall (A2:nat) (B3:nat) (C2:nat), (((ord_less_eq_nat A2) B3)->((((eq nat) B3) C2)->((ord_less_eq_nat A2) C2)))) of role axiom named fact_170_ord__le__eq__trans
% 0.68/0.87  A new axiom: (forall (A2:nat) (B3:nat) (C2:nat), (((ord_less_eq_nat A2) B3)->((((eq nat) B3) C2)->((ord_less_eq_nat A2) C2))))
% 0.68/0.87  FOF formula (forall (A2:set_nat) (B3:set_nat) (C2:set_nat), (((ord_less_eq_set_nat A2) B3)->((((eq set_nat) B3) C2)->((ord_less_eq_set_nat A2) C2)))) of role axiom named fact_171_ord__le__eq__trans
% 0.68/0.87  A new axiom: (forall (A2:set_nat) (B3:set_nat) (C2:set_nat), (((ord_less_eq_set_nat A2) B3)->((((eq set_nat) B3) C2)->((ord_less_eq_set_nat A2) C2))))
% 0.68/0.87  FOF formula (forall (A2:set_a) (B3:set_a) (C2:set_a), (((ord_less_eq_set_a A2) B3)->((((eq set_a) B3) C2)->((ord_less_eq_set_a A2) C2)))) of role axiom named fact_172_ord__le__eq__trans
% 0.68/0.87  A new axiom: (forall (A2:set_a) (B3:set_a) (C2:set_a), (((ord_less_eq_set_a A2) B3)->((((eq set_a) B3) C2)->((ord_less_eq_set_a A2) C2))))
% 0.68/0.87  FOF formula (forall (A2:product_prod_a_a) (P:(product_prod_a_a->Prop)), (((eq Prop) ((member449909584od_a_a A2) (collec645855634od_a_a P))) (P A2))) of role axiom named fact_173_mem__Collect__eq
% 0.68/0.87  A new axiom: (forall (A2:product_prod_a_a) (P:(product_prod_a_a->Prop)), (((eq Prop) ((member449909584od_a_a A2) (collec645855634od_a_a P))) (P A2)))
% 0.68/0.87  FOF formula (forall (A2:nat) (P:(nat->Prop)), (((eq Prop) ((member_nat A2) (collect_nat P))) (P A2))) of role axiom named fact_174_mem__Collect__eq
% 0.68/0.87  A new axiom: (forall (A2:nat) (P:(nat->Prop)), (((eq Prop) ((member_nat A2) (collect_nat P))) (P A2)))
% 0.68/0.87  FOF formula (forall (A:set_Product_prod_a_a), (((eq set_Product_prod_a_a) (collec645855634od_a_a (fun (X2:product_prod_a_a)=> ((member449909584od_a_a X2) A)))) A)) of role axiom named fact_175_Collect__mem__eq
% 0.68/0.87  A new axiom: (forall (A:set_Product_prod_a_a), (((eq set_Product_prod_a_a) (collec645855634od_a_a (fun (X2:product_prod_a_a)=> ((member449909584od_a_a X2) A)))) A))
% 0.68/0.87  FOF formula (forall (A:set_nat), (((eq set_nat) (collect_nat (fun (X2:nat)=> ((member_nat X2) A)))) A)) of role axiom named fact_176_Collect__mem__eq
% 0.68/0.87  A new axiom: (forall (A:set_nat), (((eq set_nat) (collect_nat (fun (X2:nat)=> ((member_nat X2) A)))) A))
% 0.68/0.87  FOF formula (forall (P:(product_prod_a_a->Prop)) (Q:(product_prod_a_a->Prop)), ((forall (X:product_prod_a_a), (((eq Prop) (P X)) (Q X)))->(((eq set_Product_prod_a_a) (collec645855634od_a_a P)) (collec645855634od_a_a Q)))) of role axiom named fact_177_Collect__cong
% 0.68/0.87  A new axiom: (forall (P:(product_prod_a_a->Prop)) (Q:(product_prod_a_a->Prop)), ((forall (X:product_prod_a_a), (((eq Prop) (P X)) (Q X)))->(((eq set_Product_prod_a_a) (collec645855634od_a_a P)) (collec645855634od_a_a Q))))
% 0.68/0.87  FOF formula (forall (P:(nat->Prop)) (Q:(nat->Prop)), ((forall (X:nat), (((eq Prop) (P X)) (Q X)))->(((eq set_nat) (collect_nat P)) (collect_nat Q)))) of role axiom named fact_178_Collect__cong
% 0.68/0.87  A new axiom: (forall (P:(nat->Prop)) (Q:(nat->Prop)), ((forall (X:nat), (((eq Prop) (P X)) (Q X)))->(((eq set_nat) (collect_nat P)) (collect_nat Q))))
% 0.68/0.87  FOF formula (forall (A2:set_Product_prod_a_a) (B3:set_Product_prod_a_a) (C2:set_Product_prod_a_a), ((((eq set_Product_prod_a_a) A2) B3)->(((ord_le1824328871od_a_a B3) C2)->((ord_le1824328871od_a_a A2) C2)))) of role axiom named fact_179_ord__eq__le__trans
% 0.68/0.87  A new axiom: (forall (A2:set_Product_prod_a_a) (B3:set_Product_prod_a_a) (C2:set_Product_prod_a_a), ((((eq set_Product_prod_a_a) A2) B3)->(((ord_le1824328871od_a_a B3) C2)->((ord_le1824328871od_a_a A2) C2))))
% 0.68/0.87  FOF formula (forall (A2:nat) (B3:nat) (C2:nat), ((((eq nat) A2) B3)->(((ord_less_eq_nat B3) C2)->((ord_less_eq_nat A2) C2)))) of role axiom named fact_180_ord__eq__le__trans
% 0.68/0.87  A new axiom: (forall (A2:nat) (B3:nat) (C2:nat), ((((eq nat) A2) B3)->(((ord_less_eq_nat B3) C2)->((ord_less_eq_nat A2) C2))))
% 0.68/0.87  FOF formula (forall (A2:set_nat) (B3:set_nat) (C2:set_nat), ((((eq set_nat) A2) B3)->(((ord_less_eq_set_nat B3) C2)->((ord_less_eq_set_nat A2) C2)))) of role axiom named fact_181_ord__eq__le__trans
% 0.68/0.87  A new axiom: (forall (A2:set_nat) (B3:set_nat) (C2:set_nat), ((((eq set_nat) A2) B3)->(((ord_less_eq_set_nat B3) C2)->((ord_less_eq_set_nat A2) C2))))
% 0.68/0.87  FOF formula (forall (A2:set_a) (B3:set_a) (C2:set_a), ((((eq set_a) A2) B3)->(((ord_less_eq_set_a B3) C2)->((ord_less_eq_set_a A2) C2)))) of role axiom named fact_182_ord__eq__le__trans
% 0.68/0.87  A new axiom: (forall (A2:set_a) (B3:set_a) (C2:set_a), ((((eq set_a) A2) B3)->(((ord_less_eq_set_a B3) C2)->((ord_less_eq_set_a A2) C2))))
% 0.68/0.87  FOF formula (((eq (set_Product_prod_a_a->(set_Product_prod_a_a->Prop))) (fun (Y:set_Product_prod_a_a) (Z:set_Product_prod_a_a)=> (((eq set_Product_prod_a_a) Y) Z))) (fun (A4:set_Product_prod_a_a) (B4:set_Product_prod_a_a)=> ((and ((ord_le1824328871od_a_a A4) B4)) ((ord_le1824328871od_a_a B4) A4)))) of role axiom named fact_183_order__class_Oorder_Oeq__iff
% 0.68/0.87  A new axiom: (((eq (set_Product_prod_a_a->(set_Product_prod_a_a->Prop))) (fun (Y:set_Product_prod_a_a) (Z:set_Product_prod_a_a)=> (((eq set_Product_prod_a_a) Y) Z))) (fun (A4:set_Product_prod_a_a) (B4:set_Product_prod_a_a)=> ((and ((ord_le1824328871od_a_a A4) B4)) ((ord_le1824328871od_a_a B4) A4))))
% 0.68/0.87  FOF formula (((eq (nat->(nat->Prop))) (fun (Y:nat) (Z:nat)=> (((eq nat) Y) Z))) (fun (A4:nat) (B4:nat)=> ((and ((ord_less_eq_nat A4) B4)) ((ord_less_eq_nat B4) A4)))) of role axiom named fact_184_order__class_Oorder_Oeq__iff
% 0.68/0.87  A new axiom: (((eq (nat->(nat->Prop))) (fun (Y:nat) (Z:nat)=> (((eq nat) Y) Z))) (fun (A4:nat) (B4:nat)=> ((and ((ord_less_eq_nat A4) B4)) ((ord_less_eq_nat B4) A4))))
% 0.68/0.87  FOF formula (((eq (set_nat->(set_nat->Prop))) (fun (Y:set_nat) (Z:set_nat)=> (((eq set_nat) Y) Z))) (fun (A4:set_nat) (B4:set_nat)=> ((and ((ord_less_eq_set_nat A4) B4)) ((ord_less_eq_set_nat B4) A4)))) of role axiom named fact_185_order__class_Oorder_Oeq__iff
% 0.68/0.87  A new axiom: (((eq (set_nat->(set_nat->Prop))) (fun (Y:set_nat) (Z:set_nat)=> (((eq set_nat) Y) Z))) (fun (A4:set_nat) (B4:set_nat)=> ((and ((ord_less_eq_set_nat A4) B4)) ((ord_less_eq_set_nat B4) A4))))
% 0.68/0.87  FOF formula (((eq (set_a->(set_a->Prop))) (fun (Y:set_a) (Z:set_a)=> (((eq set_a) Y) Z))) (fun (A4:set_a) (B4:set_a)=> ((and ((ord_less_eq_set_a A4) B4)) ((ord_less_eq_set_a B4) A4)))) of role axiom named fact_186_order__class_Oorder_Oeq__iff
% 0.68/0.87  A new axiom: (((eq (set_a->(set_a->Prop))) (fun (Y:set_a) (Z:set_a)=> (((eq set_a) Y) Z))) (fun (A4:set_a) (B4:set_a)=> ((and ((ord_less_eq_set_a A4) B4)) ((ord_less_eq_set_a B4) A4))))
% 0.68/0.87  FOF formula (forall (Y2:set_Product_prod_a_a) (X3:set_Product_prod_a_a), (((ord_le1824328871od_a_a Y2) X3)->(((eq Prop) ((ord_le1824328871od_a_a X3) Y2)) (((eq set_Product_prod_a_a) X3) Y2)))) of role axiom named fact_187_antisym__conv
% 0.68/0.87  A new axiom: (forall (Y2:set_Product_prod_a_a) (X3:set_Product_prod_a_a), (((ord_le1824328871od_a_a Y2) X3)->(((eq Prop) ((ord_le1824328871od_a_a X3) Y2)) (((eq set_Product_prod_a_a) X3) Y2))))
% 0.68/0.87  FOF formula (forall (Y2:nat) (X3:nat), (((ord_less_eq_nat Y2) X3)->(((eq Prop) ((ord_less_eq_nat X3) Y2)) (((eq nat) X3) Y2)))) of role axiom named fact_188_antisym__conv
% 0.68/0.88  A new axiom: (forall (Y2:nat) (X3:nat), (((ord_less_eq_nat Y2) X3)->(((eq Prop) ((ord_less_eq_nat X3) Y2)) (((eq nat) X3) Y2))))
% 0.68/0.88  FOF formula (forall (Y2:set_nat) (X3:set_nat), (((ord_less_eq_set_nat Y2) X3)->(((eq Prop) ((ord_less_eq_set_nat X3) Y2)) (((eq set_nat) X3) Y2)))) of role axiom named fact_189_antisym__conv
% 0.68/0.88  A new axiom: (forall (Y2:set_nat) (X3:set_nat), (((ord_less_eq_set_nat Y2) X3)->(((eq Prop) ((ord_less_eq_set_nat X3) Y2)) (((eq set_nat) X3) Y2))))
% 0.68/0.88  FOF formula (forall (Y2:set_a) (X3:set_a), (((ord_less_eq_set_a Y2) X3)->(((eq Prop) ((ord_less_eq_set_a X3) Y2)) (((eq set_a) X3) Y2)))) of role axiom named fact_190_antisym__conv
% 0.68/0.88  A new axiom: (forall (Y2:set_a) (X3:set_a), (((ord_less_eq_set_a Y2) X3)->(((eq Prop) ((ord_less_eq_set_a X3) Y2)) (((eq set_a) X3) Y2))))
% 0.68/0.88  FOF formula (forall (X3:nat) (Y2:nat) (Z2:nat), ((((ord_less_eq_nat X3) Y2)->(((ord_less_eq_nat Y2) Z2)->False))->((((ord_less_eq_nat Y2) X3)->(((ord_less_eq_nat X3) Z2)->False))->((((ord_less_eq_nat X3) Z2)->(((ord_less_eq_nat Z2) Y2)->False))->((((ord_less_eq_nat Z2) Y2)->(((ord_less_eq_nat Y2) X3)->False))->((((ord_less_eq_nat Y2) Z2)->(((ord_less_eq_nat Z2) X3)->False))->((((ord_less_eq_nat Z2) X3)->(((ord_less_eq_nat X3) Y2)->False))->False))))))) of role axiom named fact_191_le__cases3
% 0.68/0.88  A new axiom: (forall (X3:nat) (Y2:nat) (Z2:nat), ((((ord_less_eq_nat X3) Y2)->(((ord_less_eq_nat Y2) Z2)->False))->((((ord_less_eq_nat Y2) X3)->(((ord_less_eq_nat X3) Z2)->False))->((((ord_less_eq_nat X3) Z2)->(((ord_less_eq_nat Z2) Y2)->False))->((((ord_less_eq_nat Z2) Y2)->(((ord_less_eq_nat Y2) X3)->False))->((((ord_less_eq_nat Y2) Z2)->(((ord_less_eq_nat Z2) X3)->False))->((((ord_less_eq_nat Z2) X3)->(((ord_less_eq_nat X3) Y2)->False))->False)))))))
% 0.68/0.88  FOF formula (forall (A2:set_Product_prod_a_a) (B3:set_Product_prod_a_a) (C2:set_Product_prod_a_a), (((ord_le1824328871od_a_a A2) B3)->(((ord_le1824328871od_a_a B3) C2)->((ord_le1824328871od_a_a A2) C2)))) of role axiom named fact_192_order_Otrans
% 0.68/0.88  A new axiom: (forall (A2:set_Product_prod_a_a) (B3:set_Product_prod_a_a) (C2:set_Product_prod_a_a), (((ord_le1824328871od_a_a A2) B3)->(((ord_le1824328871od_a_a B3) C2)->((ord_le1824328871od_a_a A2) C2))))
% 0.68/0.88  FOF formula (forall (A2:nat) (B3:nat) (C2:nat), (((ord_less_eq_nat A2) B3)->(((ord_less_eq_nat B3) C2)->((ord_less_eq_nat A2) C2)))) of role axiom named fact_193_order_Otrans
% 0.68/0.88  A new axiom: (forall (A2:nat) (B3:nat) (C2:nat), (((ord_less_eq_nat A2) B3)->(((ord_less_eq_nat B3) C2)->((ord_less_eq_nat A2) C2))))
% 0.68/0.88  FOF formula (forall (A2:set_nat) (B3:set_nat) (C2:set_nat), (((ord_less_eq_set_nat A2) B3)->(((ord_less_eq_set_nat B3) C2)->((ord_less_eq_set_nat A2) C2)))) of role axiom named fact_194_order_Otrans
% 0.68/0.88  A new axiom: (forall (A2:set_nat) (B3:set_nat) (C2:set_nat), (((ord_less_eq_set_nat A2) B3)->(((ord_less_eq_set_nat B3) C2)->((ord_less_eq_set_nat A2) C2))))
% 0.68/0.88  FOF formula (forall (A2:set_a) (B3:set_a) (C2:set_a), (((ord_less_eq_set_a A2) B3)->(((ord_less_eq_set_a B3) C2)->((ord_less_eq_set_a A2) C2)))) of role axiom named fact_195_order_Otrans
% 0.68/0.88  A new axiom: (forall (A2:set_a) (B3:set_a) (C2:set_a), (((ord_less_eq_set_a A2) B3)->(((ord_less_eq_set_a B3) C2)->((ord_less_eq_set_a A2) C2))))
