TSTP Solution File: SEV524^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEV524^1 : TPTP v7.5.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 15:05:12 EDT 2021
% Result : Timeout 300.03s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEV524^1 : TPTP v7.5.0. Released v7.5.0.
% 0.03/0.13 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % DateTime : Fri Mar 19 12:20:22 EDT 2021
% 0.14/0.35 % CPUTime :
% 0.20/0.36 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.20/0.36 Python 2.7.5
% 0.48/0.63 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2b40b17296c8>, <kernel.DependentProduct object at 0x2745878>) of role type named c_Eps_i_tp
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_Eps_i:((fofType->Prop)->fofType)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x27463f8>, <kernel.Sort object at 0x2b40b1705638>) of role type named c_False_tp
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_False:Prop
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2b40b1729f38>, <kernel.Sort object at 0x2b40b1705638>) of role type named c_True_tp
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_True:Prop
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2b40b1729050>, <kernel.DependentProduct object at 0x2745830>) of role type named c_not_tp
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_not:(Prop->Prop)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2b40b1729320>, <kernel.DependentProduct object at 0x2745098>) of role type named c_and_tp
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_and:(Prop->(Prop->Prop))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2b40b1729f38>, <kernel.DependentProduct object at 0x2745b00>) of role type named c_or_tp
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_or:(Prop->(Prop->Prop))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2b40b1729c68>, <kernel.DependentProduct object at 0x2745b90>) of role type named c_iff_tp
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_iff:(Prop->(Prop->Prop))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2b40b1729f38>, <kernel.DependentProduct object at 0x2745830>) of role type named c_In_tp
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_In:(fofType->(fofType->Prop))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2b40b1729c68>, <kernel.DependentProduct object at 0x2745b00>) of role type named c_Subq_tp
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_Subq:(fofType->(fofType->Prop))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2b40b1729c68>, <kernel.Single object at 0x2745a70>) of role type named c_Empty_tp
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_Empty:fofType
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2745bd8>, <kernel.DependentProduct object at 0x2745710>) of role type named c_Union_tp
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_Union:(fofType->fofType)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2745830>, <kernel.DependentProduct object at 0x2745518>) of role type named c_Power_tp
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_Power:(fofType->fofType)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2745878>, <kernel.DependentProduct object at 0x27455a8>) of role type named c_Repl_tp
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_Repl:(fofType->((fofType->fofType)->fofType))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2745a70>, <kernel.DependentProduct object at 0x2745b90>) of role type named c_TransSet_tp
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_TransSet:(fofType->Prop)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2745098>, <kernel.DependentProduct object at 0x2745758>) of role type named c_atleast2_tp
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_atleast2:(fofType->Prop)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2745bd8>, <kernel.DependentProduct object at 0x2745a28>) of role type named c_atleast3_tp
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_atleast3:(fofType->Prop)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x27455a8>, <kernel.DependentProduct object at 0x2745638>) of role type named c_atleast4_tp
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_atleast4:(fofType->Prop)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2745b90>, <kernel.DependentProduct object at 0x2745e18>) of role type named c_atleast5_tp
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_atleast5:(fofType->Prop)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2745758>, <kernel.DependentProduct object at 0x2745d88>) of role type named c_atleast6_tp
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_atleast6:(fofType->Prop)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2745a28>, <kernel.DependentProduct object at 0x2745248>) of role type named c_exactly2_tp
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_exactly2:(fofType->Prop)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2745638>, <kernel.DependentProduct object at 0x2745998>) of role type named c_exactly3_tp
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring c_exactly3:(fofType->Prop)
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x2745e18>, <kernel.DependentProduct object at 0x27455f0>) of role type named c_exactly4_tp
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring c_exactly4:(fofType->Prop)
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2745d88>, <kernel.DependentProduct object at 0x2745368>) of role type named c_exactly5_tp
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring c_exactly5:(fofType->Prop)
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2745248>, <kernel.DependentProduct object at 0x2745518>) of role type named c_exu_i_tp
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring c_exu_i:((fofType->Prop)->Prop)
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2745998>, <kernel.DependentProduct object at 0x2745518>) of role type named c_reflexive_i_tp
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring c_reflexive_i:((fofType->(fofType->Prop))->Prop)
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2745f38>, <kernel.DependentProduct object at 0x2b40a9c2d7e8>) of role type named c_irreflexive_i_tp
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring c_irreflexive_i:((fofType->(fofType->Prop))->Prop)
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2745368>, <kernel.DependentProduct object at 0x2b40a9c2d7e8>) of role type named c_symmetric_i_tp
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring c_symmetric_i:((fofType->(fofType->Prop))->Prop)
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x27455f0>, <kernel.DependentProduct object at 0x2745f38>) of role type named c_antisymmetric_i_tp
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring c_antisymmetric_i:((fofType->(fofType->Prop))->Prop)
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2b40a9c2df80>, <kernel.DependentProduct object at 0x27455f0>) of role type named c_transitive_i_tp
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring c_transitive_i:((fofType->(fofType->Prop))->Prop)
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2b40a9c2de60>, <kernel.DependentProduct object at 0x27455f0>) of role type named c_eqreln_i_tp
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring c_eqreln_i:((fofType->(fofType->Prop))->Prop)
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2b40a9c2de60>, <kernel.DependentProduct object at 0x2745f38>) of role type named c_per_i_tp
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring c_per_i:((fofType->(fofType->Prop))->Prop)
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2b40b170d488>, <kernel.DependentProduct object at 0x273ddd0>) of role type named c_linear_i_tp
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring c_linear_i:((fofType->(fofType->Prop))->Prop)
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2b40b170d488>, <kernel.DependentProduct object at 0x273ddd0>) of role type named c_trichotomous_or_i_tp
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring c_trichotomous_or_i:((fofType->(fofType->Prop))->Prop)
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x27455f0>, <kernel.DependentProduct object at 0x273df38>) of role type named c_partialorder_i_tp
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring c_partialorder_i:((fofType->(fofType->Prop))->Prop)
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2745998>, <kernel.DependentProduct object at 0x273dea8>) of role type named c_totalorder_i_tp
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring c_totalorder_i:((fofType->(fofType->Prop))->Prop)
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x27455f0>, <kernel.DependentProduct object at 0x273df80>) of role type named c_strictpartialorder_i_tp
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring c_strictpartialorder_i:((fofType->(fofType->Prop))->Prop)
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2745368>, <kernel.DependentProduct object at 0x273df80>) of role type named c_stricttotalorder_i_tp
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring c_stricttotalorder_i:((fofType->(fofType->Prop))->Prop)
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x27455f0>, <kernel.DependentProduct object at 0x273df80>) of role type named c_If_i_tp
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring c_If_i:(Prop->(fofType->(fofType->fofType)))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x27455f0>, <kernel.DependentProduct object at 0x27206c8>) of role type named c_exactly1of2_tp
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring c_exactly1of2:(Prop->(Prop->Prop))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x273df38>, <kernel.DependentProduct object at 0x2720ea8>) of role type named c_exactly1of3_tp
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring c_exactly1of3:(Prop->(Prop->(Prop->Prop)))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x273ddd0>, <kernel.DependentProduct object at 0x2720ea8>) of role type named c_nIn_tp
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring c_nIn:(fofType->(fofType->Prop))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x273df38>, <kernel.DependentProduct object at 0x2720ea8>) of role type named c_nSubq_tp
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_nSubq:(fofType->(fofType->Prop))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x273de60>, <kernel.DependentProduct object at 0x27209e0>) of role type named c_UPair_tp
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_UPair:(fofType->(fofType->fofType))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x273df38>, <kernel.DependentProduct object at 0x2720bd8>) of role type named c_Sing_tp
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_Sing:(fofType->fofType)
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x273df38>, <kernel.DependentProduct object at 0x2720b00>) of role type named c_binunion_tp
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_binunion:(fofType->(fofType->fofType))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x27206c8>, <kernel.DependentProduct object at 0x27209e0>) of role type named c_SetAdjoin_tp
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_SetAdjoin:(fofType->(fofType->fofType))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2720c68>, <kernel.DependentProduct object at 0x2720b48>) of role type named c_famunion_tp
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_famunion:(fofType->((fofType->fofType)->fofType))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2720d88>, <kernel.DependentProduct object at 0x2720638>) of role type named c_Sep_tp
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_Sep:(fofType->((fofType->Prop)->fofType))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2720998>, <kernel.DependentProduct object at 0x27209e0>) of role type named c_ReplSep_tp
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_ReplSep:(fofType->((fofType->Prop)->((fofType->fofType)->fofType)))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2720e60>, <kernel.DependentProduct object at 0x2720d88>) of role type named c_binintersect_tp
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_binintersect:(fofType->(fofType->fofType))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2720b48>, <kernel.DependentProduct object at 0x2720998>) of role type named c_setminus_tp
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_setminus:(fofType->(fofType->fofType))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2720bd8>, <kernel.DependentProduct object at 0x2720e60>) of role type named c_inj_tp
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_inj:(fofType->(fofType->((fofType->fofType)->Prop)))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2720638>, <kernel.DependentProduct object at 0x2720e60>) of role type named c_bij_tp
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_bij:(fofType->(fofType->((fofType->fofType)->Prop)))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x27206c8>, <kernel.DependentProduct object at 0x2b40b172a830>) of role type named c_atleastp_tp
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_atleastp:(fofType->(fofType->Prop))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2720d88>, <kernel.DependentProduct object at 0x2b40b172aea8>) of role type named c_equip_tp
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_equip:(fofType->(fofType->Prop))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2720998>, <kernel.DependentProduct object at 0x27206c8>) of role type named c_In_rec_poly_G_i_tp
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_In_rec_poly_G_i:((fofType->((fofType->fofType)->fofType))->(fofType->(fofType->Prop)))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2720638>, <kernel.DependentProduct object at 0x2b40b172acf8>) of role type named c_In_rec_poly_i_tp
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_In_rec_poly_i:((fofType->((fofType->fofType)->fofType))->(fofType->fofType))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x29e3d40>, <kernel.DependentProduct object at 0x2720d88>) of role type named c_ordsucc_tp
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_ordsucc:(fofType->fofType)
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2b40b172acf8>, <kernel.DependentProduct object at 0x2720e60>) of role type named c_nat_p_tp
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_nat_p:(fofType->Prop)
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2b40b172a758>, <kernel.DependentProduct object at 0x2720e60>) of role type named c_nat_primrec_tp
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_nat_primrec:(fofType->((fofType->(fofType->fofType))->(fofType->fofType)))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2b40b172a830>, <kernel.DependentProduct object at 0x2720998>) of role type named c_add_nat_tp
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring c_add_nat:(fofType->(fofType->fofType))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x2b40b172a758>, <kernel.DependentProduct object at 0x2742a70>) of role type named c_mul_nat_tp
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring c_mul_nat:(fofType->(fofType->fofType))
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x2b40b172a758>, <kernel.DependentProduct object at 0x2742e60>) of role type named c_ordinal_tp
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring c_ordinal:(fofType->Prop)
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x2720d88>, <kernel.DependentProduct object at 0x2742320>) of role type named c_V__tp
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring c_V_:(fofType->fofType)
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x2720e60>, <kernel.DependentProduct object at 0x2742170>) of role type named c_Inj1_tp
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring c_Inj1:(fofType->fofType)
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x2720d88>, <kernel.DependentProduct object at 0x2742680>) of role type named c_Inj0_tp
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring c_Inj0:(fofType->fofType)
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x27206c8>, <kernel.DependentProduct object at 0x2742830>) of role type named c_Unj_tp
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring c_Unj:(fofType->fofType)
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x2720d88>, <kernel.DependentProduct object at 0x2742710>) of role type named c_combine_funcs_tp
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring c_combine_funcs:(fofType->(fofType->((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))))
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x2720d88>, <kernel.DependentProduct object at 0x2742680>) of role type named c_setsum_tp
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring c_setsum:(fofType->(fofType->fofType))
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x2742a70>, <kernel.DependentProduct object at 0x2742290>) of role type named c_proj0_tp
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring c_proj0:(fofType->fofType)
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x2742320>, <kernel.DependentProduct object at 0x27427a0>) of role type named c_proj1_tp
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring c_proj1:(fofType->fofType)
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x2742e60>, <kernel.DependentProduct object at 0x2742a70>) of role type named c_binrep_tp
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring c_binrep:(fofType->(fofType->fofType))
