TSTP Solution File: NUM821^5 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM821^5 : TPTP v7.0.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n038.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 13:11:50 EST 2018
% Result : Timeout 285.90s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM821^5 : TPTP v7.0.0. Bugfixed v5.2.0.
% 0.00/0.04 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.23 % Computer : n038.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 14:35:36 CST 2018
% 0.02/0.23 % CPUTime :
% 0.02/0.25 Python 2.7.13
% 2.80/2.99 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 2.80/2.99 FOF formula (<kernel.Constant object at 0x2b8004950ea8>, <kernel.Constant object at 0x2b800494dd40>) of role type named c0_type
% 2.80/2.99 Using role type
% 2.80/2.99 Declaring c0:fofType
% 2.80/2.99 FOF formula (<kernel.Constant object at 0x2b8004954998>, <kernel.DependentProduct object at 0x2b800494d050>) of role type named cEVEN_type
% 2.80/2.99 Using role type
% 2.80/2.99 Declaring cEVEN:(fofType->Prop)
% 2.80/2.99 FOF formula (<kernel.Constant object at 0x2b8004950ea8>, <kernel.DependentProduct object at 0x2b800494d758>) of role type named cNUMBER_type
% 2.80/2.99 Using role type
% 2.80/2.99 Declaring cNUMBER:(fofType->Prop)
% 2.80/2.99 FOF formula (<kernel.Constant object at 0x2b80049506c8>, <kernel.DependentProduct object at 0x2b800494da70>) of role type named cODD_type
% 2.80/2.99 Using role type
% 2.80/2.99 Declaring cODD:(fofType->Prop)
% 2.80/2.99 FOF formula (<kernel.Constant object at 0x2b80049506c8>, <kernel.DependentProduct object at 0x2b800494d710>) of role type named cS_type
% 2.80/2.99 Using role type
% 2.80/2.99 Declaring cS:(fofType->fofType)
% 2.80/2.99 FOF formula (<kernel.Constant object at 0x2b800494de60>, <kernel.Sort object at 0x2b8004cbcdd0>) of role type named cIND_type
% 2.80/2.99 Using role type
% 2.80/2.99 Declaring cIND:Prop
% 2.80/2.99 FOF formula (((eq Prop) cIND) (forall (Xp:(fofType->Prop)), (((and (Xp c0)) (forall (Xx:fofType), ((Xp Xx)->(Xp (cS Xx)))))->(forall (Xx:fofType), (Xp Xx))))) of role definition named cIND_def
% 2.80/2.99 A new definition: (((eq Prop) cIND) (forall (Xp:(fofType->Prop)), (((and (Xp c0)) (forall (Xx:fofType), ((Xp Xx)->(Xp (cS Xx)))))->(forall (Xx:fofType), (Xp Xx)))))
% 2.80/2.99 Defined: cIND:=(forall (Xp:(fofType->Prop)), (((and (Xp c0)) (forall (Xx:fofType), ((Xp Xx)->(Xp (cS Xx)))))->(forall (Xx:fofType), (Xp Xx))))
% 2.80/2.99 FOF formula (((and ((and ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn:fofType), ((cEVEN Xn)->(cEVEN (cS (cS Xn))))))) (cODD (cS c0)))) (forall (Xn:fofType), ((cODD Xn)->(cODD (cS (cS Xn))))))) (forall (Xn:fofType), ((iff (cNUMBER Xn)) ((or (cEVEN Xn)) (cODD Xn)))))->(forall (Xn:fofType), (cNUMBER Xn))) of role conjecture named cTHM303A
% 2.80/2.99 Conjecture to prove = (((and ((and ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn:fofType), ((cEVEN Xn)->(cEVEN (cS (cS Xn))))))) (cODD (cS c0)))) (forall (Xn:fofType), ((cODD Xn)->(cODD (cS (cS Xn))))))) (forall (Xn:fofType), ((iff (cNUMBER Xn)) ((or (cEVEN Xn)) (cODD Xn)))))->(forall (Xn:fofType), (cNUMBER Xn))):Prop
% 2.80/2.99 We need to prove ['(((and ((and ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn:fofType), ((cEVEN Xn)->(cEVEN (cS (cS Xn))))))) (cODD (cS c0)))) (forall (Xn:fofType), ((cODD Xn)->(cODD (cS (cS Xn))))))) (forall (Xn:fofType), ((iff (cNUMBER Xn)) ((or (cEVEN Xn)) (cODD Xn)))))->(forall (Xn:fofType), (cNUMBER Xn)))']
% 2.80/2.99 Parameter fofType:Type.