% 0.68/0.88  FOF formula (forall (X3:nat) (Y2:nat), ((((ord_less_eq_nat X3) Y2)->False)->((ord_less_eq_nat Y2) X3))) of role axiom named fact_196_le__cases
% 0.68/0.88  A new axiom: (forall (X3:nat) (Y2:nat), ((((ord_less_eq_nat X3) Y2)->False)->((ord_less_eq_nat Y2) X3)))
% 0.68/0.88  FOF formula (forall (X3:set_Product_prod_a_a) (Y2:set_Product_prod_a_a), ((((eq set_Product_prod_a_a) X3) Y2)->((ord_le1824328871od_a_a X3) Y2))) of role axiom named fact_197_eq__refl
% 0.68/0.88  A new axiom: (forall (X3:set_Product_prod_a_a) (Y2:set_Product_prod_a_a), ((((eq set_Product_prod_a_a) X3) Y2)->((ord_le1824328871od_a_a X3) Y2)))
% 0.68/0.88  FOF formula (forall (X3:nat) (Y2:nat), ((((eq nat) X3) Y2)->((ord_less_eq_nat X3) Y2))) of role axiom named fact_198_eq__refl
% 0.68/0.88  A new axiom: (forall (X3:nat) (Y2:nat), ((((eq nat) X3) Y2)->((ord_less_eq_nat X3) Y2)))
% 0.68/0.88  FOF formula (forall (X3:set_nat) (Y2:set_nat), ((((eq set_nat) X3) Y2)->((ord_less_eq_set_nat X3) Y2))) of role axiom named fact_199_eq__refl
% 0.68/0.89  A new axiom: (forall (X3:set_nat) (Y2:set_nat), ((((eq set_nat) X3) Y2)->((ord_less_eq_set_nat X3) Y2)))
% 0.68/0.89  FOF formula (forall (X3:set_a) (Y2:set_a), ((((eq set_a) X3) Y2)->((ord_less_eq_set_a X3) Y2))) of role axiom named fact_200_eq__refl
% 0.68/0.89  A new axiom: (forall (X3:set_a) (Y2:set_a), ((((eq set_a) X3) Y2)->((ord_less_eq_set_a X3) Y2)))
% 0.68/0.89  FOF formula (forall (X3:nat) (Y2:nat), ((or ((ord_less_eq_nat X3) Y2)) ((ord_less_eq_nat Y2) X3))) of role axiom named fact_201_linear
% 0.68/0.89  A new axiom: (forall (X3:nat) (Y2:nat), ((or ((ord_less_eq_nat X3) Y2)) ((ord_less_eq_nat Y2) X3)))
% 0.68/0.89  FOF formula (forall (X3:set_Product_prod_a_a) (Y2:set_Product_prod_a_a), (((ord_le1824328871od_a_a X3) Y2)->(((ord_le1824328871od_a_a Y2) X3)->(((eq set_Product_prod_a_a) X3) Y2)))) of role axiom named fact_202_antisym
% 0.68/0.89  A new axiom: (forall (X3:set_Product_prod_a_a) (Y2:set_Product_prod_a_a), (((ord_le1824328871od_a_a X3) Y2)->(((ord_le1824328871od_a_a Y2) X3)->(((eq set_Product_prod_a_a) X3) Y2))))
% 0.68/0.89  FOF formula (forall (X3:nat) (Y2:nat), (((ord_less_eq_nat X3) Y2)->(((ord_less_eq_nat Y2) X3)->(((eq nat) X3) Y2)))) of role axiom named fact_203_antisym
% 0.68/0.89  A new axiom: (forall (X3:nat) (Y2:nat), (((ord_less_eq_nat X3) Y2)->(((ord_less_eq_nat Y2) X3)->(((eq nat) X3) Y2))))
% 0.68/0.89  FOF formula (forall (X3:set_nat) (Y2:set_nat), (((ord_less_eq_set_nat X3) Y2)->(((ord_less_eq_set_nat Y2) X3)->(((eq set_nat) X3) Y2)))) of role axiom named fact_204_antisym
% 0.68/0.89  A new axiom: (forall (X3:set_nat) (Y2:set_nat), (((ord_less_eq_set_nat X3) Y2)->(((ord_less_eq_set_nat Y2) X3)->(((eq set_nat) X3) Y2))))
% 0.68/0.89  FOF formula (forall (X3:set_a) (Y2:set_a), (((ord_less_eq_set_a X3) Y2)->(((ord_less_eq_set_a Y2) X3)->(((eq set_a) X3) Y2)))) of role axiom named fact_205_antisym
% 0.68/0.89  A new axiom: (forall (X3:set_a) (Y2:set_a), (((ord_less_eq_set_a X3) Y2)->(((ord_less_eq_set_a Y2) X3)->(((eq set_a) X3) Y2))))
% 0.68/0.89  FOF formula (((eq (set_Product_prod_a_a->(set_Product_prod_a_a->Prop))) (fun (Y:set_Product_prod_a_a) (Z:set_Product_prod_a_a)=> (((eq set_Product_prod_a_a) Y) Z))) (fun (X2:set_Product_prod_a_a) (Y3:set_Product_prod_a_a)=> ((and ((ord_le1824328871od_a_a X2) Y3)) ((ord_le1824328871od_a_a Y3) X2)))) of role axiom named fact_206_eq__iff
% 0.68/0.89  A new axiom: (((eq (set_Product_prod_a_a->(set_Product_prod_a_a->Prop))) (fun (Y:set_Product_prod_a_a) (Z:set_Product_prod_a_a)=> (((eq set_Product_prod_a_a) Y) Z))) (fun (X2:set_Product_prod_a_a) (Y3:set_Product_prod_a_a)=> ((and ((ord_le1824328871od_a_a X2) Y3)) ((ord_le1824328871od_a_a Y3) X2))))
% 0.68/0.89  FOF formula (((eq (nat->(nat->Prop))) (fun (Y:nat) (Z:nat)=> (((eq nat) Y) Z))) (fun (X2:nat) (Y3:nat)=> ((and ((ord_less_eq_nat X2) Y3)) ((ord_less_eq_nat Y3) X2)))) of role axiom named fact_207_eq__iff
% 0.68/0.89  A new axiom: (((eq (nat->(nat->Prop))) (fun (Y:nat) (Z:nat)=> (((eq nat) Y) Z))) (fun (X2:nat) (Y3:nat)=> ((and ((ord_less_eq_nat X2) Y3)) ((ord_less_eq_nat Y3) X2))))
% 0.68/0.89  FOF formula (((eq (set_nat->(set_nat->Prop))) (fun (Y:set_nat) (Z:set_nat)=> (((eq set_nat) Y) Z))) (fun (X2:set_nat) (Y3:set_nat)=> ((and ((ord_less_eq_set_nat X2) Y3)) ((ord_less_eq_set_nat Y3) X2)))) of role axiom named fact_208_eq__iff
% 0.68/0.89  A new axiom: (((eq (set_nat->(set_nat->Prop))) (fun (Y:set_nat) (Z:set_nat)=> (((eq set_nat) Y) Z))) (fun (X2:set_nat) (Y3:set_nat)=> ((and ((ord_less_eq_set_nat X2) Y3)) ((ord_less_eq_set_nat Y3) X2))))
% 0.68/0.89  FOF formula (((eq (set_a->(set_a->Prop))) (fun (Y:set_a) (Z:set_a)=> (((eq set_a) Y) Z))) (fun (X2:set_a) (Y3:set_a)=> ((and ((ord_less_eq_set_a X2) Y3)) ((ord_less_eq_set_a Y3) X2)))) of role axiom named fact_209_eq__iff
% 0.68/0.89  A new axiom: (((eq (set_a->(set_a->Prop))) (fun (Y:set_a) (Z:set_a)=> (((eq set_a) Y) Z))) (fun (X2:set_a) (Y3:set_a)=> ((and ((ord_less_eq_set_a X2) Y3)) ((ord_less_eq_set_a Y3) X2))))
% 0.68/0.89  FOF formula (forall (A2:nat) (B3:nat) (F:(nat->nat)) (C2:nat), (((ord_less_eq_nat A2) B3)->((((eq nat) (F B3)) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C2))))) of role axiom named fact_210_ord__le__eq__subst
% 0.68/0.91  A new axiom: (forall (A2:nat) (B3:nat) (F:(nat->nat)) (C2:nat), (((ord_less_eq_nat A2) B3)->((((eq nat) (F B3)) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C2)))))
% 0.68/0.91  FOF formula (forall (A2:nat) (B3:nat) (F:(nat->set_nat)) (C2:set_nat), (((ord_less_eq_nat A2) B3)->((((eq set_nat) (F B3)) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat (F A2)) C2))))) of role axiom named fact_211_ord__le__eq__subst
% 0.68/0.91  A new axiom: (forall (A2:nat) (B3:nat) (F:(nat->set_nat)) (C2:set_nat), (((ord_less_eq_nat A2) B3)->((((eq set_nat) (F B3)) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat (F A2)) C2)))))
% 0.68/0.91  FOF formula (forall (A2:nat) (B3:nat) (F:(nat->set_a)) (C2:set_a), (((ord_less_eq_nat A2) B3)->((((eq set_a) (F B3)) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_set_a (F X)) (F Y4))))->((ord_less_eq_set_a (F A2)) C2))))) of role axiom named fact_212_ord__le__eq__subst
% 0.68/0.91  A new axiom: (forall (A2:nat) (B3:nat) (F:(nat->set_a)) (C2:set_a), (((ord_less_eq_nat A2) B3)->((((eq set_a) (F B3)) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_set_a (F X)) (F Y4))))->((ord_less_eq_set_a (F A2)) C2)))))
% 0.68/0.91  FOF formula (forall (A2:set_nat) (B3:set_nat) (F:(set_nat->nat)) (C2:nat), (((ord_less_eq_set_nat A2) B3)->((((eq nat) (F B3)) C2)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C2))))) of role axiom named fact_213_ord__le__eq__subst
% 0.68/0.91  A new axiom: (forall (A2:set_nat) (B3:set_nat) (F:(set_nat->nat)) (C2:nat), (((ord_less_eq_set_nat A2) B3)->((((eq nat) (F B3)) C2)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C2)))))
% 0.68/0.91  FOF formula (forall (A2:set_a) (B3:set_a) (F:(set_a->nat)) (C2:nat), (((ord_less_eq_set_a A2) B3)->((((eq nat) (F B3)) C2)->((forall (X:set_a) (Y4:set_a), (((ord_less_eq_set_a X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C2))))) of role axiom named fact_214_ord__le__eq__subst
% 0.68/0.91  A new axiom: (forall (A2:set_a) (B3:set_a) (F:(set_a->nat)) (C2:nat), (((ord_less_eq_set_a A2) B3)->((((eq nat) (F B3)) C2)->((forall (X:set_a) (Y4:set_a), (((ord_less_eq_set_a X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C2)))))
% 0.68/0.91  FOF formula (forall (A2:set_nat) (B3:set_nat) (F:(set_nat->set_nat)) (C2:set_nat), (((ord_less_eq_set_nat A2) B3)->((((eq set_nat) (F B3)) C2)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat (F A2)) C2))))) of role axiom named fact_215_ord__le__eq__subst
% 0.68/0.91  A new axiom: (forall (A2:set_nat) (B3:set_nat) (F:(set_nat->set_nat)) (C2:set_nat), (((ord_less_eq_set_nat A2) B3)->((((eq set_nat) (F B3)) C2)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat (F A2)) C2)))))
% 0.68/0.91  FOF formula (forall (A2:set_nat) (B3:set_nat) (F:(set_nat->set_a)) (C2:set_a), (((ord_less_eq_set_nat A2) B3)->((((eq set_a) (F B3)) C2)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_set_a (F X)) (F Y4))))->((ord_less_eq_set_a (F A2)) C2))))) of role axiom named fact_216_ord__le__eq__subst
% 0.68/0.91  A new axiom: (forall (A2:set_nat) (B3:set_nat) (F:(set_nat->set_a)) (C2:set_a), (((ord_less_eq_set_nat A2) B3)->((((eq set_a) (F B3)) C2)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_set_a (F X)) (F Y4))))->((ord_less_eq_set_a (F A2)) C2)))))
% 0.68/0.91  FOF formula (forall (A2:set_a) (B3:set_a) (F:(set_a->set_nat)) (C2:set_nat), (((ord_less_eq_set_a A2) B3)->((((eq set_nat) (F B3)) C2)->((forall (X:set_a) (Y4:set_a), (((ord_less_eq_set_a X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat (F A2)) C2))))) of role axiom named fact_217_ord__le__eq__subst
% 0.68/0.91  A new axiom: (forall (A2:set_a) (B3:set_a) (F:(set_a->set_nat)) (C2:set_nat), (((ord_less_eq_set_a A2) B3)->((((eq set_nat) (F B3)) C2)->((forall (X:set_a) (Y4:set_a), (((ord_less_eq_set_a X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat (F A2)) C2)))))
% 0.68/0.92  FOF formula (forall (A2:set_a) (B3:set_a) (F:(set_a->set_a)) (C2:set_a), (((ord_less_eq_set_a A2) B3)->((((eq set_a) (F B3)) C2)->((forall (X:set_a) (Y4:set_a), (((ord_less_eq_set_a X) Y4)->((ord_less_eq_set_a (F X)) (F Y4))))->((ord_less_eq_set_a (F A2)) C2))))) of role axiom named fact_218_ord__le__eq__subst
% 0.68/0.92  A new axiom: (forall (A2:set_a) (B3:set_a) (F:(set_a->set_a)) (C2:set_a), (((ord_less_eq_set_a A2) B3)->((((eq set_a) (F B3)) C2)->((forall (X:set_a) (Y4:set_a), (((ord_less_eq_set_a X) Y4)->((ord_less_eq_set_a (F X)) (F Y4))))->((ord_less_eq_set_a (F A2)) C2)))))
% 0.68/0.92  FOF formula (forall (A2:set_Product_prod_a_a) (B3:set_Product_prod_a_a) (F:(set_Product_prod_a_a->nat)) (C2:nat), (((ord_le1824328871od_a_a A2) B3)->((((eq nat) (F B3)) C2)->((forall (X:set_Product_prod_a_a) (Y4:set_Product_prod_a_a), (((ord_le1824328871od_a_a X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C2))))) of role axiom named fact_219_ord__le__eq__subst
% 0.68/0.92  A new axiom: (forall (A2:set_Product_prod_a_a) (B3:set_Product_prod_a_a) (F:(set_Product_prod_a_a->nat)) (C2:nat), (((ord_le1824328871od_a_a A2) B3)->((((eq nat) (F B3)) C2)->((forall (X:set_Product_prod_a_a) (Y4:set_Product_prod_a_a), (((ord_le1824328871od_a_a X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C2)))))
% 0.68/0.92  FOF formula (forall (A2:nat) (F:(nat->nat)) (B3:nat) (C2:nat), ((((eq nat) A2) (F B3))->(((ord_less_eq_nat B3) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C2)))))) of role axiom named fact_220_ord__eq__le__subst
% 0.68/0.92  A new axiom: (forall (A2:nat) (F:(nat->nat)) (B3:nat) (C2:nat), ((((eq nat) A2) (F B3))->(((ord_less_eq_nat B3) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C2))))))
