TSTP Solution File: NUM788^4 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM788^4 : TPTP v7.1.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n091.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 13:11:45 EST 2018
% Result : Timeout 300.07s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM788^4 : TPTP v7.1.0. Released v7.1.0.
% 0.00/0.04 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.23 % Computer : n091.star.cs.uiowa.edu
% 0.02/0.23 % Model : x86_64 x86_64
% 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.23 % Memory : 32218.625MB
% 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.23 % CPULimit : 300
% 0.02/0.23 % DateTime : Fri Jan 5 14:15:34 CST 2018
% 0.02/0.23 % CPUTime :
% 0.02/0.25 Python 2.7.13
% 0.07/0.51 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.07/0.51 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/NUM007^0.ax, trying next directory
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b2abf2169e0>, <kernel.DependentProduct object at 0x2b2abeb5fa28>) of role type named typ_is_of
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring is_of:(fofType->((fofType->Prop)->Prop))
% 0.07/0.51 FOF formula (((eq (fofType->((fofType->Prop)->Prop))) is_of) (fun (X0:fofType) (X1:(fofType->Prop))=> (X1 X0))) of role definition named def_is_of
% 0.07/0.51 A new definition: (((eq (fofType->((fofType->Prop)->Prop))) is_of) (fun (X0:fofType) (X1:(fofType->Prop))=> (X1 X0)))
% 0.07/0.51 Defined: is_of:=(fun (X0:fofType) (X1:(fofType->Prop))=> (X1 X0))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b2abeb5fa28>, <kernel.DependentProduct object at 0x2b2abf216e60>) of role type named typ_all_of
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring all_of:((fofType->Prop)->((fofType->Prop)->Prop))
% 0.07/0.51 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
% 0.07/0.51 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)))))
% 0.07/0.51 Defined: all_of:=(fun (X0:(fofType->Prop)) (X1:(fofType->Prop))=> (forall (X2:fofType), (((is_of X2) X0)->(X1 X2))))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b2ab6e629e0>, <kernel.DependentProduct object at 0x2b2abe7a0e18>) of role type named typ_eps
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring eps:((fofType->Prop)->fofType)
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b2abf216ea8>, <kernel.DependentProduct object at 0x2b2abe7a0680>) of role type named typ_in
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring in:(fofType->(fofType->Prop))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b2abf216a28>, <kernel.DependentProduct object at 0x2b2abe7a0680>) of role type named typ_d_Subq
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring d_Subq:(fofType->(fofType->Prop))
% 0.07/0.51 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
% 0.07/0.51 A new definition: (((eq (fofType->(fofType->Prop))) d_Subq) (fun (X0:fofType) (X1:fofType)=> (forall (X2:fofType), (((in X2) X0)->((in X2) X1)))))
% 0.07/0.51 Defined: d_Subq:=(fun (X0:fofType) (X1:fofType)=> (forall (X2:fofType), (((in X2) X0)->((in X2) X1))))
% 0.07/0.51 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
% 0.07/0.51 A new axiom: (forall (X0:fofType) (X1:fofType), (((d_Subq X0) X1)->(((d_Subq X1) X0)->(((eq fofType) X0) X1))))
% 0.07/0.51 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
% 0.07/0.51 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))))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b2abf216e60>, <kernel.Single object at 0x2b2abe79c128>) of role type named typ_emptyset
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring emptyset:fofType
% 0.07/0.51 FOF formula (((ex fofType) (fun (X0:fofType)=> ((in X0) emptyset)))->False) of role axiom named k_EmptyAx
% 0.07/0.51 A new axiom: (((ex fofType) (fun (X0:fofType)=> ((in X0) emptyset)))->False)
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b2abe79c050>, <kernel.DependentProduct object at 0x2b2abe7a0320>) of role type named typ_union
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring union:(fofType->fofType)
% 0.07/0.51 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
% 0.07/0.51 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))))))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b2abe79c050>, <kernel.DependentProduct object at 0x2b2abe7a07e8>) of role type named typ_power
% 0.07/0.51 Using role type
% 0.07/0.53 Declaring power:(fofType->fofType)
% 0.07/0.53 FOF formula (forall (X0:fofType) (X1:fofType), ((iff ((in X1) (power X0))) ((d_Subq X1) X0))) of role axiom named k_PowerEq
% 0.07/0.53 A new axiom: (forall (X0:fofType) (X1:fofType), ((iff ((in X1) (power X0))) ((d_Subq X1) X0)))
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b2abe7a07a0>, <kernel.DependentProduct object at 0x2b2abe7a0e60>) of role type named typ_repl
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring repl:(fofType->((fofType->fofType)->fofType))
% 0.07/0.53 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
% 0.07/0.53 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)))))))
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b2abe7a0128>, <kernel.DependentProduct object at 0x2b2abe7a02d8>) of role type named typ_d_Union_closed
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring d_Union_closed:(fofType->Prop)
% 0.07/0.53 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
% 0.07/0.53 A new definition: (((eq (fofType->Prop)) d_Union_closed) (fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (union X1)) X0)))))
% 0.07/0.53 Defined: d_Union_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (union X1)) X0))))
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b2abe7a02d8>, <kernel.DependentProduct object at 0x2b2abe7a0e60>) of role type named typ_d_Power_closed
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring d_Power_closed:(fofType->Prop)
% 0.07/0.53 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
% 0.07/0.53 A new definition: (((eq (fofType->Prop)) d_Power_closed) (fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (power X1)) X0)))))
% 0.07/0.53 Defined: d_Power_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (power X1)) X0))))
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b2abe7a0e60>, <kernel.DependentProduct object at 0x2b2abe7a0680>) of role type named typ_d_Repl_closed
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring d_Repl_closed:(fofType->Prop)
% 0.07/0.53 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
% 0.07/0.53 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)))))))
% 0.07/0.53 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))))))
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b2abe7a0680>, <kernel.DependentProduct object at 0x2b2abe7a0128>) of role type named typ_d_ZF_closed
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring d_ZF_closed:(fofType->Prop)
% 0.07/0.53 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
% 0.07/0.53 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))))
% 0.07/0.53 Defined: d_ZF_closed:=(fun (X0:fofType)=> ((and ((and (d_Union_closed X0)) (d_Power_closed X0))) (d_Repl_closed X0)))
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b2abe7a0830>, <kernel.DependentProduct object at 0x2b2abeaf9c20>) of role type named typ_univof
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring univof:(fofType->fofType)
% 0.07/0.53 FOF formula (forall (X0:fofType), ((in X0) (univof X0))) of role axiom named k_UnivOf_In
% 0.07/0.53 A new axiom: (forall (X0:fofType), ((in X0) (univof X0)))
% 0.07/0.53 FOF formula (forall (X0:fofType), (d_ZF_closed (univof X0))) of role axiom named k_UnivOf_ZF_closed
% 0.07/0.54 A new axiom: (forall (X0:fofType), (d_ZF_closed (univof X0)))
% 0.07/0.54 FOF formula (<kernel.Constant object at 0x2b2abe7a0128>, <kernel.DependentProduct object at 0x2b2abe7a0680>) of role type named typ_if
% 0.07/0.54 Using role type
% 0.07/0.54 Declaring if:(Prop->(fofType->(fofType->fofType)))
% 0.07/0.54 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
% 0.07/0.54 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)))))))
% 0.07/0.54 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))))))
% 0.07/0.54 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
% 0.07/0.54 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))))
% 0.07/0.54 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
% 0.07/0.54 A new axiom: (forall (X0:Prop) (X1:fofType) (X2:fofType), ((X0->False)->(((eq fofType) (((if X0) X1) X2)) X2)))
% 0.07/0.54 FOF formula (forall (X0:Prop) (X1:fofType) (X2:fofType), (X0->(((eq fofType) (((if X0) X1) X2)) X1))) of role axiom named if_i_1
% 0.07/0.54 A new axiom: (forall (X0:Prop) (X1:fofType) (X2:fofType), (X0->(((eq fofType) (((if X0) X1) X2)) X1)))
% 0.07/0.54 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
% 0.07/0.54 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)))
% 0.07/0.54 FOF formula (<kernel.Constant object at 0x2b2abe7a0ef0>, <kernel.DependentProduct object at 0x2b2abeaf9c20>) of role type named typ_nIn
% 0.07/0.54 Using role type
% 0.07/0.54 Declaring nIn:(fofType->(fofType->Prop))
% 0.07/0.54 FOF formula (((eq (fofType->(fofType->Prop))) nIn) (fun (X0:fofType) (X1:fofType)=> (((in X0) X1)->False))) of role definition named def_nIn
% 0.07/0.54 A new definition: (((eq (fofType->(fofType->Prop))) nIn) (fun (X0:fofType) (X1:fofType)=> (((in X0) X1)->False)))
% 0.07/0.54 Defined: nIn:=(fun (X0:fofType) (X1:fofType)=> (((in X0) X1)->False))
% 0.07/0.54 FOF formula (forall (X0:fofType) (X1:fofType), (((in X1) (power X0))->((d_Subq X1) X0))) of role axiom named k_PowerE
% 0.07/0.54 A new axiom: (forall (X0:fofType) (X1:fofType), (((in X1) (power X0))->((d_Subq X1) X0)))
% 0.07/0.54 FOF formula (forall (X0:fofType) (X1:fofType), (((d_Subq X1) X0)->((in X1) (power X0)))) of role axiom named k_PowerI
% 0.07/0.54 A new axiom: (forall (X0:fofType) (X1:fofType), (((d_Subq X1) X0)->((in X1) (power X0))))
% 0.07/0.54 FOF formula (forall (X0:fofType), ((in X0) (power X0))) of role axiom named k_Self_In_Power
% 0.07/0.54 A new axiom: (forall (X0:fofType), ((in X0) (power X0)))
% 0.07/0.54 FOF formula (<kernel.Constant object at 0x2b2abeaf9b90>, <kernel.DependentProduct object at 0x2b2abeaf93b0>) of role type named typ_d_UPair
% 0.07/0.54 Using role type
% 0.07/0.54 Declaring d_UPair:(fofType->(fofType->fofType))
% 0.07/0.54 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
% 0.07/0.54 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)))))
% 0.07/0.54 Defined: d_UPair:=(fun (X0:fofType) (X1:fofType)=> ((repl (power (power emptyset))) (fun (X2:fofType)=> (((if ((in emptyset) X2)) X0) X1))))
% 0.07/0.54 FOF formula (<kernel.Constant object at 0x2b2abeaf93b0>, <kernel.DependentProduct object at 0x2b2abeaf98c0>) of role type named typ_d_Sing
% 0.07/0.54 Using role type
% 0.37/0.56 Declaring d_Sing:(fofType->fofType)
% 0.37/0.56 FOF formula (((eq (fofType->fofType)) d_Sing) (fun (X0:fofType)=> ((d_UPair X0) X0))) of role definition named def_d_Sing
% 0.37/0.56 A new definition: (((eq (fofType->fofType)) d_Sing) (fun (X0:fofType)=> ((d_UPair X0) X0)))
% 0.37/0.56 Defined: d_Sing:=(fun (X0:fofType)=> ((d_UPair X0) X0))
% 0.37/0.56 FOF formula (<kernel.Constant object at 0x2b2abeaf98c0>, <kernel.DependentProduct object at 0x2b2abeaf92d8>) of role type named typ_binunion
% 0.37/0.56 Using role type
% 0.37/0.56 Declaring binunion:(fofType->(fofType->fofType))
% 0.37/0.56 FOF formula (((eq (fofType->(fofType->fofType))) binunion) (fun (X0:fofType) (X1:fofType)=> (union ((d_UPair X0) X1)))) of role definition named def_binunion
% 0.37/0.56 A new definition: (((eq (fofType->(fofType->fofType))) binunion) (fun (X0:fofType) (X1:fofType)=> (union ((d_UPair X0) X1))))
% 0.37/0.56 Defined: binunion:=(fun (X0:fofType) (X1:fofType)=> (union ((d_UPair X0) X1)))
% 0.37/0.56 FOF formula (<kernel.Constant object at 0x2b2abeaf92d8>, <kernel.DependentProduct object at 0x2b2abeaf9f80>) of role type named typ_famunion
% 0.37/0.56 Using role type
% 0.37/0.56 Declaring famunion:(fofType->((fofType->fofType)->fofType))
% 0.37/0.56 FOF formula (((eq (fofType->((fofType->fofType)->fofType))) famunion) (fun (X0:fofType) (X1:(fofType->fofType))=> (union ((repl X0) X1)))) of role definition named def_famunion
% 0.37/0.56 A new definition: (((eq (fofType->((fofType->fofType)->fofType))) famunion) (fun (X0:fofType) (X1:(fofType->fofType))=> (union ((repl X0) X1))))
% 0.37/0.56 Defined: famunion:=(fun (X0:fofType) (X1:(fofType->fofType))=> (union ((repl X0) X1)))
% 0.37/0.56 FOF formula (<kernel.Constant object at 0x2b2abeaf9f80>, <kernel.DependentProduct object at 0x2b2abeaf9b00>) of role type named typ_d_Sep
% 0.37/0.56 Using role type
% 0.37/0.56 Declaring d_Sep:(fofType->((fofType->Prop)->fofType))
% 0.37/0.56 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
% 0.37/0.56 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)))
% 0.37/0.56 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))
% 0.37/0.56 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
% 0.37/0.56 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) X0)->((X1 X2)->((in X2) ((d_Sep X0) X1)))))
% 0.37/0.56 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
% 0.37/0.56 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) ((d_Sep X0) X1))->((in X2) X0)))
% 0.37/0.56 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) ((d_Sep X0) X1))->(X1 X2))) of role axiom named k_SepE2
% 0.37/0.56 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) ((d_Sep X0) X1))->(X1 X2)))
% 0.37/0.56 FOF formula (<kernel.Constant object at 0x2b2abeaf9b90>, <kernel.DependentProduct object at 0x2b2ac1281320>) of role type named typ_d_ReplSep
% 0.37/0.56 Using role type
% 0.37/0.56 Declaring d_ReplSep:(fofType->((fofType->Prop)->((fofType->fofType)->fofType)))
% 0.37/0.56 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
% 0.37/0.56 A new definition: (((eq (fofType->((fofType->Prop)->((fofType->fofType)->fofType)))) d_ReplSep) (fun (X0:fofType) (X1:(fofType->Prop))=> (repl ((d_Sep X0) X1))))
% 0.37/0.56 Defined: d_ReplSep:=(fun (X0:fofType) (X1:(fofType->Prop))=> (repl ((d_Sep X0) X1)))
% 0.37/0.56 FOF formula (<kernel.Constant object at 0x2b2abeaf9b90>, <kernel.DependentProduct object at 0x2b2ac1281488>) of role type named typ_setminus
% 0.38/0.58 Using role type
% 0.38/0.58 Declaring setminus:(fofType->(fofType->fofType))
% 0.38/0.58 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
% 0.38/0.58 A new definition: (((eq (fofType->(fofType->fofType))) setminus) (fun (X0:fofType) (X1:fofType)=> ((d_Sep X0) (fun (X2:fofType)=> ((nIn X2) X1)))))
% 0.38/0.58 Defined: setminus:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep X0) (fun (X2:fofType)=> ((nIn X2) X1))))
% 0.38/0.58 FOF formula (<kernel.Constant object at 0x2b2abeaf9b90>, <kernel.DependentProduct object at 0x2b2ac1281440>) of role type named typ_d_In_rec_G
% 0.38/0.58 Using role type
% 0.38/0.58 Declaring d_In_rec_G:((fofType->((fofType->fofType)->fofType))->(fofType->(fofType->Prop)))
% 0.38/0.58 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
% 0.38/0.58 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)))))
% 0.38/0.58 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))))
% 0.38/0.58 FOF formula (<kernel.Constant object at 0x2b2ac1281440>, <kernel.DependentProduct object at 0x2b2ac1281710>) of role type named typ_d_In_rec
% 0.38/0.58 Using role type
% 0.38/0.58 Declaring d_In_rec:((fofType->((fofType->fofType)->fofType))->(fofType->fofType))
% 0.38/0.58 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
% 0.38/0.58 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))))
% 0.38/0.58 Defined: d_In_rec:=(fun (X0:(fofType->((fofType->fofType)->fofType))) (X1:fofType)=> (eps ((d_In_rec_G X0) X1)))
% 0.38/0.58 FOF formula (<kernel.Constant object at 0x2b2ac1281710>, <kernel.DependentProduct object at 0x2b2ac12814d0>) of role type named typ_ordsucc
% 0.38/0.58 Using role type
% 0.38/0.58 Declaring ordsucc:(fofType->fofType)
% 0.38/0.58 FOF formula (((eq (fofType->fofType)) ordsucc) (fun (X0:fofType)=> ((binunion X0) (d_Sing X0)))) of role definition named def_ordsucc
% 0.38/0.58 A new definition: (((eq (fofType->fofType)) ordsucc) (fun (X0:fofType)=> ((binunion X0) (d_Sing X0))))
% 0.38/0.58 Defined: ordsucc:=(fun (X0:fofType)=> ((binunion X0) (d_Sing X0)))
% 0.38/0.58 FOF formula (forall (X0:fofType), (not (((eq fofType) (ordsucc X0)) emptyset))) of role axiom named neq_ordsucc_0
% 0.38/0.58 A new axiom: (forall (X0:fofType), (not (((eq fofType) (ordsucc X0)) emptyset)))
% 0.38/0.58 FOF formula (forall (X0:fofType) (X1:fofType), ((((eq fofType) (ordsucc X0)) (ordsucc X1))->(((eq fofType) X0) X1))) of role axiom named ordsucc_inj
% 0.38/0.58 A new axiom: (forall (X0:fofType) (X1:fofType), ((((eq fofType) (ordsucc X0)) (ordsucc X1))->(((eq fofType) X0) X1)))
% 0.38/0.58 FOF formula ((in emptyset) (ordsucc emptyset)) of role axiom named k_In_0_1
% 0.38/0.58 A new axiom: ((in emptyset) (ordsucc emptyset))
% 0.38/0.58 FOF formula (<kernel.Constant object at 0x2b2ac1281488>, <kernel.DependentProduct object at 0x2b2ac1281200>) of role type named typ_nat_p
% 0.38/0.58 Using role type
% 0.38/0.58 Declaring nat_p:(fofType->Prop)
% 0.38/0.58 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
% 0.38/0.59 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))))))
% 0.38/0.59 Defined: nat_p:=(fun (X0:fofType)=> (forall (X1:(fofType->Prop)), ((X1 emptyset)->((forall (X2:fofType), ((X1 X2)->(X1 (ordsucc X2))))->(X1 X0)))))
% 0.38/0.59 FOF formula (forall (X0:fofType), ((nat_p X0)->(nat_p (ordsucc X0)))) of role axiom named nat_ordsucc
% 0.38/0.59 A new axiom: (forall (X0:fofType), ((nat_p X0)->(nat_p (ordsucc X0))))
% 0.38/0.59 FOF formula (nat_p (ordsucc emptyset)) of role axiom named nat_1
% 0.38/0.59 A new axiom: (nat_p (ordsucc emptyset))
% 0.38/0.59 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
% 0.38/0.59 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))))))
% 0.38/0.59 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
% 0.38/0.59 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))))))))
% 0.38/0.59 FOF formula (<kernel.Constant object at 0x2b2ac1281b00>, <kernel.Single object at 0x2b2ac1281830>) of role type named typ_omega
% 0.38/0.59 Using role type
% 0.38/0.59 Declaring omega:fofType
% 0.38/0.59 FOF formula (((eq fofType) omega) ((d_Sep (univof emptyset)) nat_p)) of role definition named def_omega
% 0.38/0.59 A new definition: (((eq fofType) omega) ((d_Sep (univof emptyset)) nat_p))
% 0.38/0.59 Defined: omega:=((d_Sep (univof emptyset)) nat_p)
% 0.38/0.59 FOF formula (forall (X0:fofType), (((in X0) omega)->(nat_p X0))) of role axiom named omega_nat_p
% 0.38/0.59 A new axiom: (forall (X0:fofType), (((in X0) omega)->(nat_p X0)))
% 0.38/0.59 FOF formula (forall (X0:fofType), ((nat_p X0)->((in X0) omega))) of role axiom named nat_p_omega
% 0.38/0.59 A new axiom: (forall (X0:fofType), ((nat_p X0)->((in X0) omega)))
% 0.38/0.59 FOF formula (<kernel.Constant object at 0x2b2ac1281638>, <kernel.DependentProduct object at 0x2b2ac1281830>) of role type named typ_d_Inj1
% 0.38/0.59 Using role type
% 0.38/0.59 Declaring d_Inj1:(fofType->fofType)
% 0.38/0.59 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
% 0.38/0.59 A new definition: (((eq (fofType->fofType)) d_Inj1) (d_In_rec (fun (X0:fofType) (X1:(fofType->fofType))=> ((binunion (d_Sing emptyset)) ((repl X0) X1)))))
% 0.38/0.59 Defined: d_Inj1:=(d_In_rec (fun (X0:fofType) (X1:(fofType->fofType))=> ((binunion (d_Sing emptyset)) ((repl X0) X1))))
% 0.38/0.59 FOF formula (<kernel.Constant object at 0x2b2ac1281b00>, <kernel.DependentProduct object at 0x2b2ac1281e60>) of role type named typ_d_Inj0
% 0.38/0.59 Using role type
% 0.38/0.59 Declaring d_Inj0:(fofType->fofType)
% 0.38/0.59 FOF formula (((eq (fofType->fofType)) d_Inj0) (fun (X0:fofType)=> ((repl X0) d_Inj1))) of role definition named def_d_Inj0
% 0.38/0.59 A new definition: (((eq (fofType->fofType)) d_Inj0) (fun (X0:fofType)=> ((repl X0) d_Inj1)))
% 0.38/0.59 Defined: d_Inj0:=(fun (X0:fofType)=> ((repl X0) d_Inj1))
% 0.38/0.59 FOF formula (<kernel.Constant object at 0x2b2ac1281e60>, <kernel.DependentProduct object at 0x2b2ac1281830>) of role type named typ_d_Unj
% 0.38/0.59 Using role type
% 0.38/0.59 Declaring d_Unj:(fofType->fofType)
% 0.38/0.59 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
% 0.38/0.59 A new definition: (((eq (fofType->fofType)) d_Unj) (d_In_rec (fun (X0:fofType)=> (repl ((setminus X0) (d_Sing emptyset))))))
% 0.38/0.59 Defined: d_Unj:=(d_In_rec (fun (X0:fofType)=> (repl ((setminus X0) (d_Sing emptyset)))))
% 0.38/0.59 FOF formula (<kernel.Constant object at 0x2b2ac1281638>, <kernel.DependentProduct object at 0x2b2ac1281830>) of role type named typ_pair
% 0.38/0.59 Using role type
% 0.38/0.59 Declaring pair:(fofType->(fofType->fofType))
% 0.38/0.59 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
% 0.38/0.61 A new definition: (((eq (fofType->(fofType->fofType))) pair) (fun (X0:fofType) (X1:fofType)=> ((binunion ((repl X0) d_Inj0)) ((repl X1) d_Inj1))))
% 0.38/0.61 Defined: pair:=(fun (X0:fofType) (X1:fofType)=> ((binunion ((repl X0) d_Inj0)) ((repl X1) d_Inj1)))
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x2b2ac1281830>, <kernel.DependentProduct object at 0x2b2ac1281518>) of role type named typ_proj0
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring proj0:(fofType->fofType)
% 0.38/0.61 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
% 0.38/0.61 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)))
% 0.38/0.61 Defined: proj0:=(fun (X0:fofType)=> (((d_ReplSep X0) (fun (X1:fofType)=> ((ex fofType) (fun (X2:fofType)=> (((eq fofType) (d_Inj0 X2)) X1))))) d_Unj))
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x2b2ac1281518>, <kernel.DependentProduct object at 0x2b2ac12817a0>) of role type named typ_proj1
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring _TPTP_proj1:(fofType->fofType)
% 0.38/0.61 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
% 0.38/0.61 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)))
% 0.38/0.61 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))
% 0.38/0.61 FOF formula (forall (X0:fofType) (X1:fofType), (((eq fofType) (proj0 ((pair X0) X1))) X0)) of role axiom named proj0_pair_eq
% 0.38/0.61 A new axiom: (forall (X0:fofType) (X1:fofType), (((eq fofType) (proj0 ((pair X0) X1))) X0))
% 0.38/0.61 FOF formula (forall (X0:fofType) (X1:fofType), (((eq fofType) (_TPTP_proj1 ((pair X0) X1))) X1)) of role axiom named proj1_pair_eq
% 0.38/0.61 A new axiom: (forall (X0:fofType) (X1:fofType), (((eq fofType) (_TPTP_proj1 ((pair X0) X1))) X1))
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x2b2ac1281ab8>, <kernel.DependentProduct object at 0x2b2ac12819e0>) of role type named typ_d_Sigma
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring d_Sigma:(fofType->((fofType->fofType)->fofType))
% 0.38/0.61 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
% 0.38/0.61 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))))))
% 0.38/0.61 Defined: d_Sigma:=(fun (X0:fofType) (X1:(fofType->fofType))=> ((famunion X0) (fun (X2:fofType)=> ((repl (X1 X2)) (pair X2)))))
% 0.38/0.61 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
% 0.38/0.61 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))))))
% 0.38/0.61 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
% 0.38/0.61 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))))))
% 0.38/0.61 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
% 0.42/0.62 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)))
% 0.42/0.62 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
% 0.42/0.62 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((in (proj0 X2)) X0)))
% 0.42/0.62 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
% 0.42/0.62 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((in (_TPTP_proj1 X2)) (X1 (proj0 X2)))))
% 0.42/0.62 FOF formula (<kernel.Constant object at 0x2b2ac1281e60>, <kernel.DependentProduct object at 0x2b2ac1281320>) of role type named typ_setprod
% 0.42/0.62 Using role type
% 0.42/0.62 Declaring setprod:(fofType->(fofType->fofType))
% 0.42/0.62 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
% 0.42/0.62 A new definition: (((eq (fofType->(fofType->fofType))) setprod) (fun (X0:fofType) (X1:fofType)=> ((d_Sigma X0) (fun (X2:fofType)=> X1))))
% 0.42/0.62 Defined: setprod:=(fun (X0:fofType) (X1:fofType)=> ((d_Sigma X0) (fun (X2:fofType)=> X1)))
% 0.42/0.62 FOF formula (<kernel.Constant object at 0x2b2ac1281ea8>, <kernel.DependentProduct object at 0x2b2ac1281518>) of role type named typ_ap
% 0.42/0.62 Using role type
% 0.42/0.62 Declaring ap:(fofType->(fofType->fofType))
% 0.42/0.62 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
% 0.42/0.62 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)))
% 0.42/0.62 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))
% 0.42/0.62 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
% 0.42/0.62 A new axiom: (forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) X0)->(((eq fofType) ((ap ((d_Sigma X0) X1)) X2)) (X1 X2))))
