TSTP Solution File: NUM743^4 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM743^4 : TPTP v7.1.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n049.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32218.625MB
% OS : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Jan 8 13:11:36 EST 2018
% Result : Timeout 300.06s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.03 % Problem : NUM743^4 : TPTP v7.1.0. Released v7.1.0.
% 0.02/0.04 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.23 % Computer : n049.star.cs.uiowa.edu
% 0.03/0.23 % Model : x86_64 x86_64
% 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.23 % Memory : 32218.625MB
% 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.03/0.23 % CPULimit : 300
% 0.03/0.23 % DateTime : Fri Jan 5 13:30:04 CST 2018
% 0.03/0.24 % CPUTime :
% 0.03/0.25 Python 2.7.13
% 0.08/0.52 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.08/0.52 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/NUM007^0.ax, trying next directory
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ad8d56de290>, <kernel.DependentProduct object at 0x2ad8d56decb0>) of role type named typ_is_of
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring is_of:(fofType->((fofType->Prop)->Prop))
% 0.08/0.52 FOF formula (((eq (fofType->((fofType->Prop)->Prop))) is_of) (fun (X0:fofType) (X1:(fofType->Prop))=> (X1 X0))) of role definition named def_is_of
% 0.08/0.52 A new definition: (((eq (fofType->((fofType->Prop)->Prop))) is_of) (fun (X0:fofType) (X1:(fofType->Prop))=> (X1 X0)))
% 0.08/0.52 Defined: is_of:=(fun (X0:fofType) (X1:(fofType->Prop))=> (X1 X0))
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ad8d56de290>, <kernel.DependentProduct object at 0x2ad8d56dec20>) of role type named typ_all_of
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring all_of:((fofType->Prop)->((fofType->Prop)->Prop))
% 0.08/0.52 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) all_of) (fun (X0:(fofType->Prop)) (X1:(fofType->Prop))=> (forall (X2:fofType), (((is_of X2) X0)->(X1 X2))))) of role definition named def_all_of
% 0.08/0.52 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) all_of) (fun (X0:(fofType->Prop)) (X1:(fofType->Prop))=> (forall (X2:fofType), (((is_of X2) X0)->(X1 X2)))))
% 0.08/0.52 Defined: all_of:=(fun (X0:(fofType->Prop)) (X1:(fofType->Prop))=> (forall (X2:fofType), (((is_of X2) X0)->(X1 X2))))
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ad8d56dec20>, <kernel.DependentProduct object at 0x2ad8d56de998>) of role type named typ_eps
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring eps:((fofType->Prop)->fofType)
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ad8d56de8c0>, <kernel.DependentProduct object at 0x2ad8d56deab8>) of role type named typ_in
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring in:(fofType->(fofType->Prop))
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ad8d56dea28>, <kernel.DependentProduct object at 0x2ad8d56dec20>) of role type named typ_d_Subq
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring d_Subq:(fofType->(fofType->Prop))
% 0.08/0.52 FOF formula (((eq (fofType->(fofType->Prop))) d_Subq) (fun (X0:fofType) (X1:fofType)=> (forall (X2:fofType), (((in X2) X0)->((in X2) X1))))) of role definition named def_d_Subq
% 0.08/0.52 A new definition: (((eq (fofType->(fofType->Prop))) d_Subq) (fun (X0:fofType) (X1:fofType)=> (forall (X2:fofType), (((in X2) X0)->((in X2) X1)))))
% 0.08/0.52 Defined: d_Subq:=(fun (X0:fofType) (X1:fofType)=> (forall (X2:fofType), (((in X2) X0)->((in X2) X1))))
% 0.08/0.52 FOF formula (forall (X0:fofType) (X1:fofType), (((d_Subq X0) X1)->(((d_Subq X1) X0)->(((eq fofType) X0) X1)))) of role axiom named set_ext
% 0.08/0.52 A new axiom: (forall (X0:fofType) (X1:fofType), (((d_Subq X0) X1)->(((d_Subq X1) X0)->(((eq fofType) X0) X1))))
% 0.08/0.52 FOF formula (forall (X0:(fofType->Prop)), ((forall (X1:fofType), ((forall (X2:fofType), (((in X2) X1)->(X0 X2)))->(X0 X1)))->(forall (X1:fofType), (X0 X1)))) of role axiom named k_In_ind
% 0.08/0.52 A new axiom: (forall (X0:(fofType->Prop)), ((forall (X1:fofType), ((forall (X2:fofType), (((in X2) X1)->(X0 X2)))->(X0 X1)))->(forall (X1:fofType), (X0 X1))))
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ad8d50175a8>, <kernel.Single object at 0x2ad8d56b8f38>) of role type named typ_emptyset
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring emptyset:fofType
% 0.08/0.52 FOF formula (((ex fofType) (fun (X0:fofType)=> ((in X0) emptyset)))->False) of role axiom named k_EmptyAx
% 0.08/0.52 A new axiom: (((ex fofType) (fun (X0:fofType)=> ((in X0) emptyset)))->False)
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ad8d56b8f38>, <kernel.DependentProduct object at 0x2ad8d56de950>) of role type named typ_union
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring union:(fofType->fofType)
% 0.08/0.52 FOF formula (forall (X0:fofType) (X1:fofType), ((iff ((in X1) (union X0))) ((ex fofType) (fun (X2:fofType)=> ((and ((in X1) X2)) ((in X2) X0)))))) of role axiom named k_UnionEq
% 0.08/0.52 A new axiom: (forall (X0:fofType) (X1:fofType), ((iff ((in X1) (union X0))) ((ex fofType) (fun (X2:fofType)=> ((and ((in X1) X2)) ((in X2) X0))))))
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ad8d56debd8>, <kernel.DependentProduct object at 0x2ad8d56de320>) of role type named typ_power
% 0.08/0.52 Using role type
% 0.08/0.53 Declaring power:(fofType->fofType)
% 0.08/0.53 FOF formula (forall (X0:fofType) (X1:fofType), ((iff ((in X1) (power X0))) ((d_Subq X1) X0))) of role axiom named k_PowerEq
% 0.08/0.53 A new axiom: (forall (X0:fofType) (X1:fofType), ((iff ((in X1) (power X0))) ((d_Subq X1) X0)))
% 0.08/0.53 FOF formula (<kernel.Constant object at 0x2ad8d56def38>, <kernel.DependentProduct object at 0x2ad8d56deea8>) of role type named typ_repl
% 0.08/0.53 Using role type
% 0.08/0.53 Declaring repl:(fofType->((fofType->fofType)->fofType))
% 0.08/0.53 FOF formula (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), ((iff ((in X2) ((repl X0) X1))) ((ex fofType) (fun (X3:fofType)=> ((and ((in X3) X0)) (((eq fofType) X2) (X1 X3))))))) of role axiom named k_ReplEq
% 0.08/0.53 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), ((iff ((in X2) ((repl X0) X1))) ((ex fofType) (fun (X3:fofType)=> ((and ((in X3) X0)) (((eq fofType) X2) (X1 X3)))))))
% 0.08/0.53 FOF formula (<kernel.Constant object at 0x2ad8d56dec68>, <kernel.DependentProduct object at 0x2ad8d56de320>) of role type named typ_d_Union_closed
% 0.08/0.53 Using role type
% 0.08/0.53 Declaring d_Union_closed:(fofType->Prop)
% 0.08/0.53 FOF formula (((eq (fofType->Prop)) d_Union_closed) (fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (union X1)) X0))))) of role definition named def_d_Union_closed
% 0.08/0.53 A new definition: (((eq (fofType->Prop)) d_Union_closed) (fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (union X1)) X0)))))
% 0.08/0.53 Defined: d_Union_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (union X1)) X0))))
% 0.08/0.53 FOF formula (<kernel.Constant object at 0x2ad8d56de2d8>, <kernel.DependentProduct object at 0x2ad8d4fc1638>) of role type named typ_d_Power_closed
% 0.08/0.53 Using role type
% 0.08/0.53 Declaring d_Power_closed:(fofType->Prop)
% 0.08/0.53 FOF formula (((eq (fofType->Prop)) d_Power_closed) (fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (power X1)) X0))))) of role definition named def_d_Power_closed
% 0.08/0.53 A new definition: (((eq (fofType->Prop)) d_Power_closed) (fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (power X1)) X0)))))
% 0.08/0.53 Defined: d_Power_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (power X1)) X0))))
% 0.08/0.53 FOF formula (<kernel.Constant object at 0x2ad8d56dec68>, <kernel.DependentProduct object at 0x2ad8d4fc1488>) of role type named typ_d_Repl_closed
% 0.08/0.53 Using role type
% 0.08/0.53 Declaring d_Repl_closed:(fofType->Prop)
% 0.08/0.53 FOF formula (((eq (fofType->Prop)) d_Repl_closed) (fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->(forall (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X1)->((in (X2 X3)) X0)))->((in ((repl X1) X2)) X0))))))) of role definition named def_d_Repl_closed
% 0.08/0.53 A new definition: (((eq (fofType->Prop)) d_Repl_closed) (fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->(forall (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X1)->((in (X2 X3)) X0)))->((in ((repl X1) X2)) X0)))))))
% 0.08/0.53 Defined: d_Repl_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->(forall (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X1)->((in (X2 X3)) X0)))->((in ((repl X1) X2)) X0))))))
% 0.08/0.53 FOF formula (<kernel.Constant object at 0x2ad8d56de998>, <kernel.DependentProduct object at 0x2ad8d4fc1488>) of role type named typ_d_ZF_closed
% 0.08/0.53 Using role type
% 0.08/0.53 Declaring d_ZF_closed:(fofType->Prop)
% 0.08/0.53 FOF formula (((eq (fofType->Prop)) d_ZF_closed) (fun (X0:fofType)=> ((and ((and (d_Union_closed X0)) (d_Power_closed X0))) (d_Repl_closed X0)))) of role definition named def_d_ZF_closed
% 0.08/0.53 A new definition: (((eq (fofType->Prop)) d_ZF_closed) (fun (X0:fofType)=> ((and ((and (d_Union_closed X0)) (d_Power_closed X0))) (d_Repl_closed X0))))
% 0.08/0.53 Defined: d_ZF_closed:=(fun (X0:fofType)=> ((and ((and (d_Union_closed X0)) (d_Power_closed X0))) (d_Repl_closed X0)))
% 0.08/0.53 FOF formula (<kernel.Constant object at 0x2ad8d56de998>, <kernel.DependentProduct object at 0x2ad8d4fc1bd8>) of role type named typ_univof
% 0.08/0.53 Using role type
% 0.08/0.53 Declaring univof:(fofType->fofType)
% 0.08/0.53 FOF formula (forall (X0:fofType), ((in X0) (univof X0))) of role axiom named k_UnivOf_In
% 0.08/0.53 A new axiom: (forall (X0:fofType), ((in X0) (univof X0)))
% 0.08/0.53 FOF formula (forall (X0:fofType), (d_ZF_closed (univof X0))) of role axiom named k_UnivOf_ZF_closed
% 0.08/0.55 A new axiom: (forall (X0:fofType), (d_ZF_closed (univof X0)))
% 0.08/0.55 FOF formula (<kernel.Constant object at 0x2ad8d4fc12d8>, <kernel.DependentProduct object at 0x2ad8d4fc1f38>) of role type named typ_if
% 0.08/0.55 Using role type
% 0.08/0.55 Declaring if:(Prop->(fofType->(fofType->fofType)))
% 0.08/0.55 FOF formula (((eq (Prop->(fofType->(fofType->fofType)))) if) (fun (X0:Prop) (X1:fofType) (X2:fofType)=> (eps (fun (X3:fofType)=> ((or ((and X0) (((eq fofType) X3) X1))) ((and (X0->False)) (((eq fofType) X3) X2))))))) of role definition named def_if
% 0.08/0.55 A new definition: (((eq (Prop->(fofType->(fofType->fofType)))) if) (fun (X0:Prop) (X1:fofType) (X2:fofType)=> (eps (fun (X3:fofType)=> ((or ((and X0) (((eq fofType) X3) X1))) ((and (X0->False)) (((eq fofType) X3) X2)))))))
% 0.08/0.55 Defined: if:=(fun (X0:Prop) (X1:fofType) (X2:fofType)=> (eps (fun (X3:fofType)=> ((or ((and X0) (((eq fofType) X3) X1))) ((and (X0->False)) (((eq fofType) X3) X2))))))
% 0.08/0.55 FOF formula (forall (X0:Prop) (X1:fofType) (X2:fofType), ((or ((and X0) (((eq fofType) (((if X0) X1) X2)) X1))) ((and (X0->False)) (((eq fofType) (((if X0) X1) X2)) X2)))) of role axiom named if_i_correct
% 0.08/0.55 A new axiom: (forall (X0:Prop) (X1:fofType) (X2:fofType), ((or ((and X0) (((eq fofType) (((if X0) X1) X2)) X1))) ((and (X0->False)) (((eq fofType) (((if X0) X1) X2)) X2))))
% 0.08/0.55 FOF formula (forall (X0:Prop) (X1:fofType) (X2:fofType), ((X0->False)->(((eq fofType) (((if X0) X1) X2)) X2))) of role axiom named if_i_0
% 0.08/0.55 A new axiom: (forall (X0:Prop) (X1:fofType) (X2:fofType), ((X0->False)->(((eq fofType) (((if X0) X1) X2)) X2)))
% 0.08/0.55 FOF formula (forall (X0:Prop) (X1:fofType) (X2:fofType), (X0->(((eq fofType) (((if X0) X1) X2)) X1))) of role axiom named if_i_1
% 0.08/0.55 A new axiom: (forall (X0:Prop) (X1:fofType) (X2:fofType), (X0->(((eq fofType) (((if X0) X1) X2)) X1)))
% 0.08/0.55 FOF formula (forall (X0:Prop) (X1:fofType) (X2:fofType), ((or (((eq fofType) (((if X0) X1) X2)) X1)) (((eq fofType) (((if X0) X1) X2)) X2))) of role axiom named if_i_or
% 0.08/0.55 A new axiom: (forall (X0:Prop) (X1:fofType) (X2:fofType), ((or (((eq fofType) (((if X0) X1) X2)) X1)) (((eq fofType) (((if X0) X1) X2)) X2)))
% 0.08/0.55 FOF formula (<kernel.Constant object at 0x2ad8d4fc1bd8>, <kernel.DependentProduct object at 0x2ad8d4fc1fc8>) of role type named typ_nIn
% 0.08/0.55 Using role type
% 0.08/0.55 Declaring nIn:(fofType->(fofType->Prop))
% 0.08/0.55 FOF formula (((eq (fofType->(fofType->Prop))) nIn) (fun (X0:fofType) (X1:fofType)=> (((in X0) X1)->False))) of role definition named def_nIn
% 0.08/0.55 A new definition: (((eq (fofType->(fofType->Prop))) nIn) (fun (X0:fofType) (X1:fofType)=> (((in X0) X1)->False)))
% 0.08/0.55 Defined: nIn:=(fun (X0:fofType) (X1:fofType)=> (((in X0) X1)->False))
% 0.08/0.55 FOF formula (forall (X0:fofType) (X1:fofType), (((in X1) (power X0))->((d_Subq X1) X0))) of role axiom named k_PowerE
% 0.08/0.55 A new axiom: (forall (X0:fofType) (X1:fofType), (((in X1) (power X0))->((d_Subq X1) X0)))
% 0.08/0.55 FOF formula (forall (X0:fofType) (X1:fofType), (((d_Subq X1) X0)->((in X1) (power X0)))) of role axiom named k_PowerI
% 0.08/0.55 A new axiom: (forall (X0:fofType) (X1:fofType), (((d_Subq X1) X0)->((in X1) (power X0))))
% 0.08/0.55 FOF formula (forall (X0:fofType), ((in X0) (power X0))) of role axiom named k_Self_In_Power
% 0.08/0.55 A new axiom: (forall (X0:fofType), ((in X0) (power X0)))
% 0.08/0.55 FOF formula (<kernel.Constant object at 0x2ad8d4fc1b00>, <kernel.DependentProduct object at 0x2ad8d4fc1bd8>) of role type named typ_d_UPair
% 0.08/0.55 Using role type
% 0.08/0.55 Declaring d_UPair:(fofType->(fofType->fofType))
% 0.08/0.55 FOF formula (((eq (fofType->(fofType->fofType))) d_UPair) (fun (X0:fofType) (X1:fofType)=> ((repl (power (power emptyset))) (fun (X2:fofType)=> (((if ((in emptyset) X2)) X0) X1))))) of role definition named def_d_UPair
% 0.08/0.55 A new definition: (((eq (fofType->(fofType->fofType))) d_UPair) (fun (X0:fofType) (X1:fofType)=> ((repl (power (power emptyset))) (fun (X2:fofType)=> (((if ((in emptyset) X2)) X0) X1)))))
% 0.08/0.55 Defined: d_UPair:=(fun (X0:fofType) (X1:fofType)=> ((repl (power (power emptyset))) (fun (X2:fofType)=> (((if ((in emptyset) X2)) X0) X1))))
% 0.08/0.55 FOF formula (<kernel.Constant object at 0x2ad8d4fc1908>, <kernel.DependentProduct object at 0x2ad8d56d36c8>) of role type named typ_d_Sing
% 0.08/0.55 Using role type
% 0.08/0.57 Declaring d_Sing:(fofType->fofType)
% 0.08/0.57 FOF formula (((eq (fofType->fofType)) d_Sing) (fun (X0:fofType)=> ((d_UPair X0) X0))) of role definition named def_d_Sing
% 0.08/0.57 A new definition: (((eq (fofType->fofType)) d_Sing) (fun (X0:fofType)=> ((d_UPair X0) X0)))
% 0.08/0.57 Defined: d_Sing:=(fun (X0:fofType)=> ((d_UPair X0) X0))
% 0.08/0.57 FOF formula (<kernel.Constant object at 0x2ad8d4fc1b00>, <kernel.DependentProduct object at 0x2ad8d56d30e0>) of role type named typ_binunion
% 0.08/0.57 Using role type
% 0.08/0.57 Declaring binunion:(fofType->(fofType->fofType))
% 0.08/0.57 FOF formula (((eq (fofType->(fofType->fofType))) binunion) (fun (X0:fofType) (X1:fofType)=> (union ((d_UPair X0) X1)))) of role definition named def_binunion
% 0.08/0.57 A new definition: (((eq (fofType->(fofType->fofType))) binunion) (fun (X0:fofType) (X1:fofType)=> (union ((d_UPair X0) X1))))
% 0.08/0.57 Defined: binunion:=(fun (X0:fofType) (X1:fofType)=> (union ((d_UPair X0) X1)))
% 0.08/0.57 FOF formula (<kernel.Constant object at 0x2ad8d4fc1518>, <kernel.DependentProduct object at 0x2ad8d56d3368>) of role type named typ_famunion
% 0.08/0.57 Using role type
% 0.08/0.57 Declaring famunion:(fofType->((fofType->fofType)->fofType))
% 0.08/0.57 FOF formula (((eq (fofType->((fofType->fofType)->fofType))) famunion) (fun (X0:fofType) (X1:(fofType->fofType))=> (union ((repl X0) X1)))) of role definition named def_famunion
% 0.08/0.57 A new definition: (((eq (fofType->((fofType->fofType)->fofType))) famunion) (fun (X0:fofType) (X1:(fofType->fofType))=> (union ((repl X0) X1))))
% 0.08/0.57 Defined: famunion:=(fun (X0:fofType) (X1:(fofType->fofType))=> (union ((repl X0) X1)))
% 0.08/0.57 FOF formula (<kernel.Constant object at 0x2ad8d4fc1518>, <kernel.DependentProduct object at 0x2ad8d56d3368>) of role type named typ_d_Sep
% 0.08/0.57 Using role type
% 0.08/0.57 Declaring d_Sep:(fofType->((fofType->Prop)->fofType))
% 0.08/0.57 FOF formula (((eq (fofType->((fofType->Prop)->fofType))) d_Sep) (fun (X0:fofType) (X1:(fofType->Prop))=> (((if ((ex fofType) (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2))))) ((repl X0) (fun (X2:fofType)=> (((if (X1 X2)) X2) (eps (fun (X3:fofType)=> ((and ((in X3) X0)) (X1 X3)))))))) emptyset))) of role definition named def_d_Sep
% 0.08/0.57 A new definition: (((eq (fofType->((fofType->Prop)->fofType))) d_Sep) (fun (X0:fofType) (X1:(fofType->Prop))=> (((if ((ex fofType) (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2))))) ((repl X0) (fun (X2:fofType)=> (((if (X1 X2)) X2) (eps (fun (X3:fofType)=> ((and ((in X3) X0)) (X1 X3)))))))) emptyset)))
% 0.08/0.57 Defined: d_Sep:=(fun (X0:fofType) (X1:(fofType->Prop))=> (((if ((ex fofType) (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2))))) ((repl X0) (fun (X2:fofType)=> (((if (X1 X2)) X2) (eps (fun (X3:fofType)=> ((and ((in X3) X0)) (X1 X3)))))))) emptyset))
% 0.08/0.57 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) X0)->((X1 X2)->((in X2) ((d_Sep X0) X1))))) of role axiom named k_SepI
% 0.08/0.57 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) X0)->((X1 X2)->((in X2) ((d_Sep X0) X1)))))
% 0.08/0.57 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) ((d_Sep X0) X1))->((in X2) X0))) of role axiom named k_SepE1
% 0.08/0.57 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) ((d_Sep X0) X1))->((in X2) X0)))
% 0.08/0.57 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) ((d_Sep X0) X1))->(X1 X2))) of role axiom named k_SepE2
% 0.08/0.57 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) ((d_Sep X0) X1))->(X1 X2)))
% 0.08/0.57 FOF formula (<kernel.Constant object at 0x2ad8d56d36c8>, <kernel.DependentProduct object at 0x2ad8d7749320>) of role type named typ_d_ReplSep
% 0.08/0.57 Using role type
% 0.08/0.57 Declaring d_ReplSep:(fofType->((fofType->Prop)->((fofType->fofType)->fofType)))
% 0.08/0.57 FOF formula (((eq (fofType->((fofType->Prop)->((fofType->fofType)->fofType)))) d_ReplSep) (fun (X0:fofType) (X1:(fofType->Prop))=> (repl ((d_Sep X0) X1)))) of role definition named def_d_ReplSep
% 0.08/0.57 A new definition: (((eq (fofType->((fofType->Prop)->((fofType->fofType)->fofType)))) d_ReplSep) (fun (X0:fofType) (X1:(fofType->Prop))=> (repl ((d_Sep X0) X1))))
% 0.08/0.57 Defined: d_ReplSep:=(fun (X0:fofType) (X1:(fofType->Prop))=> (repl ((d_Sep X0) X1)))
% 0.08/0.57 FOF formula (<kernel.Constant object at 0x2ad8d56d36c8>, <kernel.DependentProduct object at 0x2ad8d7749488>) of role type named typ_setminus
% 0.40/0.58 Using role type
% 0.40/0.58 Declaring setminus:(fofType->(fofType->fofType))
% 0.40/0.58 FOF formula (((eq (fofType->(fofType->fofType))) setminus) (fun (X0:fofType) (X1:fofType)=> ((d_Sep X0) (fun (X2:fofType)=> ((nIn X2) X1))))) of role definition named def_setminus
% 0.40/0.58 A new definition: (((eq (fofType->(fofType->fofType))) setminus) (fun (X0:fofType) (X1:fofType)=> ((d_Sep X0) (fun (X2:fofType)=> ((nIn X2) X1)))))
% 0.40/0.58 Defined: setminus:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep X0) (fun (X2:fofType)=> ((nIn X2) X1))))
% 0.40/0.58 FOF formula (<kernel.Constant object at 0x2ad8d56d36c8>, <kernel.DependentProduct object at 0x2ad8d7749440>) of role type named typ_d_In_rec_G
% 0.40/0.58 Using role type
% 0.40/0.58 Declaring d_In_rec_G:((fofType->((fofType->fofType)->fofType))->(fofType->(fofType->Prop)))
% 0.40/0.58 FOF formula (((eq ((fofType->((fofType->fofType)->fofType))->(fofType->(fofType->Prop)))) d_In_rec_G) (fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType) (X2:fofType)=> (forall (X3:(fofType->(fofType->Prop))), ((forall (X4:fofType) (X5:(fofType->fofType)), ((forall (X6:fofType), (((in X6) X4)->((X3 X6) (X5 X6))))->((X3 X4) ((X0 X4) X5))))->((X3 X1) X2))))) of role definition named def_d_In_rec_G
% 0.40/0.58 A new definition: (((eq ((fofType->((fofType->fofType)->fofType))->(fofType->(fofType->Prop)))) d_In_rec_G) (fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType) (X2:fofType)=> (forall (X3:(fofType->(fofType->Prop))), ((forall (X4:fofType) (X5:(fofType->fofType)), ((forall (X6:fofType), (((in X6) X4)->((X3 X6) (X5 X6))))->((X3 X4) ((X0 X4) X5))))->((X3 X1) X2)))))
% 0.40/0.58 Defined: d_In_rec_G:=(fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType) (X2:fofType)=> (forall (X3:(fofType->(fofType->Prop))), ((forall (X4:fofType) (X5:(fofType->fofType)), ((forall (X6:fofType), (((in X6) X4)->((X3 X6) (X5 X6))))->((X3 X4) ((X0 X4) X5))))->((X3 X1) X2))))
% 0.40/0.58 FOF formula (<kernel.Constant object at 0x2ad8d7749440>, <kernel.DependentProduct object at 0x2ad8d7749710>) of role type named typ_d_In_rec
% 0.40/0.58 Using role type
% 0.40/0.58 Declaring d_In_rec:((fofType->((fofType->fofType)->fofType))->(fofType->fofType))
% 0.40/0.58 FOF formula (((eq ((fofType->((fofType->fofType)->fofType))->(fofType->fofType))) d_In_rec) (fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType)=> (eps ((d_In_rec_G X0) X1)))) of role definition named def_d_In_rec
% 0.40/0.58 A new definition: (((eq ((fofType->((fofType->fofType)->fofType))->(fofType->fofType))) d_In_rec) (fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType)=> (eps ((d_In_rec_G X0) X1))))
% 0.40/0.58 Defined: d_In_rec:=(fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType)=> (eps ((d_In_rec_G X0) X1)))
% 0.40/0.58 FOF formula (<kernel.Constant object at 0x2ad8d7749710>, <kernel.DependentProduct object at 0x2ad8d77494d0>) of role type named typ_ordsucc
% 0.40/0.58 Using role type
% 0.40/0.58 Declaring ordsucc:(fofType->fofType)
% 0.40/0.58 FOF formula (((eq (fofType->fofType)) ordsucc) (fun (X0:fofType)=> ((binunion X0) (d_Sing X0)))) of role definition named def_ordsucc
% 0.40/0.58 A new definition: (((eq (fofType->fofType)) ordsucc) (fun (X0:fofType)=> ((binunion X0) (d_Sing X0))))
% 0.40/0.58 Defined: ordsucc:=(fun (X0:fofType)=> ((binunion X0) (d_Sing X0)))
% 0.40/0.58 FOF formula (forall (X0:fofType), (not (((eq fofType) (ordsucc X0)) emptyset))) of role axiom named neq_ordsucc_0
% 0.40/0.58 A new axiom: (forall (X0:fofType), (not (((eq fofType) (ordsucc X0)) emptyset)))
% 0.40/0.58 FOF formula (forall (X0:fofType) (X1:fofType), ((((eq fofType) (ordsucc X0)) (ordsucc X1))->(((eq fofType) X0) X1))) of role axiom named ordsucc_inj
% 0.40/0.58 A new axiom: (forall (X0:fofType) (X1:fofType), ((((eq fofType) (ordsucc X0)) (ordsucc X1))->(((eq fofType) X0) X1)))
% 0.40/0.58 FOF formula ((in emptyset) (ordsucc emptyset)) of role axiom named k_In_0_1
% 0.40/0.58 A new axiom: ((in emptyset) (ordsucc emptyset))
% 0.40/0.58 FOF formula (<kernel.Constant object at 0x2ad8d7749488>, <kernel.DependentProduct object at 0x2ad8d7749200>) of role type named typ_nat_p
% 0.40/0.58 Using role type
% 0.40/0.58 Declaring nat_p:(fofType->Prop)
% 0.40/0.58 FOF formula (((eq (fofType->Prop)) nat_p) (fun (X0:fofType)=> (forall (X1:(fofType->Prop)), ((X1 emptyset)->((forall (X2:fofType), ((X1 X2)->(X1 (ordsucc X2))))->(X1 X0)))))) of role definition named def_nat_p
% 0.40/0.60 A new definition: (((eq (fofType->Prop)) nat_p) (fun (X0:fofType)=> (forall (X1:(fofType->Prop)), ((X1 emptyset)->((forall (X2:fofType), ((X1 X2)->(X1 (ordsucc X2))))->(X1 X0))))))
% 0.40/0.60 Defined: nat_p:=(fun (X0:fofType)=> (forall (X1:(fofType->Prop)), ((X1 emptyset)->((forall (X2:fofType), ((X1 X2)->(X1 (ordsucc X2))))->(X1 X0)))))
% 0.40/0.60 FOF formula (forall (X0:fofType), ((nat_p X0)->(nat_p (ordsucc X0)))) of role axiom named nat_ordsucc
% 0.40/0.60 A new axiom: (forall (X0:fofType), ((nat_p X0)->(nat_p (ordsucc X0))))
% 0.40/0.60 FOF formula (nat_p (ordsucc emptyset)) of role axiom named nat_1
% 0.40/0.60 A new axiom: (nat_p (ordsucc emptyset))
% 0.40/0.60 FOF formula (forall (X0:(fofType->Prop)), ((X0 emptyset)->((forall (X1:fofType), ((nat_p X1)->((X0 X1)->(X0 (ordsucc X1)))))->(forall (X1:fofType), ((nat_p X1)->(X0 X1)))))) of role axiom named nat_ind
% 0.40/0.60 A new axiom: (forall (X0:(fofType->Prop)), ((X0 emptyset)->((forall (X1:fofType), ((nat_p X1)->((X0 X1)->(X0 (ordsucc X1)))))->(forall (X1:fofType), ((nat_p X1)->(X0 X1))))))
% 0.40/0.60 FOF formula (forall (X0:fofType), ((nat_p X0)->((or (((eq fofType) X0) emptyset)) ((ex fofType) (fun (X1:fofType)=> ((and (nat_p X1)) (((eq fofType) X0) (ordsucc X1)))))))) of role axiom named nat_inv
% 0.40/0.60 A new axiom: (forall (X0:fofType), ((nat_p X0)->((or (((eq fofType) X0) emptyset)) ((ex fofType) (fun (X1:fofType)=> ((and (nat_p X1)) (((eq fofType) X0) (ordsucc X1))))))))
% 0.40/0.60 FOF formula (<kernel.Constant object at 0x2ad8d7749b00>, <kernel.Single object at 0x2ad8d7749830>) of role type named typ_omega
% 0.40/0.60 Using role type
% 0.40/0.60 Declaring omega:fofType
% 0.40/0.60 FOF formula (((eq fofType) omega) ((d_Sep (univof emptyset)) nat_p)) of role definition named def_omega
% 0.40/0.60 A new definition: (((eq fofType) omega) ((d_Sep (univof emptyset)) nat_p))
% 0.40/0.60 Defined: omega:=((d_Sep (univof emptyset)) nat_p)
% 0.40/0.60 FOF formula (forall (X0:fofType), (((in X0) omega)->(nat_p X0))) of role axiom named omega_nat_p
% 0.40/0.60 A new axiom: (forall (X0:fofType), (((in X0) omega)->(nat_p X0)))
% 0.40/0.60 FOF formula (forall (X0:fofType), ((nat_p X0)->((in X0) omega))) of role axiom named nat_p_omega
% 0.40/0.60 A new axiom: (forall (X0:fofType), ((nat_p X0)->((in X0) omega)))
% 0.40/0.60 FOF formula (<kernel.Constant object at 0x2ad8d7749638>, <kernel.DependentProduct object at 0x2ad8d7749830>) of role type named typ_d_Inj1
% 0.40/0.60 Using role type
% 0.40/0.60 Declaring d_Inj1:(fofType->fofType)
% 0.40/0.60 FOF formula (((eq (fofType->fofType)) d_Inj1) (d_In_rec (fun (X0:fofType) (X1:(fofType->fofType))=> ((binunion (d_Sing emptyset)) ((repl X0) X1))))) of role definition named def_d_Inj1
% 0.40/0.60 A new definition: (((eq (fofType->fofType)) d_Inj1) (d_In_rec (fun (X0:fofType) (X1:(fofType->fofType))=> ((binunion (d_Sing emptyset)) ((repl X0) X1)))))
% 0.40/0.60 Defined: d_Inj1:=(d_In_rec (fun (X0:fofType) (X1:(fofType->fofType))=> ((binunion (d_Sing emptyset)) ((repl X0) X1))))
% 0.40/0.60 FOF formula (<kernel.Constant object at 0x2ad8d7749b00>, <kernel.DependentProduct object at 0x2ad8d7749e60>) of role type named typ_d_Inj0
% 0.40/0.60 Using role type
% 0.40/0.60 Declaring d_Inj0:(fofType->fofType)
% 0.40/0.60 FOF formula (((eq (fofType->fofType)) d_Inj0) (fun (X0:fofType)=> ((repl X0) d_Inj1))) of role definition named def_d_Inj0
% 0.40/0.60 A new definition: (((eq (fofType->fofType)) d_Inj0) (fun (X0:fofType)=> ((repl X0) d_Inj1)))
% 0.40/0.60 Defined: d_Inj0:=(fun (X0:fofType)=> ((repl X0) d_Inj1))
% 0.40/0.60 FOF formula (<kernel.Constant object at 0x2ad8d7749e60>, <kernel.DependentProduct object at 0x2ad8d7749830>) of role type named typ_d_Unj
% 0.40/0.60 Using role type
% 0.40/0.60 Declaring d_Unj:(fofType->fofType)
% 0.40/0.60 FOF formula (((eq (fofType->fofType)) d_Unj) (d_In_rec (fun (X0:fofType)=> (repl ((setminus X0) (d_Sing emptyset)))))) of role definition named def_d_Unj
% 0.40/0.60 A new definition: (((eq (fofType->fofType)) d_Unj) (d_In_rec (fun (X0:fofType)=> (repl ((setminus X0) (d_Sing emptyset))))))
% 0.40/0.60 Defined: d_Unj:=(d_In_rec (fun (X0:fofType)=> (repl ((setminus X0) (d_Sing emptyset)))))
% 0.40/0.60 FOF formula (<kernel.Constant object at 0x2ad8d7749638>, <kernel.DependentProduct object at 0x2ad8d7749830>) of role type named typ_pair
% 0.40/0.60 Using role type
% 0.40/0.60 Declaring pair:(fofType->(fofType->fofType))
% 0.40/0.60 FOF formula (((eq (fofType->(fofType->fofType))) pair) (fun (X0:fofType) (X1:fofType)=> ((binunion ((repl X0) d_Inj0)) ((repl X1) d_Inj1)))) of role definition named def_pair
% 0.43/0.61 A new definition: (((eq (fofType->(fofType->fofType))) pair) (fun (X0:fofType) (X1:fofType)=> ((binunion ((repl X0) d_Inj0)) ((repl X1) d_Inj1))))
% 0.43/0.61 Defined: pair:=(fun (X0:fofType) (X1:fofType)=> ((binunion ((repl X0) d_Inj0)) ((repl X1) d_Inj1)))
% 0.43/0.61 FOF formula (<kernel.Constant object at 0x2ad8d7749830>, <kernel.DependentProduct object at 0x2ad8d7749518>) of role type named typ_proj0
% 0.43/0.61 Using role type
% 0.43/0.61 Declaring proj0:(fofType->fofType)
% 0.43/0.61 FOF formula (((eq (fofType->fofType)) proj0) (fun (X0:fofType)=> (((d_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (d_Inj0 X2)) X1))))) d_Unj))) of role definition named def_proj0
% 0.43/0.61 A new definition: (((eq (fofType->fofType)) proj0) (fun (X0:fofType)=> (((d_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (d_Inj0 X2)) X1))))) d_Unj)))
% 0.43/0.61 Defined: proj0:=(fun (X0:fofType)=> (((d_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (d_Inj0 X2)) X1))))) d_Unj))
% 0.43/0.61 FOF formula (<kernel.Constant object at 0x2ad8d7749518>, <kernel.DependentProduct object at 0x2ad8d77497a0>) of role type named typ_proj1
% 0.43/0.61 Using role type
% 0.43/0.61 Declaring _TPTP_proj1:(fofType->fofType)
% 0.43/0.61 FOF formula (((eq (fofType->fofType)) _TPTP_proj1) (fun (X0:fofType)=> (((d_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (d_Inj1 X2)) X1))))) d_Unj))) of role definition named def_proj1