% 0.68/0.92  FOF formula (forall (A2:set_nat) (F:(nat->set_nat)) (B3:nat) (C2:nat), ((((eq set_nat) A2) (F B3))->(((ord_less_eq_nat B3) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat A2) (F C2)))))) of role axiom named fact_221_ord__eq__le__subst
% 0.68/0.92  A new axiom: (forall (A2:set_nat) (F:(nat->set_nat)) (B3:nat) (C2:nat), ((((eq set_nat) A2) (F B3))->(((ord_less_eq_nat B3) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat A2) (F C2))))))
% 0.68/0.92  FOF formula (forall (A2:set_a) (F:(nat->set_a)) (B3:nat) (C2:nat), ((((eq set_a) A2) (F B3))->(((ord_less_eq_nat B3) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_set_a (F X)) (F Y4))))->((ord_less_eq_set_a A2) (F C2)))))) of role axiom named fact_222_ord__eq__le__subst
% 0.68/0.92  A new axiom: (forall (A2:set_a) (F:(nat->set_a)) (B3:nat) (C2:nat), ((((eq set_a) A2) (F B3))->(((ord_less_eq_nat B3) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_set_a (F X)) (F Y4))))->((ord_less_eq_set_a A2) (F C2))))))
% 0.68/0.92  FOF formula (forall (A2:nat) (F:(set_nat->nat)) (B3:set_nat) (C2:set_nat), ((((eq nat) A2) (F B3))->(((ord_less_eq_set_nat B3) C2)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C2)))))) of role axiom named fact_223_ord__eq__le__subst
% 0.68/0.92  A new axiom: (forall (A2:nat) (F:(set_nat->nat)) (B3:set_nat) (C2:set_nat), ((((eq nat) A2) (F B3))->(((ord_less_eq_set_nat B3) C2)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C2))))))
% 0.68/0.92  FOF formula (forall (A2:nat) (F:(set_a->nat)) (B3:set_a) (C2:set_a), ((((eq nat) A2) (F B3))->(((ord_less_eq_set_a B3) C2)->((forall (X:set_a) (Y4:set_a), (((ord_less_eq_set_a X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C2)))))) of role axiom named fact_224_ord__eq__le__subst
% 0.68/0.92  A new axiom: (forall (A2:nat) (F:(set_a->nat)) (B3:set_a) (C2:set_a), ((((eq nat) A2) (F B3))->(((ord_less_eq_set_a B3) C2)->((forall (X:set_a) (Y4:set_a), (((ord_less_eq_set_a X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C2))))))
% 0.77/0.93  FOF formula (forall (A2:set_nat) (F:(set_nat->set_nat)) (B3:set_nat) (C2:set_nat), ((((eq set_nat) A2) (F B3))->(((ord_less_eq_set_nat B3) C2)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat A2) (F C2)))))) of role axiom named fact_225_ord__eq__le__subst
% 0.77/0.93  A new axiom: (forall (A2:set_nat) (F:(set_nat->set_nat)) (B3:set_nat) (C2:set_nat), ((((eq set_nat) A2) (F B3))->(((ord_less_eq_set_nat B3) C2)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat A2) (F C2))))))
% 0.77/0.93  FOF formula (forall (A2:set_a) (F:(set_nat->set_a)) (B3:set_nat) (C2:set_nat), ((((eq set_a) A2) (F B3))->(((ord_less_eq_set_nat B3) C2)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_set_a (F X)) (F Y4))))->((ord_less_eq_set_a A2) (F C2)))))) of role axiom named fact_226_ord__eq__le__subst
% 0.77/0.93  A new axiom: (forall (A2:set_a) (F:(set_nat->set_a)) (B3:set_nat) (C2:set_nat), ((((eq set_a) A2) (F B3))->(((ord_less_eq_set_nat B3) C2)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_set_a (F X)) (F Y4))))->((ord_less_eq_set_a A2) (F C2))))))
% 0.77/0.93  FOF formula (forall (A2:set_nat) (F:(set_a->set_nat)) (B3:set_a) (C2:set_a), ((((eq set_nat) A2) (F B3))->(((ord_less_eq_set_a B3) C2)->((forall (X:set_a) (Y4:set_a), (((ord_less_eq_set_a X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat A2) (F C2)))))) of role axiom named fact_227_ord__eq__le__subst
% 0.77/0.93  A new axiom: (forall (A2:set_nat) (F:(set_a->set_nat)) (B3:set_a) (C2:set_a), ((((eq set_nat) A2) (F B3))->(((ord_less_eq_set_a B3) C2)->((forall (X:set_a) (Y4:set_a), (((ord_less_eq_set_a X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat A2) (F C2))))))
% 0.77/0.93  FOF formula (forall (A2:set_a) (F:(set_a->set_a)) (B3:set_a) (C2:set_a), ((((eq set_a) A2) (F B3))->(((ord_less_eq_set_a B3) C2)->((forall (X:set_a) (Y4:set_a), (((ord_less_eq_set_a X) Y4)->((ord_less_eq_set_a (F X)) (F Y4))))->((ord_less_eq_set_a A2) (F C2)))))) of role axiom named fact_228_ord__eq__le__subst
% 0.77/0.93  A new axiom: (forall (A2:set_a) (F:(set_a->set_a)) (B3:set_a) (C2:set_a), ((((eq set_a) A2) (F B3))->(((ord_less_eq_set_a B3) C2)->((forall (X:set_a) (Y4:set_a), (((ord_less_eq_set_a X) Y4)->((ord_less_eq_set_a (F X)) (F Y4))))->((ord_less_eq_set_a A2) (F C2))))))
% 0.77/0.93  FOF formula (forall (A2:nat) (F:(set_Product_prod_a_a->nat)) (B3:set_Product_prod_a_a) (C2:set_Product_prod_a_a), ((((eq nat) A2) (F B3))->(((ord_le1824328871od_a_a B3) C2)->((forall (X:set_Product_prod_a_a) (Y4:set_Product_prod_a_a), (((ord_le1824328871od_a_a X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C2)))))) of role axiom named fact_229_ord__eq__le__subst
% 0.77/0.93  A new axiom: (forall (A2:nat) (F:(set_Product_prod_a_a->nat)) (B3:set_Product_prod_a_a) (C2:set_Product_prod_a_a), ((((eq nat) A2) (F B3))->(((ord_le1824328871od_a_a B3) C2)->((forall (X:set_Product_prod_a_a) (Y4:set_Product_prod_a_a), (((ord_le1824328871od_a_a X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C2))))))
% 0.77/0.93  FOF formula (forall (A2:nat) (B3:nat) (F:(nat->nat)) (C2:nat), (((ord_less_eq_nat A2) B3)->(((ord_less_eq_nat (F B3)) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C2))))) of role axiom named fact_230_order__subst2
% 0.77/0.93  A new axiom: (forall (A2:nat) (B3:nat) (F:(nat->nat)) (C2:nat), (((ord_less_eq_nat A2) B3)->(((ord_less_eq_nat (F B3)) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C2)))))
% 0.77/0.93  FOF formula (forall (A2:nat) (B3:nat) (F:(nat->set_nat)) (C2:set_nat), (((ord_less_eq_nat A2) B3)->(((ord_less_eq_set_nat (F B3)) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat (F A2)) C2))))) of role axiom named fact_231_order__subst2
% 0.77/0.94  A new axiom: (forall (A2:nat) (B3:nat) (F:(nat->set_nat)) (C2:set_nat), (((ord_less_eq_nat A2) B3)->(((ord_less_eq_set_nat (F B3)) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat (F A2)) C2)))))
% 0.77/0.94  FOF formula (forall (A2:nat) (B3:nat) (F:(nat->set_a)) (C2:set_a), (((ord_less_eq_nat A2) B3)->(((ord_less_eq_set_a (F B3)) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_set_a (F X)) (F Y4))))->((ord_less_eq_set_a (F A2)) C2))))) of role axiom named fact_232_order__subst2
% 0.77/0.94  A new axiom: (forall (A2:nat) (B3:nat) (F:(nat->set_a)) (C2:set_a), (((ord_less_eq_nat A2) B3)->(((ord_less_eq_set_a (F B3)) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_set_a (F X)) (F Y4))))->((ord_less_eq_set_a (F A2)) C2)))))
% 0.77/0.94  FOF formula (forall (A2:set_nat) (B3:set_nat) (F:(set_nat->nat)) (C2:nat), (((ord_less_eq_set_nat A2) B3)->(((ord_less_eq_nat (F B3)) C2)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C2))))) of role axiom named fact_233_order__subst2
% 0.77/0.94  A new axiom: (forall (A2:set_nat) (B3:set_nat) (F:(set_nat->nat)) (C2:nat), (((ord_less_eq_set_nat A2) B3)->(((ord_less_eq_nat (F B3)) C2)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C2)))))
% 0.77/0.94  FOF formula (forall (A2:set_a) (B3:set_a) (F:(set_a->nat)) (C2:nat), (((ord_less_eq_set_a A2) B3)->(((ord_less_eq_nat (F B3)) C2)->((forall (X:set_a) (Y4:set_a), (((ord_less_eq_set_a X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C2))))) of role axiom named fact_234_order__subst2
% 0.77/0.94  A new axiom: (forall (A2:set_a) (B3:set_a) (F:(set_a->nat)) (C2:nat), (((ord_less_eq_set_a A2) B3)->(((ord_less_eq_nat (F B3)) C2)->((forall (X:set_a) (Y4:set_a), (((ord_less_eq_set_a X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C2)))))
% 0.77/0.94  FOF formula (forall (A2:set_nat) (B3:set_nat) (F:(set_nat->set_nat)) (C2:set_nat), (((ord_less_eq_set_nat A2) B3)->(((ord_less_eq_set_nat (F B3)) C2)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat (F A2)) C2))))) of role axiom named fact_235_order__subst2
% 0.77/0.94  A new axiom: (forall (A2:set_nat) (B3:set_nat) (F:(set_nat->set_nat)) (C2:set_nat), (((ord_less_eq_set_nat A2) B3)->(((ord_less_eq_set_nat (F B3)) C2)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat (F A2)) C2)))))
% 0.77/0.94  FOF formula (forall (A2:set_nat) (B3:set_nat) (F:(set_nat->set_a)) (C2:set_a), (((ord_less_eq_set_nat A2) B3)->(((ord_less_eq_set_a (F B3)) C2)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_set_a (F X)) (F Y4))))->((ord_less_eq_set_a (F A2)) C2))))) of role axiom named fact_236_order__subst2
% 0.77/0.94  A new axiom: (forall (A2:set_nat) (B3:set_nat) (F:(set_nat->set_a)) (C2:set_a), (((ord_less_eq_set_nat A2) B3)->(((ord_less_eq_set_a (F B3)) C2)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_set_a (F X)) (F Y4))))->((ord_less_eq_set_a (F A2)) C2)))))
% 0.77/0.94  FOF formula (forall (A2:set_a) (B3:set_a) (F:(set_a->set_nat)) (C2:set_nat), (((ord_less_eq_set_a A2) B3)->(((ord_less_eq_set_nat (F B3)) C2)->((forall (X:set_a) (Y4:set_a), (((ord_less_eq_set_a X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat (F A2)) C2))))) of role axiom named fact_237_order__subst2
% 0.77/0.94  A new axiom: (forall (A2:set_a) (B3:set_a) (F:(set_a->set_nat)) (C2:set_nat), (((ord_less_eq_set_a A2) B3)->(((ord_less_eq_set_nat (F B3)) C2)->((forall (X:set_a) (Y4:set_a), (((ord_less_eq_set_a X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat (F A2)) C2)))))
% 0.77/0.94  FOF formula (forall (A2:set_a) (B3:set_a) (F:(set_a->set_a)) (C2:set_a), (((ord_less_eq_set_a A2) B3)->(((ord_less_eq_set_a (F B3)) C2)->((forall (X:set_a) (Y4:set_a), (((ord_less_eq_set_a X) Y4)->((ord_less_eq_set_a (F X)) (F Y4))))->((ord_less_eq_set_a (F A2)) C2))))) of role axiom named fact_238_order__subst2
% 0.77/0.96  A new axiom: (forall (A2:set_a) (B3:set_a) (F:(set_a->set_a)) (C2:set_a), (((ord_less_eq_set_a A2) B3)->(((ord_less_eq_set_a (F B3)) C2)->((forall (X:set_a) (Y4:set_a), (((ord_less_eq_set_a X) Y4)->((ord_less_eq_set_a (F X)) (F Y4))))->((ord_less_eq_set_a (F A2)) C2)))))
% 0.77/0.96  FOF formula (forall (A2:set_Product_prod_a_a) (B3:set_Product_prod_a_a) (F:(set_Product_prod_a_a->nat)) (C2:nat), (((ord_le1824328871od_a_a A2) B3)->(((ord_less_eq_nat (F B3)) C2)->((forall (X:set_Product_prod_a_a) (Y4:set_Product_prod_a_a), (((ord_le1824328871od_a_a X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C2))))) of role axiom named fact_239_order__subst2
% 0.77/0.96  A new axiom: (forall (A2:set_Product_prod_a_a) (B3:set_Product_prod_a_a) (F:(set_Product_prod_a_a->nat)) (C2:nat), (((ord_le1824328871od_a_a A2) B3)->(((ord_less_eq_nat (F B3)) C2)->((forall (X:set_Product_prod_a_a) (Y4:set_Product_prod_a_a), (((ord_le1824328871od_a_a X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat (F A2)) C2)))))
% 0.77/0.96  FOF formula (forall (A2:nat) (F:(nat->nat)) (B3:nat) (C2:nat), (((ord_less_eq_nat A2) (F B3))->(((ord_less_eq_nat B3) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C2)))))) of role axiom named fact_240_order__subst1