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x2742680>, <kernel.DependentProduct object at 0x27423b0>) of role type named c_lam_tp
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring c_lam:(fofType->((fofType->fofType)->fofType))
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x2742290>, <kernel.DependentProduct object at 0x2742e60>) of role type named c_setprod_tp
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring c_setprod:(fofType->(fofType->fofType))
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x27428c0>, <kernel.DependentProduct object at 0x2742680>) of role type named c_ap_tp
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring c_ap:(fofType->(fofType->fofType))
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x2742320>, <kernel.DependentProduct object at 0x27420e0>) of role type named c_setsum_p_tp
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring c_setsum_p:(fofType->Prop)
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x2742518>, <kernel.DependentProduct object at 0x27428c0>) of role type named c_tuple_p_tp
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring c_tuple_p:(fofType->(fofType->Prop))
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x2742830>, <kernel.DependentProduct object at 0x2742bd8>) of role type named c_Pi_tp
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring c_Pi:(fofType->((fofType->fofType)->fofType))
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x2742680>, <kernel.DependentProduct object at 0x2742518>) of role type named c_setexp_tp
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring c_setexp:(fofType->(fofType->fofType))
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x2742f80>, <kernel.DependentProduct object at 0x2742b48>) of role type named c_Sep2_tp
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring c_Sep2:(fofType->((fofType->fofType)->((fofType->(fofType->Prop))->fofType)))
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x2742320>, <kernel.DependentProduct object at 0x2742830>) of role type named c_set_of_pairs_tp
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring c_set_of_pairs:(fofType->Prop)
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x2742998>, <kernel.DependentProduct object at 0x2742200>) of role type named c_lam2_tp
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring c_lam2:(fofType->((fofType->fofType)->((fofType->(fofType->fofType))->fofType)))
% 0.50/0.67 FOF formula (<kernel.Constant object at 0x27428c0>, <kernel.DependentProduct object at 0x2742d40>) of role type named c_PNoEq__tp
% 0.50/0.67 Using role type
% 0.50/0.67 Declaring c_PNoEq_:(fofType->((fofType->Prop)->((fofType->Prop)->Prop)))
% 0.50/0.67 FOF formula (<kernel.Constant object at 0x2742b48>, <kernel.DependentProduct object at 0x2742830>) of role type named c_PNoLt__tp
% 0.50/0.67 Using role type
% 0.50/0.67 Declaring c_PNoLt_:(fofType->((fofType->Prop)->((fofType->Prop)->Prop)))
% 0.50/0.67 FOF formula (<kernel.Constant object at 0x2742518>, <kernel.DependentProduct object at 0x2742248>) of role type named c_PNoLt_tp
% 0.50/0.67 Using role type
% 0.50/0.67 Declaring c_PNoLt:(fofType->((fofType->Prop)->(fofType->((fofType->Prop)->Prop))))
% 0.50/0.67 FOF formula (<kernel.Constant object at 0x2742098>, <kernel.DependentProduct object at 0x27428c0>) of role type named c_PNoLe_tp
% 0.50/0.67 Using role type
% 0.50/0.67 Declaring c_PNoLe:(fofType->((fofType->Prop)->(fofType->((fofType->Prop)->Prop))))
% 0.50/0.67 FOF formula (<kernel.Constant object at 0x2740680>, <kernel.DependentProduct object at 0x2742200>) of role type named c_PNo_downc_tp
% 0.50/0.67 Using role type
% 0.50/0.67 Declaring c_PNo_downc:((fofType->((fofType->Prop)->Prop))->(fofType->((fofType->Prop)->Prop)))
% 0.50/0.67 FOF formula (<kernel.Constant object at 0x2742d40>, <kernel.DependentProduct object at 0x2742320>) of role type named c_PNo_upc_tp
% 0.50/0.67 Using role type
% 0.50/0.67 Declaring c_PNo_upc:((fofType->((fofType->Prop)->Prop))->(fofType->((fofType->Prop)->Prop)))
% 0.50/0.67 FOF formula (<kernel.Constant object at 0x27428c0>, <kernel.DependentProduct object at 0x2742830>) of role type named c_SNoElts__tp
% 0.50/0.67 Using role type
% 0.50/0.67 Declaring c_SNoElts_:(fofType->fofType)
% 0.50/0.67 FOF formula (<kernel.Constant object at 0x2742200>, <kernel.DependentProduct object at 0x2742d40>) of role type named c_SNo__tp
% 0.50/0.67 Using role type
% 0.50/0.67 Declaring c_SNo_:(fofType->(fofType->Prop))
% 0.50/0.67 FOF formula (<kernel.Constant object at 0x2742098>, <kernel.DependentProduct object at 0x2742830>) of role type named c_PSNo_tp
% 0.50/0.67 Using role type
% 0.50/0.67 Declaring c_PSNo:(fofType->((fofType->Prop)->fofType))
% 0.50/0.67 FOF formula (<kernel.Constant object at 0x2742320>, <kernel.DependentProduct object at 0x28b8248>) of role type named c_SNo_tp
% 0.50/0.67 Using role type
% 0.50/0.67 Declaring c_SNo:(fofType->Prop)
% 0.50/0.67 FOF formula (<kernel.Constant object at 0x2742d40>, <kernel.DependentProduct object at 0x28b8290>) of role type named c_SNoLev_tp
% 0.50/0.67 Using role type
% 0.50/0.67 Declaring c_SNoLev:(fofType->fofType)
% 0.50/0.67 FOF formula (<kernel.Constant object at 0x2742830>, <kernel.DependentProduct object at 0x28b8200>) of role type named c_SNoEq__tp
% 0.50/0.67 Using role type
% 0.50/0.67 Declaring c_SNoEq_:(fofType->(fofType->(fofType->Prop)))
% 0.50/0.67 FOF formula (<kernel.Constant object at 0x2742098>, <kernel.DependentProduct object at 0x28b8200>) of role type named c_SNoLt_tp
% 0.50/0.67 Using role type
% 0.50/0.67 Declaring c_SNoLt:(fofType->(fofType->Prop))
% 0.50/0.67 FOF formula (<kernel.Constant object at 0x2742830>, <kernel.DependentProduct object at 0x28b8200>) of role type named c_SNoLe_tp
% 0.50/0.67 Using role type
% 0.50/0.67 Declaring c_SNoLe:(fofType->(fofType->Prop))
% 0.50/0.67 FOF formula (<kernel.Constant object at 0x2742d40>, <kernel.DependentProduct object at 0x28b8170>) of role type named c_binop_on_tp
% 0.50/0.67 Using role type
% 0.50/0.67 Declaring c_binop_on:(fofType->((fofType->(fofType->fofType))->Prop))
% 0.50/0.67 FOF formula (<kernel.Constant object at 0x2742830>, <kernel.DependentProduct object at 0x28b8098>) of role type named c_Loop_tp
% 0.50/0.67 Using role type
% 0.50/0.67 Declaring c_Loop:(fofType->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->(fofType->Prop)))))
% 0.50/0.67 FOF formula (<kernel.Constant object at 0x2742830>, <kernel.DependentProduct object at 0x28b8368>) of role type named c_Loop_with_defs_tp
% 0.50/0.67 Using role type
% 0.50/0.67 Declaring c_Loop_with_defs:(fofType->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->(fofType->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->Prop))))))))))))))
% 0.50/0.67 FOF formula (<kernel.Constant object at 0x28b82d8>, <kernel.DependentProduct object at 0x28b8290>) of role type named c_Loop_with_defs_cex1_tp
% 0.50/0.69 Using role type
% 0.50/0.69 Declaring c_Loop_with_defs_cex1:(fofType->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->(fofType->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->Prop))))))))))))))
% 0.50/0.69 FOF formula (<kernel.Constant object at 0x28b80e0>, <kernel.DependentProduct object at 0x28b8488>) of role type named c_Loop_with_defs_cex2_tp
% 0.50/0.69 Using role type
% 0.50/0.69 Declaring c_Loop_with_defs_cex2:(fofType->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->(fofType->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->Prop))))))))))))))
% 0.50/0.69 FOF formula (<kernel.Constant object at 0x28b8128>, <kernel.DependentProduct object at 0x28b8098>) of role type named c_combinator_tp
% 0.50/0.69 Using role type
% 0.50/0.69 Declaring c_combinator:(fofType->Prop)
% 0.50/0.69 FOF formula (<kernel.Constant object at 0x28b8368>, <kernel.DependentProduct object at 0x28b80e0>) of role type named c_combinator_equiv_tp
% 0.50/0.69 Using role type
% 0.50/0.69 Declaring c_combinator_equiv:(fofType->(fofType->Prop))
% 0.50/0.69 FOF formula (<kernel.Constant object at 0x28b8290>, <kernel.DependentProduct object at 0x28b8128>) of role type named c_equip_mod_tp
% 0.50/0.69 Using role type
% 0.50/0.69 Declaring c_equip_mod:(fofType->(fofType->(fofType->Prop)))
% 0.50/0.69 FOF formula (forall (X0:(fofType->Prop)) (X1:fofType), ((X0 X1)->(X0 (c_Eps_i X0)))) of role axiom named ax1
% 0.50/0.69 A new axiom: (forall (X0:(fofType->Prop)) (X1:fofType), ((X0 X1)->(X0 (c_Eps_i X0))))
% 0.50/0.69 FOF formula (forall (X0:Prop), ((c_not (c_not X0))->X0)) of role axiom named ax2
% 0.50/0.69 A new axiom: (forall (X0:Prop), ((c_not (c_not X0))->X0))
% 0.50/0.69 FOF formula (forall (X0:Prop) (X1:Prop), (((c_iff X0) X1)->(((eq Prop) X0) X1))) of role axiom named ax3
% 0.50/0.69 A new axiom: (forall (X0:Prop) (X1:Prop), (((c_iff X0) X1)->(((eq Prop) X0) X1)))
% 0.50/0.69 FOF formula (forall (X0:fofType) (X1:fofType), (((c_Subq X0) X1)->(((c_Subq X1) X0)->(((eq fofType) X0) X1)))) of role axiom named ax4
% 0.50/0.69 A new axiom: (forall (X0:fofType) (X1:fofType), (((c_Subq X0) X1)->(((c_Subq X1) X0)->(((eq fofType) X0) X1))))
% 0.50/0.69 FOF formula (c_not ((ex fofType) (fun (X0:fofType)=> ((c_In X0) c_Empty)))) of role axiom named ax5
% 0.50/0.69 A new axiom: (c_not ((ex fofType) (fun (X0:fofType)=> ((c_In X0) c_Empty))))
% 0.50/0.69 FOF formula (forall (X0:fofType) (X1:fofType), ((c_iff ((c_In X1) (c_Union X0))) ((ex fofType) (fun (X2:fofType)=> ((c_and ((c_In X1) X2)) ((c_In X2) X0)))))) of role axiom named ax6
% 0.50/0.69 A new axiom: (forall (X0:fofType) (X1:fofType), ((c_iff ((c_In X1) (c_Union X0))) ((ex fofType) (fun (X2:fofType)=> ((c_and ((c_In X1) X2)) ((c_In X2) X0))))))
% 0.50/0.69 FOF formula (forall (X0:fofType) (X1:fofType), ((c_iff ((c_In X1) (c_Power X0))) ((c_Subq X1) X0))) of role axiom named ax7
% 0.50/0.69 A new axiom: (forall (X0:fofType) (X1:fofType), ((c_iff ((c_In X1) (c_Power X0))) ((c_Subq X1) X0)))
% 0.50/0.69 FOF formula (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), ((c_iff ((c_In X2) ((c_Repl X0) (fun (X3:fofType)=> (X1 X3))))) ((ex fofType) (fun (X3:fofType)=> ((c_and ((c_In X3) X0)) (((eq fofType) X2) (X1 X3))))))) of role axiom named ax8
% 0.50/0.69 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), ((c_iff ((c_In X2) ((c_Repl X0) (fun (X3:fofType)=> (X1 X3))))) ((ex fofType) (fun (X3:fofType)=> ((c_and ((c_In X3) X0)) (((eq fofType) X2) (X1 X3)))))))
% 0.50/0.69 FOF formula (forall (X0:(fofType->Prop)), ((forall (X1:fofType), ((X0 X1)->(forall (X2:fofType), (((c_In X2) X1)->(X0 X2)))))->((X0 c_Empty)->((forall (X1:fofType), ((X0 X1)->(X0 (c_Union X1))))->((forall (X1:fofType), ((X0 X1)->(X0 (c_Power X1))))->((forall (X1:fofType), ((X0 X1)->(forall (X2:(fofType->fofType)), ((forall (X3:fofType), (((c_In X3) X1)->(X0 (X2 X3))))->(X0 ((c_Repl X1) (fun (X3:fofType)=> (X2 X3))))))))->(forall (X1:fofType), (X0 X1)))))))) of role axiom named ax9
% 0.50/0.70 A new axiom: (forall (X0:(fofType->Prop)), ((forall (X1:fofType), ((X0 X1)->(forall (X2:fofType), (((c_In X2) X1)->(X0 X2)))))->((X0 c_Empty)->((forall (X1:fofType), ((X0 X1)->(X0 (c_Union X1))))->((forall (X1:fofType), ((X0 X1)->(X0 (c_Power X1))))->((forall (X1:fofType), ((X0 X1)->(forall (X2:(fofType->fofType)), ((forall (X3:fofType), (((c_In X3) X1)->(X0 (X2 X3))))->(X0 ((c_Repl X1) (fun (X3:fofType)=> (X2 X3))))))))->(forall (X1:fofType), (X0 X1))))))))
% 0.50/0.70 FOF formula (forall (X0:(fofType->Prop)), ((forall (X1:fofType), ((forall (X2:fofType), (((c_In X2) X1)->(X0 X2)))->(X0 X1)))->(forall (X1:fofType), (X0 X1)))) of role axiom named ax10
% 0.50/0.70 A new axiom: (forall (X0:(fofType->Prop)), ((forall (X1:fofType), ((forall (X2:fofType), (((c_In X2) X1)->(X0 X2)))->(X0 X1)))->(forall (X1:fofType), (X0 X1))))
% 0.50/0.70 FOF formula (((eq Prop) c_False) (forall (X0:Prop), X0)) of role axiom named ax11
% 0.50/0.70 A new axiom: (((eq Prop) c_False) (forall (X0:Prop), X0))
% 0.50/0.70 FOF formula (((eq Prop) c_True) (forall (X0:Prop), (X0->X0))) of role axiom named ax12
% 0.50/0.70 A new axiom: (((eq Prop) c_True) (forall (X0:Prop), (X0->X0)))
% 0.50/0.70 FOF formula (((eq (Prop->Prop)) c_not) (fun (X0:Prop)=> (X0->c_False))) of role axiom named ax13
% 0.50/0.70 A new axiom: (((eq (Prop->Prop)) c_not) (fun (X0:Prop)=> (X0->c_False)))
% 0.50/0.70 FOF formula (((eq (Prop->(Prop->Prop))) c_and) (fun (X0:Prop) (X1:Prop)=> (forall (X2:Prop), ((X0->(X1->X2))->X2)))) of role axiom named ax14
% 0.50/0.70 A new axiom: (((eq (Prop->(Prop->Prop))) c_and) (fun (X0:Prop) (X1:Prop)=> (forall (X2:Prop), ((X0->(X1->X2))->X2))))
% 0.50/0.70 FOF formula (((eq (Prop->(Prop->Prop))) c_or) (fun (X0:Prop) (X1:Prop)=> (forall (X2:Prop), ((X0->X2)->((X1->X2)->X2))))) of role axiom named ax15
% 0.50/0.70 A new axiom: (((eq (Prop->(Prop->Prop))) c_or) (fun (X0:Prop) (X1:Prop)=> (forall (X2:Prop), ((X0->X2)->((X1->X2)->X2)))))
% 0.50/0.70 FOF formula (((eq (Prop->(Prop->Prop))) c_iff) (fun (X0:Prop) (X1:Prop)=> ((c_and (X0->X1)) (X1->X0)))) of role axiom named ax16
% 0.50/0.70 A new axiom: (((eq (Prop->(Prop->Prop))) c_iff) (fun (X0:Prop) (X1:Prop)=> ((c_and (X0->X1)) (X1->X0))))
% 0.50/0.70 FOF formula (((eq (fofType->(fofType->Prop))) c_Subq) (fun (X0:fofType) (X1:fofType)=> (forall (X2:fofType), (((c_In X2) X0)->((c_In X2) X1))))) of role axiom named ax17
% 0.50/0.70 A new axiom: (((eq (fofType->(fofType->Prop))) c_Subq) (fun (X0:fofType) (X1:fofType)=> (forall (X2:fofType), (((c_In X2) X0)->((c_In X2) X1)))))
% 0.50/0.70 FOF formula (((eq (fofType->Prop)) c_TransSet) (fun (X0:fofType)=> (forall (X1:fofType), (((c_In X1) X0)->((c_Subq X1) X0))))) of role axiom named ax18
% 0.50/0.70 A new axiom: (((eq (fofType->Prop)) c_TransSet) (fun (X0:fofType)=> (forall (X1:fofType), (((c_In X1) X0)->((c_Subq X1) X0)))))
% 0.50/0.70 FOF formula (((eq (fofType->Prop)) c_atleast2) (fun (X0:fofType)=> ((ex fofType) (fun (X1:fofType)=> ((c_and ((c_In X1) X0)) (c_not ((c_Subq X0) (c_Power X1)))))))) of role axiom named ax19
% 0.50/0.70 A new axiom: (((eq (fofType->Prop)) c_atleast2) (fun (X0:fofType)=> ((ex fofType) (fun (X1:fofType)=> ((c_and ((c_In X1) X0)) (c_not ((c_Subq X0) (c_Power X1))))))))
% 0.50/0.70 FOF formula (((eq (fofType->Prop)) c_atleast3) (fun (X0:fofType)=> ((ex fofType) (fun (X1:fofType)=> ((c_and ((c_Subq X1) X0)) ((c_and (c_not ((c_Subq X0) X1))) (c_atleast2 X1))))))) of role axiom named ax20
% 0.50/0.70 A new axiom: (((eq (fofType->Prop)) c_atleast3) (fun (X0:fofType)=> ((ex fofType) (fun (X1:fofType)=> ((c_and ((c_Subq X1) X0)) ((c_and (c_not ((c_Subq X0) X1))) (c_atleast2 X1)))))))
% 0.50/0.70 FOF formula (((eq (fofType->Prop)) c_atleast4) (fun (X0:fofType)=> ((ex fofType) (fun (X1:fofType)=> ((c_and ((c_Subq X1) X0)) ((c_and (c_not ((c_Subq X0) X1))) (c_atleast3 X1))))))) of role axiom named ax21
% 0.50/0.70 A new axiom: (((eq (fofType->Prop)) c_atleast4) (fun (X0:fofType)=> ((ex fofType) (fun (X1:fofType)=> ((c_and ((c_Subq X1) X0)) ((c_and (c_not ((c_Subq X0) X1))) (c_atleast3 X1)))))))
% 0.50/0.70 FOF formula (((eq (fofType->Prop)) c_atleast5) (fun (X0:fofType)=> ((ex fofType) (fun (X1:fofType)=> ((c_and ((c_Subq X1) X0)) ((c_and (c_not ((c_Subq X0) X1))) (c_atleast4 X1))))))) of role axiom named ax22
% 0.50/0.71 A new axiom: (((eq (fofType->Prop)) c_atleast5) (fun (X0:fofType)=> ((ex fofType) (fun (X1:fofType)=> ((c_and ((c_Subq X1) X0)) ((c_and (c_not ((c_Subq X0) X1))) (c_atleast4 X1)))))))
% 0.50/0.71 FOF formula (((eq (fofType->Prop)) c_atleast6) (fun (X0:fofType)=> ((ex fofType) (fun (X1:fofType)=> ((c_and ((c_Subq X1) X0)) ((c_and (c_not ((c_Subq X0) X1))) (c_atleast5 X1))))))) of role axiom named ax23
% 0.50/0.71 A new axiom: (((eq (fofType->Prop)) c_atleast6) (fun (X0:fofType)=> ((ex fofType) (fun (X1:fofType)=> ((c_and ((c_Subq X1) X0)) ((c_and (c_not ((c_Subq X0) X1))) (c_atleast5 X1)))))))
% 0.50/0.71 FOF formula (((eq (fofType->Prop)) c_exactly2) (fun (X0:fofType)=> ((c_and (c_atleast2 X0)) (c_not (c_atleast3 X0))))) of role axiom named ax24
% 0.50/0.71 A new axiom: (((eq (fofType->Prop)) c_exactly2) (fun (X0:fofType)=> ((c_and (c_atleast2 X0)) (c_not (c_atleast3 X0)))))
% 0.50/0.71 FOF formula (((eq (fofType->Prop)) c_exactly3) (fun (X0:fofType)=> ((c_and (c_atleast3 X0)) (c_not (c_atleast4 X0))))) of role axiom named ax25
% 0.50/0.71 A new axiom: (((eq (fofType->Prop)) c_exactly3) (fun (X0:fofType)=> ((c_and (c_atleast3 X0)) (c_not (c_atleast4 X0)))))
% 0.50/0.71 FOF formula (((eq (fofType->Prop)) c_exactly4) (fun (X0:fofType)=> ((c_and (c_atleast4 X0)) (c_not (c_atleast5 X0))))) of role axiom named ax26
% 0.50/0.71 A new axiom: (((eq (fofType->Prop)) c_exactly4) (fun (X0:fofType)=> ((c_and (c_atleast4 X0)) (c_not (c_atleast5 X0)))))
% 0.50/0.71 FOF formula (((eq (fofType->Prop)) c_exactly5) (fun (X0:fofType)=> ((c_and (c_atleast5 X0)) (c_not (c_atleast6 X0))))) of role axiom named ax27
% 0.50/0.71 A new axiom: (((eq (fofType->Prop)) c_exactly5) (fun (X0:fofType)=> ((c_and (c_atleast5 X0)) (c_not (c_atleast6 X0)))))
% 0.50/0.71 FOF formula (((eq ((fofType->Prop)->Prop)) c_exu_i) (fun (X0:(fofType->Prop))=> ((c_and ((ex fofType) (fun (X1:fofType)=> (X0 X1)))) (forall (X1:fofType) (X2:fofType), ((X0 X1)->((X0 X2)->(((eq fofType) X1) X2))))))) of role axiom named ax28
% 0.50/0.71 A new axiom: (((eq ((fofType->Prop)->Prop)) c_exu_i) (fun (X0:(fofType->Prop))=> ((c_and ((ex fofType) (fun (X1:fofType)=> (X0 X1)))) (forall (X1:fofType) (X2:fofType), ((X0 X1)->((X0 X2)->(((eq fofType) X1) X2)))))))
% 0.50/0.71 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) c_reflexive_i) (fun (X0:(fofType->(fofType->Prop)))=> (forall (X1:fofType), ((X0 X1) X1)))) of role axiom named ax29