% 0.43/0.61 A new definition: (((eq (fofType->fofType)) _TPTP_proj1) (fun (X0:fofType)=> (((d_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (d_Inj1 X2)) X1))))) d_Unj)))
% 0.43/0.61 Defined: _TPTP_proj1:=(fun (X0:fofType)=> (((d_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (d_Inj1 X2)) X1))))) d_Unj))
% 0.43/0.61 FOF formula (forall (X0:fofType) (X1:fofType), (((eq fofType) (proj0 ((pair X0) X1))) X0)) of role axiom named proj0_pair_eq
% 0.43/0.61 A new axiom: (forall (X0:fofType) (X1:fofType), (((eq fofType) (proj0 ((pair X0) X1))) X0))
% 0.43/0.61 FOF formula (forall (X0:fofType) (X1:fofType), (((eq fofType) (_TPTP_proj1 ((pair X0) X1))) X1)) of role axiom named proj1_pair_eq
% 0.43/0.61 A new axiom: (forall (X0:fofType) (X1:fofType), (((eq fofType) (_TPTP_proj1 ((pair X0) X1))) X1))
% 0.43/0.61 FOF formula (<kernel.Constant object at 0x2ad8d7749ab8>, <kernel.DependentProduct object at 0x2ad8d77499e0>) of role type named typ_d_Sigma
% 0.43/0.61 Using role type
% 0.43/0.61 Declaring d_Sigma:(fofType->((fofType->fofType)->fofType))
% 0.43/0.61 FOF formula (((eq (fofType->((fofType->fofType)->fofType))) d_Sigma) (fun (X0:fofType) (X1:(fofType->fofType))=> ((famunion X0) (fun (X2:fofType)=> ((repl (X1 X2)) (pair X2)))))) of role definition named def_d_Sigma
% 0.43/0.61 A new definition: (((eq (fofType->((fofType->fofType)->fofType))) d_Sigma) (fun (X0:fofType) (X1:(fofType->fofType))=> ((famunion X0) (fun (X2:fofType)=> ((repl (X1 X2)) (pair X2))))))
% 0.43/0.61 Defined: d_Sigma:=(fun (X0:fofType) (X1:(fofType->fofType))=> ((famunion X0) (fun (X2:fofType)=> ((repl (X1 X2)) (pair X2)))))
% 0.43/0.61 FOF formula (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) X0)->(forall (X3:fofType), (((in X3) (X1 X2))->((in ((pair X2) X3)) ((d_Sigma X0) X1)))))) of role axiom named pair_Sigma
% 0.43/0.61 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) X0)->(forall (X3:fofType), (((in X3) (X1 X2))->((in ((pair X2) X3)) ((d_Sigma X0) X1))))))
% 0.43/0.61 FOF formula (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((and ((and (((eq fofType) ((pair (proj0 X2)) (_TPTP_proj1 X2))) X2)) ((in (proj0 X2)) X0))) ((in (_TPTP_proj1 X2)) (X1 (proj0 X2)))))) of role axiom named k_Sigma_eta_proj0_proj1
% 0.43/0.61 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((and ((and (((eq fofType) ((pair (proj0 X2)) (_TPTP_proj1 X2))) X2)) ((in (proj0 X2)) X0))) ((in (_TPTP_proj1 X2)) (X1 (proj0 X2))))))
% 0.43/0.61 FOF formula (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->(((eq fofType) ((pair (proj0 X2)) (_TPTP_proj1 X2))) X2))) of role axiom named proj_Sigma_eta
% 0.45/0.63 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->(((eq fofType) ((pair (proj0 X2)) (_TPTP_proj1 X2))) X2)))
% 0.45/0.63 FOF formula (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((in (proj0 X2)) X0))) of role axiom named proj0_Sigma
% 0.45/0.63 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((in (proj0 X2)) X0)))
% 0.45/0.63 FOF formula (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((in (_TPTP_proj1 X2)) (X1 (proj0 X2))))) of role axiom named proj1_Sigma
% 0.45/0.63 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((in (_TPTP_proj1 X2)) (X1 (proj0 X2)))))
% 0.45/0.63 FOF formula (<kernel.Constant object at 0x2ad8d7749e60>, <kernel.DependentProduct object at 0x2ad8d7749320>) of role type named typ_setprod
% 0.45/0.63 Using role type
% 0.45/0.63 Declaring setprod:(fofType->(fofType->fofType))
% 0.45/0.63 FOF formula (((eq (fofType->(fofType->fofType))) setprod) (fun (X0:fofType) (X1:fofType)=> ((d_Sigma X0) (fun (X2:fofType)=> X1)))) of role definition named def_setprod
% 0.45/0.63 A new definition: (((eq (fofType->(fofType->fofType))) setprod) (fun (X0:fofType) (X1:fofType)=> ((d_Sigma X0) (fun (X2:fofType)=> X1))))
% 0.45/0.63 Defined: setprod:=(fun (X0:fofType) (X1:fofType)=> ((d_Sigma X0) (fun (X2:fofType)=> X1)))
% 0.45/0.63 FOF formula (<kernel.Constant object at 0x2ad8d7749ea8>, <kernel.DependentProduct object at 0x2ad8d7749518>) of role type named typ_ap
% 0.45/0.63 Using role type
% 0.45/0.63 Declaring ap:(fofType->(fofType->fofType))
% 0.45/0.63 FOF formula (((eq (fofType->(fofType->fofType))) ap) (fun (X0:fofType) (X1:fofType)=> (((d_ReplSep X0) (fun (X2:fofType)=> ((ex fofType) (fun (X3:fofType)=> (((eq fofType) X2) ((pair X1) X3)))))) _TPTP_proj1))) of role definition named def_ap
% 0.45/0.63 A new definition: (((eq (fofType->(fofType->fofType))) ap) (fun (X0:fofType) (X1:fofType)=> (((d_ReplSep X0) (fun (X2:fofType)=> ((ex fofType) (fun (X3:fofType)=> (((eq fofType) X2) ((pair X1) X3)))))) _TPTP_proj1)))
% 0.45/0.63 Defined: ap:=(fun (X0:fofType) (X1:fofType)=> (((d_ReplSep X0) (fun (X2:fofType)=> ((ex fofType) (fun (X3:fofType)=> (((eq fofType) X2) ((pair X1) X3)))))) _TPTP_proj1))
% 0.45/0.63 FOF formula (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) X0)->(((eq fofType) ((ap ((d_Sigma X0) X1)) X2)) (X1 X2)))) of role axiom named beta
% 0.45/0.63 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) X0)->(((eq fofType) ((ap ((d_Sigma X0) X1)) X2)) (X1 X2))))
% 0.45/0.63 FOF formula (<kernel.Constant object at 0x2ad8d7749ef0>, <kernel.DependentProduct object at 0x2ad8d83465f0>) of role type named typ_pair_p
% 0.45/0.63 Using role type
% 0.45/0.63 Declaring pair_p:(fofType->Prop)
% 0.45/0.63 FOF formula (((eq (fofType->Prop)) pair_p) (fun (X0:fofType)=> (((eq fofType) ((pair ((ap X0) emptyset)) ((ap X0) (ordsucc emptyset)))) X0))) of role definition named def_pair_p
% 0.45/0.63 A new definition: (((eq (fofType->Prop)) pair_p) (fun (X0:fofType)=> (((eq fofType) ((pair ((ap X0) emptyset)) ((ap X0) (ordsucc emptyset)))) X0)))
% 0.45/0.63 Defined: pair_p:=(fun (X0:fofType)=> (((eq fofType) ((pair ((ap X0) emptyset)) ((ap X0) (ordsucc emptyset)))) X0))
% 0.45/0.63 FOF formula (<kernel.Constant object at 0x2ad8d7749ea8>, <kernel.DependentProduct object at 0x2ad8d83461b8>) of role type named typ_d_Pi
% 0.45/0.63 Using role type
% 0.45/0.63 Declaring d_Pi:(fofType->((fofType->fofType)->fofType))
% 0.45/0.63 FOF formula (((eq (fofType->((fofType->fofType)->fofType))) d_Pi) (fun (X0:fofType) (X1:(fofType->fofType))=> ((d_Sep (power ((d_Sigma X0) (fun (X2:fofType)=> (union (X1 X2)))))) (fun (X2:fofType)=> (forall (X3:fofType), (((in X3) X0)->((in ((ap X2) X3)) (X1 X3)))))))) of role definition named def_d_Pi
% 0.45/0.63 A new definition: (((eq (fofType->((fofType->fofType)->fofType))) d_Pi) (fun (X0:fofType) (X1:(fofType->fofType))=> ((d_Sep (power ((d_Sigma X0) (fun (X2:fofType)=> (union (X1 X2)))))) (fun (X2:fofType)=> (forall (X3:fofType), (((in X3) X0)->((in ((ap X2) X3)) (X1 X3))))))))
% 0.45/0.63 Defined: d_Pi:=(fun (X0:fofType) (X1:(fofType->fofType))=> ((d_Sep (power ((d_Sigma X0) (fun (X2:fofType)=> (union (X1 X2)))))) (fun (X2:fofType)=> (forall (X3:fofType), (((in X3) X0)->((in ((ap X2) X3)) (X1 X3)))))))
% 0.45/0.65 FOF formula (forall (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X0)->((in (X2 X3)) (X1 X3))))->((in ((d_Sigma X0) X2)) ((d_Pi X0) X1)))) of role axiom named lam_Pi
% 0.45/0.65 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X0)->((in (X2 X3)) (X1 X3))))->((in ((d_Sigma X0) X2)) ((d_Pi X0) X1))))
% 0.45/0.65 FOF formula (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType) (X3:fofType), (((in X2) ((d_Pi X0) X1))->(((in X3) X0)->((in ((ap X2) X3)) (X1 X3))))) of role axiom named ap_Pi
% 0.45/0.65 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType) (X3:fofType), (((in X2) ((d_Pi X0) X1))->(((in X3) X0)->((in ((ap X2) X3)) (X1 X3)))))
% 0.45/0.65 FOF formula (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Pi X0) X1))->(forall (X3:fofType), (((in X3) ((d_Pi X0) X1))->((forall (X4:fofType), (((in X4) X0)->(((eq fofType) ((ap X2) X4)) ((ap X3) X4))))->(((eq fofType) X2) X3)))))) of role axiom named k_Pi_ext
% 0.45/0.65 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Pi X0) X1))->(forall (X3:fofType), (((in X3) ((d_Pi X0) X1))->((forall (X4:fofType), (((in X4) X0)->(((eq fofType) ((ap X2) X4)) ((ap X3) X4))))->(((eq fofType) X2) X3))))))
% 0.45/0.65 FOF formula (forall (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X0)->(((eq fofType) (X1 X3)) (X2 X3))))->(((eq fofType) ((d_Sigma X0) X1)) ((d_Sigma X0) X2)))) of role axiom named xi_ext
% 0.45/0.65 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X0)->(((eq fofType) (X1 X3)) (X2 X3))))->(((eq fofType) ((d_Sigma X0) X1)) ((d_Sigma X0) X2))))
% 0.45/0.65 FOF formula (forall (X0:Prop) (X1:fofType) (X2:fofType), ((X0->((in X1) X2))->((in (((if X0) X1) emptyset)) (((if X0) X2) (ordsucc emptyset))))) of role axiom named k_If_In_01
% 0.45/0.65 A new axiom: (forall (X0:Prop) (X1:fofType) (X2:fofType), ((X0->((in X1) X2))->((in (((if X0) X1) emptyset)) (((if X0) X2) (ordsucc emptyset)))))
% 0.45/0.65 FOF formula (forall (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType), (X0->(((in X1) (((if X0) X2) X3))->((in X1) X2)))) of role axiom named k_If_In_then_E
% 0.45/0.65 A new axiom: (forall (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType), (X0->(((in X1) (((if X0) X2) X3))->((in X1) X2))))
% 0.45/0.65 FOF formula (<kernel.Constant object at 0x2ad8d8346488>, <kernel.DependentProduct object at 0x2ad8d83462d8>) of role type named typ_imp
% 0.45/0.65 Using role type
% 0.45/0.65 Declaring imp:(Prop->(Prop->Prop))
% 0.45/0.65 FOF formula (((eq (Prop->(Prop->Prop))) imp) (fun (X0:Prop) (X1:Prop)=> (X0->X1))) of role definition named def_imp
% 0.45/0.65 A new definition: (((eq (Prop->(Prop->Prop))) imp) (fun (X0:Prop) (X1:Prop)=> (X0->X1)))
% 0.45/0.65 Defined: imp:=(fun (X0:Prop) (X1:Prop)=> (X0->X1))
% 0.45/0.65 FOF formula (<kernel.Constant object at 0x2ad8d83462d8>, <kernel.DependentProduct object at 0x2ad8d8346710>) of role type named typ_d_not
% 0.45/0.65 Using role type
% 0.45/0.65 Declaring d_not:(Prop->Prop)
% 0.45/0.65 FOF formula (((eq (Prop->Prop)) d_not) (fun (X0:Prop)=> ((imp X0) False))) of role definition named def_d_not
% 0.45/0.65 A new definition: (((eq (Prop->Prop)) d_not) (fun (X0:Prop)=> ((imp X0) False)))
% 0.45/0.65 Defined: d_not:=(fun (X0:Prop)=> ((imp X0) False))
% 0.45/0.65 FOF formula (<kernel.Constant object at 0x2ad8d8346710>, <kernel.DependentProduct object at 0x2ad8d8346320>) of role type named typ_wel
% 0.45/0.65 Using role type
% 0.45/0.65 Declaring wel:(Prop->Prop)
% 0.45/0.65 FOF formula (((eq (Prop->Prop)) wel) (fun (X0:Prop)=> (d_not (d_not X0)))) of role definition named def_wel
% 0.45/0.65 A new definition: (((eq (Prop->Prop)) wel) (fun (X0:Prop)=> (d_not (d_not X0))))
% 0.45/0.65 Defined: wel:=(fun (X0:Prop)=> (d_not (d_not X0)))
% 0.45/0.65 FOF formula (forall (X0:Prop), ((wel X0)->X0)) of role axiom named l_et
% 0.45/0.65 A new axiom: (forall (X0:Prop), ((wel X0)->X0))
% 0.45/0.65 FOF formula (<kernel.Constant object at 0x2ad8d8346758>, <kernel.Sort object at 0x2ad8cd32ae18>) of role type named typ_obvious
% 0.45/0.65 Using role type
% 0.45/0.65 Declaring obvious:Prop
% 0.45/0.65 FOF formula (((eq Prop) obvious) ((imp False) False)) of role definition named def_obvious
% 0.45/0.65 A new definition: (((eq Prop) obvious) ((imp False) False))
% 0.45/0.67 Defined: obvious:=((imp False) False)
% 0.45/0.67 FOF formula (<kernel.Constant object at 0x2ad8d8346518>, <kernel.DependentProduct object at 0x2ad8d8346200>) of role type named typ_l_ec
% 0.45/0.67 Using role type
% 0.45/0.67 Declaring l_ec:(Prop->(Prop->Prop))
% 0.45/0.67 FOF formula (((eq (Prop->(Prop->Prop))) l_ec) (fun (X0:Prop) (X1:Prop)=> ((imp X0) (d_not X1)))) of role definition named def_l_ec
% 0.45/0.67 A new definition: (((eq (Prop->(Prop->Prop))) l_ec) (fun (X0:Prop) (X1:Prop)=> ((imp X0) (d_not X1))))
% 0.45/0.67 Defined: l_ec:=(fun (X0:Prop) (X1:Prop)=> ((imp X0) (d_not X1)))
% 0.45/0.67 FOF formula (<kernel.Constant object at 0x2ad8d8346200>, <kernel.DependentProduct object at 0x2ad8d8346758>) of role type named typ_d_and
% 0.45/0.67 Using role type
% 0.45/0.67 Declaring d_and:(Prop->(Prop->Prop))
% 0.45/0.67 FOF formula (((eq (Prop->(Prop->Prop))) d_and) (fun (X0:Prop) (X1:Prop)=> (d_not ((l_ec X0) X1)))) of role definition named def_d_and
% 0.45/0.67 A new definition: (((eq (Prop->(Prop->Prop))) d_and) (fun (X0:Prop) (X1:Prop)=> (d_not ((l_ec X0) X1))))
% 0.45/0.67 Defined: d_and:=(fun (X0:Prop) (X1:Prop)=> (d_not ((l_ec X0) X1)))
% 0.45/0.67 FOF formula (<kernel.Constant object at 0x2ad8d8346758>, <kernel.DependentProduct object at 0x2ad8d8346518>) of role type named typ_l_or
% 0.45/0.67 Using role type
% 0.45/0.67 Declaring l_or:(Prop->(Prop->Prop))
% 0.45/0.67 FOF formula (((eq (Prop->(Prop->Prop))) l_or) (fun (X0:Prop)=> (imp (d_not X0)))) of role definition named def_l_or
% 0.45/0.67 A new definition: (((eq (Prop->(Prop->Prop))) l_or) (fun (X0:Prop)=> (imp (d_not X0))))
% 0.45/0.67 Defined: l_or:=(fun (X0:Prop)=> (imp (d_not X0)))
% 0.45/0.67 FOF formula (<kernel.Constant object at 0x2ad8d8346518>, <kernel.DependentProduct object at 0x2ad8d8346440>) of role type named typ_orec
% 0.45/0.67 Using role type
% 0.45/0.67 Declaring orec:(Prop->(Prop->Prop))
% 0.45/0.67 FOF formula (((eq (Prop->(Prop->Prop))) orec) (fun (X0:Prop) (X1:Prop)=> ((d_and ((l_or X0) X1)) ((l_ec X0) X1)))) of role definition named def_orec
% 0.45/0.67 A new definition: (((eq (Prop->(Prop->Prop))) orec) (fun (X0:Prop) (X1:Prop)=> ((d_and ((l_or X0) X1)) ((l_ec X0) X1))))
% 0.45/0.67 Defined: orec:=(fun (X0:Prop) (X1:Prop)=> ((d_and ((l_or X0) X1)) ((l_ec X0) X1)))
% 0.45/0.67 FOF formula (<kernel.Constant object at 0x2ad8d8346440>, <kernel.DependentProduct object at 0x2ad8d8346758>) of role type named typ_l_iff
% 0.45/0.67 Using role type
% 0.45/0.67 Declaring l_iff:(Prop->(Prop->Prop))
% 0.45/0.67 FOF formula (((eq (Prop->(Prop->Prop))) l_iff) (fun (X0:Prop) (X1:Prop)=> ((d_and ((imp X0) X1)) ((imp X1) X0)))) of role definition named def_l_iff
% 0.45/0.67 A new definition: (((eq (Prop->(Prop->Prop))) l_iff) (fun (X0:Prop) (X1:Prop)=> ((d_and ((imp X0) X1)) ((imp X1) X0))))
% 0.45/0.67 Defined: l_iff:=(fun (X0:Prop) (X1:Prop)=> ((d_and ((imp X0) X1)) ((imp X1) X0)))
% 0.45/0.67 FOF formula (<kernel.Constant object at 0x2ad8d8346758>, <kernel.DependentProduct object at 0x2ad8d8346998>) of role type named typ_all
% 0.45/0.67 Using role type
% 0.45/0.67 Declaring all:(fofType->((fofType->Prop)->Prop))
% 0.45/0.67 FOF formula (((eq (fofType->((fofType->Prop)->Prop))) all) (fun (X0:fofType)=> (all_of (fun (X1:fofType)=> ((in X1) X0))))) of role definition named def_all
% 0.45/0.67 A new definition: (((eq (fofType->((fofType->Prop)->Prop))) all) (fun (X0:fofType)=> (all_of (fun (X1:fofType)=> ((in X1) X0)))))
% 0.45/0.67 Defined: all:=(fun (X0:fofType)=> (all_of (fun (X1:fofType)=> ((in X1) X0))))
% 0.45/0.67 FOF formula (<kernel.Constant object at 0x2ad8d8346998>, <kernel.DependentProduct object at 0x2ad8d8346d88>) of role type named typ_non
% 0.45/0.67 Using role type
% 0.45/0.67 Declaring non:(fofType->((fofType->Prop)->(fofType->Prop)))
% 0.45/0.67 FOF formula (((eq (fofType->((fofType->Prop)->(fofType->Prop)))) non) (fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> (d_not (X1 X2)))) of role definition named def_non
% 0.45/0.67 A new definition: (((eq (fofType->((fofType->Prop)->(fofType->Prop)))) non) (fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> (d_not (X1 X2))))
% 0.45/0.67 Defined: non:=(fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> (d_not (X1 X2)))
% 0.45/0.67 FOF formula (<kernel.Constant object at 0x2ad8d8346d88>, <kernel.DependentProduct object at 0x2ad8d83464d0>) of role type named typ_l_some
% 0.45/0.67 Using role type
% 0.45/0.67 Declaring l_some:(fofType->((fofType->Prop)->Prop))
% 0.45/0.67 FOF formula (((eq (fofType->((fofType->Prop)->Prop))) l_some) (fun (X0:fofType) (X1:(fofType->Prop))=> (d_not ((all_of (fun (X2:fofType)=> ((in X2) X0))) ((non X0) X1))))) of role definition named def_l_some
% 0.45/0.68 A new definition: (((eq (fofType->((fofType->Prop)->Prop))) l_some) (fun (X0:fofType) (X1:(fofType->Prop))=> (d_not ((all_of (fun (X2:fofType)=> ((in X2) X0))) ((non X0) X1)))))
% 0.45/0.68 Defined: l_some:=(fun (X0:fofType) (X1:(fofType->Prop))=> (d_not ((all_of (fun (X2:fofType)=> ((in X2) X0))) ((non X0) X1))))
% 0.45/0.68 FOF formula (<kernel.Constant object at 0x2ad8d83464d0>, <kernel.DependentProduct object at 0x2ad8d8346dd0>) of role type named typ_or3
% 0.45/0.68 Using role type
% 0.45/0.68 Declaring or3:(Prop->(Prop->(Prop->Prop)))
% 0.45/0.68 FOF formula (((eq (Prop->(Prop->(Prop->Prop)))) or3) (fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((l_or X0) ((l_or X1) X2)))) of role definition named def_or3
% 0.45/0.68 A new definition: (((eq (Prop->(Prop->(Prop->Prop)))) or3) (fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((l_or X0) ((l_or X1) X2))))
% 0.45/0.68 Defined: or3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((l_or X0) ((l_or X1) X2)))
% 0.45/0.68 FOF formula (<kernel.Constant object at 0x2ad8d8346dd0>, <kernel.DependentProduct object at 0x2ad8d8346f38>) of role type named typ_and3
% 0.45/0.68 Using role type
% 0.45/0.68 Declaring and3:(Prop->(Prop->(Prop->Prop)))
% 0.45/0.68 FOF formula (((eq (Prop->(Prop->(Prop->Prop)))) and3) (fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and X0) ((d_and X1) X2)))) of role definition named def_and3
% 0.45/0.68 A new definition: (((eq (Prop->(Prop->(Prop->Prop)))) and3) (fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and X0) ((d_and X1) X2))))
% 0.45/0.68 Defined: and3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and X0) ((d_and X1) X2)))
% 0.45/0.68 FOF formula (<kernel.Constant object at 0x2ad8d8346f38>, <kernel.DependentProduct object at 0x2ad8d8346e18>) of role type named typ_ec3
% 0.45/0.68 Using role type
% 0.45/0.68 Declaring ec3:(Prop->(Prop->(Prop->Prop)))
% 0.45/0.68 FOF formula (((eq (Prop->(Prop->(Prop->Prop)))) ec3) (fun (X0:Prop) (X1:Prop) (X2:Prop)=> (((and3 ((l_ec X0) X1)) ((l_ec X1) X2)) ((l_ec X2) X0)))) of role definition named def_ec3
% 0.45/0.68 A new definition: (((eq (Prop->(Prop->(Prop->Prop)))) ec3) (fun (X0:Prop) (X1:Prop) (X2:Prop)=> (((and3 ((l_ec X0) X1)) ((l_ec X1) X2)) ((l_ec X2) X0))))
% 0.45/0.68 Defined: ec3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> (((and3 ((l_ec X0) X1)) ((l_ec X1) X2)) ((l_ec X2) X0)))
% 0.45/0.68 FOF formula (<kernel.Constant object at 0x2ad8d8346e18>, <kernel.DependentProduct object at 0x2ad8d8346ea8>) of role type named typ_orec3
% 0.45/0.68 Using role type
% 0.45/0.68 Declaring orec3:(Prop->(Prop->(Prop->Prop)))
% 0.45/0.68 FOF formula (((eq (Prop->(Prop->(Prop->Prop)))) orec3) (fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and (((or3 X0) X1) X2)) (((ec3 X0) X1) X2)))) of role definition named def_orec3
% 0.45/0.68 A new definition: (((eq (Prop->(Prop->(Prop->Prop)))) orec3) (fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and (((or3 X0) X1) X2)) (((ec3 X0) X1) X2))))
% 0.45/0.68 Defined: orec3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and (((or3 X0) X1) X2)) (((ec3 X0) X1) X2)))
% 0.45/0.68 FOF formula (<kernel.Constant object at 0x2ad8d8346ea8>, <kernel.DependentProduct object at 0x2ad8d8346b90>) of role type named typ_e_is
% 0.45/0.68 Using role type
% 0.45/0.68 Declaring e_is:(fofType->(fofType->(fofType->Prop)))
% 0.45/0.68 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) e_is) (fun (X0:fofType) (X:fofType) (Y:fofType)=> (((eq fofType) X) Y))) of role definition named def_e_is
% 0.45/0.68 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) e_is) (fun (X0:fofType) (X:fofType) (Y:fofType)=> (((eq fofType) X) Y)))
% 0.45/0.68 Defined: e_is:=(fun (X0:fofType) (X:fofType) (Y:fofType)=> (((eq fofType) X) Y))
% 0.45/0.68 FOF formula (forall (X0:fofType), ((all_of (fun (X1:fofType)=> ((in X1) X0))) (fun (X1:fofType)=> (((e_is X0) X1) X1)))) of role axiom named refis
% 0.45/0.68 A new axiom: (forall (X0:fofType), ((all_of (fun (X1:fofType)=> ((in X1) X0))) (fun (X1:fofType)=> (((e_is X0) X1) X1))))
% 0.45/0.68 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X0))) (fun (X3:fofType)=> ((X1 X2)->((((e_is X0) X2) X3)->(X1 X3)))))))) of role axiom named e_isp
% 0.45/0.68 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X0))) (fun (X3:fofType)=> ((X1 X2)->((((e_is X0) X2) X3)->(X1 X3))))))))
% 0.45/0.70 FOF formula (<kernel.Constant object at 0x2ad8d8346d40>, <kernel.DependentProduct object at 0x2ad8d8346d88>) of role type named typ_amone
% 0.45/0.70 Using role type
% 0.45/0.70 Declaring amone:(fofType->((fofType->Prop)->Prop))
% 0.45/0.70 FOF formula (((eq (fofType->((fofType->Prop)->Prop))) amone) (fun (X0:fofType) (X1:(fofType->Prop))=> ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X0))) (fun (X3:fofType)=> ((X1 X2)->((X1 X3)->(((e_is X0) X2) X3))))))))) of role definition named def_amone
% 0.45/0.70 A new definition: (((eq (fofType->((fofType->Prop)->Prop))) amone) (fun (X0:fofType) (X1:(fofType->Prop))=> ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X0))) (fun (X3:fofType)=> ((X1 X2)->((X1 X3)->(((e_is X0) X2) X3)))))))))
% 0.45/0.70 Defined: amone:=(fun (X0:fofType) (X1:(fofType->Prop))=> ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X0))) (fun (X3:fofType)=> ((X1 X2)->((X1 X3)->(((e_is X0) X2) X3))))))))
% 0.45/0.70 FOF formula (<kernel.Constant object at 0x2ad8d8346d88>, <kernel.DependentProduct object at 0x2ad8d8346a70>) of role type named typ_one
% 0.45/0.70 Using role type
% 0.45/0.70 Declaring one:(fofType->((fofType->Prop)->Prop))
% 0.45/0.70 FOF formula (((eq (fofType->((fofType->Prop)->Prop))) one) (fun (X0:fofType) (X1:(fofType->Prop))=> ((d_and ((amone X0) X1)) ((l_some X0) X1)))) of role definition named def_one
% 0.45/0.70 A new definition: (((eq (fofType->((fofType->Prop)->Prop))) one) (fun (X0:fofType) (X1:(fofType->Prop))=> ((d_and ((amone X0) X1)) ((l_some X0) X1))))
% 0.45/0.70 Defined: one:=(fun (X0:fofType) (X1:(fofType->Prop))=> ((d_and ((amone X0) X1)) ((l_some X0) X1)))
% 0.45/0.70 FOF formula (<kernel.Constant object at 0x2ad8d8346a70>, <kernel.DependentProduct object at 0x2ad8d8346f38>) of role type named typ_ind
% 0.45/0.70 Using role type
% 0.45/0.70 Declaring ind:(fofType->((fofType->Prop)->fofType))
% 0.45/0.70 FOF formula (((eq (fofType->((fofType->Prop)->fofType))) ind) (fun (X0:fofType) (X1:(fofType->Prop))=> (eps (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2)))))) of role definition named def_ind
% 0.45/0.70 A new definition: (((eq (fofType->((fofType->Prop)->fofType))) ind) (fun (X0:fofType) (X1:(fofType->Prop))=> (eps (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2))))))
% 0.45/0.70 Defined: ind:=(fun (X0:fofType) (X1:(fofType->Prop))=> (eps (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2)))))
% 0.45/0.70 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)), (((one X0) X1)->((is_of ((ind X0) X1)) (fun (X2:fofType)=> ((in X2) X0))))) of role axiom named ind_p
% 0.45/0.70 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)), (((one X0) X1)->((is_of ((ind X0) X1)) (fun (X2:fofType)=> ((in X2) X0)))))
% 0.45/0.70 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)), (((one X0) X1)->(X1 ((ind X0) X1)))) of role axiom named oneax
% 0.45/0.70 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)), (((one X0) X1)->(X1 ((ind X0) X1))))
% 0.45/0.70 FOF formula (<kernel.Constant object at 0x2ad8d8346f38>, <kernel.DependentProduct object at 0x2ad8d8346560>) of role type named typ_injective
% 0.45/0.70 Using role type
% 0.45/0.70 Declaring injective:(fofType->(fofType->(fofType->Prop)))
% 0.45/0.70 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) injective) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((all X0) (fun (X4:fofType)=> ((imp (((e_is X1) ((ap X2) X3)) ((ap X2) X4))) (((e_is X0) X3) X4)))))))) of role definition named def_injective
% 0.45/0.70 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) injective) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((all X0) (fun (X4:fofType)=> ((imp (((e_is X1) ((ap X2) X3)) ((ap X2) X4))) (((e_is X0) X3) X4))))))))
% 0.45/0.70 Defined: injective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((all X0) (fun (X4:fofType)=> ((imp (((e_is X1) ((ap X2) X3)) ((ap X2) X4))) (((e_is X0) X3) X4)))))))
% 0.45/0.70 FOF formula (<kernel.Constant object at 0x2ad8d8346d88>, <kernel.DependentProduct object at 0x2ad8d834c1b8>) of role type named typ_image
% 0.45/0.70 Using role type
% 0.45/0.70 Declaring image:(fofType->(fofType->(fofType->(fofType->Prop))))
% 0.45/0.70 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) image) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((l_some X0) (fun (X4:fofType)=> (((e_is X1) X3) ((ap X2) X4)))))) of role definition named def_image
% 0.45/0.71 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) image) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((l_some X0) (fun (X4:fofType)=> (((e_is X1) X3) ((ap X2) X4))))))
% 0.45/0.71 Defined: image:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((l_some X0) (fun (X4:fofType)=> (((e_is X1) X3) ((ap X2) X4)))))
% 0.45/0.71 FOF formula (<kernel.Constant object at 0x2ad8d8346d88>, <kernel.DependentProduct object at 0x2ad8d834c200>) of role type named typ_tofs
% 0.45/0.71 Using role type
% 0.45/0.71 Declaring tofs:(fofType->(fofType->(fofType->(fofType->fofType))))
% 0.45/0.71 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) tofs) (fun (X0:fofType) (X1:fofType)=> ap)) of role definition named def_tofs
% 0.45/0.71 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) tofs) (fun (X0:fofType) (X1:fofType)=> ap))
% 0.45/0.71 Defined: tofs:=(fun (X0:fofType) (X1:fofType)=> ap)
% 0.45/0.71 FOF formula (<kernel.Constant object at 0x2ad8d8346d88>, <kernel.DependentProduct object at 0x2ad8d834c998>) of role type named typ_soft
% 0.45/0.71 Using role type
% 0.45/0.71 Declaring soft:(fofType->(fofType->(fofType->(fofType->fofType))))
% 0.45/0.71 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) soft) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X0) (fun (X4:fofType)=> (((e_is X1) X3) ((ap X2) X4)))))) of role definition named def_soft
% 0.45/0.71 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) soft) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X0) (fun (X4:fofType)=> (((e_is X1) X3) ((ap X2) X4))))))
% 0.45/0.71 Defined: soft:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X0) (fun (X4:fofType)=> (((e_is X1) X3) ((ap X2) X4)))))
% 0.45/0.71 FOF formula (<kernel.Constant object at 0x2ad8d834c998>, <kernel.DependentProduct object at 0x2ad8d834c290>) of role type named typ_inverse
% 0.45/0.71 Using role type
% 0.45/0.71 Declaring inverse:(fofType->(fofType->(fofType->fofType)))
% 0.45/0.71 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) inverse) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (fun (X3:fofType)=> (((if ((((image X0) X1) X2) X3)) ((((soft X0) X1) X2) X3)) emptyset))))) of role definition named def_inverse
% 0.45/0.71 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) inverse) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (fun (X3:fofType)=> (((if ((((image X0) X1) X2) X3)) ((((soft X0) X1) X2) X3)) emptyset)))))
% 0.45/0.71 Defined: inverse:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (fun (X3:fofType)=> (((if ((((image X0) X1) X2) X3)) ((((soft X0) X1) X2) X3)) emptyset))))
% 0.45/0.71 FOF formula (<kernel.Constant object at 0x2ad8d834c290>, <kernel.DependentProduct object at 0x2ad8d834c908>) of role type named typ_surjective
% 0.45/0.71 Using role type
% 0.45/0.71 Declaring surjective:(fofType->(fofType->(fofType->Prop)))
% 0.45/0.71 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) surjective) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X1) (((image X0) X1) X2)))) of role definition named def_surjective
% 0.45/0.71 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) surjective) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X1) (((image X0) X1) X2))))
% 0.45/0.71 Defined: surjective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X1) (((image X0) X1) X2)))
% 0.45/0.71 FOF formula (<kernel.Constant object at 0x2ad8d834c908>, <kernel.DependentProduct object at 0x2ad8d834c248>) of role type named typ_bijective
% 0.45/0.71 Using role type
% 0.45/0.71 Declaring bijective:(fofType->(fofType->(fofType->Prop)))
% 0.45/0.71 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) bijective) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and (((injective X0) X1) X2)) (((surjective X0) X1) X2)))) of role definition named def_bijective
% 0.45/0.71 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) bijective) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and (((injective X0) X1) X2)) (((surjective X0) X1) X2))))
% 0.45/0.71 Defined: bijective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and (((injective X0) X1) X2)) (((surjective X0) X1) X2)))
% 0.54/0.73 FOF formula (<kernel.Constant object at 0x2ad8d834c248>, <kernel.DependentProduct object at 0x2ad8d834c3b0>) of role type named typ_invf
% 0.54/0.73 Using role type
% 0.54/0.73 Declaring invf:(fofType->(fofType->(fofType->fofType)))
% 0.54/0.73 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) invf) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (((soft X0) X1) X2)))) of role definition named def_invf
% 0.54/0.73 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) invf) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (((soft X0) X1) X2))))
% 0.54/0.73 Defined: invf:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (((soft X0) X1) X2)))