% 0.77/0.96  A new axiom: (forall (A2:nat) (F:(nat->nat)) (B3:nat) (C2:nat), (((ord_less_eq_nat A2) (F B3))->(((ord_less_eq_nat B3) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C2))))))
% 0.77/0.96  FOF formula (forall (A2:nat) (F:(set_nat->nat)) (B3:set_nat) (C2:set_nat), (((ord_less_eq_nat A2) (F B3))->(((ord_less_eq_set_nat B3) C2)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C2)))))) of role axiom named fact_241_order__subst1
% 0.77/0.96  A new axiom: (forall (A2:nat) (F:(set_nat->nat)) (B3:set_nat) (C2:set_nat), (((ord_less_eq_nat A2) (F B3))->(((ord_less_eq_set_nat B3) C2)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C2))))))
% 0.77/0.96  FOF formula (forall (A2:nat) (F:(set_a->nat)) (B3:set_a) (C2:set_a), (((ord_less_eq_nat A2) (F B3))->(((ord_less_eq_set_a B3) C2)->((forall (X:set_a) (Y4:set_a), (((ord_less_eq_set_a X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C2)))))) of role axiom named fact_242_order__subst1
% 0.77/0.96  A new axiom: (forall (A2:nat) (F:(set_a->nat)) (B3:set_a) (C2:set_a), (((ord_less_eq_nat A2) (F B3))->(((ord_less_eq_set_a B3) C2)->((forall (X:set_a) (Y4:set_a), (((ord_less_eq_set_a X) Y4)->((ord_less_eq_nat (F X)) (F Y4))))->((ord_less_eq_nat A2) (F C2))))))
% 0.77/0.96  FOF formula (forall (A2:set_nat) (F:(nat->set_nat)) (B3:nat) (C2:nat), (((ord_less_eq_set_nat A2) (F B3))->(((ord_less_eq_nat B3) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat A2) (F C2)))))) of role axiom named fact_243_order__subst1
% 0.77/0.96  A new axiom: (forall (A2:set_nat) (F:(nat->set_nat)) (B3:nat) (C2:nat), (((ord_less_eq_set_nat A2) (F B3))->(((ord_less_eq_nat B3) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat A2) (F C2))))))
% 0.77/0.96  FOF formula (forall (A2:set_a) (F:(nat->set_a)) (B3:nat) (C2:nat), (((ord_less_eq_set_a A2) (F B3))->(((ord_less_eq_nat B3) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_set_a (F X)) (F Y4))))->((ord_less_eq_set_a A2) (F C2)))))) of role axiom named fact_244_order__subst1
% 0.77/0.96  A new axiom: (forall (A2:set_a) (F:(nat->set_a)) (B3:nat) (C2:nat), (((ord_less_eq_set_a A2) (F B3))->(((ord_less_eq_nat B3) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_less_eq_set_a (F X)) (F Y4))))->((ord_less_eq_set_a A2) (F C2))))))
% 0.77/0.96  FOF formula (forall (A2:set_nat) (F:(set_nat->set_nat)) (B3:set_nat) (C2:set_nat), (((ord_less_eq_set_nat A2) (F B3))->(((ord_less_eq_set_nat B3) C2)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat A2) (F C2)))))) of role axiom named fact_245_order__subst1
% 0.77/0.97  A new axiom: (forall (A2:set_nat) (F:(set_nat->set_nat)) (B3:set_nat) (C2:set_nat), (((ord_less_eq_set_nat A2) (F B3))->(((ord_less_eq_set_nat B3) C2)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat A2) (F C2))))))
% 0.77/0.97  FOF formula (forall (A2:set_nat) (F:(set_a->set_nat)) (B3:set_a) (C2:set_a), (((ord_less_eq_set_nat A2) (F B3))->(((ord_less_eq_set_a B3) C2)->((forall (X:set_a) (Y4:set_a), (((ord_less_eq_set_a X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat A2) (F C2)))))) of role axiom named fact_246_order__subst1
% 0.77/0.97  A new axiom: (forall (A2:set_nat) (F:(set_a->set_nat)) (B3:set_a) (C2:set_a), (((ord_less_eq_set_nat A2) (F B3))->(((ord_less_eq_set_a B3) C2)->((forall (X:set_a) (Y4:set_a), (((ord_less_eq_set_a X) Y4)->((ord_less_eq_set_nat (F X)) (F Y4))))->((ord_less_eq_set_nat A2) (F C2))))))
% 0.77/0.97  FOF formula (forall (A2:set_a) (F:(set_nat->set_a)) (B3:set_nat) (C2:set_nat), (((ord_less_eq_set_a A2) (F B3))->(((ord_less_eq_set_nat B3) C2)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_set_a (F X)) (F Y4))))->((ord_less_eq_set_a A2) (F C2)))))) of role axiom named fact_247_order__subst1
% 0.77/0.97  A new axiom: (forall (A2:set_a) (F:(set_nat->set_a)) (B3:set_nat) (C2:set_nat), (((ord_less_eq_set_a A2) (F B3))->(((ord_less_eq_set_nat B3) C2)->((forall (X:set_nat) (Y4:set_nat), (((ord_less_eq_set_nat X) Y4)->((ord_less_eq_set_a (F X)) (F Y4))))->((ord_less_eq_set_a A2) (F C2))))))
% 0.77/0.97  FOF formula (forall (A2:set_a) (F:(set_a->set_a)) (B3:set_a) (C2:set_a), (((ord_less_eq_set_a A2) (F B3))->(((ord_less_eq_set_a B3) C2)->((forall (X:set_a) (Y4:set_a), (((ord_less_eq_set_a X) Y4)->((ord_less_eq_set_a (F X)) (F Y4))))->((ord_less_eq_set_a A2) (F C2)))))) of role axiom named fact_248_order__subst1
% 0.77/0.97  A new axiom: (forall (A2:set_a) (F:(set_a->set_a)) (B3:set_a) (C2:set_a), (((ord_less_eq_set_a A2) (F B3))->(((ord_less_eq_set_a B3) C2)->((forall (X:set_a) (Y4:set_a), (((ord_less_eq_set_a X) Y4)->((ord_less_eq_set_a (F X)) (F Y4))))->((ord_less_eq_set_a A2) (F C2))))))
% 0.77/0.97  FOF formula (forall (A2:set_Product_prod_a_a) (F:(nat->set_Product_prod_a_a)) (B3:nat) (C2:nat), (((ord_le1824328871od_a_a A2) (F B3))->(((ord_less_eq_nat B3) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_le1824328871od_a_a (F X)) (F Y4))))->((ord_le1824328871od_a_a A2) (F C2)))))) of role axiom named fact_249_order__subst1
% 0.77/0.97  A new axiom: (forall (A2:set_Product_prod_a_a) (F:(nat->set_Product_prod_a_a)) (B3:nat) (C2:nat), (((ord_le1824328871od_a_a A2) (F B3))->(((ord_less_eq_nat B3) C2)->((forall (X:nat) (Y4:nat), (((ord_less_eq_nat X) Y4)->((ord_le1824328871od_a_a (F X)) (F Y4))))->((ord_le1824328871od_a_a A2) (F C2))))))
% 0.77/0.97  FOF formula (forall (P:(product_prod_a_a->Prop)) (Q:(product_prod_a_a->Prop)), (((eq Prop) ((ord_le1824328871od_a_a (collec645855634od_a_a P)) (collec645855634od_a_a Q))) (forall (X2:product_prod_a_a), ((P X2)->(Q X2))))) of role axiom named fact_250_Collect__mono__iff
% 0.77/0.97  A new axiom: (forall (P:(product_prod_a_a->Prop)) (Q:(product_prod_a_a->Prop)), (((eq Prop) ((ord_le1824328871od_a_a (collec645855634od_a_a P)) (collec645855634od_a_a Q))) (forall (X2:product_prod_a_a), ((P X2)->(Q X2)))))
% 0.77/0.97  FOF formula (forall (P:(nat->Prop)) (Q:(nat->Prop)), (((eq Prop) ((ord_less_eq_set_nat (collect_nat P)) (collect_nat Q))) (forall (X2:nat), ((P X2)->(Q X2))))) of role axiom named fact_251_Collect__mono__iff
% 0.77/0.97  A new axiom: (forall (P:(nat->Prop)) (Q:(nat->Prop)), (((eq Prop) ((ord_less_eq_set_nat (collect_nat P)) (collect_nat Q))) (forall (X2:nat), ((P X2)->(Q X2)))))
% 0.77/0.97  FOF formula (forall (P:(a->Prop)) (Q:(a->Prop)), (((eq Prop) ((ord_less_eq_set_a (collect_a P)) (collect_a Q))) (forall (X2:a), ((P X2)->(Q X2))))) of role axiom named fact_252_Collect__mono__iff
% 0.77/0.97  A new axiom: (forall (P:(a->Prop)) (Q:(a->Prop)), (((eq Prop) ((ord_less_eq_set_a (collect_a P)) (collect_a Q))) (forall (X2:a), ((P X2)->(Q X2)))))
% 0.77/0.97  FOF formula (((eq (set_Product_prod_a_a->(set_Product_prod_a_a->Prop))) (fun (Y:set_Product_prod_a_a) (Z:set_Product_prod_a_a)=> (((eq set_Product_prod_a_a) Y) Z))) (fun (A5:set_Product_prod_a_a) (B2:set_Product_prod_a_a)=> ((and ((ord_le1824328871od_a_a A5) B2)) ((ord_le1824328871od_a_a B2) A5)))) of role axiom named fact_253_set__eq__subset
% 0.77/0.97  A new axiom: (((eq (set_Product_prod_a_a->(set_Product_prod_a_a->Prop))) (fun (Y:set_Product_prod_a_a) (Z:set_Product_prod_a_a)=> (((eq set_Product_prod_a_a) Y) Z))) (fun (A5:set_Product_prod_a_a) (B2:set_Product_prod_a_a)=> ((and ((ord_le1824328871od_a_a A5) B2)) ((ord_le1824328871od_a_a B2) A5))))
% 0.77/0.97  FOF formula (((eq (set_nat->(set_nat->Prop))) (fun (Y:set_nat) (Z:set_nat)=> (((eq set_nat) Y) Z))) (fun (A5:set_nat) (B2:set_nat)=> ((and ((ord_less_eq_set_nat A5) B2)) ((ord_less_eq_set_nat B2) A5)))) of role axiom named fact_254_set__eq__subset
% 0.77/0.97  A new axiom: (((eq (set_nat->(set_nat->Prop))) (fun (Y:set_nat) (Z:set_nat)=> (((eq set_nat) Y) Z))) (fun (A5:set_nat) (B2:set_nat)=> ((and ((ord_less_eq_set_nat A5) B2)) ((ord_less_eq_set_nat B2) A5))))
% 0.77/0.97  FOF formula (((eq (set_a->(set_a->Prop))) (fun (Y:set_a) (Z:set_a)=> (((eq set_a) Y) Z))) (fun (A5:set_a) (B2:set_a)=> ((and ((ord_less_eq_set_a A5) B2)) ((ord_less_eq_set_a B2) A5)))) of role axiom named fact_255_set__eq__subset
% 0.77/0.97  A new axiom: (((eq (set_a->(set_a->Prop))) (fun (Y:set_a) (Z:set_a)=> (((eq set_a) Y) Z))) (fun (A5:set_a) (B2:set_a)=> ((and ((ord_less_eq_set_a A5) B2)) ((ord_less_eq_set_a B2) A5))))
% 0.77/0.97  FOF formula (forall (A:set_Product_prod_a_a) (B:set_Product_prod_a_a) (C:set_Product_prod_a_a), (((ord_le1824328871od_a_a A) B)->(((ord_le1824328871od_a_a B) C)->((ord_le1824328871od_a_a A) C)))) of role axiom named fact_256_subset__trans
% 0.77/0.97  A new axiom: (forall (A:set_Product_prod_a_a) (B:set_Product_prod_a_a) (C:set_Product_prod_a_a), (((ord_le1824328871od_a_a A) B)->(((ord_le1824328871od_a_a B) C)->((ord_le1824328871od_a_a A) C))))
% 0.77/0.97  FOF formula (forall (A:set_nat) (B:set_nat) (C:set_nat), (((ord_less_eq_set_nat A) B)->(((ord_less_eq_set_nat B) C)->((ord_less_eq_set_nat A) C)))) of role axiom named fact_257_subset__trans
% 0.77/0.97  A new axiom: (forall (A:set_nat) (B:set_nat) (C:set_nat), (((ord_less_eq_set_nat A) B)->(((ord_less_eq_set_nat B) C)->((ord_less_eq_set_nat A) C))))
% 0.77/0.97  FOF formula (forall (A:set_a) (B:set_a) (C:set_a), (((ord_less_eq_set_a A) B)->(((ord_less_eq_set_a B) C)->((ord_less_eq_set_a A) C)))) of role axiom named fact_258_subset__trans
% 0.77/0.97  A new axiom: (forall (A:set_a) (B:set_a) (C:set_a), (((ord_less_eq_set_a A) B)->(((ord_less_eq_set_a B) C)->((ord_less_eq_set_a A) C))))
% 0.77/0.97  FOF formula (forall (P:(product_prod_a_a->Prop)) (Q:(product_prod_a_a->Prop)), ((forall (X:product_prod_a_a), ((P X)->(Q X)))->((ord_le1824328871od_a_a (collec645855634od_a_a P)) (collec645855634od_a_a Q)))) of role axiom named fact_259_Collect__mono
% 0.77/0.97  A new axiom: (forall (P:(product_prod_a_a->Prop)) (Q:(product_prod_a_a->Prop)), ((forall (X:product_prod_a_a), ((P X)->(Q X)))->((ord_le1824328871od_a_a (collec645855634od_a_a P)) (collec645855634od_a_a Q))))
% 0.77/0.97  FOF formula (forall (P:(nat->Prop)) (Q:(nat->Prop)), ((forall (X:nat), ((P X)->(Q X)))->((ord_less_eq_set_nat (collect_nat P)) (collect_nat Q)))) of role axiom named fact_260_Collect__mono
% 0.77/0.97  A new axiom: (forall (P:(nat->Prop)) (Q:(nat->Prop)), ((forall (X:nat), ((P X)->(Q X)))->((ord_less_eq_set_nat (collect_nat P)) (collect_nat Q))))
% 0.77/0.97  FOF formula (forall (P:(a->Prop)) (Q:(a->Prop)), ((forall (X:a), ((P X)->(Q X)))->((ord_less_eq_set_a (collect_a P)) (collect_a Q)))) of role axiom named fact_261_Collect__mono
% 0.77/0.97  A new axiom: (forall (P:(a->Prop)) (Q:(a->Prop)), ((forall (X:a), ((P X)->(Q X)))->((ord_less_eq_set_a (collect_a P)) (collect_a Q))))
% 0.77/0.97  FOF formula (forall (A:set_Product_prod_a_a), ((ord_le1824328871od_a_a A) A)) of role axiom named fact_262_subset__refl
% 0.77/0.97  A new axiom: (forall (A:set_Product_prod_a_a), ((ord_le1824328871od_a_a A) A))
% 0.77/0.97  FOF formula (forall (A:set_nat), ((ord_less_eq_set_nat A) A)) of role axiom named fact_263_subset__refl