% 0.50/0.71 A new axiom: (((eq ((fofType->(fofType->Prop))->Prop)) c_reflexive_i) (fun (X0:(fofType->(fofType->Prop)))=> (forall (X1:fofType), ((X0 X1) X1))))
% 0.50/0.71 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) c_irreflexive_i) (fun (X0:(fofType->(fofType->Prop)))=> (forall (X1:fofType), (c_not ((X0 X1) X1))))) of role axiom named ax30
% 0.50/0.71 A new axiom: (((eq ((fofType->(fofType->Prop))->Prop)) c_irreflexive_i) (fun (X0:(fofType->(fofType->Prop)))=> (forall (X1:fofType), (c_not ((X0 X1) X1)))))
% 0.50/0.71 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) c_symmetric_i) (fun (X0:(fofType->(fofType->Prop)))=> (forall (X1:fofType) (X2:fofType), (((X0 X1) X2)->((X0 X2) X1))))) of role axiom named ax31
% 0.50/0.71 A new axiom: (((eq ((fofType->(fofType->Prop))->Prop)) c_symmetric_i) (fun (X0:(fofType->(fofType->Prop)))=> (forall (X1:fofType) (X2:fofType), (((X0 X1) X2)->((X0 X2) X1)))))
% 0.50/0.71 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) c_antisymmetric_i) (fun (X0:(fofType->(fofType->Prop)))=> (forall (X1:fofType) (X2:fofType), (((X0 X1) X2)->(((X0 X2) X1)->(((eq fofType) X1) X2)))))) of role axiom named ax32
% 0.50/0.71 A new axiom: (((eq ((fofType->(fofType->Prop))->Prop)) c_antisymmetric_i) (fun (X0:(fofType->(fofType->Prop)))=> (forall (X1:fofType) (X2:fofType), (((X0 X1) X2)->(((X0 X2) X1)->(((eq fofType) X1) X2))))))
% 0.50/0.71 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) c_transitive_i) (fun (X0:(fofType->(fofType->Prop)))=> (forall (X1:fofType) (X2:fofType) (X3:fofType), (((X0 X1) X2)->(((X0 X2) X3)->((X0 X1) X3)))))) of role axiom named ax33
% 0.50/0.71 A new axiom: (((eq ((fofType->(fofType->Prop))->Prop)) c_transitive_i) (fun (X0:(fofType->(fofType->Prop)))=> (forall (X1:fofType) (X2:fofType) (X3:fofType), (((X0 X1) X2)->(((X0 X2) X3)->((X0 X1) X3))))))
% 0.57/0.73 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) c_eqreln_i) (fun (X0:(fofType->(fofType->Prop)))=> ((c_and ((c_and (c_reflexive_i X0)) (c_symmetric_i X0))) (c_transitive_i X0)))) of role axiom named ax34
% 0.57/0.73 A new axiom: (((eq ((fofType->(fofType->Prop))->Prop)) c_eqreln_i) (fun (X0:(fofType->(fofType->Prop)))=> ((c_and ((c_and (c_reflexive_i X0)) (c_symmetric_i X0))) (c_transitive_i X0))))
% 0.57/0.73 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) c_per_i) (fun (X0:(fofType->(fofType->Prop)))=> ((c_and (c_symmetric_i X0)) (c_transitive_i X0)))) of role axiom named ax35
% 0.57/0.73 A new axiom: (((eq ((fofType->(fofType->Prop))->Prop)) c_per_i) (fun (X0:(fofType->(fofType->Prop)))=> ((c_and (c_symmetric_i X0)) (c_transitive_i X0))))
% 0.57/0.73 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) c_linear_i) (fun (X0:(fofType->(fofType->Prop)))=> (forall (X1:fofType) (X2:fofType), ((c_or ((X0 X1) X2)) ((X0 X2) X1))))) of role axiom named ax36
% 0.57/0.73 A new axiom: (((eq ((fofType->(fofType->Prop))->Prop)) c_linear_i) (fun (X0:(fofType->(fofType->Prop)))=> (forall (X1:fofType) (X2:fofType), ((c_or ((X0 X1) X2)) ((X0 X2) X1)))))
% 0.57/0.73 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) c_trichotomous_or_i) (fun (X0:(fofType->(fofType->Prop)))=> (forall (X1:fofType) (X2:fofType), ((c_or ((c_or ((X0 X1) X2)) (((eq fofType) X1) X2))) ((X0 X2) X1))))) of role axiom named ax37
% 0.57/0.73 A new axiom: (((eq ((fofType->(fofType->Prop))->Prop)) c_trichotomous_or_i) (fun (X0:(fofType->(fofType->Prop)))=> (forall (X1:fofType) (X2:fofType), ((c_or ((c_or ((X0 X1) X2)) (((eq fofType) X1) X2))) ((X0 X2) X1)))))
% 0.57/0.73 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) c_partialorder_i) (fun (X0:(fofType->(fofType->Prop)))=> ((c_and ((c_and (c_reflexive_i X0)) (c_antisymmetric_i X0))) (c_transitive_i X0)))) of role axiom named ax38
% 0.57/0.73 A new axiom: (((eq ((fofType->(fofType->Prop))->Prop)) c_partialorder_i) (fun (X0:(fofType->(fofType->Prop)))=> ((c_and ((c_and (c_reflexive_i X0)) (c_antisymmetric_i X0))) (c_transitive_i X0))))
% 0.57/0.73 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) c_totalorder_i) (fun (X0:(fofType->(fofType->Prop)))=> ((c_and (c_partialorder_i X0)) (c_linear_i X0)))) of role axiom named ax39
% 0.57/0.73 A new axiom: (((eq ((fofType->(fofType->Prop))->Prop)) c_totalorder_i) (fun (X0:(fofType->(fofType->Prop)))=> ((c_and (c_partialorder_i X0)) (c_linear_i X0))))
% 0.57/0.73 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) c_strictpartialorder_i) (fun (X0:(fofType->(fofType->Prop)))=> ((c_and (c_irreflexive_i X0)) (c_transitive_i X0)))) of role axiom named ax40
% 0.57/0.73 A new axiom: (((eq ((fofType->(fofType->Prop))->Prop)) c_strictpartialorder_i) (fun (X0:(fofType->(fofType->Prop)))=> ((c_and (c_irreflexive_i X0)) (c_transitive_i X0))))
% 0.57/0.73 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) c_stricttotalorder_i) (fun (X0:(fofType->(fofType->Prop)))=> ((c_and (c_strictpartialorder_i X0)) (c_trichotomous_or_i X0)))) of role axiom named ax41
% 0.57/0.73 A new axiom: (((eq ((fofType->(fofType->Prop))->Prop)) c_stricttotalorder_i) (fun (X0:(fofType->(fofType->Prop)))=> ((c_and (c_strictpartialorder_i X0)) (c_trichotomous_or_i X0))))
% 0.57/0.73 FOF formula (((eq (Prop->(fofType->(fofType->fofType)))) c_If_i) (fun (X0:Prop) (X1:fofType) (X2:fofType)=> (c_Eps_i (fun (X3:fofType)=> ((c_or ((c_and X0) (((eq fofType) X3) X1))) ((c_and (c_not X0)) (((eq fofType) X3) X2))))))) of role axiom named ax42
% 0.57/0.73 A new axiom: (((eq (Prop->(fofType->(fofType->fofType)))) c_If_i) (fun (X0:Prop) (X1:fofType) (X2:fofType)=> (c_Eps_i (fun (X3:fofType)=> ((c_or ((c_and X0) (((eq fofType) X3) X1))) ((c_and (c_not X0)) (((eq fofType) X3) X2)))))))
% 0.57/0.73 FOF formula (((eq (Prop->(Prop->Prop))) c_exactly1of2) (fun (X0:Prop) (X1:Prop)=> ((c_or ((c_and X0) (c_not X1))) ((c_and (c_not X0)) X1)))) of role axiom named ax43
% 0.57/0.73 A new axiom: (((eq (Prop->(Prop->Prop))) c_exactly1of2) (fun (X0:Prop) (X1:Prop)=> ((c_or ((c_and X0) (c_not X1))) ((c_and (c_not X0)) X1))))
% 0.57/0.73 FOF formula (((eq (Prop->(Prop->(Prop->Prop)))) c_exactly1of3) (fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((c_or ((c_and ((c_exactly1of2 X0) X1)) (c_not X2))) ((c_and ((c_and (c_not X0)) (c_not X1))) X2)))) of role axiom named ax44
% 0.57/0.74 A new axiom: (((eq (Prop->(Prop->(Prop->Prop)))) c_exactly1of3) (fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((c_or ((c_and ((c_exactly1of2 X0) X1)) (c_not X2))) ((c_and ((c_and (c_not X0)) (c_not X1))) X2))))
% 0.57/0.74 FOF formula (((eq (fofType->(fofType->Prop))) c_nIn) (fun (X0:fofType) (X1:fofType)=> (c_not ((c_In X0) X1)))) of role axiom named ax45
% 0.57/0.74 A new axiom: (((eq (fofType->(fofType->Prop))) c_nIn) (fun (X0:fofType) (X1:fofType)=> (c_not ((c_In X0) X1))))
% 0.57/0.74 FOF formula (((eq (fofType->(fofType->Prop))) c_nSubq) (fun (X0:fofType) (X1:fofType)=> (c_not ((c_Subq X0) X1)))) of role axiom named ax46
% 0.57/0.74 A new axiom: (((eq (fofType->(fofType->Prop))) c_nSubq) (fun (X0:fofType) (X1:fofType)=> (c_not ((c_Subq X0) X1))))
% 0.57/0.74 FOF formula (((eq (fofType->(fofType->fofType))) c_UPair) (fun (X0:fofType) (X1:fofType)=> ((c_Repl (c_Power (c_Power c_Empty))) (fun (X2:fofType)=> (((c_If_i ((c_In c_Empty) X2)) X0) X1))))) of role axiom named ax47
% 0.57/0.74 A new axiom: (((eq (fofType->(fofType->fofType))) c_UPair) (fun (X0:fofType) (X1:fofType)=> ((c_Repl (c_Power (c_Power c_Empty))) (fun (X2:fofType)=> (((c_If_i ((c_In c_Empty) X2)) X0) X1)))))
% 0.57/0.74 FOF formula (((eq (fofType->fofType)) c_Sing) (fun (X0:fofType)=> ((c_UPair X0) X0))) of role axiom named ax48
% 0.57/0.74 A new axiom: (((eq (fofType->fofType)) c_Sing) (fun (X0:fofType)=> ((c_UPair X0) X0)))
% 0.57/0.74 FOF formula (((eq (fofType->(fofType->fofType))) c_binunion) (fun (X0:fofType) (X1:fofType)=> (c_Union ((c_UPair X0) X1)))) of role axiom named ax49
% 0.57/0.74 A new axiom: (((eq (fofType->(fofType->fofType))) c_binunion) (fun (X0:fofType) (X1:fofType)=> (c_Union ((c_UPair X0) X1))))
% 0.57/0.74 FOF formula (((eq (fofType->(fofType->fofType))) c_SetAdjoin) (fun (X0:fofType) (X1:fofType)=> ((c_binunion X0) (c_Sing X1)))) of role axiom named ax50
% 0.57/0.74 A new axiom: (((eq (fofType->(fofType->fofType))) c_SetAdjoin) (fun (X0:fofType) (X1:fofType)=> ((c_binunion X0) (c_Sing X1))))
% 0.57/0.74 FOF formula (((eq (fofType->((fofType->fofType)->fofType))) c_famunion) (fun (X0:fofType) (X1:(fofType->fofType))=> (c_Union ((c_Repl X0) (fun (X2:fofType)=> (X1 X2)))))) of role axiom named ax51
% 0.57/0.74 A new axiom: (((eq (fofType->((fofType->fofType)->fofType))) c_famunion) (fun (X0:fofType) (X1:(fofType->fofType))=> (c_Union ((c_Repl X0) (fun (X2:fofType)=> (X1 X2))))))
% 0.57/0.74 FOF formula (((eq (fofType->((fofType->Prop)->fofType))) c_Sep) (fun (X0:fofType) (X1:(fofType->Prop))=> (((c_If_i ((ex fofType) (fun (X2:fofType)=> ((c_and ((c_In X2) X0)) (X1 X2))))) ((c_Repl X0) (fun (X2:fofType)=> ((fun (X3:fofType)=> (((c_If_i (X1 X3)) X3) (c_Eps_i (fun (X4:fofType)=> ((c_and ((c_In X4) X0)) (X1 X4)))))) X2)))) c_Empty))) of role axiom named ax52
% 0.57/0.74 A new axiom: (((eq (fofType->((fofType->Prop)->fofType))) c_Sep) (fun (X0:fofType) (X1:(fofType->Prop))=> (((c_If_i ((ex fofType) (fun (X2:fofType)=> ((c_and ((c_In X2) X0)) (X1 X2))))) ((c_Repl X0) (fun (X2:fofType)=> ((fun (X3:fofType)=> (((c_If_i (X1 X3)) X3) (c_Eps_i (fun (X4:fofType)=> ((c_and ((c_In X4) X0)) (X1 X4)))))) X2)))) c_Empty)))
% 0.57/0.74 FOF formula (((eq (fofType->((fofType->Prop)->((fofType->fofType)->fofType)))) c_ReplSep) (fun (X0:fofType) (X1:(fofType->Prop)) (X2:(fofType->fofType))=> ((c_Repl ((c_Sep X0) (fun (X3:fofType)=> (X1 X3)))) (fun (X3:fofType)=> (X2 X3))))) of role axiom named ax53
% 0.57/0.74 A new axiom: (((eq (fofType->((fofType->Prop)->((fofType->fofType)->fofType)))) c_ReplSep) (fun (X0:fofType) (X1:(fofType->Prop)) (X2:(fofType->fofType))=> ((c_Repl ((c_Sep X0) (fun (X3:fofType)=> (X1 X3)))) (fun (X3:fofType)=> (X2 X3)))))
% 0.57/0.74 FOF formula (((eq (fofType->(fofType->fofType))) c_binintersect) (fun (X0:fofType) (X1:fofType)=> ((c_Sep X0) (fun (X2:fofType)=> ((c_In X2) X1))))) of role axiom named ax54
% 0.57/0.74 A new axiom: (((eq (fofType->(fofType->fofType))) c_binintersect) (fun (X0:fofType) (X1:fofType)=> ((c_Sep X0) (fun (X2:fofType)=> ((c_In X2) X1)))))
% 0.57/0.74 FOF formula (((eq (fofType->(fofType->fofType))) c_setminus) (fun (X0:fofType) (X1:fofType)=> ((c_Sep X0) (fun (X2:fofType)=> ((c_nIn X2) X1))))) of role axiom named ax55
% 0.57/0.74 A new axiom: (((eq (fofType->(fofType->fofType))) c_setminus) (fun (X0:fofType) (X1:fofType)=> ((c_Sep X0) (fun (X2:fofType)=> ((c_nIn X2) X1)))))
% 0.57/0.76 FOF formula (((eq (fofType->(fofType->((fofType->fofType)->Prop)))) c_inj) (fun (X0:fofType) (X1:fofType) (X2:(fofType->fofType))=> ((c_and (forall (X3:fofType), (((c_In X3) X0)->((c_In (X2 X3)) X1)))) (forall (X3:fofType), (((c_In X3) X0)->(forall (X4:fofType), (((c_In X4) X0)->((((eq fofType) (X2 X3)) (X2 X4))->(((eq fofType) X3) X4))))))))) of role axiom named ax56
% 0.57/0.76 A new axiom: (((eq (fofType->(fofType->((fofType->fofType)->Prop)))) c_inj) (fun (X0:fofType) (X1:fofType) (X2:(fofType->fofType))=> ((c_and (forall (X3:fofType), (((c_In X3) X0)->((c_In (X2 X3)) X1)))) (forall (X3:fofType), (((c_In X3) X0)->(forall (X4:fofType), (((c_In X4) X0)->((((eq fofType) (X2 X3)) (X2 X4))->(((eq fofType) X3) X4)))))))))
% 0.57/0.76 FOF formula (((eq (fofType->(fofType->((fofType->fofType)->Prop)))) c_bij) (fun (X0:fofType) (X1:fofType) (X2:(fofType->fofType))=> ((c_and (((c_inj X0) X1) X2)) (forall (X3:fofType), (((c_In X3) X1)->((ex fofType) (fun (X4:fofType)=> ((c_and ((c_In X4) X0)) (((eq fofType) (X2 X4)) X3))))))))) of role axiom named ax57
% 0.57/0.76 A new axiom: (((eq (fofType->(fofType->((fofType->fofType)->Prop)))) c_bij) (fun (X0:fofType) (X1:fofType) (X2:(fofType->fofType))=> ((c_and (((c_inj X0) X1) X2)) (forall (X3:fofType), (((c_In X3) X1)->((ex fofType) (fun (X4:fofType)=> ((c_and ((c_In X4) X0)) (((eq fofType) (X2 X4)) X3)))))))))
% 0.57/0.76 FOF formula (((eq (fofType->(fofType->Prop))) c_atleastp) (fun (X0:fofType) (X1:fofType)=> ((ex (fofType->fofType)) (fun (X2:(fofType->fofType))=> (((c_inj X0) X1) X2))))) of role axiom named ax58
% 0.57/0.76 A new axiom: (((eq (fofType->(fofType->Prop))) c_atleastp) (fun (X0:fofType) (X1:fofType)=> ((ex (fofType->fofType)) (fun (X2:(fofType->fofType))=> (((c_inj X0) X1) X2)))))
% 0.57/0.76 FOF formula (((eq (fofType->(fofType->Prop))) c_equip) (fun (X0:fofType) (X1:fofType)=> ((ex (fofType->fofType)) (fun (X2:(fofType->fofType))=> (((c_bij X0) X1) X2))))) of role axiom named ax59
% 0.57/0.76 A new axiom: (((eq (fofType->(fofType->Prop))) c_equip) (fun (X0:fofType) (X1:fofType)=> ((ex (fofType->fofType)) (fun (X2:(fofType->fofType))=> (((c_bij X0) X1) X2)))))
% 0.57/0.76 FOF formula (((eq ((fofType->((fofType->fofType)->fofType))->(fofType->(fofType->Prop)))) c_In_rec_poly_G_i) (fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType) (X2:fofType)=> (forall (X3:(fofType->(fofType->Prop))), ((forall (X4:fofType) (X5:(fofType->fofType)), ((forall (X6:fofType), (((c_In X6) X4)->((X3 X6) (X5 X6))))->((X3 X4) ((X0 X4) X5))))->((X3 X1) X2))))) of role axiom named ax60
% 0.57/0.76 A new axiom: (((eq ((fofType->((fofType->fofType)->fofType))->(fofType->(fofType->Prop)))) c_In_rec_poly_G_i) (fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType) (X2:fofType)=> (forall (X3:(fofType->(fofType->Prop))), ((forall (X4:fofType) (X5:(fofType->fofType)), ((forall (X6:fofType), (((c_In X6) X4)->((X3 X6) (X5 X6))))->((X3 X4) ((X0 X4) X5))))->((X3 X1) X2)))))
% 0.57/0.76 FOF formula (((eq ((fofType->((fofType->fofType)->fofType))->(fofType->fofType))) c_In_rec_poly_i) (fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType)=> (c_Eps_i (fun (X2:fofType)=> (((c_In_rec_poly_G_i X0) X1) X2))))) of role axiom named ax61
% 0.57/0.76 A new axiom: (((eq ((fofType->((fofType->fofType)->fofType))->(fofType->fofType))) c_In_rec_poly_i) (fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType)=> (c_Eps_i (fun (X2:fofType)=> (((c_In_rec_poly_G_i X0) X1) X2)))))
% 0.57/0.76 FOF formula (((eq (fofType->fofType)) c_ordsucc) (fun (X0:fofType)=> ((c_binunion X0) (c_Sing X0)))) of role axiom named ax62
% 0.57/0.76 A new axiom: (((eq (fofType->fofType)) c_ordsucc) (fun (X0:fofType)=> ((c_binunion X0) (c_Sing X0))))
% 0.57/0.76 FOF formula (((eq (fofType->Prop)) c_nat_p) (fun (X0:fofType)=> (forall (X1:(fofType->Prop)), ((X1 c_Empty)->((forall (X2:fofType), ((X1 X2)->(X1 (c_ordsucc X2))))->(X1 X0)))))) of role axiom named ax63
% 0.57/0.76 A new axiom: (((eq (fofType->Prop)) c_nat_p) (fun (X0:fofType)=> (forall (X1:(fofType->Prop)), ((X1 c_Empty)->((forall (X2:fofType), ((X1 X2)->(X1 (c_ordsucc X2))))->(X1 X0))))))
% 0.57/0.76 FOF formula (((eq (fofType->((fofType->(fofType->fofType))->(fofType->fofType)))) c_nat_primrec) (fun (X0:fofType) (X1:(fofType->(fofType->fofType)))=> (c_In_rec_poly_i (fun (X2:fofType) (X3:(fofType->fofType))=> (((c_If_i ((c_In (c_Union X2)) X2)) ((X1 (c_Union X2)) (X3 (c_Union X2)))) X0))))) of role axiom named ax64
% 0.61/0.77 A new axiom: (((eq (fofType->((fofType->(fofType->fofType))->(fofType->fofType)))) c_nat_primrec) (fun (X0:fofType) (X1:(fofType->(fofType->fofType)))=> (c_In_rec_poly_i (fun (X2:fofType) (X3:(fofType->fofType))=> (((c_If_i ((c_In (c_Union X2)) X2)) ((X1 (c_Union X2)) (X3 (c_Union X2)))) X0)))))
% 0.61/0.77 FOF formula (((eq (fofType->(fofType->fofType))) c_add_nat) (fun (X0:fofType) (X1:fofType)=> (((c_nat_primrec X0) (fun (X2:fofType) (X3:fofType)=> (c_ordsucc X3))) X1))) of role axiom named ax65
% 0.61/0.77 A new axiom: (((eq (fofType->(fofType->fofType))) c_add_nat) (fun (X0:fofType) (X1:fofType)=> (((c_nat_primrec X0) (fun (X2:fofType) (X3:fofType)=> (c_ordsucc X3))) X1)))
% 0.61/0.77 FOF formula (((eq (fofType->(fofType->fofType))) c_mul_nat) (fun (X0:fofType) (X1:fofType)=> (((c_nat_primrec c_Empty) (fun (X2:fofType) (X3:fofType)=> ((c_add_nat X0) X3))) X1))) of role axiom named ax66
% 0.61/0.77 A new axiom: (((eq (fofType->(fofType->fofType))) c_mul_nat) (fun (X0:fofType) (X1:fofType)=> (((c_nat_primrec c_Empty) (fun (X2:fofType) (X3:fofType)=> ((c_add_nat X0) X3))) X1)))
% 0.61/0.77 FOF formula (((eq (fofType->Prop)) c_ordinal) (fun (X0:fofType)=> ((c_and (c_TransSet X0)) (forall (X1:fofType), (((c_In X1) X0)->(c_TransSet X1)))))) of role axiom named ax67
% 0.61/0.77 A new axiom: (((eq (fofType->Prop)) c_ordinal) (fun (X0:fofType)=> ((c_and (c_TransSet X0)) (forall (X1:fofType), (((c_In X1) X0)->(c_TransSet X1))))))
% 0.61/0.77 FOF formula (((eq (fofType->fofType)) c_V_) (c_In_rec_poly_i (fun (X0:fofType) (X1:(fofType->fofType))=> ((c_famunion X0) (fun (X2:fofType)=> (c_Power (X1 X2))))))) of role axiom named ax68
% 0.61/0.77 A new axiom: (((eq (fofType->fofType)) c_V_) (c_In_rec_poly_i (fun (X0:fofType) (X1:(fofType->fofType))=> ((c_famunion X0) (fun (X2:fofType)=> (c_Power (X1 X2)))))))
% 0.61/0.77 FOF formula (((eq (fofType->fofType)) c_Inj1) (c_In_rec_poly_i (fun (X0:fofType) (X1:(fofType->fofType))=> ((c_binunion (c_Sing c_Empty)) ((c_Repl X0) (fun (X2:fofType)=> (X1 X2))))))) of role axiom named ax69
% 0.61/0.77 A new axiom: (((eq (fofType->fofType)) c_Inj1) (c_In_rec_poly_i (fun (X0:fofType) (X1:(fofType->fofType))=> ((c_binunion (c_Sing c_Empty)) ((c_Repl X0) (fun (X2:fofType)=> (X1 X2)))))))
% 0.61/0.77 FOF formula (((eq (fofType->fofType)) c_Inj0) (fun (X0:fofType)=> ((c_Repl X0) (fun (X1:fofType)=> (c_Inj1 X1))))) of role axiom named ax70
% 0.61/0.77 A new axiom: (((eq (fofType->fofType)) c_Inj0) (fun (X0:fofType)=> ((c_Repl X0) (fun (X1:fofType)=> (c_Inj1 X1)))))