% 0.42/0.62 FOF formula (<kernel.Constant object at 0x2b2ac1281ef0>, <kernel.DependentProduct object at 0x2b2ac1e7e5f0>) of role type named typ_pair_p
% 0.42/0.62 Using role type
% 0.42/0.62 Declaring pair_p:(fofType->Prop)
% 0.42/0.62 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
% 0.42/0.62 A new definition: (((eq (fofType->Prop)) pair_p) (fun (X0:fofType)=> (((eq fofType) ((pair ((ap X0) emptyset)) ((ap X0) (ordsucc emptyset)))) X0)))
% 0.42/0.62 Defined: pair_p:=(fun (X0:fofType)=> (((eq fofType) ((pair ((ap X0) emptyset)) ((ap X0) (ordsucc emptyset)))) X0))
% 0.42/0.62 FOF formula (<kernel.Constant object at 0x2b2ac1281ea8>, <kernel.DependentProduct object at 0x2b2ac1e7e1b8>) of role type named typ_d_Pi
% 0.42/0.62 Using role type
% 0.42/0.62 Declaring d_Pi:(fofType->((fofType->fofType)->fofType))
% 0.42/0.62 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
% 0.42/0.62 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))))))))
% 0.42/0.62 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 0x2b2ac1e7e488>, <kernel.DependentProduct object at 0x2b2ac1e7e2d8>) 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 0x2b2ac1e7e2d8>, <kernel.DependentProduct object at 0x2b2ac1e7e710>) 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 0x2b2ac1e7e710>, <kernel.DependentProduct object at 0x2b2ac1e7e320>) 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 0x2b2ac1e7e758>, <kernel.Sort object at 0x2b2ab6e65c20>) 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))
% 0.45/0.66 Defined: obvious:=((imp False) False)
% 0.45/0.66 FOF formula (<kernel.Constant object at 0x2b2ac1e7e518>, <kernel.DependentProduct object at 0x2b2ac1e7e200>) of role type named typ_l_ec
% 0.45/0.66 Using role type
% 0.45/0.66 Declaring l_ec:(Prop->(Prop->Prop))
% 0.45/0.66 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
% 0.45/0.66 A new definition: (((eq (Prop->(Prop->Prop))) l_ec) (fun (X0:Prop) (X1:Prop)=> ((imp X0) (d_not X1))))
% 0.45/0.66 Defined: l_ec:=(fun (X0:Prop) (X1:Prop)=> ((imp X0) (d_not X1)))
% 0.45/0.66 FOF formula (<kernel.Constant object at 0x2b2ac1e7e200>, <kernel.DependentProduct object at 0x2b2ac1e7e758>) of role type named typ_d_and
% 0.45/0.66 Using role type
% 0.45/0.66 Declaring d_and:(Prop->(Prop->Prop))
% 0.45/0.66 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
% 0.45/0.66 A new definition: (((eq (Prop->(Prop->Prop))) d_and) (fun (X0:Prop) (X1:Prop)=> (d_not ((l_ec X0) X1))))
% 0.45/0.66 Defined: d_and:=(fun (X0:Prop) (X1:Prop)=> (d_not ((l_ec X0) X1)))
% 0.45/0.66 FOF formula (<kernel.Constant object at 0x2b2ac1e7e758>, <kernel.DependentProduct object at 0x2b2ac1e7e518>) of role type named typ_l_or
% 0.45/0.66 Using role type
% 0.45/0.66 Declaring l_or:(Prop->(Prop->Prop))
% 0.45/0.66 FOF formula (((eq (Prop->(Prop->Prop))) l_or) (fun (X0:Prop)=> (imp (d_not X0)))) of role definition named def_l_or
% 0.45/0.66 A new definition: (((eq (Prop->(Prop->Prop))) l_or) (fun (X0:Prop)=> (imp (d_not X0))))
% 0.45/0.66 Defined: l_or:=(fun (X0:Prop)=> (imp (d_not X0)))
% 0.45/0.66 FOF formula (<kernel.Constant object at 0x2b2ac1e7e518>, <kernel.DependentProduct object at 0x2b2ac1e7e440>) of role type named typ_orec
% 0.45/0.66 Using role type
% 0.45/0.66 Declaring orec:(Prop->(Prop->Prop))
% 0.45/0.66 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
% 0.45/0.66 A new definition: (((eq (Prop->(Prop->Prop))) orec) (fun (X0:Prop) (X1:Prop)=> ((d_and ((l_or X0) X1)) ((l_ec X0) X1))))
% 0.45/0.66 Defined: orec:=(fun (X0:Prop) (X1:Prop)=> ((d_and ((l_or X0) X1)) ((l_ec X0) X1)))
% 0.45/0.66 FOF formula (<kernel.Constant object at 0x2b2ac1e7e440>, <kernel.DependentProduct object at 0x2b2ac1e7e758>) of role type named typ_l_iff
% 0.45/0.66 Using role type
% 0.45/0.66 Declaring l_iff:(Prop->(Prop->Prop))
% 0.45/0.66 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
% 0.45/0.66 A new definition: (((eq (Prop->(Prop->Prop))) l_iff) (fun (X0:Prop) (X1:Prop)=> ((d_and ((imp X0) X1)) ((imp X1) X0))))
% 0.45/0.66 Defined: l_iff:=(fun (X0:Prop) (X1:Prop)=> ((d_and ((imp X0) X1)) ((imp X1) X0)))
% 0.45/0.66 FOF formula (<kernel.Constant object at 0x2b2ac1e7e758>, <kernel.DependentProduct object at 0x2b2ac1e7e998>) of role type named typ_all
% 0.45/0.66 Using role type
% 0.45/0.66 Declaring all:(fofType->((fofType->Prop)->Prop))
% 0.45/0.66 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
% 0.45/0.66 A new definition: (((eq (fofType->((fofType->Prop)->Prop))) all) (fun (X0:fofType)=> (all_of (fun (X1:fofType)=> ((in X1) X0)))))
% 0.45/0.66 Defined: all:=(fun (X0:fofType)=> (all_of (fun (X1:fofType)=> ((in X1) X0))))
% 0.45/0.66 FOF formula (<kernel.Constant object at 0x2b2ac1e7e998>, <kernel.DependentProduct object at 0x2b2ac1e7ed88>) of role type named typ_non
% 0.45/0.66 Using role type
% 0.45/0.66 Declaring non:(fofType->((fofType->Prop)->(fofType->Prop)))
% 0.45/0.66 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
% 0.45/0.66 A new definition: (((eq (fofType->((fofType->Prop)->(fofType->Prop)))) non) (fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> (d_not (X1 X2))))
% 0.45/0.66 Defined: non:=(fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> (d_not (X1 X2)))
% 0.45/0.66 FOF formula (<kernel.Constant object at 0x2b2ac1e7ed88>, <kernel.DependentProduct object at 0x2b2ac1e7e4d0>) of role type named typ_l_some
% 0.45/0.66 Using role type
% 0.45/0.66 Declaring l_some:(fofType->((fofType->Prop)->Prop))
% 0.45/0.66 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 0x2b2ac1e7e4d0>, <kernel.DependentProduct object at 0x2b2ac1e7edd0>) 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 0x2b2ac1e7edd0>, <kernel.DependentProduct object at 0x2b2ac1e7ef38>) 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 0x2b2ac1e7ef38>, <kernel.DependentProduct object at 0x2b2ac1e7ee18>) 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 0x2b2ac1e7ee18>, <kernel.DependentProduct object at 0x2b2ac1e7eea8>) 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 0x2b2ac1e7eea8>, <kernel.DependentProduct object at 0x2b2ac1e7eb90>) 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))))))))
% 0.45/0.69 FOF formula (<kernel.Constant object at 0x2b2ac1e7ed40>, <kernel.DependentProduct object at 0x2b2ac1e7ed88>) of role type named typ_amone
% 0.45/0.69 Using role type
% 0.45/0.69 Declaring amone:(fofType->((fofType->Prop)->Prop))
% 0.45/0.69 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
% 0.45/0.69 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)))))))))
% 0.45/0.69 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))))))))
% 0.45/0.69 FOF formula (<kernel.Constant object at 0x2b2ac1e7ed88>, <kernel.DependentProduct object at 0x2b2ac1e7ea70>) of role type named typ_one
% 0.45/0.69 Using role type
% 0.45/0.69 Declaring one:(fofType->((fofType->Prop)->Prop))
% 0.45/0.69 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
% 0.45/0.69 A new definition: (((eq (fofType->((fofType->Prop)->Prop))) one) (fun (X0:fofType) (X1:(fofType->Prop))=> ((d_and ((amone X0) X1)) ((l_some X0) X1))))
% 0.45/0.69 Defined: one:=(fun (X0:fofType) (X1:(fofType->Prop))=> ((d_and ((amone X0) X1)) ((l_some X0) X1)))
% 0.45/0.69 FOF formula (<kernel.Constant object at 0x2b2ac1e7ea70>, <kernel.DependentProduct object at 0x2b2ac1e7ef38>) of role type named typ_ind
% 0.45/0.69 Using role type
% 0.45/0.69 Declaring ind:(fofType->((fofType->Prop)->fofType))
% 0.45/0.69 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
% 0.45/0.69 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))))))
% 0.45/0.69 Defined: ind:=(fun (X0:fofType) (X1:(fofType->Prop))=> (eps (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2)))))
% 0.45/0.69 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
% 0.45/0.69 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)), (((one X0) X1)->((is_of ((ind X0) X1)) (fun (X2:fofType)=> ((in X2) X0)))))
% 0.45/0.69 FOF formula (forall (X0:fofType) (X1:(fofType->Prop)), (((one X0) X1)->(X1 ((ind X0) X1)))) of role axiom named oneax
% 0.45/0.69 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)), (((one X0) X1)->(X1 ((ind X0) X1))))
% 0.45/0.69 FOF formula (<kernel.Constant object at 0x2b2ac1e7ef38>, <kernel.DependentProduct object at 0x2b2ac1e7e560>) of role type named typ_injective
% 0.45/0.69 Using role type
% 0.45/0.69 Declaring injective:(fofType->(fofType->(fofType->Prop)))
% 0.45/0.69 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
% 0.45/0.69 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))))))))
% 0.45/0.69 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)))))))
% 0.45/0.69 FOF formula (<kernel.Constant object at 0x2b2ac1e7ed88>, <kernel.DependentProduct object at 0x2b2ac1e841b8>) of role type named typ_image
% 0.45/0.69 Using role type
% 0.45/0.69 Declaring image:(fofType->(fofType->(fofType->(fofType->Prop))))
% 0.45/0.69 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 0x2b2ac1e7ed88>, <kernel.DependentProduct object at 0x2b2ac1e84200>) 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 0x2b2ac1e7ed88>, <kernel.DependentProduct object at 0x2b2ac1e84998>) 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 0x2b2ac1e84998>, <kernel.DependentProduct object at 0x2b2ac1e84290>) 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 0x2b2ac1e84290>, <kernel.DependentProduct object at 0x2b2ac1e84908>) 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 0x2b2ac1e84908>, <kernel.DependentProduct object at 0x2b2ac1e84248>) 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)))
% 0.53/0.73 FOF formula (<kernel.Constant object at 0x2b2ac1e84248>, <kernel.DependentProduct object at 0x2b2ac1e843b0>) of role type named typ_invf
% 0.53/0.73 Using role type
% 0.53/0.73 Declaring invf:(fofType->(fofType->(fofType->fofType)))
% 0.53/0.73 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
% 0.53/0.73 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) invf) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (((soft X0) X1) X2))))
% 0.53/0.73 Defined: invf:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (((soft X0) X1) X2)))
% 0.53/0.73 FOF formula (<kernel.Constant object at 0x2b2ac1e843b0>, <kernel.DependentProduct object at 0x2b2ac1e84290>) of role type named typ_inj_h
% 0.53/0.73 Using role type
% 0.53/0.73 Declaring inj_h:(fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))
% 0.53/0.73 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
% 0.53/0.73 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))))))
% 0.53/0.73 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)))))
% 0.53/0.73 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
% 0.53/0.73 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)))))))
% 0.53/0.73 FOF formula (<kernel.Constant object at 0x2b2ac1e84ab8>, <kernel.DependentProduct object at 0x2b2ac1e842d8>) of role type named typ_e_in
% 0.53/0.73 Using role type
% 0.53/0.73 Declaring e_in:(fofType->((fofType->Prop)->(fofType->fofType)))
% 0.53/0.73 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
% 0.53/0.73 A new definition: (((eq (fofType->((fofType->Prop)->(fofType->fofType)))) e_in) (fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> X2))
% 0.53/0.73 Defined: e_in:=(fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> X2)
% 0.53/0.73 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
% 0.53/0.73 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))))))
% 0.53/0.73 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
% 0.53/0.73 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)))))
% 0.53/0.73 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
% 0.53/0.73 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))))
% 0.53/0.73 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
% 0.53/0.74 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)))))
% 0.53/0.74 FOF formula (<kernel.Constant object at 0x2b2ac1e84098>, <kernel.DependentProduct object at 0x2b2ac1e84e18>) of role type named typ_out
% 0.53/0.74 Using role type
% 0.53/0.74 Declaring out:(fofType->((fofType->Prop)->(fofType->fofType)))
% 0.53/0.74 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
% 0.53/0.74 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)))))
% 0.53/0.74 Defined: out:=(fun (X0:fofType) (X1:(fofType->Prop))=> (((soft ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1))))
% 0.53/0.74 FOF formula (<kernel.Constant object at 0x2b2ac1e84e18>, <kernel.DependentProduct object at 0x2b2ac1e84758>) of role type named typ_d_pair
% 0.53/0.74 Using role type
% 0.53/0.74 Declaring d_pair:(fofType->(fofType->(fofType->(fofType->fofType))))
% 0.53/0.74 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) d_pair) (fun (X0:fofType) (X1:fofType)=> pair)) of role definition named def_d_pair
% 0.53/0.74 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) d_pair) (fun (X0:fofType) (X1:fofType)=> pair))
% 0.53/0.74 Defined: d_pair:=(fun (X0:fofType) (X1:fofType)=> pair)
% 0.53/0.74 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
% 0.53/0.74 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)))))))))
% 0.53/0.74 FOF formula (<kernel.Constant object at 0x2b2ac1e84b00>, <kernel.DependentProduct object at 0x2b2ac1e84c68>) of role type named typ_first
% 0.53/0.74 Using role type
% 0.53/0.74 Declaring first:(fofType->(fofType->(fofType->fofType)))
% 0.53/0.74 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) first) (fun (X0:fofType) (X1:fofType)=> proj0)) of role definition named def_first
% 0.53/0.74 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) first) (fun (X0:fofType) (X1:fofType)=> proj0))
% 0.53/0.74 Defined: first:=(fun (X0:fofType) (X1:fofType)=> proj0)
% 0.53/0.74 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
% 0.53/0.74 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))))))
% 0.53/0.74 FOF formula (<kernel.Constant object at 0x2b2ac1e84098>, <kernel.DependentProduct object at 0x2b2ac1e84710>) of role type named typ_second
% 0.53/0.74 Using role type
% 0.53/0.74 Declaring second:(fofType->(fofType->(fofType->fofType)))
% 0.53/0.74 FOF formula (((eq (fofType->(fofType->(fofType->fofType)))) second) (fun (X0:fofType) (X1:fofType)=> _TPTP_proj1)) of role definition named def_second
% 0.53/0.74 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) second) (fun (X0:fofType) (X1:fofType)=> _TPTP_proj1))
% 0.53/0.74 Defined: second:=(fun (X0:fofType) (X1:fofType)=> _TPTP_proj1)
% 0.53/0.74 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
% 0.53/0.74 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))))))
% 0.53/0.76 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
% 0.53/0.76 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))))
% 0.53/0.76 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
% 0.53/0.76 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))))))
% 0.53/0.76 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
% 0.53/0.76 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))))))
% 0.53/0.76 FOF formula (<kernel.Constant object at 0x2b2ac1e84ef0>, <kernel.DependentProduct object at 0x2b2ac1e84680>) of role type named typ_prop1
% 0.53/0.76 Using role type
% 0.53/0.76 Declaring prop1:(Prop->(fofType->(fofType->(fofType->(fofType->Prop)))))
% 0.53/0.76 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
% 0.53/0.76 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)))))
% 0.53/0.76 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))))
% 0.53/0.76 FOF formula (<kernel.Constant object at 0x2b2ac1e84680>, <kernel.DependentProduct object at 0x2b2ac1e84ef0>) of role type named typ_ite
% 0.53/0.76 Using role type
% 0.53/0.76 Declaring ite:(Prop->(fofType->(fofType->(fofType->fofType))))
% 0.53/0.76 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
% 0.53/0.76 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))))
% 0.53/0.76 Defined: ite:=(fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X1) ((((prop1 X0) X1) X2) X3)))
% 0.53/0.76 FOF formula (<kernel.Constant object at 0x2b2ac1e84ef0>, <kernel.DependentProduct object at 0x2b2ac1e84488>) of role type named typ_wissel_wa
% 0.53/0.76 Using role type
% 0.53/0.76 Declaring wissel_wa:(fofType->(fofType->(fofType->(fofType->fofType))))
% 0.53/0.76 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
% 0.53/0.76 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)))
% 0.53/0.76 Defined: wissel_wa:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((ite (((e_is X0) X3) X1)) X0) X2) X3))
% 0.53/0.76 FOF formula (<kernel.Constant object at 0x2b2ac1e84488>, <kernel.DependentProduct object at 0x2b2ac1e84fc8>) of role type named typ_wissel_wb
% 0.59/0.78 Using role type
% 0.59/0.78 Declaring wissel_wb:(fofType->(fofType->(fofType->(fofType->fofType))))
% 0.59/0.78 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
% 0.59/0.78 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))))
% 0.59/0.78 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)))
% 0.59/0.78 FOF formula (<kernel.Constant object at 0x2b2ac1e84fc8>, <kernel.DependentProduct object at 0x2b2ac1e84d88>) of role type named typ_wissel
% 0.59/0.78 Using role type
% 0.59/0.78 Declaring wissel:(fofType->(fofType->(fofType->fofType)))
% 0.59/0.78 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
% 0.59/0.78 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) wissel) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X0) (((wissel_wb X0) X1) X2))))
% 0.59/0.78 Defined: wissel:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X0) (((wissel_wb X0) X1) X2)))
% 0.59/0.78 FOF formula (<kernel.Constant object at 0x2b2ac1e84878>, <kernel.DependentProduct object at 0x2b2ac1e84830>) of role type named typ_changef
% 0.59/0.78 Using role type
% 0.59/0.78 Declaring changef:(fofType->(fofType->(fofType->(fofType->(fofType->fofType)))))
% 0.59/0.78 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
% 0.59/0.78 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))))))
% 0.59/0.78 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)))))
% 0.59/0.78 FOF formula (<kernel.Constant object at 0x2b2ac1e84248>, <kernel.DependentProduct object at 0x2b2ac1e84d88>) of role type named typ_r_ec
% 0.59/0.78 Using role type
% 0.59/0.78 Declaring r_ec:(Prop->(Prop->Prop))
% 0.59/0.78 FOF formula (((eq (Prop->(Prop->Prop))) r_ec) (fun (X0:Prop) (X1:Prop)=> (X0->(d_not X1)))) of role definition named def_r_ec
% 0.59/0.78 A new definition: (((eq (Prop->(Prop->Prop))) r_ec) (fun (X0:Prop) (X1:Prop)=> (X0->(d_not X1))))
% 0.59/0.78 Defined: r_ec:=(fun (X0:Prop) (X1:Prop)=> (X0->(d_not X1)))
% 0.59/0.78 FOF formula (<kernel.Constant object at 0x2b2ac1e84d88>, <kernel.DependentProduct object at 0x2b2ac1e84830>) of role type named typ_esti
% 0.59/0.78 Using role type
% 0.59/0.78 Declaring esti:(fofType->(fofType->(fofType->Prop)))
% 0.59/0.78 FOF formula (((eq (fofType->(fofType->(fofType->Prop)))) esti) (fun (X0:fofType)=> in)) of role definition named def_esti
% 0.59/0.78 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) esti) (fun (X0:fofType)=> in))
% 0.59/0.78 Defined: esti:=(fun (X0:fofType)=> in)
% 0.59/0.78 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
% 0.59/0.78 A new axiom: (forall (X0:fofType) (X1:(fofType->Prop)), ((is_of ((d_Sep X0) X1)) (fun (X2:fofType)=> ((in X2) (power X0)))))
% 0.59/0.78 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
% 0.59/0.78 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))))))
% 0.59/0.78 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
% 0.59/0.80 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)))))
% 0.59/0.80 FOF formula (<kernel.Constant object at 0x2b2ac1e84830>, <kernel.DependentProduct object at 0x2b2ac1e8b638>) of role type named typ_empty
% 0.59/0.80 Using role type
% 0.59/0.80 Declaring empty:(fofType->(fofType->Prop))
% 0.59/0.80 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
% 0.59/0.80 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))))))
% 0.59/0.80 Defined: empty:=(fun (X0:fofType) (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) X0))) ((non X0) (fun (X2:fofType)=> (((esti X0) X2) X1)))))
% 0.59/0.80 FOF formula (<kernel.Constant object at 0x2b2ac1e84830>, <kernel.DependentProduct object at 0x2b2ac1e8b440>) of role type named typ_nonempty
% 0.59/0.80 Using role type
% 0.59/0.80 Declaring nonempty:(fofType->(fofType->Prop))
% 0.59/0.80 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
% 0.59/0.80 A new definition: (((eq (fofType->(fofType->Prop))) nonempty) (fun (X0:fofType) (X1:fofType)=> ((l_some X0) (fun (X2:fofType)=> (((esti X0) X2) X1)))))
% 0.59/0.80 Defined: nonempty:=(fun (X0:fofType) (X1:fofType)=> ((l_some X0) (fun (X2:fofType)=> (((esti X0) X2) X1))))
% 0.59/0.80 FOF formula (<kernel.Constant object at 0x2b2ac1e84830>, <kernel.DependentProduct object at 0x2b2ac1e8b098>) of role type named typ_incl
% 0.59/0.80 Using role type
% 0.59/0.80 Declaring incl:(fofType->(fofType->(fofType->Prop)))
% 0.59/0.80 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
% 0.59/0.80 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))))))
% 0.59/0.80 Defined: incl:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X0) (fun (X3:fofType)=> ((imp (((esti X0) X3) X1)) (((esti X0) X3) X2)))))
% 0.59/0.80 FOF formula (<kernel.Constant object at 0x2b2ac1e8b098>, <kernel.DependentProduct object at 0x2b2ac1e8b638>) of role type named typ_st_disj
% 0.59/0.80 Using role type
% 0.59/0.80 Declaring st_disj:(fofType->(fofType->(fofType->Prop)))
% 0.59/0.80 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
% 0.59/0.80 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))))))
% 0.59/0.80 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)))))
% 0.59/0.80 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
% 0.59/0.80 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))))))))
% 0.59/0.80 FOF formula (<kernel.Constant object at 0x2b2ac1e8b2d8>, <kernel.DependentProduct object at 0x2b2ac1e8b710>) of role type named typ_nissetprop
% 0.59/0.80 Using role type
% 0.59/0.80 Declaring nissetprop:(fofType->(fofType->(fofType->(fofType->Prop))))
% 0.59/0.80 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
% 0.59/0.81 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)))))
% 0.59/0.81 Defined: nissetprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((d_and (((esti X0) X3) X1)) (d_not (((esti X0) X3) X2))))
% 0.59/0.81 FOF formula (<kernel.Constant object at 0x2b2ac1e8b710>, <kernel.DependentProduct object at 0x2b2ac1e8b098>) of role type named typ_unmore
% 0.59/0.81 Using role type
% 0.59/0.81 Declaring unmore:(fofType->(fofType->(fofType->fofType)))
% 0.59/0.81 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
% 0.59/0.81 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))))))))
% 0.59/0.81 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)))))))
% 0.59/0.81 FOF formula (<kernel.Constant object at 0x2b2ac1e8b098>, <kernel.DependentProduct object at 0x2b2ac1e8b908>) of role type named typ_ecelt
% 0.59/0.81 Using role type
% 0.59/0.81 Declaring ecelt:(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 0.59/0.81 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
% 0.59/0.81 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))))
% 0.59/0.81 Defined: ecelt:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((d_Sep X0) (X1 X2)))
% 0.59/0.81 FOF formula (<kernel.Constant object at 0x2b2ac1e8b908>, <kernel.DependentProduct object at 0x2b2ac1e8b8c0>) of role type named typ_ecp
% 0.59/0.81 Using role type
% 0.59/0.81 Declaring ecp:(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% 0.59/0.81 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
% 0.59/0.81 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))))
% 0.59/0.81 Defined: ecp:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType)=> (((e_is (power X0)) X2) (((ecelt X0) X1) X3)))
% 0.59/0.81 FOF formula (<kernel.Constant object at 0x2b2ac1e8b8c0>, <kernel.DependentProduct object at 0x2b2ac1e8bc20>) of role type named typ_anec
% 0.59/0.81 Using role type
% 0.59/0.81 Declaring anec:(fofType->((fofType->(fofType->Prop))->(fofType->Prop)))
% 0.59/0.81 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
% 0.59/0.81 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))))
% 0.59/0.81 Defined: anec:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((l_some X0) (((ecp X0) X1) X2)))
% 0.59/0.81 FOF formula (<kernel.Constant object at 0x2b2ac1e8bc20>, <kernel.DependentProduct object at 0x2b2ac1e8b908>) of role type named typ_ect
% 0.59/0.81 Using role type
% 0.59/0.81 Declaring ect:(fofType->((fofType->(fofType->Prop))->fofType))
% 0.59/0.81 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
% 0.59/0.81 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->fofType))) ect) (fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((d_Sep (power X0)) ((anec X0) X1))))
% 0.59/0.83 Defined: ect:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((d_Sep (power X0)) ((anec X0) X1)))
% 0.59/0.83 FOF formula (<kernel.Constant object at 0x2b2ac1e8b908>, <kernel.DependentProduct object at 0x2b2ac1e8b560>) of role type named typ_ectset
% 0.59/0.83 Using role type
% 0.59/0.83 Declaring ectset:(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 0.59/0.83 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