% 0.83/0.98  A new axiom: (forall (A:set_nat), ((ord_less_eq_set_nat A) A))
% 0.83/0.98  FOF formula (forall (A:set_a), ((ord_less_eq_set_a A) A)) of role axiom named fact_264_subset__refl
% 0.83/0.98  A new axiom: (forall (A:set_a), ((ord_less_eq_set_a A) A))
% 0.83/0.98  FOF formula (((eq (set_Product_prod_a_a->(set_Product_prod_a_a->Prop))) ord_le1824328871od_a_a) (fun (A5:set_Product_prod_a_a) (B2:set_Product_prod_a_a)=> (forall (T2:product_prod_a_a), (((member449909584od_a_a T2) A5)->((member449909584od_a_a T2) B2))))) of role axiom named fact_265_subset__iff
% 0.83/0.98  A new axiom: (((eq (set_Product_prod_a_a->(set_Product_prod_a_a->Prop))) ord_le1824328871od_a_a) (fun (A5:set_Product_prod_a_a) (B2:set_Product_prod_a_a)=> (forall (T2:product_prod_a_a), (((member449909584od_a_a T2) A5)->((member449909584od_a_a T2) B2)))))
% 0.83/0.98  FOF formula (((eq (set_nat->(set_nat->Prop))) ord_less_eq_set_nat) (fun (A5:set_nat) (B2:set_nat)=> (forall (T2:nat), (((member_nat T2) A5)->((member_nat T2) B2))))) of role axiom named fact_266_subset__iff
% 0.83/0.98  A new axiom: (((eq (set_nat->(set_nat->Prop))) ord_less_eq_set_nat) (fun (A5:set_nat) (B2:set_nat)=> (forall (T2:nat), (((member_nat T2) A5)->((member_nat T2) B2)))))
% 0.83/0.98  FOF formula (((eq (set_a->(set_a->Prop))) ord_less_eq_set_a) (fun (A5:set_a) (B2:set_a)=> (forall (T2:a), (((member_a T2) A5)->((member_a T2) B2))))) of role axiom named fact_267_subset__iff
% 0.83/0.98  A new axiom: (((eq (set_a->(set_a->Prop))) ord_less_eq_set_a) (fun (A5:set_a) (B2:set_a)=> (forall (T2:a), (((member_a T2) A5)->((member_a T2) B2)))))
% 0.83/0.98  FOF formula (forall (A:set_Product_prod_a_a) (B:set_Product_prod_a_a), ((((eq set_Product_prod_a_a) A) B)->((ord_le1824328871od_a_a B) A))) of role axiom named fact_268_equalityD2
% 0.83/0.98  A new axiom: (forall (A:set_Product_prod_a_a) (B:set_Product_prod_a_a), ((((eq set_Product_prod_a_a) A) B)->((ord_le1824328871od_a_a B) A)))
% 0.83/0.98  FOF formula (forall (A:set_nat) (B:set_nat), ((((eq set_nat) A) B)->((ord_less_eq_set_nat B) A))) of role axiom named fact_269_equalityD2
% 0.83/0.98  A new axiom: (forall (A:set_nat) (B:set_nat), ((((eq set_nat) A) B)->((ord_less_eq_set_nat B) A)))
% 0.83/0.98  FOF formula (forall (A:set_a) (B:set_a), ((((eq set_a) A) B)->((ord_less_eq_set_a B) A))) of role axiom named fact_270_equalityD2
% 0.83/0.98  A new axiom: (forall (A:set_a) (B:set_a), ((((eq set_a) A) B)->((ord_less_eq_set_a B) A)))
% 0.83/0.98  FOF formula (forall (A:set_Product_prod_a_a) (B:set_Product_prod_a_a), ((((eq set_Product_prod_a_a) A) B)->((ord_le1824328871od_a_a A) B))) of role axiom named fact_271_equalityD1
% 0.83/0.98  A new axiom: (forall (A:set_Product_prod_a_a) (B:set_Product_prod_a_a), ((((eq set_Product_prod_a_a) A) B)->((ord_le1824328871od_a_a A) B)))
% 0.83/0.98  FOF formula (forall (A:set_nat) (B:set_nat), ((((eq set_nat) A) B)->((ord_less_eq_set_nat A) B))) of role axiom named fact_272_equalityD1
% 0.83/0.98  A new axiom: (forall (A:set_nat) (B:set_nat), ((((eq set_nat) A) B)->((ord_less_eq_set_nat A) B)))
% 0.83/0.98  FOF formula (forall (A:set_a) (B:set_a), ((((eq set_a) A) B)->((ord_less_eq_set_a A) B))) of role axiom named fact_273_equalityD1
% 0.83/0.98  A new axiom: (forall (A:set_a) (B:set_a), ((((eq set_a) A) B)->((ord_less_eq_set_a A) B)))
% 0.83/0.98  FOF formula (((eq (set_Product_prod_a_a->(set_Product_prod_a_a->Prop))) ord_le1824328871od_a_a) (fun (A5:set_Product_prod_a_a) (B2:set_Product_prod_a_a)=> (forall (X2:product_prod_a_a), (((member449909584od_a_a X2) A5)->((member449909584od_a_a X2) B2))))) of role axiom named fact_274_subset__eq
% 0.83/0.98  A new axiom: (((eq (set_Product_prod_a_a->(set_Product_prod_a_a->Prop))) ord_le1824328871od_a_a) (fun (A5:set_Product_prod_a_a) (B2:set_Product_prod_a_a)=> (forall (X2:product_prod_a_a), (((member449909584od_a_a X2) A5)->((member449909584od_a_a X2) B2)))))
% 0.83/0.98  FOF formula (((eq (set_nat->(set_nat->Prop))) ord_less_eq_set_nat) (fun (A5:set_nat) (B2:set_nat)=> (forall (X2:nat), (((member_nat X2) A5)->((member_nat X2) B2))))) of role axiom named fact_275_subset__eq
% 0.83/0.98  A new axiom: (((eq (set_nat->(set_nat->Prop))) ord_less_eq_set_nat) (fun (A5:set_nat) (B2:set_nat)=> (forall (X2:nat), (((member_nat X2) A5)->((member_nat X2) B2)))))
% 0.83/0.98  FOF formula (((eq (set_a->(set_a->Prop))) ord_less_eq_set_a) (fun (A5:set_a) (B2:set_a)=> (forall (X2:a), (((member_a X2) A5)->((member_a X2) B2))))) of role axiom named fact_276_subset__eq
% 0.83/0.99  A new axiom: (((eq (set_a->(set_a->Prop))) ord_less_eq_set_a) (fun (A5:set_a) (B2:set_a)=> (forall (X2:a), (((member_a X2) A5)->((member_a X2) B2)))))
% 0.83/0.99  FOF formula (forall (A:set_Product_prod_a_a) (B:set_Product_prod_a_a), ((((eq set_Product_prod_a_a) A) B)->((((ord_le1824328871od_a_a A) B)->(((ord_le1824328871od_a_a B) A)->False))->False))) of role axiom named fact_277_equalityE
% 0.83/0.99  A new axiom: (forall (A:set_Product_prod_a_a) (B:set_Product_prod_a_a), ((((eq set_Product_prod_a_a) A) B)->((((ord_le1824328871od_a_a A) B)->(((ord_le1824328871od_a_a B) A)->False))->False)))
% 0.83/0.99  FOF formula (forall (A:set_nat) (B:set_nat), ((((eq set_nat) A) B)->((((ord_less_eq_set_nat A) B)->(((ord_less_eq_set_nat B) A)->False))->False))) of role axiom named fact_278_equalityE
% 0.83/0.99  A new axiom: (forall (A:set_nat) (B:set_nat), ((((eq set_nat) A) B)->((((ord_less_eq_set_nat A) B)->(((ord_less_eq_set_nat B) A)->False))->False)))
% 0.83/0.99  FOF formula (forall (A:set_a) (B:set_a), ((((eq set_a) A) B)->((((ord_less_eq_set_a A) B)->(((ord_less_eq_set_a B) A)->False))->False))) of role axiom named fact_279_equalityE
% 0.83/0.99  A new axiom: (forall (A:set_a) (B:set_a), ((((eq set_a) A) B)->((((ord_less_eq_set_a A) B)->(((ord_less_eq_set_a B) A)->False))->False)))
% 0.83/0.99  FOF formula (forall (A:set_Product_prod_a_a) (B:set_Product_prod_a_a) (C2:product_prod_a_a), (((ord_le1824328871od_a_a A) B)->(((member449909584od_a_a C2) A)->((member449909584od_a_a C2) B)))) of role axiom named fact_280_subsetD
% 0.83/0.99  A new axiom: (forall (A:set_Product_prod_a_a) (B:set_Product_prod_a_a) (C2:product_prod_a_a), (((ord_le1824328871od_a_a A) B)->(((member449909584od_a_a C2) A)->((member449909584od_a_a C2) B))))
% 0.83/0.99  FOF formula (forall (A:set_nat) (B:set_nat) (C2:nat), (((ord_less_eq_set_nat A) B)->(((member_nat C2) A)->((member_nat C2) B)))) of role axiom named fact_281_subsetD
% 0.83/0.99  A new axiom: (forall (A:set_nat) (B:set_nat) (C2:nat), (((ord_less_eq_set_nat A) B)->(((member_nat C2) A)->((member_nat C2) B))))
% 0.83/0.99  FOF formula (forall (A:set_a) (B:set_a) (C2:a), (((ord_less_eq_set_a A) B)->(((member_a C2) A)->((member_a C2) B)))) of role axiom named fact_282_subsetD
% 0.83/0.99  A new axiom: (forall (A:set_a) (B:set_a) (C2:a), (((ord_less_eq_set_a A) B)->(((member_a C2) A)->((member_a C2) B))))
% 0.83/0.99  FOF formula (forall (A:set_Product_prod_a_a) (B:set_Product_prod_a_a) (X3:product_prod_a_a), (((ord_le1824328871od_a_a A) B)->(((member449909584od_a_a X3) A)->((member449909584od_a_a X3) B)))) of role axiom named fact_283_in__mono
% 0.83/0.99  A new axiom: (forall (A:set_Product_prod_a_a) (B:set_Product_prod_a_a) (X3:product_prod_a_a), (((ord_le1824328871od_a_a A) B)->(((member449909584od_a_a X3) A)->((member449909584od_a_a X3) B))))
% 0.83/0.99  FOF formula (forall (A:set_nat) (B:set_nat) (X3:nat), (((ord_less_eq_set_nat A) B)->(((member_nat X3) A)->((member_nat X3) B)))) of role axiom named fact_284_in__mono
% 0.83/0.99  A new axiom: (forall (A:set_nat) (B:set_nat) (X3:nat), (((ord_less_eq_set_nat A) B)->(((member_nat X3) A)->((member_nat X3) B))))
% 0.83/0.99  FOF formula (forall (A:set_a) (B:set_a) (X3:a), (((ord_less_eq_set_a A) B)->(((member_a X3) A)->((member_a X3) B)))) of role axiom named fact_285_in__mono
% 0.83/0.99  A new axiom: (forall (A:set_a) (B:set_a) (X3:a), (((ord_less_eq_set_a A) B)->(((member_a X3) A)->((member_a X3) B))))
% 0.83/0.99  FOF formula (forall (R:set_Product_prod_a_a) (S:set_Product_prod_a_a), (((eq Prop) ((ord_le1347718902_a_a_o (fun (X2:product_prod_a_a)=> ((member449909584od_a_a X2) R))) (fun (X2:product_prod_a_a)=> ((member449909584od_a_a X2) S)))) ((ord_le1824328871od_a_a R) S))) of role axiom named fact_286_pred__subset__eq
% 0.83/0.99  A new axiom: (forall (R:set_Product_prod_a_a) (S:set_Product_prod_a_a), (((eq Prop) ((ord_le1347718902_a_a_o (fun (X2:product_prod_a_a)=> ((member449909584od_a_a X2) R))) (fun (X2:product_prod_a_a)=> ((member449909584od_a_a X2) S)))) ((ord_le1824328871od_a_a R) S)))
% 0.83/0.99  FOF formula (forall (R:set_nat) (S:set_nat), (((eq Prop) ((ord_less_eq_nat_o (fun (X2:nat)=> ((member_nat X2) R))) (fun (X2:nat)=> ((member_nat X2) S)))) ((ord_less_eq_set_nat R) S))) of role axiom named fact_287_pred__subset__eq
% 0.83/1.00  A new axiom: (forall (R:set_nat) (S:set_nat), (((eq Prop) ((ord_less_eq_nat_o (fun (X2:nat)=> ((member_nat X2) R))) (fun (X2:nat)=> ((member_nat X2) S)))) ((ord_less_eq_set_nat R) S)))
% 0.83/1.00  FOF formula (forall (R:set_a) (S:set_a), (((eq Prop) ((ord_less_eq_a_o (fun (X2:a)=> ((member_a X2) R))) (fun (X2:a)=> ((member_a X2) S)))) ((ord_less_eq_set_a R) S))) of role axiom named fact_288_pred__subset__eq
% 0.83/1.00  A new axiom: (forall (R:set_a) (S:set_a), (((eq Prop) ((ord_less_eq_a_o (fun (X2:a)=> ((member_a X2) R))) (fun (X2:a)=> ((member_a X2) S)))) ((ord_less_eq_set_a R) S)))
% 0.83/1.00  FOF formula (forall (R2:pair_p125712459t_unit), (((eq pair_p125712459t_unit) R2) (((pair_p1621517565t_unit (pair_p1047056820t_unit R2)) (pair_p133601421t_unit R2)) (pair_p1896222615t_unit R2)))) of role axiom named fact_289_pair__pre__digraph_Osurjective
% 0.83/1.00  A new axiom: (forall (R2:pair_p125712459t_unit), (((eq pair_p125712459t_unit) R2) (((pair_p1621517565t_unit (pair_p1047056820t_unit R2)) (pair_p133601421t_unit R2)) (pair_p1896222615t_unit R2))))
% 0.83/1.00  FOF formula (forall (R2:pair_p1914262621t_unit), (((eq pair_p1914262621t_unit) R2) (((pair_p1167410509t_unit (pair_p1677060310t_unit R2)) (pair_p715279805t_unit R2)) (pair_p69470259t_unit R2)))) of role axiom named fact_290_pair__pre__digraph_Osurjective
% 0.83/1.00  A new axiom: (forall (R2:pair_p1914262621t_unit), (((eq pair_p1914262621t_unit) R2) (((pair_p1167410509t_unit (pair_p1677060310t_unit R2)) (pair_p715279805t_unit R2)) (pair_p69470259t_unit R2))))
% 0.83/1.00  FOF formula (forall (R2:pair_p1765063010t_unit), (((eq pair_p1765063010t_unit) R2) (((pair_p398687508t_unit (pair_p447552203t_unit R2)) (pair_p1783210148t_unit R2)) (pair_p1984658862t_unit R2)))) of role axiom named fact_291_pair__pre__digraph_Osurjective
% 0.83/1.00  A new axiom: (forall (R2:pair_p1765063010t_unit), (((eq pair_p1765063010t_unit) R2) (((pair_p398687508t_unit (pair_p447552203t_unit R2)) (pair_p1783210148t_unit R2)) (pair_p1984658862t_unit R2))))