% 0.61/0.77 FOF formula (((eq (fofType->fofType)) c_Unj) (c_In_rec_poly_i (fun (X0:fofType) (X1:(fofType->fofType))=> ((c_Repl ((c_setminus X0) (c_Sing c_Empty))) (fun (X2:fofType)=> (X1 X2)))))) of role axiom named ax71
% 0.61/0.77 A new axiom: (((eq (fofType->fofType)) c_Unj) (c_In_rec_poly_i (fun (X0:fofType) (X1:(fofType->fofType))=> ((c_Repl ((c_setminus X0) (c_Sing c_Empty))) (fun (X2:fofType)=> (X1 X2))))))
% 0.61/0.77 FOF formula (((eq (fofType->(fofType->((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))))) c_combine_funcs) (fun (X0:fofType) (X1:fofType) (X2:(fofType->fofType)) (X3:(fofType->fofType)) (X4:fofType)=> (((c_If_i (((eq fofType) X4) (c_Inj0 (c_Unj X4)))) (X2 (c_Unj X4))) (X3 (c_Unj X4))))) of role axiom named ax72
% 0.61/0.77 A new axiom: (((eq (fofType->(fofType->((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))))) c_combine_funcs) (fun (X0:fofType) (X1:fofType) (X2:(fofType->fofType)) (X3:(fofType->fofType)) (X4:fofType)=> (((c_If_i (((eq fofType) X4) (c_Inj0 (c_Unj X4)))) (X2 (c_Unj X4))) (X3 (c_Unj X4)))))
% 0.61/0.77 FOF formula (((eq (fofType->(fofType->fofType))) c_setsum) (fun (X0:fofType) (X1:fofType)=> ((c_binunion ((c_Repl X0) (fun (X2:fofType)=> (c_Inj0 X2)))) ((c_Repl X1) (fun (X2:fofType)=> (c_Inj1 X2)))))) of role axiom named ax73
% 0.61/0.77 A new axiom: (((eq (fofType->(fofType->fofType))) c_setsum) (fun (X0:fofType) (X1:fofType)=> ((c_binunion ((c_Repl X0) (fun (X2:fofType)=> (c_Inj0 X2)))) ((c_Repl X1) (fun (X2:fofType)=> (c_Inj1 X2))))))
% 0.61/0.77 FOF formula (((eq (fofType->fofType)) c_proj0) (fun (X0:fofType)=> (((c_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (c_Inj0 X2)) X1))))) (fun (X1:fofType)=> (c_Unj X1))))) of role axiom named ax74
% 0.61/0.78 A new axiom: (((eq (fofType->fofType)) c_proj0) (fun (X0:fofType)=> (((c_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (c_Inj0 X2)) X1))))) (fun (X1:fofType)=> (c_Unj X1)))))
% 0.61/0.78 FOF formula (((eq (fofType->fofType)) c_proj1) (fun (X0:fofType)=> (((c_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (c_Inj1 X2)) X1))))) (fun (X1:fofType)=> (c_Unj X1))))) of role axiom named ax75
% 0.61/0.78 A new axiom: (((eq (fofType->fofType)) c_proj1) (fun (X0:fofType)=> (((c_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (c_Inj1 X2)) X1))))) (fun (X1:fofType)=> (c_Unj X1)))))
% 0.61/0.78 FOF formula (((eq (fofType->(fofType->fofType))) c_binrep) (fun (X0:fofType) (X1:fofType)=> ((c_setsum X0) (c_Power X1)))) of role axiom named ax76
% 0.61/0.78 A new axiom: (((eq (fofType->(fofType->fofType))) c_binrep) (fun (X0:fofType) (X1:fofType)=> ((c_setsum X0) (c_Power X1))))
% 0.61/0.78 FOF formula (((eq (fofType->((fofType->fofType)->fofType))) c_lam) (fun (X0:fofType) (X1:(fofType->fofType))=> ((c_famunion X0) (fun (X2:fofType)=> ((c_Repl (X1 X2)) (fun (X3:fofType)=> ((c_setsum X2) X3))))))) of role axiom named ax77
% 0.61/0.78 A new axiom: (((eq (fofType->((fofType->fofType)->fofType))) c_lam) (fun (X0:fofType) (X1:(fofType->fofType))=> ((c_famunion X0) (fun (X2:fofType)=> ((c_Repl (X1 X2)) (fun (X3:fofType)=> ((c_setsum X2) X3)))))))
% 0.61/0.78 FOF formula (((eq (fofType->(fofType->fofType))) c_setprod) (fun (X0:fofType) (X1:fofType)=> ((c_lam X0) (fun (X2:fofType)=> X1)))) of role axiom named ax78
% 0.61/0.78 A new axiom: (((eq (fofType->(fofType->fofType))) c_setprod) (fun (X0:fofType) (X1:fofType)=> ((c_lam X0) (fun (X2:fofType)=> X1))))
% 0.61/0.78 FOF formula (((eq (fofType->(fofType->fofType))) c_ap) (fun (X0:fofType) (X1:fofType)=> (((c_ReplSep X0) (fun (X2:fofType)=> ((ex fofType) (fun (X3:fofType)=> (((eq fofType) X2) ((c_setsum X1) X3)))))) (fun (X2:fofType)=> (c_proj1 X2))))) of role axiom named ax79
% 0.61/0.78 A new axiom: (((eq (fofType->(fofType->fofType))) c_ap) (fun (X0:fofType) (X1:fofType)=> (((c_ReplSep X0) (fun (X2:fofType)=> ((ex fofType) (fun (X3:fofType)=> (((eq fofType) X2) ((c_setsum X1) X3)))))) (fun (X2:fofType)=> (c_proj1 X2)))))
% 0.61/0.78 FOF formula (((eq (fofType->Prop)) c_setsum_p) (fun (X0:fofType)=> (((eq fofType) ((c_setsum ((c_ap X0) c_Empty)) ((c_ap X0) (c_ordsucc c_Empty)))) X0))) of role axiom named ax80
% 0.61/0.78 A new axiom: (((eq (fofType->Prop)) c_setsum_p) (fun (X0:fofType)=> (((eq fofType) ((c_setsum ((c_ap X0) c_Empty)) ((c_ap X0) (c_ordsucc c_Empty)))) X0)))
% 0.61/0.78 FOF formula (((eq (fofType->(fofType->Prop))) c_tuple_p) (fun (X0:fofType) (X1:fofType)=> (forall (X2:fofType), (((c_In X2) X1)->((ex fofType) (fun (X3:fofType)=> ((c_and ((c_In X3) X0)) ((ex fofType) (fun (X4:fofType)=> (((eq fofType) X2) ((c_setsum X3) X4))))))))))) of role axiom named ax81
% 0.61/0.78 A new axiom: (((eq (fofType->(fofType->Prop))) c_tuple_p) (fun (X0:fofType) (X1:fofType)=> (forall (X2:fofType), (((c_In X2) X1)->((ex fofType) (fun (X3:fofType)=> ((c_and ((c_In X3) X0)) ((ex fofType) (fun (X4:fofType)=> (((eq fofType) X2) ((c_setsum X3) X4)))))))))))
% 0.61/0.78 FOF formula (((eq (fofType->((fofType->fofType)->fofType))) c_Pi) (fun (X0:fofType) (X1:(fofType->fofType))=> ((c_Sep (c_Power ((c_lam X0) (fun (X2:fofType)=> (c_Union (X1 X2)))))) (fun (X2:fofType)=> (forall (X3:fofType), (((c_In X3) X0)->((c_In ((c_ap X2) X3)) (X1 X3)))))))) of role axiom named ax82
% 0.61/0.78 A new axiom: (((eq (fofType->((fofType->fofType)->fofType))) c_Pi) (fun (X0:fofType) (X1:(fofType->fofType))=> ((c_Sep (c_Power ((c_lam X0) (fun (X2:fofType)=> (c_Union (X1 X2)))))) (fun (X2:fofType)=> (forall (X3:fofType), (((c_In X3) X0)->((c_In ((c_ap X2) X3)) (X1 X3))))))))
% 0.61/0.78 FOF formula (((eq (fofType->(fofType->fofType))) c_setexp) (fun (X0:fofType) (X1:fofType)=> ((c_Pi X1) (fun (X2:fofType)=> X0)))) of role axiom named ax83
% 0.61/0.78 A new axiom: (((eq (fofType->(fofType->fofType))) c_setexp) (fun (X0:fofType) (X1:fofType)=> ((c_Pi X1) (fun (X2:fofType)=> X0))))
% 0.61/0.79 FOF formula (((eq (fofType->((fofType->fofType)->((fofType->(fofType->Prop))->fofType)))) c_Sep2) (fun (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->(fofType->Prop)))=> ((c_Sep ((c_lam X0) (fun (X3:fofType)=> (X1 X3)))) (fun (X3:fofType)=> ((X2 ((c_ap X3) c_Empty)) ((c_ap X3) (c_ordsucc c_Empty))))))) of role axiom named ax84
% 0.61/0.79 A new axiom: (((eq (fofType->((fofType->fofType)->((fofType->(fofType->Prop))->fofType)))) c_Sep2) (fun (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->(fofType->Prop)))=> ((c_Sep ((c_lam X0) (fun (X3:fofType)=> (X1 X3)))) (fun (X3:fofType)=> ((X2 ((c_ap X3) c_Empty)) ((c_ap X3) (c_ordsucc c_Empty)))))))
% 0.61/0.79 FOF formula (((eq (fofType->Prop)) c_set_of_pairs) (fun (X0:fofType)=> (forall (X1:fofType), (((c_In X1) X0)->((ex fofType) (fun (X2:fofType)=> ((ex fofType) (fun (X3:fofType)=> (((eq fofType) X1) ((c_lam (c_ordsucc (c_ordsucc c_Empty))) (fun (X4:fofType)=> (((c_If_i (((eq fofType) X4) c_Empty)) X2) X3)))))))))))) of role axiom named ax85
% 0.61/0.79 A new axiom: (((eq (fofType->Prop)) c_set_of_pairs) (fun (X0:fofType)=> (forall (X1:fofType), (((c_In X1) X0)->((ex fofType) (fun (X2:fofType)=> ((ex fofType) (fun (X3:fofType)=> (((eq fofType) X1) ((c_lam (c_ordsucc (c_ordsucc c_Empty))) (fun (X4:fofType)=> (((c_If_i (((eq fofType) X4) c_Empty)) X2) X3))))))))))))
% 0.61/0.79 FOF formula (((eq (fofType->((fofType->fofType)->((fofType->(fofType->fofType))->fofType)))) c_lam2) (fun (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->(fofType->fofType)))=> ((c_lam X0) (fun (X3:fofType)=> ((c_lam (X1 X3)) (fun (X4:fofType)=> ((X2 X3) X4))))))) of role axiom named ax86
% 0.61/0.79 A new axiom: (((eq (fofType->((fofType->fofType)->((fofType->(fofType->fofType))->fofType)))) c_lam2) (fun (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->(fofType->fofType)))=> ((c_lam X0) (fun (X3:fofType)=> ((c_lam (X1 X3)) (fun (X4:fofType)=> ((X2 X3) X4)))))))
% 0.61/0.79 FOF formula (((eq (fofType->((fofType->Prop)->((fofType->Prop)->Prop)))) c_PNoEq_) (fun (X0:fofType) (X1:(fofType->Prop)) (X2:(fofType->Prop))=> (forall (X3:fofType), (((c_In X3) X0)->((c_iff (X1 X3)) (X2 X3)))))) of role axiom named ax87
% 0.61/0.79 A new axiom: (((eq (fofType->((fofType->Prop)->((fofType->Prop)->Prop)))) c_PNoEq_) (fun (X0:fofType) (X1:(fofType->Prop)) (X2:(fofType->Prop))=> (forall (X3:fofType), (((c_In X3) X0)->((c_iff (X1 X3)) (X2 X3))))))
% 0.61/0.79 FOF formula (((eq (fofType->((fofType->Prop)->((fofType->Prop)->Prop)))) c_PNoLt_) (fun (X0:fofType) (X1:(fofType->Prop)) (X2:(fofType->Prop))=> ((ex fofType) (fun (X3:fofType)=> ((c_and ((c_In X3) X0)) ((c_and ((c_and (((c_PNoEq_ X3) X1) X2)) (c_not (X1 X3)))) (X2 X3))))))) of role axiom named ax88
% 0.61/0.79 A new axiom: (((eq (fofType->((fofType->Prop)->((fofType->Prop)->Prop)))) c_PNoLt_) (fun (X0:fofType) (X1:(fofType->Prop)) (X2:(fofType->Prop))=> ((ex fofType) (fun (X3:fofType)=> ((c_and ((c_In X3) X0)) ((c_and ((c_and (((c_PNoEq_ X3) X1) X2)) (c_not (X1 X3)))) (X2 X3)))))))
% 0.61/0.79 FOF formula (((eq (fofType->((fofType->Prop)->(fofType->((fofType->Prop)->Prop))))) c_PNoLt) (fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType) (X3:(fofType->Prop))=> ((c_or ((c_or (((c_PNoLt_ ((c_binintersect X0) X2)) X1) X3)) ((c_and ((c_and ((c_In X0) X2)) (((c_PNoEq_ X0) X1) X3))) (X3 X0)))) ((c_and ((c_and ((c_In X2) X0)) (((c_PNoEq_ X2) X1) X3))) (c_not (X1 X2)))))) of role axiom named ax89
% 0.61/0.79 A new axiom: (((eq (fofType->((fofType->Prop)->(fofType->((fofType->Prop)->Prop))))) c_PNoLt) (fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType) (X3:(fofType->Prop))=> ((c_or ((c_or (((c_PNoLt_ ((c_binintersect X0) X2)) X1) X3)) ((c_and ((c_and ((c_In X0) X2)) (((c_PNoEq_ X0) X1) X3))) (X3 X0)))) ((c_and ((c_and ((c_In X2) X0)) (((c_PNoEq_ X2) X1) X3))) (c_not (X1 X2))))))
% 0.61/0.79 FOF formula (((eq (fofType->((fofType->Prop)->(fofType->((fofType->Prop)->Prop))))) c_PNoLe) (fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType) (X3:(fofType->Prop))=> ((c_or ((((c_PNoLt X0) X1) X2) X3)) ((c_and (((eq fofType) X0) X2)) (((c_PNoEq_ X0) X1) X3))))) of role axiom named ax90
% 0.61/0.79 A new axiom: (((eq (fofType->((fofType->Prop)->(fofType->((fofType->Prop)->Prop))))) c_PNoLe) (fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType) (X3:(fofType->Prop))=> ((c_or ((((c_PNoLt X0) X1) X2) X3)) ((c_and (((eq fofType) X0) X2)) (((c_PNoEq_ X0) X1) X3)))))
% 0.61/0.81 FOF formula (((eq ((fofType->((fofType->Prop)->Prop))->(fofType->((fofType->Prop)->Prop)))) c_PNo_downc) (fun (X0:(fofType->((fofType->Prop)->Prop))) (X1:fofType) (X2:(fofType->Prop))=> ((ex fofType) (fun (X3:fofType)=> ((c_and (c_ordinal X3)) ((ex (fofType->Prop)) (fun (X4:(fofType->Prop))=> ((c_and ((X0 X3) X4)) ((((c_PNoLe X1) X2) X3) X4))))))))) of role axiom named ax91
% 0.61/0.81 A new axiom: (((eq ((fofType->((fofType->Prop)->Prop))->(fofType->((fofType->Prop)->Prop)))) c_PNo_downc) (fun (X0:(fofType->((fofType->Prop)->Prop))) (X1:fofType) (X2:(fofType->Prop))=> ((ex fofType) (fun (X3:fofType)=> ((c_and (c_ordinal X3)) ((ex (fofType->Prop)) (fun (X4:(fofType->Prop))=> ((c_and ((X0 X3) X4)) ((((c_PNoLe X1) X2) X3) X4)))))))))
% 0.61/0.81 FOF formula (((eq ((fofType->((fofType->Prop)->Prop))->(fofType->((fofType->Prop)->Prop)))) c_PNo_upc) (fun (X0:(fofType->((fofType->Prop)->Prop))) (X1:fofType) (X2:(fofType->Prop))=> ((ex fofType) (fun (X3:fofType)=> ((c_and (c_ordinal X3)) ((ex (fofType->Prop)) (fun (X4:(fofType->Prop))=> ((c_and ((X0 X3) X4)) ((((c_PNoLe X3) X4) X1) X2))))))))) of role axiom named ax92
% 0.61/0.81 A new axiom: (((eq ((fofType->((fofType->Prop)->Prop))->(fofType->((fofType->Prop)->Prop)))) c_PNo_upc) (fun (X0:(fofType->((fofType->Prop)->Prop))) (X1:fofType) (X2:(fofType->Prop))=> ((ex fofType) (fun (X3:fofType)=> ((c_and (c_ordinal X3)) ((ex (fofType->Prop)) (fun (X4:(fofType->Prop))=> ((c_and ((X0 X3) X4)) ((((c_PNoLe X3) X4) X1) X2)))))))))
% 0.61/0.81 FOF formula (((eq (fofType->fofType)) c_SNoElts_) (fun (X0:fofType)=> ((c_binunion X0) ((c_Repl X0) (fun (X1:fofType)=> ((fun (X2:fofType)=> ((c_SetAdjoin X2) (c_Sing (c_ordsucc c_Empty)))) X1)))))) of role axiom named ax93
% 0.61/0.81 A new axiom: (((eq (fofType->fofType)) c_SNoElts_) (fun (X0:fofType)=> ((c_binunion X0) ((c_Repl X0) (fun (X1:fofType)=> ((fun (X2:fofType)=> ((c_SetAdjoin X2) (c_Sing (c_ordsucc c_Empty)))) X1))))))
% 0.61/0.81 FOF formula (((eq (fofType->(fofType->Prop))) c_SNo_) (fun (X0:fofType) (X1:fofType)=> ((c_and ((c_Subq X1) (c_SNoElts_ X0))) (forall (X2:fofType), (((c_In X2) X0)->((c_exactly1of2 ((c_In ((fun (X3:fofType)=> ((c_SetAdjoin X3) (c_Sing (c_ordsucc c_Empty)))) X2)) X1)) ((c_In X2) X1))))))) of role axiom named ax94
% 0.61/0.81 A new axiom: (((eq (fofType->(fofType->Prop))) c_SNo_) (fun (X0:fofType) (X1:fofType)=> ((c_and ((c_Subq X1) (c_SNoElts_ X0))) (forall (X2:fofType), (((c_In X2) X0)->((c_exactly1of2 ((c_In ((fun (X3:fofType)=> ((c_SetAdjoin X3) (c_Sing (c_ordsucc c_Empty)))) X2)) X1)) ((c_In X2) X1)))))))
% 0.61/0.81 FOF formula (((eq (fofType->((fofType->Prop)->fofType))) c_PSNo) (fun (X0:fofType) (X1:(fofType->Prop))=> ((c_binunion ((c_Sep X0) (fun (X2:fofType)=> (X1 X2)))) (((c_ReplSep X0) (fun (X2:fofType)=> (c_not (X1 X2)))) (fun (X2:fofType)=> ((fun (X3:fofType)=> ((c_SetAdjoin X3) (c_Sing (c_ordsucc c_Empty)))) X2)))))) of role axiom named ax95
% 0.61/0.81 A new axiom: (((eq (fofType->((fofType->Prop)->fofType))) c_PSNo) (fun (X0:fofType) (X1:(fofType->Prop))=> ((c_binunion ((c_Sep X0) (fun (X2:fofType)=> (X1 X2)))) (((c_ReplSep X0) (fun (X2:fofType)=> (c_not (X1 X2)))) (fun (X2:fofType)=> ((fun (X3:fofType)=> ((c_SetAdjoin X3) (c_Sing (c_ordsucc c_Empty)))) X2))))))
% 0.61/0.81 FOF formula (((eq (fofType->Prop)) c_SNo) (fun (X0:fofType)=> ((ex fofType) (fun (X1:fofType)=> ((c_and (c_ordinal X1)) ((c_SNo_ X1) X0)))))) of role axiom named ax96
% 0.61/0.81 A new axiom: (((eq (fofType->Prop)) c_SNo) (fun (X0:fofType)=> ((ex fofType) (fun (X1:fofType)=> ((c_and (c_ordinal X1)) ((c_SNo_ X1) X0))))))
% 0.61/0.81 FOF formula (((eq (fofType->fofType)) c_SNoLev) (fun (X0:fofType)=> (c_Eps_i (fun (X1:fofType)=> ((c_and (c_ordinal X1)) ((c_SNo_ X1) X0)))))) of role axiom named ax97
% 0.61/0.81 A new axiom: (((eq (fofType->fofType)) c_SNoLev) (fun (X0:fofType)=> (c_Eps_i (fun (X1:fofType)=> ((c_and (c_ordinal X1)) ((c_SNo_ X1) X0))))))
% 0.61/0.81 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) c_SNoEq_) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((c_PNoEq_ X0) (fun (X3:fofType)=> ((c_In X3) X1))) (fun (X3:fofType)=> ((c_In X3) X2))))) of role axiom named ax98
% 0.61/0.83 A new axiom: (((eq (fofType->(fofType->(fofType->Prop)))) c_SNoEq_) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((c_PNoEq_ X0) (fun (X3:fofType)=> ((c_In X3) X1))) (fun (X3:fofType)=> ((c_In X3) X2)))))
% 0.61/0.83 FOF formula (((eq (fofType->(fofType->Prop))) c_SNoLt) (fun (X0:fofType) (X1:fofType)=> ((((c_PNoLt (c_SNoLev X0)) (fun (X2:fofType)=> ((c_In X2) X0))) (c_SNoLev X1)) (fun (X2:fofType)=> ((c_In X2) X1))))) of role axiom named ax99
% 0.61/0.83 A new axiom: (((eq (fofType->(fofType->Prop))) c_SNoLt) (fun (X0:fofType) (X1:fofType)=> ((((c_PNoLt (c_SNoLev X0)) (fun (X2:fofType)=> ((c_In X2) X0))) (c_SNoLev X1)) (fun (X2:fofType)=> ((c_In X2) X1)))))
% 0.61/0.83 FOF formula (((eq (fofType->(fofType->Prop))) c_SNoLe) (fun (X0:fofType) (X1:fofType)=> ((((c_PNoLe (c_SNoLev X0)) (fun (X2:fofType)=> ((c_In X2) X0))) (c_SNoLev X1)) (fun (X2:fofType)=> ((c_In X2) X1))))) of role axiom named ax100
% 0.61/0.83 A new axiom: (((eq (fofType->(fofType->Prop))) c_SNoLe) (fun (X0:fofType) (X1:fofType)=> ((((c_PNoLe (c_SNoLev X0)) (fun (X2:fofType)=> ((c_In X2) X0))) (c_SNoLev X1)) (fun (X2:fofType)=> ((c_In X2) X1)))))
% 0.61/0.83 FOF formula (((eq (fofType->((fofType->(fofType->fofType))->Prop))) c_binop_on) (fun (X0:fofType) (X1:(fofType->(fofType->fofType)))=> (forall (X2:fofType), (((c_In X2) X0)->(forall (X3:fofType), (((c_In X3) X0)->((c_In ((X1 X2) X3)) X0))))))) of role axiom named ax101
% 0.61/0.83 A new axiom: (((eq (fofType->((fofType->(fofType->fofType))->Prop))) c_binop_on) (fun (X0:fofType) (X1:(fofType->(fofType->fofType)))=> (forall (X2:fofType), (((c_In X2) X0)->(forall (X3:fofType), (((c_In X3) X0)->((c_In ((X1 X2) X3)) X0)))))))
% 0.61/0.83 FOF formula (((eq (fofType->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->(fofType->Prop)))))) c_Loop) (fun (X0:fofType) (X1:(fofType->(fofType->fofType))) (X2:(fofType->(fofType->fofType))) (X3:(fofType->(fofType->fofType))) (X4:fofType)=> ((c_and ((c_and ((c_and ((c_and ((c_binop_on X0) X1)) ((c_binop_on X0) X2))) ((c_binop_on X0) X3))) (forall (X5:fofType), (((c_In X5) X0)->((c_and (((eq fofType) ((X1 X4) X5)) X5)) (((eq fofType) ((X1 X5) X4)) X5)))))) (forall (X5:fofType), (((c_In X5) X0)->(forall (X6:fofType), (((c_In X6) X0)->((c_and ((c_and ((c_and (((eq fofType) ((X2 X5) ((X1 X5) X6))) X6)) (((eq fofType) ((X1 X5) ((X2 X5) X6))) X6))) (((eq fofType) ((X3 ((X1 X5) X6)) X6)) X5))) (((eq fofType) ((X1 ((X3 X5) X6)) X6)) X5))))))))) of role axiom named ax102
% 0.61/0.83 A new axiom: (((eq (fofType->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->(fofType->Prop)))))) c_Loop) (fun (X0:fofType) (X1:(fofType->(fofType->fofType))) (X2:(fofType->(fofType->fofType))) (X3:(fofType->(fofType->fofType))) (X4:fofType)=> ((c_and ((c_and ((c_and ((c_and ((c_binop_on X0) X1)) ((c_binop_on X0) X2))) ((c_binop_on X0) X3))) (forall (X5:fofType), (((c_In X5) X0)->((c_and (((eq fofType) ((X1 X4) X5)) X5)) (((eq fofType) ((X1 X5) X4)) X5)))))) (forall (X5:fofType), (((c_In X5) X0)->(forall (X6:fofType), (((c_In X6) X0)->((c_and ((c_and ((c_and (((eq fofType) ((X2 X5) ((X1 X5) X6))) X6)) (((eq fofType) ((X1 X5) ((X2 X5) X6))) X6))) (((eq fofType) ((X3 ((X1 X5) X6)) X6)) X5))) (((eq fofType) ((X1 ((X3 X5) X6)) X6)) X5)))))))))