% 0.59/0.83 A new definition: (((eq (fofType->((fofType->(fofType->Prop))->(fofType->fofType)))) ectset) (fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((out (power X0)) ((anec X0) X1))))
% 0.59/0.83 Defined: ectset:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((out (power X0)) ((anec X0) X1)))
% 0.59/0.83 FOF formula (<kernel.Constant object at 0x2b2ac1e8b560>, <kernel.DependentProduct object at 0x2b2ac1e8b3b0>) of role type named typ_ectelt
% 0.59/0.83 Using role type
% 0.59/0.83 Declaring ectelt:(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 0.59/0.83 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
% 0.59/0.83 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))))
% 0.59/0.83 Defined: ectelt:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((ectset X0) X1) (((ecelt X0) X1) X2)))
% 0.59/0.83 FOF formula (<kernel.Constant object at 0x2b2ac1e8b3b0>, <kernel.DependentProduct object at 0x2b2ac1e8bb00>) of role type named typ_ecect
% 0.59/0.83 Using role type
% 0.59/0.83 Declaring ecect:(fofType->((fofType->(fofType->Prop))->(fofType->fofType)))
% 0.59/0.83 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
% 0.59/0.83 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))))
% 0.59/0.83 Defined: ecect:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((e_in (power X0)) ((anec X0) X1)))
% 0.59/0.83 FOF formula (<kernel.Constant object at 0x2b2ac1e8bb00>, <kernel.DependentProduct object at 0x2b2ac1e8b320>) of role type named typ_fixfu
% 0.59/0.83 Using role type
% 0.59/0.83 Declaring fixfu:(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% 0.59/0.83 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
% 0.59/0.83 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)))))))))
% 0.59/0.83 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))))))))
% 0.59/0.83 FOF formula (<kernel.Constant object at 0x2b2ac1e8b320>, <kernel.DependentProduct object at 0x2b2ac1e8b998>) of role type named typ_d_10_prop1
% 0.59/0.83 Using role type
% 0.59/0.83 Declaring d_10_prop1:(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->(fofType->Prop)))))))
% 0.59/0.83 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
% 0.59/0.84 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))))
% 0.59/0.84 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)))
% 0.59/0.84 FOF formula (<kernel.Constant object at 0x2b2ac1e8b998>, <kernel.DependentProduct object at 0x2b2ac1e8bbd8>) of role type named typ_prop2
% 0.59/0.84 Using role type
% 0.59/0.84 Declaring prop2:(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->Prop))))))
% 0.59/0.84 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
% 0.59/0.84 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))))
% 0.59/0.84 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)))
% 0.59/0.84 FOF formula (<kernel.Constant object at 0x2b2ac1e8bbd8>, <kernel.DependentProduct object at 0x2b2ac1e8be18>) of role type named typ_indeq
% 0.59/0.84 Using role type
% 0.59/0.84 Declaring indeq:(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType)))))
% 0.59/0.84 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
% 0.59/0.84 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))))
% 0.59/0.84 Defined: indeq:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType) (X3:fofType) (X4:fofType)=> ((ind X2) (((((prop2 X0) X1) X2) X3) X4)))
% 0.59/0.84 FOF formula (<kernel.Constant object at 0x2b2ac1e8be18>, <kernel.DependentProduct object at 0x2b2ac1e8bd88>) of role type named typ_fixfu2
% 0.59/0.84 Using role type
% 0.59/0.84 Declaring fixfu2:(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->Prop))))
% 0.59/0.84 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
% 0.59/0.84 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))))))))))))))
% 0.59/0.84 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)))))))))))))
% 0.66/0.85 FOF formula (<kernel.Constant object at 0x2b2ac1e8bd88>, <kernel.DependentProduct object at 0x2b2ac1e8b0e0>) of role type named typ_d_11_i
% 0.66/0.85 Using role type
% 0.66/0.85 Declaring d_11_i:(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->fofType)))))
% 0.66/0.85 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
% 0.66/0.85 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)))))
% 0.66/0.85 Defined: d_11_i:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((indeq X0) X1) ((d_Pi X0) (fun (X3:fofType)=> X2))))
% 0.66/0.85 FOF formula (<kernel.Constant object at 0x2b2ac1e8b0e0>, <kernel.DependentProduct object at 0x2b2ac1e8b9e0>) of role type named typ_indeq2
% 0.66/0.85 Using role type
% 0.66/0.85 Declaring indeq2:(fofType->((fofType->(fofType->Prop))->(fofType->(fofType->(fofType->(fofType->fofType))))))
% 0.66/0.85 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
% 0.66/0.85 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))))
% 0.66/0.85 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)))
% 0.66/0.85 FOF formula (<kernel.Constant object at 0x2b2ac1e8b9e0>, <kernel.Single object at 0x2b2ac1e8b0e0>) of role type named typ_nat
% 0.66/0.85 Using role type
% 0.66/0.85 Declaring nat:fofType
% 0.66/0.85 FOF formula (((eq fofType) nat) ((d_Sep omega) (fun (X0:fofType)=> (not (((eq fofType) X0) emptyset))))) of role definition named def_nat
% 0.66/0.85 A new definition: (((eq fofType) nat) ((d_Sep omega) (fun (X0:fofType)=> (not (((eq fofType) X0) emptyset)))))
% 0.66/0.85 Defined: nat:=((d_Sep omega) (fun (X0:fofType)=> (not (((eq fofType) X0) emptyset))))
% 0.66/0.85 FOF formula (<kernel.Constant object at 0x2b2ac1e8b0e0>, <kernel.DependentProduct object at 0x2b2ac1e8bb00>) of role type named typ_n_is
% 0.66/0.85 Using role type
% 0.66/0.85 Declaring n_is:(fofType->(fofType->Prop))
% 0.66/0.85 FOF formula (((eq (fofType->(fofType->Prop))) n_is) (e_is nat)) of role definition named def_n_is
% 0.66/0.85 A new definition: (((eq (fofType->(fofType->Prop))) n_is) (e_is nat))
% 0.66/0.85 Defined: n_is:=(e_is nat)
% 0.66/0.85 FOF formula (<kernel.Constant object at 0x2b2ac1e8b998>, <kernel.DependentProduct object at 0x2b2ac1e8bf38>) of role type named typ_nis
% 0.66/0.85 Using role type
% 0.66/0.85 Declaring nis:(fofType->(fofType->Prop))
% 0.66/0.85 FOF formula (((eq (fofType->(fofType->Prop))) nis) (fun (X0:fofType) (X1:fofType)=> (d_not ((n_is X0) X1)))) of role definition named def_nis
% 0.66/0.85 A new definition: (((eq (fofType->(fofType->Prop))) nis) (fun (X0:fofType) (X1:fofType)=> (d_not ((n_is X0) X1))))
% 0.66/0.85 Defined: nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((n_is X0) X1)))
% 0.66/0.85 FOF formula (<kernel.Constant object at 0x2b2ac1e8bf38>, <kernel.DependentProduct object at 0x2b2ac1e8bb00>) of role type named typ_n_in
% 0.66/0.85 Using role type
% 0.66/0.85 Declaring n_in:(fofType->(fofType->Prop))
% 0.66/0.85 FOF formula (((eq (fofType->(fofType->Prop))) n_in) (esti nat)) of role definition named def_n_in
% 0.66/0.85 A new definition: (((eq (fofType->(fofType->Prop))) n_in) (esti nat))
% 0.68/0.87 Defined: n_in:=(esti nat)
% 0.68/0.87 FOF formula (<kernel.Constant object at 0x2b2ac1e8bd40>, <kernel.DependentProduct object at 0x2b2ac1e8bb00>) of role type named typ_n_some
% 0.68/0.87 Using role type
% 0.68/0.87 Declaring n_some:((fofType->Prop)->Prop)
% 0.68/0.87 FOF formula (((eq ((fofType->Prop)->Prop)) n_some) (l_some nat)) of role definition named def_n_some
% 0.68/0.87 A new definition: (((eq ((fofType->Prop)->Prop)) n_some) (l_some nat))
% 0.68/0.87 Defined: n_some:=(l_some nat)
% 0.68/0.87 FOF formula (<kernel.Constant object at 0x2b2ac1e8bf80>, <kernel.DependentProduct object at 0x2b2ac1e8bb00>) of role type named typ_n_all
% 0.68/0.87 Using role type
% 0.68/0.87 Declaring n_all:((fofType->Prop)->Prop)
% 0.68/0.87 FOF formula (((eq ((fofType->Prop)->Prop)) n_all) (all nat)) of role definition named def_n_all
% 0.68/0.87 A new definition: (((eq ((fofType->Prop)->Prop)) n_all) (all nat))
% 0.68/0.87 Defined: n_all:=(all nat)
% 0.68/0.87 FOF formula (<kernel.Constant object at 0x2b2ac1e8bd40>, <kernel.DependentProduct object at 0x2b2ac1e8be18>) of role type named typ_n_one
% 0.68/0.87 Using role type
% 0.68/0.87 Declaring n_one:((fofType->Prop)->Prop)
% 0.68/0.87 FOF formula (((eq ((fofType->Prop)->Prop)) n_one) (one nat)) of role definition named def_n_one
% 0.68/0.87 A new definition: (((eq ((fofType->Prop)->Prop)) n_one) (one nat))
% 0.68/0.87 Defined: n_one:=(one nat)
% 0.68/0.87 FOF formula (<kernel.Constant object at 0x2b2ac1e8b8c0>, <kernel.Single object at 0x2b2ac1e8bd40>) of role type named typ_n_1
% 0.68/0.87 Using role type
% 0.68/0.87 Declaring n_1:fofType
% 0.68/0.87 FOF formula (((eq fofType) n_1) (ordsucc emptyset)) of role definition named def_n_1
% 0.68/0.87 A new definition: (((eq fofType) n_1) (ordsucc emptyset))
% 0.68/0.87 Defined: n_1:=(ordsucc emptyset)
% 0.68/0.87 FOF formula ((is_of n_1) (fun (X0:fofType)=> ((in X0) nat))) of role axiom named n_1_p
% 0.68/0.87 A new axiom: ((is_of n_1) (fun (X0:fofType)=> ((in X0) nat)))
% 0.68/0.87 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
% 0.68/0.87 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((is_of (ordsucc X0)) (fun (X1:fofType)=> ((in X1) nat)))))
% 0.68/0.87 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) n_1))) of role axiom named n_ax3
% 0.68/0.87 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) n_1)))
% 0.68/0.87 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
% 0.68/0.87 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))))))
% 0.68/0.87 FOF formula (<kernel.Constant object at 0x2b2ac1e8bd40>, <kernel.DependentProduct object at 0x2b2ac1e90290>) of role type named typ_cond1
% 0.68/0.87 Using role type
% 0.68/0.87 Declaring cond1:(fofType->Prop)
% 0.68/0.87 FOF formula (((eq (fofType->Prop)) cond1) (n_in n_1)) of role definition named def_cond1
% 0.68/0.87 A new definition: (((eq (fofType->Prop)) cond1) (n_in n_1))
% 0.68/0.87 Defined: cond1:=(n_in n_1)
% 0.68/0.87 FOF formula (<kernel.Constant object at 0x2b2ac1e90998>, <kernel.DependentProduct object at 0x2b2ac1e904d0>) of role type named typ_cond2
% 0.68/0.87 Using role type
% 0.68/0.87 Declaring cond2:(fofType->Prop)
% 0.68/0.87 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
% 0.68/0.87 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))))))
% 0.68/0.87 Defined: cond2:=(fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((imp ((n_in X1) X0)) ((n_in (ordsucc X1)) X0)))))
% 0.68/0.87 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
% 0.68/0.87 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)))))))
% 0.68/0.87 FOF formula (<kernel.Constant object at 0x2b2ac1e902d8>, <kernel.DependentProduct object at 0x2b2ac1e90878>) of role type named typ_i1_s
% 0.68/0.89 Using role type
% 0.68/0.89 Declaring i1_s:((fofType->Prop)->fofType)
% 0.68/0.89 FOF formula (((eq ((fofType->Prop)->fofType)) i1_s) (d_Sep nat)) of role definition named def_i1_s
% 0.68/0.89 A new definition: (((eq ((fofType->Prop)->fofType)) i1_s) (d_Sep nat))
% 0.68/0.89 Defined: i1_s:=(d_Sep nat)
% 0.68/0.89 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/NUM007^1.ax, trying next directory
% 0.68/0.89 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
% 0.68/0.89 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)))))))
% 0.68/0.89 FOF formula (<kernel.Constant object at 0x2b2abf1f0b00>, <kernel.DependentProduct object at 0x2b2abf216d40>) of role type named typ_d_22_prop1
% 0.68/0.89 Using role type
% 0.68/0.89 Declaring d_22_prop1:(fofType->Prop)
% 0.68/0.89 FOF formula (((eq (fofType->Prop)) d_22_prop1) (fun (X0:fofType)=> ((nis (ordsucc X0)) X0))) of role definition named def_d_22_prop1
% 0.68/0.89 A new definition: (((eq (fofType->Prop)) d_22_prop1) (fun (X0:fofType)=> ((nis (ordsucc X0)) X0)))
% 0.68/0.89 Defined: d_22_prop1:=(fun (X0:fofType)=> ((nis (ordsucc X0)) X0))
% 0.68/0.89 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) X0))) of role axiom named satz2
% 0.68/0.89 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) X0)))
% 0.68/0.89 FOF formula (<kernel.Constant object at 0x2b2abe79c128>, <kernel.DependentProduct object at 0x2b2abf216c68>) of role type named typ_d_23_prop1
% 0.68/0.89 Using role type
% 0.68/0.89 Declaring d_23_prop1:(fofType->Prop)
% 0.68/0.89 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
% 0.68/0.89 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)))))))
% 0.68/0.89 Defined: d_23_prop1:=(fun (X0:fofType)=> ((l_or ((n_is X0) n_1)) (n_some (fun (X1:fofType)=> ((n_is X0) (ordsucc X1))))))
% 0.68/0.89 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
% 0.68/0.89 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)))))))
% 0.68/0.89 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
% 0.68/0.89 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)))))))
% 0.68/0.89 FOF formula (<kernel.Constant object at 0x2b2abf216e60>, <kernel.DependentProduct object at 0x2b2abe7a0170>) of role type named typ_d_24_prop1
% 0.68/0.89 Using role type
% 0.68/0.89 Declaring d_24_prop1:(fofType->Prop)
% 0.68/0.89 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
% 0.68/0.89 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)))))))
% 0.68/0.89 Defined: d_24_prop1:=(fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((n_is ((ap X0) (ordsucc X1))) (ordsucc ((ap X0) X1))))))
% 0.68/0.89 FOF formula (<kernel.Constant object at 0x2b2abf216c20>, <kernel.DependentProduct object at 0x2b2abe7a0170>) of role type named typ_d_24_prop2
% 0.68/0.89 Using role type
% 0.68/0.89 Declaring d_24_prop2:(fofType->(fofType->Prop))
% 0.68/0.89 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
% 0.68/0.89 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))))
% 0.68/0.90 Defined: d_24_prop2:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) (ordsucc X0))) (d_24_prop1 X1)))
% 0.68/0.90 FOF formula (<kernel.Constant object at 0x2b2abf216c20>, <kernel.DependentProduct object at 0x2b2abe7a0e18>) of role type named typ_prop3
% 0.68/0.90 Using role type
% 0.68/0.90 Declaring prop3:(fofType->(fofType->(fofType->Prop)))
% 0.68/0.90 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
% 0.68/0.90 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) prop3) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((ap X0) X2)) ((ap X1) X2))))
% 0.68/0.90 Defined: prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((ap X0) X2)) ((ap X1) X2)))
% 0.68/0.90 FOF formula (<kernel.Constant object at 0x2b2abf216c20>, <kernel.DependentProduct object at 0x2b2abe7a02d8>) of role type named typ_prop4
% 0.68/0.90 Using role type
% 0.68/0.90 Declaring prop4:(fofType->Prop)
% 0.68/0.90 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
% 0.68/0.90 A new definition: (((eq (fofType->Prop)) prop4) (fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0))))
% 0.68/0.90 Defined: prop4:=(fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0)))
% 0.68/0.90 FOF formula (<kernel.Constant object at 0x2b2abe7a02d8>, <kernel.DependentProduct object at 0x2b2abe7a0320>) of role type named typ_d_24_g
% 0.68/0.90 Using role type
% 0.68/0.90 Declaring d_24_g:(fofType->fofType)
% 0.68/0.90 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
% 0.68/0.90 A new definition: (((eq (fofType->fofType)) d_24_g) (fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> (ordsucc ((ap X0) X1))))))
% 0.68/0.90 Defined: d_24_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> (ordsucc ((ap X0) X1)))))
% 0.68/0.90 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
% 0.68/0.90 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))))))))))
% 0.68/0.90 FOF formula (<kernel.Constant object at 0x2b2abe7a0680>, <kernel.DependentProduct object at 0x2b2abe7a0ef0>) of role type named typ_plus
% 0.68/0.90 Using role type
% 0.68/0.90 Declaring plus:(fofType->fofType)
% 0.68/0.90 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
% 0.68/0.90 A new definition: (((eq (fofType->fofType)) plus) (fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0))))
% 0.68/0.90 Defined: plus:=(fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0)))
% 0.68/0.90 FOF formula (<kernel.Constant object at 0x2b2abe7a0ef0>, <kernel.DependentProduct object at 0x2b2abe7a0830>) of role type named typ_n_pl
% 0.68/0.90 Using role type
% 0.68/0.90 Declaring n_pl:(fofType->(fofType->fofType))
% 0.68/0.90 FOF formula (((eq (fofType->(fofType->fofType))) n_pl) (fun (X0:fofType)=> (ap (plus X0)))) of role definition named def_n_pl
% 0.68/0.90 A new definition: (((eq (fofType->(fofType->fofType))) n_pl) (fun (X0:fofType)=> (ap (plus X0))))
% 0.68/0.90 Defined: n_pl:=(fun (X0:fofType)=> (ap (plus X0)))
% 0.68/0.90 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
% 0.68/0.90 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_pl X0) n_1)) (ordsucc X0))))
% 0.68/0.90 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
% 0.72/0.92 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)))))))
% 0.72/0.92 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
% 0.72/0.92 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_pl n_1) X0)) (ordsucc X0))))
% 0.72/0.92 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
% 0.72/0.92 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)))))))
% 0.72/0.92 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
% 0.72/0.92 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is (ordsucc X0)) ((n_pl X0) n_1))))
% 0.72/0.92 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
% 0.72/0.92 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)))))))
% 0.72/0.92 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
% 0.72/0.92 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is (ordsucc X0)) ((n_pl n_1) X0))))
% 0.72/0.92 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
% 0.72/0.92 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))))))
% 0.72/0.92 FOF formula (<kernel.Constant object at 0x2b2abe7a07e8>, <kernel.DependentProduct object at 0x2b2abeaf9290>) of role type named typ_d_25_prop1
% 0.72/0.92 Using role type
% 0.72/0.92 Declaring d_25_prop1:(fofType->(fofType->(fofType->Prop)))
% 0.72/0.92 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
% 0.72/0.92 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)))))
% 0.72/0.92 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))))
% 0.72/0.92 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
% 0.72/0.92 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)))))))))
% 0.72/0.92 FOF formula (<kernel.Constant object at 0x2b2abe7a07e8>, <kernel.DependentProduct object at 0x2b2abeaf9248>) of role type named typ_d_26_prop1
% 0.72/0.92 Using role type
% 0.72/0.92 Declaring d_26_prop1:(fofType->(fofType->Prop))
% 0.72/0.92 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
% 0.72/0.92 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))))
% 0.75/0.94 Defined: d_26_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_pl X0) X1)) ((n_pl X1) X0)))
% 0.75/0.94 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
% 0.75/0.94 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))))))
% 0.75/0.94 FOF formula (<kernel.Constant object at 0x2b2abeaf9908>, <kernel.DependentProduct object at 0x2b2abeaf9cb0>) of role type named typ_d_27_prop1
% 0.75/0.94 Using role type
% 0.75/0.94 Declaring d_27_prop1:(fofType->(fofType->Prop))
% 0.75/0.94 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
% 0.75/0.94 A new definition: (((eq (fofType->(fofType->Prop))) d_27_prop1) (fun (X0:fofType) (X1:fofType)=> ((nis X1) ((n_pl X0) X1))))
% 0.75/0.94 Defined: d_27_prop1:=(fun (X0:fofType) (X1:fofType)=> ((nis X1) ((n_pl X0) X1)))
% 0.75/0.94 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
% 0.75/0.94 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))))))
% 0.75/0.94 FOF formula (<kernel.Constant object at 0x2b2abeaf9c20>, <kernel.DependentProduct object at 0x2b2abeaf9290>) of role type named typ_d_28_prop1
% 0.75/0.94 Using role type
% 0.75/0.94 Declaring d_28_prop1:(fofType->(fofType->(fofType->Prop)))
% 0.75/0.94 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
% 0.75/0.94 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))))
% 0.75/0.94 Defined: d_28_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((nis ((n_pl X0) X1)) ((n_pl X0) X2)))
% 0.75/0.94 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
% 0.75/0.94 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)))))))))
% 0.75/0.94 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
% 0.75/0.94 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))))))))
% 0.75/0.94 FOF formula (<kernel.Constant object at 0x2b2abeaf9680>, <kernel.DependentProduct object at 0x2b2abeaf9908>) of role type named typ_diffprop
% 0.75/0.94 Using role type
% 0.75/0.94 Declaring diffprop:(fofType->(fofType->(fofType->Prop)))
% 0.75/0.94 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
% 0.75/0.94 A new definition: (((eq (fofType->(fofType->(fofType->Prop)))) diffprop) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))))
% 0.75/0.94 Defined: diffprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is X0) ((n_pl X1) X2)))
% 0.75/0.94 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 0x2b2abeaf9908>, <kernel.DependentProduct object at 0x2b2abeaf9c20>) 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 0x2b2abeaf9f80>, <kernel.DependentProduct object at 0x2b2ac1281200>) 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 0x2b2abeaf9908>, <kernel.DependentProduct object at 0x2b2ac1281c20>) 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 0x2b2ac1281d40>, <kernel.DependentProduct object at 0x2b2ac12813f8>) 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 0x2b2ac12813f8>, <kernel.DependentProduct object at 0x2b2ac1281680>) 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
% 0.75/1.01 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)))))))
% 0.75/1.01 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
% 0.75/1.01 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))))))
% 0.75/1.01 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
% 0.75/1.01 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))))))
% 0.75/1.01 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
% 0.75/1.01 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)))))))
% 0.75/1.01 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
% 0.75/1.01 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)))))))
% 0.75/1.01 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
% 0.75/1.01 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))))))
% 0.75/1.01 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
% 0.75/1.01 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))))))
% 0.75/1.01 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
% 0.75/1.01 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)))))))))
% 0.75/1.01 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
% 0.75/1.01 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)))))))))
% 0.75/1.01 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
% 0.83/1.04 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)=> (((iii X0) X1)->(((lessis X1) X2)->((iii X0) X2)))))))))
% 0.83/1.04 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
% 0.83/1.04 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)))))))))
% 0.83/1.04 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
% 0.83/1.04 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)))))))))
% 0.83/1.04 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
% 0.83/1.04 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)))))))))
% 0.83/1.04 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
% 0.83/1.04 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)))))
% 0.83/1.04 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
% 0.83/1.04 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))))))
% 0.83/1.04 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((d_29_ii (ordsucc X0)) X0))) of role axiom named satz18b
% 0.83/1.04 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((d_29_ii (ordsucc X0)) X0)))
% 0.83/1.04 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((iii X0) (ordsucc X0)))) of role axiom named satz18c
% 0.83/1.04 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((iii X0) (ordsucc X0))))
% 0.83/1.04 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
% 0.83/1.04 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)))))))))
% 0.83/1.04 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
% 0.83/1.06 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)))))))))
% 0.83/1.06 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
% 0.83/1.06 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)))))))))
% 0.83/1.06 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
% 0.83/1.06 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)))))))))
% 0.83/1.06 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
% 0.83/1.06 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)))))))))
% 0.83/1.06 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
% 0.83/1.06 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)))))))))
% 0.83/1.06 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
% 0.83/1.06 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))))))))))))