% 0.83/1.00  FOF formula (forall (X3:product_prod_a_a) (A:set_a) (B:set_a), (((eq Prop) ((member449909584od_a_a X3) ((product_product_a_a A) B))) ((member449909584od_a_a X3) ((product_Sigma_a_a A) (fun (Uu:a)=> B))))) of role axiom named fact_292_member__product
% 0.83/1.00  A new axiom: (forall (X3:product_prod_a_a) (A:set_a) (B:set_a), (((eq Prop) ((member449909584od_a_a X3) ((product_product_a_a A) B))) ((member449909584od_a_a X3) ((product_Sigma_a_a A) (fun (Uu:a)=> B)))))
% 0.83/1.00  FOF formula (((eq (set_a->(set_a->set_Product_prod_a_a))) product_product_a_a) (fun (A5:set_a) (B2:set_a)=> ((product_Sigma_a_a A5) (fun (Uu:a)=> B2)))) of role axiom named fact_293_Product__Type_Oproduct__def
% 0.83/1.00  A new axiom: (((eq (set_a->(set_a->set_Product_prod_a_a))) product_product_a_a) (fun (A5:set_a) (B2:set_a)=> ((product_Sigma_a_a A5) (fun (Uu:a)=> B2))))
% 0.83/1.00  FOF formula (forall (B:set_Product_prod_a_a) (A:set_Product_prod_a_a) (P:(product_prod_a_a->Prop)), (((ord_le1824328871od_a_a B) A)->(((eq Prop) ((ord_le1824328871od_a_a B) (collec645855634od_a_a (fun (X2:product_prod_a_a)=> ((and ((member449909584od_a_a X2) A)) (P X2)))))) (forall (X2:product_prod_a_a), (((member449909584od_a_a X2) B)->(P X2)))))) of role axiom named fact_294_subset__Collect__iff
% 0.83/1.00  A new axiom: (forall (B:set_Product_prod_a_a) (A:set_Product_prod_a_a) (P:(product_prod_a_a->Prop)), (((ord_le1824328871od_a_a B) A)->(((eq Prop) ((ord_le1824328871od_a_a B) (collec645855634od_a_a (fun (X2:product_prod_a_a)=> ((and ((member449909584od_a_a X2) A)) (P X2)))))) (forall (X2:product_prod_a_a), (((member449909584od_a_a X2) B)->(P X2))))))
% 0.83/1.00  FOF formula (forall (B:set_nat) (A:set_nat) (P:(nat->Prop)), (((ord_less_eq_set_nat B) A)->(((eq Prop) ((ord_less_eq_set_nat B) (collect_nat (fun (X2:nat)=> ((and ((member_nat X2) A)) (P X2)))))) (forall (X2:nat), (((member_nat X2) B)->(P X2)))))) of role axiom named fact_295_subset__Collect__iff
% 0.83/1.00  A new axiom: (forall (B:set_nat) (A:set_nat) (P:(nat->Prop)), (((ord_less_eq_set_nat B) A)->(((eq Prop) ((ord_less_eq_set_nat B) (collect_nat (fun (X2:nat)=> ((and ((member_nat X2) A)) (P X2)))))) (forall (X2:nat), (((member_nat X2) B)->(P X2))))))
% 0.83/1.00  FOF formula (forall (B:set_a) (A:set_a) (P:(a->Prop)), (((ord_less_eq_set_a B) A)->(((eq Prop) ((ord_less_eq_set_a B) (collect_a (fun (X2:a)=> ((and ((member_a X2) A)) (P X2)))))) (forall (X2:a), (((member_a X2) B)->(P X2)))))) of role axiom named fact_296_subset__Collect__iff
% 0.83/1.01  A new axiom: (forall (B:set_a) (A:set_a) (P:(a->Prop)), (((ord_less_eq_set_a B) A)->(((eq Prop) ((ord_less_eq_set_a B) (collect_a (fun (X2:a)=> ((and ((member_a X2) A)) (P X2)))))) (forall (X2:a), (((member_a X2) B)->(P X2))))))
% 0.83/1.01  FOF formula (forall (B:set_Product_prod_a_a) (A:set_Product_prod_a_a) (Q:(product_prod_a_a->Prop)) (P:(product_prod_a_a->Prop)), (((ord_le1824328871od_a_a B) A)->((forall (X:product_prod_a_a), (((member449909584od_a_a X) B)->((Q X)->(P X))))->((ord_le1824328871od_a_a (collec645855634od_a_a (fun (X2:product_prod_a_a)=> ((and ((member449909584od_a_a X2) B)) (Q X2))))) (collec645855634od_a_a (fun (X2:product_prod_a_a)=> ((and ((member449909584od_a_a X2) A)) (P X2)))))))) of role axiom named fact_297_subset__CollectI
% 0.83/1.01  A new axiom: (forall (B:set_Product_prod_a_a) (A:set_Product_prod_a_a) (Q:(product_prod_a_a->Prop)) (P:(product_prod_a_a->Prop)), (((ord_le1824328871od_a_a B) A)->((forall (X:product_prod_a_a), (((member449909584od_a_a X) B)->((Q X)->(P X))))->((ord_le1824328871od_a_a (collec645855634od_a_a (fun (X2:product_prod_a_a)=> ((and ((member449909584od_a_a X2) B)) (Q X2))))) (collec645855634od_a_a (fun (X2:product_prod_a_a)=> ((and ((member449909584od_a_a X2) A)) (P X2))))))))
% 0.83/1.01  FOF formula (forall (B:set_nat) (A:set_nat) (Q:(nat->Prop)) (P:(nat->Prop)), (((ord_less_eq_set_nat B) A)->((forall (X:nat), (((member_nat X) B)->((Q X)->(P X))))->((ord_less_eq_set_nat (collect_nat (fun (X2:nat)=> ((and ((member_nat X2) B)) (Q X2))))) (collect_nat (fun (X2:nat)=> ((and ((member_nat X2) A)) (P X2)))))))) of role axiom named fact_298_subset__CollectI
% 0.83/1.01  A new axiom: (forall (B:set_nat) (A:set_nat) (Q:(nat->Prop)) (P:(nat->Prop)), (((ord_less_eq_set_nat B) A)->((forall (X:nat), (((member_nat X) B)->((Q X)->(P X))))->((ord_less_eq_set_nat (collect_nat (fun (X2:nat)=> ((and ((member_nat X2) B)) (Q X2))))) (collect_nat (fun (X2:nat)=> ((and ((member_nat X2) A)) (P X2))))))))
% 0.83/1.01  FOF formula (forall (B:set_a) (A:set_a) (Q:(a->Prop)) (P:(a->Prop)), (((ord_less_eq_set_a B) A)->((forall (X:a), (((member_a X) B)->((Q X)->(P X))))->((ord_less_eq_set_a (collect_a (fun (X2:a)=> ((and ((member_a X2) B)) (Q X2))))) (collect_a (fun (X2:a)=> ((and ((member_a X2) A)) (P X2)))))))) of role axiom named fact_299_subset__CollectI
% 0.83/1.01  A new axiom: (forall (B:set_a) (A:set_a) (Q:(a->Prop)) (P:(a->Prop)), (((ord_less_eq_set_a B) A)->((forall (X:a), (((member_a X) B)->((Q X)->(P X))))->((ord_less_eq_set_a (collect_a (fun (X2:a)=> ((and ((member_a X2) B)) (Q X2))))) (collect_a (fun (X2:a)=> ((and ((member_a X2) A)) (P X2))))))))
% 0.83/1.01  FOF formula (forall (X4:set_Product_prod_a_a) (P:(product_prod_a_a->Prop)), ((ord_le1824328871od_a_a (collec645855634od_a_a (fun (X2:product_prod_a_a)=> ((and ((member449909584od_a_a X2) X4)) (P X2))))) X4)) of role axiom named fact_300_Collect__restrict
% 0.83/1.01  A new axiom: (forall (X4:set_Product_prod_a_a) (P:(product_prod_a_a->Prop)), ((ord_le1824328871od_a_a (collec645855634od_a_a (fun (X2:product_prod_a_a)=> ((and ((member449909584od_a_a X2) X4)) (P X2))))) X4))
% 0.83/1.01  FOF formula (forall (X4:set_nat) (P:(nat->Prop)), ((ord_less_eq_set_nat (collect_nat (fun (X2:nat)=> ((and ((member_nat X2) X4)) (P X2))))) X4)) of role axiom named fact_301_Collect__restrict
% 0.83/1.01  A new axiom: (forall (X4:set_nat) (P:(nat->Prop)), ((ord_less_eq_set_nat (collect_nat (fun (X2:nat)=> ((and ((member_nat X2) X4)) (P X2))))) X4))
% 0.83/1.01  FOF formula (forall (X4:set_a) (P:(a->Prop)), ((ord_less_eq_set_a (collect_a (fun (X2:a)=> ((and ((member_a X2) X4)) (P X2))))) X4)) of role axiom named fact_302_Collect__restrict
% 0.83/1.01  A new axiom: (forall (X4:set_a) (P:(a->Prop)), ((ord_less_eq_set_a (collect_a (fun (X2:a)=> ((and ((member_a X2) X4)) (P X2))))) X4))
% 0.83/1.01  FOF formula (forall (X3:product_prod_a_a) (Z3:set_Product_prod_a_a) (X4:set_Product_prod_a_a) (P:(product_prod_a_a->Prop)), (((member449909584od_a_a X3) Z3)->(((ord_le1824328871od_a_a Z3) (collec645855634od_a_a (fun (X2:product_prod_a_a)=> ((and ((member449909584od_a_a X2) X4)) (P X2)))))->(P X3)))) of role axiom named fact_303_prop__restrict
% 0.83/1.02  A new axiom: (forall (X3:product_prod_a_a) (Z3:set_Product_prod_a_a) (X4:set_Product_prod_a_a) (P:(product_prod_a_a->Prop)), (((member449909584od_a_a X3) Z3)->(((ord_le1824328871od_a_a Z3) (collec645855634od_a_a (fun (X2:product_prod_a_a)=> ((and ((member449909584od_a_a X2) X4)) (P X2)))))->(P X3))))
% 0.83/1.02  FOF formula (forall (X3:nat) (Z3:set_nat) (X4:set_nat) (P:(nat->Prop)), (((member_nat X3) Z3)->(((ord_less_eq_set_nat Z3) (collect_nat (fun (X2:nat)=> ((and ((member_nat X2) X4)) (P X2)))))->(P X3)))) of role axiom named fact_304_prop__restrict
% 0.83/1.02  A new axiom: (forall (X3:nat) (Z3:set_nat) (X4:set_nat) (P:(nat->Prop)), (((member_nat X3) Z3)->(((ord_less_eq_set_nat Z3) (collect_nat (fun (X2:nat)=> ((and ((member_nat X2) X4)) (P X2)))))->(P X3))))
% 0.83/1.02  FOF formula (forall (X3:a) (Z3:set_a) (X4:set_a) (P:(a->Prop)), (((member_a X3) Z3)->(((ord_less_eq_set_a Z3) (collect_a (fun (X2:a)=> ((and ((member_a X2) X4)) (P X2)))))->(P X3)))) of role axiom named fact_305_prop__restrict
% 0.83/1.02  A new axiom: (forall (X3:a) (Z3:set_a) (X4:set_a) (P:(a->Prop)), (((member_a X3) Z3)->(((ord_less_eq_set_a Z3) (collect_a (fun (X2:a)=> ((and ((member_a X2) X4)) (P X2)))))->(P X3))))
% 0.83/1.02  FOF formula (forall (A:set_Product_prod_a_a) (P:(product_prod_a_a->Prop)) (Q:(product_prod_a_a->Prop)), (((eq Prop) ((ord_le1824328871od_a_a A) (collec645855634od_a_a (fun (X2:product_prod_a_a)=> ((and (P X2)) (Q X2)))))) ((and ((ord_le1824328871od_a_a A) (collec645855634od_a_a P))) ((ord_le1824328871od_a_a A) (collec645855634od_a_a Q))))) of role axiom named fact_306_conj__subset__def
% 0.83/1.02  A new axiom: (forall (A:set_Product_prod_a_a) (P:(product_prod_a_a->Prop)) (Q:(product_prod_a_a->Prop)), (((eq Prop) ((ord_le1824328871od_a_a A) (collec645855634od_a_a (fun (X2:product_prod_a_a)=> ((and (P X2)) (Q X2)))))) ((and ((ord_le1824328871od_a_a A) (collec645855634od_a_a P))) ((ord_le1824328871od_a_a A) (collec645855634od_a_a Q)))))
% 0.83/1.02  FOF formula (forall (A:set_nat) (P:(nat->Prop)) (Q:(nat->Prop)), (((eq Prop) ((ord_less_eq_set_nat A) (collect_nat (fun (X2:nat)=> ((and (P X2)) (Q X2)))))) ((and ((ord_less_eq_set_nat A) (collect_nat P))) ((ord_less_eq_set_nat A) (collect_nat Q))))) of role axiom named fact_307_conj__subset__def
% 0.83/1.02  A new axiom: (forall (A:set_nat) (P:(nat->Prop)) (Q:(nat->Prop)), (((eq Prop) ((ord_less_eq_set_nat A) (collect_nat (fun (X2:nat)=> ((and (P X2)) (Q X2)))))) ((and ((ord_less_eq_set_nat A) (collect_nat P))) ((ord_less_eq_set_nat A) (collect_nat Q)))))
% 0.83/1.02  FOF formula (forall (A:set_a) (P:(a->Prop)) (Q:(a->Prop)), (((eq Prop) ((ord_less_eq_set_a A) (collect_a (fun (X2:a)=> ((and (P X2)) (Q X2)))))) ((and ((ord_less_eq_set_a A) (collect_a P))) ((ord_less_eq_set_a A) (collect_a Q))))) of role axiom named fact_308_conj__subset__def
% 0.83/1.02  A new axiom: (forall (A:set_a) (P:(a->Prop)) (Q:(a->Prop)), (((eq Prop) ((ord_less_eq_set_a A) (collect_a (fun (X2:a)=> ((and (P X2)) (Q X2)))))) ((and ((ord_less_eq_set_a A) (collect_a P))) ((ord_less_eq_set_a A) (collect_a Q)))))
% 0.83/1.02  FOF formula (forall (Pverts:set_a) (Parcs:set_Product_prod_a_a) (More:product_unit), (((eq set_Product_prod_a_a) (pair_p133601421t_unit (((pair_p1621517565t_unit Pverts) Parcs) More))) Parcs)) of role axiom named fact_309_pair__pre__digraph_Oselect__convs_I2_J
% 0.83/1.02  A new axiom: (forall (Pverts:set_a) (Parcs:set_Product_prod_a_a) (More:product_unit), (((eq set_Product_prod_a_a) (pair_p133601421t_unit (((pair_p1621517565t_unit Pverts) Parcs) More))) Parcs))
% 0.83/1.02  FOF formula (forall (Pverts:set_nat) (Parcs:set_Pr1986765409at_nat) (More:product_unit), (((eq set_Pr1986765409at_nat) (pair_p715279805t_unit (((pair_p1167410509t_unit Pverts) Parcs) More))) Parcs)) of role axiom named fact_310_pair__pre__digraph_Oselect__convs_I2_J
% 0.83/1.02  A new axiom: (forall (Pverts:set_nat) (Parcs:set_Pr1986765409at_nat) (More:product_unit), (((eq set_Pr1986765409at_nat) (pair_p715279805t_unit (((pair_p1167410509t_unit Pverts) Parcs) More))) Parcs))