% 0.54/0.73 FOF formula (<kernel.Constant object at 0x2ad8d834c3b0>, <kernel.DependentProduct object at 0x2ad8d834c290>) of role type named typ_inj_h
% 0.54/0.73 Using role type
% 0.54/0.73 Declaring inj_h:(fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))
% 0.54/0.73 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))) inj_h) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_Sigma X0) (fun (X5:fofType)=> ((ap X4) ((ap X3) X5)))))) of role definition named def_inj_h
% 0.54/0.73 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))) inj_h) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_Sigma X0) (fun (X5:fofType)=> ((ap X4) ((ap X3) X5))))))
% 0.54/0.73 Defined: inj_h:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_Sigma X0) (fun (X5:fofType)=> ((ap X4) ((ap X3) X5)))))
% 0.54/0.73 FOF formula (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Pi X0) (fun (X3:fofType)=> X1))))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) ((d_Pi X0) (fun (X4:fofType)=> X1))))) (fun (X3:fofType)=> (((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> (((e_is X1) ((ap X2) X4)) ((ap X3) X4))))->(((e_is ((d_Pi X0) (fun (X4:fofType)=> X1))) X2) X3))))))) of role axiom named e_fisi
% 0.54/0.73 A new axiom: (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Pi X0) (fun (X3:fofType)=> X1))))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) ((d_Pi X0) (fun (X4:fofType)=> X1))))) (fun (X3:fofType)=> (((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> (((e_is X1) ((ap X2) X4)) ((ap X3) X4))))->(((e_is ((d_Pi X0) (fun (X4:fofType)=> X1))) X2) X3)))))))
% 0.54/0.73 FOF formula (<kernel.Constant object at 0x2ad8d834cab8>, <kernel.DependentProduct object at 0x2ad8d834c2d8>) of role type named typ_e_in
% 0.54/0.73 Using role type
% 0.54/0.73 Declaring e_in:(fofType->((fofType->Prop)->(fofType->fofType)))
% 0.54/0.73 FOF formula (((eq (fofType->((fofType->Prop)->(fofType->fofType)))) e_in) (fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> X2)) of role definition named def_e_in
% 0.54/0.73 A new definition: (((eq (fofType->((fofType->Prop)->(fofType->fofType)))) e_in) (fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> X2))
% 0.54/0.73 Defined: e_in:=(fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> X2)
% 0.54/0.73 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Sep X0) X1)))) (fun (X2:fofType)=> ((is_of (((e_in X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X0)))))) of role axiom named e_in_p
% 0.54/0.73 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Sep X0) X1)))) (fun (X2:fofType)=> ((is_of (((e_in X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X0))))))
% 0.54/0.73 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Sep X0) X1)))) (fun (X2:fofType)=> (X1 (((e_in X0) X1) X2))))) of role axiom named e_inp
% 0.54/0.73 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Sep X0) X1)))) (fun (X2:fofType)=> (X1 (((e_in X0) X1) X2)))))
% 0.54/0.73 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)), (((injective ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1)))) of role axiom named otax1
% 0.54/0.73 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)), (((injective ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1))))
% 0.54/0.73 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((X1 X2)->((((image ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1))) X2))))) of role axiom named otax2
% 0.54/0.75 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((X1 X2)->((((image ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1))) X2)))))
% 0.54/0.75 FOF formula (<kernel.Constant object at 0x2ad8d834c098>, <kernel.DependentProduct object at 0x2ad8d834ce18>) of role type named typ_out
% 0.54/0.75 Using role type
% 0.54/0.75 Declaring out:(fofType->((fofType->Prop)->(fofType->fofType)))
% 0.54/0.75 FOF formula (((eq (fofType->((fofType->Prop)->(fofType->fofType)))) out) (fun (X0:fofType) (X1:(fofType->Prop))=> (((soft ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1))))) of role definition named def_out
% 0.54/0.75 A new definition: (((eq (fofType->((fofType->Prop)->(fofType->fofType)))) out) (fun (X0:fofType) (X1:(fofType->Prop))=> (((soft ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1)))))
% 0.54/0.75 Defined: out:=(fun (X0:fofType) (X1:(fofType->Prop))=> (((soft ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1))))
% 0.54/0.75 FOF formula (<kernel.Constant object at 0x2ad8d834ce18>, <kernel.DependentProduct object at 0x2ad8d834c758>) of role type named typ_d_pair
% 0.54/0.75 Using role type
% 0.54/0.75 Declaring d_pair:(fofType->(fofType->(fofType->(fofType->fofType))))
% 0.54/0.75 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) d_pair) (fun (X0:fofType) (X1:fofType)=> pair)) of role definition named def_d_pair
% 0.54/0.75 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) d_pair) (fun (X0:fofType) (X1:fofType)=> pair))
% 0.54/0.75 Defined: d_pair:=(fun (X0:fofType) (X1:fofType)=> pair)
% 0.54/0.75 FOF formula (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> ((is_of ((((d_pair X0) X1) X2) X3)) (fun (X4:fofType)=> ((in X4) ((setprod X0) X1))))))))) of role axiom named e_pair_p
% 0.54/0.75 A new axiom: (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> ((is_of ((((d_pair X0) X1) X2) X3)) (fun (X4:fofType)=> ((in X4) ((setprod X0) X1)))))))))
% 0.54/0.75 FOF formula (<kernel.Constant object at 0x2ad8d834cb00>, <kernel.DependentProduct object at 0x2ad8d834cc68>) of role type named typ_first
% 0.54/0.75 Using role type
% 0.54/0.75 Declaring first:(fofType->(fofType->(fofType->fofType)))
% 0.54/0.75 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) first) (fun (X0:fofType) (X1:fofType)=> proj0)) of role definition named def_first
% 0.54/0.75 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) first) (fun (X0:fofType) (X1:fofType)=> proj0))
% 0.54/0.75 Defined: first:=(fun (X0:fofType) (X1:fofType)=> proj0)
% 0.54/0.75 FOF formula (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> ((is_of (((first X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X0)))))) of role axiom named first_p
% 0.54/0.75 A new axiom: (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> ((is_of (((first X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X0))))))
% 0.54/0.75 FOF formula (<kernel.Constant object at 0x2ad8d834c098>, <kernel.DependentProduct object at 0x2ad8d834c710>) of role type named typ_second
% 0.54/0.75 Using role type
% 0.54/0.75 Declaring second:(fofType->(fofType->(fofType->fofType)))
% 0.54/0.75 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) second) (fun (X0:fofType) (X1:fofType)=> _TPTP_proj1)) of role definition named def_second
% 0.54/0.75 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) second) (fun (X0:fofType) (X1:fofType)=> _TPTP_proj1))
% 0.54/0.75 Defined: second:=(fun (X0:fofType) (X1:fofType)=> _TPTP_proj1)
% 0.54/0.75 FOF formula (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> ((is_of (((second X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X1)))))) of role axiom named second_p
% 0.54/0.75 A new axiom: (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> ((is_of (((second X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X1))))))
% 0.54/0.77 FOF formula (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> (((e_is ((setprod X0) X1)) ((((d_pair X0) X1) (((first X0) X1) X2)) (((second X0) X1) X2))) X2)))) of role axiom named pairis1
% 0.54/0.77 A new axiom: (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> (((e_is ((setprod X0) X1)) ((((d_pair X0) X1) (((first X0) X1) X2)) (((second X0) X1) X2))) X2))))
% 0.54/0.77 FOF formula (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> (((e_is X0) (((first X0) X1) ((((d_pair X0) X1) X2) X3))) X2)))))) of role axiom named firstis1
% 0.54/0.77 A new axiom: (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> (((e_is X0) (((first X0) X1) ((((d_pair X0) X1) X2) X3))) X2))))))
% 0.54/0.77 FOF formula (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> (((e_is X1) (((second X0) X1) ((((d_pair X0) X1) X2) X3))) X3)))))) of role axiom named secondis1
% 0.54/0.77 A new axiom: (forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> (((e_is X1) (((second X0) X1) ((((d_pair X0) X1) X2) X3))) X3))))))
% 0.54/0.77 FOF formula (<kernel.Constant object at 0x2ad8d834cef0>, <kernel.DependentProduct object at 0x2ad8d834c680>) of role type named typ_prop1
% 0.54/0.77 Using role type
% 0.54/0.77 Declaring prop1:(Prop->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 0.54/0.77 FOF formula (((eq (Prop->(fofType->(fofType->(fofType->(fofType->Prop)))))) prop1) (fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_and ((imp X0) (((e_is X1) X4) X2))) ((imp (d_not X0)) (((e_is X1) X4) X3))))) of role definition named def_prop1
% 0.54/0.77 A new definition: (((eq (Prop->(fofType->(fofType->(fofType->(fofType->Prop)))))) prop1) (fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_and ((imp X0) (((e_is X1) X4) X2))) ((imp (d_not X0)) (((e_is X1) X4) X3)))))
% 0.54/0.77 Defined: prop1:=(fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_and ((imp X0) (((e_is X1) X4) X2))) ((imp (d_not X0)) (((e_is X1) X4) X3))))
% 0.54/0.77 FOF formula (<kernel.Constant object at 0x2ad8d834c680>, <kernel.DependentProduct object at 0x2ad8d834cef0>) of role type named typ_ite
% 0.54/0.77 Using role type
% 0.54/0.77 Declaring ite:(Prop->(fofType->(fofType->(fofType->fofType))))
% 0.54/0.77 FOF formula (((eq (Prop->(fofType->(fofType->(fofType->fofType))))) ite) (fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X1) ((((prop1 X0) X1) X2) X3)))) of role definition named def_ite
% 0.54/0.77 A new definition: (((eq (Prop->(fofType->(fofType->(fofType->fofType))))) ite) (fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X1) ((((prop1 X0) X1) X2) X3))))
% 0.54/0.77 Defined: ite:=(fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X1) ((((prop1 X0) X1) X2) X3)))
% 0.54/0.77 FOF formula (<kernel.Constant object at 0x2ad8d834cef0>, <kernel.DependentProduct object at 0x2ad8d834c488>) of role type named typ_wissel_wa
% 0.54/0.77 Using role type
% 0.54/0.77 Declaring wissel_wa:(fofType->(fofType->(fofType->(fofType->fofType))))
% 0.54/0.77 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) wissel_wa) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((ite (((e_is X0) X3) X1)) X0) X2) X3))) of role definition named def_wissel_wa
% 0.54/0.77 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) wissel_wa) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((ite (((e_is X0) X3) X1)) X0) X2) X3)))
% 0.54/0.77 Defined: wissel_wa:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((ite (((e_is X0) X3) X1)) X0) X2) X3))
% 0.54/0.77 FOF formula (<kernel.Constant object at 0x2ad8d834c488>, <kernel.DependentProduct object at 0x2ad8d834cfc8>) of role type named typ_wissel_wb
% 0.60/0.79 Using role type
% 0.60/0.79 Declaring wissel_wb:(fofType->(fofType->(fofType->(fofType->fofType))))
% 0.60/0.79 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) wissel_wb) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((ite (((e_is X0) X3) X2)) X0) X1) ((((wissel_wa X0) X1) X2) X3)))) of role definition named def_wissel_wb
% 0.60/0.79 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) wissel_wb) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((ite (((e_is X0) X3) X2)) X0) X1) ((((wissel_wa X0) X1) X2) X3))))
% 0.60/0.79 Defined: wissel_wb:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((ite (((e_is X0) X3) X2)) X0) X1) ((((wissel_wa X0) X1) X2) X3)))
% 0.60/0.79 FOF formula (<kernel.Constant object at 0x2ad8d834cfc8>, <kernel.DependentProduct object at 0x2ad8d834cd88>) of role type named typ_wissel
% 0.60/0.79 Using role type
% 0.60/0.79 Declaring wissel:(fofType->(fofType->(fofType->fofType)))
% 0.60/0.79 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) wissel) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X0) (((wissel_wb X0) X1) X2)))) of role definition named def_wissel
% 0.60/0.79 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) wissel) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X0) (((wissel_wb X0) X1) X2))))
% 0.60/0.79 Defined: wissel:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X0) (((wissel_wb X0) X1) X2)))
% 0.60/0.79 FOF formula (<kernel.Constant object at 0x2ad8d834c878>, <kernel.DependentProduct object at 0x2ad8d834c830>) of role type named typ_changef
% 0.60/0.79 Using role type
% 0.60/0.79 Declaring changef:(fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))
% 0.60/0.79 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))) changef) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_Sigma X0) (fun (X5:fofType)=> ((ap X2) ((ap (((wissel X0) X3) X4)) X5)))))) of role definition named def_changef
% 0.60/0.79 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))) changef) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_Sigma X0) (fun (X5:fofType)=> ((ap X2) ((ap (((wissel X0) X3) X4)) X5))))))
% 0.60/0.79 Defined: changef:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_Sigma X0) (fun (X5:fofType)=> ((ap X2) ((ap (((wissel X0) X3) X4)) X5)))))
% 0.60/0.79 FOF formula (<kernel.Constant object at 0x2ad8d834c248>, <kernel.DependentProduct object at 0x2ad8d834cd88>) of role type named typ_r_ec
% 0.60/0.79 Using role type
% 0.60/0.79 Declaring r_ec:(Prop->(Prop->Prop))
% 0.60/0.79 FOF formula (((eq (Prop->(Prop->Prop))) r_ec) (fun (X0:Prop) (X1:Prop)=> (X0->(d_not X1)))) of role definition named def_r_ec
% 0.60/0.79 A new definition: (((eq (Prop->(Prop->Prop))) r_ec) (fun (X0:Prop) (X1:Prop)=> (X0->(d_not X1))))
% 0.60/0.79 Defined: r_ec:=(fun (X0:Prop) (X1:Prop)=> (X0->(d_not X1)))
% 0.60/0.79 FOF formula (<kernel.Constant object at 0x2ad8d834cd88>, <kernel.DependentProduct object at 0x2ad8d834c830>) of role type named typ_esti
% 0.60/0.79 Using role type
% 0.60/0.79 Declaring esti:(fofType->(fofType->(fofType->Prop)))
% 0.60/0.79 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) esti) (fun (X0:fofType)=> in)) of role definition named def_esti
% 0.60/0.79 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) esti) (fun (X0:fofType)=> in))
% 0.60/0.79 Defined: esti:=(fun (X0:fofType)=> in)
% 0.60/0.79 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)), ((is_of ((d_Sep X0) X1)) (fun (X2:fofType)=> ((in X2) (power X0))))) of role axiom named setof_p
% 0.60/0.79 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)), ((is_of ((d_Sep X0) X1)) (fun (X2:fofType)=> ((in X2) (power X0)))))
% 0.60/0.79 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((X1 X2)->(((esti X0) X2) ((d_Sep X0) X1)))))) of role axiom named estii
% 0.60/0.79 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((X1 X2)->(((esti X0) X2) ((d_Sep X0) X1))))))
% 0.60/0.79 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((((esti X0) X2) ((d_Sep X0) X1))->(X1 X2))))) of role axiom named estie
% 0.60/0.80 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((((esti X0) X2) ((d_Sep X0) X1))->(X1 X2)))))
% 0.60/0.80 FOF formula (<kernel.Constant object at 0x2ad8d834c830>, <kernel.DependentProduct object at 0x2ad8d8353638>) of role type named typ_empty
% 0.60/0.80 Using role type
% 0.60/0.80 Declaring empty:(fofType->(fofType->Prop))
% 0.60/0.80 FOF formula (((eq (fofType->(fofType->Prop))) empty) (fun (X0:fofType) (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) X0))) ((non X0) (fun (X2:fofType)=> (((esti X0) X2) X1)))))) of role definition named def_empty
% 0.60/0.80 A new definition: (((eq (fofType->(fofType->Prop))) empty) (fun (X0:fofType) (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) X0))) ((non X0) (fun (X2:fofType)=> (((esti X0) X2) X1))))))
% 0.60/0.80 Defined: empty:=(fun (X0:fofType) (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) X0))) ((non X0) (fun (X2:fofType)=> (((esti X0) X2) X1)))))
% 0.60/0.80 FOF formula (<kernel.Constant object at 0x2ad8d834c830>, <kernel.DependentProduct object at 0x2ad8d8353440>) of role type named typ_nonempty
% 0.60/0.80 Using role type
% 0.60/0.80 Declaring nonempty:(fofType->(fofType->Prop))
% 0.60/0.80 FOF formula (((eq (fofType->(fofType->Prop))) nonempty) (fun (X0:fofType) (X1:fofType)=> ((l_some X0) (fun (X2:fofType)=> (((esti X0) X2) X1))))) of role definition named def_nonempty
% 0.60/0.80 A new definition: (((eq (fofType->(fofType->Prop))) nonempty) (fun (X0:fofType) (X1:fofType)=> ((l_some X0) (fun (X2:fofType)=> (((esti X0) X2) X1)))))
% 0.60/0.80 Defined: nonempty:=(fun (X0:fofType) (X1:fofType)=> ((l_some X0) (fun (X2:fofType)=> (((esti X0) X2) X1))))
% 0.60/0.80 FOF formula (<kernel.Constant object at 0x2ad8d834c830>, <kernel.DependentProduct object at 0x2ad8d8353098>) of role type named typ_incl
% 0.60/0.80 Using role type
% 0.60/0.80 Declaring incl:(fofType->(fofType->(fofType->Prop)))
% 0.60/0.80 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) incl) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((imp (((esti X0) X3) X1)) (((esti X0) X3) X2)))))) of role definition named def_incl
% 0.60/0.80 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) incl) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((imp (((esti X0) X3) X1)) (((esti X0) X3) X2))))))
% 0.60/0.80 Defined: incl:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((imp (((esti X0) X3) X1)) (((esti X0) X3) X2)))))
% 0.60/0.80 FOF formula (<kernel.Constant object at 0x2ad8d8353098>, <kernel.DependentProduct object at 0x2ad8d8353638>) of role type named typ_st_disj
% 0.60/0.80 Using role type
% 0.60/0.80 Declaring st_disj:(fofType->(fofType->(fofType->Prop)))
% 0.60/0.80 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) st_disj) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((l_ec (((esti X0) X3) X1)) (((esti X0) X3) X2)))))) of role definition named def_st_disj
% 0.60/0.80 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) st_disj) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((l_ec (((esti X0) X3) X1)) (((esti X0) X3) X2))))))
% 0.60/0.80 Defined: st_disj:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((l_ec (((esti X0) X3) X1)) (((esti X0) X3) X2)))))
% 0.60/0.80 FOF formula (forall (X0:fofType), ((all_of (fun (X1:fofType)=> ((in X1) (power X0)))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) (power X0)))) (fun (X2:fofType)=> ((((incl X0) X1) X2)->((((incl X0) X2) X1)->(((e_is (power X0)) X1) X2)))))))) of role axiom named isseti
% 0.60/0.80 A new axiom: (forall (X0:fofType), ((all_of (fun (X1:fofType)=> ((in X1) (power X0)))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) (power X0)))) (fun (X2:fofType)=> ((((incl X0) X1) X2)->((((incl X0) X2) X1)->(((e_is (power X0)) X1) X2))))))))
% 0.60/0.80 FOF formula (<kernel.Constant object at 0x2ad8d83532d8>, <kernel.DependentProduct object at 0x2ad8d8353710>) of role type named typ_nissetprop
% 0.60/0.80 Using role type
% 0.60/0.80 Declaring nissetprop:(fofType->(fofType->(fofType->(fofType->Prop))))
% 0.60/0.80 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) nissetprop) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_and (((esti X0) X3) X1)) (d_not (((esti X0) X3) X2))))) of role definition named def_nissetprop
% 0.60/0.82 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) nissetprop) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_and (((esti X0) X3) X1)) (d_not (((esti X0) X3) X2)))))
% 0.60/0.82 Defined: nissetprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_and (((esti X0) X3) X1)) (d_not (((esti X0) X3) X2))))
% 0.60/0.82 FOF formula (<kernel.Constant object at 0x2ad8d8353710>, <kernel.DependentProduct object at 0x2ad8d8353098>) of role type named typ_unmore
% 0.60/0.82 Using role type
% 0.60/0.82 Declaring unmore:(fofType->(fofType->(fofType->fofType)))
% 0.60/0.82 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) unmore) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sep X0) (fun (X3:fofType)=> ((l_some X1) (fun (X4:fofType)=> (((esti X0) X3) ((ap X2) X4)))))))) of role definition named def_unmore
% 0.60/0.82 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) unmore) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sep X0) (fun (X3:fofType)=> ((l_some X1) (fun (X4:fofType)=> (((esti X0) X3) ((ap X2) X4))))))))
% 0.60/0.82 Defined: unmore:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sep X0) (fun (X3:fofType)=> ((l_some X1) (fun (X4:fofType)=> (((esti X0) X3) ((ap X2) X4)))))))
% 0.60/0.82 FOF formula (<kernel.Constant object at 0x2ad8d8353098>, <kernel.DependentProduct object at 0x2ad8d8353908>) of role type named typ_ecelt
% 0.60/0.82 Using role type
% 0.60/0.82 Declaring ecelt:(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 0.60/0.82 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->fofType)))) ecelt) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((d_Sep X0) (X1 X2)))) of role definition named def_ecelt
% 0.60/0.82 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->fofType)))) ecelt) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((d_Sep X0) (X1 X2))))
% 0.60/0.82 Defined: ecelt:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((d_Sep X0) (X1 X2)))
% 0.60/0.82 FOF formula (<kernel.Constant object at 0x2ad8d8353908>, <kernel.DependentProduct object at 0x2ad8d83538c0>) of role type named typ_ecp
% 0.60/0.82 Using role type
% 0.60/0.82 Declaring ecp:(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% 0.60/0.82 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))) ecp) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> (((e_is (power X0)) X2) (((ecelt X0) X1) X3)))) of role definition named def_ecp
% 0.60/0.82 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))) ecp) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> (((e_is (power X0)) X2) (((ecelt X0) X1) X3))))
% 0.60/0.82 Defined: ecp:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> (((e_is (power X0)) X2) (((ecelt X0) X1) X3)))
% 0.60/0.82 FOF formula (<kernel.Constant object at 0x2ad8d83538c0>, <kernel.DependentProduct object at 0x2ad8d8353c20>) of role type named typ_anec
% 0.60/0.82 Using role type
% 0.60/0.82 Declaring anec:(fofType->((fofType->(fofType->Prop))->(fofType->Prop)))
% 0.60/0.82 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->Prop)))) anec) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((l_some X0) (((ecp X0) X1) X2)))) of role definition named def_anec
% 0.60/0.82 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->Prop)))) anec) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((l_some X0) (((ecp X0) X1) X2))))
% 0.60/0.82 Defined: anec:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((l_some X0) (((ecp X0) X1) X2)))
% 0.60/0.82 FOF formula (<kernel.Constant object at 0x2ad8d8353c20>, <kernel.DependentProduct object at 0x2ad8d8353908>) of role type named typ_ect
% 0.60/0.82 Using role type
% 0.60/0.82 Declaring ect:(fofType->((fofType->(fofType->Prop))->fofType))
% 0.60/0.82 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->fofType))) ect) (fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((d_Sep (power X0)) ((anec X0) X1)))) of role definition named def_ect
% 0.60/0.82 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->fofType))) ect) (fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((d_Sep (power X0)) ((anec X0) X1))))
% 0.60/0.83 Defined: ect:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((d_Sep (power X0)) ((anec X0) X1)))
% 0.60/0.83 FOF formula (<kernel.Constant object at 0x2ad8d8353908>, <kernel.DependentProduct object at 0x2ad8d8353560>) of role type named typ_ectset
% 0.60/0.83 Using role type
% 0.60/0.83 Declaring ectset:(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 0.60/0.83 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->fofType)))) ectset) (fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((out (power X0)) ((anec X0) X1)))) of role definition named def_ectset
% 0.60/0.83 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->fofType)))) ectset) (fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((out (power X0)) ((anec X0) X1))))
% 0.60/0.83 Defined: ectset:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((out (power X0)) ((anec X0) X1)))
% 0.60/0.83 FOF formula (<kernel.Constant object at 0x2ad8d8353560>, <kernel.DependentProduct object at 0x2ad8d83533b0>) of role type named typ_ectelt
% 0.60/0.83 Using role type
% 0.60/0.83 Declaring ectelt:(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 0.60/0.83 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->fofType)))) ectelt) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((ectset X0) X1) (((ecelt X0) X1) X2)))) of role definition named def_ectelt
% 0.60/0.83 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->fofType)))) ectelt) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((ectset X0) X1) (((ecelt X0) X1) X2))))
% 0.60/0.83 Defined: ectelt:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((ectset X0) X1) (((ecelt X0) X1) X2)))
% 0.60/0.83 FOF formula (<kernel.Constant object at 0x2ad8d83533b0>, <kernel.DependentProduct object at 0x2ad8d8353b00>) of role type named typ_ecect
% 0.60/0.83 Using role type
% 0.60/0.83 Declaring ecect:(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 0.60/0.83 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->fofType)))) ecect) (fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((e_in (power X0)) ((anec X0) X1)))) of role definition named def_ecect
% 0.60/0.83 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->fofType)))) ecect) (fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((e_in (power X0)) ((anec X0) X1))))
% 0.60/0.83 Defined: ecect:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((e_in (power X0)) ((anec X0) X1)))
% 0.60/0.83 FOF formula (<kernel.Constant object at 0x2ad8d8353b00>, <kernel.DependentProduct object at 0x2ad8d8353320>) of role type named typ_fixfu
% 0.60/0.83 Using role type
% 0.60/0.83 Declaring fixfu:(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% 0.60/0.83 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))) fixfu) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> ((all_of (fun (X5:fofType)=> ((in X5) X0))) (fun (X5:fofType)=> (((X1 X4) X5)->(((e_is X2) ((ap X3) X4)) ((ap X3) X5))))))))) of role definition named def_fixfu
% 0.60/0.83 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))) fixfu) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> ((all_of (fun (X5:fofType)=> ((in X5) X0))) (fun (X5:fofType)=> (((X1 X4) X5)->(((e_is X2) ((ap X3) X4)) ((ap X3) X5)))))))))
% 0.60/0.83 Defined: fixfu:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> ((all_of (fun (X5:fofType)=> ((in X5) X0))) (fun (X5:fofType)=> (((X1 X4) X5)->(((e_is X2) ((ap X3) X4)) ((ap X3) X5))))))))
% 0.60/0.83 FOF formula (<kernel.Constant object at 0x2ad8d8353320>, <kernel.DependentProduct object at 0x2ad8d8353998>) of role type named typ_d_10_prop1
% 0.60/0.83 Using role type
% 0.60/0.83 Declaring d_10_prop1:(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))))
% 0.60/0.83 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))))) d_10_prop1) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType) (X5:fofType) (X6:fofType)=> ((d_and (((esti X0) X6) (((ecect X0) X1) X4))) (((e_is X2) ((ap X3) X6)) X5)))) of role definition named def_d_10_prop1
% 0.60/0.85 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))))) d_10_prop1) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType) (X5:fofType) (X6:fofType)=> ((d_and (((esti X0) X6) (((ecect X0) X1) X4))) (((e_is X2) ((ap X3) X6)) X5))))
% 0.60/0.85 Defined: d_10_prop1:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType) (X5:fofType) (X6:fofType)=> ((d_and (((esti X0) X6) (((ecect X0) X1) X4))) (((e_is X2) ((ap X3) X6)) X5)))
% 0.60/0.85 FOF formula (<kernel.Constant object at 0x2ad8d8353998>, <kernel.DependentProduct object at 0x2ad8d8353bd8>) of role type named typ_prop2
% 0.60/0.85 Using role type
% 0.60/0.85 Declaring prop2:(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->Prop))))))
% 0.60/0.85 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->Prop))))))) prop2) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType) (X5:fofType)=> ((l_some X0) ((((((d_10_prop1 X0) X1) X2) X3) X4) X5)))) of role definition named def_prop2
% 0.60/0.85 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->Prop))))))) prop2) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType) (X5:fofType)=> ((l_some X0) ((((((d_10_prop1 X0) X1) X2) X3) X4) X5))))
% 0.60/0.85 Defined: prop2:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType) (X5:fofType)=> ((l_some X0) ((((((d_10_prop1 X0) X1) X2) X3) X4) X5)))
% 0.60/0.85 FOF formula (<kernel.Constant object at 0x2ad8d8353bd8>, <kernel.DependentProduct object at 0x2ad8d8353e18>) of role type named typ_indeq
% 0.60/0.85 Using role type
% 0.60/0.85 Declaring indeq:(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType)))))
% 0.60/0.85 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType)))))) indeq) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType)=> ((ind X2) (((((prop2 X0) X1) X2) X3) X4)))) of role definition named def_indeq
% 0.60/0.85 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType)))))) indeq) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType)=> ((ind X2) (((((prop2 X0) X1) X2) X3) X4))))
% 0.60/0.85 Defined: indeq:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType)=> ((ind X2) (((((prop2 X0) X1) X2) X3) X4)))