% 0.83/1.06 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
% 0.83/1.06 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))))))))))))
% 0.90/1.09 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
% 0.90/1.09 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))))))))))))
% 0.90/1.09 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
% 0.90/1.09 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))))))))))))
% 0.90/1.09 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
% 0.90/1.09 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)))))))))
% 0.90/1.09 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
% 0.90/1.09 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)))))))))
% 0.90/1.09 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
% 0.90/1.09 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)))))))))
% 0.90/1.09 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
% 0.90/1.09 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)))))))))
% 0.90/1.09 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
% 0.90/1.12 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 X0) X2)) ((n_pl X1) X2))->((d_29_ii X0) X1))))))))
% 0.90/1.12 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
% 0.90/1.12 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))))))))
% 0.90/1.12 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
% 0.90/1.12 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))))))))
% 0.90/1.12 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
% 0.90/1.12 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))))))))
% 0.90/1.12 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
% 0.90/1.12 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))))))))
% 0.90/1.12 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
% 0.90/1.12 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))))))))
% 0.90/1.12 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
% 0.90/1.12 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))))))))))))
% 0.90/1.12 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
% 0.90/1.14 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))))))))))))
% 0.90/1.14 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
% 0.90/1.14 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))))))))))))
% 0.90/1.14 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
% 0.90/1.14 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))))))))))))
% 0.90/1.14 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
% 0.90/1.14 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))))))))))))
% 0.90/1.14 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
% 0.90/1.14 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))))))))))))
% 0.90/1.14 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
% 0.90/1.14 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))))))))))))
% 0.97/1.16 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
% 0.97/1.16 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))))))))))))
% 0.97/1.16 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((moreis X0) n_1))) of role axiom named satz24
% 0.97/1.16 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((moreis X0) n_1)))
% 0.97/1.16 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (lessis n_1)) of role axiom named satz24a
% 0.97/1.16 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (lessis n_1))
% 0.97/1.16 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
% 0.97/1.16 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((d_29_ii (ordsucc X0)) n_1)))
% 0.97/1.16 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((iii n_1) (ordsucc X0)))) of role axiom named satz24c
% 0.97/1.16 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((iii n_1) (ordsucc X0))))
% 0.97/1.16 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
% 0.97/1.16 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)))))))
% 0.97/1.16 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
% 0.97/1.16 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)))))))
% 0.97/1.16 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
% 0.97/1.16 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))))))
% 0.97/1.16 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
% 0.97/1.16 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))))))
% 0.97/1.16 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
% 0.97/1.16 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))))))
% 0.97/1.16 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
% 0.98/1.18 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))))))
% 0.98/1.18 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
% 0.98/1.18 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))))))
% 0.98/1.18 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
% 0.98/1.18 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))))))
% 0.98/1.18 FOF formula (<kernel.Constant object at 0x2b2ac1e5f8c0>, <kernel.DependentProduct object at 0x2b2ac1e5f560>) of role type named typ_lbprop
% 0.98/1.18 Using role type
% 0.98/1.18 Declaring lbprop:((fofType->Prop)->(fofType->(fofType->Prop)))
% 0.98/1.18 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
% 0.98/1.18 A new definition: (((eq ((fofType->Prop)->(fofType->(fofType->Prop)))) lbprop) (fun (X0:(fofType->Prop)) (X1:fofType) (X2:fofType)=> ((imp (X0 X2)) ((lessis X1) X2))))
% 0.98/1.18 Defined: lbprop:=(fun (X0:(fofType->Prop)) (X1:fofType) (X2:fofType)=> ((imp (X0 X2)) ((lessis X1) X2)))
% 0.98/1.18 FOF formula (<kernel.Constant object at 0x2b2ac1e5f560>, <kernel.DependentProduct object at 0x2b2ac1e5f638>) of role type named typ_n_lb
% 0.98/1.18 Using role type
% 0.98/1.18 Declaring n_lb:((fofType->Prop)->(fofType->Prop))
% 0.98/1.18 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
% 0.98/1.18 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) n_lb) (fun (X0:(fofType->Prop)) (X1:fofType)=> (n_all ((lbprop X0) X1))))
% 0.98/1.18 Defined: n_lb:=(fun (X0:(fofType->Prop)) (X1:fofType)=> (n_all ((lbprop X0) X1)))
% 0.98/1.18 FOF formula (<kernel.Constant object at 0x2b2ac1e5f638>, <kernel.DependentProduct object at 0x2b2ac1e5fe18>) of role type named typ_min
% 0.98/1.18 Using role type
% 0.98/1.18 Declaring min:((fofType->Prop)->(fofType->Prop))
% 0.98/1.18 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
% 0.98/1.18 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) min) (fun (X0:(fofType->Prop)) (X1:fofType)=> ((d_and ((n_lb X0) X1)) (X0 X1))))
% 0.98/1.18 Defined: min:=(fun (X0:(fofType->Prop)) (X1:fofType)=> ((d_and ((n_lb X0) X1)) (X0 X1)))
% 0.98/1.18 FOF formula (forall (X0:(fofType->Prop)), ((n_some X0)->(n_some (min X0)))) of role axiom named satz27
% 0.98/1.18 A new axiom: (forall (X0:(fofType->Prop)), ((n_some X0)->(n_some (min X0))))
% 0.98/1.18 FOF formula (forall (X0:(fofType->Prop)), ((n_some X0)->(n_one (min X0)))) of role axiom named satz27a
% 0.98/1.18 A new axiom: (forall (X0:(fofType->Prop)), ((n_some X0)->(n_one (min X0))))
% 0.98/1.18 FOF formula (<kernel.Constant object at 0x2b2ac1e5fd88>, <kernel.DependentProduct object at 0x2b2ac1e5fcf8>) of role type named typ_d_428_prop1
% 0.98/1.18 Using role type
% 0.98/1.18 Declaring d_428_prop1:(fofType->(fofType->Prop))
% 0.98/1.18 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
% 0.98/1.18 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))))))
% 0.98/1.18 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)))))
% 0.98/1.18 FOF formula (<kernel.Constant object at 0x2b2ac1e5fcf8>, <kernel.DependentProduct object at 0x2b2ac1e5f950>) of role type named typ_d_428_prop2
% 0.98/1.20 Using role type
% 0.98/1.20 Declaring d_428_prop2:(fofType->(fofType->Prop))
% 0.98/1.20 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
% 0.98/1.20 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))))
% 0.98/1.20 Defined: d_428_prop2:=(fun (X0:fofType) (X1:fofType)=> ((d_and ((n_is ((ap X1) n_1)) X0)) ((d_428_prop1 X0) X1)))
% 0.98/1.20 FOF formula (<kernel.Constant object at 0x2b2ac1e5f950>, <kernel.DependentProduct object at 0x2b2ac1e5f908>) of role type named typ_d_428_prop4
% 0.98/1.20 Using role type
% 0.98/1.20 Declaring d_428_prop4:(fofType->Prop)
% 0.98/1.20 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
% 0.98/1.20 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))))
% 0.98/1.20 Defined: d_428_prop4:=(fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0)))
% 0.98/1.20 FOF formula (<kernel.Constant object at 0x2b2ac1e5f908>, <kernel.Single object at 0x2b2ac1e5f950>) of role type named typ_d_428_id
% 0.98/1.20 Using role type
% 0.98/1.20 Declaring d_428_id:fofType
% 0.98/1.20 FOF formula (((eq fofType) d_428_id) ((d_Sigma nat) (fun (X0:fofType)=> X0))) of role definition named def_d_428_id
% 0.98/1.20 A new definition: (((eq fofType) d_428_id) ((d_Sigma nat) (fun (X0:fofType)=> X0)))
% 0.98/1.20 Defined: d_428_id:=((d_Sigma nat) (fun (X0:fofType)=> X0))
% 0.98/1.20 FOF formula (<kernel.Constant object at 0x2b2ac1e5f950>, <kernel.DependentProduct object at 0x2b2ac1e5f440>) of role type named typ_d_428_g
% 0.98/1.20 Using role type
% 0.98/1.20 Declaring d_428_g:(fofType->fofType)
% 0.98/1.20 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
% 0.98/1.20 A new definition: (((eq (fofType->fofType)) d_428_g) (fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> ((n_pl ((ap X0) X1)) X1)))))
% 0.98/1.20 Defined: d_428_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> ((n_pl ((ap X0) X1)) X1))))
% 0.98/1.20 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
% 0.98/1.20 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)))))))))
% 0.98/1.20 FOF formula (<kernel.Constant object at 0x2b2ac1e5f560>, <kernel.DependentProduct object at 0x2b2ac1e5fea8>) of role type named typ_times
% 0.98/1.20 Using role type
% 0.98/1.20 Declaring times:(fofType->fofType)
% 0.98/1.20 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
% 0.98/1.20 A new definition: (((eq (fofType->fofType)) times) (fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0))))
% 0.98/1.20 Defined: times:=(fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0)))
% 0.98/1.20 FOF formula (<kernel.Constant object at 0x2b2ac1e5fea8>, <kernel.DependentProduct object at 0x2b2ac1e5f638>) of role type named typ_n_ts
% 0.98/1.20 Using role type
% 0.98/1.20 Declaring n_ts:(fofType->(fofType->fofType))
% 0.98/1.20 FOF formula (((eq (fofType->(fofType->fofType))) n_ts) (fun (X0:fofType)=> (ap (times X0)))) of role definition named def_n_ts
% 0.98/1.20 A new definition: (((eq (fofType->(fofType->fofType))) n_ts) (fun (X0:fofType)=> (ap (times X0))))
% 0.98/1.20 Defined: n_ts:=(fun (X0:fofType)=> (ap (times X0)))
% 0.98/1.20 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
% 0.98/1.20 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_ts X0) n_1)) X0)))
% 1.02/1.22 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
% 1.02/1.22 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))))))
% 1.02/1.22 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
% 1.02/1.22 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_ts n_1) X0)) X0)))
% 1.02/1.22 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
% 1.02/1.22 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))))))
% 1.02/1.22 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
% 1.02/1.22 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is X0) ((n_ts X0) n_1))))
% 1.02/1.22 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
% 1.02/1.22 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)))))))
% 1.02/1.22 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
% 1.02/1.22 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is X0) ((n_ts n_1) X0))))
% 1.02/1.22 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
% 1.02/1.22 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))))))
% 1.02/1.22 FOF formula (<kernel.Constant object at 0x2b2ac1e5fb00>, <kernel.DependentProduct object at 0x2b2ac1e7d290>) of role type named typ_d_429_prop1
% 1.02/1.22 Using role type
% 1.02/1.22 Declaring d_429_prop1:(fofType->(fofType->Prop))
% 1.02/1.22 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
% 1.02/1.22 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))))
% 1.02/1.22 Defined: d_429_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts X0) X1)) ((n_ts X1) X0)))
% 1.02/1.22 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
% 1.02/1.22 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))))))
% 1.02/1.22 FOF formula (<kernel.Constant object at 0x2b2ac1e5f7e8>, <kernel.DependentProduct object at 0x2b2ac1e7d2d8>) of role type named typ_d_430_prop1
% 1.02/1.22 Using role type
% 1.02/1.22 Declaring d_430_prop1:(fofType->(fofType->(fofType->Prop)))
% 1.02/1.22 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
% 1.02/1.22 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)))))
% 1.04/1.24 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))))
% 1.04/1.24 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
% 1.04/1.24 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)))))))))
% 1.04/1.24 FOF formula (<kernel.Constant object at 0x2b2ac1e5fb00>, <kernel.DependentProduct object at 0x2b2ac1e7d440>) of role type named typ_d_431_prop1
% 1.04/1.24 Using role type
% 1.04/1.24 Declaring d_431_prop1:(fofType->(fofType->(fofType->Prop)))
% 1.04/1.24 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
% 1.04/1.24 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)))))
% 1.04/1.24 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))))
% 1.04/1.24 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
% 1.04/1.24 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)))))))))
% 1.04/1.24 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
% 1.04/1.24 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)))))))))
% 1.04/1.24 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
% 1.04/1.24 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)))))))))
% 1.04/1.24 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
% 1.04/1.24 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)))))))))
% 1.04/1.24 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
% 1.04/1.27 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)))))))))
% 1.04/1.27 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
% 1.04/1.27 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)))))))))
% 1.04/1.27 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
% 1.04/1.27 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)))))))))
% 1.04/1.27 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
% 1.04/1.27 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))))))))))))
% 1.04/1.27 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
% 1.04/1.27 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))))))))))))
% 1.04/1.27 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
% 1.04/1.27 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))))))))))))
% 1.04/1.27 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
% 1.04/1.29 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))))))))))))
% 1.04/1.29 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
% 1.04/1.29 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)))))))))
% 1.04/1.29 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
% 1.04/1.29 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)))))))))
% 1.04/1.29 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
% 1.04/1.29 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)))))))))
% 1.04/1.29 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
% 1.04/1.29 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)))))))))
% 1.04/1.29 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
% 1.04/1.29 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))))))))
% 1.04/1.29 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
% 1.04/1.29 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))))))))
% 1.04/1.29 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
% 1.13/1.32 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))))))))
% 1.13/1.32 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
% 1.13/1.32 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))))))))))))
% 1.13/1.32 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
% 1.13/1.32 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))))))))))))
% 1.13/1.32 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
% 1.13/1.32 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))))))))))))
% 1.13/1.32 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
% 1.13/1.32 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))))))))))))
% 1.13/1.32 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
% 1.13/1.32 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))))))))))))
% 1.13/1.32 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
% 1.13/1.34 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))))))))))))
% 1.13/1.34 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
% 1.13/1.34 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))))))))))))
% 1.13/1.34 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
% 1.13/1.34 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))))))))))))
% 1.13/1.34 FOF formula (<kernel.Constant object at 0x2b2ac1e7d758>, <kernel.DependentProduct object at 0x2b2ac1e7d320>) of role type named typ_n_mn
% 1.13/1.34 Using role type
% 1.13/1.34 Declaring n_mn:(fofType->(fofType->fofType))
% 1.13/1.34 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
% 1.13/1.34 A new definition: (((eq (fofType->(fofType->fofType))) n_mn) (fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop X0) X1))))
% 1.13/1.34 Defined: n_mn:=(fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop X0) X1)))
% 1.13/1.34 FOF formula (<kernel.Constant object at 0x2b2ac1e7d320>, <kernel.DependentProduct object at 0x2b2ac1e7d2d8>) of role type named typ_d_1to
% 1.13/1.34 Using role type
% 1.13/1.34 Declaring d_1to:(fofType->fofType)
% 1.13/1.34 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
% 1.13/1.34 A new definition: (((eq (fofType->fofType)) d_1to) (fun (X0:fofType)=> ((d_Sep nat) (fun (X1:fofType)=> ((lessis X1) X0)))))
% 1.13/1.34 Defined: d_1to:=(fun (X0:fofType)=> ((d_Sep nat) (fun (X1:fofType)=> ((lessis X1) X0))))
% 1.13/1.34 FOF formula (<kernel.Constant object at 0x2b2ac1e7d2d8>, <kernel.DependentProduct object at 0x2b2ac1e7d560>) of role type named typ_outn
% 1.13/1.34 Using role type
% 1.13/1.34 Declaring outn:(fofType->(fofType->fofType))
% 1.13/1.34 FOF formula (((eq (fofType->(fofType->fofType))) outn) (fun (X0:fofType)=> ((out nat) (fun (X1:fofType)=> ((lessis X1) X0))))) of role definition named def_outn
% 1.13/1.34 A new definition: (((eq (fofType->(fofType->fofType))) outn) (fun (X0:fofType)=> ((out nat) (fun (X1:fofType)=> ((lessis X1) X0)))))
% 1.13/1.34 Defined: outn:=(fun (X0:fofType)=> ((out nat) (fun (X1:fofType)=> ((lessis X1) X0))))
% 1.13/1.34 FOF formula (<kernel.Constant object at 0x2b2ac1e7d560>, <kernel.DependentProduct object at 0x2b2ac1e7dc68>) of role type named typ_inn
% 1.13/1.34 Using role type
% 1.13/1.34 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
% 1.13/1.35 A new definition: (((eq (fofType->(fofType->fofType))) inn) (fun (X0:fofType)=> ((e_in nat) (fun (X1:fofType)=> ((lessis X1) X0)))))
% 1.13/1.35 Defined: inn:=(fun (X0:fofType)=> ((e_in nat) (fun (X1:fofType)=> ((lessis X1) X0))))
% 1.13/1.35 FOF formula (<kernel.Constant object at 0x2b2ac1e7dc68>, <kernel.Single object at 0x2b2ac1e7d560>) of role type named typ_n_1o
% 1.13/1.35 Using role type
% 1.13/1.35 Declaring n_1o:fofType
% 1.13/1.35 FOF formula (((eq fofType) n_1o) ((outn n_1) n_1)) of role definition named def_n_1o
% 1.13/1.35 A new definition: (((eq fofType) n_1o) ((outn n_1) n_1))
% 1.13/1.35 Defined: n_1o:=((outn n_1) n_1)
% 1.13/1.35 FOF formula (<kernel.Constant object at 0x2b2ac1e7d560>, <kernel.DependentProduct object at 0x2b2ac1e7dcb0>) of role type named typ_singlet_u0
% 1.13/1.35 Using role type
% 1.13/1.35 Declaring singlet_u0:(fofType->fofType)
% 1.13/1.35 FOF formula (((eq (fofType->fofType)) singlet_u0) (inn n_1)) of role definition named def_singlet_u0
% 1.13/1.35 A new definition: (((eq (fofType->fofType)) singlet_u0) (inn n_1))
% 1.13/1.35 Defined: singlet_u0:=(inn n_1)
% 1.13/1.35 FOF formula (<kernel.Constant object at 0x2b2ac1e7d2d8>, <kernel.Single object at 0x2b2ac1e7d560>) of role type named typ_n_2
% 1.13/1.35 Using role type
% 1.13/1.35 Declaring n_2:fofType
% 1.13/1.35 FOF formula (((eq fofType) n_2) ((n_pl n_1) n_1)) of role definition named def_n_2
% 1.13/1.35 A new definition: (((eq fofType) n_2) ((n_pl n_1) n_1))
% 1.13/1.35 Defined: n_2:=((n_pl n_1) n_1)
% 1.13/1.35 FOF formula (<kernel.Constant object at 0x2b2ac1e7d560>, <kernel.Single object at 0x2b2ac1e7d2d8>) of role type named typ_n_1t
% 1.13/1.35 Using role type
% 1.13/1.35 Declaring n_1t:fofType
% 1.13/1.35 FOF formula (((eq fofType) n_1t) ((outn n_2) n_1)) of role definition named def_n_1t
% 1.13/1.35 A new definition: (((eq fofType) n_1t) ((outn n_2) n_1))
% 1.13/1.35 Defined: n_1t:=((outn n_2) n_1)
% 1.13/1.35 FOF formula (<kernel.Constant object at 0x2b2ac1e7d2d8>, <kernel.Single object at 0x2b2ac1e7d560>) of role type named typ_n_2t
% 1.13/1.35 Using role type
% 1.13/1.35 Declaring n_2t:fofType
% 1.13/1.35 FOF formula (((eq fofType) n_2t) ((outn n_2) n_2)) of role definition named def_n_2t
% 1.13/1.35 A new definition: (((eq fofType) n_2t) ((outn n_2) n_2))
% 1.13/1.35 Defined: n_2t:=((outn n_2) n_2)
% 1.13/1.35 FOF formula (<kernel.Constant object at 0x2b2ac1e7d560>, <kernel.DependentProduct object at 0x2b2ac1e7dd40>) of role type named typ_pair_u0
% 1.13/1.35 Using role type
% 1.13/1.35 Declaring pair_u0:(fofType->fofType)
% 1.13/1.35 FOF formula (((eq (fofType->fofType)) pair_u0) (inn n_2)) of role definition named def_pair_u0
% 1.13/1.35 A new definition: (((eq (fofType->fofType)) pair_u0) (inn n_2))
% 1.13/1.35 Defined: pair_u0:=(inn n_2)
% 1.13/1.35 FOF formula (<kernel.Constant object at 0x2b2ac1e7db90>, <kernel.DependentProduct object at 0x2b2abeacc128>) of role type named typ_pair1type
% 1.13/1.35 Using role type
% 1.13/1.35 Declaring pair1type:(fofType->fofType)
% 1.13/1.35 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
% 1.13/1.35 A new definition: (((eq (fofType->fofType)) pair1type) (fun (X0:fofType)=> ((d_Pi (d_1to n_2)) (fun (X1:fofType)=> X0))))
% 1.13/1.35 Defined: pair1type:=(fun (X0:fofType)=> ((d_Pi (d_1to n_2)) (fun (X1:fofType)=> X0)))
% 1.13/1.35 FOF formula (<kernel.Constant object at 0x2b2ac1e7d560>, <kernel.DependentProduct object at 0x2b2ac1e7d2d8>) of role type named typ_pair1
% 1.13/1.35 Using role type
% 1.13/1.35 Declaring pair1:(fofType->(fofType->(fofType->fofType)))
% 1.13/1.35 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
% 1.13/1.35 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)))))
% 1.13/1.35 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))))
% 1.13/1.35 FOF formula (<kernel.Constant object at 0x2b2ac1e7d3b0>, <kernel.DependentProduct object at 0x2b2abeacc128>) of role type named typ_first1
% 1.13/1.35 Using role type
% 1.13/1.35 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
% 1.13/1.36 A new definition: (((eq (fofType->(fofType->fofType))) first1) (fun (X0:fofType) (X1:fofType)=> ((ap X1) n_1t)))
% 1.13/1.36 Defined: first1:=(fun (X0:fofType) (X1:fofType)=> ((ap X1) n_1t))
% 1.13/1.36 FOF formula (<kernel.Constant object at 0x2b2ac1e7d3b0>, <kernel.DependentProduct object at 0x2b2abeacc440>) of role type named typ_second1
% 1.13/1.36 Using role type
% 1.13/1.36 Declaring second1:(fofType->(fofType->fofType))
% 1.13/1.36 FOF formula (((eq (fofType->(fofType->fofType))) second1) (fun (X0:fofType) (X1:fofType)=> ((ap X1) n_2t))) of role definition named def_second1
% 1.13/1.36 A new definition: (((eq (fofType->(fofType->fofType))) second1) (fun (X0:fofType) (X1:fofType)=> ((ap X1) n_2t)))
% 1.13/1.36 Defined: second1:=(fun (X0:fofType) (X1:fofType)=> ((ap X1) n_2t))
% 1.13/1.36 FOF formula (<kernel.Constant object at 0x2b2ac1e7d3b0>, <kernel.DependentProduct object at 0x2b2abeacc1b8>) of role type named typ_pair_q0
% 1.13/1.36 Using role type
% 1.13/1.36 Declaring pair_q0:(fofType->(fofType->fofType))
% 1.13/1.36 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
% 1.13/1.36 A new definition: (((eq (fofType->(fofType->fofType))) pair_q0) (fun (X0:fofType) (X1:fofType)=> (((pair1 X0) ((first1 X0) X1)) ((second1 X0) X1))))
% 1.13/1.36 Defined: pair_q0:=(fun (X0:fofType) (X1:fofType)=> (((pair1 X0) ((first1 X0) X1)) ((second1 X0) X1)))
% 1.13/1.36 FOF formula (<kernel.Constant object at 0x2b2abeacc1b8>, <kernel.DependentProduct object at 0x2b2abeacc560>) of role type named typ_d_1out
% 1.13/1.36 Using role type
% 1.13/1.36 Declaring d_1out:(fofType->fofType)
% 1.13/1.36 FOF formula (((eq (fofType->fofType)) d_1out) (fun (X0:fofType)=> ((outn X0) n_1))) of role definition named def_d_1out
% 1.13/1.36 A new definition: (((eq (fofType->fofType)) d_1out) (fun (X0:fofType)=> ((outn X0) n_1)))
% 1.13/1.36 Defined: d_1out:=(fun (X0:fofType)=> ((outn X0) n_1))