% 0.61/0.83 FOF formula (((eq (fofType->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->(fofType->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->Prop))))))))))))))) c_Loop_with_defs) (fun (X0:fofType) (X1:(fofType->(fofType->fofType))) (X2:(fofType->(fofType->fofType))) (X3:(fofType->(fofType->fofType))) (X4:fofType) (X5:(fofType->(fofType->fofType))) (X6:(fofType->(fofType->(fofType->fofType)))) (X7:(fofType->(fofType->fofType))) (X8:(fofType->(fofType->(fofType->fofType)))) (X9:(fofType->(fofType->(fofType->fofType)))) (X10:(fofType->(fofType->fofType))) (X11:(fofType->(fofType->fofType))) (X12:(fofType->(fofType->fofType))) (X13:(fofType->(fofType->fofType)))=> ((c_and ((c_and ((c_and ((c_and (((((c_Loop X0) X1) X2) X3) X4)) (forall (X14:fofType), (((c_In X14) X0)->(forall (X15:fofType), (((c_In X15) X0)->(((eq fofType) ((X5 X14) X15)) ((X2 ((X1 X15) X14)) ((X1 X14) X15))))))))) (forall (X14:fofType), (((c_In X14) X0)->(forall (X15:fofType), (((c_In X15) X0)->(forall (X16:fofType), (((c_In X16) X0)->(((eq fofType) (((X6 X14) X15) X16)) ((X2 ((X1 X14) ((X1 X15) X16))) ((X1 ((X1 X14) X15)) X16))))))))))) (forall (X14:fofType), (((c_In X14) X0)->(forall (X15:fofType), (((c_In X15) X0)->((c_and ((c_and ((c_and ((c_and (((eq fofType) ((X7 X14) X15)) ((X2 X14) ((X1 X15) X14)))) (((eq fofType) ((X10 X14) X15)) ((X1 X14) ((X1 X15) ((X2 X14) X4)))))) (((eq fofType) ((X11 X14) X15)) ((X1 ((X1 ((X3 X4) X14)) X15)) X14)))) (((eq fofType) ((X12 X14) X15)) ((X1 ((X2 X14) X15)) ((X2 ((X2 X14) X4)) X4))))) (((eq fofType) ((X13 X14) X15)) ((X1 ((X3 X4) ((X3 X4) X14))) ((X3 X15) X14)))))))))) (forall (X14:fofType), (((c_In X14) X0)->(forall (X15:fofType), (((c_In X15) X0)->(forall (X16:fofType), (((c_In X16) X0)->((c_and (((eq fofType) (((X8 X14) X15) X16)) ((X2 ((X1 X15) X14)) ((X1 X15) ((X1 X14) X16))))) (((eq fofType) (((X9 X14) X15) X16)) ((X3 ((X1 ((X1 X16) X14)) X15)) ((X1 X14) X15))))))))))))) of role axiom named ax103
% 0.61/0.83 A new axiom: (((eq (fofType->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->(fofType->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->Prop))))))))))))))) c_Loop_with_defs) (fun (X0:fofType) (X1:(fofType->(fofType->fofType))) (X2:(fofType->(fofType->fofType))) (X3:(fofType->(fofType->fofType))) (X4:fofType) (X5:(fofType->(fofType->fofType))) (X6:(fofType->(fofType->(fofType->fofType)))) (X7:(fofType->(fofType->fofType))) (X8:(fofType->(fofType->(fofType->fofType)))) (X9:(fofType->(fofType->(fofType->fofType)))) (X10:(fofType->(fofType->fofType))) (X11:(fofType->(fofType->fofType))) (X12:(fofType->(fofType->fofType))) (X13:(fofType->(fofType->fofType)))=> ((c_and ((c_and ((c_and ((c_and (((((c_Loop X0) X1) X2) X3) X4)) (forall (X14:fofType), (((c_In X14) X0)->(forall (X15:fofType), (((c_In X15) X0)->(((eq fofType) ((X5 X14) X15)) ((X2 ((X1 X15) X14)) ((X1 X14) X15))))))))) (forall (X14:fofType), (((c_In X14) X0)->(forall (X15:fofType), (((c_In X15) X0)->(forall (X16:fofType), (((c_In X16) X0)->(((eq fofType) (((X6 X14) X15) X16)) ((X2 ((X1 X14) ((X1 X15) X16))) ((X1 ((X1 X14) X15)) X16))))))))))) (forall (X14:fofType), (((c_In X14) X0)->(forall (X15:fofType), (((c_In X15) X0)->((c_and ((c_and ((c_and ((c_and (((eq fofType) ((X7 X14) X15)) ((X2 X14) ((X1 X15) X14)))) (((eq fofType) ((X10 X14) X15)) ((X1 X14) ((X1 X15) ((X2 X14) X4)))))) (((eq fofType) ((X11 X14) X15)) ((X1 ((X1 ((X3 X4) X14)) X15)) X14)))) (((eq fofType) ((X12 X14) X15)) ((X1 ((X2 X14) X15)) ((X2 ((X2 X14) X4)) X4))))) (((eq fofType) ((X13 X14) X15)) ((X1 ((X3 X4) ((X3 X4) X14))) ((X3 X15) X14)))))))))) (forall (X14:fofType), (((c_In X14) X0)->(forall (X15:fofType), (((c_In X15) X0)->(forall (X16:fofType), (((c_In X16) X0)->((c_and (((eq fofType) (((X8 X14) X15) X16)) ((X2 ((X1 X15) X14)) ((X1 X15) ((X1 X14) X16))))) (((eq fofType) (((X9 X14) X15) X16)) ((X3 ((X1 ((X1 X16) X14)) X15)) ((X1 X14) X15)))))))))))))
% 0.61/0.83 FOF formula (((eq (fofType->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->(fofType->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->Prop))))))))))))))) c_Loop_with_defs_cex1) (fun (X0:fofType) (X1:(fofType->(fofType->fofType))) (X2:(fofType->(fofType->fofType))) (X3:(fofType->(fofType->fofType))) (X4:fofType) (X5:(fofType->(fofType->fofType))) (X6:(fofType->(fofType->(fofType->fofType)))) (X7:(fofType->(fofType->fofType))) (X8:(fofType->(fofType->(fofType->fofType)))) (X9:(fofType->(fofType->(fofType->fofType)))) (X10:(fofType->(fofType->fofType))) (X11:(fofType->(fofType->fofType))) (X12:(fofType->(fofType->fofType))) (X13:(fofType->(fofType->fofType)))=> ((c_and ((((((((((((((c_Loop_with_defs X0) X1) X2) X3) X4) X5) X6) X7) X8) X9) X10) X11) X12) X13)) ((ex fofType) (fun (X14:fofType)=> ((c_and ((c_In X14) X0)) ((ex fofType) (fun (X15:fofType)=> ((c_and ((c_In X15) X0)) ((ex fofType) (fun (X16:fofType)=> ((c_and ((c_In X16) X0)) ((ex fofType) (fun (X17:fofType)=> ((c_and ((c_In X17) X0)) (c_not (((eq fofType) ((X5 ((X1 ((X2 (((X8 X15) X16) X14)) X4)) X14)) X17)) X4))))))))))))))))) of role axiom named ax104
% 0.68/0.84 A new axiom: (((eq (fofType->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->(fofType->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->Prop))))))))))))))) c_Loop_with_defs_cex1) (fun (X0:fofType) (X1:(fofType->(fofType->fofType))) (X2:(fofType->(fofType->fofType))) (X3:(fofType->(fofType->fofType))) (X4:fofType) (X5:(fofType->(fofType->fofType))) (X6:(fofType->(fofType->(fofType->fofType)))) (X7:(fofType->(fofType->fofType))) (X8:(fofType->(fofType->(fofType->fofType)))) (X9:(fofType->(fofType->(fofType->fofType)))) (X10:(fofType->(fofType->fofType))) (X11:(fofType->(fofType->fofType))) (X12:(fofType->(fofType->fofType))) (X13:(fofType->(fofType->fofType)))=> ((c_and ((((((((((((((c_Loop_with_defs X0) X1) X2) X3) X4) X5) X6) X7) X8) X9) X10) X11) X12) X13)) ((ex fofType) (fun (X14:fofType)=> ((c_and ((c_In X14) X0)) ((ex fofType) (fun (X15:fofType)=> ((c_and ((c_In X15) X0)) ((ex fofType) (fun (X16:fofType)=> ((c_and ((c_In X16) X0)) ((ex fofType) (fun (X17:fofType)=> ((c_and ((c_In X17) X0)) (c_not (((eq fofType) ((X5 ((X1 ((X2 (((X8 X15) X16) X14)) X4)) X14)) X17)) X4)))))))))))))))))
% 0.68/0.84 FOF formula (((eq (fofType->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->(fofType->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->Prop))))))))))))))) c_Loop_with_defs_cex2) (fun (X0:fofType) (X1:(fofType->(fofType->fofType))) (X2:(fofType->(fofType->fofType))) (X3:(fofType->(fofType->fofType))) (X4:fofType) (X5:(fofType->(fofType->fofType))) (X6:(fofType->(fofType->(fofType->fofType)))) (X7:(fofType->(fofType->fofType))) (X8:(fofType->(fofType->(fofType->fofType)))) (X9:(fofType->(fofType->(fofType->fofType)))) (X10:(fofType->(fofType->fofType))) (X11:(fofType->(fofType->fofType))) (X12:(fofType->(fofType->fofType))) (X13:(fofType->(fofType->fofType)))=> ((c_and ((((((((((((((c_Loop_with_defs X0) X1) X2) X3) X4) X5) X6) X7) X8) X9) X10) X11) X12) X13)) ((ex fofType) (fun (X14:fofType)=> ((c_and ((c_In X14) X0)) ((ex fofType) (fun (X15:fofType)=> ((c_and ((c_In X15) X0)) ((ex fofType) (fun (X16:fofType)=> ((c_and ((c_In X16) X0)) ((ex fofType) (fun (X17:fofType)=> ((c_and ((c_In X17) X0)) ((ex fofType) (fun (X18:fofType)=> ((c_and ((c_In X18) X0)) (c_not (((eq fofType) (((X6 X18) ((X1 ((X3 X4) X14)) (((X9 X15) X16) X14))) X17)) X4)))))))))))))))))))) of role axiom named ax105
% 0.68/0.84 A new axiom: (((eq (fofType->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->(fofType->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->Prop))))))))))))))) c_Loop_with_defs_cex2) (fun (X0:fofType) (X1:(fofType->(fofType->fofType))) (X2:(fofType->(fofType->fofType))) (X3:(fofType->(fofType->fofType))) (X4:fofType) (X5:(fofType->(fofType->fofType))) (X6:(fofType->(fofType->(fofType->fofType)))) (X7:(fofType->(fofType->fofType))) (X8:(fofType->(fofType->(fofType->fofType)))) (X9:(fofType->(fofType->(fofType->fofType)))) (X10:(fofType->(fofType->fofType))) (X11:(fofType->(fofType->fofType))) (X12:(fofType->(fofType->fofType))) (X13:(fofType->(fofType->fofType)))=> ((c_and ((((((((((((((c_Loop_with_defs X0) X1) X2) X3) X4) X5) X6) X7) X8) X9) X10) X11) X12) X13)) ((ex fofType) (fun (X14:fofType)=> ((c_and ((c_In X14) X0)) ((ex fofType) (fun (X15:fofType)=> ((c_and ((c_In X15) X0)) ((ex fofType) (fun (X16:fofType)=> ((c_and ((c_In X16) X0)) ((ex fofType) (fun (X17:fofType)=> ((c_and ((c_In X17) X0)) ((ex fofType) (fun (X18:fofType)=> ((c_and ((c_In X18) X0)) (c_not (((eq fofType) (((X6 X18) ((X1 ((X3 X4) X14)) (((X9 X15) X16) X14))) X17)) X4))))))))))))))))))))
% 0.68/0.85 FOF formula (((eq (fofType->Prop)) c_combinator) (fun (X0:fofType)=> (forall (X1:(fofType->Prop)), ((X1 (c_Inj0 c_Empty))->((X1 (c_Inj0 (c_Power c_Empty)))->((forall (X2:fofType) (X3:fofType), ((X1 X2)->((X1 X3)->(X1 (c_Inj1 ((c_setsum X2) X3))))))->(X1 X0))))))) of role axiom named ax106
% 0.68/0.85 A new axiom: (((eq (fofType->Prop)) c_combinator) (fun (X0:fofType)=> (forall (X1:(fofType->Prop)), ((X1 (c_Inj0 c_Empty))->((X1 (c_Inj0 (c_Power c_Empty)))->((forall (X2:fofType) (X3:fofType), ((X1 X2)->((X1 X3)->(X1 (c_Inj1 ((c_setsum X2) X3))))))->(X1 X0)))))))
% 0.68/0.85 FOF formula (((eq (fofType->(fofType->Prop))) c_combinator_equiv) (fun (X0:fofType) (X1:fofType)=> (forall (X2:(fofType->(fofType->Prop))), ((((fun (X3:fofType) (X4:fofType) (X5:(fofType->(fofType->fofType)))=> ((c_per_i X2)->((forall (X6:fofType), ((c_combinator X6)->((X2 X6) X6)))->((forall (X6:fofType) (X7:fofType) (X8:fofType) (X9:fofType), ((c_combinator X6)->((c_combinator X7)->((c_combinator X8)->((c_combinator X9)->(((X2 X6) X8)->(((X2 X7) X9)->((X2 ((X5 X6) X7)) ((X5 X8) X9)))))))))->((forall (X6:fofType) (X7:fofType), ((X2 ((X5 ((X5 X3) X6)) X7)) X6))->((forall (X6:fofType) (X7:fofType) (X8:fofType), ((X2 ((X5 ((X5 ((X5 X4) X6)) X7)) X8)) ((X5 ((X5 X6) X8)) ((X5 X7) X8))))->((X2 X0) X1))))))) (c_Inj0 c_Empty)) (c_Inj0 (c_Power c_Empty))) (fun (X3:fofType) (X4:fofType)=> (c_Inj1 ((c_setsum X3) X4))))))) of role axiom named ax107
% 0.68/0.85 A new axiom: (((eq (fofType->(fofType->Prop))) c_combinator_equiv) (fun (X0:fofType) (X1:fofType)=> (forall (X2:(fofType->(fofType->Prop))), ((((fun (X3:fofType) (X4:fofType) (X5:(fofType->(fofType->fofType)))=> ((c_per_i X2)->((forall (X6:fofType), ((c_combinator X6)->((X2 X6) X6)))->((forall (X6:fofType) (X7:fofType) (X8:fofType) (X9:fofType), ((c_combinator X6)->((c_combinator X7)->((c_combinator X8)->((c_combinator X9)->(((X2 X6) X8)->(((X2 X7) X9)->((X2 ((X5 X6) X7)) ((X5 X8) X9)))))))))->((forall (X6:fofType) (X7:fofType), ((X2 ((X5 ((X5 X3) X6)) X7)) X6))->((forall (X6:fofType) (X7:fofType) (X8:fofType), ((X2 ((X5 ((X5 ((X5 X4) X6)) X7)) X8)) ((X5 ((X5 X6) X8)) ((X5 X7) X8))))->((X2 X0) X1))))))) (c_Inj0 c_Empty)) (c_Inj0 (c_Power c_Empty))) (fun (X3:fofType) (X4:fofType)=> (c_Inj1 ((c_setsum X3) X4)))))))
% 0.68/0.85 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) c_equip_mod) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((ex fofType) (fun (X3:fofType)=> ((ex fofType) (fun (X4:fofType)=> ((c_or ((c_and ((c_equip ((c_setsum X0) X3)) X1)) ((c_equip ((c_setprod X4) X3)) X2))) ((c_and ((c_equip ((c_setsum X1) X3)) X0)) ((c_equip ((c_setprod X4) X3)) X2))))))))) of role axiom named ax108
% 0.68/0.85 A new axiom: (((eq (fofType->(fofType->(fofType->Prop)))) c_equip_mod) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((ex fofType) (fun (X3:fofType)=> ((ex fofType) (fun (X4:fofType)=> ((c_or ((c_and ((c_equip ((c_setsum X0) X3)) X1)) ((c_equip ((c_setprod X4) X3)) X2))) ((c_and ((c_equip ((c_setsum X1) X3)) X0)) ((c_equip ((c_setprod X4) X3)) X2)))))))))
% 0.72/0.88 FOF formula (c_not (forall (X0:((fofType->(fofType->(((fofType->fofType)->(fofType->fofType))->fofType)))->(fofType->(fofType->Prop)))) (X1:((fofType->(((fofType->fofType)->fofType)->fofType))->(fofType->Prop))) (X2:((fofType->fofType)->(((((fofType->fofType)->fofType)->fofType)->((fofType->(fofType->fofType))->(fofType->(fofType->fofType))))->(fofType->Prop)))) (X3:((fofType->((fofType->(fofType->fofType))->fofType))->(fofType->(fofType->Prop)))), ((forall (X4:(((fofType->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))->fofType)) (X5:fofType) (X6:fofType), (fofType->(((c_In (c_Inj0 X6)) ((c_setsum ((c_setsum c_Empty) c_Empty)) ((c_setsum X6) (c_Inj0 ((c_setsum c_Empty) c_Empty)))))->((((X2 (fun (X8:fofType)=> (c_Inj0 (c_Inj0 c_Empty)))) (fun (X8:(((fofType->fofType)->fofType)->fofType)) (X9:(fofType->(fofType->fofType))) (X10:fofType) (X11:fofType)=> X10)) ((c_setsum (X4 (fun (X8:(fofType->(fofType->fofType))) (X9:(fofType->fofType)) (X10:fofType)=> (c_Inj0 ((c_setsum c_Empty) c_Empty))))) c_Empty))->(((X3 (fun (X8:fofType) (X9:(fofType->(fofType->fofType)))=> (c_Inj0 X8))) X5) ((c_setsum ((c_setsum ((c_setsum c_Empty) ((c_setsum c_Empty) c_Empty))) (c_Inj0 c_Empty))) c_Empty))))))->((forall (X4:((((fofType->fofType)->(fofType->fofType))->fofType)->fofType)), ((fofType->fofType)->(forall (X6:fofType) (X7:fofType), ((((X3 (fun (X8:fofType) (X9:(fofType->(fofType->fofType)))=> c_Empty)) X7) ((c_setsum ((c_setsum ((c_setsum ((c_setsum c_Empty) c_Empty)) c_Empty)) ((c_setsum ((c_setsum c_Empty) c_Empty)) (c_Inj0 c_Empty)))) ((c_setsum c_Empty) (c_Inj1 ((c_setsum c_Empty) c_Empty)))))->(((X3 (fun (X8:fofType) (X9:(fofType->(fofType->fofType)))=> X7)) ((c_setsum (X4 (fun (X8:((fofType->fofType)->(fofType->fofType)))=> X7))) X6)) (c_Inj0 (c_Inj1 ((c_setsum ((c_setsum c_Empty) c_Empty)) ((c_setsum c_Empty) c_Empty)))))))))->((fofType->(forall (X5:(fofType->(((fofType->fofType)->(fofType->fofType))->fofType))) (X6:((((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))->((fofType->(fofType->fofType))->fofType))) (X7:fofType), (((c_In (c_Inj0 c_Empty)) ((c_setsum c_Empty) ((X5 (c_Inj0 ((c_setsum c_Empty) c_Empty))) (fun (X8:(fofType->fofType)) (X9:fofType)=> (c_Inj0 c_Empty)))))->((((X0 (fun (X8:fofType) (X9:fofType) (X10:((fofType->fofType)->(fofType->fofType)))=> X8)) X7) ((X6 (fun (X8:((fofType->fofType)->(fofType->fofType))) (X9:(fofType->fofType)) (X10:fofType)=> (c_Inj1 c_Empty))) (fun (X8:fofType) (X9:fofType)=> c_Empty)))->(((X2 (fun (X8:fofType)=> X8)) (fun (X8:(((fofType->fofType)->fofType)->fofType)) (X9:(fofType->(fofType->fofType))) (X10:fofType) (X11:fofType)=> X10)) ((c_setsum (c_Inj0 c_Empty)) ((X6 (fun (X8:((fofType->fofType)->(fofType->fofType))) (X9:(fofType->fofType)) (X10:fofType)=> (c_Inj0 c_Empty))) (fun (X8:fofType) (X9:fofType)=> X9))))))))->((forall (X4:(fofType->(fofType->fofType))) (X5:(fofType->fofType)) (X6:fofType), ((fofType->fofType)->(((c_In (c_Inj0 (c_Inj1 c_Empty))) ((c_setsum ((c_setsum (c_Inj0 c_Empty)) ((c_setsum ((c_setsum c_Empty) c_Empty)) ((c_setsum c_Empty) c_Empty)))) ((c_setsum c_Empty) ((c_setsum (c_Inj0 c_Empty)) ((X4 c_Empty) c_Empty)))))->((((X2 (fun (X8:fofType)=> c_Empty)) (fun (X8:(((fofType->fofType)->fofType)->fofType)) (X9:(fofType->(fofType->fofType))) (X10:fofType) (X11:fofType)=> c_Empty)) ((c_setsum ((c_setsum c_Empty) ((c_setsum ((c_setsum c_Empty) c_Empty)) (c_Inj0 c_Empty)))) (c_Inj1 X6)))->((X1 (fun (X8:fofType) (X9:((fofType->fofType)->fofType))=> (c_Inj0 c_Empty))) ((X4 c_Empty) (X5 ((c_setsum (c_Inj1 c_Empty)) c_Empty))))))))->((fofType->((fofType->fofType)->((fofType->fofType)->(fofType->((((X3 (fun (X8:fofType) (X9:(fofType->(fofType->fofType)))=> c_Empty)) c_Empty) c_Empty)->((X1 (fun (X8:fofType) (X9:((fofType->fofType)->fofType))=> (X9 (fun (X10:fofType)=> ((c_setsum (c_Inj1 (c_Inj0 c_Empty))) ((c_setsum c_Empty) c_Empty)))))) c_Empty))))))->((forall (X4:fofType) (X5:fofType) (X6:fofType) (X7:fofType), (((c_In (c_Inj0 X6)) ((c_setsum ((c_setsum X4) ((c_setsum X5) ((c_setsum c_Empty) c_Empty)))) (c_Inj1 ((c_setsum X5) c_Empty))))->(((X1 (fun (X8:fofType) (X9:((fofType->fofType)->fofType))=> X7)) c_Empty)->(((X2 (fun (X8:fofType)=> c_Empty)) (fun (X8:(((fofType->fofType)->fofType)->fofType)) (X9:(fofType->(fofType->fofType))) (X10:fofType) (X11:fofType)=> ((c_setsum c_Empty) c_Empty))) X5))))->((forall (X4:((((fofType->fofType)->(fofType->fofType))->fofType)->fofType)) (X5:fofType), (fofType->(fofType->(((c_In (c_Inj1 c_Empty)) X5)->(((X1 (fun (X8:fofType) (X9:((fofType->fofType)->fofType))=> c_Empty)) c_Empty)->(((X0 (fun (X8:fofType) (X9:fofType) (X10:((fofType->fofType)->(fofType->fofType)))=> (c_Inj1 c_Empty))) (c_Inj1 (c_Inj1 (X4 (fun (X8:((fofType->fofType)->(fofType->fofType)))=> c_Empty))))) (c_Inj1 ((c_setsum ((c_setsum (c_Inj0 c_Empty)) c_Empty)) (c_Inj1 (c_Inj0 c_Empty))))))))))->((forall (X4:(fofType->fofType)), (fofType->((fofType->fofType)->(forall (X7:fofType), ((((X0 (fun (X8:fofType) (X9:fofType) (X10:((fofType->fofType)->(fofType->fofType)))=> c_Empty)) (X4 c_Empty)) X7)->c_False)))))->c_False)))))))))) of role conjecture named conj