% 0.60/0.85 FOF formula (<kernel.Constant object at 0x2ad8d8353e18>, <kernel.DependentProduct object at 0x2ad8d8353d88>) of role type named typ_fixfu2
% 0.60/0.85 Using role type
% 0.60/0.85 Declaring fixfu2:(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% 0.60/0.85 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))) fixfu2) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> ((all_of (fun (X5:fofType)=> ((in X5) X0))) (fun (X5:fofType)=> ((all_of (fun (X6:fofType)=> ((in X6) X0))) (fun (X6:fofType)=> ((all_of (fun (X7:fofType)=> ((in X7) X0))) (fun (X7:fofType)=> (((X1 X4) X5)->(((X1 X6) X7)->(((e_is X2) ((ap ((ap X3) X4)) X6)) ((ap ((ap X3) X5)) X7)))))))))))))) of role definition named def_fixfu2
% 0.60/0.85 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))) fixfu2) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> ((all_of (fun (X5:fofType)=> ((in X5) X0))) (fun (X5:fofType)=> ((all_of (fun (X6:fofType)=> ((in X6) X0))) (fun (X6:fofType)=> ((all_of (fun (X7:fofType)=> ((in X7) X0))) (fun (X7:fofType)=> (((X1 X4) X5)->(((X1 X6) X7)->(((e_is X2) ((ap ((ap X3) X4)) X6)) ((ap ((ap X3) X5)) X7))))))))))))))
% 0.60/0.85 Defined: fixfu2:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> ((all_of (fun (X5:fofType)=> ((in X5) X0))) (fun (X5:fofType)=> ((all_of (fun (X6:fofType)=> ((in X6) X0))) (fun (X6:fofType)=> ((all_of (fun (X7:fofType)=> ((in X7) X0))) (fun (X7:fofType)=> (((X1 X4) X5)->(((X1 X6) X7)->(((e_is X2) ((ap ((ap X3) X4)) X6)) ((ap ((ap X3) X5)) X7)))))))))))))
% 0.60/0.86 FOF formula (<kernel.Constant object at 0x2ad8d8353d88>, <kernel.DependentProduct object at 0x2ad8d83530e0>) of role type named typ_d_11_i
% 0.60/0.86 Using role type
% 0.60/0.86 Declaring d_11_i:(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType)))))
% 0.60/0.86 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType)))))) d_11_i) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((indeq X0) X1) ((d_Pi X0) (fun (X3:fofType)=> X2))))) of role definition named def_d_11_i
% 0.60/0.86 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType)))))) d_11_i) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((indeq X0) X1) ((d_Pi X0) (fun (X3:fofType)=> X2)))))
% 0.60/0.86 Defined: d_11_i:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((indeq X0) X1) ((d_Pi X0) (fun (X3:fofType)=> X2))))
% 0.60/0.86 FOF formula (<kernel.Constant object at 0x2ad8d83530e0>, <kernel.DependentProduct object at 0x2ad8d83539e0>) of role type named typ_indeq2
% 0.60/0.86 Using role type
% 0.60/0.86 Declaring indeq2:(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->fofType))))))
% 0.60/0.86 FOF formula (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->fofType))))))) indeq2) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType)=> ((((indeq X0) X1) X2) (((((d_11_i X0) X1) X2) X3) X4)))) of role definition named def_indeq2
% 0.60/0.86 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->fofType))))))) indeq2) (fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType)=> ((((indeq X0) X1) X2) (((((d_11_i X0) X1) X2) X3) X4))))
% 0.60/0.86 Defined: indeq2:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType)=> ((((indeq X0) X1) X2) (((((d_11_i X0) X1) X2) X3) X4)))
% 0.60/0.86 FOF formula (<kernel.Constant object at 0x2ad8d83539e0>, <kernel.Single object at 0x2ad8d83530e0>) of role type named typ_nat
% 0.60/0.86 Using role type
% 0.60/0.86 Declaring nat:fofType
% 0.60/0.86 FOF formula (((eq fofType) nat) ((d_Sep omega) (fun (X0:fofType)=> (not (((eq fofType) X0) emptyset))))) of role definition named def_nat
% 0.60/0.86 A new definition: (((eq fofType) nat) ((d_Sep omega) (fun (X0:fofType)=> (not (((eq fofType) X0) emptyset)))))
% 0.60/0.86 Defined: nat:=((d_Sep omega) (fun (X0:fofType)=> (not (((eq fofType) X0) emptyset))))
% 0.60/0.86 FOF formula (<kernel.Constant object at 0x2ad8d83530e0>, <kernel.DependentProduct object at 0x2ad8d8353b00>) of role type named typ_n_is
% 0.60/0.86 Using role type
% 0.60/0.86 Declaring n_is:(fofType->(fofType->Prop))
% 0.60/0.86 FOF formula (((eq (fofType->(fofType->Prop))) n_is) (e_is nat)) of role definition named def_n_is
% 0.60/0.86 A new definition: (((eq (fofType->(fofType->Prop))) n_is) (e_is nat))
% 0.60/0.86 Defined: n_is:=(e_is nat)
% 0.60/0.86 FOF formula (<kernel.Constant object at 0x2ad8d8353998>, <kernel.DependentProduct object at 0x2ad8d8353f38>) of role type named typ_nis
% 0.60/0.86 Using role type
% 0.60/0.86 Declaring nis:(fofType->(fofType->Prop))
% 0.60/0.86 FOF formula (((eq (fofType->(fofType->Prop))) nis) (fun (X0:fofType) (X1:fofType)=> (d_not ((n_is X0) X1)))) of role definition named def_nis
% 0.60/0.86 A new definition: (((eq (fofType->(fofType->Prop))) nis) (fun (X0:fofType) (X1:fofType)=> (d_not ((n_is X0) X1))))
% 0.60/0.86 Defined: nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((n_is X0) X1)))
% 0.60/0.86 FOF formula (<kernel.Constant object at 0x2ad8d8353f38>, <kernel.DependentProduct object at 0x2ad8d8353b00>) of role type named typ_n_in
% 0.60/0.86 Using role type
% 0.60/0.86 Declaring n_in:(fofType->(fofType->Prop))
% 0.60/0.86 FOF formula (((eq (fofType->(fofType->Prop))) n_in) (esti nat)) of role definition named def_n_in
% 0.60/0.86 A new definition: (((eq (fofType->(fofType->Prop))) n_in) (esti nat))
% 0.68/0.88 Defined: n_in:=(esti nat)
% 0.68/0.88 FOF formula (<kernel.Constant object at 0x2ad8d8353d40>, <kernel.DependentProduct object at 0x2ad8d8353b00>) of role type named typ_n_some
% 0.68/0.88 Using role type
% 0.68/0.88 Declaring n_some:((fofType->Prop)->Prop)
% 0.68/0.88 FOF formula (((eq ((fofType->Prop)->Prop)) n_some) (l_some nat)) of role definition named def_n_some
% 0.68/0.88 A new definition: (((eq ((fofType->Prop)->Prop)) n_some) (l_some nat))
% 0.68/0.88 Defined: n_some:=(l_some nat)
% 0.68/0.88 FOF formula (<kernel.Constant object at 0x2ad8d8353f80>, <kernel.DependentProduct object at 0x2ad8d8353b00>) of role type named typ_n_all
% 0.68/0.88 Using role type
% 0.68/0.88 Declaring n_all:((fofType->Prop)->Prop)
% 0.68/0.88 FOF formula (((eq ((fofType->Prop)->Prop)) n_all) (all nat)) of role definition named def_n_all
% 0.68/0.88 A new definition: (((eq ((fofType->Prop)->Prop)) n_all) (all nat))
% 0.68/0.88 Defined: n_all:=(all nat)
% 0.68/0.88 FOF formula (<kernel.Constant object at 0x2ad8d8353d40>, <kernel.DependentProduct object at 0x2ad8d8353e18>) of role type named typ_n_one
% 0.68/0.88 Using role type
% 0.68/0.88 Declaring n_one:((fofType->Prop)->Prop)
% 0.68/0.88 FOF formula (((eq ((fofType->Prop)->Prop)) n_one) (one nat)) of role definition named def_n_one
% 0.68/0.88 A new definition: (((eq ((fofType->Prop)->Prop)) n_one) (one nat))
% 0.68/0.88 Defined: n_one:=(one nat)
% 0.68/0.88 FOF formula (<kernel.Constant object at 0x2ad8d83538c0>, <kernel.Single object at 0x2ad8d8353d40>) of role type named typ_n_1
% 0.68/0.88 Using role type
% 0.68/0.88 Declaring n_1:fofType
% 0.68/0.88 FOF formula (((eq fofType) n_1) (ordsucc emptyset)) of role definition named def_n_1
% 0.68/0.88 A new definition: (((eq fofType) n_1) (ordsucc emptyset))
% 0.68/0.88 Defined: n_1:=(ordsucc emptyset)
% 0.68/0.88 FOF formula ((is_of n_1) (fun (X0:fofType)=> ((in X0) nat))) of role axiom named n_1_p
% 0.68/0.88 A new axiom: ((is_of n_1) (fun (X0:fofType)=> ((in X0) nat)))
% 0.68/0.88 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((is_of (ordsucc X0)) (fun (X1:fofType)=> ((in X1) nat))))) of role axiom named suc_p
% 0.68/0.88 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((is_of (ordsucc X0)) (fun (X1:fofType)=> ((in X1) nat)))))
% 0.68/0.88 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) n_1))) of role axiom named n_ax3
% 0.68/0.88 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) n_1)))
% 0.68/0.88 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((n_is (ordsucc X0)) (ordsucc X1))->((n_is X0) X1)))))) of role axiom named n_ax4
% 0.68/0.88 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((n_is (ordsucc X0)) (ordsucc X1))->((n_is X0) X1))))))
% 0.68/0.88 FOF formula (<kernel.Constant object at 0x2ad8d8353d40>, <kernel.DependentProduct object at 0x2ad8d8358290>) of role type named typ_cond1
% 0.68/0.88 Using role type
% 0.68/0.88 Declaring cond1:(fofType->Prop)
% 0.68/0.88 FOF formula (((eq (fofType->Prop)) cond1) (n_in n_1)) of role definition named def_cond1
% 0.68/0.88 A new definition: (((eq (fofType->Prop)) cond1) (n_in n_1))
% 0.68/0.88 Defined: cond1:=(n_in n_1)
% 0.68/0.88 FOF formula (<kernel.Constant object at 0x2ad8d8358998>, <kernel.DependentProduct object at 0x2ad8d83584d0>) of role type named typ_cond2
% 0.68/0.88 Using role type
% 0.68/0.88 Declaring cond2:(fofType->Prop)
% 0.68/0.88 FOF formula (((eq (fofType->Prop)) cond2) (fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((imp ((n_in X1) X0)) ((n_in (ordsucc X1)) X0)))))) of role definition named def_cond2
% 0.68/0.88 A new definition: (((eq (fofType->Prop)) cond2) (fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((imp ((n_in X1) X0)) ((n_in (ordsucc X1)) X0))))))
% 0.68/0.88 Defined: cond2:=(fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((imp ((n_in X1) X0)) ((n_in (ordsucc X1)) X0)))))
% 0.68/0.88 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) (power nat)))) (fun (X0:fofType)=> ((cond1 X0)->((cond2 X0)->((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_in X1) X0))))))) of role axiom named n_ax5
% 0.68/0.88 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) (power nat)))) (fun (X0:fofType)=> ((cond1 X0)->((cond2 X0)->((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_in X1) X0)))))))
% 0.68/0.88 FOF formula (<kernel.Constant object at 0x2ad8d83582d8>, <kernel.DependentProduct object at 0x2ad8d8358878>) of role type named typ_i1_s
% 0.70/0.89 Using role type
% 0.70/0.89 Declaring i1_s:((fofType->Prop)->fofType)
% 0.70/0.89 FOF formula (((eq ((fofType->Prop)->fofType)) i1_s) (d_Sep nat)) of role definition named def_i1_s
% 0.70/0.89 A new definition: (((eq ((fofType->Prop)->fofType)) i1_s) (d_Sep nat))
% 0.70/0.89 Defined: i1_s:=(d_Sep nat)
% 0.70/0.89 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((nis X0) X1)->((nis (ordsucc X0)) (ordsucc X1))))))) of role axiom named satz1
% 0.70/0.89 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((nis X0) X1)->((nis (ordsucc X0)) (ordsucc X1)))))))
% 0.70/0.89 FOF formula (<kernel.Constant object at 0x2ad8d4c65ea8>, <kernel.DependentProduct object at 0x2ad8d56b8fc8>) of role type named typ_d_22_prop1
% 0.70/0.89 Using role type
% 0.70/0.89 Declaring d_22_prop1:(fofType->Prop)
% 0.70/0.89 FOF formula (((eq (fofType->Prop)) d_22_prop1) (fun (X0:fofType)=> ((nis (ordsucc X0)) X0))) of role definition named def_d_22_prop1
% 0.70/0.89 A new definition: (((eq (fofType->Prop)) d_22_prop1) (fun (X0:fofType)=> ((nis (ordsucc X0)) X0)))
% 0.70/0.89 Defined: d_22_prop1:=(fun (X0:fofType)=> ((nis (ordsucc X0)) X0))
% 0.70/0.89 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) X0))) of role axiom named satz2
% 0.70/0.89 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) X0)))
% 0.70/0.89 FOF formula (<kernel.Constant object at 0x2ad8d50175a8>, <kernel.DependentProduct object at 0x2ad8d56de7e8>) of role type named typ_d_23_prop1
% 0.70/0.89 Using role type
% 0.70/0.89 Declaring d_23_prop1:(fofType->Prop)
% 0.70/0.89 FOF formula (((eq (fofType->Prop)) d_23_prop1) (fun (X0:fofType)=> ((l_or ((n_is X0) n_1)) (n_some (fun (X1:fofType)=> ((n_is X0) (ordsucc X1))))))) of role definition named def_d_23_prop1
% 0.70/0.89 A new definition: (((eq (fofType->Prop)) d_23_prop1) (fun (X0:fofType)=> ((l_or ((n_is X0) n_1)) (n_some (fun (X1:fofType)=> ((n_is X0) (ordsucc X1)))))))
% 0.70/0.89 Defined: d_23_prop1:=(fun (X0:fofType)=> ((l_or ((n_is X0) n_1)) (n_some (fun (X1:fofType)=> ((n_is X0) (ordsucc X1))))))
% 0.70/0.89 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> (((nis X0) n_1)->(n_some (fun (X1:fofType)=> ((n_is X0) (ordsucc X1))))))) of role axiom named satz3
% 0.70/0.89 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> (((nis X0) n_1)->(n_some (fun (X1:fofType)=> ((n_is X0) (ordsucc X1)))))))
% 0.70/0.89 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> (((nis X0) n_1)->(n_one (fun (X1:fofType)=> ((n_is X0) (ordsucc X1))))))) of role axiom named satz3a
% 0.70/0.89 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> (((nis X0) n_1)->(n_one (fun (X1:fofType)=> ((n_is X0) (ordsucc X1)))))))
% 0.70/0.89 FOF formula (<kernel.Constant object at 0x2ad8d56e4830>, <kernel.DependentProduct object at 0x2ad8d56de248>) of role type named typ_d_24_prop1
% 0.70/0.89 Using role type
% 0.70/0.89 Declaring d_24_prop1:(fofType->Prop)
% 0.70/0.89 FOF formula (((eq (fofType->Prop)) d_24_prop1) (fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((n_is ((ap X0) (ordsucc X1))) (ordsucc ((ap X0) X1))))))) of role definition named def_d_24_prop1
% 0.70/0.89 A new definition: (((eq (fofType->Prop)) d_24_prop1) (fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((n_is ((ap X0) (ordsucc X1))) (ordsucc ((ap X0) X1)))))))
% 0.70/0.89 Defined: d_24_prop1:=(fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((n_is ((ap X0) (ordsucc X1))) (ordsucc ((ap X0) X1))))))
% 0.70/0.89 FOF formula (<kernel.Constant object at 0x2ad8d56b8fc8>, <kernel.DependentProduct object at 0x2ad8d56de1b8>) of role type named typ_d_24_prop2
% 0.70/0.89 Using role type
% 0.70/0.89 Declaring d_24_prop2:(fofType->(fofType->Prop))
% 0.70/0.89 FOF formula (((eq (fofType->(fofType->Prop))) d_24_prop2) (fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc X0))) (d_24_prop1 X1)))) of role definition named def_d_24_prop2
% 0.70/0.89 A new definition: (((eq (fofType->(fofType->Prop))) d_24_prop2) (fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc X0))) (d_24_prop1 X1))))
% 0.70/0.89 Defined: d_24_prop2:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc X0))) (d_24_prop1 X1)))
% 0.70/0.91 FOF formula (<kernel.Constant object at 0x2ad8d56b8f38>, <kernel.DependentProduct object at 0x2ad8d56de7e8>) of role type named typ_prop3
% 0.70/0.91 Using role type
% 0.70/0.91 Declaring prop3:(fofType->(fofType->(fofType->Prop)))
% 0.70/0.91 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) prop3) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((ap X0) X2)) ((ap X1) X2)))) of role definition named def_prop3
% 0.70/0.91 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) prop3) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((ap X0) X2)) ((ap X1) X2))))
% 0.70/0.91 Defined: prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((ap X0) X2)) ((ap X1) X2)))
% 0.70/0.91 FOF formula (<kernel.Constant object at 0x2ad8d56de7e8>, <kernel.DependentProduct object at 0x2ad8d56de758>) of role type named typ_prop4
% 0.70/0.91 Using role type
% 0.70/0.91 Declaring prop4:(fofType->Prop)
% 0.70/0.91 FOF formula (((eq (fofType->Prop)) prop4) (fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0)))) of role definition named def_prop4
% 0.70/0.91 A new definition: (((eq (fofType->Prop)) prop4) (fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0))))
% 0.70/0.91 Defined: prop4:=(fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0)))
% 0.70/0.91 FOF formula (<kernel.Constant object at 0x2ad8d56de758>, <kernel.DependentProduct object at 0x2ad8d56de3b0>) of role type named typ_d_24_g
% 0.70/0.91 Using role type
% 0.70/0.91 Declaring d_24_g:(fofType->fofType)
% 0.70/0.91 FOF formula (((eq (fofType->fofType)) d_24_g) (fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> (ordsucc ((ap X0) X1)))))) of role definition named def_d_24_g
% 0.70/0.91 A new definition: (((eq (fofType->fofType)) d_24_g) (fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> (ordsucc ((ap X0) X1))))))
% 0.70/0.91 Defined: d_24_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> (ordsucc ((ap X0) X1)))))
% 0.70/0.91 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((one ((d_Pi nat) (fun (X1:fofType)=> nat))) (fun (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc X0))) (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) (ordsucc ((ap X1) X2)))))))))) of role axiom named satz4
% 0.70/0.91 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((one ((d_Pi nat) (fun (X1:fofType)=> nat))) (fun (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc X0))) (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) (ordsucc ((ap X1) X2))))))))))
% 0.70/0.91 FOF formula (<kernel.Constant object at 0x2ad8d56de170>, <kernel.DependentProduct object at 0x2ad8d56deb48>) of role type named typ_plus
% 0.70/0.91 Using role type
% 0.70/0.91 Declaring plus:(fofType->fofType)
% 0.70/0.91 FOF formula (((eq (fofType->fofType)) plus) (fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0)))) of role definition named def_plus
% 0.70/0.91 A new definition: (((eq (fofType->fofType)) plus) (fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0))))
% 0.70/0.91 Defined: plus:=(fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0)))
% 0.70/0.91 FOF formula (<kernel.Constant object at 0x2ad8d56deb48>, <kernel.DependentProduct object at 0x2ad8d56de3f8>) of role type named typ_n_pl
% 0.70/0.91 Using role type
% 0.70/0.91 Declaring n_pl:(fofType->(fofType->fofType))
% 0.70/0.91 FOF formula (((eq (fofType->(fofType->fofType))) n_pl) (fun (X0:fofType)=> (ap (plus X0)))) of role definition named def_n_pl
% 0.70/0.91 A new definition: (((eq (fofType->(fofType->fofType))) n_pl) (fun (X0:fofType)=> (ap (plus X0))))
% 0.70/0.91 Defined: n_pl:=(fun (X0:fofType)=> (ap (plus X0)))
% 0.70/0.91 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_pl X0) n_1)) (ordsucc X0)))) of role axiom named satz4a
% 0.70/0.91 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_pl X0) n_1)) (ordsucc X0))))
% 0.70/0.91 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl X0) (ordsucc X1))) (ordsucc ((n_pl X0) X1))))))) of role axiom named satz4b
% 0.70/0.91 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl X0) (ordsucc X1))) (ordsucc ((n_pl X0) X1)))))))
% 0.75/0.93 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_pl n_1) X0)) (ordsucc X0)))) of role axiom named satz4c
% 0.75/0.93 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_pl n_1) X0)) (ordsucc X0))))
% 0.75/0.93 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl (ordsucc X0)) X1)) (ordsucc ((n_pl X0) X1))))))) of role axiom named satz4d
% 0.75/0.93 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl (ordsucc X0)) X1)) (ordsucc ((n_pl X0) X1)))))))
% 0.75/0.93 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is (ordsucc X0)) ((n_pl X0) n_1)))) of role axiom named satz4e
% 0.75/0.93 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is (ordsucc X0)) ((n_pl X0) n_1))))
% 0.75/0.93 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is (ordsucc ((n_pl X0) X1))) ((n_pl X0) (ordsucc X1))))))) of role axiom named satz4f
% 0.75/0.93 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is (ordsucc ((n_pl X0) X1))) ((n_pl X0) (ordsucc X1)))))))
% 0.75/0.93 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is (ordsucc X0)) ((n_pl n_1) X0)))) of role axiom named satz4g
% 0.75/0.93 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is (ordsucc X0)) ((n_pl n_1) X0))))
% 0.75/0.93 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is (ordsucc ((n_pl X0) X1))) ((n_pl (ordsucc X0)) X1)))))) of role axiom named satz4h
% 0.75/0.93 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is (ordsucc ((n_pl X0) X1))) ((n_pl (ordsucc X0)) X1))))))
% 0.75/0.93 FOF formula (<kernel.Constant object at 0x2ad8d56dec20>, <kernel.DependentProduct object at 0x2ad8d56deef0>) of role type named typ_d_25_prop1
% 0.75/0.93 Using role type
% 0.75/0.93 Declaring d_25_prop1:(fofType->(fofType->(fofType->Prop)))
% 0.75/0.93 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) d_25_prop1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_pl ((n_pl X0) X1)) X2)) ((n_pl X0) ((n_pl X1) X2))))) of role definition named def_d_25_prop1
% 0.75/0.93 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) d_25_prop1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_pl ((n_pl X0) X1)) X2)) ((n_pl X0) ((n_pl X1) X2)))))
% 0.75/0.93 Defined: d_25_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_pl ((n_pl X0) X1)) X2)) ((n_pl X0) ((n_pl X1) X2))))
% 0.75/0.93 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_pl ((n_pl X0) X1)) X2)) ((n_pl X0) ((n_pl X1) X2))))))))) of role axiom named satz5
% 0.75/0.93 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_pl ((n_pl X0) X1)) X2)) ((n_pl X0) ((n_pl X1) X2)))))))))
% 0.75/0.93 FOF formula (<kernel.Constant object at 0x2ad8d56de128>, <kernel.DependentProduct object at 0x2ad8d56de290>) of role type named typ_d_26_prop1
% 0.75/0.93 Using role type
% 0.75/0.93 Declaring d_26_prop1:(fofType->(fofType->Prop))
% 0.75/0.93 FOF formula (((eq (fofType->(fofType->Prop))) d_26_prop1) (fun (X0:fofType) (X1:fofType)=> ((n_is ((n_pl X0) X1)) ((n_pl X1) X0)))) of role definition named def_d_26_prop1
% 0.75/0.93 A new definition: (((eq (fofType->(fofType->Prop))) d_26_prop1) (fun (X0:fofType) (X1:fofType)=> ((n_is ((n_pl X0) X1)) ((n_pl X1) X0))))
% 0.75/0.93 Defined: d_26_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_pl X0) X1)) ((n_pl X1) X0)))
% 0.75/0.95 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl X0) X1)) ((n_pl X1) X0)))))) of role axiom named satz6
% 0.75/0.95 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl X0) X1)) ((n_pl X1) X0))))))
% 0.75/0.95 FOF formula (<kernel.Constant object at 0x2ad8d56de998>, <kernel.DependentProduct object at 0x2ad8d56de638>) of role type named typ_d_27_prop1
% 0.75/0.95 Using role type
% 0.75/0.95 Declaring d_27_prop1:(fofType->(fofType->Prop))
% 0.75/0.95 FOF formula (((eq (fofType->(fofType->Prop))) d_27_prop1) (fun (X0:fofType) (X1:fofType)=> ((nis X1) ((n_pl X0) X1)))) of role definition named def_d_27_prop1
% 0.75/0.95 A new definition: (((eq (fofType->(fofType->Prop))) d_27_prop1) (fun (X0:fofType) (X1:fofType)=> ((nis X1) ((n_pl X0) X1))))
% 0.75/0.95 Defined: d_27_prop1:=(fun (X0:fofType) (X1:fofType)=> ((nis X1) ((n_pl X0) X1)))
% 0.75/0.95 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((nis X1) ((n_pl X0) X1)))))) of role axiom named satz7
% 0.75/0.95 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((nis X1) ((n_pl X0) X1))))))
% 0.75/0.95 FOF formula (<kernel.Constant object at 0x2ad8d56de128>, <kernel.DependentProduct object at 0x2ad8d56debd8>) of role type named typ_d_28_prop1
% 0.75/0.95 Using role type
% 0.75/0.95 Declaring d_28_prop1:(fofType->(fofType->(fofType->Prop)))
% 0.75/0.95 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) d_28_prop1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((nis ((n_pl X0) X1)) ((n_pl X0) X2)))) of role definition named def_d_28_prop1
% 0.75/0.95 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) d_28_prop1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((nis ((n_pl X0) X1)) ((n_pl X0) X2))))
% 0.75/0.95 Defined: d_28_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((nis ((n_pl X0) X1)) ((n_pl X0) X2)))
% 0.75/0.95 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((nis X1) X2)->((nis ((n_pl X0) X1)) ((n_pl X0) X2))))))))) of role axiom named satz8
% 0.75/0.95 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((nis X1) X2)->((nis ((n_pl X0) X1)) ((n_pl X0) X2)))))))))
% 0.75/0.95 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X0) X1)) ((n_pl X0) X2))->((n_is X1) X2)))))))) of role axiom named satz8a
% 0.75/0.95 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X0) X1)) ((n_pl X0) X2))->((n_is X1) X2))))))))
% 0.75/0.95 FOF formula (<kernel.Constant object at 0x2ad8d56de4d0>, <kernel.DependentProduct object at 0x2ad8d56dec20>) of role type named typ_diffprop
% 0.75/0.95 Using role type
% 0.75/0.95 Declaring diffprop:(fofType->(fofType->(fofType->Prop)))
% 0.75/0.95 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) diffprop) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is X0) ((n_pl X1) X2)))) of role definition named def_diffprop
% 0.75/0.95 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) diffprop) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))))
% 0.75/0.95 Defined: diffprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is X0) ((n_pl X1) X2)))
% 0.75/0.95 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((amone nat) (fun (X2:fofType)=> ((n_is X0) ((n_pl X1) X2)))))))) of role axiom named satz8b
% 0.75/0.97 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((amone nat) (fun (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))))))))
% 0.75/0.97 FOF formula (<kernel.Constant object at 0x2ad8d56dec20>, <kernel.DependentProduct object at 0x2ad8d56deb48>) of role type named typ_d_29_ii
% 0.75/0.97 Using role type
% 0.75/0.97 Declaring d_29_ii:(fofType->(fofType->Prop))
% 0.75/0.97 FOF formula (((eq (fofType->(fofType->Prop))) d_29_ii) (fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X0) X1)))) of role definition named def_d_29_ii
% 0.75/0.97 A new definition: (((eq (fofType->(fofType->Prop))) d_29_ii) (fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X0) X1))))
% 0.75/0.97 Defined: d_29_ii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X0) X1)))
% 0.75/0.97 FOF formula (<kernel.Constant object at 0x2ad8d56debd8>, <kernel.DependentProduct object at 0x2ad8d4fc1290>) of role type named typ_iii
% 0.75/0.97 Using role type
% 0.75/0.97 Declaring iii:(fofType->(fofType->Prop))
% 0.75/0.97 FOF formula (((eq (fofType->(fofType->Prop))) iii) (fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X1) X0)))) of role definition named def_iii
% 0.75/0.97 A new definition: (((eq (fofType->(fofType->Prop))) iii) (fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X1) X0))))
% 0.75/0.97 Defined: iii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X1) X0)))
% 0.75/0.97 FOF formula (<kernel.Constant object at 0x2ad8d56de128>, <kernel.DependentProduct object at 0x2ad8d4fc1a28>) of role type named typ_d_29_prop1
% 0.75/0.97 Using role type
% 0.75/0.97 Declaring d_29_prop1:(fofType->(fofType->Prop))
% 0.75/0.97 FOF formula (((eq (fofType->(fofType->Prop))) d_29_prop1) (fun (X0:fofType) (X1:fofType)=> (((or3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1)))) of role definition named def_d_29_prop1
% 0.75/0.97 A new definition: (((eq (fofType->(fofType->Prop))) d_29_prop1) (fun (X0:fofType) (X1:fofType)=> (((or3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))))
% 0.75/0.97 Defined: d_29_prop1:=(fun (X0:fofType) (X1:fofType)=> (((or3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1)))
% 0.75/0.97 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((orec3 ((n_is X0) X1)) (n_some (fun (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))))) (n_some (fun (X2:fofType)=> ((n_is X1) ((n_pl X0) X2))))))))) of role axiom named satz9
% 0.75/0.97 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((orec3 ((n_is X0) X1)) (n_some (fun (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))))) (n_some (fun (X2:fofType)=> ((n_is X1) ((n_pl X0) X2)))))))))
% 0.75/0.97 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((or3 ((n_is X0) X1)) (n_some ((diffprop X0) X1))) (n_some ((diffprop X1) X0))))))) of role axiom named satz9a
% 0.75/0.97 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((or3 ((n_is X0) X1)) (n_some ((diffprop X0) X1))) (n_some ((diffprop X1) X0)))))))
% 0.75/0.97 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((ec3 ((n_is X0) X1)) (n_some ((diffprop X0) X1))) (n_some ((diffprop X1) X0))))))) of role axiom named satz9b
% 0.75/0.97 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((ec3 ((n_is X0) X1)) (n_some ((diffprop X0) X1))) (n_some ((diffprop X1) X0)))))))
% 0.75/0.97 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((orec3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1)))))) of role axiom named satz10
% 0.75/0.97 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((orec3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))))))
% 0.75/0.97 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((or3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1)))))) of role axiom named satz10a
% 0.75/0.99 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((or3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))))))
% 0.75/0.99 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((ec3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1)))))) of role axiom named satz10b
% 0.75/0.99 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((ec3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))))))
% 0.75/0.99 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->((iii X1) X0)))))) of role axiom named satz11
% 0.75/0.99 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->((iii X1) X0))))))
% 0.75/0.99 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->((d_29_ii X1) X0)))))) of role axiom named satz12
% 0.75/0.99 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->((d_29_ii X1) X0))))))
% 0.75/0.99 FOF formula (<kernel.Constant object at 0x2ad8d4fc1488>, <kernel.DependentProduct object at 0x2ad8d4fc12d8>) of role type named typ_moreis
% 0.75/0.99 Using role type
% 0.75/0.99 Declaring moreis:(fofType->(fofType->Prop))
% 0.75/0.99 FOF formula (((eq (fofType->(fofType->Prop))) moreis) (fun (X0:fofType) (X1:fofType)=> ((l_or ((d_29_ii X0) X1)) ((n_is X0) X1)))) of role definition named def_moreis
% 0.75/0.99 A new definition: (((eq (fofType->(fofType->Prop))) moreis) (fun (X0:fofType) (X1:fofType)=> ((l_or ((d_29_ii X0) X1)) ((n_is X0) X1))))