% 1.13/1.36 FOF formula (<kernel.Constant object at 0x2b2abeacc560>, <kernel.DependentProduct object at 0x2b2abeacc050>) of role type named typ_xout
% 1.13/1.36 Using role type
% 1.13/1.36 Declaring xout:(fofType->fofType)
% 1.13/1.36 FOF formula (((eq (fofType->fofType)) xout) (fun (X0:fofType)=> ((outn X0) X0))) of role definition named def_xout
% 1.13/1.36 A new definition: (((eq (fofType->fofType)) xout) (fun (X0:fofType)=> ((outn X0) X0)))
% 1.13/1.36 Defined: xout:=(fun (X0:fofType)=> ((outn X0) X0))
% 1.13/1.36 FOF formula (<kernel.Constant object at 0x2b2abeacc050>, <kernel.DependentProduct object at 0x2b2abeacc2d8>) of role type named typ_left1to
% 1.13/1.36 Using role type
% 1.13/1.36 Declaring left1to:(fofType->(fofType->(fofType->fofType)))
% 1.13/1.36 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
% 1.13/1.36 A new definition: (((eq (fofType->(fofType->(fofType->fofType)))) left1to) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn X0) ((inn X1) X2))))
% 1.13/1.36 Defined: left1to:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn X0) ((inn X1) X2)))
% 1.13/1.36 FOF formula (<kernel.Constant object at 0x2b2abeacc2d8>, <kernel.DependentProduct object at 0x2b2abeacc7a0>) of role type named typ_right1to
% 1.13/1.36 Using role type
% 1.13/1.36 Declaring right1to:(fofType->(fofType->(fofType->fofType)))
% 1.13/1.36 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
% 1.13/1.36 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)))))
% 1.13/1.36 Defined: right1to:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn ((n_pl X0) X1)) ((n_pl X0) ((inn X1) X2))))
% 1.13/1.36 FOF formula (<kernel.Constant object at 0x2b2abeacc7a0>, <kernel.DependentProduct object at 0x2b2abeacc8c0>) of role type named typ_left
% 1.13/1.36 Using role type
% 1.13/1.36 Declaring left:(fofType->(fofType->(fofType->(fofType->fofType))))
% 1.13/1.36 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
% 1.13/1.37 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))))))
% 1.13/1.37 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)))))
% 1.13/1.37 FOF formula (<kernel.Constant object at 0x2b2abeacc8c0>, <kernel.DependentProduct object at 0x2b2abeacc248>) of role type named typ_right
% 1.13/1.37 Using role type
% 1.13/1.37 Declaring right:(fofType->(fofType->(fofType->(fofType->fofType))))
% 1.13/1.37 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
% 1.13/1.37 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))))))
% 1.13/1.37 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)))))
% 1.13/1.37 FOF formula (<kernel.Constant object at 0x2b2abeacc248>, <kernel.DependentProduct object at 0x2b2abeacc4d0>) of role type named typ_left_f1
% 1.13/1.37 Using role type
% 1.13/1.37 Declaring left_f1:(fofType->(fofType->(fofType->(fofType->fofType))))
% 1.13/1.37 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
% 1.13/1.37 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) left_f1) (fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((left X0) X2) X1)))
% 1.13/1.37 Defined: left_f1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((left X0) X2) X1))
% 1.13/1.37 FOF formula (<kernel.Constant object at 0x2b2abeacc4d0>, <kernel.DependentProduct object at 0x2b2abeacc0e0>) of role type named typ_left_f2
% 1.13/1.37 Using role type
% 1.13/1.37 Declaring left_f2:(fofType->(fofType->(fofType->(fofType->fofType))))
% 1.13/1.37 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
% 1.13/1.37 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))))
% 1.13/1.37 Defined: left_f2:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((left X0) X1) X2) ((((left_f1 X0) X1) X2) X3)))
% 1.13/1.37 FOF formula (<kernel.Constant object at 0x2b2abeacc0e0>, <kernel.Single object at 0x2b2abeacc4d0>) of role type named typ_frac
% 1.13/1.37 Using role type
% 1.13/1.37 Declaring frac:fofType
% 1.13/1.37 FOF formula (((eq fofType) frac) (pair1type nat)) of role definition named def_frac
% 1.13/1.37 A new definition: (((eq fofType) frac) (pair1type nat))
% 1.13/1.37 Defined: frac:=(pair1type nat)
% 1.13/1.37 FOF formula (<kernel.Constant object at 0x2b2abeacc950>, <kernel.DependentProduct object at 0x2b2abeacc998>) of role type named typ_n_fr
% 1.13/1.37 Using role type
% 1.13/1.37 Declaring n_fr:(fofType->(fofType->fofType))
% 1.13/1.37 FOF formula (((eq (fofType->(fofType->fofType))) n_fr) (pair1 nat)) of role definition named def_n_fr
% 1.13/1.37 A new definition: (((eq (fofType->(fofType->fofType))) n_fr) (pair1 nat))
% 1.13/1.37 Defined: n_fr:=(pair1 nat)
% 1.13/1.37 FOF formula (<kernel.Constant object at 0x2b2abeacc7a0>, <kernel.DependentProduct object at 0x2b2abeacc440>) of role type named typ_num
% 1.13/1.37 Using role type
% 1.13/1.37 Declaring num:(fofType->fofType)
% 1.13/1.37 FOF formula (((eq (fofType->fofType)) num) (first1 nat)) of role definition named def_num
% 1.13/1.37 A new definition: (((eq (fofType->fofType)) num) (first1 nat))
% 1.13/1.37 Defined: num:=(first1 nat)
% 1.13/1.37 FOF formula (<kernel.Constant object at 0x2b2abeacca70>, <kernel.DependentProduct object at 0x2b2abeacc248>) of role type named typ_den
% 1.13/1.37 Using role type
% 1.13/1.37 Declaring den:(fofType->fofType)
% 1.13/1.37 FOF formula (((eq (fofType->fofType)) den) (second1 nat)) of role definition named def_den
% 1.19/1.40 A new definition: (((eq (fofType->fofType)) den) (second1 nat))
% 1.19/1.40 Defined: den:=(second1 nat)
% 1.19/1.40 FOF formula (<kernel.Constant object at 0x2b2abeacc4d0>, <kernel.DependentProduct object at 0x2b2abeacc710>) of role type named typ_n_eq
% 1.19/1.40 Using role type
% 1.19/1.40 Declaring n_eq:(fofType->(fofType->Prop))
% 1.19/1.40 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
% 1.19/1.40 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)))))
% 1.19/1.40 Defined: n_eq:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0))))
% 1.19/1.40 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((n_eq X0) X0))) of role axiom named satz37
% 1.19/1.40 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((n_eq X0) X0)))
% 1.19/1.40 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
% 1.19/1.40 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))))))
% 1.19/1.40 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
% 1.19/1.40 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)))))))))
% 1.19/1.40 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
% 1.19/1.40 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)))))))
% 1.19/1.40 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
% 1.19/1.40 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)))))
% 1.19/1.40 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
% 1.19/1.40 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)))))))))
% 1.19/1.40 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
% 1.19/1.40 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))))))))
% 1.19/1.40 FOF formula (<kernel.Constant object at 0x2b2abeacca70>, <kernel.DependentProduct object at 0x2b2abeaccd40>) of role type named typ_moref
% 1.19/1.42 Using role type
% 1.19/1.42 Declaring moref:(fofType->(fofType->Prop))
% 1.19/1.42 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
% 1.19/1.42 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)))))
% 1.19/1.42 Defined: moref:=(fun (X0:fofType) (X1:fofType)=> ((d_29_ii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0))))
% 1.19/1.42 FOF formula (<kernel.Constant object at 0x2b2abeaccd40>, <kernel.DependentProduct object at 0x2b2abeacc248>) of role type named typ_lessf
% 1.19/1.42 Using role type
% 1.19/1.42 Declaring lessf:(fofType->(fofType->Prop))
% 1.19/1.42 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
% 1.19/1.42 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)))))
% 1.19/1.42 Defined: lessf:=(fun (X0:fofType) (X1:fofType)=> ((iii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0))))
% 1.19/1.42 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
% 1.19/1.42 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))))))
% 1.19/1.42 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
% 1.19/1.42 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))))))
% 1.19/1.42 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
% 1.19/1.42 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))))))
% 1.19/1.42 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
% 1.19/1.42 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))))))
% 1.19/1.42 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
% 1.19/1.42 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))))))
% 1.19/1.42 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
% 1.19/1.42 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))))))))))))
% 1.19/1.42 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
% 1.19/1.44 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))))))))))))
% 1.19/1.44 FOF formula (<kernel.Constant object at 0x2b2abeaccfc8>, <kernel.DependentProduct object at 0x2b2abeacce60>) of role type named typ_moreq
% 1.19/1.44 Using role type
% 1.19/1.44 Declaring moreq:(fofType->(fofType->Prop))
% 1.19/1.44 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
% 1.19/1.44 A new definition: (((eq (fofType->(fofType->Prop))) moreq) (fun (X0:fofType) (X1:fofType)=> ((l_or ((moref X0) X1)) ((n_eq X0) X1))))
% 1.19/1.44 Defined: moreq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((moref X0) X1)) ((n_eq X0) X1)))
% 1.19/1.44 FOF formula (<kernel.Constant object at 0x2b2abeacc518>, <kernel.DependentProduct object at 0x2b2abeaccb90>) of role type named typ_lesseq
% 1.19/1.44 Using role type
% 1.19/1.44 Declaring lesseq:(fofType->(fofType->Prop))
% 1.19/1.44 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
% 1.19/1.44 A new definition: (((eq (fofType->(fofType->Prop))) lesseq) (fun (X0:fofType) (X1:fofType)=> ((l_or ((lessf X0) X1)) ((n_eq X0) X1))))
% 1.19/1.44 Defined: lesseq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((lessf X0) X1)) ((n_eq X0) X1)))
% 1.19/1.44 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
% 1.19/1.44 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)))))))
% 1.19/1.44 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
% 1.19/1.44 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)))))))
% 1.19/1.44 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
% 1.19/1.44 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))))))
% 1.19/1.44 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
% 1.19/1.44 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))))))
% 1.19/1.44 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
% 1.19/1.44 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)))))))
% 1.19/1.44 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
% 1.27/1.47 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)))))))
% 1.27/1.47 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
% 1.27/1.47 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))))))
% 1.27/1.47 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
% 1.27/1.47 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))))))
% 1.27/1.47 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
% 1.27/1.47 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))))))))))))
% 1.27/1.47 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
% 1.27/1.47 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))))))))))))
% 1.27/1.47 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
% 1.27/1.47 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))))))
% 1.27/1.47 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
% 1.27/1.47 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))))))
% 1.27/1.47 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
% 1.27/1.47 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)))))))))
% 1.27/1.47 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
% 1.28/1.49 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)))))))))
% 1.28/1.49 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 axiom named satz51b
% 1.28/1.49 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)=> (((lessf X0) X1)->(((lesseq X1) X2)->((lessf X0) X2)))))))))
% 1.28/1.49 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)=> (((moreq X0) X1)->(((moref X1) X2)->((moref X0) X2))))))))) of role axiom named satz51c
% 1.28/1.49 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)=> (((moreq X0) X1)->(((moref X1) X2)->((moref X0) X2)))))))))
% 1.28/1.49 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)=> (((moref X0) X1)->(((moreq X1) X2)->((moref X0) X2))))))))) of role axiom named satz51d
% 1.28/1.49 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)=> (((moref X0) X1)->(((moreq X1) X2)->((moref X0) X2)))))))))
% 1.28/1.49 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)=> (((lesseq X0) X1)->(((lesseq X1) X2)->((lesseq X0) X2))))))))) of role axiom named satz52
% 1.28/1.49 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)->(((lesseq X1) X2)->((lesseq X0) X2)))))))))
% 1.28/1.49 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((l_some frac) (fun (X1:fofType)=> ((moref X1) X0))))) of role axiom named satz53
% 1.28/1.49 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((l_some frac) (fun (X1:fofType)=> ((moref X1) X0)))))
% 1.28/1.49 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((l_some frac) (fun (X1:fofType)=> ((lessf X1) X0))))) of role axiom named satz54
% 1.28/1.49 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((l_some frac) (fun (X1:fofType)=> ((lessf X1) X0)))))
% 1.28/1.49 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> (((lessf X0) X1)->((l_some frac) (fun (X2:fofType)=> ((d_and ((lessf X0) X2)) ((lessf X2) X1))))))))) of role axiom named satz55
% 1.28/1.49 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)=> (((lessf X0) X1)->((l_some frac) (fun (X2:fofType)=> ((d_and ((lessf X0) X2)) ((lessf X2) X1)))))))))
% 1.28/1.49 FOF formula (<kernel.Constant object at 0x2b2abead0320>, <kernel.DependentProduct object at 0x2b2abead0d40>) of role type named typ_n_pf
% 1.28/1.49 Using role type
% 1.28/1.49 Declaring n_pf:(fofType->(fofType->fofType))
% 1.28/1.49 FOF formula (((eq (fofType->(fofType->fofType))) n_pf) (fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_pl ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))) ((n_ts (den X0)) (den X1))))) of role definition named def_n_pf
% 1.32/1.52 A new definition: (((eq (fofType->(fofType->fofType))) n_pf) (fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_pl ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))) ((n_ts (den X0)) (den X1)))))
% 1.32/1.52 Defined: n_pf:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_pl ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))) ((n_ts (den X0)) (den X1))))
% 1.32/1.52 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)=> (((n_eq X0) X1)->(((n_eq X2) X3)->((n_eq ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))) of role axiom named satz56
% 1.32/1.52 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)=> (((n_eq X0) X1)->(((n_eq X2) X3)->((n_eq ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 1.32/1.52 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_pf ((n_fr X0) X2)) ((n_fr X1) X2))) ((n_fr ((n_pl X0) X1)) X2)))))))) of role axiom named satz57
% 1.32/1.52 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_pf ((n_fr X0) X2)) ((n_fr X1) X2))) ((n_fr ((n_pl X0) X1)) X2))))))))
% 1.32/1.52 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_pl X0) X1)) X2)) ((n_pf ((n_fr X0) X2)) ((n_fr X1) X2))))))))) of role axiom named satz57a
% 1.32/1.52 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_pl X0) X1)) X2)) ((n_pf ((n_fr X0) X2)) ((n_fr X1) X2)))))))))
% 1.32/1.52 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 ((n_pf X0) X1)) ((n_pf X1) X0)))))) of role axiom named satz58
% 1.32/1.52 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 ((n_pf X0) X1)) ((n_pf X1) X0))))))
% 1.32/1.52 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 ((n_pf ((n_pf X0) X1)) X2)) ((n_pf X0) ((n_pf X1) X2))))))))) of role axiom named satz59
% 1.32/1.52 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 ((n_pf ((n_pf X0) X1)) X2)) ((n_pf X0) ((n_pf X1) X2)))))))))
% 1.32/1.52 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 ((n_pf X0) X1)) X0))))) of role axiom named satz60
% 1.32/1.52 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 ((n_pf X0) X1)) X0)))))
% 1.32/1.52 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) ((n_pf X0) X1)))))) of role axiom named satz60a
% 1.32/1.52 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) ((n_pf X0) X1))))))
% 1.34/1.54 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)=> (((moref X0) X1)->((moref ((n_pf X0) X2)) ((n_pf X1) X2))))))))) of role axiom named satz61
% 1.34/1.54 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)=> (((moref X0) X1)->((moref ((n_pf X0) X2)) ((n_pf X1) X2)))))))))
% 1.34/1.54 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 ((n_pf X0) X2)) ((n_pf X1) X2))))))))) of role axiom named satz62b
% 1.34/1.54 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 ((n_pf X0) X2)) ((n_pf X1) X2)))))))))
% 1.34/1.54 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 ((n_pf X0) X2)) ((n_pf X1) X2))))))))) of role axiom named satz62c
% 1.34/1.54 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 ((n_pf X0) X2)) ((n_pf X1) X2)))))))))
% 1.34/1.54 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)=> (((moref X0) X1)->((moref ((n_pf X2) X0)) ((n_pf X2) X1))))))))) of role axiom named satz62d
% 1.34/1.54 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)=> (((moref X0) X1)->((moref ((n_pf X2) X0)) ((n_pf X2) X1)))))))))
% 1.34/1.54 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 ((n_pf X2) X0)) ((n_pf X2) X1))))))))) of role axiom named satz62e
% 1.34/1.54 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 ((n_pf X2) X0)) ((n_pf X2) X1)))))))))
% 1.34/1.54 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 ((n_pf X2) X0)) ((n_pf X2) X1))))))))) of role axiom named satz62f
% 1.34/1.54 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 ((n_pf X2) X0)) ((n_pf X2) X1)))))))))
% 1.34/1.54 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)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))) of role axiom named satz62g
% 1.34/1.54 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)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 1.34/1.57 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)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_pf X2) X0)) ((n_pf X3) X1)))))))))))) of role axiom named satz62h
% 1.34/1.57 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)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_pf X2) X0)) ((n_pf X3) X1))))))))))))
% 1.34/1.57 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)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))) of role axiom named satz62j
% 1.34/1.57 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)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 1.34/1.57 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)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X2) X0)) ((n_pf X3) X1)))))))))))) of role axiom named satz62k
% 1.34/1.57 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)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X2) X0)) ((n_pf X3) X1))))))))))))
% 1.34/1.57 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)=> (((moref ((n_pf X0) X2)) ((n_pf X1) X2))->((moref X0) X1)))))))) of role axiom named satz63a
% 1.34/1.57 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)=> (((moref ((n_pf X0) X2)) ((n_pf X1) X2))->((moref X0) X1))))))))
% 1.34/1.57 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 ((n_pf X0) X2)) ((n_pf X1) X2))->((n_eq X0) X1)))))))) of role axiom named satz63b
% 1.34/1.57 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 ((n_pf X0) X2)) ((n_pf X1) X2))->((n_eq X0) X1))))))))
% 1.34/1.57 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 ((n_pf X0) X2)) ((n_pf X1) X2))->((lessf X0) X1)))))))) of role axiom named satz63c
% 1.34/1.57 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 ((n_pf X0) X2)) ((n_pf X1) X2))->((lessf X0) X1))))))))
% 1.34/1.60 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)=> (((moref ((n_pf X2) X0)) ((n_pf X2) X1))->((moref X0) X1)))))))) of role axiom named satz63d
% 1.34/1.60 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)=> (((moref ((n_pf X2) X0)) ((n_pf X2) X1))->((moref X0) X1))))))))
% 1.34/1.60 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 ((n_pf X2) X0)) ((n_pf X2) X1))->((n_eq X0) X1)))))))) of role axiom named satz63e
% 1.34/1.60 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 ((n_pf X2) X0)) ((n_pf X2) X1))->((n_eq X0) X1))))))))
% 1.34/1.60 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 ((n_pf X2) X0)) ((n_pf X2) X1))->((lessf X0) X1)))))))) of role axiom named satz63f
% 1.34/1.60 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 ((n_pf X2) X0)) ((n_pf X2) X1))->((lessf X0) X1))))))))
% 1.34/1.60 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)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))) of role axiom named satz64
% 1.34/1.60 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)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 1.34/1.60 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)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))) of role axiom named satz64a
% 1.34/1.60 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)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 1.34/1.60 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)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))) of role axiom named satz65a
% 1.34/1.60 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)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 1.34/1.60 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)->(((moreq X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))) of role axiom named satz65b
% 1.34/1.62 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)->(((moreq X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 1.34/1.62 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)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))) of role axiom named satz65c
% 1.34/1.62 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)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 1.34/1.62 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)->(((lesseq X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))) of role axiom named satz65d
% 1.34/1.62 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)->(((lesseq X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 1.34/1.62 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)->(((moreq X2) X3)->((moreq ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))) of role axiom named satz66
% 1.34/1.62 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)->(((moreq X2) X3)->((moreq ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 1.34/1.62 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)->(((lesseq X2) X3)->((lesseq ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))) of role axiom named satz66a
% 1.34/1.62 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)->(((lesseq X2) X3)->((lesseq ((n_pf X0) X2)) ((n_pf X1) X3))))))))))))
% 1.34/1.62 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)=> (((n_eq ((n_pf X1) X2)) X0)->(((n_eq ((n_pf X1) X3)) X0)->((n_eq X2) X3))))))))))) of role axiom named satz67b
% 1.43/1.64 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)=> (((n_eq ((n_pf X1) X2)) X0)->(((n_eq ((n_pf X1) X3)) X0)->((n_eq X2) X3)))))))))))
% 1.43/1.64 FOF formula (<kernel.Constant object at 0x2b2abead0fc8>, <kernel.DependentProduct object at 0x2b2abead03f8>) of role type named typ_d_367_vo
% 1.43/1.64 Using role type
% 1.43/1.64 Declaring d_367_vo:(fofType->(fofType->fofType))
% 1.43/1.64 FOF formula (((eq (fofType->(fofType->fofType))) d_367_vo) (fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))))) of role definition named def_d_367_vo
% 1.43/1.64 A new definition: (((eq (fofType->(fofType->fofType))) d_367_vo) (fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0))))))
% 1.43/1.64 Defined: d_367_vo:=(fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))))
% 1.43/1.64 FOF formula (<kernel.Constant object at 0x2b2abead0758>, <kernel.DependentProduct object at 0x2b2abead61b8>) of role type named typ_d_367_w
% 1.43/1.64 Using role type
% 1.43/1.64 Declaring d_367_w:(fofType->(fofType->fofType))
% 1.43/1.64 FOF formula (((eq (fofType->(fofType->fofType))) d_367_w) (fun (X0:fofType) (X1:fofType)=> ((n_fr ((d_367_vo X0) X1)) ((n_ts (den X0)) (den X1))))) of role definition named def_d_367_w
% 1.43/1.64 A new definition: (((eq (fofType->(fofType->fofType))) d_367_w) (fun (X0:fofType) (X1:fofType)=> ((n_fr ((d_367_vo X0) X1)) ((n_ts (den X0)) (den X1)))))
% 1.43/1.64 Defined: d_367_w:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((d_367_vo X0) X1)) ((n_ts (den X0)) (den X1))))
% 1.43/1.64 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)->((l_some frac) (fun (X2:fofType)=> ((n_eq ((n_pf X1) X2)) X0)))))))) of role axiom named satz67a