% 0.72/0.88 Conjecture to prove = (c_not (forall (X0:((fofType->(fofType->(((fofType->fofType)->(fofType->fofType))->fofType)))->(fofType->(fofType->Prop)))) (X1:((fofType->(((fofType->fofType)->fofType)->fofType))->(fofType->Prop))) (X2:((fofType->fofType)->(((((fofType->fofType)->fofType)->fofType)->((fofType->(fofType->fofType))->(fofType->(fofType->fofType))))->(fofType->Prop)))) (X3:((fofType->((fofType->(fofType->fofType))->fofType))->(fofType->(fofType->Prop)))), ((forall (X4:(((fofType->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))->fofType)) (X5:fofType) (X6:fofType), (fofType->(((c_In (c_Inj0 X6)) ((c_setsum ((c_setsum c_Empty) c_Empty)) ((c_setsum X6) (c_Inj0 ((c_setsum c_Empty) c_Empty)))))->((((X2 (fun (X8:fofType)=> (c_Inj0 (c_Inj0 c_Empty)))) (fun (X8:(((fofType->fofType)->fofType)->fofType)) (X9:(fofType->(fofType->fofType))) (X10:fofType) (X11:fofType)=> X10)) ((c_setsum (X4 (fun (X8:(fofType->(fofType->fofType))) (X9:(fofType->fofType)) (X10:fofType)=> (c_Inj0 ((c_setsum c_Empty) c_Empty))))) c_Empty))->(((X3 (fun (X8:fofType) (X9:(fofType->(fofType->fofType)))=> (c_Inj0 X8))) X5) ((c_setsum ((c_setsum ((c_setsum c_Empty) ((c_setsum c_Empty) c_Empty))) (c_Inj0 c_Empty))) c_Empty))))))->((forall (X4:((((fofType->fofType)->(fofType->fofType))->fofType)->fofType)), ((fofType->fofType)->(forall (X6:fofType) (X7:fofType), ((((X3 (fun (X8:fofType) (X9:(fofType->(fofType->fofType)))=> c_Empty)) X7) ((c_setsum ((c_setsum ((c_setsum ((c_setsum c_Empty) c_Empty)) c_Empty)) ((c_setsum ((c_setsum c_Empty) c_Empty)) (c_Inj0 c_Empty)))) ((c_setsum c_Empty) (c_Inj1 ((c_setsum c_Empty) c_Empty)))))->(((X3 (fun (X8:fofType) (X9:(fofType->(fofType->fofType)))=> X7)) ((c_setsum (X4 (fun (X8:((fofType->fofType)->(fofType->fofType)))=> X7))) X6)) (c_Inj0 (c_Inj1 ((c_setsum ((c_setsum c_Empty) c_Empty)) ((c_setsum c_Empty) c_Empty)))))))))->((fofType->(forall (X5:(fofType->(((fofType->fofType)->(fofType->fofType))->fofType))) (X6:((((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))->((fofType->(fofType->fofType))->fofType))) (X7:fofType), (((c_In (c_Inj0 c_Empty)) ((c_setsum c_Empty) ((X5 (c_Inj0 ((c_setsum c_Empty) c_Empty))) (fun (X8:(fofType->fofType)) (X9:fofType)=> (c_Inj0 c_Empty)))))->((((X0 (fun (X8:fofType) (X9:fofType) (X10:((fofType->fofType)->(fofType->fofType)))=> X8)) X7) ((X6 (fun (X8:((fofType->fofType)->(fofType->fofType))) (X9:(fofType->fofType)) (X10:fofType)=> (c_Inj1 c_Empty))) (fun (X8:fofType) (X9:fofType)=> c_Empty)))->(((X2 (fun (X8:fofType)=> X8)) (fun (X8:(((fofType->fofType)->fofType)->fofType)) (X9:(fofType->(fofType->fofType))) (X10:fofType) (X11:fofType)=> X10)) ((c_setsum (c_Inj0 c_Empty)) ((X6 (fun (X8:((fofType->fofType)->(fofType->fofType))) (X9:(fofType->fofType)) (X10:fofType)=> (c_Inj0 c_Empty))) (fun (X8:fofType) (X9:fofType)=> X9))))))))->((forall (X4:(fofType->(fofType->fofType))) (X5:(fofType->fofType)) (X6:fofType), ((fofType->fofType)->(((c_In (c_Inj0 (c_Inj1 c_Empty))) ((c_setsum ((c_setsum (c_Inj0 c_Empty)) ((c_setsum ((c_setsum c_Empty) c_Empty)) ((c_setsum c_Empty) c_Empty)))) ((c_setsum c_Empty) ((c_setsum (c_Inj0 c_Empty)) ((X4 c_Empty) c_Empty)))))->((((X2 (fun (X8:fofType)=> c_Empty)) (fun (X8:(((fofType->fofType)->fofType)->fofType)) (X9:(fofType->(fofType->fofType))) (X10:fofType) (X11:fofType)=> c_Empty)) ((c_setsum ((c_setsum c_Empty) ((c_setsum ((c_setsum c_Empty) c_Empty)) (c_Inj0 c_Empty)))) (c_Inj1 X6)))->((X1 (fun (X8:fofType) (X9:((fofType->fofType)->fofType))=> (c_Inj0 c_Empty))) ((X4 c_Empty) (X5 ((c_setsum (c_Inj1 c_Empty)) c_Empty))))))))->((fofType->((fofType->fofType)->((fofType->fofType)->(fofType->((((X3 (fun (X8:fofType) (X9:(fofType->(fofType->fofType)))=> c_Empty)) c_Empty) c_Empty)->((X1 (fun (X8:fofType) (X9:((fofType->fofType)->fofType))=> (X9 (fun (X10:fofType)=> ((c_setsum (c_Inj1 (c_Inj0 c_Empty))) ((c_setsum c_Empty) c_Empty)))))) c_Empty))))))->((forall (X4:fofType) (X5:fofType) (X6:fofType) (X7:fofType), (((c_In (c_Inj0 X6)) ((c_setsum ((c_setsum X4) ((c_setsum X5) ((c_setsum c_Empty) c_Empty)))) (c_Inj1 ((c_setsum X5) c_Empty))))->(((X1 (fun (X8:fofType) (X9:((fofType->fofType)->fofType))=> X7)) c_Empty)->(((X2 (fun (X8:fofType)=> c_Empty)) (fun (X8:(((fofType->fofType)->fofType)->fofType)) (X9:(fofType->(fofType->fofType))) (X10:fofType) (X11:fofType)=> ((c_setsum c_Empty) c_Empty))) X5))))->((forall (X4:((((fofType->fofType)->(fofType->fofType))->fofType)->fofType)) (X5:fofType), (fofType->(fofType->(((c_In (c_Inj1 c_Empty)) X5)->(((X1 (fun (X8:fofType) (X9:((fofType->fofType)->fofType))=> c_Empty)) c_Empty)->(((X0 (fun (X8:fofType) (X9:fofType) (X10:((fofType->fofType)->(fofType->fofType)))=> (c_Inj1 c_Empty))) (c_Inj1 (c_Inj1 (X4 (fun (X8:((fofType->fofType)->(fofType->fofType)))=> c_Empty))))) (c_Inj1 ((c_setsum ((c_setsum (c_Inj0 c_Empty)) c_Empty)) (c_Inj1 (c_Inj0 c_Empty))))))))))->((forall (X4:(fofType->fofType)), (fofType->((fofType->fofType)->(forall (X7:fofType), ((((X0 (fun (X8:fofType) (X9:fofType) (X10:((fofType->fofType)->(fofType->fofType)))=> c_Empty)) (X4 c_Empty)) X7)->c_False)))))->c_False)))))))))):Prop
% 0.72/0.89 We need to prove ['(c_not (forall (X0:((fofType->(fofType->(((fofType->fofType)->(fofType->fofType))->fofType)))->(fofType->(fofType->Prop)))) (X1:((fofType->(((fofType->fofType)->fofType)->fofType))->(fofType->Prop))) (X2:((fofType->fofType)->(((((fofType->fofType)->fofType)->fofType)->((fofType->(fofType->fofType))->(fofType->(fofType->fofType))))->(fofType->Prop)))) (X3:((fofType->((fofType->(fofType->fofType))->fofType))->(fofType->(fofType->Prop)))), ((forall (X4:(((fofType->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))->fofType)) (X5:fofType) (X6:fofType), (fofType->(((c_In (c_Inj0 X6)) ((c_setsum ((c_setsum c_Empty) c_Empty)) ((c_setsum X6) (c_Inj0 ((c_setsum c_Empty) c_Empty)))))->((((X2 (fun (X8:fofType)=> (c_Inj0 (c_Inj0 c_Empty)))) (fun (X8:(((fofType->fofType)->fofType)->fofType)) (X9:(fofType->(fofType->fofType))) (X10:fofType) (X11:fofType)=> X10)) ((c_setsum (X4 (fun (X8:(fofType->(fofType->fofType))) (X9:(fofType->fofType)) (X10:fofType)=> (c_Inj0 ((c_setsum c_Empty) c_Empty))))) c_Empty))->(((X3 (fun (X8:fofType) (X9:(fofType->(fofType->fofType)))=> (c_Inj0 X8))) X5) ((c_setsum ((c_setsum ((c_setsum c_Empty) ((c_setsum c_Empty) c_Empty))) (c_Inj0 c_Empty))) c_Empty))))))->((forall (X4:((((fofType->fofType)->(fofType->fofType))->fofType)->fofType)), ((fofType->fofType)->(forall (X6:fofType) (X7:fofType), ((((X3 (fun (X8:fofType) (X9:(fofType->(fofType->fofType)))=> c_Empty)) X7) ((c_setsum ((c_setsum ((c_setsum ((c_setsum c_Empty) c_Empty)) c_Empty)) ((c_setsum ((c_setsum c_Empty) c_Empty)) (c_Inj0 c_Empty)))) ((c_setsum c_Empty) (c_Inj1 ((c_setsum c_Empty) c_Empty)))))->(((X3 (fun (X8:fofType) (X9:(fofType->(fofType->fofType)))=> X7)) ((c_setsum (X4 (fun (X8:((fofType->fofType)->(fofType->fofType)))=> X7))) X6)) (c_Inj0 (c_Inj1 ((c_setsum ((c_setsum c_Empty) c_Empty)) ((c_setsum c_Empty) c_Empty)))))))))->((fofType->(forall (X5:(fofType->(((fofType->fofType)->(fofType->fofType))->fofType))) (X6:((((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))->((fofType->(fofType->fofType))->fofType))) (X7:fofType), (((c_In (c_Inj0 c_Empty)) ((c_setsum c_Empty) ((X5 (c_Inj0 ((c_setsum c_Empty) c_Empty))) (fun (X8:(fofType->fofType)) (X9:fofType)=> (c_Inj0 c_Empty)))))->((((X0 (fun (X8:fofType) (X9:fofType) (X10:((fofType->fofType)->(fofType->fofType)))=> X8)) X7) ((X6 (fun (X8:((fofType->fofType)->(fofType->fofType))) (X9:(fofType->fofType)) (X10:fofType)=> (c_Inj1 c_Empty))) (fun (X8:fofType) (X9:fofType)=> c_Empty)))->(((X2 (fun (X8:fofType)=> X8)) (fun (X8:(((fofType->fofType)->fofType)->fofType)) (X9:(fofType->(fofType->fofType))) (X10:fofType) (X11:fofType)=> X10)) ((c_setsum (c_Inj0 c_Empty)) ((X6 (fun (X8:((fofType->fofType)->(fofType->fofType))) (X9:(fofType->fofType)) (X10:fofType)=> (c_Inj0 c_Empty))) (fun (X8:fofType) (X9:fofType)=> X9))))))))->((forall (X4:(fofType->(fofType->fofType))) (X5:(fofType->fofType)) (X6:fofType), ((fofType->fofType)->(((c_In (c_Inj0 (c_Inj1 c_Empty))) ((c_setsum ((c_setsum (c_Inj0 c_Empty)) ((c_setsum ((c_setsum c_Empty) c_Empty)) ((c_setsum c_Empty) c_Empty)))) ((c_setsum c_Empty) ((c_setsum (c_Inj0 c_Empty)) ((X4 c_Empty) c_Empty)))))->((((X2 (fun (X8:fofType)=> c_Empty)) (fun (X8:(((fofType->fofType)->fofType)->fofType)) (X9:(fofType->(fofType->fofType))) (X10:fofType) (X11:fofType)=> c_Empty)) ((c_setsum ((c_setsum c_Empty) ((c_setsum ((c_setsum c_Empty) c_Empty)) (c_Inj0 c_Empty)))) (c_Inj1 X6)))->((X1 (fun (X8:fofType) (X9:((fofType->fofType)->fofType))=> (c_Inj0 c_Empty))) ((X4 c_Empty) (X5 ((c_setsum (c_Inj1 c_Empty)) c_Empty))))))))->((fofType->((fofType->fofType)->((fofType->fofType)->(fofType->((((X3 (fun (X8:fofType) (X9:(fofType->(fofType->fofType)))=> c_Empty)) c_Empty) c_Empty)->((X1 (fun (X8:fofType) (X9:((fofType->fofType)->fofType))=> (X9 (fun (X10:fofType)=> ((c_setsum (c_Inj1 (c_Inj0 c_Empty))) ((c_setsum c_Empty) c_Empty)))))) c_Empty))))))->((forall (X4:fofType) (X5:fofType) (X6:fofType) (X7:fofType), (((c_In (c_Inj0 X6)) ((c_setsum ((c_setsum X4) ((c_setsum X5) ((c_setsum c_Empty) c_Empty)))) (c_Inj1 ((c_setsum X5) c_Empty))))->(((X1 (fun (X8:fofType) (X9:((fofType->fofType)->fofType))=> X7)) c_Empty)->(((X2 (fun (X8:fofType)=> c_Empty)) (fun (X8:(((fofType->fofType)->fofType)->fofType)) (X9:(fofType->(fofType->fofType))) (X10:fofType) (X11:fofType)=> ((c_setsum c_Empty) c_Empty))) X5))))->((forall (X4:((((fofType->fofType)->(fofType->fofType))->fofType)->fofType)) (X5:fofType), (fofType->(fofType->(((c_In (c_Inj1 c_Empty)) X5)->(((X1 (fun (X8:fofType) (X9:((fofType->fofType)->fofType))=> c_Empty)) c_Empty)->(((X0 (fun (X8:fofType) (X9:fofType) (X10:((fofType->fofType)->(fofType->fofType)))=> (c_Inj1 c_Empty))) (c_Inj1 (c_Inj1 (X4 (fun (X8:((fofType->fofType)->(fofType->fofType)))=> c_Empty))))) (c_Inj1 ((c_setsum ((c_setsum (c_Inj0 c_Empty)) c_Empty)) (c_Inj1 (c_Inj0 c_Empty))))))))))->((forall (X4:(fofType->fofType)), (fofType->((fofType->fofType)->(forall (X7:fofType), ((((X0 (fun (X8:fofType) (X9:fofType) (X10:((fofType->fofType)->(fofType->fofType)))=> c_Empty)) (X4 c_Empty)) X7)->c_False)))))->c_False))))))))))']
% 0.72/0.89 Parameter fofType:Type.
% 0.72/0.89 Parameter c_Eps_i:((fofType->Prop)->fofType).
% 0.72/0.89 Parameter c_False:Prop.
% 0.72/0.89 Parameter c_True:Prop.
% 0.72/0.89 Parameter c_not:(Prop->Prop).
% 0.72/0.89 Parameter c_and:(Prop->(Prop->Prop)).
% 0.72/0.89 Parameter c_or:(Prop->(Prop->Prop)).
% 0.72/0.89 Parameter c_iff:(Prop->(Prop->Prop)).
% 0.72/0.89 Parameter c_In:(fofType->(fofType->Prop)).
% 0.72/0.89 Parameter c_Subq:(fofType->(fofType->Prop)).
% 0.72/0.89 Parameter c_Empty:fofType.
% 0.72/0.89 Parameter c_Union:(fofType->fofType).
% 0.72/0.89 Parameter c_Power:(fofType->fofType).
% 0.72/0.89 Parameter c_Repl:(fofType->((fofType->fofType)->fofType)).
% 0.72/0.89 Parameter c_TransSet:(fofType->Prop).
% 0.72/0.89 Parameter c_atleast2:(fofType->Prop).
% 0.72/0.89 Parameter c_atleast3:(fofType->Prop).
% 0.72/0.89 Parameter c_atleast4:(fofType->Prop).
% 0.72/0.89 Parameter c_atleast5:(fofType->Prop).
% 0.72/0.89 Parameter c_atleast6:(fofType->Prop).
% 0.72/0.89 Parameter c_exactly2:(fofType->Prop).
% 0.72/0.89 Parameter c_exactly3:(fofType->Prop).
% 0.72/0.89 Parameter c_exactly4:(fofType->Prop).
% 0.72/0.89 Parameter c_exactly5:(fofType->Prop).
% 0.72/0.89 Parameter c_exu_i:((fofType->Prop)->Prop).
% 0.72/0.89 Parameter c_reflexive_i:((fofType->(fofType->Prop))->Prop).
% 0.72/0.89 Parameter c_irreflexive_i:((fofType->(fofType->Prop))->Prop).
% 0.72/0.89 Parameter c_symmetric_i:((fofType->(fofType->Prop))->Prop).
% 0.72/0.89 Parameter c_antisymmetric_i:((fofType->(fofType->Prop))->Prop).
% 0.72/0.89 Parameter c_transitive_i:((fofType->(fofType->Prop))->Prop).
% 0.72/0.89 Parameter c_eqreln_i:((fofType->(fofType->Prop))->Prop).
% 0.72/0.89 Parameter c_per_i:((fofType->(fofType->Prop))->Prop).
% 0.72/0.89 Parameter c_linear_i:((fofType->(fofType->Prop))->Prop).
% 0.72/0.89 Parameter c_trichotomous_or_i:((fofType->(fofType->Prop))->Prop).
% 0.72/0.89 Parameter c_partialorder_i:((fofType->(fofType->Prop))->Prop).
% 0.72/0.89 Parameter c_totalorder_i:((fofType->(fofType->Prop))->Prop).
% 0.72/0.89 Parameter c_strictpartialorder_i:((fofType->(fofType->Prop))->Prop).
% 0.72/0.89 Parameter c_stricttotalorder_i:((fofType->(fofType->Prop))->Prop).
% 0.72/0.89 Parameter c_If_i:(Prop->(fofType->(fofType->fofType))).
% 0.72/0.89 Parameter c_exactly1of2:(Prop->(Prop->Prop)).
% 0.72/0.89 Parameter c_exactly1of3:(Prop->(Prop->(Prop->Prop))).
% 0.72/0.89 Parameter c_nIn:(fofType->(fofType->Prop)).
% 0.72/0.89 Parameter c_nSubq:(fofType->(fofType->Prop)).
% 0.72/0.89 Parameter c_UPair:(fofType->(fofType->fofType)).
% 0.72/0.89 Parameter c_Sing:(fofType->fofType).
% 0.72/0.89 Parameter c_binunion:(fofType->(fofType->fofType)).
% 0.72/0.89 Parameter c_SetAdjoin:(fofType->(fofType->fofType)).
% 0.72/0.89 Parameter c_famunion:(fofType->((fofType->fofType)->fofType)).
% 0.72/0.89 Parameter c_Sep:(fofType->((fofType->Prop)->fofType)).
% 0.72/0.89 Parameter c_ReplSep:(fofType->((fofType->Prop)->((fofType->fofType)->fofType))).
% 0.72/0.89 Parameter c_binintersect:(fofType->(fofType->fofType)).
% 0.72/0.89 Parameter c_setminus:(fofType->(fofType->fofType)).
% 0.72/0.89 Parameter c_inj:(fofType->(fofType->((fofType->fofType)->Prop))).
% 0.72/0.89 Parameter c_bij:(fofType->(fofType->((fofType->fofType)->Prop))).
% 0.72/0.89 Parameter c_atleastp:(fofType->(fofType->Prop)).
% 0.72/0.89 Parameter c_equip:(fofType->(fofType->Prop)).
% 0.72/0.89 Parameter c_In_rec_poly_G_i:((fofType->((fofType->fofType)->fofType))->(fofType->(fofType->Prop))).
% 0.72/0.89 Parameter c_In_rec_poly_i:((fofType->((fofType->fofType)->fofType))->(fofType->fofType)).
% 0.72/0.89 Parameter c_ordsucc:(fofType->fofType).
% 0.72/0.89 Parameter c_nat_p:(fofType->Prop).
% 0.72/0.89 Parameter c_nat_primrec:(fofType->((fofType->(fofType->fofType))->(fofType->fofType))).
% 0.72/0.89 Parameter c_add_nat:(fofType->(fofType->fofType)).
% 0.72/0.89 Parameter c_mul_nat:(fofType->(fofType->fofType)).
% 0.72/0.89 Parameter c_ordinal:(fofType->Prop).
% 0.72/0.89 Parameter c_V_:(fofType->fofType).
% 0.72/0.89 Parameter c_Inj1:(fofType->fofType).
% 0.72/0.89 Parameter c_Inj0:(fofType->fofType).
% 0.72/0.89 Parameter c_Unj:(fofType->fofType).
% 0.72/0.89 Parameter c_combine_funcs:(fofType->(fofType->((fofType->fofType)->((fofType->fofType)->(fofType->fofType))))).
% 0.72/0.89 Parameter c_setsum:(fofType->(fofType->fofType)).
% 0.72/0.89 Parameter c_proj0:(fofType->fofType).
% 0.72/0.89 Parameter c_proj1:(fofType->fofType).
% 0.72/0.89 Parameter c_binrep:(fofType->(fofType->fofType)).
% 0.72/0.89 Parameter c_lam:(fofType->((fofType->fofType)->fofType)).
% 0.72/0.89 Parameter c_setprod:(fofType->(fofType->fofType)).
% 0.72/0.89 Parameter c_ap:(fofType->(fofType->fofType)).
% 0.72/0.89 Parameter c_setsum_p:(fofType->Prop).
% 0.72/0.89 Parameter c_tuple_p:(fofType->(fofType->Prop)).
% 0.72/0.89 Parameter c_Pi:(fofType->((fofType->fofType)->fofType)).
% 0.72/0.89 Parameter c_setexp:(fofType->(fofType->fofType)).
% 0.72/0.89 Parameter c_Sep2:(fofType->((fofType->fofType)->((fofType->(fofType->Prop))->fofType))).
% 0.72/0.89 Parameter c_set_of_pairs:(fofType->Prop).
% 0.72/0.89 Parameter c_lam2:(fofType->((fofType->fofType)->((fofType->(fofType->fofType))->fofType))).
% 0.72/0.89 Parameter c_PNoEq_:(fofType->((fofType->Prop)->((fofType->Prop)->Prop))).
% 0.72/0.89 Parameter c_PNoLt_:(fofType->((fofType->Prop)->((fofType->Prop)->Prop))).
% 0.72/0.89 Parameter c_PNoLt:(fofType->((fofType->Prop)->(fofType->((fofType->Prop)->Prop)))).
% 0.72/0.89 Parameter c_PNoLe:(fofType->((fofType->Prop)->(fofType->((fofType->Prop)->Prop)))).
% 0.72/0.89 Parameter c_PNo_downc:((fofType->((fofType->Prop)->Prop))->(fofType->((fofType->Prop)->Prop))).
% 0.72/0.89 Parameter c_PNo_upc:((fofType->((fofType->Prop)->Prop))->(fofType->((fofType->Prop)->Prop))).
% 0.72/0.89 Parameter c_SNoElts_:(fofType->fofType).
% 0.72/0.89 Parameter c_SNo_:(fofType->(fofType->Prop)).
% 0.72/0.89 Parameter c_PSNo:(fofType->((fofType->Prop)->fofType)).
% 0.72/0.89 Parameter c_SNo:(fofType->Prop).
% 0.72/0.89 Parameter c_SNoLev:(fofType->fofType).
% 0.72/0.89 Parameter c_SNoEq_:(fofType->(fofType->(fofType->Prop))).
% 0.72/0.89 Parameter c_SNoLt:(fofType->(fofType->Prop)).
% 0.72/0.89 Parameter c_SNoLe:(fofType->(fofType->Prop)).
% 0.72/0.89 Parameter c_binop_on:(fofType->((fofType->(fofType->fofType))->Prop)).
% 0.72/0.89 Parameter c_Loop:(fofType->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->(fofType->Prop))))).
% 0.72/0.89 Parameter c_Loop_with_defs:(fofType->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->(fofType->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->Prop)))))))))))))).
% 0.72/0.89 Parameter c_Loop_with_defs_cex1:(fofType->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->(fofType->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->Prop)))))))))))))).
% 0.72/0.89 Parameter c_Loop_with_defs_cex2:(fofType->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->(fofType->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->Prop)))))))))))))).
% 0.72/0.89 Parameter c_combinator:(fofType->Prop).
% 0.72/0.89 Parameter c_combinator_equiv:(fofType->(fofType->Prop)).
% 0.72/0.89 Parameter c_equip_mod:(fofType->(fofType->(fofType->Prop))).
% 0.72/0.89 Axiom ax1:(forall (X0:(fofType->Prop)) (X1:fofType), ((X0 X1)->(X0 (c_Eps_i X0)))).
% 0.72/0.89 Axiom ax2:(forall (X0:Prop), ((c_not (c_not X0))->X0)).
% 0.72/0.89 Axiom ax3:(forall (X0:Prop) (X1:Prop), (((c_iff X0) X1)->(((eq Prop) X0) X1))).
% 0.72/0.89 Axiom ax4:(forall (X0:fofType) (X1:fofType), (((c_Subq X0) X1)->(((c_Subq X1) X0)->(((eq fofType) X0) X1)))).
% 0.72/0.89 Axiom ax5:(c_not ((ex fofType) (fun (X0:fofType)=> ((c_In X0) c_Empty)))).
% 0.72/0.89 Axiom ax6:(forall (X0:fofType) (X1:fofType), ((c_iff ((c_In X1) (c_Union X0))) ((ex fofType) (fun (X2:fofType)=> ((c_and ((c_In X1) X2)) ((c_In X2) X0)))))).
% 0.72/0.89 Axiom ax7:(forall (X0:fofType) (X1:fofType), ((c_iff ((c_In X1) (c_Power X0))) ((c_Subq X1) X0))).
% 0.72/0.89 Axiom ax8:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), ((c_iff ((c_In X2) ((c_Repl X0) (fun (X3:fofType)=> (X1 X3))))) ((ex fofType) (fun (X3:fofType)=> ((c_and ((c_In X3) X0)) (((eq fofType) X2) (X1 X3))))))).