% 0.75/0.99 Defined: moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((d_29_ii X0) X1)) ((n_is X0) X1)))
% 0.75/0.99 FOF formula (<kernel.Constant object at 0x2ad8d4fc12d8>, <kernel.DependentProduct object at 0x2ad8d4fc1bd8>) of role type named typ_lessis
% 0.75/0.99 Using role type
% 0.75/0.99 Declaring lessis:(fofType->(fofType->Prop))
% 0.75/0.99 FOF formula (((eq (fofType->(fofType->Prop))) lessis) (fun (X0:fofType) (X1:fofType)=> ((l_or ((iii X0) X1)) ((n_is X0) X1)))) of role definition named def_lessis
% 0.75/0.99 A new definition: (((eq (fofType->(fofType->Prop))) lessis) (fun (X0:fofType) (X1:fofType)=> ((l_or ((iii X0) X1)) ((n_is X0) X1))))
% 0.75/0.99 Defined: lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((iii X0) X1)) ((n_is X0) X1)))
% 0.75/0.99 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moreis X0) X1)->((lessis X1) X0)))))) of role axiom named satz13
% 0.75/0.99 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moreis X0) X1)->((lessis X1) X0))))))
% 0.75/0.99 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessis X0) X1)->((moreis X1) X0)))))) of role axiom named satz14
% 0.75/0.99 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessis X0) X1)->((moreis X1) X0))))))
% 0.75/0.99 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moreis X0) X1)->(d_not ((iii X0) X1))))))) of role axiom named satz10c
% 0.75/0.99 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moreis X0) X1)->(d_not ((iii X0) X1)))))))
% 0.75/0.99 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessis X0) X1)->(d_not ((d_29_ii X0) X1))))))) of role axiom named satz10d
% 0.84/1.02 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessis X0) X1)->(d_not ((d_29_ii X0) X1)))))))
% 0.84/1.02 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((d_29_ii X0) X1))->((lessis X0) X1)))))) of role axiom named satz10e
% 0.84/1.02 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((d_29_ii X0) X1))->((lessis X0) X1))))))
% 0.84/1.02 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((iii X0) X1))->((moreis X0) X1)))))) of role axiom named satz10f
% 0.84/1.02 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((iii X0) X1))->((moreis X0) X1))))))
% 0.84/1.02 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->(d_not ((lessis X0) X1))))))) of role axiom named satz10g
% 0.84/1.02 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->(d_not ((lessis X0) X1)))))))
% 0.84/1.02 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->(d_not ((moreis X0) X1))))))) of role axiom named satz10h
% 0.84/1.02 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->(d_not ((moreis X0) X1)))))))
% 0.84/1.02 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((moreis X0) X1))->((iii X0) X1)))))) of role axiom named satz10j
% 0.84/1.02 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((moreis X0) X1))->((iii X0) X1))))))
% 0.84/1.02 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((lessis X0) X1))->((d_29_ii X0) X1)))))) of role axiom named satz10k
% 0.84/1.02 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((lessis X0) X1))->((d_29_ii X0) X1))))))
% 0.84/1.02 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->(((iii X1) X2)->((iii X0) X2))))))))) of role axiom named satz15
% 0.84/1.02 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->(((iii X1) X2)->((iii X0) X2)))))))))
% 0.84/1.02 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->(((iii X1) X2)->((iii X0) X2))))))))) of role axiom named satz16a
% 0.84/1.02 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->(((iii X1) X2)->((iii X0) X2)))))))))
% 0.84/1.02 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->(((lessis X1) X2)->((iii X0) X2))))))))) of role axiom named satz16b
% 0.84/1.02 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->(((lessis X1) X2)->((iii X0) X2)))))))))
% 0.84/1.04 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->(((d_29_ii X1) X2)->((d_29_ii X0) X2))))))))) of role axiom named satz16c
% 0.84/1.04 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->(((d_29_ii X1) X2)->((d_29_ii X0) X2)))))))))
% 0.84/1.04 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->(((moreis X1) X2)->((d_29_ii X0) X2))))))))) of role axiom named satz16d
% 0.84/1.04 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->(((moreis X1) X2)->((d_29_ii X0) X2)))))))))
% 0.84/1.04 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->(((lessis X1) X2)->((lessis X0) X2))))))))) of role axiom named satz17
% 0.84/1.04 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->(((lessis X1) X2)->((lessis X0) X2)))))))))
% 0.84/1.04 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_29_ii ((n_pl X0) X1)) X0))))) of role axiom named satz18
% 0.84/1.04 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_29_ii ((n_pl X0) X1)) X0)))))
% 0.84/1.04 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((iii X0) ((n_pl X0) X1)))))) of role axiom named satz18a
% 0.84/1.04 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((iii X0) ((n_pl X0) X1))))))
% 0.84/1.04 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((d_29_ii (ordsucc X0)) X0))) of role axiom named satz18b
% 0.84/1.04 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((d_29_ii (ordsucc X0)) X0)))
% 0.84/1.04 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((iii X0) (ordsucc X0)))) of role axiom named satz18c
% 0.84/1.04 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((iii X0) (ordsucc X0))))
% 0.84/1.04 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X2))))))))) of role axiom named satz19a
% 0.84/1.04 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 0.84/1.04 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_pl X0) X2)) ((n_pl X1) X2))))))))) of role axiom named satz19b
% 0.84/1.04 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 0.84/1.07 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_pl X0) X2)) ((n_pl X1) X2))))))))) of role axiom named satz19c
% 0.84/1.07 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 0.84/1.07 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_pl X2) X0)) ((n_pl X2) X1))))))))) of role axiom named satz19d
% 0.84/1.07 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 0.84/1.07 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_pl X2) X0)) ((n_pl X2) X1))))))))) of role axiom named satz19e
% 0.84/1.07 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 0.84/1.07 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_pl X2) X0)) ((n_pl X2) X1))))))))) of role axiom named satz19f
% 0.84/1.07 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 0.84/1.07 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))) of role axiom named satz19g
% 0.84/1.07 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 0.84/1.07 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X2) X0)) ((n_pl X3) X1)))))))))))) of role axiom named satz19h
% 0.84/1.07 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X2) X0)) ((n_pl X3) X1))))))))))))
% 0.84/1.07 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))) of role axiom named satz19j
% 0.91/1.10 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 0.91/1.10 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_pl X2) X0)) ((n_pl X3) X1)))))))))))) of role axiom named satz19k
% 0.91/1.10 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_pl X2) X0)) ((n_pl X3) X1))))))))))))
% 0.91/1.10 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_pl X0) X2)) ((n_pl X1) X2))))))))) of role axiom named satz19l
% 0.91/1.10 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 0.91/1.10 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_pl X2) X0)) ((n_pl X2) X1))))))))) of role axiom named satz19m
% 0.91/1.10 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 0.91/1.10 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_pl X0) X2)) ((n_pl X1) X2))))))))) of role axiom named satz19n
% 0.91/1.10 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_pl X0) X2)) ((n_pl X1) X2)))))))))
% 0.91/1.10 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_pl X2) X0)) ((n_pl X2) X1))))))))) of role axiom named satz19o
% 0.91/1.10 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_pl X2) X0)) ((n_pl X2) X1)))))))))
% 0.91/1.10 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X2))->((d_29_ii X0) X1)))))))) of role axiom named satz20a
% 0.91/1.10 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X2))->((d_29_ii X0) X1))))))))
% 0.91/1.12 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X0) X2)) ((n_pl X1) X2))->((n_is X0) X1)))))))) of role axiom named satz20b
% 0.91/1.12 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X0) X2)) ((n_pl X1) X2))->((n_is X0) X1))))))))
% 0.91/1.12 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_pl X0) X2)) ((n_pl X1) X2))->((iii X0) X1)))))))) of role axiom named satz20c
% 0.91/1.12 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_pl X0) X2)) ((n_pl X1) X2))->((iii X0) X1))))))))
% 0.91/1.12 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_pl X2) X0)) ((n_pl X2) X1))->((d_29_ii X0) X1)))))))) of role axiom named satz20d
% 0.91/1.12 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_pl X2) X0)) ((n_pl X2) X1))->((d_29_ii X0) X1))))))))
% 0.91/1.12 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X2) X0)) ((n_pl X2) X1))->((n_is X0) X1)))))))) of role axiom named satz20e
% 0.91/1.12 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X2) X0)) ((n_pl X2) X1))->((n_is X0) X1))))))))
% 0.91/1.12 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_pl X2) X0)) ((n_pl X2) X1))->((iii X0) X1)))))))) of role axiom named satz20f
% 0.91/1.12 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_pl X2) X0)) ((n_pl X2) X1))->((iii X0) X1))))))))
% 0.91/1.12 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))) of role axiom named satz21
% 0.91/1.12 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 0.91/1.12 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))) of role axiom named satz21a
% 0.91/1.15 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 0.91/1.15 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))) of role axiom named satz22a
% 0.91/1.15 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 0.91/1.15 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((moreis X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))) of role axiom named satz22b
% 0.91/1.15 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((moreis X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 0.91/1.15 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))) of role axiom named satz22c
% 0.91/1.15 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 0.91/1.15 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((lessis X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))) of role axiom named satz22d
% 0.91/1.15 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((lessis X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 0.91/1.15 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((moreis X2) X3)->((moreis ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))) of role axiom named satz23
% 0.91/1.15 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((moreis X2) X3)->((moreis ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 0.99/1.17 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((lessis X2) X3)->((lessis ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))) of role axiom named satz23a
% 0.99/1.17 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((lessis X2) X3)->((lessis ((n_pl X0) X2)) ((n_pl X1) X3))))))))))))
% 0.99/1.17 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((moreis X0) n_1))) of role axiom named satz24
% 0.99/1.17 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((moreis X0) n_1)))
% 0.99/1.17 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (lessis n_1)) of role axiom named satz24a
% 0.99/1.17 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (lessis n_1))
% 0.99/1.17 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((d_29_ii (ordsucc X0)) n_1))) of role axiom named satz24b
% 0.99/1.17 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((d_29_ii (ordsucc X0)) n_1)))
% 0.99/1.17 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((iii n_1) (ordsucc X0)))) of role axiom named satz24c
% 0.99/1.17 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((iii n_1) (ordsucc X0))))
% 0.99/1.17 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X1) X0)->((moreis X1) ((n_pl X0) n_1))))))) of role axiom named satz25
% 0.99/1.17 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X1) X0)->((moreis X1) ((n_pl X0) n_1)))))))
% 0.99/1.17 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X1) X0)->((moreis X1) (ordsucc X0))))))) of role axiom named satz25a
% 0.99/1.17 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X1) X0)->((moreis X1) (ordsucc X0)))))))
% 0.99/1.17 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) X0)->((lessis ((n_pl X1) n_1)) X0)))))) of role axiom named satz25b
% 0.99/1.17 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) X0)->((lessis ((n_pl X1) n_1)) X0))))))
% 0.99/1.17 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) X0)->((lessis (ordsucc X1)) X0)))))) of role axiom named satz25c
% 0.99/1.17 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) X0)->((lessis (ordsucc X1)) X0))))))
% 0.99/1.17 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) ((n_pl X0) n_1))->((lessis X1) X0)))))) of role axiom named satz26
% 0.99/1.17 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) ((n_pl X0) n_1))->((lessis X1) X0))))))
% 0.99/1.17 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) (ordsucc X0))->((lessis X1) X0)))))) of role axiom named satz26a
% 0.99/1.17 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) (ordsucc X0))->((lessis X1) X0))))))
% 1.00/1.19 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii ((n_pl X1) n_1)) X0)->((moreis X1) X0)))))) of role axiom named satz26b
% 1.00/1.19 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii ((n_pl X1) n_1)) X0)->((moreis X1) X0))))))
% 1.00/1.19 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii (ordsucc X1)) X0)->((moreis X1) X0)))))) of role axiom named satz26c
% 1.00/1.19 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii (ordsucc X1)) X0)->((moreis X1) X0))))))
% 1.00/1.19 FOF formula (<kernel.Constant object at 0x2ad8d77492d8>, <kernel.DependentProduct object at 0x2ad8d7749e18>) of role type named typ_lbprop
% 1.00/1.19 Using role type
% 1.00/1.19 Declaring lbprop:((fofType->Prop)->(fofType->(fofType->Prop)))
% 1.00/1.19 FOF formula (((eq ((fofType->Prop)->(fofType->(fofType->Prop)))) lbprop) (fun (X0:(fofType->Prop)) (X1:fofType) (X2:fofType)=> ((imp (X0 X2)) ((lessis X1) X2)))) of role definition named def_lbprop
% 1.00/1.19 A new definition: (((eq ((fofType->Prop)->(fofType->(fofType->Prop)))) lbprop) (fun (X0:(fofType->Prop)) (X1:fofType) (X2:fofType)=> ((imp (X0 X2)) ((lessis X1) X2))))
% 1.00/1.19 Defined: lbprop:=(fun (X0:(fofType->Prop)) (X1:fofType) (X2:fofType)=> ((imp (X0 X2)) ((lessis X1) X2)))
% 1.00/1.19 FOF formula (<kernel.Constant object at 0x2ad8d7749320>, <kernel.DependentProduct object at 0x2ad8d7749e60>) of role type named typ_n_lb
% 1.00/1.19 Using role type
% 1.00/1.19 Declaring n_lb:((fofType->Prop)->(fofType->Prop))
% 1.00/1.19 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) n_lb) (fun (X0:(fofType->Prop)) (X1:fofType)=> (n_all ((lbprop X0) X1)))) of role definition named def_n_lb
% 1.00/1.19 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) n_lb) (fun (X0:(fofType->Prop)) (X1:fofType)=> (n_all ((lbprop X0) X1))))
% 1.00/1.19 Defined: n_lb:=(fun (X0:(fofType->Prop)) (X1:fofType)=> (n_all ((lbprop X0) X1)))
% 1.00/1.19 FOF formula (<kernel.Constant object at 0x2ad8d7749e18>, <kernel.DependentProduct object at 0x2ad8d8358440>) of role type named typ_min
% 1.00/1.19 Using role type
% 1.00/1.19 Declaring min:((fofType->Prop)->(fofType->Prop))
% 1.00/1.19 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) min) (fun (X0:(fofType->Prop)) (X1:fofType)=> ((d_and ((n_lb X0) X1)) (X0 X1)))) of role definition named def_min
% 1.00/1.19 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) min) (fun (X0:(fofType->Prop)) (X1:fofType)=> ((d_and ((n_lb X0) X1)) (X0 X1))))
% 1.00/1.19 Defined: min:=(fun (X0:(fofType->Prop)) (X1:fofType)=> ((d_and ((n_lb X0) X1)) (X0 X1)))
% 1.00/1.19 FOF formula (forall (X0:(fofType->Prop)), ((n_some X0)->(n_some (min X0)))) of role axiom named satz27
% 1.00/1.19 A new axiom: (forall (X0:(fofType->Prop)), ((n_some X0)->(n_some (min X0))))
% 1.00/1.19 FOF formula (forall (X0:(fofType->Prop)), ((n_some X0)->(n_one (min X0)))) of role axiom named satz27a
% 1.00/1.19 A new axiom: (forall (X0:(fofType->Prop)), ((n_some X0)->(n_one (min X0))))
% 1.00/1.19 FOF formula (<kernel.Constant object at 0x2ad8d7749e18>, <kernel.DependentProduct object at 0x2ad8d83585f0>) of role type named typ_d_428_prop1
% 1.00/1.19 Using role type
% 1.00/1.19 Declaring d_428_prop1:(fofType->(fofType->Prop))
% 1.00/1.19 FOF formula (((eq (fofType->(fofType->Prop))) d_428_prop1) (fun (X0:fofType) (X1:fofType)=> (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) ((n_pl ((ap X1) X2)) X0)))))) of role definition named def_d_428_prop1
% 1.00/1.19 A new definition: (((eq (fofType->(fofType->Prop))) d_428_prop1) (fun (X0:fofType) (X1:fofType)=> (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) ((n_pl ((ap X1) X2)) X0))))))
% 1.00/1.19 Defined: d_428_prop1:=(fun (X0:fofType) (X1:fofType)=> (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) ((n_pl ((ap X1) X2)) X0)))))
% 1.00/1.19 FOF formula (<kernel.Constant object at 0x2ad8d7749e18>, <kernel.DependentProduct object at 0x2ad8d8358098>) of role type named typ_d_428_prop2
% 1.00/1.19 Using role type
% 1.00/1.19 Declaring d_428_prop2:(fofType->(fofType->Prop))
% 1.00/1.21 FOF formula (((eq (fofType->(fofType->Prop))) d_428_prop2) (fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) X0)) ((d_428_prop1 X0) X1)))) of role definition named def_d_428_prop2
% 1.00/1.21 A new definition: (((eq (fofType->(fofType->Prop))) d_428_prop2) (fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) X0)) ((d_428_prop1 X0) X1))))
% 1.00/1.21 Defined: d_428_prop2:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) X0)) ((d_428_prop1 X0) X1)))
% 1.00/1.21 FOF formula (<kernel.Constant object at 0x2ad8d8358098>, <kernel.DependentProduct object at 0x2ad8d83580e0>) of role type named typ_d_428_prop4
% 1.00/1.21 Using role type
% 1.00/1.21 Declaring d_428_prop4:(fofType->Prop)
% 1.00/1.21 FOF formula (((eq (fofType->Prop)) d_428_prop4) (fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0)))) of role definition named def_d_428_prop4
% 1.00/1.21 A new definition: (((eq (fofType->Prop)) d_428_prop4) (fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0))))
% 1.00/1.21 Defined: d_428_prop4:=(fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0)))
% 1.00/1.21 FOF formula (<kernel.Constant object at 0x2ad8d83580e0>, <kernel.Single object at 0x2ad8d8358098>) of role type named typ_d_428_id
% 1.00/1.21 Using role type
% 1.00/1.21 Declaring d_428_id:fofType
% 1.00/1.21 FOF formula (((eq fofType) d_428_id) ((d_Sigma nat) (fun (X0:fofType)=> X0))) of role definition named def_d_428_id
% 1.00/1.21 A new definition: (((eq fofType) d_428_id) ((d_Sigma nat) (fun (X0:fofType)=> X0)))
% 1.00/1.21 Defined: d_428_id:=((d_Sigma nat) (fun (X0:fofType)=> X0))
% 1.00/1.21 FOF formula (<kernel.Constant object at 0x2ad8d8358098>, <kernel.DependentProduct object at 0x2ad8d8358320>) of role type named typ_d_428_g
% 1.00/1.21 Using role type
% 1.00/1.21 Declaring d_428_g:(fofType->fofType)
% 1.00/1.21 FOF formula (((eq (fofType->fofType)) d_428_g) (fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> ((n_pl ((ap X0) X1)) X1))))) of role definition named def_d_428_g
% 1.00/1.21 A new definition: (((eq (fofType->fofType)) d_428_g) (fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> ((n_pl ((ap X0) X1)) X1)))))
% 1.00/1.21 Defined: d_428_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> ((n_pl ((ap X0) X1)) X1))))
% 1.00/1.21 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((one ((d_Pi nat) (fun (X1:fofType)=> nat))) (fun (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) X0)) (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) ((n_pl ((ap X1) X2)) X0))))))))) of role axiom named satz28
% 1.00/1.21 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((one ((d_Pi nat) (fun (X1:fofType)=> nat))) (fun (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) X0)) (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) ((n_pl ((ap X1) X2)) X0)))))))))
% 1.00/1.21 FOF formula (<kernel.Constant object at 0x2ad8d8358200>, <kernel.DependentProduct object at 0x2ad8d8358518>) of role type named typ_times
% 1.00/1.21 Using role type
% 1.00/1.21 Declaring times:(fofType->fofType)
% 1.00/1.21 FOF formula (((eq (fofType->fofType)) times) (fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0)))) of role definition named def_times
% 1.00/1.21 A new definition: (((eq (fofType->fofType)) times) (fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0))))
% 1.00/1.21 Defined: times:=(fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0)))
% 1.00/1.21 FOF formula (<kernel.Constant object at 0x2ad8d8358518>, <kernel.DependentProduct object at 0x2ad8d83585f0>) of role type named typ_n_ts
% 1.00/1.21 Using role type
% 1.00/1.21 Declaring n_ts:(fofType->(fofType->fofType))
% 1.00/1.21 FOF formula (((eq (fofType->(fofType->fofType))) n_ts) (fun (X0:fofType)=> (ap (times X0)))) of role definition named def_n_ts
% 1.00/1.21 A new definition: (((eq (fofType->(fofType->fofType))) n_ts) (fun (X0:fofType)=> (ap (times X0))))
% 1.00/1.21 Defined: n_ts:=(fun (X0:fofType)=> (ap (times X0)))
% 1.00/1.21 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_ts X0) n_1)) X0))) of role axiom named satz28a
% 1.00/1.21 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_ts X0) n_1)) X0)))
% 1.00/1.21 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts X0) (ordsucc X1))) ((n_pl ((n_ts X0) X1)) X0)))))) of role axiom named satz28b
% 1.04/1.23 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts X0) (ordsucc X1))) ((n_pl ((n_ts X0) X1)) X0))))))
% 1.04/1.23 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_ts n_1) X0)) X0))) of role axiom named satz28c
% 1.04/1.23 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_ts n_1) X0)) X0)))
% 1.04/1.23 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts (ordsucc X0)) X1)) ((n_pl ((n_ts X0) X1)) X1)))))) of role axiom named satz28d
% 1.04/1.23 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts (ordsucc X0)) X1)) ((n_pl ((n_ts X0) X1)) X1))))))
% 1.04/1.23 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is X0) ((n_ts X0) n_1)))) of role axiom named satz28e
% 1.04/1.23 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is X0) ((n_ts X0) n_1))))
% 1.04/1.23 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl ((n_ts X0) X1)) X0)) ((n_ts X0) (ordsucc X1))))))) of role axiom named satz28f
% 1.04/1.23 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl ((n_ts X0) X1)) X0)) ((n_ts X0) (ordsucc X1)))))))
% 1.04/1.23 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is X0) ((n_ts n_1) X0)))) of role axiom named satz28g
% 1.04/1.23 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is X0) ((n_ts n_1) X0))))
% 1.04/1.23 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl ((n_ts X0) X1)) X1)) ((n_ts (ordsucc X0)) X1)))))) of role axiom named satz28h
% 1.04/1.23 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl ((n_ts X0) X1)) X1)) ((n_ts (ordsucc X0)) X1))))))
% 1.04/1.23 FOF formula (<kernel.Constant object at 0x2ad8d8358950>, <kernel.DependentProduct object at 0x2ad8d8358758>) of role type named typ_d_429_prop1
% 1.04/1.23 Using role type
% 1.04/1.23 Declaring d_429_prop1:(fofType->(fofType->Prop))
% 1.04/1.23 FOF formula (((eq (fofType->(fofType->Prop))) d_429_prop1) (fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts X0) X1)) ((n_ts X1) X0)))) of role definition named def_d_429_prop1
% 1.04/1.23 A new definition: (((eq (fofType->(fofType->Prop))) d_429_prop1) (fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts X0) X1)) ((n_ts X1) X0))))
% 1.04/1.23 Defined: d_429_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts X0) X1)) ((n_ts X1) X0)))
% 1.04/1.23 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts X0) X1)) ((n_ts X1) X0)))))) of role axiom named satz29
% 1.04/1.23 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts X0) X1)) ((n_ts X1) X0))))))
% 1.04/1.23 FOF formula (<kernel.Constant object at 0x2ad8d8358b48>, <kernel.DependentProduct object at 0x2ad8d8358200>) of role type named typ_d_430_prop1
% 1.04/1.23 Using role type
% 1.04/1.23 Declaring d_430_prop1:(fofType->(fofType->(fofType->Prop)))
% 1.04/1.23 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) d_430_prop1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_ts X0) ((n_pl X1) X2))) ((n_pl ((n_ts X0) X1)) ((n_ts X0) X2))))) of role definition named def_d_430_prop1
% 1.04/1.23 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) d_430_prop1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_ts X0) ((n_pl X1) X2))) ((n_pl ((n_ts X0) X1)) ((n_ts X0) X2)))))
% 1.04/1.25 Defined: d_430_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_ts X0) ((n_pl X1) X2))) ((n_pl ((n_ts X0) X1)) ((n_ts X0) X2))))
% 1.04/1.25 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_ts X0) ((n_pl X1) X2))) ((n_pl ((n_ts X0) X1)) ((n_ts X0) X2))))))))) of role axiom named satz30
% 1.04/1.25 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_ts X0) ((n_pl X1) X2))) ((n_pl ((n_ts X0) X1)) ((n_ts X0) X2)))))))))
% 1.04/1.25 FOF formula (<kernel.Constant object at 0x2ad8d8358dd0>, <kernel.DependentProduct object at 0x2ad8d8358bd8>) of role type named typ_d_431_prop1
% 1.04/1.25 Using role type
% 1.04/1.25 Declaring d_431_prop1:(fofType->(fofType->(fofType->Prop)))
% 1.04/1.25 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) d_431_prop1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_ts ((n_ts X0) X1)) X2)) ((n_ts X0) ((n_ts X1) X2))))) of role definition named def_d_431_prop1
% 1.04/1.25 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) d_431_prop1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_ts ((n_ts X0) X1)) X2)) ((n_ts X0) ((n_ts X1) X2)))))
% 1.04/1.25 Defined: d_431_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_ts ((n_ts X0) X1)) X2)) ((n_ts X0) ((n_ts X1) X2))))
% 1.04/1.25 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_ts ((n_ts X0) X1)) X2)) ((n_ts X0) ((n_ts X1) X2))))))))) of role axiom named satz31
% 1.04/1.25 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_ts ((n_ts X0) X1)) X2)) ((n_ts X0) ((n_ts X1) X2)))))))))
% 1.04/1.25 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X2))))))))) of role axiom named satz32a
% 1.04/1.25 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 1.04/1.25 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_ts X0) X2)) ((n_ts X1) X2))))))))) of role axiom named satz32b
% 1.04/1.25 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 1.04/1.25 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_ts X0) X2)) ((n_ts X1) X2))))))))) of role axiom named satz32c
% 1.04/1.25 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 1.04/1.25 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_ts X2) X0)) ((n_ts X2) X1))))))))) of role axiom named satz32d
% 1.04/1.28 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 1.04/1.28 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_ts X2) X0)) ((n_ts X2) X1))))))))) of role axiom named satz32e
% 1.04/1.28 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 1.04/1.28 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_ts X2) X0)) ((n_ts X2) X1))))))))) of role axiom named satz32f
% 1.04/1.28 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 1.04/1.28 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))) of role axiom named satz32g
% 1.04/1.28 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 1.04/1.28 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X2) X0)) ((n_ts X3) X1)))))))))))) of role axiom named satz32h
% 1.04/1.28 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X2) X0)) ((n_ts X3) X1))))))))))))
% 1.04/1.28 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))) of role axiom named satz32j
% 1.04/1.28 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 1.04/1.28 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_ts X2) X0)) ((n_ts X3) X1)))))))))))) of role axiom named satz32k
% 1.04/1.28 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_ts X2) X0)) ((n_ts X3) X1))))))))))))
% 1.04/1.30 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_ts X0) X2)) ((n_ts X1) X2))))))))) of role axiom named satz32l
% 1.04/1.30 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 1.04/1.30 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_ts X2) X0)) ((n_ts X2) X1))))))))) of role axiom named satz32m
% 1.04/1.30 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 1.04/1.30 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_ts X0) X2)) ((n_ts X1) X2))))))))) of role axiom named satz32n
% 1.04/1.30 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 1.04/1.30 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_ts X2) X0)) ((n_ts X2) X1))))))))) of role axiom named satz32o