% 2.80/2.99 Parameter c0:fofType.
% 2.80/2.99 Parameter cEVEN:(fofType->Prop).
% 2.80/2.99 Parameter cNUMBER:(fofType->Prop).
% 2.80/2.99 Parameter cODD:(fofType->Prop).
% 2.80/2.99 Parameter cS:(fofType->fofType).
% 2.80/2.99 Definition cIND:=(forall (Xp:(fofType->Prop)), (((and (Xp c0)) (forall (Xx:fofType), ((Xp Xx)->(Xp (cS Xx)))))->(forall (Xx:fofType), (Xp Xx)))):Prop.
% 2.80/2.99 Trying to prove (((and ((and ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn:fofType), ((cEVEN Xn)->(cEVEN (cS (cS Xn))))))) (cODD (cS c0)))) (forall (Xn:fofType), ((cODD Xn)->(cODD (cS (cS Xn))))))) (forall (Xn:fofType), ((iff (cNUMBER Xn)) ((or (cEVEN Xn)) (cODD Xn)))))->(forall (Xn:fofType), (cNUMBER Xn)))
% 2.80/2.99 Found x30:(cNUMBER Xn0)
% 2.80/2.99 Instantiate: Xn0:=Xn:fofType
% 2.80/2.99 Found x30 as proof of (cNUMBER Xn)
% 2.80/2.99 Found x30:=(x3 x20):(cNUMBER Xn0)
% 2.80/2.99 Instantiate: Xn0:=Xn:fofType
% 2.80/2.99 Found (x3 x20) as proof of (cNUMBER Xn)
% 2.80/2.99 Found (x3 x20) as proof of (cNUMBER Xn)
% 2.80/2.99 Found x30:=(x3 x20):(cNUMBER Xn0)
% 2.80/2.99 Instantiate: Xn0:=Xn:fofType
% 2.80/2.99 Found (x3 x20) as proof of (cNUMBER Xn)
% 2.80/2.99 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 2.80/2.99 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x20)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 2.80/2.99 Found x30:=(x3 x20):(cNUMBER Xn0)
% 2.80/2.99 Found (x3 x20) as proof of (cNUMBER Xn)
% 2.80/2.99 Found (x3 x20) as proof of (cNUMBER Xn)
% 2.80/2.99 Found (x3 x20) as proof of (cNUMBER Xn)
% 2.80/2.99 Found x30:=(x3 x20):(cNUMBER Xn0)
% 6.43/6.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 6.43/6.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 6.43/6.65 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 6.43/6.65 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x20)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 6.43/6.65 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 6.43/6.65 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 6.43/6.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 6.43/6.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 6.43/6.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 6.43/6.65 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 6.43/6.65 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 6.43/6.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 6.43/6.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 6.43/6.65 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 6.43/6.65 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x20)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 6.43/6.65 Found x50:(cNUMBER Xn0)
% 6.43/6.65 Instantiate: Xn0:=Xn:fofType
% 6.43/6.65 Found x50 as proof of (cNUMBER Xn)
% 6.43/6.65 Found x30:(cNUMBER Xn0)
% 6.43/6.65 Instantiate: Xn0:=Xn:fofType
% 6.43/6.65 Found x30 as proof of (cNUMBER Xn)
% 6.43/6.65 Found x30:(cNUMBER Xn0)
% 6.43/6.65 Instantiate: Xn0:=Xn:fofType
% 6.43/6.65 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 6.43/6.65 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 6.43/6.65 Found x50:=(x5 x40):(cNUMBER Xn0)
% 6.43/6.65 Instantiate: Xn0:=Xn:fofType
% 6.43/6.65 Found (x5 x40) as proof of (cNUMBER Xn)
% 6.43/6.65 Found (x5 x40) as proof of (cNUMBER Xn)
% 6.43/6.65 Found x30:(cNUMBER Xn0)
% 6.43/6.65 Instantiate: Xn0:=Xn:fofType
% 6.43/6.65 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 6.43/6.65 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 6.43/6.65 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 6.43/6.65 Found x30:=(x3 x20):(cNUMBER Xn0)
% 6.43/6.65 Instantiate: Xn0:=Xn:fofType
% 6.43/6.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 6.43/6.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 6.43/6.65 Found x50:=(x5 x40):(cNUMBER Xn0)