% 0.83/1.02  FOF formula (forall (Pverts:set_Product_prod_a_a) (Parcs:set_Pr1948701895od_a_a) (More:product_unit), (((eq set_Pr1948701895od_a_a) (pair_p1783210148t_unit (((pair_p398687508t_unit Pverts) Parcs) More))) Parcs)) of role axiom named fact_311_pair__pre__digraph_Oselect__convs_I2_J
% 0.83/1.03  A new axiom: (forall (Pverts:set_Product_prod_a_a) (Parcs:set_Pr1948701895od_a_a) (More:product_unit), (((eq set_Pr1948701895od_a_a) (pair_p1783210148t_unit (((pair_p398687508t_unit Pverts) Parcs) More))) Parcs))
% 0.83/1.03  FOF formula (forall (Pverts:set_a) (Parcs:set_Product_prod_a_a) (More:product_unit), (((eq set_a) (pair_p1047056820t_unit (((pair_p1621517565t_unit Pverts) Parcs) More))) Pverts)) of role axiom named fact_312_pair__pre__digraph_Oselect__convs_I1_J
% 0.83/1.03  A new axiom: (forall (Pverts:set_a) (Parcs:set_Product_prod_a_a) (More:product_unit), (((eq set_a) (pair_p1047056820t_unit (((pair_p1621517565t_unit Pverts) Parcs) More))) Pverts))
% 0.83/1.03  FOF formula (forall (Pverts:set_nat) (Parcs:set_Pr1986765409at_nat) (More:product_unit), (((eq set_nat) (pair_p1677060310t_unit (((pair_p1167410509t_unit Pverts) Parcs) More))) Pverts)) of role axiom named fact_313_pair__pre__digraph_Oselect__convs_I1_J
% 0.83/1.03  A new axiom: (forall (Pverts:set_nat) (Parcs:set_Pr1986765409at_nat) (More:product_unit), (((eq set_nat) (pair_p1677060310t_unit (((pair_p1167410509t_unit Pverts) Parcs) More))) Pverts))
% 0.83/1.03  FOF formula (forall (Pverts:set_Product_prod_a_a) (Parcs:set_Pr1948701895od_a_a) (More:product_unit), (((eq set_Product_prod_a_a) (pair_p447552203t_unit (((pair_p398687508t_unit Pverts) Parcs) More))) Pverts)) of role axiom named fact_314_pair__pre__digraph_Oselect__convs_I1_J
% 0.83/1.03  A new axiom: (forall (Pverts:set_Product_prod_a_a) (Parcs:set_Pr1948701895od_a_a) (More:product_unit), (((eq set_Product_prod_a_a) (pair_p447552203t_unit (((pair_p398687508t_unit Pverts) Parcs) More))) Pverts))
% 0.83/1.03  FOF formula (((eq (set_Pr1986765409at_nat->set_se1612935105at_nat)) finite361944167at_nat) (fun (A5:set_Pr1986765409at_nat)=> (collec1606769740at_nat (fun (X5:set_Pr1986765409at_nat)=> ((and ((ord_le841296385at_nat X5) A5)) (finite772653738at_nat X5)))))) of role axiom named fact_315_Fpow__def
% 0.83/1.03  A new axiom: (((eq (set_Pr1986765409at_nat->set_se1612935105at_nat)) finite361944167at_nat) (fun (A5:set_Pr1986765409at_nat)=> (collec1606769740at_nat (fun (X5:set_Pr1986765409at_nat)=> ((and ((ord_le841296385at_nat X5) A5)) (finite772653738at_nat X5))))))
% 0.83/1.03  FOF formula (((eq (set_Pr1948701895od_a_a->set_se958357159od_a_a)) finite702915405od_a_a) (fun (A5:set_Pr1948701895od_a_a)=> (collec453062450od_a_a (fun (X5:set_Pr1948701895od_a_a)=> ((and ((ord_le456379495od_a_a X5) A5)) (finite1664988688od_a_a X5)))))) of role axiom named fact_316_Fpow__def
% 0.83/1.03  A new axiom: (((eq (set_Pr1948701895od_a_a->set_se958357159od_a_a)) finite702915405od_a_a) (fun (A5:set_Pr1948701895od_a_a)=> (collec453062450od_a_a (fun (X5:set_Pr1948701895od_a_a)=> ((and ((ord_le456379495od_a_a X5) A5)) (finite1664988688od_a_a X5))))))
% 0.83/1.03  FOF formula (((eq (set_Product_prod_a_a->set_se1596668135od_a_a)) finite351630733od_a_a) (fun (A5:set_Product_prod_a_a)=> (collec183727474od_a_a (fun (X5:set_Product_prod_a_a)=> ((and ((ord_le1824328871od_a_a X5) A5)) (finite179568208od_a_a X5)))))) of role axiom named fact_317_Fpow__def
% 0.83/1.03  A new axiom: (((eq (set_Product_prod_a_a->set_se1596668135od_a_a)) finite351630733od_a_a) (fun (A5:set_Product_prod_a_a)=> (collec183727474od_a_a (fun (X5:set_Product_prod_a_a)=> ((and ((ord_le1824328871od_a_a X5) A5)) (finite179568208od_a_a X5))))))
% 0.83/1.03  FOF formula (((eq (set_nat->set_set_nat)) finite_Fpow_nat) (fun (A5:set_nat)=> (collect_set_nat (fun (X5:set_nat)=> ((and ((ord_less_eq_set_nat X5) A5)) (finite_finite_nat X5)))))) of role axiom named fact_318_Fpow__def
% 0.83/1.03  A new axiom: (((eq (set_nat->set_set_nat)) finite_Fpow_nat) (fun (A5:set_nat)=> (collect_set_nat (fun (X5:set_nat)=> ((and ((ord_less_eq_set_nat X5) A5)) (finite_finite_nat X5))))))
% 0.83/1.03  FOF formula (((eq (set_a->set_set_a)) finite_Fpow_a) (fun (A5:set_a)=> (collect_set_a (fun (X5:set_a)=> ((and ((ord_less_eq_set_a X5) A5)) (finite_finite_a X5)))))) of role axiom named fact_319_Fpow__def
% 0.83/1.03  A new axiom: (((eq (set_a->set_set_a)) finite_Fpow_a) (fun (A5:set_a)=> (collect_set_a (fun (X5:set_a)=> ((and ((ord_less_eq_set_a X5) A5)) (finite_finite_a X5))))))
% 0.83/1.03  FOF formula (((eq (pair_p125712459t_unit->Prop)) pair_p1802376898raph_a) (fun (G:pair_p125712459t_unit)=> ((and (pair_p68905728raph_a G)) (pair_p1864019935ioms_a G)))) of role axiom named fact_320_pair__fin__digraph__def
% 0.83/1.03  A new axiom: (((eq (pair_p125712459t_unit->Prop)) pair_p1802376898raph_a) (fun (G:pair_p125712459t_unit)=> ((and (pair_p68905728raph_a G)) (pair_p1864019935ioms_a G))))
% 0.83/1.03  FOF formula (((eq (pair_p1914262621t_unit->Prop)) pair_p128415500ph_nat) (fun (G:pair_p1914262621t_unit)=> ((and (pair_p1515597646ph_nat G)) (pair_p1027063983ms_nat G)))) of role axiom named fact_321_pair__fin__digraph__def
% 0.83/1.03  A new axiom: (((eq (pair_p1914262621t_unit->Prop)) pair_p128415500ph_nat) (fun (G:pair_p1914262621t_unit)=> ((and (pair_p1515597646ph_nat G)) (pair_p1027063983ms_nat G))))
% 0.83/1.03  FOF formula (((eq (pair_p1765063010t_unit->Prop)) pair_p374947051od_a_a) (fun (G:pair_p1765063010t_unit)=> ((and (pair_p646030121od_a_a G)) (pair_p504738056od_a_a G)))) of role axiom named fact_322_pair__fin__digraph__def
% 0.83/1.03  A new axiom: (((eq (pair_p1765063010t_unit->Prop)) pair_p374947051od_a_a) (fun (G:pair_p1765063010t_unit)=> ((and (pair_p646030121od_a_a G)) (pair_p504738056od_a_a G))))
% 0.83/1.03  FOF formula (forall (G2:pair_p125712459t_unit), ((pair_p68905728raph_a G2)->((pair_p1864019935ioms_a G2)->(pair_p1802376898raph_a G2)))) of role axiom named fact_323_pair__fin__digraph_Ointro
% 0.83/1.03  A new axiom: (forall (G2:pair_p125712459t_unit), ((pair_p68905728raph_a G2)->((pair_p1864019935ioms_a G2)->(pair_p1802376898raph_a G2))))
% 0.83/1.03  FOF formula (forall (G2:pair_p1914262621t_unit), ((pair_p1515597646ph_nat G2)->((pair_p1027063983ms_nat G2)->(pair_p128415500ph_nat G2)))) of role axiom named fact_324_pair__fin__digraph_Ointro
% 0.83/1.03  A new axiom: (forall (G2:pair_p1914262621t_unit), ((pair_p1515597646ph_nat G2)->((pair_p1027063983ms_nat G2)->(pair_p128415500ph_nat G2))))
% 0.83/1.03  FOF formula (forall (G2:pair_p1765063010t_unit), ((pair_p646030121od_a_a G2)->((pair_p504738056od_a_a G2)->(pair_p374947051od_a_a G2)))) of role axiom named fact_325_pair__fin__digraph_Ointro
% 0.83/1.03  A new axiom: (forall (G2:pair_p1765063010t_unit), ((pair_p646030121od_a_a G2)->((pair_p504738056od_a_a G2)->(pair_p374947051od_a_a G2))))
% 0.83/1.03  FOF formula (forall (A:set_a) (B:set_nat), (((eq Prop) (finite1743148308_a_nat ((product_Sigma_a_nat A) (fun (Uu:a)=> B)))) ((or ((or (((eq set_a) A) bot_bot_set_a)) (((eq set_nat) B) bot_bot_set_nat))) ((and (finite_finite_a A)) (finite_finite_nat B))))) of role axiom named fact_326_finite__cartesian__product__iff
% 0.83/1.03  A new axiom: (forall (A:set_a) (B:set_nat), (((eq Prop) (finite1743148308_a_nat ((product_Sigma_a_nat A) (fun (Uu:a)=> B)))) ((or ((or (((eq set_a) A) bot_bot_set_a)) (((eq set_nat) B) bot_bot_set_nat))) ((and (finite_finite_a A)) (finite_finite_nat B)))))
% 0.83/1.03  FOF formula (forall (A:set_nat) (B:set_a), (((eq Prop) (finite1808550458_nat_a ((product_Sigma_nat_a A) (fun (Uu:nat)=> B)))) ((or ((or (((eq set_nat) A) bot_bot_set_nat)) (((eq set_a) B) bot_bot_set_a))) ((and (finite_finite_nat A)) (finite_finite_a B))))) of role axiom named fact_327_finite__cartesian__product__iff
% 0.83/1.03  A new axiom: (forall (A:set_nat) (B:set_a), (((eq Prop) (finite1808550458_nat_a ((product_Sigma_nat_a A) (fun (Uu:nat)=> B)))) ((or ((or (((eq set_nat) A) bot_bot_set_nat)) (((eq set_a) B) bot_bot_set_a))) ((and (finite_finite_nat A)) (finite_finite_a B)))))
% 0.83/1.03  FOF formula (forall (A:set_nat) (B:set_nat), (((eq Prop) (finite772653738at_nat ((produc45129834at_nat A) (fun (Uu:nat)=> B)))) ((or ((or (((eq set_nat) A) bot_bot_set_nat)) (((eq set_nat) B) bot_bot_set_nat))) ((and (finite_finite_nat A)) (finite_finite_nat B))))) of role axiom named fact_328_finite__cartesian__product__iff
% 0.83/1.03  A new axiom: (forall (A:set_nat) (B:set_nat), (((eq Prop) (finite772653738at_nat ((produc45129834at_nat A) (fun (Uu:nat)=> B)))) ((or ((or (((eq set_nat) A) bot_bot_set_nat)) (((eq set_nat) B) bot_bot_set_nat))) ((and (finite_finite_nat A)) (finite_finite_nat B)))))
% 0.83/1.03  FOF formula (forall (A:set_a) (B:set_a), (((eq Prop) (finite179568208od_a_a ((product_Sigma_a_a A) (fun (Uu:a)=> B)))) ((or ((or (((eq set_a) A) bot_bot_set_a)) (((eq set_a) B) bot_bot_set_a))) ((and (finite_finite_a A)) (finite_finite_a B))))) of role axiom named fact_329_finite__cartesian__product__iff
% 0.83/1.04  A new axiom: (forall (A:set_a) (B:set_a), (((eq Prop) (finite179568208od_a_a ((product_Sigma_a_a A) (fun (Uu:a)=> B)))) ((or ((or (((eq set_a) A) bot_bot_set_a)) (((eq set_a) B) bot_bot_set_a))) ((and (finite_finite_a A)) (finite_finite_a B)))))
% 0.83/1.04  FOF formula (forall (A:set_Product_prod_a_a) (B:set_a), (((eq Prop) (finite1919032935_a_a_a ((produc1282482655_a_a_a A) (fun (Uu:product_prod_a_a)=> B)))) ((or ((or (((eq set_Product_prod_a_a) A) bot_bo2131659635od_a_a)) (((eq set_a) B) bot_bot_set_a))) ((and (finite179568208od_a_a A)) (finite_finite_a B))))) of role axiom named fact_330_finite__cartesian__product__iff
% 0.83/1.04  A new axiom: (forall (A:set_Product_prod_a_a) (B:set_a), (((eq Prop) (finite1919032935_a_a_a ((produc1282482655_a_a_a A) (fun (Uu:product_prod_a_a)=> B)))) ((or ((or (((eq set_Product_prod_a_a) A) bot_bo2131659635od_a_a)) (((eq set_a) B) bot_bot_set_a))) ((and (finite179568208od_a_a A)) (finite_finite_a B)))))
% 0.83/1.04  FOF formula (forall (A:set_Product_prod_a_a) (B:set_nat), (((eq Prop) (finite1837575485_a_nat ((produc931712687_a_nat A) (fun (Uu:product_prod_a_a)=> B)))) ((or ((or (((eq set_Product_prod_a_a) A) bot_bo2131659635od_a_a)) (((eq set_nat) B) bot_bot_set_nat))) ((and (finite179568208od_a_a A)) (finite_finite_nat B))))) of role axiom named fact_331_finite__cartesian__product__iff
% 0.83/1.04  A new axiom: (forall (A:set_Product_prod_a_a) (B:set_nat), (((eq Prop) (finite1837575485_a_nat ((produc931712687_a_nat A) (fun (Uu:product_prod_a_a)=> B)))) ((or ((or (((eq set_Product_prod_a_a) A) bot_bo2131659635od_a_a)) (((eq set_nat) B) bot_bot_set_nat))) ((and (finite179568208od_a_a A)) (finite_finite_nat B)))))