% 1.04/1.30 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_ts X2) X0)) ((n_ts X2) X1)))))))))
% 1.04/1.30 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X2))->((d_29_ii X0) X1)))))))) of role axiom named satz33a
% 1.04/1.30 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X2))->((d_29_ii X0) X1))))))))
% 1.04/1.30 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_ts X0) X2)) ((n_ts X1) X2))->((n_is X0) X1)))))))) of role axiom named satz33b
% 1.04/1.30 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_ts X0) X2)) ((n_ts X1) X2))->((n_is X0) X1))))))))
% 1.04/1.30 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_ts X0) X2)) ((n_ts X1) X2))->((iii X0) X1)))))))) of role axiom named satz33c
% 1.04/1.30 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_ts X0) X2)) ((n_ts X1) X2))->((iii X0) X1))))))))
% 1.13/1.33 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))) of role axiom named satz34
% 1.13/1.33 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 1.13/1.33 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))) of role axiom named satz34a
% 1.13/1.33 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 1.13/1.33 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))) of role axiom named satz35a
% 1.13/1.33 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 1.13/1.33 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((moreis X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))) of role axiom named satz35b
% 1.13/1.33 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((moreis X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 1.13/1.33 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))) of role axiom named satz35c
% 1.13/1.33 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 1.13/1.33 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((lessis X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))) of role axiom named satz35d
% 1.13/1.35 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((lessis X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 1.13/1.35 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((moreis X2) X3)->((moreis ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))) of role axiom named satz36
% 1.13/1.35 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((moreis X2) X3)->((moreis ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 1.13/1.35 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((lessis X2) X3)->((lessis ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))) of role axiom named satz36a
% 1.13/1.35 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((lessis X2) X3)->((lessis ((n_ts X0) X2)) ((n_ts X1) X3))))))))))))
% 1.13/1.35 FOF formula (<kernel.Constant object at 0x2ad8d83582d8>, <kernel.DependentProduct object at 0x2ad8d8346320>) of role type named typ_n_mn
% 1.13/1.35 Using role type
% 1.13/1.35 Declaring n_mn:(fofType->(fofType->fofType))
% 1.13/1.35 FOF formula (((eq (fofType->(fofType->fofType))) n_mn) (fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop X0) X1)))) of role definition named def_n_mn
% 1.13/1.35 A new definition: (((eq (fofType->(fofType->fofType))) n_mn) (fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop X0) X1))))
% 1.13/1.35 Defined: n_mn:=(fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop X0) X1)))
% 1.13/1.35 FOF formula (<kernel.Constant object at 0x2ad8d8358878>, <kernel.DependentProduct object at 0x2ad8d8346440>) of role type named typ_d_1to
% 1.13/1.35 Using role type
% 1.13/1.35 Declaring d_1to:(fofType->fofType)
% 1.13/1.35 FOF formula (((eq (fofType->fofType)) d_1to) (fun (X0:fofType)=> ((d_Sep nat) (fun (X1:fofType)=> ((lessis X1) X0))))) of role definition named def_d_1to
% 1.13/1.35 A new definition: (((eq (fofType->fofType)) d_1to) (fun (X0:fofType)=> ((d_Sep nat) (fun (X1:fofType)=> ((lessis X1) X0)))))
% 1.13/1.35 Defined: d_1to:=(fun (X0:fofType)=> ((d_Sep nat) (fun (X1:fofType)=> ((lessis X1) X0))))
% 1.13/1.35 FOF formula (<kernel.Constant object at 0x2ad8d8346440>, <kernel.DependentProduct object at 0x2ad8d8346950>) of role type named typ_outn
% 1.13/1.35 Using role type
% 1.13/1.35 Declaring outn:(fofType->(fofType->fofType))
% 1.13/1.35 FOF formula (((eq (fofType->(fofType->fofType))) outn) (fun (X0:fofType)=> ((out nat) (fun (X1:fofType)=> ((lessis X1) X0))))) of role definition named def_outn
% 1.13/1.35 A new definition: (((eq (fofType->(fofType->fofType))) outn) (fun (X0:fofType)=> ((out nat) (fun (X1:fofType)=> ((lessis X1) X0)))))
% 1.13/1.35 Defined: outn:=(fun (X0:fofType)=> ((out nat) (fun (X1:fofType)=> ((lessis X1) X0))))
% 1.13/1.35 FOF formula (<kernel.Constant object at 0x2ad8d8346950>, <kernel.DependentProduct object at 0x2ad8d8346710>) of role type named typ_inn
% 1.13/1.35 Using role type
% 1.13/1.35 Declaring inn:(fofType->(fofType->fofType))
% 1.13/1.35 FOF formula (((eq (fofType->(fofType->fofType))) inn) (fun (X0:fofType)=> ((e_in nat) (fun (X1:fofType)=> ((lessis X1) X0))))) of role definition named def_inn
% 1.13/1.36 A new definition: (((eq (fofType->(fofType->fofType))) inn) (fun (X0:fofType)=> ((e_in nat) (fun (X1:fofType)=> ((lessis X1) X0)))))
% 1.13/1.36 Defined: inn:=(fun (X0:fofType)=> ((e_in nat) (fun (X1:fofType)=> ((lessis X1) X0))))
% 1.13/1.36 FOF formula (<kernel.Constant object at 0x2ad8d8346710>, <kernel.Single object at 0x2ad8d8346950>) of role type named typ_n_1o
% 1.13/1.36 Using role type
% 1.13/1.36 Declaring n_1o:fofType
% 1.13/1.36 FOF formula (((eq fofType) n_1o) ((outn n_1) n_1)) of role definition named def_n_1o
% 1.13/1.36 A new definition: (((eq fofType) n_1o) ((outn n_1) n_1))
% 1.13/1.36 Defined: n_1o:=((outn n_1) n_1)
% 1.13/1.36 FOF formula (<kernel.Constant object at 0x2ad8d8346950>, <kernel.DependentProduct object at 0x2ad8d83460e0>) of role type named typ_singlet_u0
% 1.13/1.36 Using role type
% 1.13/1.36 Declaring singlet_u0:(fofType->fofType)
% 1.13/1.36 FOF formula (((eq (fofType->fofType)) singlet_u0) (inn n_1)) of role definition named def_singlet_u0
% 1.13/1.36 A new definition: (((eq (fofType->fofType)) singlet_u0) (inn n_1))
% 1.13/1.36 Defined: singlet_u0:=(inn n_1)
% 1.13/1.36 FOF formula (<kernel.Constant object at 0x2ad8d8346440>, <kernel.Single object at 0x2ad8d8346950>) of role type named typ_n_2
% 1.13/1.36 Using role type
% 1.13/1.36 Declaring n_2:fofType
% 1.13/1.36 FOF formula (((eq fofType) n_2) ((n_pl n_1) n_1)) of role definition named def_n_2
% 1.13/1.36 A new definition: (((eq fofType) n_2) ((n_pl n_1) n_1))
% 1.13/1.36 Defined: n_2:=((n_pl n_1) n_1)
% 1.13/1.36 FOF formula (<kernel.Constant object at 0x2ad8d8346950>, <kernel.Single object at 0x2ad8d8346440>) of role type named typ_n_1t
% 1.13/1.36 Using role type
% 1.13/1.36 Declaring n_1t:fofType
% 1.13/1.36 FOF formula (((eq fofType) n_1t) ((outn n_2) n_1)) of role definition named def_n_1t
% 1.13/1.36 A new definition: (((eq fofType) n_1t) ((outn n_2) n_1))
% 1.13/1.36 Defined: n_1t:=((outn n_2) n_1)
% 1.13/1.36 FOF formula (<kernel.Constant object at 0x2ad8d8346440>, <kernel.Single object at 0x2ad8d8346950>) of role type named typ_n_2t
% 1.13/1.36 Using role type
% 1.13/1.36 Declaring n_2t:fofType
% 1.13/1.36 FOF formula (((eq fofType) n_2t) ((outn n_2) n_2)) of role definition named def_n_2t
% 1.13/1.36 A new definition: (((eq fofType) n_2t) ((outn n_2) n_2))
% 1.13/1.36 Defined: n_2t:=((outn n_2) n_2)
% 1.13/1.36 FOF formula (<kernel.Constant object at 0x2ad8d8346950>, <kernel.DependentProduct object at 0x2ad8d83463b0>) of role type named typ_pair_u0
% 1.13/1.36 Using role type
% 1.13/1.36 Declaring pair_u0:(fofType->fofType)
% 1.13/1.36 FOF formula (((eq (fofType->fofType)) pair_u0) (inn n_2)) of role definition named def_pair_u0
% 1.13/1.36 A new definition: (((eq (fofType->fofType)) pair_u0) (inn n_2))
% 1.13/1.36 Defined: pair_u0:=(inn n_2)
% 1.13/1.36 FOF formula (<kernel.Constant object at 0x2ad8d8346758>, <kernel.DependentProduct object at 0x2ad8d8346b00>) of role type named typ_pair1type
% 1.13/1.36 Using role type
% 1.13/1.36 Declaring pair1type:(fofType->fofType)
% 1.13/1.36 FOF formula (((eq (fofType->fofType)) pair1type) (fun (X0:fofType)=> ((d_Pi (d_1to n_2)) (fun (X1:fofType)=> X0)))) of role definition named def_pair1type
% 1.13/1.36 A new definition: (((eq (fofType->fofType)) pair1type) (fun (X0:fofType)=> ((d_Pi (d_1to n_2)) (fun (X1:fofType)=> X0))))
% 1.13/1.36 Defined: pair1type:=(fun (X0:fofType)=> ((d_Pi (d_1to n_2)) (fun (X1:fofType)=> X0)))
% 1.13/1.36 FOF formula (<kernel.Constant object at 0x2ad8d8346b00>, <kernel.DependentProduct object at 0x2ad8d8346440>) of role type named typ_pair1
% 1.13/1.36 Using role type
% 1.13/1.36 Declaring pair1:(fofType->(fofType->(fofType->fofType)))
% 1.13/1.36 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) pair1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma (d_1to n_2)) (fun (X3:fofType)=> ((((ite (((e_is (d_1to n_2)) X3) n_1t)) X0) X1) X2))))) of role definition named def_pair1
% 1.13/1.36 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) pair1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma (d_1to n_2)) (fun (X3:fofType)=> ((((ite (((e_is (d_1to n_2)) X3) n_1t)) X0) X1) X2)))))
% 1.13/1.36 Defined: pair1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma (d_1to n_2)) (fun (X3:fofType)=> ((((ite (((e_is (d_1to n_2)) X3) n_1t)) X0) X1) X2))))
% 1.13/1.36 FOF formula (<kernel.Constant object at 0x2ad8d8346440>, <kernel.DependentProduct object at 0x2ad8d83467a0>) of role type named typ_first1
% 1.13/1.36 Using role type
% 1.13/1.36 Declaring first1:(fofType->(fofType->fofType))
% 1.13/1.36 FOF formula (((eq (fofType->(fofType->fofType))) first1) (fun (X0:fofType) (X1:fofType)=> ((ap X1) n_1t))) of role definition named def_first1
% 1.13/1.37 A new definition: (((eq (fofType->(fofType->fofType))) first1) (fun (X0:fofType) (X1:fofType)=> ((ap X1) n_1t)))
% 1.13/1.37 Defined: first1:=(fun (X0:fofType) (X1:fofType)=> ((ap X1) n_1t))
% 1.13/1.37 FOF formula (<kernel.Constant object at 0x2ad8d83467a0>, <kernel.DependentProduct object at 0x2ad8d8346518>) of role type named typ_second1
% 1.13/1.37 Using role type
% 1.13/1.37 Declaring second1:(fofType->(fofType->fofType))
% 1.13/1.37 FOF formula (((eq (fofType->(fofType->fofType))) second1) (fun (X0:fofType) (X1:fofType)=> ((ap X1) n_2t))) of role definition named def_second1
% 1.13/1.37 A new definition: (((eq (fofType->(fofType->fofType))) second1) (fun (X0:fofType) (X1:fofType)=> ((ap X1) n_2t)))
% 1.13/1.37 Defined: second1:=(fun (X0:fofType) (X1:fofType)=> ((ap X1) n_2t))
% 1.13/1.37 FOF formula (<kernel.Constant object at 0x2ad8d8346518>, <kernel.DependentProduct object at 0x2ad8d83468c0>) of role type named typ_pair_q0
% 1.13/1.37 Using role type
% 1.13/1.37 Declaring pair_q0:(fofType->(fofType->fofType))
% 1.13/1.37 FOF formula (((eq (fofType->(fofType->fofType))) pair_q0) (fun (X0:fofType) (X1:fofType)=> (((pair1 X0) ((first1 X0) X1)) ((second1 X0) X1)))) of role definition named def_pair_q0
% 1.13/1.37 A new definition: (((eq (fofType->(fofType->fofType))) pair_q0) (fun (X0:fofType) (X1:fofType)=> (((pair1 X0) ((first1 X0) X1)) ((second1 X0) X1))))
% 1.13/1.37 Defined: pair_q0:=(fun (X0:fofType) (X1:fofType)=> (((pair1 X0) ((first1 X0) X1)) ((second1 X0) X1)))
% 1.13/1.37 FOF formula (<kernel.Constant object at 0x2ad8d83468c0>, <kernel.DependentProduct object at 0x2ad8d8346cf8>) of role type named typ_d_1out
% 1.13/1.37 Using role type
% 1.13/1.37 Declaring d_1out:(fofType->fofType)
% 1.13/1.37 FOF formula (((eq (fofType->fofType)) d_1out) (fun (X0:fofType)=> ((outn X0) n_1))) of role definition named def_d_1out
% 1.13/1.37 A new definition: (((eq (fofType->fofType)) d_1out) (fun (X0:fofType)=> ((outn X0) n_1)))
% 1.13/1.37 Defined: d_1out:=(fun (X0:fofType)=> ((outn X0) n_1))
% 1.13/1.37 FOF formula (<kernel.Constant object at 0x2ad8d8346cf8>, <kernel.DependentProduct object at 0x2ad8d83464d0>) of role type named typ_xout
% 1.13/1.37 Using role type
% 1.13/1.37 Declaring xout:(fofType->fofType)
% 1.13/1.37 FOF formula (((eq (fofType->fofType)) xout) (fun (X0:fofType)=> ((outn X0) X0))) of role definition named def_xout
% 1.13/1.37 A new definition: (((eq (fofType->fofType)) xout) (fun (X0:fofType)=> ((outn X0) X0)))
% 1.13/1.37 Defined: xout:=(fun (X0:fofType)=> ((outn X0) X0))
% 1.13/1.37 FOF formula (<kernel.Constant object at 0x2ad8d83464d0>, <kernel.DependentProduct object at 0x2ad8d8346560>) of role type named typ_left1to
% 1.13/1.37 Using role type
% 1.13/1.37 Declaring left1to:(fofType->(fofType->(fofType->fofType)))
% 1.13/1.37 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) left1to) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn X0) ((inn X1) X2)))) of role definition named def_left1to
% 1.13/1.37 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) left1to) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn X0) ((inn X1) X2))))
% 1.13/1.37 Defined: left1to:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn X0) ((inn X1) X2)))
% 1.13/1.37 FOF formula (<kernel.Constant object at 0x2ad8d8346560>, <kernel.DependentProduct object at 0x2ad8d8346f38>) of role type named typ_right1to
% 1.13/1.37 Using role type
% 1.13/1.37 Declaring right1to:(fofType->(fofType->(fofType->fofType)))
% 1.13/1.37 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) right1to) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn ((n_pl X0) X1)) ((n_pl X0) ((inn X1) X2))))) of role definition named def_right1to
% 1.13/1.37 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) right1to) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn ((n_pl X0) X1)) ((n_pl X0) ((inn X1) X2)))))
% 1.13/1.37 Defined: right1to:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn ((n_pl X0) X1)) ((n_pl X0) ((inn X1) X2))))
% 1.13/1.37 FOF formula (<kernel.Constant object at 0x2ad8d8346f38>, <kernel.DependentProduct object at 0x2ad8d83468c0>) of role type named typ_left
% 1.13/1.37 Using role type
% 1.13/1.37 Declaring left:(fofType->(fofType->(fofType->(fofType->fofType))))
% 1.13/1.37 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) left) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to X2)) (fun (X4:fofType)=> ((ap X3) (((left1to X1) X2) X4)))))) of role definition named def_left
% 1.20/1.38 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) left) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to X2)) (fun (X4:fofType)=> ((ap X3) (((left1to X1) X2) X4))))))
% 1.20/1.38 Defined: left:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to X2)) (fun (X4:fofType)=> ((ap X3) (((left1to X1) X2) X4)))))
% 1.20/1.38 FOF formula (<kernel.Constant object at 0x2ad8d83468c0>, <kernel.DependentProduct object at 0x2ad8d8346c68>) of role type named typ_right
% 1.20/1.38 Using role type
% 1.20/1.38 Declaring right:(fofType->(fofType->(fofType->(fofType->fofType))))
% 1.20/1.38 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) right) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to X2)) (fun (X4:fofType)=> ((ap X3) (((right1to X1) X2) X4)))))) of role definition named def_right
% 1.20/1.38 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) right) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to X2)) (fun (X4:fofType)=> ((ap X3) (((right1to X1) X2) X4))))))
% 1.20/1.38 Defined: right:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to X2)) (fun (X4:fofType)=> ((ap X3) (((right1to X1) X2) X4)))))
% 1.20/1.38 FOF formula (<kernel.Constant object at 0x2ad8d8346c68>, <kernel.DependentProduct object at 0x2ad8d8346440>) of role type named typ_left_f1
% 1.20/1.38 Using role type
% 1.20/1.38 Declaring left_f1:(fofType->(fofType->(fofType->(fofType->fofType))))
% 1.20/1.38 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) left_f1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((left X0) X2) X1))) of role definition named def_left_f1
% 1.20/1.38 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) left_f1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((left X0) X2) X1)))
% 1.20/1.38 Defined: left_f1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((left X0) X2) X1))
% 1.20/1.38 FOF formula (<kernel.Constant object at 0x2ad8d8346ea8>, <kernel.DependentProduct object at 0x2ad8d8346f38>) of role type named typ_left_f2
% 1.20/1.38 Using role type
% 1.20/1.38 Declaring left_f2:(fofType->(fofType->(fofType->(fofType->fofType))))
% 1.20/1.38 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) left_f2) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((left X0) X1) X2) ((((left_f1 X0) X1) X2) X3)))) of role definition named def_left_f2
% 1.20/1.38 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) left_f2) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((left X0) X1) X2) ((((left_f1 X0) X1) X2) X3))))
% 1.20/1.38 Defined: left_f2:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((left X0) X1) X2) ((((left_f1 X0) X1) X2) X3)))
% 1.20/1.38 FOF formula (<kernel.Constant object at 0x2ad8d8346f38>, <kernel.Single object at 0x2ad8d8346ea8>) of role type named typ_frac
% 1.20/1.38 Using role type
% 1.20/1.38 Declaring frac:fofType
% 1.20/1.38 FOF formula (((eq fofType) frac) (pair1type nat)) of role definition named def_frac
% 1.20/1.38 A new definition: (((eq fofType) frac) (pair1type nat))
% 1.20/1.38 Defined: frac:=(pair1type nat)
% 1.20/1.38 FOF formula (<kernel.Constant object at 0x2ad8d8346cb0>, <kernel.DependentProduct object at 0x2ad8d8346fc8>) of role type named typ_n_fr
% 1.20/1.38 Using role type
% 1.20/1.38 Declaring n_fr:(fofType->(fofType->fofType))
% 1.20/1.38 FOF formula (((eq (fofType->(fofType->fofType))) n_fr) (pair1 nat)) of role definition named def_n_fr
% 1.20/1.38 A new definition: (((eq (fofType->(fofType->fofType))) n_fr) (pair1 nat))
% 1.20/1.38 Defined: n_fr:=(pair1 nat)
% 1.20/1.38 FOF formula (<kernel.Constant object at 0x2ad8d83468c0>, <kernel.DependentProduct object at 0x2ad8d8353128>) of role type named typ_num
% 1.20/1.38 Using role type
% 1.20/1.38 Declaring num:(fofType->fofType)
% 1.20/1.38 FOF formula (((eq (fofType->fofType)) num) (first1 nat)) of role definition named def_num
% 1.20/1.38 A new definition: (((eq (fofType->fofType)) num) (first1 nat))
% 1.20/1.38 Defined: num:=(first1 nat)
% 1.20/1.38 FOF formula (<kernel.Constant object at 0x2ad8d8346cb0>, <kernel.DependentProduct object at 0x2ad8d8353128>) of role type named typ_den
% 1.20/1.38 Using role type
% 1.20/1.38 Declaring den:(fofType->fofType)
% 1.20/1.38 FOF formula (((eq (fofType->fofType)) den) (second1 nat)) of role definition named def_den
% 1.20/1.38 A new definition: (((eq (fofType->fofType)) den) (second1 nat))
% 1.20/1.41 Defined: den:=(second1 nat)
% 1.20/1.41 FOF formula (<kernel.Constant object at 0x2ad8d8346f38>, <kernel.DependentProduct object at 0x2ad8d8353290>) of role type named typ_n_eq
% 1.20/1.41 Using role type
% 1.20/1.41 Declaring n_eq:(fofType->(fofType->Prop))
% 1.20/1.41 FOF formula (((eq (fofType->(fofType->Prop))) n_eq) (fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0))))) of role definition named def_n_eq
% 1.20/1.41 A new definition: (((eq (fofType->(fofType->Prop))) n_eq) (fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))))
% 1.20/1.41 Defined: n_eq:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0))))
% 1.20/1.41 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((n_eq X0) X0))) of role axiom named satz37
% 1.20/1.41 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((n_eq X0) X0)))
% 1.20/1.41 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((n_eq X0) X1)->((n_eq X1) X0)))))) of role axiom named satz38
% 1.20/1.41 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((n_eq X0) X1)->((n_eq X1) X0))))))
% 1.20/1.41 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->(((n_eq X1) X2)->((n_eq X0) X2))))))))) of role axiom named satz39
% 1.20/1.41 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->(((n_eq X1) X2)->((n_eq X0) X2)))))))))
% 1.20/1.41 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq X0) ((n_fr ((n_ts (num X0)) X1)) ((n_ts (den X0)) X1))))))) of role axiom named satz40
% 1.20/1.41 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq X0) ((n_fr ((n_ts (num X0)) X1)) ((n_ts (den X0)) X1)))))))
% 1.20/1.41 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq ((n_fr ((n_ts (num X0)) X1)) ((n_ts (den X0)) X1))) X0))))) of role axiom named satz40a
% 1.20/1.41 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq ((n_fr ((n_ts (num X0)) X1)) ((n_ts (den X0)) X1))) X0)))))
% 1.20/1.41 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr X0) X1)) ((n_fr ((n_ts X0) X2)) ((n_ts X1) X2))))))))) of role axiom named satz40b
% 1.20/1.41 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr X0) X1)) ((n_fr ((n_ts X0) X2)) ((n_ts X1) X2)))))))))
% 1.20/1.41 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr ((n_ts X0) X2)) ((n_ts X1) X2))) ((n_fr X0) X1)))))))) of role axiom named satz40c
% 1.20/1.41 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr ((n_ts X0) X2)) ((n_ts X1) X2))) ((n_fr X0) X1))))))))
% 1.20/1.41 FOF formula (<kernel.Constant object at 0x2ad8d8353878>, <kernel.DependentProduct object at 0x2ad8d83539e0>) of role type named typ_moref
% 1.20/1.41 Using role type
% 1.20/1.41 Declaring moref:(fofType->(fofType->Prop))
% 1.20/1.43 FOF formula (((eq (fofType->(fofType->Prop))) moref) (fun (X0:fofType) (X1:fofType)=> ((d_29_ii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0))))) of role definition named def_moref
% 1.20/1.43 A new definition: (((eq (fofType->(fofType->Prop))) moref) (fun (X0:fofType) (X1:fofType)=> ((d_29_ii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))))
% 1.20/1.43 Defined: moref:=(fun (X0:fofType) (X1:fofType)=> ((d_29_ii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0))))
% 1.20/1.43 FOF formula (<kernel.Constant object at 0x2ad8d83539e0>, <kernel.DependentProduct object at 0x2ad8d8353248>) of role type named typ_lessf
% 1.20/1.43 Using role type
% 1.20/1.43 Declaring lessf:(fofType->(fofType->Prop))
% 1.20/1.43 FOF formula (((eq (fofType->(fofType->Prop))) lessf) (fun (X0:fofType) (X1:fofType)=> ((iii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0))))) of role definition named def_lessf
% 1.20/1.43 A new definition: (((eq (fofType->(fofType->Prop))) lessf) (fun (X0:fofType) (X1:fofType)=> ((iii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))))
% 1.20/1.43 Defined: lessf:=(fun (X0:fofType) (X1:fofType)=> ((iii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0))))
% 1.20/1.43 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((orec3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1)))))) of role axiom named satz41
% 1.20/1.43 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((orec3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1))))))
% 1.20/1.43 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((or3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1)))))) of role axiom named satz41a
% 1.20/1.43 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((or3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1))))))
% 1.20/1.43 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((ec3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1)))))) of role axiom named satz41b
% 1.20/1.43 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((ec3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1))))))
% 1.20/1.43 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((lessf X1) X0)))))) of role axiom named satz42
% 1.20/1.43 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((lessf X1) X0))))))
% 1.20/1.43 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->((moref X1) X0)))))) of role axiom named satz43
% 1.20/1.43 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->((moref X1) X0))))))
% 1.20/1.43 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((moref X2) X3)))))))))))) of role axiom named satz44
% 1.20/1.43 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((moref X2) X3))))))))))))
% 1.20/1.43 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((lessf X2) X3)))))))))))) of role axiom named satz45
% 1.20/1.45 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((lessf X2) X3))))))))))))
% 1.20/1.45 FOF formula (<kernel.Constant object at 0x2ad8d8353b00>, <kernel.DependentProduct object at 0x2ad8d83535f0>) of role type named typ_moreq
% 1.20/1.45 Using role type
% 1.20/1.45 Declaring moreq:(fofType->(fofType->Prop))
% 1.20/1.45 FOF formula (((eq (fofType->(fofType->Prop))) moreq) (fun (X0:fofType) (X1:fofType)=> ((l_or ((moref X0) X1)) ((n_eq X0) X1)))) of role definition named def_moreq
% 1.20/1.45 A new definition: (((eq (fofType->(fofType->Prop))) moreq) (fun (X0:fofType) (X1:fofType)=> ((l_or ((moref X0) X1)) ((n_eq X0) X1))))
% 1.20/1.45 Defined: moreq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((moref X0) X1)) ((n_eq X0) X1)))
% 1.20/1.45 FOF formula (<kernel.Constant object at 0x2ad8d83535f0>, <kernel.DependentProduct object at 0x2ad8d83537a0>) of role type named typ_lesseq
% 1.20/1.45 Using role type
% 1.20/1.45 Declaring lesseq:(fofType->(fofType->Prop))
% 1.20/1.45 FOF formula (((eq (fofType->(fofType->Prop))) lesseq) (fun (X0:fofType) (X1:fofType)=> ((l_or ((lessf X0) X1)) ((n_eq X0) X1)))) of role definition named def_lesseq
% 1.20/1.45 A new definition: (((eq (fofType->(fofType->Prop))) lesseq) (fun (X0:fofType) (X1:fofType)=> ((l_or ((lessf X0) X1)) ((n_eq X0) X1))))
% 1.20/1.45 Defined: lesseq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((lessf X0) X1)) ((n_eq X0) X1)))
% 1.20/1.45 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moreq X0) X1)->(d_not ((lessf X0) X1))))))) of role axiom named satz41c
% 1.20/1.45 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moreq X0) X1)->(d_not ((lessf X0) X1)))))))
% 1.20/1.45 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lesseq X0) X1)->(d_not ((moref X0) X1))))))) of role axiom named satz41d
% 1.20/1.45 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lesseq X0) X1)->(d_not ((moref X0) X1)))))))
% 1.20/1.45 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((moref X0) X1))->((lesseq X0) X1)))))) of role axiom named satz41e
% 1.20/1.45 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((moref X0) X1))->((lesseq X0) X1))))))
% 1.20/1.45 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((lessf X0) X1))->((moreq X0) X1)))))) of role axiom named satz41f
% 1.20/1.45 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((lessf X0) X1))->((moreq X0) X1))))))
% 1.20/1.45 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->(d_not ((lesseq X0) X1))))))) of role axiom named satz41g
% 1.20/1.45 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->(d_not ((lesseq X0) X1)))))))
% 1.20/1.45 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->(d_not ((moreq X0) X1))))))) of role axiom named satz41h
% 1.29/1.48 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->(d_not ((moreq X0) X1)))))))
% 1.29/1.48 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((moreq X0) X1))->((lessf X0) X1)))))) of role axiom named satz41j
% 1.29/1.48 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((moreq X0) X1))->((lessf X0) X1))))))
% 1.29/1.48 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((lesseq X0) X1))->((moref X0) X1)))))) of role axiom named satz41k
% 1.29/1.48 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((lesseq X0) X1))->((moref X0) X1))))))
% 1.29/1.48 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((moreq X2) X3)))))))))))) of role axiom named satz46
% 1.29/1.48 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moreq X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((moreq X2) X3))))))))))))
% 1.29/1.48 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((lesseq X2) X3)))))))))))) of role axiom named satz47
% 1.29/1.48 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lesseq X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((lesseq X2) X3))))))))))))
% 1.29/1.48 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moreq X0) X1)->((lesseq X1) X0)))))) of role axiom named satz48
% 1.29/1.48 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moreq X0) X1)->((lesseq X1) X0))))))
% 1.29/1.48 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lesseq X0) X1)->((moreq X1) X0)))))) of role axiom named satz49
% 1.29/1.48 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lesseq X0) X1)->((moreq X1) X0))))))
% 1.29/1.48 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->(((lessf X1) X2)->((lessf X0) X2))))))))) of role axiom named satz50
% 1.29/1.48 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->(((lessf X1) X2)->((lessf X0) X2)))))))))
% 1.29/1.48 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lesseq X0) X1)->(((lessf X1) X2)->((lessf X0) X2))))))))) of role axiom named satz51a
% 1.30/1.49 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lesseq X0) X1)->(((lessf X1) X2)->((lessf X0) X2)))))))))
% 1.30/1.49 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->(((lesseq X1) X2)->((lessf X0) X2))))))))) of role conjecture named satz51b
% 1.30/1.49 Conjecture to prove = ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->(((lesseq X1) X2)->((lessf X0) X2))))))))):Prop
% 1.30/1.49 We need to prove ['((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((lessf X0) X1)->(((lesseq X1) X2)->((lessf X0) X2)))))))))']
% 1.30/1.49 Parameter fofType:Type.