% 6.43/6.65 Instantiate: Xn0:=Xn:fofType
% 6.43/6.65 Found (x5 x40) as proof of (cNUMBER Xn)
% 6.43/6.65 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 6.43/6.65 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 6.43/6.65 Found x30:=(x3 x20):(cNUMBER Xn0)
% 6.43/6.65 Instantiate: Xn0:=Xn:fofType
% 6.43/6.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 6.43/6.65 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 6.43/6.65 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 6.43/6.65 Found x50:=(x5 x40):(cNUMBER Xn0)
% 6.43/6.65 Found (x5 x40) as proof of (cNUMBER Xn)
% 6.43/6.65 Found (x5 x40) as proof of (cNUMBER Xn)
% 6.43/6.65 Found (x5 x40) as proof of (cNUMBER Xn)
% 6.43/6.65 Found x30:=(x3 x20):(cNUMBER Xn0)
% 6.43/6.65 Instantiate: Xn0:=Xn:fofType
% 6.43/6.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 6.43/6.65 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 6.43/6.65 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 6.43/6.65 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 9.55/9.78 Found x30:=(x3 x20):(cNUMBER Xn0)
% 9.55/9.78 Found (x3 x20) as proof of (cNUMBER Xn)
% 9.55/9.78 Found (x3 x20) as proof of (cNUMBER Xn)
% 9.55/9.78 Found (x3 x20) as proof of (cNUMBER Xn)
% 9.55/9.78 Found x50:=(x5 x40):(cNUMBER Xn0)
% 9.55/9.78 Found (x5 x40) as proof of (cNUMBER Xn)
% 9.55/9.78 Found (x5 x40) as proof of (cNUMBER Xn)
% 9.55/9.78 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 9.55/9.78 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 9.55/9.78 Found x30:=(x3 x20):(cNUMBER Xn0)
% 9.55/9.78 Found (x3 x20) as proof of (cNUMBER Xn)
% 9.55/9.78 Found (x3 x20) as proof of (cNUMBER Xn)
% 9.55/9.78 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 9.55/9.78 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 9.55/9.78 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 9.55/9.78 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 9.55/9.78 Found (x5 x40) as proof of (cNUMBER Xn)
% 9.55/9.78 Found (x5 x40) as proof of (cNUMBER Xn)
% 9.55/9.78 Found (x5 x40) as proof of (cNUMBER Xn)
% 9.55/9.78 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 9.55/9.78 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 9.55/9.78 Found (x3 x20) as proof of (cNUMBER Xn)
% 9.55/9.78 Found (x3 x20) as proof of (cNUMBER Xn)
% 9.55/9.78 Found (x3 x20) as proof of (cNUMBER Xn)
% 9.55/9.78 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 9.55/9.78 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 9.55/9.78 Found (x5 x40) as proof of (cNUMBER Xn)
% 9.55/9.78 Found (x5 x40) as proof of (cNUMBER Xn)
% 9.55/9.78 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 9.55/9.78 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 9.55/9.78 Found x30:=(x3 x20):(cNUMBER Xn0)
% 9.55/9.78 Found (x3 x20) as proof of (cNUMBER Xn)
% 9.55/9.78 Found (x3 x20) as proof of (cNUMBER Xn)
% 9.55/9.78 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 9.55/9.78 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 9.55/9.78 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 9.55/9.78 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 9.55/9.78 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 9.55/9.78 Found (x3 x20) as proof of (cNUMBER Xn)
% 9.55/9.78 Found (x3 x20) as proof of (cNUMBER Xn)
% 9.55/9.78 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 9.55/9.78 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 9.55/9.78 Found x30:(cNUMBER Xn0)
% 9.55/9.78 Instantiate: Xn0:=Xn:fofType
% 9.55/9.78 Found x30 as proof of (cNUMBER Xn)
% 9.55/9.78 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 9.55/9.78 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 9.55/9.78 Found (x3 x20) as proof of (cNUMBER Xn)
% 9.55/9.78 Found (x3 x20) as proof of (cNUMBER Xn)