% 1.43/1.64 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)->((l_some frac) (fun (X2:fofType)=> ((n_eq ((n_pf X1) X2)) X0))))))))
% 1.43/1.64 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)->((n_eq ((n_pf X1) ((d_367_w X0) X1))) X0)))))) of role axiom named k_satz67c
% 1.43/1.64 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)->((n_eq ((n_pf X1) ((d_367_w X0) X1))) X0))))))
% 1.43/1.64 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)->((n_eq X0) ((n_pf X1) ((d_367_w X0) X1)))))))) of role axiom named satz67d
% 1.43/1.64 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)->((n_eq X0) ((n_pf X1) ((d_367_w X0) X1))))))))
% 1.43/1.64 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)=> (((moref X0) X1)->(((n_eq ((n_pf X1) X2)) X0)->((n_eq X2) ((d_367_w X0) X1)))))))))) of role axiom named satz67e
% 1.43/1.64 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)=> (((moref X0) X1)->(((n_eq ((n_pf X1) X2)) X0)->((n_eq X2) ((d_367_w X0) X1))))))))))
% 1.43/1.64 FOF formula (<kernel.Constant object at 0x2b2abead0758>, <kernel.DependentProduct object at 0x2b2abead6440>) of role type named typ_n_tf
% 1.43/1.64 Using role type
% 1.43/1.64 Declaring n_tf:(fofType->(fofType->fofType))
% 1.43/1.64 FOF formula (((eq (fofType->(fofType->fofType))) n_tf) (fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_ts (num X0)) (num X1))) ((n_ts (den X0)) (den X1))))) of role definition named def_n_tf
% 1.43/1.67 A new definition: (((eq (fofType->(fofType->fofType))) n_tf) (fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_ts (num X0)) (num X1))) ((n_ts (den X0)) (den X1)))))
% 1.43/1.67 Defined: n_tf:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_ts (num X0)) (num X1))) ((n_ts (den X0)) (den X1))))
% 1.43/1.67 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)=> (((n_eq X0) X1)->(((n_eq X2) X3)->((n_eq ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))) of role axiom named satz68
% 1.43/1.67 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)=> (((n_eq X0) X1)->(((n_eq X2) X3)->((n_eq ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 1.43/1.67 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 ((n_tf X0) X1)) ((n_tf X1) X0)))))) of role axiom named satz69
% 1.43/1.67 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 ((n_tf X0) X1)) ((n_tf X1) X0))))))
% 1.43/1.67 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 ((n_tf ((n_tf X0) X1)) X2)) ((n_tf X0) ((n_tf X1) X2))))))))) of role axiom named satz70
% 1.43/1.67 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 ((n_tf ((n_tf X0) X1)) X2)) ((n_tf X0) ((n_tf X1) X2)))))))))
% 1.43/1.67 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 ((n_tf X0) ((n_pf X1) X2))) ((n_pf ((n_tf X0) X1)) ((n_tf X0) X2))))))))) of role axiom named satz71
% 1.43/1.67 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 ((n_tf X0) ((n_pf X1) X2))) ((n_pf ((n_tf X0) X1)) ((n_tf X0) X2)))))))))
% 1.43/1.67 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)=> (((moref X0) X1)->((moref ((n_tf X0) X2)) ((n_tf X1) X2))))))))) of role axiom named satz72a
% 1.43/1.67 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)=> (((moref X0) X1)->((moref ((n_tf X0) X2)) ((n_tf X1) X2)))))))))
% 1.43/1.67 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 ((n_tf X0) X2)) ((n_tf X1) X2))))))))) of role axiom named satz72b
% 1.43/1.67 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 ((n_tf X0) X2)) ((n_tf X1) X2)))))))))
% 1.43/1.67 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 ((n_tf X0) X2)) ((n_tf X1) X2))))))))) of role axiom named satz72c
% 1.50/1.69 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 ((n_tf X0) X2)) ((n_tf X1) X2)))))))))
% 1.50/1.69 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)=> (((moref X0) X1)->((moref ((n_tf X2) X0)) ((n_tf X2) X1))))))))) of role axiom named satz72d
% 1.50/1.69 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)=> (((moref X0) X1)->((moref ((n_tf X2) X0)) ((n_tf X2) X1)))))))))
% 1.50/1.69 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 ((n_tf X2) X0)) ((n_tf X2) X1))))))))) of role axiom named satz72e
% 1.50/1.69 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 ((n_tf X2) X0)) ((n_tf X2) X1)))))))))
% 1.50/1.69 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 ((n_tf X2) X0)) ((n_tf X2) X1))))))))) of role axiom named satz72f
% 1.50/1.69 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 ((n_tf X2) X0)) ((n_tf X2) X1)))))))))
% 1.50/1.69 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)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))) of role axiom named satz72g
% 1.50/1.69 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)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 1.50/1.69 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)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_tf X2) X0)) ((n_tf X3) X1)))))))))))) of role axiom named satz72h
% 1.50/1.69 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)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_tf X2) X0)) ((n_tf X3) X1))))))))))))
% 1.50/1.69 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)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))) of role axiom named satz72j
% 1.50/1.69 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)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 1.50/1.72 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)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X2) X0)) ((n_tf X3) X1)))))))))))) of role axiom named satz72k
% 1.50/1.72 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)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X2) X0)) ((n_tf X3) X1))))))))))))
% 1.50/1.72 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)=> (((moref ((n_tf X0) X2)) ((n_tf X1) X2))->((moref X0) X1)))))))) of role axiom named satz73a
% 1.50/1.72 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)=> (((moref ((n_tf X0) X2)) ((n_tf X1) X2))->((moref X0) X1))))))))
% 1.50/1.72 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 ((n_tf X0) X2)) ((n_tf X1) X2))->((n_eq X0) X1)))))))) of role axiom named satz73b
% 1.50/1.72 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 ((n_tf X0) X2)) ((n_tf X1) X2))->((n_eq X0) X1))))))))
% 1.50/1.72 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 ((n_tf X0) X2)) ((n_tf X1) X2))->((lessf X0) X1)))))))) of role axiom named satz73c
% 1.50/1.72 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 ((n_tf X0) X2)) ((n_tf X1) X2))->((lessf X0) X1))))))))
% 1.50/1.72 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)=> (((moref ((n_tf X2) X0)) ((n_tf X2) X1))->((moref X0) X1)))))))) of role axiom named satz73d
% 1.50/1.72 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)=> (((moref ((n_tf X2) X0)) ((n_tf X2) X1))->((moref X0) X1))))))))
% 1.50/1.72 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 ((n_tf X2) X0)) ((n_tf X2) X1))->((n_eq X0) X1)))))))) of role axiom named satz73e
% 1.50/1.72 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 ((n_tf X2) X0)) ((n_tf X2) X1))->((n_eq X0) X1))))))))
% 1.50/1.72 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 ((n_tf X2) X0)) ((n_tf X2) X1))->((lessf X0) X1)))))))) of role axiom named satz73f
% 1.50/1.74 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 ((n_tf X2) X0)) ((n_tf X2) X1))->((lessf X0) X1))))))))
% 1.50/1.74 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)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))) of role axiom named satz74
% 1.50/1.74 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)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 1.50/1.74 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)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))) of role axiom named satz74a
% 1.50/1.74 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)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 1.50/1.74 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)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))) of role axiom named satz75a
% 1.50/1.74 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)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 1.50/1.74 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)->(((moreq X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))) of role axiom named satz75b
% 1.50/1.74 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)->(((moreq X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 1.50/1.74 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)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))) of role axiom named satz75c
% 1.50/1.74 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)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 1.57/1.77 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)->(((lesseq X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))) of role axiom named satz75d
% 1.57/1.77 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)->(((lesseq X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 1.57/1.77 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)->(((moreq X2) X3)->((moreq ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))) of role axiom named satz76
% 1.57/1.77 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)->(((moreq X2) X3)->((moreq ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 1.57/1.77 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)->(((lesseq X2) X3)->((lesseq ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))) of role axiom named satz76a
% 1.57/1.77 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)->(((lesseq X2) X3)->((lesseq ((n_tf X0) X2)) ((n_tf X1) X3))))))))))))
% 1.57/1.77 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)=> (((n_eq ((n_tf X1) X2)) X0)->(((n_eq ((n_tf X1) X3)) X0)->((n_eq X2) X3))))))))))) of role axiom named satz77b
% 1.57/1.77 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)=> (((n_eq ((n_tf X1) X2)) X0)->(((n_eq ((n_tf X1) X3)) X0)->((n_eq X2) X3)))))))))))
% 1.57/1.77 FOF formula (<kernel.Constant object at 0x2b2abead6170>, <kernel.DependentProduct object at 0x2b2abead6518>) of role type named typ_d_477_v
% 1.57/1.77 Using role type
% 1.57/1.77 Declaring d_477_v:(fofType->(fofType->fofType))
% 1.57/1.77 FOF formula (((eq (fofType->(fofType->fofType))) d_477_v) (fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_ts (num X0)) (den X1))) ((n_ts (den X0)) (num X1))))) of role definition named def_d_477_v
% 1.57/1.77 A new definition: (((eq (fofType->(fofType->fofType))) d_477_v) (fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_ts (num X0)) (den X1))) ((n_ts (den X0)) (num X1)))))
% 1.57/1.77 Defined: d_477_v:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_ts (num X0)) (den X1))) ((n_ts (den X0)) (num X1))))
% 1.57/1.77 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((n_eq ((n_tf X1) X2)) X0))))))) of role axiom named satz77a
% 1.57/1.77 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)=> ((l_some frac) (fun (X2:fofType)=> ((n_eq ((n_tf X1) X2)) X0)))))))
% 1.58/1.78 FOF formula (<kernel.Constant object at 0x2b2abeb5fa28>, <kernel.DependentProduct object at 0x2b2abf216b48>) of role type named typ_inf
% 1.58/1.78 Using role type
% 1.58/1.78 Declaring inf:(fofType->(fofType->Prop))
% 1.58/1.78 FOF formula (((eq (fofType->(fofType->Prop))) inf) (esti frac)) of role definition named def_inf
% 1.58/1.78 A new definition: (((eq (fofType->(fofType->Prop))) inf) (esti frac))
% 1.58/1.78 Defined: inf:=(esti frac)
% 1.58/1.78 FOF formula (<kernel.Constant object at 0x2b2abe79ca28>, <kernel.Single object at 0x2b2abf216440>) of role type named typ_rat
% 1.58/1.78 Using role type
% 1.58/1.78 Declaring rat:fofType
% 1.58/1.78 FOF formula (((eq fofType) rat) ((ect frac) n_eq)) of role definition named def_rat
% 1.58/1.78 A new definition: (((eq fofType) rat) ((ect frac) n_eq))
% 1.58/1.78 Defined: rat:=((ect frac) n_eq)
% 1.58/1.78 FOF formula (<kernel.Constant object at 0x2b2abe79c1b8>, <kernel.DependentProduct object at 0x2b2abf216cf8>) of role type named typ_rt_is
% 1.58/1.78 Using role type
% 1.58/1.78 Declaring rt_is:(fofType->(fofType->Prop))
% 1.58/1.78 FOF formula (((eq (fofType->(fofType->Prop))) rt_is) (e_is rat)) of role definition named def_rt_is
% 1.58/1.78 A new definition: (((eq (fofType->(fofType->Prop))) rt_is) (e_is rat))
% 1.58/1.78 Defined: rt_is:=(e_is rat)
% 1.58/1.78 FOF formula (<kernel.Constant object at 0x2b2abf216b48>, <kernel.DependentProduct object at 0x2b2abf216b00>) of role type named typ_rt_nis
% 1.58/1.78 Using role type
% 1.58/1.78 Declaring rt_nis:(fofType->(fofType->Prop))
% 1.58/1.78 FOF formula (((eq (fofType->(fofType->Prop))) rt_nis) (fun (X0:fofType) (X1:fofType)=> (d_not ((rt_is X0) X1)))) of role definition named def_rt_nis
% 1.58/1.78 A new definition: (((eq (fofType->(fofType->Prop))) rt_nis) (fun (X0:fofType) (X1:fofType)=> (d_not ((rt_is X0) X1))))
% 1.58/1.78 Defined: rt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rt_is X0) X1)))
% 1.58/1.78 FOF formula (<kernel.Constant object at 0x2b2abf216b00>, <kernel.DependentProduct object at 0x2b2abf2167e8>) of role type named typ_rt_some
% 1.58/1.78 Using role type
% 1.58/1.78 Declaring rt_some:((fofType->Prop)->Prop)
% 1.58/1.78 FOF formula (((eq ((fofType->Prop)->Prop)) rt_some) (l_some rat)) of role definition named def_rt_some
% 1.58/1.78 A new definition: (((eq ((fofType->Prop)->Prop)) rt_some) (l_some rat))
% 1.58/1.78 Defined: rt_some:=(l_some rat)
% 1.58/1.78 FOF formula (<kernel.Constant object at 0x2b2abf2164d0>, <kernel.DependentProduct object at 0x2b2abf2167e8>) of role type named typ_rt_all
% 1.58/1.78 Using role type
% 1.58/1.78 Declaring rt_all:((fofType->Prop)->Prop)
% 1.58/1.78 FOF formula (((eq ((fofType->Prop)->Prop)) rt_all) (all rat)) of role definition named def_rt_all
% 1.58/1.78 A new definition: (((eq ((fofType->Prop)->Prop)) rt_all) (all rat))
% 1.58/1.78 Defined: rt_all:=(all rat)
% 1.58/1.78 FOF formula (<kernel.Constant object at 0x2b2abf216cb0>, <kernel.DependentProduct object at 0x2b2abf2167e8>) of role type named typ_rt_one
% 1.58/1.78 Using role type
% 1.58/1.78 Declaring rt_one:((fofType->Prop)->Prop)
% 1.58/1.78 FOF formula (((eq ((fofType->Prop)->Prop)) rt_one) (one rat)) of role definition named def_rt_one
% 1.58/1.78 A new definition: (((eq ((fofType->Prop)->Prop)) rt_one) (one rat))
% 1.58/1.78 Defined: rt_one:=(one rat)
% 1.58/1.78 FOF formula (<kernel.Constant object at 0x2b2abf216b48>, <kernel.DependentProduct object at 0x2b2abf216908>) of role type named typ_rt_in
% 1.58/1.78 Using role type
% 1.58/1.78 Declaring rt_in:(fofType->(fofType->Prop))
% 1.58/1.78 FOF formula (((eq (fofType->(fofType->Prop))) rt_in) (esti rat)) of role definition named def_rt_in
% 1.58/1.78 A new definition: (((eq (fofType->(fofType->Prop))) rt_in) (esti rat))
% 1.58/1.78 Defined: rt_in:=(esti rat)
% 1.58/1.78 FOF formula (<kernel.Constant object at 0x2b2abf216b00>, <kernel.DependentProduct object at 0x2b2abf2163f8>) of role type named typ_ratof
% 1.58/1.78 Using role type
% 1.58/1.78 Declaring ratof:(fofType->fofType)
% 1.58/1.78 FOF formula (((eq (fofType->fofType)) ratof) ((ectelt frac) n_eq)) of role definition named def_ratof
% 1.58/1.78 A new definition: (((eq (fofType->fofType)) ratof) ((ectelt frac) n_eq))
% 1.58/1.78 Defined: ratof:=((ectelt frac) n_eq)
% 1.58/1.78 FOF formula (<kernel.Constant object at 0x2b2abf2163f8>, <kernel.DependentProduct object at 0x2b2abf2168c0>) of role type named typ_class
% 1.58/1.78 Using role type
% 1.58/1.78 Declaring class:(fofType->fofType)
% 1.58/1.78 FOF formula (((eq (fofType->fofType)) class) ((ecect frac) n_eq)) of role definition named def_class
% 1.58/1.78 A new definition: (((eq (fofType->fofType)) class) ((ecect frac) n_eq))
% 1.58/1.78 Defined: class:=((ecect frac) n_eq)
% 1.58/1.80 FOF formula (<kernel.Constant object at 0x2b2abf2168c0>, <kernel.DependentProduct object at 0x2b2abf216758>) of role type named typ_fixf
% 1.58/1.80 Using role type
% 1.58/1.80 Declaring fixf:(fofType->(fofType->Prop))
% 1.58/1.80 FOF formula (((eq (fofType->(fofType->Prop))) fixf) ((fixfu2 frac) n_eq)) of role definition named def_fixf
% 1.58/1.80 A new definition: (((eq (fofType->(fofType->Prop))) fixf) ((fixfu2 frac) n_eq))
% 1.58/1.80 Defined: fixf:=((fixfu2 frac) n_eq)
% 1.58/1.80 FOF formula (<kernel.Constant object at 0x2b2abf216758>, <kernel.DependentProduct object at 0x2b2abf216998>) of role type named typ_indrat
% 1.58/1.80 Using role type
% 1.58/1.80 Declaring indrat:(fofType->(fofType->(fofType->(fofType->fofType))))
% 1.58/1.80 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) indrat) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((((indeq2 frac) n_eq) X2) X3) X0) X1))) of role definition named def_indrat
% 1.58/1.80 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->fofType))))) indrat) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((((indeq2 frac) n_eq) X2) X3) X0) X1)))
% 1.58/1.80 Defined: indrat:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((((indeq2 frac) n_eq) X2) X3) X0) X1))
% 1.58/1.80 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((rt_is X0) X0))) of role axiom named satz78
% 1.58/1.80 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((rt_is X0) X0)))
% 1.58/1.80 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_is X0) X1)->((rt_is X1) X0)))))) of role axiom named satz79
% 1.58/1.80 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_is X0) X1)->((rt_is X1) X0))))))
% 1.58/1.80 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->(((rt_is X1) X2)->((rt_is X0) X2))))))))) of role axiom named satz80
% 1.58/1.80 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->(((rt_is X1) X2)->((rt_is X0) X2)))))))))
% 1.58/1.80 FOF formula (<kernel.Constant object at 0x2b2abf216ea8>, <kernel.DependentProduct object at 0x2b2abf216710>) of role type named typ_rt_more
% 1.58/1.80 Using role type
% 1.58/1.80 Declaring rt_more:(fofType->(fofType->Prop))
% 1.58/1.80 FOF formula (((eq (fofType->(fofType->Prop))) rt_more) (fun (X0:fofType) (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((l_some frac) (fun (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((moref X2) X3)))))))) of role definition named def_rt_more
% 1.58/1.80 A new definition: (((eq (fofType->(fofType->Prop))) rt_more) (fun (X0:fofType) (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((l_some frac) (fun (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((moref X2) X3))))))))
% 1.58/1.80 Defined: rt_more:=(fun (X0:fofType) (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((l_some frac) (fun (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((moref X2) X3)))))))
% 1.58/1.80 FOF formula (<kernel.Constant object at 0x2b2abf216710>, <kernel.DependentProduct object at 0x2b2abf216a28>) of role type named typ_propm
% 1.58/1.80 Using role type
% 1.58/1.80 Declaring propm:(fofType->(fofType->(fofType->(fofType->Prop))))
% 1.58/1.80 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) propm) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((moref X2) X3)))) of role definition named def_propm
% 1.58/1.80 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) propm) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((moref X2) X3))))
% 1.58/1.80 Defined: propm:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((moref X2) X3)))
% 1.58/1.80 FOF formula (<kernel.Constant object at 0x2b2abf216a28>, <kernel.DependentProduct object at 0x2b2abf216ef0>) of role type named typ_rt_less
% 1.61/1.82 Using role type
% 1.61/1.82 Declaring rt_less:(fofType->(fofType->Prop))
% 1.61/1.82 FOF formula (((eq (fofType->(fofType->Prop))) rt_less) (fun (X0:fofType) (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((l_some frac) (fun (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((lessf X2) X3)))))))) of role definition named def_rt_less
% 1.61/1.82 A new definition: (((eq (fofType->(fofType->Prop))) rt_less) (fun (X0:fofType) (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((l_some frac) (fun (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((lessf X2) X3))))))))
% 1.61/1.82 Defined: rt_less:=(fun (X0:fofType) (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((l_some frac) (fun (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((lessf X2) X3)))))))
% 1.61/1.82 FOF formula (<kernel.Constant object at 0x2b2abf2169e0>, <kernel.DependentProduct object at 0x2b2abf216b90>) of role type named typ_propl
% 1.61/1.82 Using role type
% 1.61/1.82 Declaring propl:(fofType->(fofType->(fofType->(fofType->Prop))))
% 1.61/1.82 FOF formula (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) propl) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((lessf X2) X3)))) of role definition named def_propl
% 1.61/1.82 A new definition: (((eq (fofType->(fofType->(fofType->(fofType->Prop))))) propl) (fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((lessf X2) X3))))
% 1.61/1.82 Defined: propl:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((lessf X2) X3)))
% 1.61/1.82 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((orec3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1)))))) of role axiom named satz81
% 1.61/1.82 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((orec3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1))))))
% 1.61/1.82 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((or3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1)))))) of role axiom named satz81a
% 1.61/1.82 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((or3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1))))))
% 1.61/1.82 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((ec3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1)))))) of role axiom named satz81b
% 1.61/1.82 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((ec3 ((rt_is X0) X1)) ((rt_more X0) X1)) ((rt_less X0) X1))))))
% 1.61/1.82 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_less X1) X0)))))) of role axiom named satz82
% 1.61/1.82 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->((rt_less X1) X0))))))
% 1.61/1.82 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->((rt_more X1) X0)))))) of role axiom named satz83
% 1.61/1.82 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_less X0) X1)->((rt_more X1) X0))))))
% 1.61/1.82 FOF formula (<kernel.Constant object at 0x2b2abf216b90>, <kernel.DependentProduct object at 0x2b2abe7a0320>) of role type named typ_rt_moreis
% 1.61/1.82 Using role type
% 1.61/1.82 Declaring rt_moreis:(fofType->(fofType->Prop))
% 1.61/1.82 FOF formula (((eq (fofType->(fofType->Prop))) rt_moreis) (fun (X0:fofType) (X1:fofType)=> ((l_or ((rt_more X0) X1)) ((rt_is X0) X1)))) of role definition named def_rt_moreis
% 1.64/1.83 A new definition: (((eq (fofType->(fofType->Prop))) rt_moreis) (fun (X0:fofType) (X1:fofType)=> ((l_or ((rt_more X0) X1)) ((rt_is X0) X1))))
% 1.64/1.83 Defined: rt_moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rt_more X0) X1)) ((rt_is X0) X1)))
% 1.64/1.83 FOF formula (<kernel.Constant object at 0x2b2abf216b90>, <kernel.DependentProduct object at 0x2b2abe7a0bd8>) of role type named typ_rt_lessis
% 1.64/1.83 Using role type
% 1.64/1.83 Declaring rt_lessis:(fofType->(fofType->Prop))
% 1.64/1.83 FOF formula (((eq (fofType->(fofType->Prop))) rt_lessis) (fun (X0:fofType) (X1:fofType)=> ((l_or ((rt_less X0) X1)) ((rt_is X0) X1)))) of role definition named def_rt_lessis
% 1.64/1.83 A new definition: (((eq (fofType->(fofType->Prop))) rt_lessis) (fun (X0:fofType) (X1:fofType)=> ((l_or ((rt_less X0) X1)) ((rt_is X0) X1))))
% 1.64/1.83 Defined: rt_lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((rt_less X0) X1)) ((rt_is X0) X1)))
% 1.64/1.83 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_moreis X0) X1)->(d_not ((rt_less X0) X1))))))) of role axiom named satz81c
% 1.64/1.83 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_moreis X0) X1)->(d_not ((rt_less X0) X1)))))))
% 1.64/1.83 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_lessis X0) X1)->(d_not ((rt_more X0) X1))))))) of role axiom named satz81d
% 1.64/1.83 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_lessis X0) X1)->(d_not ((rt_more X0) X1)))))))
% 1.64/1.83 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_more X0) X1))->((rt_lessis X0) X1)))))) of role axiom named satz81e
% 1.64/1.83 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_more X0) X1))->((rt_lessis X0) X1))))))
% 1.64/1.83 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_less X0) X1))->((rt_moreis X0) X1)))))) of role axiom named satz81f
% 1.64/1.83 A new axiom: ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((d_not ((rt_less X0) X1))->((rt_moreis X0) X1))))))
% 1.64/1.83 FOF formula ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->(d_not ((rt_lessis X0) X1))))))) of role conjecture named satz81g
% 1.64/1.83 Conjecture to prove = ((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->(d_not ((rt_lessis X0) X1))))))):Prop
% 1.64/1.83 We need to prove ['((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_more X0) X1)->(d_not ((rt_lessis X0) X1)))))))']
% 1.64/1.83 Parameter fofType:Type.