% 1.30/1.49 Definition is_of:=(fun (X0:fofType) (X1:(fofType->Prop))=> (X1 X0)):(fofType->((fofType->Prop)->Prop)).
% 1.30/1.49 Definition all_of:=(fun (X0:(fofType->Prop)) (X1:(fofType->Prop))=> (forall (X2:fofType), (((is_of X2) X0)->(X1 X2)))):((fofType->Prop)->((fofType->Prop)->Prop)).
% 1.30/1.49 Parameter eps:((fofType->Prop)->fofType).
% 1.30/1.49 Parameter in:(fofType->(fofType->Prop)).
% 1.30/1.49 Definition d_Subq:=(fun (X0:fofType) (X1:fofType)=> (forall (X2:fofType), (((in X2) X0)->((in X2) X1)))):(fofType->(fofType->Prop)).
% 1.30/1.49 Axiom set_ext:(forall (X0:fofType) (X1:fofType), (((d_Subq X0) X1)->(((d_Subq X1) X0)->(((eq fofType) X0) X1)))).
% 1.30/1.49 Axiom k_In_ind:(forall (X0:(fofType->Prop)), ((forall (X1:fofType), ((forall (X2:fofType), (((in X2) X1)->(X0 X2)))->(X0 X1)))->(forall (X1:fofType), (X0 X1)))).
% 1.30/1.49 Parameter emptyset:fofType.
% 1.30/1.49 Axiom k_EmptyAx:(((ex fofType) (fun (X0:fofType)=> ((in X0) emptyset)))->False).
% 1.30/1.49 Parameter union:(fofType->fofType).
% 1.30/1.49 Axiom k_UnionEq:(forall (X0:fofType) (X1:fofType), ((iff ((in X1) (union X0))) ((ex fofType) (fun (X2:fofType)=> ((and ((in X1) X2)) ((in X2) X0)))))).
% 1.30/1.49 Parameter power:(fofType->fofType).
% 1.30/1.49 Axiom k_PowerEq:(forall (X0:fofType) (X1:fofType), ((iff ((in X1) (power X0))) ((d_Subq X1) X0))).
% 1.30/1.49 Parameter repl:(fofType->((fofType->fofType)->fofType)).
% 1.30/1.49 Axiom k_ReplEq:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), ((iff ((in X2) ((repl X0) X1))) ((ex fofType) (fun (X3:fofType)=> ((and ((in X3) X0)) (((eq fofType) X2) (X1 X3))))))).
% 1.30/1.49 Definition d_Union_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (union X1)) X0)))):(fofType->Prop).
% 1.30/1.49 Definition d_Power_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (power X1)) X0)))):(fofType->Prop).
% 1.30/1.49 Definition d_Repl_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->(forall (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X1)->((in (X2 X3)) X0)))->((in ((repl X1) X2)) X0)))))):(fofType->Prop).
% 1.30/1.49 Definition d_ZF_closed:=(fun (X0:fofType)=> ((and ((and (d_Union_closed X0)) (d_Power_closed X0))) (d_Repl_closed X0))):(fofType->Prop).
% 1.30/1.49 Parameter univof:(fofType->fofType).
% 1.30/1.49 Axiom k_UnivOf_In:(forall (X0:fofType), ((in X0) (univof X0))).
% 1.30/1.49 Axiom k_UnivOf_ZF_closed:(forall (X0:fofType), (d_ZF_closed (univof X0))).
% 1.30/1.49 Definition if:=(fun (X0:Prop) (X1:fofType) (X2:fofType)=> (eps (fun (X3:fofType)=> ((or ((and X0) (((eq fofType) X3) X1))) ((and (X0->False)) (((eq fofType) X3) X2)))))):(Prop->(fofType->(fofType->fofType))).
% 1.30/1.49 Axiom if_i_correct:(forall (X0:Prop) (X1:fofType) (X2:fofType), ((or ((and X0) (((eq fofType) (((if X0) X1) X2)) X1))) ((and (X0->False)) (((eq fofType) (((if X0) X1) X2)) X2)))).
% 1.30/1.49 Axiom if_i_0:(forall (X0:Prop) (X1:fofType) (X2:fofType), ((X0->False)->(((eq fofType) (((if X0) X1) X2)) X2))).
% 1.30/1.49 Axiom if_i_1:(forall (X0:Prop) (X1:fofType) (X2:fofType), (X0->(((eq fofType) (((if X0) X1) X2)) X1))).
% 1.30/1.49 Axiom if_i_or:(forall (X0:Prop) (X1:fofType) (X2:fofType), ((or (((eq fofType) (((if X0) X1) X2)) X1)) (((eq fofType) (((if X0) X1) X2)) X2))).
% 1.30/1.49 Definition nIn:=(fun (X0:fofType) (X1:fofType)=> (((in X0) X1)->False)):(fofType->(fofType->Prop)).
% 1.30/1.49 Axiom k_PowerE:(forall (X0:fofType) (X1:fofType), (((in X1) (power X0))->((d_Subq X1) X0))).
% 1.30/1.49 Axiom k_PowerI:(forall (X0:fofType) (X1:fofType), (((d_Subq X1) X0)->((in X1) (power X0)))).
% 1.30/1.49 Axiom k_Self_In_Power:(forall (X0:fofType), ((in X0) (power X0))).
% 1.30/1.49 Definition d_UPair:=(fun (X0:fofType) (X1:fofType)=> ((repl (power (power emptyset))) (fun (X2:fofType)=> (((if ((in emptyset) X2)) X0) X1)))):(fofType->(fofType->fofType)).
% 1.30/1.49 Definition d_Sing:=(fun (X0:fofType)=> ((d_UPair X0) X0)):(fofType->fofType).
% 1.30/1.49 Definition binunion:=(fun (X0:fofType) (X1:fofType)=> (union ((d_UPair X0) X1))):(fofType->(fofType->fofType)).
% 1.30/1.49 Definition famunion:=(fun (X0:fofType) (X1:(fofType->fofType))=> (union ((repl X0) X1))):(fofType->((fofType->fofType)->fofType)).
% 1.30/1.49 Definition d_Sep:=(fun (X0:fofType) (X1:(fofType->Prop))=> (((if ((ex fofType) (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2))))) ((repl X0) (fun (X2:fofType)=> (((if (X1 X2)) X2) (eps (fun (X3:fofType)=> ((and ((in X3) X0)) (X1 X3)))))))) emptyset)):(fofType->((fofType->Prop)->fofType)).
% 1.30/1.49 Axiom k_SepI:(forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) X0)->((X1 X2)->((in X2) ((d_Sep X0) X1))))).
% 1.30/1.49 Axiom k_SepE1:(forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) ((d_Sep X0) X1))->((in X2) X0))).
% 1.30/1.49 Axiom k_SepE2:(forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) ((d_Sep X0) X1))->(X1 X2))).
% 1.30/1.49 Definition d_ReplSep:=(fun (X0:fofType) (X1:(fofType->Prop))=> (repl ((d_Sep X0) X1))):(fofType->((fofType->Prop)->((fofType->fofType)->fofType))).
% 1.30/1.49 Definition setminus:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep X0) (fun (X2:fofType)=> ((nIn X2) X1)))):(fofType->(fofType->fofType)).
% 1.30/1.49 Definition d_In_rec_G:=(fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType) (X2:fofType)=> (forall (X3:(fofType->(fofType->Prop))), ((forall (X4:fofType) (X5:(fofType->fofType)), ((forall (X6:fofType), (((in X6) X4)->((X3 X6) (X5 X6))))->((X3 X4) ((X0 X4) X5))))->((X3 X1) X2)))):((fofType->((fofType->fofType)->fofType))->(fofType->(fofType->Prop))).
% 1.30/1.49 Definition d_In_rec:=(fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType)=> (eps ((d_In_rec_G X0) X1))):((fofType->((fofType->fofType)->fofType))->(fofType->fofType)).
% 1.30/1.49 Definition ordsucc:=(fun (X0:fofType)=> ((binunion X0) (d_Sing X0))):(fofType->fofType).
% 1.30/1.49 Axiom neq_ordsucc_0:(forall (X0:fofType), (not (((eq fofType) (ordsucc X0)) emptyset))).
% 1.30/1.49 Axiom ordsucc_inj:(forall (X0:fofType) (X1:fofType), ((((eq fofType) (ordsucc X0)) (ordsucc X1))->(((eq fofType) X0) X1))).
% 1.30/1.49 Axiom k_In_0_1:((in emptyset) (ordsucc emptyset)).
% 1.30/1.49 Definition nat_p:=(fun (X0:fofType)=> (forall (X1:(fofType->Prop)), ((X1 emptyset)->((forall (X2:fofType), ((X1 X2)->(X1 (ordsucc X2))))->(X1 X0))))):(fofType->Prop).
% 1.30/1.49 Axiom nat_ordsucc:(forall (X0:fofType), ((nat_p X0)->(nat_p (ordsucc X0)))).
% 1.30/1.49 Axiom nat_1:(nat_p (ordsucc emptyset)).
% 1.30/1.49 Axiom nat_ind:(forall (X0:(fofType->Prop)), ((X0 emptyset)->((forall (X1:fofType), ((nat_p X1)->((X0 X1)->(X0 (ordsucc X1)))))->(forall (X1:fofType), ((nat_p X1)->(X0 X1)))))).
% 1.30/1.49 Axiom nat_inv:(forall (X0:fofType), ((nat_p X0)->((or (((eq fofType) X0) emptyset)) ((ex fofType) (fun (X1:fofType)=> ((and (nat_p X1)) (((eq fofType) X0) (ordsucc X1)))))))).
% 1.30/1.49 Definition omega:=((d_Sep (univof emptyset)) nat_p):fofType.
% 1.30/1.49 Axiom omega_nat_p:(forall (X0:fofType), (((in X0) omega)->(nat_p X0))).
% 1.30/1.49 Axiom nat_p_omega:(forall (X0:fofType), ((nat_p X0)->((in X0) omega))).
% 1.30/1.49 Definition d_Inj1:=(d_In_rec (fun (X0:fofType) (X1:(fofType->fofType))=> ((binunion (d_Sing emptyset)) ((repl X0) X1)))):(fofType->fofType).
% 1.30/1.49 Definition d_Inj0:=(fun (X0:fofType)=> ((repl X0) d_Inj1)):(fofType->fofType).
% 1.30/1.49 Definition d_Unj:=(d_In_rec (fun (X0:fofType)=> (repl ((setminus X0) (d_Sing emptyset))))):(fofType->fofType).
% 1.30/1.49 Definition pair:=(fun (X0:fofType) (X1:fofType)=> ((binunion ((repl X0) d_Inj0)) ((repl X1) d_Inj1))):(fofType->(fofType->fofType)).
% 1.30/1.49 Definition proj0:=(fun (X0:fofType)=> (((d_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (d_Inj0 X2)) X1))))) d_Unj)):(fofType->fofType).
% 1.30/1.49 Definition _TPTP_proj1:=(fun (X0:fofType)=> (((d_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (d_Inj1 X2)) X1))))) d_Unj)):(fofType->fofType).
% 1.30/1.49 Axiom proj0_pair_eq:(forall (X0:fofType) (X1:fofType), (((eq fofType) (proj0 ((pair X0) X1))) X0)).
% 1.30/1.49 Axiom proj1_pair_eq:(forall (X0:fofType) (X1:fofType), (((eq fofType) (_TPTP_proj1 ((pair X0) X1))) X1)).
% 1.30/1.49 Definition d_Sigma:=(fun (X0:fofType) (X1:(fofType->fofType))=> ((famunion X0) (fun (X2:fofType)=> ((repl (X1 X2)) (pair X2))))):(fofType->((fofType->fofType)->fofType)).
% 1.30/1.49 Axiom pair_Sigma:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) X0)->(forall (X3:fofType), (((in X3) (X1 X2))->((in ((pair X2) X3)) ((d_Sigma X0) X1)))))).
% 1.30/1.49 Axiom k_Sigma_eta_proj0_proj1:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((and ((and (((eq fofType) ((pair (proj0 X2)) (_TPTP_proj1 X2))) X2)) ((in (proj0 X2)) X0))) ((in (_TPTP_proj1 X2)) (X1 (proj0 X2)))))).
% 1.30/1.49 Axiom proj_Sigma_eta:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->(((eq fofType) ((pair (proj0 X2)) (_TPTP_proj1 X2))) X2))).
% 1.30/1.49 Axiom proj0_Sigma:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((in (proj0 X2)) X0))).
% 1.30/1.49 Axiom proj1_Sigma:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((in (_TPTP_proj1 X2)) (X1 (proj0 X2))))).
% 1.30/1.49 Definition setprod:=(fun (X0:fofType) (X1:fofType)=> ((d_Sigma X0) (fun (X2:fofType)=> X1))):(fofType->(fofType->fofType)).
% 1.30/1.49 Definition ap:=(fun (X0:fofType) (X1:fofType)=> (((d_ReplSep X0) (fun (X2:fofType)=> ((ex fofType) (fun (X3:fofType)=> (((eq fofType) X2) ((pair X1) X3)))))) _TPTP_proj1)):(fofType->(fofType->fofType)).
% 1.30/1.49 Axiom beta:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) X0)->(((eq fofType) ((ap ((d_Sigma X0) X1)) X2)) (X1 X2)))).
% 1.30/1.49 Definition pair_p:=(fun (X0:fofType)=> (((eq fofType) ((pair ((ap X0) emptyset)) ((ap X0) (ordsucc emptyset)))) X0)):(fofType->Prop).
% 1.30/1.49 Definition d_Pi:=(fun (X0:fofType) (X1:(fofType->fofType))=> ((d_Sep (power ((d_Sigma X0) (fun (X2:fofType)=> (union (X1 X2)))))) (fun (X2:fofType)=> (forall (X3:fofType), (((in X3) X0)->((in ((ap X2) X3)) (X1 X3))))))):(fofType->((fofType->fofType)->fofType)).
% 1.30/1.49 Axiom lam_Pi:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X0)->((in (X2 X3)) (X1 X3))))->((in ((d_Sigma X0) X2)) ((d_Pi X0) X1)))).
% 1.30/1.49 Axiom ap_Pi:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType) (X3:fofType), (((in X2) ((d_Pi X0) X1))->(((in X3) X0)->((in ((ap X2) X3)) (X1 X3))))).
% 1.30/1.49 Axiom k_Pi_ext:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Pi X0) X1))->(forall (X3:fofType), (((in X3) ((d_Pi X0) X1))->((forall (X4:fofType), (((in X4) X0)->(((eq fofType) ((ap X2) X4)) ((ap X3) X4))))->(((eq fofType) X2) X3)))))).
% 1.30/1.49 Axiom xi_ext:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:(fofType->fofType)), ((forall (X3:fofType), (((in X3) X0)->(((eq fofType) (X1 X3)) (X2 X3))))->(((eq fofType) ((d_Sigma X0) X1)) ((d_Sigma X0) X2)))).
% 1.30/1.49 Axiom k_If_In_01:(forall (X0:Prop) (X1:fofType) (X2:fofType), ((X0->((in X1) X2))->((in (((if X0) X1) emptyset)) (((if X0) X2) (ordsucc emptyset))))).
% 1.30/1.49 Axiom k_If_In_then_E:(forall (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType), (X0->(((in X1) (((if X0) X2) X3))->((in X1) X2)))).
% 1.30/1.49 Definition imp:=(fun (X0:Prop) (X1:Prop)=> (X0->X1)):(Prop->(Prop->Prop)).
% 1.30/1.49 Definition d_not:=(fun (X0:Prop)=> ((imp X0) False)):(Prop->Prop).
% 1.30/1.49 Definition wel:=(fun (X0:Prop)=> (d_not (d_not X0))):(Prop->Prop).
% 1.30/1.49 Axiom l_et:(forall (X0:Prop), ((wel X0)->X0)).
% 1.30/1.49 Definition obvious:=((imp False) False):Prop.
% 1.30/1.49 Definition l_ec:=(fun (X0:Prop) (X1:Prop)=> ((imp X0) (d_not X1))):(Prop->(Prop->Prop)).
% 1.30/1.49 Definition d_and:=(fun (X0:Prop) (X1:Prop)=> (d_not ((l_ec X0) X1))):(Prop->(Prop->Prop)).
% 1.30/1.49 Definition l_or:=(fun (X0:Prop)=> (imp (d_not X0))):(Prop->(Prop->Prop)).
% 1.30/1.49 Definition orec:=(fun (X0:Prop) (X1:Prop)=> ((d_and ((l_or X0) X1)) ((l_ec X0) X1))):(Prop->(Prop->Prop)).
% 1.30/1.49 Definition l_iff:=(fun (X0:Prop) (X1:Prop)=> ((d_and ((imp X0) X1)) ((imp X1) X0))):(Prop->(Prop->Prop)).
% 1.30/1.49 Definition all:=(fun (X0:fofType)=> (all_of (fun (X1:fofType)=> ((in X1) X0)))):(fofType->((fofType->Prop)->Prop)).
% 1.30/1.49 Definition non:=(fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> (d_not (X1 X2))):(fofType->((fofType->Prop)->(fofType->Prop))).
% 1.30/1.49 Definition l_some:=(fun (X0:fofType) (X1:(fofType->Prop))=> (d_not ((all_of (fun (X2:fofType)=> ((in X2) X0))) ((non X0) X1)))):(fofType->((fofType->Prop)->Prop)).
% 1.30/1.49 Definition or3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((l_or X0) ((l_or X1) X2))):(Prop->(Prop->(Prop->Prop))).
% 1.30/1.49 Definition and3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and X0) ((d_and X1) X2))):(Prop->(Prop->(Prop->Prop))).
% 1.30/1.49 Definition ec3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> (((and3 ((l_ec X0) X1)) ((l_ec X1) X2)) ((l_ec X2) X0))):(Prop->(Prop->(Prop->Prop))).
% 1.30/1.49 Definition orec3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and (((or3 X0) X1) X2)) (((ec3 X0) X1) X2))):(Prop->(Prop->(Prop->Prop))).
% 1.30/1.49 Definition e_is:=(fun (X0:fofType) (X:fofType) (Y:fofType)=> (((eq fofType) X) Y)):(fofType->(fofType->(fofType->Prop))).
% 1.30/1.49 Axiom refis:(forall (X0:fofType), ((all_of (fun (X1:fofType)=> ((in X1) X0))) (fun (X1:fofType)=> (((e_is X0) X1) X1)))).
% 1.30/1.49 Axiom e_isp:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X0))) (fun (X3:fofType)=> ((X1 X2)->((((e_is X0) X2) X3)->(X1 X3)))))))).
% 1.30/1.49 Definition amone:=(fun (X0:fofType) (X1:(fofType->Prop))=> ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X0))) (fun (X3:fofType)=> ((X1 X2)->((X1 X3)->(((e_is X0) X2) X3)))))))):(fofType->((fofType->Prop)->Prop)).
% 1.30/1.49 Definition one:=(fun (X0:fofType) (X1:(fofType->Prop))=> ((d_and ((amone X0) X1)) ((l_some X0) X1))):(fofType->((fofType->Prop)->Prop)).
% 1.30/1.49 Definition ind:=(fun (X0:fofType) (X1:(fofType->Prop))=> (eps (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2))))):(fofType->((fofType->Prop)->fofType)).
% 1.30/1.49 Axiom ind_p:(forall (X0:fofType) (X1:(fofType->Prop)), (((one X0) X1)->((is_of ((ind X0) X1)) (fun (X2:fofType)=> ((in X2) X0))))).
% 1.30/1.49 Axiom oneax:(forall (X0:fofType) (X1:(fofType->Prop)), (((one X0) X1)->(X1 ((ind X0) X1)))).
% 1.30/1.49 Definition injective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((all X0) (fun (X4:fofType)=> ((imp (((e_is X1) ((ap X2) X3)) ((ap X2) X4))) (((e_is X0) X3) X4))))))):(fofType->(fofType->(fofType->Prop))).
% 1.30/1.49 Definition image:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((l_some X0) (fun (X4:fofType)=> (((e_is X1) X3) ((ap X2) X4))))):(fofType->(fofType->(fofType->(fofType->Prop)))).
% 1.30/1.49 Definition tofs:=(fun (X0:fofType) (X1:fofType)=> ap):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 1.30/1.49 Definition soft:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X0) (fun (X4:fofType)=> (((e_is X1) X3) ((ap X2) X4))))):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 1.30/1.49 Definition inverse:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (fun (X3:fofType)=> (((if ((((image X0) X1) X2) X3)) ((((soft X0) X1) X2) X3)) emptyset)))):(fofType->(fofType->(fofType->fofType))).
% 1.30/1.49 Definition surjective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X1) (((image X0) X1) X2))):(fofType->(fofType->(fofType->Prop))).
% 1.30/1.49 Definition bijective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and (((injective X0) X1) X2)) (((surjective X0) X1) X2))):(fofType->(fofType->(fofType->Prop))).
% 1.30/1.49 Definition invf:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (((soft X0) X1) X2))):(fofType->(fofType->(fofType->fofType))).
% 1.30/1.49 Definition inj_h:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_Sigma X0) (fun (X5:fofType)=> ((ap X4) ((ap X3) X5))))):(fofType->(fofType->(fofType->(fofType->(fofType->fofType))))).
% 1.30/1.49 Axiom e_fisi:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Pi X0) (fun (X3:fofType)=> X1))))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) ((d_Pi X0) (fun (X4:fofType)=> X1))))) (fun (X3:fofType)=> (((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> (((e_is X1) ((ap X2) X4)) ((ap X3) X4))))->(((e_is ((d_Pi X0) (fun (X4:fofType)=> X1))) X2) X3))))))).
% 1.30/1.49 Definition e_in:=(fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> X2):(fofType->((fofType->Prop)->(fofType->fofType))).
% 1.30/1.49 Axiom e_in_p:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Sep X0) X1)))) (fun (X2:fofType)=> ((is_of (((e_in X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X0)))))).
% 1.30/1.49 Axiom e_inp:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) ((d_Sep X0) X1)))) (fun (X2:fofType)=> (X1 (((e_in X0) X1) X2))))).
% 1.30/1.49 Axiom otax1:(forall (X0:fofType) (X1:(fofType->Prop)), (((injective ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1)))).
% 1.30/1.49 Axiom otax2:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((X1 X2)->((((image ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1))) X2))))).
% 1.30/1.49 Definition out:=(fun (X0:fofType) (X1:(fofType->Prop))=> (((soft ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1)))):(fofType->((fofType->Prop)->(fofType->fofType))).
% 1.30/1.49 Definition d_pair:=(fun (X0:fofType) (X1:fofType)=> pair):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 1.30/1.49 Axiom e_pair_p:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> ((is_of ((((d_pair X0) X1) X2) X3)) (fun (X4:fofType)=> ((in X4) ((setprod X0) X1))))))))).
% 1.30/1.49 Definition first:=(fun (X0:fofType) (X1:fofType)=> proj0):(fofType->(fofType->(fofType->fofType))).
% 1.30/1.49 Axiom first_p:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> ((is_of (((first X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X0)))))).
% 1.30/1.49 Definition second:=(fun (X0:fofType) (X1:fofType)=> _TPTP_proj1):(fofType->(fofType->(fofType->fofType))).
% 1.30/1.49 Axiom second_p:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> ((is_of (((second X0) X1) X2)) (fun (X3:fofType)=> ((in X3) X1)))))).
% 1.30/1.49 Axiom pairis1:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) ((setprod X0) X1)))) (fun (X2:fofType)=> (((e_is ((setprod X0) X1)) ((((d_pair X0) X1) (((first X0) X1) X2)) (((second X0) X1) X2))) X2)))).
% 1.30/1.49 Axiom firstis1:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> (((e_is X0) (((first X0) X1) ((((d_pair X0) X1) X2) X3))) X2)))))).
% 1.30/1.49 Axiom secondis1:(forall (X0:fofType) (X1:fofType), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) X1))) (fun (X3:fofType)=> (((e_is X1) (((second X0) X1) ((((d_pair X0) X1) X2) X3))) X3)))))).
% 1.30/1.49 Definition prop1:=(fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_and ((imp X0) (((e_is X1) X4) X2))) ((imp (d_not X0)) (((e_is X1) X4) X3)))):(Prop->(fofType->(fofType->(fofType->(fofType->Prop))))).
% 1.30/1.49 Definition ite:=(fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X1) ((((prop1 X0) X1) X2) X3))):(Prop->(fofType->(fofType->(fofType->fofType)))).
% 1.30/1.49 Definition wissel_wa:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((ite (((e_is X0) X3) X1)) X0) X2) X3)):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 1.30/1.49 Definition wissel_wb:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((ite (((e_is X0) X3) X2)) X0) X1) ((((wissel_wa X0) X1) X2) X3))):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 1.30/1.49 Definition wissel:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X0) (((wissel_wb X0) X1) X2))):(fofType->(fofType->(fofType->fofType))).
% 1.30/1.49 Definition changef:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType) (X4:fofType)=> ((d_Sigma X0) (fun (X5:fofType)=> ((ap X2) ((ap (((wissel X0) X3) X4)) X5))))):(fofType->(fofType->(fofType->(fofType->(fofType->fofType))))).
% 1.30/1.50 Definition r_ec:=(fun (X0:Prop) (X1:Prop)=> (X0->(d_not X1))):(Prop->(Prop->Prop)).
% 1.30/1.50 Definition esti:=(fun (X0:fofType)=> in):(fofType->(fofType->(fofType->Prop))).
% 1.30/1.50 Axiom setof_p:(forall (X0:fofType) (X1:(fofType->Prop)), ((is_of ((d_Sep X0) X1)) (fun (X2:fofType)=> ((in X2) (power X0))))).
% 1.30/1.50 Axiom estii:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((X1 X2)->(((esti X0) X2) ((d_Sep X0) X1)))))).
% 1.30/1.50 Axiom estie:(forall (X0:fofType) (X1:(fofType->Prop)), ((all_of (fun (X2:fofType)=> ((in X2) X0))) (fun (X2:fofType)=> ((((esti X0) X2) ((d_Sep X0) X1))->(X1 X2))))).
% 1.30/1.50 Definition empty:=(fun (X0:fofType) (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) X0))) ((non X0) (fun (X2:fofType)=> (((esti X0) X2) X1))))):(fofType->(fofType->Prop)).
% 1.30/1.50 Definition nonempty:=(fun (X0:fofType) (X1:fofType)=> ((l_some X0) (fun (X2:fofType)=> (((esti X0) X2) X1)))):(fofType->(fofType->Prop)).
% 1.30/1.50 Definition incl:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((imp (((esti X0) X3) X1)) (((esti X0) X3) X2))))):(fofType->(fofType->(fofType->Prop))).
% 1.30/1.50 Definition st_disj:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((l_ec (((esti X0) X3) X1)) (((esti X0) X3) X2))))):(fofType->(fofType->(fofType->Prop))).
% 1.30/1.50 Axiom isseti:(forall (X0:fofType), ((all_of (fun (X1:fofType)=> ((in X1) (power X0)))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) (power X0)))) (fun (X2:fofType)=> ((((incl X0) X1) X2)->((((incl X0) X2) X1)->(((e_is (power X0)) X1) X2)))))))).
% 1.30/1.50 Definition nissetprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_and (((esti X0) X3) X1)) (d_not (((esti X0) X3) X2)))):(fofType->(fofType->(fofType->(fofType->Prop)))).