% 9.55/9.78 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 9.55/9.78 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 11.45/11.63 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 11.45/11.63 Found x30:(cNUMBER Xn0)
% 11.45/11.63 Instantiate: Xn0:=Xn:fofType
% 11.45/11.63 Found (fun (x7:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 11.45/11.63 Found (fun (x7:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 11.45/11.63 Found x70:(cNUMBER Xn0)
% 11.45/11.63 Instantiate: Xn0:=Xn:fofType
% 11.45/11.63 Found x70 as proof of (cNUMBER Xn)
% 11.45/11.63 Found x50:(cNUMBER Xn0)
% 11.45/11.63 Instantiate: Xn0:=Xn:fofType
% 11.45/11.63 Found x50 as proof of (cNUMBER Xn)
% 11.45/11.63 Found x30:(cNUMBER Xn0)
% 11.45/11.63 Instantiate: Xn0:=Xn:fofType
% 11.45/11.63 Found (fun (x7:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 11.45/11.63 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 11.45/11.63 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> x30) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 11.45/11.63 Found x30:=(x3 x20):(cNUMBER Xn0)
% 11.45/11.63 Instantiate: Xn0:=Xn:fofType
% 11.45/11.63 Found (x3 x20) as proof of (cNUMBER Xn)
% 11.45/11.63 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 11.45/11.63 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 11.45/11.63 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 11.45/11.63 Found (and_rect20 (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 11.45/11.63 Found ((and_rect2 (cNUMBER Xn)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 11.45/11.63 Found (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 11.45/11.63 Found (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 13.29/13.48 Found x30:=(x3 x20):(cNUMBER Xn0)
% 13.29/13.48 Instantiate: Xn0:=Xn:fofType
% 13.29/13.48 Found (x3 x20) as proof of (cNUMBER Xn)
% 13.29/13.48 Found (x3 x20) as proof of (cNUMBER Xn)
% 13.29/13.48 Found x50:(cNUMBER Xn0)
% 13.29/13.48 Instantiate: Xn0:=Xn:fofType
% 13.29/13.48 Found (fun (x7:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 13.29/13.48 Found (fun (x7:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 13.29/13.48 Found x30:=(x3 x20):(cNUMBER Xn0)
% 13.29/13.48 Instantiate: Xn0:=Xn:fofType
% 13.29/13.48 Found (x3 x20) as proof of (cNUMBER Xn)
% 13.29/13.48 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 13.29/13.48 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 13.29/13.48 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 13.29/13.48 Found (and_rect20 (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 13.29/13.48 Found ((and_rect2 (cNUMBER Xn)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 13.29/13.48 Found (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 13.29/13.48 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 13.29/13.48 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)))) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 13.29/13.48 Found x30:=(x3 x20):(cNUMBER Xn0)
% 13.29/13.48 Instantiate: Xn0:=Xn:fofType
% 13.29/13.48 Found (x3 x20) as proof of (cNUMBER Xn)
% 13.29/13.48 Found (fun (x7:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 15.03/15.25 Found (fun (x7:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 15.03/15.25 Found x50:(cNUMBER Xn0)
% 15.03/15.25 Instantiate: Xn0:=Xn:fofType
% 15.03/15.25 Found (fun (x7:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 15.03/15.25 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 15.03/15.25 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> x50) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 15.03/15.25 Found x70:=(x7 x60):(cNUMBER Xn0)
% 15.03/15.25 Instantiate: Xn0:=Xn:fofType
% 15.03/15.25 Found (x7 x60) as proof of (cNUMBER Xn)
% 15.03/15.25 Found (x7 x60) as proof of (cNUMBER Xn)