% 0.72/0.89 Axiom ax9:(forall (X0:(fofType->Prop)), ((forall (X1:fofType), ((X0 X1)->(forall (X2:fofType), (((c_In X2) X1)->(X0 X2)))))->((X0 c_Empty)->((forall (X1:fofType), ((X0 X1)->(X0 (c_Union X1))))->((forall (X1:fofType), ((X0 X1)->(X0 (c_Power X1))))->((forall (X1:fofType), ((X0 X1)->(forall (X2:(fofType->fofType)), ((forall (X3:fofType), (((c_In X3) X1)->(X0 (X2 X3))))->(X0 ((c_Repl X1) (fun (X3:fofType)=> (X2 X3))))))))->(forall (X1:fofType), (X0 X1)))))))).
% 0.72/0.89 Axiom ax10:(forall (X0:(fofType->Prop)), ((forall (X1:fofType), ((forall (X2:fofType), (((c_In X2) X1)->(X0 X2)))->(X0 X1)))->(forall (X1:fofType), (X0 X1)))).
% 0.72/0.89 Axiom ax11:(((eq Prop) c_False) (forall (X0:Prop), X0)).
% 0.72/0.89 Axiom ax12:(((eq Prop) c_True) (forall (X0:Prop), (X0->X0))).
% 0.72/0.89 Axiom ax13:(((eq (Prop->Prop)) c_not) (fun (X0:Prop)=> (X0->c_False))).
% 0.72/0.89 Axiom ax14:(((eq (Prop->(Prop->Prop))) c_and) (fun (X0:Prop) (X1:Prop)=> (forall (X2:Prop), ((X0->(X1->X2))->X2)))).
% 0.72/0.89 Axiom ax15:(((eq (Prop->(Prop->Prop))) c_or) (fun (X0:Prop) (X1:Prop)=> (forall (X2:Prop), ((X0->X2)->((X1->X2)->X2))))).
% 0.72/0.89 Axiom ax16:(((eq (Prop->(Prop->Prop))) c_iff) (fun (X0:Prop) (X1:Prop)=> ((c_and (X0->X1)) (X1->X0)))).
% 0.72/0.89 Axiom ax17:(((eq (fofType->(fofType->Prop))) c_Subq) (fun (X0:fofType) (X1:fofType)=> (forall (X2:fofType), (((c_In X2) X0)->((c_In X2) X1))))).
% 0.72/0.89 Axiom ax18:(((eq (fofType->Prop)) c_TransSet) (fun (X0:fofType)=> (forall (X1:fofType), (((c_In X1) X0)->((c_Subq X1) X0))))).
% 0.72/0.89 Axiom ax19:(((eq (fofType->Prop)) c_atleast2) (fun (X0:fofType)=> ((ex fofType) (fun (X1:fofType)=> ((c_and ((c_In X1) X0)) (c_not ((c_Subq X0) (c_Power X1)))))))).
% 0.72/0.89 Axiom ax20:(((eq (fofType->Prop)) c_atleast3) (fun (X0:fofType)=> ((ex fofType) (fun (X1:fofType)=> ((c_and ((c_Subq X1) X0)) ((c_and (c_not ((c_Subq X0) X1))) (c_atleast2 X1))))))).
% 0.72/0.89 Axiom ax21:(((eq (fofType->Prop)) c_atleast4) (fun (X0:fofType)=> ((ex fofType) (fun (X1:fofType)=> ((c_and ((c_Subq X1) X0)) ((c_and (c_not ((c_Subq X0) X1))) (c_atleast3 X1))))))).
% 0.72/0.89 Axiom ax22:(((eq (fofType->Prop)) c_atleast5) (fun (X0:fofType)=> ((ex fofType) (fun (X1:fofType)=> ((c_and ((c_Subq X1) X0)) ((c_and (c_not ((c_Subq X0) X1))) (c_atleast4 X1))))))).
% 0.72/0.89 Axiom ax23:(((eq (fofType->Prop)) c_atleast6) (fun (X0:fofType)=> ((ex fofType) (fun (X1:fofType)=> ((c_and ((c_Subq X1) X0)) ((c_and (c_not ((c_Subq X0) X1))) (c_atleast5 X1))))))).
% 0.72/0.89 Axiom ax24:(((eq (fofType->Prop)) c_exactly2) (fun (X0:fofType)=> ((c_and (c_atleast2 X0)) (c_not (c_atleast3 X0))))).
% 0.72/0.89 Axiom ax25:(((eq (fofType->Prop)) c_exactly3) (fun (X0:fofType)=> ((c_and (c_atleast3 X0)) (c_not (c_atleast4 X0))))).
% 0.72/0.89 Axiom ax26:(((eq (fofType->Prop)) c_exactly4) (fun (X0:fofType)=> ((c_and (c_atleast4 X0)) (c_not (c_atleast5 X0))))).
% 0.72/0.89 Axiom ax27:(((eq (fofType->Prop)) c_exactly5) (fun (X0:fofType)=> ((c_and (c_atleast5 X0)) (c_not (c_atleast6 X0))))).
% 0.72/0.89 Axiom ax28:(((eq ((fofType->Prop)->Prop)) c_exu_i) (fun (X0:(fofType->Prop))=> ((c_and ((ex fofType) (fun (X1:fofType)=> (X0 X1)))) (forall (X1:fofType) (X2:fofType), ((X0 X1)->((X0 X2)->(((eq fofType) X1) X2))))))).
% 0.72/0.89 Axiom ax29:(((eq ((fofType->(fofType->Prop))->Prop)) c_reflexive_i) (fun (X0:(fofType->(fofType->Prop)))=> (forall (X1:fofType), ((X0 X1) X1)))).
% 0.72/0.89 Axiom ax30:(((eq ((fofType->(fofType->Prop))->Prop)) c_irreflexive_i) (fun (X0:(fofType->(fofType->Prop)))=> (forall (X1:fofType), (c_not ((X0 X1) X1))))).
% 0.72/0.89 Axiom ax31:(((eq ((fofType->(fofType->Prop))->Prop)) c_symmetric_i) (fun (X0:(fofType->(fofType->Prop)))=> (forall (X1:fofType) (X2:fofType), (((X0 X1) X2)->((X0 X2) X1))))).
% 0.72/0.89 Axiom ax32:(((eq ((fofType->(fofType->Prop))->Prop)) c_antisymmetric_i) (fun (X0:(fofType->(fofType->Prop)))=> (forall (X1:fofType) (X2:fofType), (((X0 X1) X2)->(((X0 X2) X1)->(((eq fofType) X1) X2)))))).
% 0.72/0.89 Axiom ax33:(((eq ((fofType->(fofType->Prop))->Prop)) c_transitive_i) (fun (X0:(fofType->(fofType->Prop)))=> (forall (X1:fofType) (X2:fofType) (X3:fofType), (((X0 X1) X2)->(((X0 X2) X3)->((X0 X1) X3)))))).
% 0.72/0.89 Axiom ax34:(((eq ((fofType->(fofType->Prop))->Prop)) c_eqreln_i) (fun (X0:(fofType->(fofType->Prop)))=> ((c_and ((c_and (c_reflexive_i X0)) (c_symmetric_i X0))) (c_transitive_i X0)))).
% 0.72/0.89 Axiom ax35:(((eq ((fofType->(fofType->Prop))->Prop)) c_per_i) (fun (X0:(fofType->(fofType->Prop)))=> ((c_and (c_symmetric_i X0)) (c_transitive_i X0)))).
% 0.72/0.89 Axiom ax36:(((eq ((fofType->(fofType->Prop))->Prop)) c_linear_i) (fun (X0:(fofType->(fofType->Prop)))=> (forall (X1:fofType) (X2:fofType), ((c_or ((X0 X1) X2)) ((X0 X2) X1))))).
% 0.72/0.89 Axiom ax37:(((eq ((fofType->(fofType->Prop))->Prop)) c_trichotomous_or_i) (fun (X0:(fofType->(fofType->Prop)))=> (forall (X1:fofType) (X2:fofType), ((c_or ((c_or ((X0 X1) X2)) (((eq fofType) X1) X2))) ((X0 X2) X1))))).
% 0.72/0.89 Axiom ax38:(((eq ((fofType->(fofType->Prop))->Prop)) c_partialorder_i) (fun (X0:(fofType->(fofType->Prop)))=> ((c_and ((c_and (c_reflexive_i X0)) (c_antisymmetric_i X0))) (c_transitive_i X0)))).
% 0.72/0.89 Axiom ax39:(((eq ((fofType->(fofType->Prop))->Prop)) c_totalorder_i) (fun (X0:(fofType->(fofType->Prop)))=> ((c_and (c_partialorder_i X0)) (c_linear_i X0)))).
% 0.72/0.89 Axiom ax40:(((eq ((fofType->(fofType->Prop))->Prop)) c_strictpartialorder_i) (fun (X0:(fofType->(fofType->Prop)))=> ((c_and (c_irreflexive_i X0)) (c_transitive_i X0)))).
% 0.72/0.89 Axiom ax41:(((eq ((fofType->(fofType->Prop))->Prop)) c_stricttotalorder_i) (fun (X0:(fofType->(fofType->Prop)))=> ((c_and (c_strictpartialorder_i X0)) (c_trichotomous_or_i X0)))).
% 0.72/0.89 Axiom ax42:(((eq (Prop->(fofType->(fofType->fofType)))) c_If_i) (fun (X0:Prop) (X1:fofType) (X2:fofType)=> (c_Eps_i (fun (X3:fofType)=> ((c_or ((c_and X0) (((eq fofType) X3) X1))) ((c_and (c_not X0)) (((eq fofType) X3) X2))))))).
% 0.72/0.89 Axiom ax43:(((eq (Prop->(Prop->Prop))) c_exactly1of2) (fun (X0:Prop) (X1:Prop)=> ((c_or ((c_and X0) (c_not X1))) ((c_and (c_not X0)) X1)))).
% 0.72/0.89 Axiom ax44:(((eq (Prop->(Prop->(Prop->Prop)))) c_exactly1of3) (fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((c_or ((c_and ((c_exactly1of2 X0) X1)) (c_not X2))) ((c_and ((c_and (c_not X0)) (c_not X1))) X2)))).
% 0.72/0.89 Axiom ax45:(((eq (fofType->(fofType->Prop))) c_nIn) (fun (X0:fofType) (X1:fofType)=> (c_not ((c_In X0) X1)))).
% 0.72/0.89 Axiom ax46:(((eq (fofType->(fofType->Prop))) c_nSubq) (fun (X0:fofType) (X1:fofType)=> (c_not ((c_Subq X0) X1)))).
% 0.72/0.89 Axiom ax47:(((eq (fofType->(fofType->fofType))) c_UPair) (fun (X0:fofType) (X1:fofType)=> ((c_Repl (c_Power (c_Power c_Empty))) (fun (X2:fofType)=> (((c_If_i ((c_In c_Empty) X2)) X0) X1))))).
% 0.72/0.89 Axiom ax48:(((eq (fofType->fofType)) c_Sing) (fun (X0:fofType)=> ((c_UPair X0) X0))).
% 0.72/0.89 Axiom ax49:(((eq (fofType->(fofType->fofType))) c_binunion) (fun (X0:fofType) (X1:fofType)=> (c_Union ((c_UPair X0) X1)))).
% 0.72/0.89 Axiom ax50:(((eq (fofType->(fofType->fofType))) c_SetAdjoin) (fun (X0:fofType) (X1:fofType)=> ((c_binunion X0) (c_Sing X1)))).
% 0.72/0.89 Axiom ax51:(((eq (fofType->((fofType->fofType)->fofType))) c_famunion) (fun (X0:fofType) (X1:(fofType->fofType))=> (c_Union ((c_Repl X0) (fun (X2:fofType)=> (X1 X2)))))).
% 0.72/0.89 Axiom ax52:(((eq (fofType->((fofType->Prop)->fofType))) c_Sep) (fun (X0:fofType) (X1:(fofType->Prop))=> (((c_If_i ((ex fofType) (fun (X2:fofType)=> ((c_and ((c_In X2) X0)) (X1 X2))))) ((c_Repl X0) (fun (X2:fofType)=> ((fun (X3:fofType)=> (((c_If_i (X1 X3)) X3) (c_Eps_i (fun (X4:fofType)=> ((c_and ((c_In X4) X0)) (X1 X4)))))) X2)))) c_Empty))).
% 0.72/0.89 Axiom ax53:(((eq (fofType->((fofType->Prop)->((fofType->fofType)->fofType)))) c_ReplSep) (fun (X0:fofType) (X1:(fofType->Prop)) (X2:(fofType->fofType))=> ((c_Repl ((c_Sep X0) (fun (X3:fofType)=> (X1 X3)))) (fun (X3:fofType)=> (X2 X3))))).
% 0.72/0.89 Axiom ax54:(((eq (fofType->(fofType->fofType))) c_binintersect) (fun (X0:fofType) (X1:fofType)=> ((c_Sep X0) (fun (X2:fofType)=> ((c_In X2) X1))))).
% 0.72/0.89 Axiom ax55:(((eq (fofType->(fofType->fofType))) c_setminus) (fun (X0:fofType) (X1:fofType)=> ((c_Sep X0) (fun (X2:fofType)=> ((c_nIn X2) X1))))).
% 0.72/0.89 Axiom ax56:(((eq (fofType->(fofType->((fofType->fofType)->Prop)))) c_inj) (fun (X0:fofType) (X1:fofType) (X2:(fofType->fofType))=> ((c_and (forall (X3:fofType), (((c_In X3) X0)->((c_In (X2 X3)) X1)))) (forall (X3:fofType), (((c_In X3) X0)->(forall (X4:fofType), (((c_In X4) X0)->((((eq fofType) (X2 X3)) (X2 X4))->(((eq fofType) X3) X4))))))))).
% 0.72/0.89 Axiom ax57:(((eq (fofType->(fofType->((fofType->fofType)->Prop)))) c_bij) (fun (X0:fofType) (X1:fofType) (X2:(fofType->fofType))=> ((c_and (((c_inj X0) X1) X2)) (forall (X3:fofType), (((c_In X3) X1)->((ex fofType) (fun (X4:fofType)=> ((c_and ((c_In X4) X0)) (((eq fofType) (X2 X4)) X3))))))))).
% 0.72/0.89 Axiom ax58:(((eq (fofType->(fofType->Prop))) c_atleastp) (fun (X0:fofType) (X1:fofType)=> ((ex (fofType->fofType)) (fun (X2:(fofType->fofType))=> (((c_inj X0) X1) X2))))).
% 0.72/0.89 Axiom ax59:(((eq (fofType->(fofType->Prop))) c_equip) (fun (X0:fofType) (X1:fofType)=> ((ex (fofType->fofType)) (fun (X2:(fofType->fofType))=> (((c_bij X0) X1) X2))))).
% 0.72/0.89 Axiom ax60:(((eq ((fofType->((fofType->fofType)->fofType))->(fofType->(fofType->Prop)))) c_In_rec_poly_G_i) (fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType) (X2:fofType)=> (forall (X3:(fofType->(fofType->Prop))), ((forall (X4:fofType) (X5:(fofType->fofType)), ((forall (X6:fofType), (((c_In X6) X4)->((X3 X6) (X5 X6))))->((X3 X4) ((X0 X4) X5))))->((X3 X1) X2))))).
% 0.72/0.89 Axiom ax61:(((eq ((fofType->((fofType->fofType)->fofType))->(fofType->fofType))) c_In_rec_poly_i) (fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType)=> (c_Eps_i (fun (X2:fofType)=> (((c_In_rec_poly_G_i X0) X1) X2))))).
% 0.72/0.89 Axiom ax62:(((eq (fofType->fofType)) c_ordsucc) (fun (X0:fofType)=> ((c_binunion X0) (c_Sing X0)))).
% 0.72/0.89 Axiom ax63:(((eq (fofType->Prop)) c_nat_p) (fun (X0:fofType)=> (forall (X1:(fofType->Prop)), ((X1 c_Empty)->((forall (X2:fofType), ((X1 X2)->(X1 (c_ordsucc X2))))->(X1 X0)))))).
% 0.72/0.89 Axiom ax64:(((eq (fofType->((fofType->(fofType->fofType))->(fofType->fofType)))) c_nat_primrec) (fun (X0:fofType) (X1:(fofType->(fofType->fofType)))=> (c_In_rec_poly_i (fun (X2:fofType) (X3:(fofType->fofType))=> (((c_If_i ((c_In (c_Union X2)) X2)) ((X1 (c_Union X2)) (X3 (c_Union X2)))) X0))))).
% 0.72/0.89 Axiom ax65:(((eq (fofType->(fofType->fofType))) c_add_nat) (fun (X0:fofType) (X1:fofType)=> (((c_nat_primrec X0) (fun (X2:fofType) (X3:fofType)=> (c_ordsucc X3))) X1))).
% 0.72/0.89 Axiom ax66:(((eq (fofType->(fofType->fofType))) c_mul_nat) (fun (X0:fofType) (X1:fofType)=> (((c_nat_primrec c_Empty) (fun (X2:fofType) (X3:fofType)=> ((c_add_nat X0) X3))) X1))).
% 0.72/0.89 Axiom ax67:(((eq (fofType->Prop)) c_ordinal) (fun (X0:fofType)=> ((c_and (c_TransSet X0)) (forall (X1:fofType), (((c_In X1) X0)->(c_TransSet X1)))))).
% 0.72/0.89 Axiom ax68:(((eq (fofType->fofType)) c_V_) (c_In_rec_poly_i (fun (X0:fofType) (X1:(fofType->fofType))=> ((c_famunion X0) (fun (X2:fofType)=> (c_Power (X1 X2))))))).
% 0.72/0.89 Axiom ax69:(((eq (fofType->fofType)) c_Inj1) (c_In_rec_poly_i (fun (X0:fofType) (X1:(fofType->fofType))=> ((c_binunion (c_Sing c_Empty)) ((c_Repl X0) (fun (X2:fofType)=> (X1 X2))))))).
% 0.72/0.89 Axiom ax70:(((eq (fofType->fofType)) c_Inj0) (fun (X0:fofType)=> ((c_Repl X0) (fun (X1:fofType)=> (c_Inj1 X1))))).
% 0.72/0.89 Axiom ax71:(((eq (fofType->fofType)) c_Unj) (c_In_rec_poly_i (fun (X0:fofType) (X1:(fofType->fofType))=> ((c_Repl ((c_setminus X0) (c_Sing c_Empty))) (fun (X2:fofType)=> (X1 X2)))))).
% 0.72/0.89 Axiom ax72:(((eq (fofType->(fofType->((fofType->fofType)->((fofType->fofType)->(fofType->fofType)))))) c_combine_funcs) (fun (X0:fofType) (X1:fofType) (X2:(fofType->fofType)) (X3:(fofType->fofType)) (X4:fofType)=> (((c_If_i (((eq fofType) X4) (c_Inj0 (c_Unj X4)))) (X2 (c_Unj X4))) (X3 (c_Unj X4))))).
% 0.72/0.89 Axiom ax73:(((eq (fofType->(fofType->fofType))) c_setsum) (fun (X0:fofType) (X1:fofType)=> ((c_binunion ((c_Repl X0) (fun (X2:fofType)=> (c_Inj0 X2)))) ((c_Repl X1) (fun (X2:fofType)=> (c_Inj1 X2)))))).
% 0.72/0.89 Axiom ax74:(((eq (fofType->fofType)) c_proj0) (fun (X0:fofType)=> (((c_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (c_Inj0 X2)) X1))))) (fun (X1:fofType)=> (c_Unj X1))))).
% 0.72/0.89 Axiom ax75:(((eq (fofType->fofType)) c_proj1) (fun (X0:fofType)=> (((c_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (c_Inj1 X2)) X1))))) (fun (X1:fofType)=> (c_Unj X1))))).
% 0.72/0.89 Axiom ax76:(((eq (fofType->(fofType->fofType))) c_binrep) (fun (X0:fofType) (X1:fofType)=> ((c_setsum X0) (c_Power X1)))).
% 0.72/0.89 Axiom ax77:(((eq (fofType->((fofType->fofType)->fofType))) c_lam) (fun (X0:fofType) (X1:(fofType->fofType))=> ((c_famunion X0) (fun (X2:fofType)=> ((c_Repl (X1 X2)) (fun (X3:fofType)=> ((c_setsum X2) X3))))))).
% 0.72/0.89 Axiom ax78:(((eq (fofType->(fofType->fofType))) c_setprod) (fun (X0:fofType) (X1:fofType)=> ((c_lam X0) (fun (X2:fofType)=> X1)))).
% 0.72/0.89 Axiom ax79:(((eq (fofType->(fofType->fofType))) c_ap) (fun (X0:fofType) (X1:fofType)=> (((c_ReplSep X0) (fun (X2:fofType)=> ((ex fofType) (fun (X3:fofType)=> (((eq fofType) X2) ((c_setsum X1) X3)))))) (fun (X2:fofType)=> (c_proj1 X2))))).
% 0.72/0.89 Axiom ax80:(((eq (fofType->Prop)) c_setsum_p) (fun (X0:fofType)=> (((eq fofType) ((c_setsum ((c_ap X0) c_Empty)) ((c_ap X0) (c_ordsucc c_Empty)))) X0))).
% 0.72/0.89 Axiom ax81:(((eq (fofType->(fofType->Prop))) c_tuple_p) (fun (X0:fofType) (X1:fofType)=> (forall (X2:fofType), (((c_In X2) X1)->((ex fofType) (fun (X3:fofType)=> ((c_and ((c_In X3) X0)) ((ex fofType) (fun (X4:fofType)=> (((eq fofType) X2) ((c_setsum X3) X4))))))))))).
% 0.72/0.89 Axiom ax82:(((eq (fofType->((fofType->fofType)->fofType))) c_Pi) (fun (X0:fofType) (X1:(fofType->fofType))=> ((c_Sep (c_Power ((c_lam X0) (fun (X2:fofType)=> (c_Union (X1 X2)))))) (fun (X2:fofType)=> (forall (X3:fofType), (((c_In X3) X0)->((c_In ((c_ap X2) X3)) (X1 X3)))))))).
% 0.72/0.89 Axiom ax83:(((eq (fofType->(fofType->fofType))) c_setexp) (fun (X0:fofType) (X1:fofType)=> ((c_Pi X1) (fun (X2:fofType)=> X0)))).
% 0.72/0.90 Axiom ax84:(((eq (fofType->((fofType->fofType)->((fofType->(fofType->Prop))->fofType)))) c_Sep2) (fun (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->(fofType->Prop)))=> ((c_Sep ((c_lam X0) (fun (X3:fofType)=> (X1 X3)))) (fun (X3:fofType)=> ((X2 ((c_ap X3) c_Empty)) ((c_ap X3) (c_ordsucc c_Empty))))))).