% 1.64/1.83 Definition is_of:=(fun (X0:fofType) (X1:(fofType->Prop))=> (X1 X0)):(fofType->((fofType->Prop)->Prop)).
% 1.64/1.83 Definition all_of:=(fun (X0:(fofType->Prop)) (X1:(fofType->Prop))=> (forall (X2:fofType), (((is_of X2) X0)->(X1 X2)))):((fofType->Prop)->((fofType->Prop)->Prop)).
% 1.64/1.83 Parameter eps:((fofType->Prop)->fofType).
% 1.64/1.83 Parameter in:(fofType->(fofType->Prop)).
% 1.64/1.83 Definition d_Subq:=(fun (X0:fofType) (X1:fofType)=> (forall (X2:fofType), (((in X2) X0)->((in X2) X1)))):(fofType->(fofType->Prop)).
% 1.64/1.83 Axiom set_ext:(forall (X0:fofType) (X1:fofType), (((d_Subq X0) X1)->(((d_Subq X1) X0)->(((eq fofType) X0) X1)))).
% 1.64/1.83 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)))).
% 1.64/1.83 Parameter emptyset:fofType.
% 1.64/1.83 Axiom k_EmptyAx:(((ex fofType) (fun (X0:fofType)=> ((in X0) emptyset)))->False).
% 1.64/1.83 Parameter union:(fofType->fofType).
% 1.64/1.83 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)))))).
% 1.64/1.83 Parameter power:(fofType->fofType).
% 1.64/1.83 Axiom k_PowerEq:(forall (X0:fofType) (X1:fofType), ((iff ((in X1) (power X0))) ((d_Subq X1) X0))).
% 1.64/1.83 Parameter repl:(fofType->((fofType->fofType)->fofType)).
% 1.64/1.83 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))))))).
% 1.64/1.83 Definition d_Union_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (union X1)) X0)))):(fofType->Prop).
% 1.64/1.83 Definition d_Power_closed:=(fun (X0:fofType)=> (forall (X1:fofType), (((in X1) X0)->((in (power X1)) X0)))):(fofType->Prop).
% 1.64/1.83 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).
% 1.64/1.83 Definition d_ZF_closed:=(fun (X0:fofType)=> ((and ((and (d_Union_closed X0)) (d_Power_closed X0))) (d_Repl_closed X0))):(fofType->Prop).
% 1.64/1.83 Parameter univof:(fofType->fofType).
% 1.64/1.83 Axiom k_UnivOf_In:(forall (X0:fofType), ((in X0) (univof X0))).
% 1.64/1.83 Axiom k_UnivOf_ZF_closed:(forall (X0:fofType), (d_ZF_closed (univof X0))).
% 1.64/1.83 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))).
% 1.64/1.83 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)))).
% 1.64/1.83 Axiom if_i_0:(forall (X0:Prop) (X1:fofType) (X2:fofType), ((X0->False)->(((eq fofType) (((if X0) X1) X2)) X2))).
% 1.64/1.83 Axiom if_i_1:(forall (X0:Prop) (X1:fofType) (X2:fofType), (X0->(((eq fofType) (((if X0) X1) X2)) X1))).
% 1.64/1.83 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))).
% 1.64/1.83 Definition nIn:=(fun (X0:fofType) (X1:fofType)=> (((in X0) X1)->False)):(fofType->(fofType->Prop)).
% 1.64/1.83 Axiom k_PowerE:(forall (X0:fofType) (X1:fofType), (((in X1) (power X0))->((d_Subq X1) X0))).
% 1.64/1.83 Axiom k_PowerI:(forall (X0:fofType) (X1:fofType), (((d_Subq X1) X0)->((in X1) (power X0)))).
% 1.64/1.83 Axiom k_Self_In_Power:(forall (X0:fofType), ((in X0) (power X0))).
% 1.64/1.83 Definition d_UPair:=(fun (X0:fofType) (X1:fofType)=> ((repl (power (power emptyset))) (fun (X2:fofType)=> (((if ((in emptyset) X2)) X0) X1)))):(fofType->(fofType->fofType)).
% 1.64/1.83 Definition d_Sing:=(fun (X0:fofType)=> ((d_UPair X0) X0)):(fofType->fofType).
% 1.64/1.83 Definition binunion:=(fun (X0:fofType) (X1:fofType)=> (union ((d_UPair X0) X1))):(fofType->(fofType->fofType)).
% 1.64/1.83 Definition famunion:=(fun (X0:fofType) (X1:(fofType->fofType))=> (union ((repl X0) X1))):(fofType->((fofType->fofType)->fofType)).
% 1.64/1.83 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)).
% 1.64/1.83 Axiom k_SepI:(forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) X0)->((X1 X2)->((in X2) ((d_Sep X0) X1))))).
% 1.64/1.83 Axiom k_SepE1:(forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) ((d_Sep X0) X1))->((in X2) X0))).
% 1.64/1.83 Axiom k_SepE2:(forall (X0:fofType) (X1:(fofType->Prop)) (X2:fofType), (((in X2) ((d_Sep X0) X1))->(X1 X2))).
% 1.64/1.83 Definition d_ReplSep:=(fun (X0:fofType) (X1:(fofType->Prop))=> (repl ((d_Sep X0) X1))):(fofType->((fofType->Prop)->((fofType->fofType)->fofType))).
% 1.64/1.83 Definition setminus:=(fun (X0:fofType) (X1:fofType)=> ((d_Sep X0) (fun (X2:fofType)=> ((nIn X2) X1)))):(fofType->(fofType->fofType)).
% 1.64/1.83 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))).
% 1.64/1.84 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)).
% 1.64/1.84 Definition ordsucc:=(fun (X0:fofType)=> ((binunion X0) (d_Sing X0))):(fofType->fofType).
% 1.64/1.84 Axiom neq_ordsucc_0:(forall (X0:fofType), (not (((eq fofType) (ordsucc X0)) emptyset))).
% 1.64/1.84 Axiom ordsucc_inj:(forall (X0:fofType) (X1:fofType), ((((eq fofType) (ordsucc X0)) (ordsucc X1))->(((eq fofType) X0) X1))).
% 1.64/1.84 Axiom k_In_0_1:((in emptyset) (ordsucc emptyset)).
% 1.64/1.84 Definition nat_p:=(fun (X0:fofType)=> (forall (X1:(fofType->Prop)), ((X1 emptyset)->((forall (X2:fofType), ((X1 X2)->(X1 (ordsucc X2))))->(X1 X0))))):(fofType->Prop).
% 1.64/1.84 Axiom nat_ordsucc:(forall (X0:fofType), ((nat_p X0)->(nat_p (ordsucc X0)))).
% 1.64/1.84 Axiom nat_1:(nat_p (ordsucc emptyset)).
% 1.64/1.84 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)))))).
% 1.64/1.84 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)))))))).
% 1.64/1.84 Definition omega:=((d_Sep (univof emptyset)) nat_p):fofType.
% 1.64/1.84 Axiom omega_nat_p:(forall (X0:fofType), (((in X0) omega)->(nat_p X0))).
% 1.64/1.84 Axiom nat_p_omega:(forall (X0:fofType), ((nat_p X0)->((in X0) omega))).
% 1.64/1.84 Definition d_Inj1:=(d_In_rec (fun (X0:fofType) (X1:(fofType->fofType))=> ((binunion (d_Sing emptyset)) ((repl X0) X1)))):(fofType->fofType).
% 1.64/1.84 Definition d_Inj0:=(fun (X0:fofType)=> ((repl X0) d_Inj1)):(fofType->fofType).
% 1.64/1.84 Definition d_Unj:=(d_In_rec (fun (X0:fofType)=> (repl ((setminus X0) (d_Sing emptyset))))):(fofType->fofType).
% 1.64/1.84 Definition pair:=(fun (X0:fofType) (X1:fofType)=> ((binunion ((repl X0) d_Inj0)) ((repl X1) d_Inj1))):(fofType->(fofType->fofType)).
% 1.64/1.84 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).
% 1.64/1.84 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).
% 1.64/1.84 Axiom proj0_pair_eq:(forall (X0:fofType) (X1:fofType), (((eq fofType) (proj0 ((pair X0) X1))) X0)).
% 1.64/1.84 Axiom proj1_pair_eq:(forall (X0:fofType) (X1:fofType), (((eq fofType) (_TPTP_proj1 ((pair X0) X1))) X1)).
% 1.64/1.84 Definition d_Sigma:=(fun (X0:fofType) (X1:(fofType->fofType))=> ((famunion X0) (fun (X2:fofType)=> ((repl (X1 X2)) (pair X2))))):(fofType->((fofType->fofType)->fofType)).
% 1.64/1.84 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)))))).
% 1.64/1.84 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)))))).
% 1.64/1.84 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))).
% 1.64/1.84 Axiom proj0_Sigma:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((in (proj0 X2)) X0))).
% 1.64/1.84 Axiom proj1_Sigma:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) ((d_Sigma X0) X1))->((in (_TPTP_proj1 X2)) (X1 (proj0 X2))))).
% 1.64/1.84 Definition setprod:=(fun (X0:fofType) (X1:fofType)=> ((d_Sigma X0) (fun (X2:fofType)=> X1))):(fofType->(fofType->fofType)).
% 1.64/1.84 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)).
% 1.64/1.84 Axiom beta:(forall (X0:fofType) (X1:(fofType->fofType)) (X2:fofType), (((in X2) X0)->(((eq fofType) ((ap ((d_Sigma X0) X1)) X2)) (X1 X2)))).
% 1.64/1.84 Definition pair_p:=(fun (X0:fofType)=> (((eq fofType) ((pair ((ap X0) emptyset)) ((ap X0) (ordsucc emptyset)))) X0)):(fofType->Prop).
% 1.64/1.84 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)).
% 1.64/1.84 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)))).
% 1.64/1.84 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))))).
% 1.64/1.84 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)))))).
% 1.64/1.84 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)))).
% 1.64/1.84 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))))).
% 1.64/1.84 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)))).
% 1.64/1.84 Definition imp:=(fun (X0:Prop) (X1:Prop)=> (X0->X1)):(Prop->(Prop->Prop)).
% 1.64/1.84 Definition d_not:=(fun (X0:Prop)=> ((imp X0) False)):(Prop->Prop).
% 1.64/1.84 Definition wel:=(fun (X0:Prop)=> (d_not (d_not X0))):(Prop->Prop).
% 1.64/1.84 Axiom l_et:(forall (X0:Prop), ((wel X0)->X0)).
% 1.64/1.84 Definition obvious:=((imp False) False):Prop.
% 1.64/1.84 Definition l_ec:=(fun (X0:Prop) (X1:Prop)=> ((imp X0) (d_not X1))):(Prop->(Prop->Prop)).
% 1.64/1.84 Definition d_and:=(fun (X0:Prop) (X1:Prop)=> (d_not ((l_ec X0) X1))):(Prop->(Prop->Prop)).
% 1.64/1.84 Definition l_or:=(fun (X0:Prop)=> (imp (d_not X0))):(Prop->(Prop->Prop)).
% 1.64/1.84 Definition orec:=(fun (X0:Prop) (X1:Prop)=> ((d_and ((l_or X0) X1)) ((l_ec X0) X1))):(Prop->(Prop->Prop)).
% 1.64/1.84 Definition l_iff:=(fun (X0:Prop) (X1:Prop)=> ((d_and ((imp X0) X1)) ((imp X1) X0))):(Prop->(Prop->Prop)).
% 1.64/1.84 Definition all:=(fun (X0:fofType)=> (all_of (fun (X1:fofType)=> ((in X1) X0)))):(fofType->((fofType->Prop)->Prop)).
% 1.64/1.84 Definition non:=(fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> (d_not (X1 X2))):(fofType->((fofType->Prop)->(fofType->Prop))).
% 1.64/1.84 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)).
% 1.64/1.84 Definition or3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((l_or X0) ((l_or X1) X2))):(Prop->(Prop->(Prop->Prop))).
% 1.64/1.84 Definition and3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and X0) ((d_and X1) X2))):(Prop->(Prop->(Prop->Prop))).
% 1.64/1.84 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))).
% 1.64/1.84 Definition orec3:=(fun (X0:Prop) (X1:Prop) (X2:Prop)=> ((d_and (((or3 X0) X1) X2)) (((ec3 X0) X1) X2))):(Prop->(Prop->(Prop->Prop))).
% 1.64/1.84 Definition e_is:=(fun (X0:fofType) (X:fofType) (Y:fofType)=> (((eq fofType) X) Y)):(fofType->(fofType->(fofType->Prop))).
% 1.64/1.84 Axiom refis:(forall (X0:fofType), ((all_of (fun (X1:fofType)=> ((in X1) X0))) (fun (X1:fofType)=> (((e_is X0) X1) X1)))).
% 1.64/1.84 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)))))))).
% 1.64/1.84 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)).
% 1.64/1.84 Definition one:=(fun (X0:fofType) (X1:(fofType->Prop))=> ((d_and ((amone X0) X1)) ((l_some X0) X1))):(fofType->((fofType->Prop)->Prop)).
% 1.64/1.84 Definition ind:=(fun (X0:fofType) (X1:(fofType->Prop))=> (eps (fun (X2:fofType)=> ((and ((in X2) X0)) (X1 X2))))):(fofType->((fofType->Prop)->fofType)).
% 1.64/1.84 Axiom ind_p:(forall (X0:fofType) (X1:(fofType->Prop)), (((one X0) X1)->((is_of ((ind X0) X1)) (fun (X2:fofType)=> ((in X2) X0))))).
% 1.64/1.84 Axiom oneax:(forall (X0:fofType) (X1:(fofType->Prop)), (((one X0) X1)->(X1 ((ind X0) X1)))).
% 1.64/1.84 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))).
% 1.64/1.84 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)))).
% 1.64/1.84 Definition tofs:=(fun (X0:fofType) (X1:fofType)=> ap):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 1.64/1.84 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)))).
% 1.64/1.84 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))).
% 1.64/1.84 Definition surjective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((all X1) (((image X0) X1) X2))):(fofType->(fofType->(fofType->Prop))).
% 1.64/1.84 Definition bijective:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_and (((injective X0) X1) X2)) (((surjective X0) X1) X2))):(fofType->(fofType->(fofType->Prop))).
% 1.64/1.84 Definition invf:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X1) (((soft X0) X1) X2))):(fofType->(fofType->(fofType->fofType))).
% 1.64/1.84 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))))).
% 1.64/1.84 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))))))).
% 1.64/1.84 Definition e_in:=(fun (X0:fofType) (X1:(fofType->Prop)) (X2:fofType)=> X2):(fofType->((fofType->Prop)->(fofType->fofType))).
% 1.64/1.84 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)))))).
% 1.64/1.84 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))))).
% 1.64/1.84 Axiom otax1:(forall (X0:fofType) (X1:(fofType->Prop)), (((injective ((d_Sep X0) X1)) X0) ((d_Sigma ((d_Sep X0) X1)) ((e_in X0) X1)))).
% 1.64/1.84 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))))).
% 1.64/1.84 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))).
% 1.64/1.84 Definition d_pair:=(fun (X0:fofType) (X1:fofType)=> pair):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 1.64/1.84 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))))))))).
% 1.64/1.84 Definition first:=(fun (X0:fofType) (X1:fofType)=> proj0):(fofType->(fofType->(fofType->fofType))).
% 1.64/1.84 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)))))).
% 1.64/1.84 Definition second:=(fun (X0:fofType) (X1:fofType)=> _TPTP_proj1):(fofType->(fofType->(fofType->fofType))).
% 1.64/1.84 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)))))).
% 1.64/1.84 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)))).
% 1.64/1.84 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)))))).
% 1.64/1.84 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)))))).
% 1.64/1.84 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))))).
% 1.64/1.84 Definition ite:=(fun (X0:Prop) (X1:fofType) (X2:fofType) (X3:fofType)=> ((ind X1) ((((prop1 X0) X1) X2) X3))):(Prop->(fofType->(fofType->(fofType->fofType)))).
% 1.64/1.84 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)))).
% 1.64/1.84 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)))).
% 1.64/1.84 Definition wissel:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((d_Sigma X0) (((wissel_wb X0) X1) X2))):(fofType->(fofType->(fofType->fofType))).
% 1.64/1.84 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))))).
% 1.64/1.84 Definition r_ec:=(fun (X0:Prop) (X1:Prop)=> (X0->(d_not X1))):(Prop->(Prop->Prop)).
% 1.64/1.84 Definition esti:=(fun (X0:fofType)=> in):(fofType->(fofType->(fofType->Prop))).
% 1.64/1.84 Axiom setof_p:(forall (X0:fofType) (X1:(fofType->Prop)), ((is_of ((d_Sep X0) X1)) (fun (X2:fofType)=> ((in X2) (power X0))))).
% 1.64/1.84 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)))))).
% 1.64/1.84 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))))).
% 1.64/1.84 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)).
% 1.64/1.84 Definition nonempty:=(fun (X0:fofType) (X1:fofType)=> ((l_some X0) (fun (X2:fofType)=> (((esti X0) X2) X1)))):(fofType->(fofType->Prop)).
% 1.64/1.84 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))).
% 1.64/1.84 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))).
% 1.64/1.84 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)))))))).
% 1.64/1.84 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)))).
% 1.64/1.84 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))).
% 1.64/1.85 Definition ecelt:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((d_Sep X0) (X1 X2))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType))).
% 1.64/1.85 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)))).
% 1.64/1.85 Definition anec:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> ((l_some X0) (((ecp X0) X1) X2))):(fofType->((fofType->(fofType->Prop))->(fofType->Prop))).
% 1.64/1.85 Definition ect:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((d_Sep (power X0)) ((anec X0) X1))):(fofType->((fofType->(fofType->Prop))->fofType)).
% 1.64/1.85 Definition ectset:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((out (power X0)) ((anec X0) X1))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType))).
% 1.64/1.85 Definition ectelt:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop))) (X2:fofType)=> (((ectset X0) X1) (((ecelt X0) X1) X2))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType))).
% 1.64/1.85 Definition ecect:=(fun (X0:fofType) (X1:(fofType->(fofType->Prop)))=> ((e_in (power X0)) ((anec X0) X1))):(fofType->((fofType->(fofType->Prop))->(fofType->fofType))).
% 1.64/1.85 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)))).
% 1.64/1.85 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))))))).
% 1.64/1.85 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)))))).
% 1.64/1.85 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))))).
% 1.64/1.85 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)))).
% 1.64/1.85 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))))).
% 1.64/1.85 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)))))).
% 1.64/1.85 Definition nat:=((d_Sep omega) (fun (X0:fofType)=> (not (((eq fofType) X0) emptyset)))):fofType.
% 1.64/1.85 Definition n_is:=(e_is nat):(fofType->(fofType->Prop)).
% 1.64/1.85 Definition nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((n_is X0) X1))):(fofType->(fofType->Prop)).
% 1.64/1.85 Definition n_in:=(esti nat):(fofType->(fofType->Prop)).
% 1.64/1.85 Definition n_some:=(l_some nat):((fofType->Prop)->Prop).
% 1.64/1.85 Definition n_all:=(all nat):((fofType->Prop)->Prop).
% 1.64/1.85 Definition n_one:=(one nat):((fofType->Prop)->Prop).
% 1.64/1.85 Definition n_1:=(ordsucc emptyset):fofType.
% 1.64/1.85 Axiom n_1_p:((is_of n_1) (fun (X0:fofType)=> ((in X0) nat))).
% 1.64/1.85 Axiom suc_p:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((is_of (ordsucc X0)) (fun (X1:fofType)=> ((in X1) nat))))).
% 1.64/1.85 Axiom n_ax3:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) n_1))).
% 1.64/1.85 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)))))).
% 1.64/1.85 Definition cond1:=(n_in n_1):(fofType->Prop).
% 1.64/1.85 Definition cond2:=(fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((imp ((n_in X1) X0)) ((n_in (ordsucc X1)) X0))))):(fofType->Prop).
% 1.64/1.85 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))))))).
% 1.64/1.85 Definition i1_s:=(d_Sep nat):((fofType->Prop)->fofType).
% 1.64/1.85 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))))))).
% 1.64/1.85 Definition d_22_prop1:=(fun (X0:fofType)=> ((nis (ordsucc X0)) X0)):(fofType->Prop).
% 1.64/1.85 Axiom satz2:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((nis (ordsucc X0)) X0))).
% 1.64/1.85 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).
% 1.64/1.85 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))))))).
% 1.64/1.85 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))))))).
% 1.64/1.85 Definition d_24_prop1:=(fun (X0:fofType)=> (n_all (fun (X1:fofType)=> ((n_is ((ap X0) (ordsucc X1))) (ordsucc ((ap X0) X1)))))):(fofType->Prop).
% 1.64/1.85 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)).
% 1.64/1.85 Definition prop3:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is ((ap X0) X2)) ((ap X1) X2))):(fofType->(fofType->(fofType->Prop))).
% 1.64/1.85 Definition prop4:=(fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0))):(fofType->Prop).
% 1.64/1.85 Definition d_24_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> (ordsucc ((ap X0) X1))))):(fofType->fofType).
% 1.64/1.85 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)))))))))).
% 1.64/1.85 Definition plus:=(fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_24_prop2 X0))):(fofType->fofType).
% 1.64/1.85 Definition n_pl:=(fun (X0:fofType)=> (ap (plus X0))):(fofType->(fofType->fofType)).
% 1.64/1.85 Axiom satz4a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_pl X0) n_1)) (ordsucc X0)))).
% 1.64/1.85 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))))))).
% 1.64/1.85 Axiom satz4c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_pl n_1) X0)) (ordsucc X0)))).
% 1.64/1.85 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))))))).
% 1.64/1.85 Axiom satz4e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is (ordsucc X0)) ((n_pl X0) n_1)))).
% 1.64/1.85 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))))))).
% 1.64/1.85 Axiom satz4g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is (ordsucc X0)) ((n_pl n_1) X0)))).
% 1.64/1.85 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)))))).
% 1.64/1.85 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))).
% 1.64/1.85 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))))))))).
% 1.64/1.85 Definition d_26_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_pl X0) X1)) ((n_pl X1) X0))):(fofType->(fofType->Prop)).
% 1.64/1.85 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)))))).
% 1.64/1.85 Definition d_27_prop1:=(fun (X0:fofType) (X1:fofType)=> ((nis X1) ((n_pl X0) X1))):(fofType->(fofType->Prop)).
% 1.64/1.85 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)))))).
% 1.64/1.85 Definition d_28_prop1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((nis ((n_pl X0) X1)) ((n_pl X0) X2))):(fofType->(fofType->(fofType->Prop))).
% 1.64/1.85 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))))))))).
% 1.64/1.85 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)))))))).
% 1.64/1.85 Definition diffprop:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((n_is X0) ((n_pl X1) X2))):(fofType->(fofType->(fofType->Prop))).
% 1.64/1.85 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)))))))).
% 1.64/1.85 Definition d_29_ii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X0) X1))):(fofType->(fofType->Prop)).
% 1.64/1.85 Definition iii:=(fun (X0:fofType) (X1:fofType)=> (n_some ((diffprop X1) X0))):(fofType->(fofType->Prop)).
% 1.64/1.85 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)).
% 1.64/1.85 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))))))))).
% 1.64/1.85 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))))))).
% 1.64/1.85 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))))))).
% 1.64/1.85 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)))))).
% 1.64/1.85 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)))))).
% 1.64/1.85 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)))))).
% 1.64/1.85 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)))))).
% 1.64/1.85 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)))))).
% 1.64/1.85 Definition moreis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((d_29_ii X0) X1)) ((n_is X0) X1))):(fofType->(fofType->Prop)).
% 1.64/1.85 Definition lessis:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((iii X0) X1)) ((n_is X0) X1))):(fofType->(fofType->Prop)).
% 1.64/1.85 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)))))).
% 1.64/1.85 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)))))).
% 1.64/1.85 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))))))).
% 1.64/1.85 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))))))).
% 1.64/1.85 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)))))).
% 1.64/1.85 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)))))).
% 1.64/1.85 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))))))).
% 1.64/1.85 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))))))).
% 1.64/1.85 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)))))).
% 1.64/1.85 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)))))).
% 1.64/1.85 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))))))))).
% 1.64/1.85 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))))))))).
% 1.64/1.85 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))))))))).
% 1.64/1.85 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))))))))).
% 1.64/1.85 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))))))))).
% 1.64/1.85 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))))))))).
% 1.64/1.85 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))))).