% 15.03/15.25 Found x50:=(x5 x40):(cNUMBER Xn0)
% 15.03/15.25 Instantiate: Xn0:=Xn:fofType
% 15.03/15.25 Found (x5 x40) as proof of (cNUMBER Xn)
% 15.03/15.25 Found (x5 x40) as proof of (cNUMBER Xn)
% 15.03/15.25 Found x30:=(x3 x20):(cNUMBER Xn0)
% 15.03/15.25 Instantiate: Xn0:=Xn:fofType
% 15.03/15.25 Found (x3 x20) as proof of (cNUMBER Xn)
% 15.03/15.25 Found (fun (x7:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 15.03/15.25 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 15.03/15.25 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 15.03/15.25 Found x30:=(x3 x20):(cNUMBER Xn0)
% 15.03/15.25 Found (x3 x20) as proof of (cNUMBER Xn)
% 15.03/15.25 Found (x3 x20) as proof of (cNUMBER Xn)
% 15.03/15.25 Found (x3 x20) as proof of (cNUMBER Xn)
% 15.03/15.25 Found x70:=(x7 x60):(cNUMBER Xn0)
% 15.03/15.25 Instantiate: Xn0:=Xn:fofType
% 15.03/15.25 Found (x7 x60) as proof of (cNUMBER Xn)
% 15.03/15.25 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 15.03/15.25 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 15.03/15.25 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 15.03/15.25 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 15.03/15.25 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 15.03/15.25 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 15.03/15.25 Found (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 15.03/15.25 Found (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 15.03/15.25 Found (and_rect30 (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 15.03/15.25 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 15.03/15.25 Found (((fun (P:Type) (x5:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x5) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 15.03/15.25 Found (((fun (P:Type) (x5:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x5) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 16.64/16.85 Found x50:=(x5 x40):(cNUMBER Xn0)
% 16.64/16.85 Instantiate: Xn0:=Xn:fofType
% 16.64/16.85 Found (x5 x40) as proof of (cNUMBER Xn)
% 16.64/16.85 Found (fun (x7:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 16.64/16.85 Found (fun (x7:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 16.64/16.85 Found x30:=(x3 x20):(cNUMBER Xn0)
% 16.64/16.85 Found (x3 x20) as proof of (cNUMBER Xn)
% 16.64/16.85 Found (x3 x20) as proof of (cNUMBER Xn)
% 16.64/16.85 Found (fun (x7:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 16.64/16.85 Found (fun (x7:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 16.64/16.85 Found x70:=(x7 x60):(cNUMBER Xn0)
% 16.64/16.85 Found (x7 x60) as proof of (cNUMBER Xn)
% 16.64/16.85 Found (x7 x60) as proof of (cNUMBER Xn)
% 16.64/16.85 Found (x7 x60) as proof of (cNUMBER Xn)
% 16.64/16.85 Found x50:=(x5 x40):(cNUMBER Xn0)
% 16.64/16.85 Instantiate: Xn0:=Xn:fofType
% 16.64/16.85 Found (x5 x40) as proof of (cNUMBER Xn)
% 16.64/16.85 Found (fun (x7:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 16.64/16.85 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 16.64/16.85 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x40)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 16.64/16.85 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 16.64/16.85 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 16.64/16.85 Found (x3 x20) as proof of (cNUMBER Xn)
% 16.64/16.85 Found (x3 x20) as proof of (cNUMBER Xn)
% 16.64/16.85 Found (x3 x20) as proof of (cNUMBER Xn)
% 16.64/16.85 Found x50:=(x5 x40):(cNUMBER Xn0)
% 16.64/16.85 Found (x5 x40) as proof of (cNUMBER Xn)
% 16.64/16.85 Found (x5 x40) as proof of (cNUMBER Xn)
% 16.64/16.85 Found (x5 x40) as proof of (cNUMBER Xn)
% 16.64/16.85 Found x30:=(x3 x20):(cNUMBER Xn0)
% 16.64/16.85 Found (x3 x20) as proof of (cNUMBER Xn)
% 16.64/16.85 Found (x3 x20) as proof of (cNUMBER Xn)