% 1.30/1.50 Definition unmore:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sep X0) (fun (X3:fofType)=> ((l_some X1) (fun (X4:fofType)=> (((esti X0) X3) ((ap X2) X4))))))):(fofType->(fofType->(fofType->fofType))).
% 1.30/1.50 Definition ecelt:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((d_Sep X0) (X1 X2))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType))).
% 1.30/1.50 Definition ecp:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> (((e_is (power X0)) X2) (((ecelt X0) X1) X3))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))).
% 1.30/1.50 Definition anec:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((l_some X0) (((ecp X0) X1) X2))):(fofType->((fofType->(fofType->Prop))->(fofType->Prop))).
% 1.30/1.50 Definition ect:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((d_Sep (power X0)) ((anec X0) X1))):(fofType->((fofType->(fofType->Prop))->fofType)).
% 1.30/1.50 Definition ectset:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((out (power X0)) ((anec X0) X1))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType))).
% 1.30/1.50 Definition ectelt:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((ectset X0) X1) (((ecelt X0) X1) X2))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType))).
% 1.30/1.50 Definition ecect:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((e_in (power X0)) ((anec X0) X1))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType))).
% 1.30/1.50 Definition fixfu:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> ((all_of (fun (X5:fofType)=> ((in X5) X0))) (fun (X5:fofType)=> (((X1 X4) X5)->(((e_is X2) ((ap X3) X4)) ((ap X3) X5)))))))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))).
% 1.30/1.50 Definition d_10_prop1:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType) (X5:fofType) (X6:fofType)=> ((d_and (((esti X0) X6) (((ecect X0) X1) X4))) (((e_is X2) ((ap X3) X6)) X5))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->(fofType->Prop))))))).
% 1.30/1.50 Definition prop2:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType) (X5:fofType)=> ((l_some X0) ((((((d_10_prop1 X0) X1) X2) X3) X4) X5))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->Prop)))))).
% 1.30/1.50 Definition indeq:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType)=> ((ind X2) (((((prop2 X0) X1) X2) X3) X4))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType))))).
% 1.30/1.50 Definition fixfu2:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> ((all_of (fun (X4:fofType)=> ((in X4) X0))) (fun (X4:fofType)=> ((all_of (fun (X5:fofType)=> ((in X5) X0))) (fun (X5:fofType)=> ((all_of (fun (X6:fofType)=> ((in X6) X0))) (fun (X6:fofType)=> ((all_of (fun (X7:fofType)=> ((in X7) X0))) (fun (X7:fofType)=> (((X1 X4) X5)->(((X1 X6) X7)->(((e_is X2) ((ap ((ap X3) X4)) X6)) ((ap ((ap X3) X5)) X7))))))))))))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop)))).
% 1.30/1.50 Definition d_11_i:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((indeq X0) X1) ((d_Pi X0) (fun (X3:fofType)=> X2)))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType))))).
% 1.30/1.50 Definition indeq2:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType)=> ((((indeq X0) X1) X2) (((((d_11_i X0) X1) X2) X3) X4))):(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->fofType)))))).
% 1.30/1.50 Definition nat:=((d_Sep omega) (fun (X0:fofType)=> (not (((eq fofType) X0) emptyset)))):fofType.
% 1.30/1.50 Definition n_is:=(e_is nat):(fofType->(fofType->Prop)).
% 1.30/1.50 Definition nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((n_is X0) X1))):(fofType->(fofType->Prop)).
% 1.30/1.50 Definition n_in:=(esti nat):(fofType->(fofType->Prop)).
% 1.30/1.50 Definition n_some:=(l_some nat):((fofType->Prop)->Prop).
% 1.30/1.50 Definition n_all:=(all nat):((fofType->Prop)->Prop).
% 1.30/1.50 Definition n_one:=(one nat):((fofType->Prop)->Prop).
% 1.30/1.50 Definition n_1:=(ordsucc emptyset):fofType.
% 1.30/1.50 Axiom n_1_p:((is_of n_1) (fun (X0:fofType)=> ((in X0) nat))).
% 1.30/1.50 Axiom suc_p:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((is_of (ordsucc X0)) (fun (X1:fofType)=> ((in X1) nat))))).
% 1.30/1.50 Axiom n_ax3:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) n_1))).
% 1.30/1.50 Axiom n_ax4:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((n_is (ordsucc X0)) (ordsucc X1))->((n_is X0) X1)))))).
% 1.30/1.50 Definition cond1:=(n_in n_1):(fofType->Prop).
% 1.30/1.50 Definition cond2:=(fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((imp ((n_in X1) X0)) ((n_in (ordsucc X1)) X0))))):(fofType->Prop).
% 1.30/1.50 Axiom n_ax5:((all_of (fun (X0:fofType)=> ((in X0) (power nat)))) (fun (X0:fofType)=> ((cond1 X0)->((cond2 X0)->((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_in X1) X0))))))).
% 1.30/1.50 Definition i1_s:=(d_Sep nat):((fofType->Prop)->fofType).
% 1.30/1.50 Axiom satz1:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((nis X0) X1)->((nis (ordsucc X0)) (ordsucc X1))))))).
% 1.30/1.50 Definition d_22_prop1:=(fun (X0:fofType)=> ((nis (ordsucc X0)) X0)):(fofType->Prop).
% 1.30/1.50 Axiom satz2:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) X0))).
% 1.30/1.50 Definition d_23_prop1:=(fun (X0:fofType)=> ((l_or ((n_is X0) n_1)) (n_some (fun (X1:fofType)=> ((n_is X0) (ordsucc X1)))))):(fofType->Prop).
% 1.30/1.50 Axiom satz3:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> (((nis X0) n_1)->(n_some (fun (X1:fofType)=> ((n_is X0) (ordsucc X1))))))).
% 1.30/1.50 Axiom satz3a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> (((nis X0) n_1)->(n_one (fun (X1:fofType)=> ((n_is X0) (ordsucc X1))))))).
% 1.30/1.50 Definition d_24_prop1:=(fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((n_is ((ap X0) (ordsucc X1))) (ordsucc ((ap X0) X1)))))):(fofType->Prop).
% 1.30/1.50 Definition d_24_prop2:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc X0))) (d_24_prop1 X1))):(fofType->(fofType->Prop)).
% 1.30/1.50 Definition prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((ap X0) X2)) ((ap X1) X2))):(fofType->(fofType->(fofType->Prop))).
% 1.30/1.50 Definition prop4:=(fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0))):(fofType->Prop).
% 1.30/1.50 Definition d_24_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> (ordsucc ((ap X0) X1))))):(fofType->fofType).
% 1.30/1.50 Axiom satz4:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((one ((d_Pi nat) (fun (X1:fofType)=> nat))) (fun (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc X0))) (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) (ordsucc ((ap X1) X2)))))))))).
% 1.30/1.50 Definition plus:=(fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0))):(fofType->fofType).
% 1.30/1.50 Definition n_pl:=(fun (X0:fofType)=> (ap (plus X0))):(fofType->(fofType->fofType)).
% 1.30/1.50 Axiom satz4a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_pl X0) n_1)) (ordsucc X0)))).
% 1.30/1.50 Axiom satz4b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl X0) (ordsucc X1))) (ordsucc ((n_pl X0) X1))))))).
% 1.30/1.50 Axiom satz4c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_pl n_1) X0)) (ordsucc X0)))).
% 1.30/1.50 Axiom satz4d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl (ordsucc X0)) X1)) (ordsucc ((n_pl X0) X1))))))).
% 1.30/1.50 Axiom satz4e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is (ordsucc X0)) ((n_pl X0) n_1)))).
% 1.30/1.50 Axiom satz4f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is (ordsucc ((n_pl X0) X1))) ((n_pl X0) (ordsucc X1))))))).
% 1.30/1.50 Axiom satz4g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is (ordsucc X0)) ((n_pl n_1) X0)))).
% 1.30/1.50 Axiom satz4h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is (ordsucc ((n_pl X0) X1))) ((n_pl (ordsucc X0)) X1)))))).
% 1.30/1.50 Definition d_25_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_pl ((n_pl X0) X1)) X2)) ((n_pl X0) ((n_pl X1) X2)))):(fofType->(fofType->(fofType->Prop))).
% 1.30/1.50 Axiom satz5:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_pl ((n_pl X0) X1)) X2)) ((n_pl X0) ((n_pl X1) X2))))))))).
% 1.30/1.50 Definition d_26_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_pl X0) X1)) ((n_pl X1) X0))):(fofType->(fofType->Prop)).
% 1.30/1.50 Axiom satz6:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl X0) X1)) ((n_pl X1) X0)))))).
% 1.30/1.50 Definition d_27_prop1:=(fun (X0:fofType) (X1:fofType)=> ((nis X1) ((n_pl X0) X1))):(fofType->(fofType->Prop)).
% 1.30/1.50 Axiom satz7:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((nis X1) ((n_pl X0) X1)))))).
% 1.30/1.50 Definition d_28_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((nis ((n_pl X0) X1)) ((n_pl X0) X2))):(fofType->(fofType->(fofType->Prop))).
% 1.30/1.50 Axiom satz8:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((nis X1) X2)->((nis ((n_pl X0) X1)) ((n_pl X0) X2))))))))).
% 1.30/1.50 Axiom satz8a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X0) X1)) ((n_pl X0) X2))->((n_is X1) X2)))))))).
% 1.30/1.50 Definition diffprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))):(fofType->(fofType->(fofType->Prop))).
% 1.30/1.50 Axiom satz8b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((amone nat) (fun (X2:fofType)=> ((n_is X0) ((n_pl X1) X2)))))))).
% 1.30/1.50 Definition d_29_ii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X0) X1))):(fofType->(fofType->Prop)).
% 1.30/1.50 Definition iii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X1) X0))):(fofType->(fofType->Prop)).
% 1.30/1.50 Definition d_29_prop1:=(fun (X0:fofType) (X1:fofType)=> (((or3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1))):(fofType->(fofType->Prop)).
% 1.30/1.50 Axiom satz9:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((orec3 ((n_is X0) X1)) (n_some (fun (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))))) (n_some (fun (X2:fofType)=> ((n_is X1) ((n_pl X0) X2))))))))).
% 1.30/1.50 Axiom satz9a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((or3 ((n_is X0) X1)) (n_some ((diffprop X0) X1))) (n_some ((diffprop X1) X0))))))).
% 1.30/1.50 Axiom satz9b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((ec3 ((n_is X0) X1)) (n_some ((diffprop X0) X1))) (n_some ((diffprop X1) X0))))))).
% 1.30/1.50 Axiom satz10:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((orec3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1)))))).
% 1.30/1.50 Axiom satz10a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((or3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1)))))).
% 1.30/1.50 Axiom satz10b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((ec3 ((n_is X0) X1)) ((d_29_ii X0) X1)) ((iii X0) X1)))))).
% 1.30/1.50 Axiom satz11:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->((iii X1) X0)))))).
% 1.30/1.50 Axiom satz12:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->((d_29_ii X1) X0)))))).
% 1.30/1.50 Definition moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((d_29_ii X0) X1)) ((n_is X0) X1))):(fofType->(fofType->Prop)).
% 1.30/1.50 Definition lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((iii X0) X1)) ((n_is X0) X1))):(fofType->(fofType->Prop)).
% 1.30/1.50 Axiom satz13:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moreis X0) X1)->((lessis X1) X0)))))).
% 1.30/1.50 Axiom satz14:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessis X0) X1)->((moreis X1) X0)))))).
% 1.30/1.50 Axiom satz10c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((moreis X0) X1)->(d_not ((iii X0) X1))))))).
% 1.30/1.50 Axiom satz10d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((lessis X0) X1)->(d_not ((d_29_ii X0) X1))))))).
% 1.30/1.50 Axiom satz10e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((d_29_ii X0) X1))->((lessis X0) X1)))))).
% 1.30/1.50 Axiom satz10f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((iii X0) X1))->((moreis X0) X1)))))).
% 1.30/1.50 Axiom satz10g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X0) X1)->(d_not ((lessis X0) X1))))))).
% 1.30/1.50 Axiom satz10h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X0) X1)->(d_not ((moreis X0) X1))))))).
% 1.30/1.50 Axiom satz10j:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((moreis X0) X1))->((iii X0) X1)))))).
% 1.30/1.50 Axiom satz10k:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_not ((lessis X0) X1))->((d_29_ii X0) X1)))))).
% 1.30/1.51 Axiom satz15:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->(((iii X1) X2)->((iii X0) X2))))))))).
% 1.30/1.51 Axiom satz16a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->(((iii X1) X2)->((iii X0) X2))))))))).
% 1.30/1.51 Axiom satz16b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->(((lessis X1) X2)->((iii X0) X2))))))))).
% 1.30/1.51 Axiom satz16c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->(((d_29_ii X1) X2)->((d_29_ii X0) X2))))))))).
% 1.30/1.51 Axiom satz16d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->(((moreis X1) X2)->((d_29_ii X0) X2))))))))).
% 1.30/1.51 Axiom satz17:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->(((lessis X1) X2)->((lessis X0) X2))))))))).
% 1.30/1.51 Axiom satz18:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((d_29_ii ((n_pl X0) X1)) X0))))).
% 1.30/1.51 Axiom satz18a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((iii X0) ((n_pl X0) X1)))))).
% 1.30/1.51 Axiom satz18b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((d_29_ii (ordsucc X0)) X0))).
% 1.30/1.51 Axiom satz18c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((iii X0) (ordsucc X0)))).
% 1.30/1.51 Axiom satz19a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X2))))))))).
% 1.30/1.51 Axiom satz19b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_pl X0) X2)) ((n_pl X1) X2))))))))).
% 1.30/1.51 Axiom satz19c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_pl X0) X2)) ((n_pl X1) X2))))))))).
% 1.30/1.51 Axiom satz19d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_pl X2) X0)) ((n_pl X2) X1))))))))).
% 1.30/1.51 Axiom satz19e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_pl X2) X0)) ((n_pl X2) X1))))))))).
% 1.30/1.51 Axiom satz19f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_pl X2) X0)) ((n_pl X2) X1))))))))).
% 1.30/1.51 Axiom satz19g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))).
% 1.30/1.51 Axiom satz19h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X2) X0)) ((n_pl X3) X1)))))))))))).
% 1.30/1.51 Axiom satz19j:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))).
% 1.30/1.51 Axiom satz19k:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_pl X2) X0)) ((n_pl X3) X1)))))))))))).
% 1.30/1.51 Axiom satz19l:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_pl X0) X2)) ((n_pl X1) X2))))))))).
% 1.30/1.51 Axiom satz19m:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_pl X2) X0)) ((n_pl X2) X1))))))))).
% 1.30/1.51 Axiom satz19n:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_pl X0) X2)) ((n_pl X1) X2))))))))).
% 1.30/1.51 Axiom satz19o:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_pl X2) X0)) ((n_pl X2) X1))))))))).
% 1.30/1.51 Axiom satz20a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X2))->((d_29_ii X0) X1)))))))).
% 1.30/1.51 Axiom satz20b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X0) X2)) ((n_pl X1) X2))->((n_is X0) X1)))))))).
% 1.30/1.51 Axiom satz20c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_pl X0) X2)) ((n_pl X1) X2))->((iii X0) X1)))))))).
% 1.30/1.51 Axiom satz20d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_pl X2) X0)) ((n_pl X2) X1))->((d_29_ii X0) X1)))))))).
% 1.30/1.51 Axiom satz20e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_pl X2) X0)) ((n_pl X2) X1))->((n_is X0) X1)))))))).
% 1.30/1.51 Axiom satz20f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_pl X2) X0)) ((n_pl X2) X1))->((iii X0) X1)))))))).
% 1.33/1.51 Axiom satz21:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))).
% 1.33/1.51 Axiom satz21a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))).
% 1.33/1.51 Axiom satz22a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))).
% 1.33/1.51 Axiom satz22b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((moreis X2) X3)->((d_29_ii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))).
% 1.33/1.51 Axiom satz22c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((iii X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))).
% 1.33/1.51 Axiom satz22d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((lessis X2) X3)->((iii ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))).
% 1.33/1.51 Axiom satz23:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((moreis X2) X3)->((moreis ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))).
% 1.33/1.51 Axiom satz23a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((lessis X2) X3)->((lessis ((n_pl X0) X2)) ((n_pl X1) X3)))))))))))).
% 1.33/1.51 Axiom satz24:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((moreis X0) n_1))).
% 1.33/1.51 Axiom satz24a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (lessis n_1)).
% 1.33/1.51 Axiom satz24b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((d_29_ii (ordsucc X0)) n_1))).
% 1.33/1.51 Axiom satz24c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((iii n_1) (ordsucc X0)))).
% 1.33/1.51 Axiom satz25:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X1) X0)->((moreis X1) ((n_pl X0) n_1))))))).
% 1.33/1.51 Axiom satz25a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii X1) X0)->((moreis X1) (ordsucc X0))))))).
% 1.33/1.51 Axiom satz25b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) X0)->((lessis ((n_pl X1) n_1)) X0)))))).
% 1.33/1.51 Axiom satz25c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) X0)->((lessis (ordsucc X1)) X0)))))).
% 1.33/1.51 Axiom satz26:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) ((n_pl X0) n_1))->((lessis X1) X0)))))).
% 1.33/1.51 Axiom satz26a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((iii X1) (ordsucc X0))->((lessis X1) X0)))))).
% 1.33/1.51 Axiom satz26b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii ((n_pl X1) n_1)) X0)->((moreis X1) X0)))))).
% 1.33/1.51 Axiom satz26c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> (((d_29_ii (ordsucc X1)) X0)->((moreis X1) X0)))))).
% 1.33/1.51 Definition lbprop:=(fun (X0:(fofType->Prop)) (X1:fofType) (X2:fofType)=> ((imp (X0 X2)) ((lessis X1) X2))):((fofType->Prop)->(fofType->(fofType->Prop))).
% 1.33/1.51 Definition n_lb:=(fun (X0:(fofType->Prop)) (X1:fofType)=> (n_all ((lbprop X0) X1))):((fofType->Prop)->(fofType->Prop)).
% 1.33/1.51 Definition min:=(fun (X0:(fofType->Prop)) (X1:fofType)=> ((d_and ((n_lb X0) X1)) (X0 X1))):((fofType->Prop)->(fofType->Prop)).
% 1.33/1.51 Axiom satz27:(forall (X0:(fofType->Prop)), ((n_some X0)->(n_some (min X0)))).
% 1.33/1.51 Axiom satz27a:(forall (X0:(fofType->Prop)), ((n_some X0)->(n_one (min X0)))).
% 1.33/1.51 Definition d_428_prop1:=(fun (X0:fofType) (X1:fofType)=> (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) ((n_pl ((ap X1) X2)) X0))))):(fofType->(fofType->Prop)).
% 1.33/1.51 Definition d_428_prop2:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) X0)) ((d_428_prop1 X0) X1))):(fofType->(fofType->Prop)).
% 1.33/1.51 Definition d_428_prop4:=(fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0))):(fofType->Prop).
% 1.33/1.51 Definition d_428_id:=((d_Sigma nat) (fun (X0:fofType)=> X0)):fofType.
% 1.33/1.51 Definition d_428_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> ((n_pl ((ap X0) X1)) X1)))):(fofType->fofType).
% 1.33/1.51 Axiom satz28:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((one ((d_Pi nat) (fun (X1:fofType)=> nat))) (fun (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) X0)) (n_all (fun (X2:fofType)=> ((n_is ((ap X1) (ordsucc X2))) ((n_pl ((ap X1) X2)) X0))))))))).
% 1.33/1.51 Definition times:=(fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0))):(fofType->fofType).
% 1.33/1.51 Definition n_ts:=(fun (X0:fofType)=> (ap (times X0))):(fofType->(fofType->fofType)).
% 1.33/1.51 Axiom satz28a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_ts X0) n_1)) X0))).
% 1.33/1.51 Axiom satz28b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts X0) (ordsucc X1))) ((n_pl ((n_ts X0) X1)) X0)))))).
% 1.33/1.51 Axiom satz28c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_ts n_1) X0)) X0))).
% 1.33/1.51 Axiom satz28d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts (ordsucc X0)) X1)) ((n_pl ((n_ts X0) X1)) X1)))))).
% 1.33/1.51 Axiom satz28e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is X0) ((n_ts X0) n_1)))).
% 1.33/1.51 Axiom satz28f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl ((n_ts X0) X1)) X0)) ((n_ts X0) (ordsucc X1))))))).
% 1.33/1.51 Axiom satz28g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is X0) ((n_ts n_1) X0)))).
% 1.33/1.51 Axiom satz28h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_pl ((n_ts X0) X1)) X1)) ((n_ts (ordsucc X0)) X1)))))).
% 1.33/1.51 Definition d_429_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts X0) X1)) ((n_ts X1) X0))):(fofType->(fofType->Prop)).
% 1.33/1.51 Axiom satz29:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_is ((n_ts X0) X1)) ((n_ts X1) X0)))))).
% 1.33/1.51 Definition d_430_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_ts X0) ((n_pl X1) X2))) ((n_pl ((n_ts X0) X1)) ((n_ts X0) X2)))):(fofType->(fofType->(fofType->Prop))).
% 1.33/1.52 Axiom satz30:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_ts X0) ((n_pl X1) X2))) ((n_pl ((n_ts X0) X1)) ((n_ts X0) X2))))))))).
% 1.33/1.52 Definition d_431_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((n_ts ((n_ts X0) X1)) X2)) ((n_ts X0) ((n_ts X1) X2)))):(fofType->(fofType->(fofType->Prop))).
% 1.33/1.52 Axiom satz31:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_is ((n_ts ((n_ts X0) X1)) X2)) ((n_ts X0) ((n_ts X1) X2))))))))).
% 1.33/1.52 Axiom satz32a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X2))))))))).
% 1.33/1.52 Axiom satz32b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_ts X0) X2)) ((n_ts X1) X2))))))))).
% 1.33/1.52 Axiom satz32c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_ts X0) X2)) ((n_ts X1) X2))))))))).
% 1.33/1.52 Axiom satz32d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii X0) X1)->((d_29_ii ((n_ts X2) X0)) ((n_ts X2) X1))))))))).
% 1.33/1.52 Axiom satz32e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is X0) X1)->((n_is ((n_ts X2) X0)) ((n_ts X2) X1))))))))).
% 1.33/1.52 Axiom satz32f:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii X0) X1)->((iii ((n_ts X2) X0)) ((n_ts X2) X1))))))))).
% 1.33/1.52 Axiom satz32g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))).
% 1.33/1.52 Axiom satz32h:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X2) X0)) ((n_ts X3) X1)))))))))))).
% 1.33/1.52 Axiom satz32j:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))).
% 1.33/1.52 Axiom satz32k:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((n_is X0) X1)->(((iii X2) X3)->((iii ((n_ts X2) X0)) ((n_ts X3) X1)))))))))))).
% 1.33/1.52 Axiom satz32l:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_ts X0) X2)) ((n_ts X1) X2))))))))).
% 1.33/1.52 Axiom satz32m:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((moreis X0) X1)->((moreis ((n_ts X2) X0)) ((n_ts X2) X1))))))))).
% 1.33/1.52 Axiom satz32n:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_ts X0) X2)) ((n_ts X1) X2))))))))).
% 1.33/1.52 Axiom satz32o:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((lessis X0) X1)->((lessis ((n_ts X2) X0)) ((n_ts X2) X1))))))))).
% 1.33/1.52 Axiom satz33a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X2))->((d_29_ii X0) X1)))))))).
% 1.33/1.52 Axiom satz33b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((n_is ((n_ts X0) X2)) ((n_ts X1) X2))->((n_is X0) X1)))))))).
% 1.33/1.52 Axiom satz33c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> (((iii ((n_ts X0) X2)) ((n_ts X1) X2))->((iii X0) X1)))))))).
% 1.33/1.52 Axiom satz34:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))).
% 1.33/1.52 Axiom satz34a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))).
% 1.33/1.52 Axiom satz35a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((d_29_ii X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))).
% 1.33/1.52 Axiom satz35b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((d_29_ii X0) X1)->(((moreis X2) X3)->((d_29_ii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))).
% 1.33/1.52 Axiom satz35c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((iii X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))).
% 1.33/1.52 Axiom satz35d:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((iii X0) X1)->(((lessis X2) X3)->((iii ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))).
% 1.33/1.52 Axiom satz36:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((moreis X0) X1)->(((moreis X2) X3)->((moreis ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))).
% 1.33/1.52 Axiom satz36a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) nat))) (fun (X3:fofType)=> (((lessis X0) X1)->(((lessis X2) X3)->((lessis ((n_ts X0) X2)) ((n_ts X1) X3)))))))))))).
% 1.33/1.52 Definition n_mn:=(fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop X0) X1))):(fofType->(fofType->fofType)).
% 1.33/1.52 Definition d_1to:=(fun (X0:fofType)=> ((d_Sep nat) (fun (X1:fofType)=> ((lessis X1) X0)))):(fofType->fofType).
% 1.33/1.52 Definition outn:=(fun (X0:fofType)=> ((out nat) (fun (X1:fofType)=> ((lessis X1) X0)))):(fofType->(fofType->fofType)).
% 1.33/1.52 Definition inn:=(fun (X0:fofType)=> ((e_in nat) (fun (X1:fofType)=> ((lessis X1) X0)))):(fofType->(fofType->fofType)).
% 1.33/1.52 Definition n_1o:=((outn n_1) n_1):fofType.
% 1.33/1.52 Definition singlet_u0:=(inn n_1):(fofType->fofType).
% 1.33/1.52 Definition n_2:=((n_pl n_1) n_1):fofType.
% 1.33/1.52 Definition n_1t:=((outn n_2) n_1):fofType.
% 1.33/1.52 Definition n_2t:=((outn n_2) n_2):fofType.
% 1.33/1.52 Definition pair_u0:=(inn n_2):(fofType->fofType).
% 1.33/1.52 Definition pair1type:=(fun (X0:fofType)=> ((d_Pi (d_1to n_2)) (fun (X1:fofType)=> X0))):(fofType->fofType).
% 1.33/1.52 Definition pair1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma (d_1to n_2)) (fun (X3:fofType)=> ((((ite (((e_is (d_1to n_2)) X3) n_1t)) X0) X1) X2)))):(fofType->(fofType->(fofType->fofType))).
% 1.33/1.52 Definition first1:=(fun (X0:fofType) (X1:fofType)=> ((ap X1) n_1t)):(fofType->(fofType->fofType)).
% 1.33/1.52 Definition second1:=(fun (X0:fofType) (X1:fofType)=> ((ap X1) n_2t)):(fofType->(fofType->fofType)).
% 1.33/1.52 Definition pair_q0:=(fun (X0:fofType) (X1:fofType)=> (((pair1 X0) ((first1 X0) X1)) ((second1 X0) X1))):(fofType->(fofType->fofType)).
% 1.33/1.52 Definition d_1out:=(fun (X0:fofType)=> ((outn X0) n_1)):(fofType->fofType).
% 1.33/1.52 Definition xout:=(fun (X0:fofType)=> ((outn X0) X0)):(fofType->fofType).
% 1.33/1.52 Definition left1to:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn X0) ((inn X1) X2))):(fofType->(fofType->(fofType->fofType))).
% 1.33/1.52 Definition right1to:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn ((n_pl X0) X1)) ((n_pl X0) ((inn X1) X2)))):(fofType->(fofType->(fofType->fofType))).
% 1.33/1.52 Definition left:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to X2)) (fun (X4:fofType)=> ((ap X3) (((left1to X1) X2) X4))))):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 1.33/1.52 Definition right:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_Sigma (d_1to X2)) (fun (X4:fofType)=> ((ap X3) (((right1to X1) X2) X4))))):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 1.33/1.52 Definition left_f1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((left X0) X2) X1)):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 1.33/1.52 Definition left_f2:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((left X0) X1) X2) ((((left_f1 X0) X1) X2) X3))):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 1.33/1.52 Definition frac:=(pair1type nat):fofType.
% 1.33/1.52 Definition n_fr:=(pair1 nat):(fofType->(fofType->fofType)).
% 1.33/1.52 Definition num:=(first1 nat):(fofType->fofType).
% 1.33/1.52 Definition den:=(second1 nat):(fofType->fofType).
% 1.33/1.52 Definition n_eq:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))):(fofType->(fofType->Prop)).
% 1.33/1.52 Axiom satz37:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((n_eq X0) X0))).
% 1.33/1.52 Axiom satz38:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((n_eq X0) X1)->((n_eq X1) X0)))))).
% 1.33/1.52 Axiom satz39:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> (((n_eq X0) X1)->(((n_eq X1) X2)->((n_eq X0) X2))))))))).
% 1.33/1.52 Axiom satz40:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq X0) ((n_fr ((n_ts (num X0)) X1)) ((n_ts (den X0)) X1))))))).
% 1.33/1.52 Axiom satz40a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((n_eq ((n_fr ((n_ts (num X0)) X1)) ((n_ts (den X0)) X1))) X0))))).
% 1.33/1.52 Axiom satz40b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr X0) X1)) ((n_fr ((n_ts X0) X2)) ((n_ts X1) X2))))))))).
% 1.33/1.52 Axiom satz40c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) nat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) nat))) (fun (X2:fofType)=> ((n_eq ((n_fr ((n_ts X0) X2)) ((n_ts X1) X2))) ((n_fr X0) X1)))))))).
% 1.33/1.52 Definition moref:=(fun (X0:fofType) (X1:fofType)=> ((d_29_ii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))):(fofType->(fofType->Prop)).
% 1.33/1.52 Definition lessf:=(fun (X0:fofType) (X1:fofType)=> ((iii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))):(fofType->(fofType->Prop)).
% 1.33/1.52 Axiom satz41:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((orec3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1)))))).
% 1.33/1.52 Axiom satz41a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((or3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1)))))).
% 1.33/1.52 Axiom satz41b:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((ec3 ((n_eq X0) X1)) ((moref X0) X1)) ((lessf X0) X1)))))).
% 1.33/1.52 Axiom satz42:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X0) X1)->((lessf X1) X0)))))).
% 1.33/1.52 Axiom satz43:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->((moref X1) X0)))))).
% 1.33/1.52 Axiom satz44:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((moref X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((moref X2) X3)))))))))))).
% 1.33/1.52 Axiom satz45:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) frac))) (fun (X2:fofType)=> ((all_of (fun (X3:fofType)=> ((in X3) frac))) (fun (X3:fofType)=> (((lessf X0) X1)->(((n_eq X0) X2)->(((n_eq X1) X3)->((lessf X2) X3)))))))))))).
% 1.33/1.52 Definition moreq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((moref X0) X1)) ((n_eq X0) X1))):(fofType->(fofType->Prop)).
% 1.33/1.52 Definition lesseq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((lessf X0) X1)) ((n_eq X0) X1))):(fofType->(fofType->Prop)).
% 1.33/1.52 Axiom satz41c:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moreq X0) X1)->(d_not ((lessf X0) X1))))))).
% 1.33/1.52 Axiom satz41d:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lesseq X0) X1)->(d_not ((moref X0) X1))))))).
% 1.33/1.52 Axiom satz41e:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((moref X0) X1))->((lesseq X0) X1)))))).
% 1.33/1.52 Axiom satz41f:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((d_not ((lessf X0) X1))->((moreq X0) X1)))))).
% 1.33/1.52 Axiom satz41g:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((moref X
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