% 0.83/1.04  FOF formula (forall (A:set_a) (B:set_Product_prod_a_a), (((eq Prop) (finite676513017od_a_a ((produc520147185od_a_a A) (fun (Uu:a)=> B)))) ((or ((or (((eq set_a) A) bot_bot_set_a)) (((eq set_Product_prod_a_a) B) bot_bo2131659635od_a_a))) ((and (finite_finite_a A)) (finite179568208od_a_a B))))) of role axiom named fact_332_finite__cartesian__product__iff
% 0.83/1.04  A new axiom: (forall (A:set_a) (B:set_Product_prod_a_a), (((eq Prop) (finite676513017od_a_a ((produc520147185od_a_a A) (fun (Uu:a)=> B)))) ((or ((or (((eq set_a) A) bot_bot_set_a)) (((eq set_Product_prod_a_a) B) bot_bo2131659635od_a_a))) ((and (finite_finite_a A)) (finite179568208od_a_a B)))))
% 0.83/1.04  FOF formula (forall (A:set_a) (B:set_Pr1986765409at_nat), (((eq Prop) (finite942416723at_nat ((produc292491723at_nat A) (fun (Uu:a)=> B)))) ((or ((or (((eq set_a) A) bot_bot_set_a)) (((eq set_Pr1986765409at_nat) B) bot_bo2130386637at_nat))) ((and (finite_finite_a A)) (finite772653738at_nat B))))) of role axiom named fact_333_finite__cartesian__product__iff
% 0.83/1.04  A new axiom: (forall (A:set_a) (B:set_Pr1986765409at_nat), (((eq Prop) (finite942416723at_nat ((produc292491723at_nat A) (fun (Uu:a)=> B)))) ((or ((or (((eq set_a) A) bot_bot_set_a)) (((eq set_Pr1986765409at_nat) B) bot_bo2130386637at_nat))) ((and (finite_finite_a A)) (finite772653738at_nat B)))))
% 0.83/1.04  FOF formula (forall (A:set_nat) (B:set_Product_prod_a_a), (((eq Prop) (finite1297454819od_a_a ((produc1182842125od_a_a A) (fun (Uu:nat)=> B)))) ((or ((or (((eq set_nat) A) bot_bot_set_nat)) (((eq set_Product_prod_a_a) B) bot_bo2131659635od_a_a))) ((and (finite_finite_nat A)) (finite179568208od_a_a B))))) of role axiom named fact_334_finite__cartesian__product__iff
% 0.83/1.04  A new axiom: (forall (A:set_nat) (B:set_Product_prod_a_a), (((eq Prop) (finite1297454819od_a_a ((produc1182842125od_a_a A) (fun (Uu:nat)=> B)))) ((or ((or (((eq set_nat) A) bot_bot_set_nat)) (((eq set_Product_prod_a_a) B) bot_bo2131659635od_a_a))) ((and (finite_finite_nat A)) (finite179568208od_a_a B)))))
% 0.83/1.04  FOF formula (forall (A:set_nat) (B:set_Pr1986765409at_nat), (((eq Prop) (finite277291581at_nat ((produc894163943at_nat A) (fun (Uu:nat)=> B)))) ((or ((or (((eq set_nat) A) bot_bot_set_nat)) (((eq set_Pr1986765409at_nat) B) bot_bo2130386637at_nat))) ((and (finite_finite_nat A)) (finite772653738at_nat B))))) of role axiom named fact_335_finite__cartesian__product__iff
% 0.83/1.05  A new axiom: (forall (A:set_nat) (B:set_Pr1986765409at_nat), (((eq Prop) (finite277291581at_nat ((produc894163943at_nat A) (fun (Uu:nat)=> B)))) ((or ((or (((eq set_nat) A) bot_bot_set_nat)) (((eq set_Pr1986765409at_nat) B) bot_bo2130386637at_nat))) ((and (finite_finite_nat A)) (finite772653738at_nat B)))))
% 0.83/1.05  FOF formula (forall (C2:product_prod_a_a), (((member449909584od_a_a C2) bot_bo2131659635od_a_a)->False)) of role axiom named fact_336_empty__iff
% 0.83/1.05  A new axiom: (forall (C2:product_prod_a_a), (((member449909584od_a_a C2) bot_bo2131659635od_a_a)->False))
% 0.83/1.05  FOF formula (forall (C2:nat), (((member_nat C2) bot_bot_set_nat)->False)) of role axiom named fact_337_empty__iff
% 0.83/1.05  A new axiom: (forall (C2:nat), (((member_nat C2) bot_bot_set_nat)->False))
% 0.83/1.05  FOF formula (forall (A:set_Product_prod_a_a), (((eq Prop) (forall (X2:product_prod_a_a), (((member449909584od_a_a X2) A)->False))) (((eq set_Product_prod_a_a) A) bot_bo2131659635od_a_a))) of role axiom named fact_338_all__not__in__conv
% 0.83/1.05  A new axiom: (forall (A:set_Product_prod_a_a), (((eq Prop) (forall (X2:product_prod_a_a), (((member449909584od_a_a X2) A)->False))) (((eq set_Product_prod_a_a) A) bot_bo2131659635od_a_a)))
% 0.83/1.05  FOF formula (forall (A:set_nat), (((eq Prop) (forall (X2:nat), (((member_nat X2) A)->False))) (((eq set_nat) A) bot_bot_set_nat))) of role axiom named fact_339_all__not__in__conv
% 0.83/1.05  A new axiom: (forall (A:set_nat), (((eq Prop) (forall (X2:nat), (((member_nat X2) A)->False))) (((eq set_nat) A) bot_bot_set_nat)))
% 0.83/1.05  FOF formula (forall (P:(product_prod_a_a->Prop)), (((eq Prop) (((eq set_Product_prod_a_a) (collec645855634od_a_a P)) bot_bo2131659635od_a_a)) (forall (X2:product_prod_a_a), ((P X2)->False)))) of role axiom named fact_340_Collect__empty__eq
% 0.83/1.05  A new axiom: (forall (P:(product_prod_a_a->Prop)), (((eq Prop) (((eq set_Product_prod_a_a) (collec645855634od_a_a P)) bot_bo2131659635od_a_a)) (forall (X2:product_prod_a_a), ((P X2)->False))))
% 0.83/1.05  FOF formula (forall (P:(nat->Prop)), (((eq Prop) (((eq set_nat) (collect_nat P)) bot_bot_set_nat)) (forall (X2:nat), ((P X2)->False)))) of role axiom named fact_341_Collect__empty__eq
% 0.83/1.05  A new axiom: (forall (P:(nat->Prop)), (((eq Prop) (((eq set_nat) (collect_nat P)) bot_bot_set_nat)) (forall (X2:nat), ((P X2)->False))))
% 0.83/1.05  FOF formula (forall (P:(product_prod_a_a->Prop)), (((eq Prop) (((eq set_Product_prod_a_a) bot_bo2131659635od_a_a) (collec645855634od_a_a P))) (forall (X2:product_prod_a_a), ((P X2)->False)))) of role axiom named fact_342_empty__Collect__eq
% 0.83/1.05  A new axiom: (forall (P:(product_prod_a_a->Prop)), (((eq Prop) (((eq set_Product_prod_a_a) bot_bo2131659635od_a_a) (collec645855634od_a_a P))) (forall (X2:product_prod_a_a), ((P X2)->False))))
% 0.83/1.05  FOF formula (forall (P:(nat->Prop)), (((eq Prop) (((eq set_nat) bot_bot_set_nat) (collect_nat P))) (forall (X2:nat), ((P X2)->False)))) of role axiom named fact_343_empty__Collect__eq
% 0.83/1.05  A new axiom: (forall (P:(nat->Prop)), (((eq Prop) (((eq set_nat) bot_bot_set_nat) (collect_nat P))) (forall (X2:nat), ((P X2)->False))))
% 0.83/1.05  FOF formula (forall (A:set_Product_prod_a_a), ((ord_le1824328871od_a_a bot_bo2131659635od_a_a) A)) of role axiom named fact_344_empty__subsetI
% 0.83/1.05  A new axiom: (forall (A:set_Product_prod_a_a), ((ord_le1824328871od_a_a bot_bo2131659635od_a_a) A))
% 0.83/1.05  FOF formula (forall (A:set_nat), ((ord_less_eq_set_nat bot_bot_set_nat) A)) of role axiom named fact_345_empty__subsetI
% 0.83/1.05  A new axiom: (forall (A:set_nat), ((ord_less_eq_set_nat bot_bot_set_nat) A))
% 0.83/1.05  FOF formula (forall (A:set_a), ((ord_less_eq_set_a bot_bot_set_a) A)) of role axiom named fact_346_empty__subsetI
% 0.83/1.05  A new axiom: (forall (A:set_a), ((ord_less_eq_set_a bot_bot_set_a) A))
% 0.83/1.05  FOF formula (forall (A:set_a), (((eq Prop) ((ord_less_eq_set_a A) bot_bot_set_a)) (((eq set_a) A) bot_bot_set_a))) of role axiom named fact_347_subset__empty
% 0.83/1.05  A new axiom: (forall (A:set_a), (((eq Prop) ((ord_less_eq_set_a A) bot_bot_set_a)) (((eq set_a) A) bot_bot_set_a)))
% 0.83/1.05  FOF formula ((and ((and (finite_finite_a (pair_p1047056820t_unit g))) (((eq nat) (finite_card_a (pair_p1047056820t_unit g))) n))) (((eq set_Product_prod_a_a) (pair_p133601421t_unit g)) (collec645855634od_a_a (produc1833107820_a_a_o (fun (U:a) (V:a)=> ((and ((member449909584od_a_a ((product_Pair_a_a U) V)) ((product_Sigma_a_a (pair_p1047056820t_unit g)) (fun (Uu:a)=> (pair_p1047056820t_unit g))))) (not (((eq a) U) V)))))))) of role axiom named fact_348_calculation
% 0.83/1.05  A new axiom: ((and ((and (finite_finite_a (pair_p1047056820t_unit g))) (((eq nat) (finite_card_a (pair_p1047056820t_unit g))) n))) (((eq set_Product_prod_a_a) (pair_p133601421t_unit g)) (collec645855634od_a_a (produc1833107820_a_a_o (fun (U:a) (V:a)=> ((and ((member449909584od_a_a ((product_Pair_a_a U) V)) ((product_Sigma_a_a (pair_p1047056820t_unit g)) (fun (Uu:a)=> (pair_p1047056820t_unit g))))) (not (((eq a) U) V))))))))
% 0.83/1.05  FOF formula (forall (K:nat), (finite_finite_nat (collect_nat (fun (N:nat)=> ((ord_less_eq_nat N) K))))) of role axiom named fact_349_finite__Collect__le__nat
% 0.83/1.05  A new axiom: (forall (K:nat), (finite_finite_nat (collect_nat (fun (N:nat)=> ((ord_less_eq_nat N) K)))))
% 0.83/1.05  FOF formula (((eq (set_nat->Prop)) finite_finite_nat) (fun (N2:set_nat)=> ((ex nat) (fun (M:nat)=> (forall (X2:nat), (((member_nat X2) N2)->((ord_less_eq_nat X2) M))))))) of role axiom named fact_350_finite__nat__set__iff__bounded__le
% 0.83/1.05  A new axiom: (((eq (set_nat->Prop)) finite_finite_nat) (fun (N2:set_nat)=> ((ex nat) (fun (M:nat)=> (forall (X2:nat), (((member_nat X2) N2)->((ord_less_eq_nat X2) M)))))))
% 0.83/1.05  FOF formula (forall (S:set_nat), (((eq Prop) ((finite_finite_nat S)->False)) (forall (M:nat), ((ex nat) (fun (N:nat)=> ((and ((ord_less_eq_nat M) N)) ((member_nat N) S))))))) of role axiom named fact_351_infinite__nat__iff__unbounded__le
% 0.83/1.05  A new axiom: (forall (S:set_nat), (((eq Prop) ((finite_finite_nat S)->False)) (forall (M:nat), ((ex nat) (fun (N:nat)=> ((and ((ord_less_eq_nat M) N)) ((member_nat N) S)))))))
% 0.83/1.05  <<< nat] :
% 0.83/1.05              ( ( P @ X )
% 0.83/1.05             => ( ord_less_eq_nat @ X @ M2 ) )
% 0.83/1.05         => ~ !>>>!!!<<< [M3: nat] :
% 0.83/1.05                ( ( P @ M3 )
% 0.83/1.05               => ~ ! [X6: nat] :
% 0.83/1.05                    >>>
% 0.83/1.05  statestack=[0, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 11, 22, 30, 36, 43, 50, 99, 113, 185, 229, 265, 285, 300, 221, 120, 187, 221, 120, 187, 124]
% 0.83/1.05  symstack=[$end, TPTP_file_pre, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, 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TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, TPTP_input, LexToken(THF,'thf',1,131932), LexToken(LPAR,'(',1,131935), name, LexToken(COMMA,',',1,131962), formula_role, LexToken(COMMA,',',1,131968), LexToken(LPAR,'(',1,131969), thf_quantified_formula_PRE, thf_quantifier, LexToken(LBRACKET,'[',1,131977), thf_variable_list, LexToken(RBRACKET,']',1,132005), LexToken(COLON,':',1,132007), LexToken(LPAR,'(',1,132015), thf_unitary_formula, thf_pair_connective, LexToken(LPAR,'(',1,132036), thf_unitary_formula, thf_pair_connective, unary_connective]
% 0.83/1.05  Unexpected exception Syntax error at '!':BANG
% 0.83/1.05  Traceback (most recent call last):
% 0.83/1.05    File "CASC.py", line 79, in <module>
% 0.83/1.05      problem=TPTP.TPTPproblem(env=environment,debug=1,file=file)
% 0.83/1.05    File "/export/starexec/sandbox/solver/bin/TPTP.py", line 38, in __init__
% 0.83/1.05      parser.parse(file.read(),debug=0,lexer=lexer)
% 0.83/1.05    File "/export/starexec/sandbox/solver/bin/ply/yacc.py", line 265, in parse
% 0.83/1.05      return self.parseopt_notrack(input,lexer,debug,tracking,tokenfunc)
% 0.83/1.05    File "/export/starexec/sandbox/solver/bin/ply/yacc.py", line 1047, in parseopt_notrack
% 0.83/1.05      tok = self.errorfunc(errtoken)
% 0.83/1.05    File "/export/starexec/sandbox/solver/bin/TPTPparser.py", line 2099, in p_error
% 0.83/1.05      raise TPTPParsingError("Syntax error at '%s':%s" % (t.value,t.type))
% 0.83/1.05  TPTPparser.TPTPParsingError: Syntax error at '!':BANG
%------------------------------------------------------------------------------