% 1.64/1.85 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)))))).
% 1.64/1.86 Axiom satz18b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((d_29_ii (ordsucc X0)) X0))).
% 1.64/1.86 Axiom satz18c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((iii X0) (ordsucc X0)))).
% 1.64/1.86 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))))))))).
% 1.64/1.86 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))))))))).
% 1.64/1.86 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))))))))).
% 1.64/1.86 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))))))))).
% 1.64/1.86 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))))))))).
% 1.64/1.86 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))))))))).
% 1.64/1.86 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)))))))))))).
% 1.64/1.86 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)))))))))))).
% 1.64/1.86 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)))))))))))).
% 1.64/1.86 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)))))))))))).
% 1.64/1.86 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))))))))).
% 1.64/1.86 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))))))))).
% 1.64/1.86 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))))))))).
% 1.64/1.86 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))))))))).
% 1.64/1.86 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)))))))).
% 1.64/1.86 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)))))))).
% 1.64/1.86 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)))))))).
% 1.64/1.86 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)))))))).
% 1.64/1.86 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)))))))).
% 1.64/1.86 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)))))))).
% 1.64/1.86 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)))))))))))).
% 1.64/1.86 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)))))))))))).
% 1.64/1.86 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)))))))))))).
% 1.64/1.86 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)))))))))))).
% 1.64/1.86 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)))))))))))).
% 1.64/1.86 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)))))))))))).
% 1.64/1.86 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)))))))))))).
% 1.64/1.86 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)))))))))))).
% 1.64/1.86 Axiom satz24:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((moreis X0) n_1))).
% 1.64/1.86 Axiom satz24a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (lessis n_1)).
% 1.64/1.86 Axiom satz24b:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((d_29_ii (ordsucc X0)) n_1))).
% 1.64/1.86 Axiom satz24c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((iii n_1) (ordsucc X0)))).
% 1.64/1.86 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))))))).
% 1.64/1.86 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))))))).
% 1.64/1.86 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)))))).
% 1.64/1.86 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)))))).
% 1.64/1.86 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)))))).
% 1.64/1.86 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)))))).
% 1.64/1.86 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)))))).
% 1.64/1.86 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)))))).
% 1.64/1.86 Definition lbprop:=(fun (X0:(fofType->Prop)) (X1:fofType) (X2:fofType)=> ((imp (X0 X2)) ((lessis X1) X2))):((fofType->Prop)->(fofType->(fofType->Prop))).
% 1.64/1.86 Definition n_lb:=(fun (X0:(fofType->Prop)) (X1:fofType)=> (n_all ((lbprop X0) X1))):((fofType->Prop)->(fofType->Prop)).
% 1.64/1.86 Definition min:=(fun (X0:(fofType->Prop)) (X1:fofType)=> ((d_and ((n_lb X0) X1)) (X0 X1))):((fofType->Prop)->(fofType->Prop)).
% 1.64/1.86 Axiom satz27:(forall (X0:(fofType->Prop)), ((n_some X0)->(n_some (min X0)))).
% 1.64/1.86 Axiom satz27a:(forall (X0:(fofType->Prop)), ((n_some X0)->(n_one (min X0)))).
% 1.64/1.86 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)).
% 1.64/1.86 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)).
% 1.64/1.86 Definition d_428_prop4:=(fun (X0:fofType)=> ((l_some ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0))):(fofType->Prop).
% 1.64/1.86 Definition d_428_id:=((d_Sigma nat) (fun (X0:fofType)=> X0)):fofType.
% 1.64/1.86 Definition d_428_g:=(fun (X0:fofType)=> ((d_Sigma nat) (fun (X1:fofType)=> ((n_pl ((ap X0) X1)) X1)))):(fofType->fofType).
% 1.64/1.86 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))))))))).
% 1.64/1.86 Definition times:=(fun (X0:fofType)=> ((ind ((d_Pi nat) (fun (X1:fofType)=> nat))) (d_428_prop2 X0))):(fofType->fofType).
% 1.64/1.86 Definition n_ts:=(fun (X0:fofType)=> (ap (times X0))):(fofType->(fofType->fofType)).
% 1.64/1.86 Axiom satz28a:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_ts X0) n_1)) X0))).
% 1.64/1.86 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)))))).
% 1.64/1.86 Axiom satz28c:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is ((n_ts n_1) X0)) X0))).
% 1.64/1.86 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)))))).
% 1.64/1.86 Axiom satz28e:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is X0) ((n_ts X0) n_1)))).
% 1.64/1.86 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))))))).
% 1.64/1.86 Axiom satz28g:((all_of (fun (X0:fofType)=> ((in X0) nat))) (fun (X0:fofType)=> ((n_is X0) ((n_ts n_1) X0)))).
% 1.64/1.86 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)))))).
% 1.64/1.86 Definition d_429_prop1:=(fun (X0:fofType) (X1:fofType)=> ((n_is ((n_ts X0) X1)) ((n_ts X1) X0))):(fofType->(fofType->Prop)).
% 1.64/1.86 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)))))).
% 1.64/1.86 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))).
% 1.64/1.86 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))))))))).
% 1.64/1.86 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))).
% 1.64/1.86 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))))))))).
% 1.64/1.86 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))))))))).
% 1.64/1.86 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))))))))).
% 1.64/1.86 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))))))))).
% 1.64/1.86 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))))))))).
% 1.64/1.86 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))))))))).
% 1.64/1.86 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))))))))).
% 1.64/1.86 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)))))))))))).
% 1.64/1.86 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)))))))))))).
% 1.64/1.86 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)))))))))))).
% 1.64/1.86 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)))))))))))).
% 1.64/1.86 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))))))))).
% 1.64/1.86 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))))))))).
% 1.64/1.86 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))))))))).
% 1.64/1.86 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))))))))).
% 1.64/1.86 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)))))))).
% 1.64/1.86 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)))))))).
% 1.64/1.86 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)))))))).
% 1.64/1.86 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)))))))))))).
% 1.64/1.87 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)))))))))))).
% 1.64/1.87 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)))))))))))).
% 1.64/1.87 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)))))))))))).
% 1.64/1.87 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)))))))))))).
% 1.64/1.87 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)))))))))))).
% 1.64/1.87 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)))))))))))).
% 1.64/1.87 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)))))))))))).
% 1.64/1.87 Definition n_mn:=(fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop X0) X1))):(fofType->(fofType->fofType)).
% 1.64/1.87 Definition d_1to:=(fun (X0:fofType)=> ((d_Sep nat) (fun (X1:fofType)=> ((lessis X1) X0)))):(fofType->fofType).
% 1.64/1.87 Definition outn:=(fun (X0:fofType)=> ((out nat) (fun (X1:fofType)=> ((lessis X1) X0)))):(fofType->(fofType->fofType)).
% 1.64/1.87 Definition inn:=(fun (X0:fofType)=> ((e_in nat) (fun (X1:fofType)=> ((lessis X1) X0)))):(fofType->(fofType->fofType)).
% 1.64/1.87 Definition n_1o:=((outn n_1) n_1):fofType.
% 1.64/1.87 Definition singlet_u0:=(inn n_1):(fofType->fofType).
% 1.64/1.87 Definition n_2:=((n_pl n_1) n_1):fofType.
% 1.64/1.87 Definition n_1t:=((outn n_2) n_1):fofType.
% 1.64/1.87 Definition n_2t:=((outn n_2) n_2):fofType.
% 1.64/1.87 Definition pair_u0:=(inn n_2):(fofType->fofType).
% 1.64/1.87 Definition pair1type:=(fun (X0:fofType)=> ((d_Pi (d_1to n_2)) (fun (X1:fofType)=> X0))):(fofType->fofType).
% 1.64/1.87 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))).
% 1.64/1.87 Definition first1:=(fun (X0:fofType) (X1:fofType)=> ((ap X1) n_1t)):(fofType->(fofType->fofType)).
% 1.64/1.87 Definition second1:=(fun (X0:fofType) (X1:fofType)=> ((ap X1) n_2t)):(fofType->(fofType->fofType)).
% 1.64/1.87 Definition pair_q0:=(fun (X0:fofType) (X1:fofType)=> (((pair1 X0) ((first1 X0) X1)) ((second1 X0) X1))):(fofType->(fofType->fofType)).
% 1.64/1.87 Definition d_1out:=(fun (X0:fofType)=> ((outn X0) n_1)):(fofType->fofType).
% 1.64/1.87 Definition xout:=(fun (X0:fofType)=> ((outn X0) X0)):(fofType->fofType).
% 1.64/1.87 Definition left1to:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn X0) ((inn X1) X2))):(fofType->(fofType->(fofType->fofType))).
% 1.64/1.87 Definition right1to:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> ((outn ((n_pl X0) X1)) ((n_pl X0) ((inn X1) X2)))):(fofType->(fofType->(fofType->fofType))).
% 1.64/1.87 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)))).
% 1.64/1.87 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)))).
% 1.64/1.87 Definition left_f1:=(fun (X0:fofType) (X1:fofType) (X2:fofType)=> (((left X0) X2) X1)):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 1.64/1.87 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)))).
% 1.64/1.87 Definition frac:=(pair1type nat):fofType.
% 1.64/1.87 Definition n_fr:=(pair1 nat):(fofType->(fofType->fofType)).
% 1.64/1.87 Definition num:=(first1 nat):(fofType->fofType).
% 1.64/1.87 Definition den:=(second1 nat):(fofType->fofType).
% 1.64/1.87 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)).
% 1.64/1.87 Axiom satz37:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((n_eq X0) X0))).
% 1.64/1.87 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)))))).
% 1.64/1.87 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))))))))).
% 1.64/1.87 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))))))).
% 1.64/1.87 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))))).
% 1.64/1.87 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))))))))).
% 1.64/1.87 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)))))))).
% 1.64/1.87 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)).
% 1.64/1.87 Definition lessf:=(fun (X0:fofType) (X1:fofType)=> ((iii ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))):(fofType->(fofType->Prop)).
% 1.64/1.87 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)))))).
% 1.64/1.87 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)))))).
% 1.64/1.87 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)))))).
% 1.64/1.87 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)))))).
% 1.64/1.87 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)))))).
% 1.64/1.87 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)))))))))))).
% 1.64/1.87 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)))))))))))).
% 1.64/1.87 Definition moreq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((moref X0) X1)) ((n_eq X0) X1))):(fofType->(fofType->Prop)).
% 1.64/1.87 Definition lesseq:=(fun (X0:fofType) (X1:fofType)=> ((l_or ((lessf X0) X1)) ((n_eq X0) X1))):(fofType->(fofType->Prop)).
% 1.64/1.87 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))))))).
% 1.64/1.87 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))))))).
% 1.64/1.87 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)))))).
% 1.64/1.87 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)))))).
% 1.64/1.87 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 X0) X1)->(d_not ((lesseq X0) X1))))))).
% 1.64/1.87 Axiom satz41h:((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))))))).
% 1.64/1.87 Axiom satz41j:((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)))))).
% 1.64/1.87 Axiom satz41k:((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)))))).
% 1.64/1.87 Axiom satz46:((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)))))))))))).
% 1.64/1.87 Axiom satz47:((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)))))))))))).
% 1.64/1.87 Axiom satz48:((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)))))).
% 1.64/1.87 Axiom satz49:((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)))))).
% 1.64/1.87 Axiom satz50:((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))))))))).
% 1.64/1.87 Axiom satz51a:((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))))))))).
% 1.64/1.87 Axiom satz51b:((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))))))))).
% 1.64/1.87 Axiom satz51c:((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)=> (((moreq X0) X1)->(((moref X1) X2)->((moref X0) X2))))))))).
% 1.64/1.87 Axiom satz51d:((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)=> (((moref X0) X1)->(((moreq X1) X2)->((moref X0) X2))))))))).
% 1.64/1.87 Axiom satz52:((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)->(((lesseq X1) X2)->((lesseq X0) X2))))))))).
% 1.64/1.87 Axiom satz53:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((l_some frac) (fun (X1:fofType)=> ((moref X1) X0))))).
% 1.64/1.87 Axiom satz54:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((l_some frac) (fun (X1:fofType)=> ((lessf X1) X0))))).
% 1.64/1.87 Axiom satz55:((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)->((l_some frac) (fun (X2:fofType)=> ((d_and ((lessf X0) X2)) ((lessf X2) X1))))))))).
% 1.64/1.87 Definition n_pf:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_pl ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0)))) ((n_ts (den X0)) (den X1)))):(fofType->(fofType->fofType)).
% 1.64/1.87 Axiom satz56:((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)=> (((n_eq X0) X1)->(((n_eq X2) X3)->((n_eq ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))).
% 1.64/1.87 Axiom satz57:((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_pf ((n_fr X0) X2)) ((n_fr X1) X2))) ((n_fr ((n_pl X0) X1)) X2)))))))).
% 1.64/1.87 Axiom satz57a:((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_pl X0) X1)) X2)) ((n_pf ((n_fr X0) X2)) ((n_fr X1) X2))))))))).
% 1.64/1.87 Axiom satz58:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((n_eq ((n_pf X0) X1)) ((n_pf X1) X0)))))).
% 1.64/1.87 Axiom satz59:((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 ((n_pf ((n_pf X0) X1)) X2)) ((n_pf X0) ((n_pf X1) X2))))))))).
% 1.64/1.87 Axiom satz60:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((moref ((n_pf X0) X1)) X0))))).
% 1.64/1.87 Axiom satz60a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((lessf X0) ((n_pf X0) X1)))))).
% 1.64/1.87 Axiom satz61:((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)=> (((moref X0) X1)->((moref ((n_pf X0) X2)) ((n_pf X1) X2))))))))).
% 1.64/1.88 Axiom satz62b:((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 ((n_pf X0) X2)) ((n_pf X1) X2))))))))).
% 1.64/1.88 Axiom satz62c:((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 ((n_pf X0) X2)) ((n_pf X1) X2))))))))).
% 1.64/1.88 Axiom satz62d:((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)=> (((moref X0) X1)->((moref ((n_pf X2) X0)) ((n_pf X2) X1))))))))).
% 1.64/1.88 Axiom satz62e:((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 ((n_pf X2) X0)) ((n_pf X2) X1))))))))).
% 1.64/1.88 Axiom satz62f:((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 ((n_pf X2) X0)) ((n_pf X2) X1))))))))).
% 1.64/1.88 Axiom satz62g:((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)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))).
% 1.64/1.88 Axiom satz62h:((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)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_pf X2) X0)) ((n_pf X3) X1)))))))))))).
% 1.64/1.88 Axiom satz62j:((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)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))).
% 1.64/1.88 Axiom satz62k:((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)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_pf X2) X0)) ((n_pf X3) X1)))))))))))).
% 1.64/1.88 Axiom satz63a:((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)=> (((moref ((n_pf X0) X2)) ((n_pf X1) X2))->((moref X0) X1)))))))).
% 1.64/1.88 Axiom satz63b:((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 ((n_pf X0) X2)) ((n_pf X1) X2))->((n_eq X0) X1)))))))).
% 1.64/1.88 Axiom satz63c:((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 ((n_pf X0) X2)) ((n_pf X1) X2))->((lessf X0) X1)))))))).
% 1.64/1.88 Axiom satz63d:((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)=> (((moref ((n_pf X2) X0)) ((n_pf X2) X1))->((moref X0) X1)))))))).
% 1.64/1.88 Axiom satz63e:((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 ((n_pf X2) X0)) ((n_pf X2) X1))->((n_eq X0) X1)))))))).
% 1.64/1.88 Axiom satz63f:((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 ((n_pf X2) X0)) ((n_pf X2) X1))->((lessf X0) X1)))))))).
% 1.64/1.88 Axiom satz64:((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)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))).
% 1.64/1.88 Axiom satz64a:((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)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))).
% 1.64/1.88 Axiom satz65a:((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)->(((moref X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))).
% 1.64/1.88 Axiom satz65b:((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)->(((moreq X2) X3)->((moref ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))).
% 1.64/1.88 Axiom satz65c:((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)->(((lessf X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))).
% 1.64/1.88 Axiom satz65d:((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)->(((lesseq X2) X3)->((lessf ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))).
% 1.64/1.88 Axiom satz66:((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)->(((moreq X2) X3)->((moreq ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))).
% 1.64/1.88 Axiom satz66a:((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)->(((lesseq X2) X3)->((lesseq ((n_pf X0) X2)) ((n_pf X1) X3)))))))))))).
% 1.64/1.88 Axiom satz67b:((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)=> (((n_eq ((n_pf X1) X2)) X0)->(((n_eq ((n_pf X1) X3)) X0)->((n_eq X2) X3))))))))))).
% 1.64/1.88 Definition d_367_vo:=(fun (X0:fofType) (X1:fofType)=> ((ind nat) ((diffprop ((n_ts (num X0)) (den X1))) ((n_ts (num X1)) (den X0))))):(fofType->(fofType->fofType)).
% 1.64/1.88 Definition d_367_w:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((d_367_vo X0) X1)) ((n_ts (den X0)) (den X1)))):(fofType->(fofType->fofType)).
% 1.64/1.88 Axiom satz67a:((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)->((l_some frac) (fun (X2:fofType)=> ((n_eq ((n_pf X1) X2)) X0)))))))).
% 1.64/1.88 Axiom k_satz67c:((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)->((n_eq ((n_pf X1) ((d_367_w X0) X1))) X0)))))).
% 1.64/1.88 Axiom satz67d:((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)->((n_eq X0) ((n_pf X1) ((d_367_w X0) X1)))))))).
% 1.64/1.88 Axiom satz67e:((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)=> (((moref X0) X1)->(((n_eq ((n_pf X1) X2)) X0)->((n_eq X2) ((d_367_w X0) X1)))))))))).
% 1.64/1.88 Definition n_tf:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_ts (num X0)) (num X1))) ((n_ts (den X0)) (den X1)))):(fofType->(fofType->fofType)).
% 1.64/1.88 Axiom satz68:((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)=> (((n_eq X0) X1)->(((n_eq X2) X3)->((n_eq ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))).
% 1.64/1.88 Axiom satz69:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((n_eq ((n_tf X0) X1)) ((n_tf X1) X0)))))).
% 1.64/1.88 Axiom satz70:((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 ((n_tf ((n_tf X0) X1)) X2)) ((n_tf X0) ((n_tf X1) X2))))))))).
% 1.64/1.88 Axiom satz71:((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 ((n_tf X0) ((n_pf X1) X2))) ((n_pf ((n_tf X0) X1)) ((n_tf X0) X2))))))))).
% 1.64/1.88 Axiom satz72a:((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)=> (((moref X0) X1)->((moref ((n_tf X0) X2)) ((n_tf X1) X2))))))))).
% 1.64/1.88 Axiom satz72b:((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 ((n_tf X0) X2)) ((n_tf X1) X2))))))))).
% 1.64/1.88 Axiom satz72c:((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 ((n_tf X0) X2)) ((n_tf X1) X2))))))))).
% 1.64/1.88 Axiom satz72d:((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)=> (((moref X0) X1)->((moref ((n_tf X2) X0)) ((n_tf X2) X1))))))))).
% 1.64/1.88 Axiom satz72e:((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 ((n_tf X2) X0)) ((n_tf X2) X1))))))))).
% 1.64/1.88 Axiom satz72f:((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 ((n_tf X2) X0)) ((n_tf X2) X1))))))))).
% 1.64/1.88 Axiom satz72g:((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)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))).
% 1.64/1.88 Axiom satz72h:((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)=> (((n_eq X0) X1)->(((moref X2) X3)->((moref ((n_tf X2) X0)) ((n_tf X3) X1)))))))))))).
% 1.64/1.88 Axiom satz72j:((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)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))).
% 1.64/1.88 Axiom satz72k:((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)=> (((n_eq X0) X1)->(((lessf X2) X3)->((lessf ((n_tf X2) X0)) ((n_tf X3) X1)))))))))))).
% 1.64/1.88 Axiom satz73a:((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)=> (((moref ((n_tf X0) X2)) ((n_tf X1) X2))->((moref X0) X1)))))))).
% 1.64/1.88 Axiom satz73b:((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 ((n_tf X0) X2)) ((n_tf X1) X2))->((n_eq X0) X1)))))))).
% 1.64/1.88 Axiom satz73c:((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 ((n_tf X0) X2)) ((n_tf X1) X2))->((lessf X0) X1)))))))).
% 1.64/1.88 Axiom satz73d:((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)=> (((moref ((n_tf X2) X0)) ((n_tf X2) X1))->((moref X0) X1)))))))).
% 1.64/1.88 Axiom satz73e:((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 ((n_tf X2) X0)) ((n_tf X2) X1))->((n_eq X0) X1)))))))).
% 1.64/1.88 Axiom satz73f:((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 ((n_tf X2) X0)) ((n_tf X2) X1))->((lessf X0) X1)))))))).
% 1.64/1.88 Axiom satz74:((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)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))).
% 1.64/1.88 Axiom satz74a:((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)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))).
% 1.64/1.88 Axiom satz75a:((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)->(((moref X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))).
% 1.64/1.88 Axiom satz75b:((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)->(((moreq X2) X3)->((moref ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))).
% 1.64/1.88 Axiom satz75c:((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)->(((lessf X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))).
% 1.64/1.88 Axiom satz75d:((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)->(((lesseq X2) X3)->((lessf ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))).
% 1.64/1.88 Axiom satz76:((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)->(((moreq X2) X3)->((moreq ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))).
% 1.64/1.88 Axiom satz76a:((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)->(((lesseq X2) X3)->((lesseq ((n_tf X0) X2)) ((n_tf X1) X3)))))))))))).
% 1.64/1.88 Axiom satz77b:((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)=> (((n_eq ((n_tf X1) X2)) X0)->(((n_eq ((n_tf X1) X3)) X0)->((n_eq X2) X3))))))))))).
% 1.64/1.88 Definition d_477_v:=(fun (X0:fofType) (X1:fofType)=> ((n_fr ((n_ts (num X0)) (den X1))) ((n_ts (den X0)) (num X1)))):(fofType->(fofType->fofType)).
% 1.64/1.88 Axiom satz77a:((all_of (fun (X0:fofType)=> ((in X0) frac))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) frac))) (fun (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((n_eq ((n_tf X1) X2)) X0))))))).
% 1.64/1.88 Definition inf:=(esti frac):(fofType->(fofType->Prop)).
% 1.64/1.88 Definition rat:=((ect frac) n_eq):fofType.
% 1.64/1.88 Definition rt_is:=(e_is rat):(fofType->(fofType->Prop)).
% 1.64/1.88 Definition rt_nis:=(fun (X0:fofType) (X1:fofType)=> (d_not ((rt_is X0) X1))):(fofType->(fofType->Prop)).
% 1.64/1.88 Definition rt_some:=(l_some rat):((fofType->Prop)->Prop).
% 1.64/1.88 Definition rt_all:=(all rat):((fofType->Prop)->Prop).
% 1.64/1.88 Definition rt_one:=(one rat):((fofType->Prop)->Prop).
% 1.64/1.88 Definition rt_in:=(esti rat):(fofType->(fofType->Prop)).
% 1.64/1.88 Definition ratof:=((ectelt frac) n_eq):(fofType->fofType).
% 1.64/1.88 Definition class:=((ecect frac) n_eq):(fofType->fofType).
% 1.64/1.88 Definition fixf:=((fixfu2 frac) n_eq):(fofType->(fofType->Prop)).
% 1.64/1.88 Definition indrat:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> ((((((indeq2 frac) n_eq) X2) X3) X0) X1)):(fofType->(fofType->(fofType->(fofType->fofType)))).
% 1.64/1.88 Axiom satz78:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((rt_is X0) X0))).
% 1.64/1.88 Axiom satz79:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> (((rt_is X0) X1)->((rt_is X1) X0)))))).
% 1.64/1.88 Axiom satz80:((all_of (fun (X0:fofType)=> ((in X0) rat))) (fun (X0:fofType)=> ((all_of (fun (X1:fofType)=> ((in X1) rat))) (fun (X1:fofType)=> ((all_of (fun (X2:fofType)=> ((in X2) rat))) (fun (X2:fofType)=> (((rt_is X0) X1)->(((rt_is X1) X2)->((rt_is X0) X2))))))))).
% 1.64/1.88 Definition rt_more:=(fun (X0:fofType) (X1:fofType)=> ((l_some frac) (fun (X2:fofType)=> ((l_some frac) (fun (X3:fofType)=> (((and3 ((inf X2) (class X0))) ((inf X3) (class X1))) ((moref X2) X3))))))):(fofType->(fofType->Prop)).
% 1.64/1.88 Definition propm:=(fun (X0:fofType) (X1:fofType) (X2:fofType) (X3:fofType)=> (((and3 ((inf X2) (class X0)
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