% 16.64/16.85 Found (fun (x7:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 16.64/16.85 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 16.64/16.85 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 16.64/16.85 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 16.64/16.85 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 16.64/16.85 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 16.64/16.85 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 16.64/16.85 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 16.64/16.85 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 16.64/16.85 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 16.64/16.85 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 19.52/19.77 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 19.52/19.77 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 19.52/19.77 Found x70:=(x7 x60):(cNUMBER Xn0)
% 19.52/19.77 Found (x7 x60) as proof of (cNUMBER Xn)
% 19.52/19.77 Found (x7 x60) as proof of (cNUMBER Xn)
% 19.52/19.77 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 19.52/19.77 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 19.52/19.77 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 19.52/19.77 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 19.52/19.77 Found (x3 x20) as proof of (cNUMBER Xn)
% 19.52/19.77 Found (x3 x20) as proof of (cNUMBER Xn)
% 19.52/19.77 Found (fun (x7:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 19.52/19.77 Found (fun (x7:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 19.52/19.77 Found x50:=(x5 x40):(cNUMBER Xn0)
% 19.52/19.77 Found (x5 x40) as proof of (cNUMBER Xn)
% 19.52/19.77 Found (x5 x40) as proof of (cNUMBER Xn)
% 19.52/19.77 Found (fun (x7:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 19.52/19.77 Found (fun (x7:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 19.52/19.77 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 19.52/19.77 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 19.52/19.77 Found (x7 x60) as proof of (cNUMBER Xn)
% 19.52/19.77 Found (x7 x60) as proof of (cNUMBER Xn)
% 19.52/19.77 Found (x7 x60) as proof of (cNUMBER Xn)
% 19.52/19.77 Found x30:(cNUMBER Xn0)
% 19.52/19.77 Instantiate: Xn0:=Xn:fofType
% 19.52/19.77 Found x30 as proof of (cNUMBER Xn)
% 19.52/19.77 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 19.52/19.77 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 19.52/19.77 Found (x5 x40) as proof of (cNUMBER Xn)
% 19.52/19.77 Found (x5 x40) as proof of (cNUMBER Xn)
% 19.52/19.77 Found (x5 x40) as proof of (cNUMBER Xn)
% 19.52/19.77 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 19.52/19.77 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 19.52/19.77 Found (x3 x20) as proof of (cNUMBER Xn)
% 19.52/19.77 Found (x3 x20) as proof of (cNUMBER Xn)
% 19.52/19.77 Found (fun (x7:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 19.52/19.77 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 19.52/19.77 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 19.52/19.77 Found x50:=(x5 x40):(cNUMBER Xn0)
% 19.52/19.77 Found (x5 x40) as proof of (cNUMBER Xn)
% 19.52/19.77 Found (x5 x40) as proof of (cNUMBER Xn)
% 19.52/19.77 Found (fun (x7:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 19.52/19.77 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 19.52/19.77 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x40)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 19.52/19.77 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 19.52/19.77 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 19.52/19.77 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 20.90/21.13 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 20.90/21.13 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 20.90/21.13 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 20.90/21.13 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 20.90/21.13 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 20.90/21.13 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 20.90/21.13 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 20.90/21.13 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 20.90/21.13 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 20.90/21.13 Found (x7 x60) as proof of (cNUMBER Xn)