% 0.72/0.90 Axiom ax85:(((eq (fofType->Prop)) c_set_of_pairs) (fun (X0:fofType)=> (forall (X1:fofType), (((c_In X1) X0)->((ex fofType) (fun (X2:fofType)=> ((ex fofType) (fun (X3:fofType)=> (((eq fofType) X1) ((c_lam (c_ordsucc (c_ordsucc c_Empty))) (fun (X4:fofType)=> (((c_If_i (((eq fofType) X4) c_Empty)) X2) X3)))))))))))).
% 0.72/0.90 Axiom ax86:(((eq (fofType->((fofType->fofType)->((fofType->(fofType->fofType))->fofType)))) c_lam2) (fun (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->(fofType->fofType)))=> ((c_lam X0) (fun (X3:fofType)=> ((c_lam (X1 X3)) (fun (X4:fofType)=> ((X2 X3) X4))))))).
% 0.72/0.90 Axiom ax87:(((eq (fofType->((fofType->Prop)->((fofType->Prop)->Prop)))) c_PNoEq_) (fun (X0:fofType) (X1:(fofType->Prop)) (X2:(fofType->Prop))=> (forall (X3:fofType), (((c_In X3) X0)->((c_iff (X1 X3)) (X2 X3)))))).
% 0.72/0.90 Axiom ax88:(((eq (fofType->((fofType->Prop)->((fofType->Prop)->Prop)))) c_PNoLt_) (fun (X0:fofType) (X1:(fofType->Prop)) (X2:(fofType->Prop))=> ((ex fofType) (fun (X3:fofType)=> ((c_and ((c_In X3) X0)) ((c_and ((c_and (((c_PNoEq_ X3) X1) X2)) (c_not (X1 X3)))) (X2 X3))))))).
% 0.72/0.90 Axiom ax89:(((eq (fofType->((fofType->Prop)->(fofType->((fofType->Prop)->Prop))))) c_PNoLt) (fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType) (X3:(fofType->Prop))=> ((c_or ((c_or (((c_PNoLt_ ((c_binintersect X0) X2)) X1) X3)) ((c_and ((c_and ((c_In X0) X2)) (((c_PNoEq_ X0) X1) X3))) (X3 X0)))) ((c_and ((c_and ((c_In X2) X0)) (((c_PNoEq_ X2) X1) X3))) (c_not (X1 X2)))))).
% 0.72/0.90 Axiom ax90:(((eq (fofType->((fofType->Prop)->(fofType->((fofType->Prop)->Prop))))) c_PNoLe) (fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType) (X3:(fofType->Prop))=> ((c_or ((((c_PNoLt X0) X1) X2) X3)) ((c_and (((eq fofType) X0) X2)) (((c_PNoEq_ X0) X1) X3))))).
% 0.72/0.90 Axiom ax91:(((eq ((fofType->((fofType->Prop)->Prop))->(fofType->((fofType->Prop)->Prop)))) c_PNo_downc) (fun (X0:(fofType->((fofType->Prop)->Prop))) (X1:fofType) (X2:(fofType->Prop))=> ((ex fofType) (fun (X3:fofType)=> ((c_and (c_ordinal X3)) ((ex (fofType->Prop)) (fun (X4:(fofType->Prop))=> ((c_and ((X0 X3) X4)) ((((c_PNoLe X1) X2) X3) X4))))))))).
% 0.72/0.90 Axiom ax92:(((eq ((fofType->((fofType->Prop)->Prop))->(fofType->((fofType->Prop)->Prop)))) c_PNo_upc) (fun (X0:(fofType->((fofType->Prop)->Prop))) (X1:fofType) (X2:(fofType->Prop))=> ((ex fofType) (fun (X3:fofType)=> ((c_and (c_ordinal X3)) ((ex (fofType->Prop)) (fun (X4:(fofType->Prop))=> ((c_and ((X0 X3) X4)) ((((c_PNoLe X3) X4) X1) X2))))))))).
% 0.72/0.90 Axiom ax93:(((eq (fofType->fofType)) c_SNoElts_) (fun (X0:fofType)=> ((c_binunion X0) ((c_Repl X0) (fun (X1:fofType)=> ((fun (X2:fofType)=> ((c_SetAdjoin X2) (c_Sing (c_ordsucc c_Empty)))) X1)))))).
% 0.72/0.90 Axiom ax94:(((eq (fofType->(fofType->Prop))) c_SNo_) (fun (X0:fofType) (X1:fofType)=> ((c_and ((c_Subq X1) (c_SNoElts_ X0))) (forall (X2:fofType), (((c_In X2) X0)->((c_exactly1of2 ((c_In ((fun (X3:fofType)=> ((c_SetAdjoin X3) (c_Sing (c_ordsucc c_Empty)))) X2)) X1)) ((c_In X2) X1))))))).
% 0.72/0.90 Axiom ax95:(((eq (fofType->((fofType->Prop)->fofType))) c_PSNo) (fun (X0:fofType) (X1:(fofType->Prop))=> ((c_binunion ((c_Sep X0) (fun (X2:fofType)=> (X1 X2)))) (((c_ReplSep X0) (fun (X2:fofType)=> (c_not (X1 X2)))) (fun (X2:fofType)=> ((fun (X3:fofType)=> ((c_SetAdjoin X3) (c_Sing (c_ordsucc c_Empty)))) X2)))))).
% 0.72/0.90 Axiom ax96:(((eq (fofType->Prop)) c_SNo) (fun (X0:fofType)=> ((ex fofType) (fun (X1:fofType)=> ((c_and (c_ordinal X1)) ((c_SNo_ X1) X0)))))).
% 0.72/0.90 Axiom ax97:(((eq (fofType->fofType)) c_SNoLev) (fun (X0:fofType)=> (c_Eps_i (fun (X1:fofType)=> ((c_and (c_ordinal X1)) ((c_SNo_ X1) X0)))))).
% 0.72/0.90 Axiom ax98:(((eq (fofType->(fofType->(fofType->Prop)))) c_SNoEq_) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((c_PNoEq_ X0) (fun (X3:fofType)=> ((c_In X3) X1))) (fun (X3:fofType)=> ((c_In X3) X2))))).
% 0.72/0.90 Axiom ax99:(((eq (fofType->(fofType->Prop))) c_SNoLt) (fun (X0:fofType) (X1:fofType)=> ((((c_PNoLt (c_SNoLev X0)) (fun (X2:fofType)=> ((c_In X2) X0))) (c_SNoLev X1)) (fun (X2:fofType)=> ((c_In X2) X1))))).
% 0.72/0.90 Axiom ax100:(((eq (fofType->(fofType->Prop))) c_SNoLe) (fun (X0:fofType) (X1:fofType)=> ((((c_PNoLe (c_SNoLev X0)) (fun (X2:fofType)=> ((c_In X2) X0))) (c_SNoLev X1)) (fun (X2:fofType)=> ((c_In X2) X1))))).
% 0.72/0.90 Axiom ax101:(((eq (fofType->((fofType->(fofType->fofType))->Prop))) c_binop_on) (fun (X0:fofType) (X1:(fofType->(fofType->fofType)))=> (forall (X2:fofType), (((c_In X2) X0)->(forall (X3:fofType), (((c_In X3) X0)->((c_In ((X1 X2) X3)) X0))))))).
% 0.72/0.90 Axiom ax102:(((eq (fofType->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->(fofType->Prop)))))) c_Loop) (fun (X0:fofType) (X1:(fofType->(fofType->fofType))) (X2:(fofType->(fofType->fofType))) (X3:(fofType->(fofType->fofType))) (X4:fofType)=> ((c_and ((c_and ((c_and ((c_and ((c_binop_on X0) X1)) ((c_binop_on X0) X2))) ((c_binop_on X0) X3))) (forall (X5:fofType), (((c_In X5) X0)->((c_and (((eq fofType) ((X1 X4) X5)) X5)) (((eq fofType) ((X1 X5) X4)) X5)))))) (forall (X5:fofType), (((c_In X5) X0)->(forall (X6:fofType), (((c_In X6) X0)->((c_and ((c_and ((c_and (((eq fofType) ((X2 X5) ((X1 X5) X6))) X6)) (((eq fofType) ((X1 X5) ((X2 X5) X6))) X6))) (((eq fofType) ((X3 ((X1 X5) X6)) X6)) X5))) (((eq fofType) ((X1 ((X3 X5) X6)) X6)) X5))))))))).
% 0.72/0.90 Axiom ax103:(((eq (fofType->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->(fofType->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->Prop))))))))))))))) c_Loop_with_defs) (fun (X0:fofType) (X1:(fofType->(fofType->fofType))) (X2:(fofType->(fofType->fofType))) (X3:(fofType->(fofType->fofType))) (X4:fofType) (X5:(fofType->(fofType->fofType))) (X6:(fofType->(fofType->(fofType->fofType)))) (X7:(fofType->(fofType->fofType))) (X8:(fofType->(fofType->(fofType->fofType)))) (X9:(fofType->(fofType->(fofType->fofType)))) (X10:(fofType->(fofType->fofType))) (X11:(fofType->(fofType->fofType))) (X12:(fofType->(fofType->fofType))) (X13:(fofType->(fofType->fofType)))=> ((c_and ((c_and ((c_and ((c_and (((((c_Loop X0) X1) X2) X3) X4)) (forall (X14:fofType), (((c_In X14) X0)->(forall (X15:fofType), (((c_In X15) X0)->(((eq fofType) ((X5 X14) X15)) ((X2 ((X1 X15) X14)) ((X1 X14) X15))))))))) (forall (X14:fofType), (((c_In X14) X0)->(forall (X15:fofType), (((c_In X15) X0)->(forall (X16:fofType), (((c_In X16) X0)->(((eq fofType) (((X6 X14) X15) X16)) ((X2 ((X1 X14) ((X1 X15) X16))) ((X1 ((X1 X14) X15)) X16))))))))))) (forall (X14:fofType), (((c_In X14) X0)->(forall (X15:fofType), (((c_In X15) X0)->((c_and ((c_and ((c_and ((c_and (((eq fofType) ((X7 X14) X15)) ((X2 X14) ((X1 X15) X14)))) (((eq fofType) ((X10 X14) X15)) ((X1 X14) ((X1 X15) ((X2 X14) X4)))))) (((eq fofType) ((X11 X14) X15)) ((X1 ((X1 ((X3 X4) X14)) X15)) X14)))) (((eq fofType) ((X12 X14) X15)) ((X1 ((X2 X14) X15)) ((X2 ((X2 X14) X4)) X4))))) (((eq fofType) ((X13 X14) X15)) ((X1 ((X3 X4) ((X3 X4) X14))) ((X3 X15) X14)))))))))) (forall (X14:fofType), (((c_In X14) X0)->(forall (X15:fofType), (((c_In X15) X0)->(forall (X16:fofType), (((c_In X16) X0)->((c_and (((eq fofType) (((X8 X14) X15) X16)) ((X2 ((X1 X15) X14)) ((X1 X15) ((X1 X14) X16))))) (((eq fofType) (((X9 X14) X15) X16)) ((X3 ((X1 ((X1 X16) X14)) X15)) ((X1 X14) X15))))))))))))).
% 0.72/0.90 Axiom ax104:(((eq (fofType->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->(fofType->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->Prop))))))))))))))) c_Loop_with_defs_cex1) (fun (X0:fofType) (X1:(fofType->(fofType->fofType))) (X2:(fofType->(fofType->fofType))) (X3:(fofType->(fofType->fofType))) (X4:fofType) (X5:(fofType->(fofType->fofType))) (X6:(fofType->(fofType->(fofType->fofType)))) (X7:(fofType->(fofType->fofType))) (X8:(fofType->(fofType->(fofType->fofType)))) (X9:(fofType->(fofType->(fofType->fofType)))) (X10:(fofType->(fofType->fofType))) (X11:(fofType->(fofType->fofType))) (X12:(fofType->(fofType->fofType))) (X13:(fofType->(fofType->fofType)))=> ((c_and ((((((((((((((c_Loop_with_defs X0) X1) X2) X3) X4) X5) X6) X7) X8) X9) X10) X11) X12) X13)) ((ex fofType) (fun (X14:fofType)=> ((c_and ((c_In X14) X0)) ((ex fofType) (fun (X15:fofType)=> ((c_and ((c_In X15) X0)) ((ex fofType) (fun (X16:fofType)=> ((c_and ((c_In X16) X0)) ((ex fofType) (fun (X17:fofType)=> ((c_and ((c_In X17) X0)) (c_not (((eq fofType) ((X5 ((X1 ((X2 (((X8 X15) X16) X14)) X4)) X14)) X17)) X4))))))))))))))))).
% 0.72/0.91 Axiom ax105:(((eq (fofType->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->(fofType->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->(fofType->fofType)))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->((fofType->(fofType->fofType))->Prop))))))))))))))) c_Loop_with_defs_cex2) (fun (X0:fofType) (X1:(fofType->(fofType->fofType))) (X2:(fofType->(fofType->fofType))) (X3:(fofType->(fofType->fofType))) (X4:fofType) (X5:(fofType->(fofType->fofType))) (X6:(fofType->(fofType->(fofType->fofType)))) (X7:(fofType->(fofType->fofType))) (X8:(fofType->(fofType->(fofType->fofType)))) (X9:(fofType->(fofType->(fofType->fofType)))) (X10:(fofType->(fofType->fofType))) (X11:(fofType->(fofType->fofType))) (X12:(fofType->(fofType->fofType))) (X13:(fofType->(fofType->fofType)))=> ((c_and ((((((((((((((c_Loop_with_defs X0) X1) X2) X3) X4) X5) X6) X7) X8) X9) X10) X11) X12) X13)) ((ex fofType) (fun (X14:fofType)=> ((c_and ((c_In X14) X0)) ((ex fofType) (fun (X15:fofType)=> ((c_and ((c_In X15) X0)) ((ex fofType) (fun (X16:fofType)=> ((c_and ((c_In X16) X0)) ((ex fofType) (fun (X17:fofType)=> ((c_and ((c_In X17) X0)) ((ex fofType) (fun (X18:fofType)=> ((c_and ((c_In X18) X0)) (c_not (((eq fofType) (((X6 X18) ((X1 ((X3 X4) X14)) (((X9 X15) X16) X14))) X17)) X4)))))))))))))))))))).
% 0.72/0.91 Axiom ax106:(((eq (fofType->Prop)) c_combinator) (fun (X0:fofType)=> (forall (X1:(fofType->Prop)), ((X1 (c_Inj0 c_Empty))->((X1 (c_Inj0 (c_Power c_Empty)))->((forall (X2:fofType) (X3:fofType), ((X1 X2)->((X1 X3)->(X1 (c_Inj1 ((c_setsum X2) X3))))))->(X1 X0))))))).
% 0.72/0.91 Axiom ax107:(((eq (fofType->(fofType->Prop))) c_combinator_equiv) (fun (X0:fofType) (X1:fofType)=> (forall (X2:(fofType->(fofType->Prop))), ((((fun (X3:fofType) (X4:fofType) (X5:(fofType->(fofType->fofType)))=> ((c_per_i X2)->((forall (X6:fofType), ((c_combinator X6)->((X2 X6) X6)))->((forall (X6:fofType) (X7:fofType) (X8:fofType) (X9:fofType), ((c_combinator X6)->((c_combinator X7)->((c_combinator X8)->((c_combinator X9)->(((X2 X6) X8)->(((X2 X7) X9)->((X2 ((X5 X6) X7)) ((X5 X8) X9)))))))))->((forall (X6:fofType) (X7:fofType), ((X2 ((X5 ((X5 X3) X6)) X7)) X6))->((forall (X6:fofType) (X7:fofType) (X8:fofType), ((X2 ((X5 ((X5 ((X5 X4) X6)) X7)) X8)) ((X5 ((X5 X6) X8)) ((X5 X7) X8))))->((X2 X0) X1))))))) (c_Inj0 c_Empty)) (c_Inj0 (c_Power c_Empty))) (fun (X3:fofType) (X4:fofType)=> (c_Inj1 ((c_setsum X3) X4))))))).
% 0.72/0.91 Axiom ax108:(((eq (fofType->(fofType->(fofType->Prop)))) c_equip_mod) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((ex fofType) (fun (X3:fofType)=> ((ex fofType) (fun (X4:fofType)=> ((c_or ((c_and ((c_equip ((c_setsum X0) X3)) X1)) ((c_equip ((c_setprod X4) X3)) X2))) ((c_and ((c_equip ((c_setsum X1) X3)) X0)) ((c_equip ((c_setprod X4) X3)) X2))))))))).
% 0.72/0.91 Trying to prove (c_not (forall (X0:((fofType->(fofType->(((fofType->fofType)->(fofType->fofType))->fofType)))->(fofType->(fofType->Prop)))) (X1:((fofType->(((fofType->fofType)->fofType)->fofType))->(fofType->Prop))) (X2:((fofType->fofType)->(((((fofType->fofType)->fofType)->fofType)->((fofType->(fofType->fofType))->(fofType->(fofType->fofType))))->(fofType->Prop)))) (X3:((fofType->((fofType->(fofType->fofType))->fofType))->(fofType->(fofType->Prop)))), ((forall (X4:(((fofType->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))->fofType)) (X5:fofType) (X6:fofType), (fofType->(((c_In (c_Inj0 X6)) ((c_setsum ((c_setsum c_Empty) c_Empty)) ((c_setsum X6) (c_Inj0 ((c_setsum c_Empty) c_Empty)))))->((((X2 (fun (X8:fofType)=> (c_Inj0 (c_Inj0 c_Empty)))) (fun (X8:(((fofType->fofType)->fofType)->fofType)) (X9:(fofType->(fofType->fofType))) (X10:fofType) (X11:fofType)=> X10)) ((c_setsum (X4 (fun (X8:(fofType->(fofType->fofType))) (X9:(fofType->fofType)) (X10:fofType)=> (c_Inj0 ((c_setsum c_Empty) c_Empty))))) c_Empty))->(((X3 (fun (X8:fofType) (X9:(fofType->(fofType->fofType)))=> (c_Inj0 X8))) X5) ((c_setsum ((c_setsum ((c_setsum c_Empty) ((c_setsum c_Empty) c_Empty))) (c_Inj0 c_Empty))) c_Empty))))))->((forall (X4:((((fofType->fofType)->(fofType->fofType))->fofType)->fofType)), ((fofType->fofType)->(forall (X6:fofType) (X7:fofType), ((((X3 (fun (X8:fofType) (X9:(fofType->(fofType->fofType)))=> c_Empty)) X7) ((c_setsum ((c_setsum ((c_setsum ((c_setsum c_Empty) c_Empty)) c_Empty)) ((c_setsum ((c_setsum c_Empty) c_Empty)) (c_Inj0 c_Empty)))) ((c_setsum c_Empty) (c_Inj1 ((c_setsum c_Empty) c_Empty)))))->(((X3 (fun (X8:fofType) (X9:(fofType->(fofType->fofType)))=> X7)) ((c_setsum (X4 (fun (X8:((fofType->fofType)->(fofType->fofType)))=> X7))) X6)) (c_Inj0 (c_Inj1 ((c_setsum ((c_setsum c_Empty) c_Empty)) ((c_setsum c_Empty) c_Empty)))))))))->((fofType->(forall (X5:(fofType->(((fofType->fofType)->(fofType->fofType))->fofType))) (X6:((((fofType->fofType)->(fofType->fofType))->((fofType->fofType)->(fofType->fofType)))->((fofType->(fofType->fofType))->fofType))) (X7:fofType), (((c_In (c_Inj0 c_Empty)) ((c_setsum c_Empty) ((X5 (c_Inj0 ((c_setsum c_Empty) c_Empty))) (fun (X8:(fofType->fofType)) (X9:fofType)=> (c_Inj0 c_Empty)))))->((((X0 (fun (X8:fofType) (X9:fofType) (X10:((fofType->fofType)->(fofType->fofType)))=> X8)) X7) ((X6 (fun (X8:((fofType->fofType)->(fofType->fofType))) (X9:(fofType->fofType)) (X10:fofType)=> (c_Inj1 c_Empty))) (fun (X8:fofType) (X9:fofType)=> c_Empty)))->(((X2 (fun (X8:fofType)=> X8)) (fun (X8:(((fofType->fofType)->fofType)->fofType)) (X9:(fofType->(fofType->fofType))) (X10:fofType) (X11:fofType)=> X10)) ((c_setsum (c_Inj0 c_Empty)) ((X6 (fun (X8:((fofType->fofType)->(fofType->fofType))) (X9:(fofType->fofType)) (X10:fofType)=> (c_Inj0 c_Empty))) (fun (X8:fofType) (X9:fofType)=> X9))))))))->((forall (X4:(fofType->(fofType->fofType))) (X5:(fofType->fofType)) (X6:fofType), ((fofType->fofType)->(((c_In (c_Inj0 (c_Inj1 c_Empty))) ((c_setsum ((c_setsum (c_Inj0 c_Empty)) ((c_setsum ((c_setsum c_Empty) c_Empty)) ((c_setsum c_Empty) c_Empty)))) ((c_setsum c_Empty) ((c_setsum (c_Inj0 c_Empty)) ((X4 c_Empty) c_Empty)))))->((((X2 (fun (X8:fofType)=> c_Empty)) (fun (X8:(((fofType->fofType)->fofType)->fofType)) (X9:(fofType->(fofType->fofType))) (X10:fofType) (X11:fofType)=> c_Empty)) ((c_setsum ((c_setsum c_Empty) ((c_setsum ((c_setsum c_Empty) c_Empty)) (c_Inj0 c_Empty)))) (c_Inj1 X6)))->((X1 (fun (X8:fofType) (X9:((fofType->fofType)->fofType))=> (c_Inj0 c_Empty))) ((X4 c_Empty) (X5 ((c_setsum (c_Inj1 c_Empty)) c_Empty))))))))->((fofType->((fofType->fofType)->((fofType->fofType)->(fofType->((((X3 (fun (X8:fofType) (X9:(fofType->(fofType->fofType)))=> c_Empty)) c_Empty) c_Empty)->((X1 (fun (X8:fofType) (X9:((fofType->fofType)->fofType))=> (X9 (fun (X10:fofType)=> ((c_setsum (c_Inj1 (c_Inj0 c_Empty))) ((c_setsum c_Empty) c_Empty)))))) c_Empty))))))->((forall (X4:fofType) (X5:fofType) (X6:fofType) (X7:fofType), (((c_In (c_Inj0 X6)) ((c_setsum ((c_setsum X4) ((c_setsum X5) ((c_setsum c_Empty) c_Empty)))) (c_Inj1 ((c_setsum X5) c_Empty))))->(((X1 (fun (X8:fofType) (X9:((fofType->fofType)->fofType))=> X7)) c_Empty)->(((X2 (fun (X8:fofType)=> c_Empty)) (fun (X8:(((fo
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