% 20.90/21.13 Found (x7 x60) as proof of (cNUMBER Xn)
% 20.90/21.13 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 20.90/21.13 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 20.90/21.13 Found x30:=(x3 x20):(cNUMBER Xn0)
% 20.90/21.13 Found (x3 x20) as proof of (cNUMBER Xn0)
% 20.90/21.13 Found (x3 x20) as proof of (cNUMBER Xn0)
% 20.90/21.13 Found x30:=(x3 x21):(cNUMBER Xn0)
% 20.90/21.13 Instantiate: Xn0:=Xn:fofType
% 20.90/21.13 Found (x3 x21) as proof of (cNUMBER Xn)
% 20.90/21.13 Found (x3 x21) as proof of (cNUMBER Xn)
% 20.90/21.13 Found x30:=(x3 x21):(cNUMBER Xn0)
% 20.90/21.13 Found (x3 x21) as proof of (cNUMBER Xn)
% 20.90/21.13 Found (x3 x21) as proof of (cNUMBER Xn)
% 20.90/21.13 Found (x3 x21) as proof of (cNUMBER Xn)
% 20.90/21.13 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 20.90/21.13 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 20.90/21.13 Found (x3 x21) as proof of (cNUMBER Xn)
% 20.90/21.13 Found (x3 x21) as proof of (cNUMBER Xn)
% 20.90/21.13 Found (x3 x21) as proof of (cNUMBER Xn)
% 20.90/21.13 Found x30:(cNUMBER Xn0)
% 20.90/21.13 Instantiate: Xn0:=Xn:fofType
% 20.90/21.13 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 20.90/21.13 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 20.90/21.13 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 20.90/21.13 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 20.90/21.13 Found (x5 x40) as proof of (cNUMBER Xn)
% 20.90/21.13 Found (x5 x40) as proof of (cNUMBER Xn)
% 20.90/21.13 Found (fun (x7:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 20.90/21.13 Found (fun (x7:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 20.90/21.13 Found x30:=(x3 x20):(cNUMBER Xn0)
% 20.90/21.13 Instantiate: Xn0:=Xn:fofType
% 20.90/21.13 Found (x3 x20) as proof of (cNUMBER Xn)
% 20.90/21.13 Found (fun (x7:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 20.90/21.13 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 22.33/22.52 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 22.33/22.52 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 22.33/22.52 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 22.33/22.52 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 22.33/22.52 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 22.33/22.52 Found x30:=(x3 x20):(cNUMBER Xn0)
% 22.33/22.52 Found (x3 x20) as proof of (cNUMBER Xn0)
% 22.33/22.52 Found (x3 x20) as proof of (cNUMBER Xn0)
% 22.33/22.52 Found x30:=(x3 x21):(cNUMBER Xn0)
% 22.33/22.52 Instantiate: Xn0:=Xn:fofType
% 22.33/22.52 Found (x3 x21) as proof of (cNUMBER Xn)
% 22.33/22.52 Found (x3 x21) as proof of (cNUMBER Xn)
% 22.33/22.52 Found x30:=(x3 x21):(cNUMBER Xn0)
% 22.33/22.52 Found (x3 x21) as proof of (cNUMBER Xn)
% 22.33/22.52 Found (x3 x21) as proof of (cNUMBER Xn)
% 22.33/22.52 Found (x3 x21) as proof of (cNUMBER Xn)
% 22.33/22.52 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 22.33/22.52 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 22.33/22.52 Found (x3 x21) as proof of (cNUMBER Xn)
% 22.33/22.52 Found (x3 x21) as proof of (cNUMBER Xn)
% 22.33/22.52 Found (x3 x21) as proof of (cNUMBER Xn)
% 22.33/22.52 Found x50:(cNUMBER Xn0)
% 22.33/22.52 Instantiate: Xn0:=Xn:fofType
% 22.33/22.52 Found x50 as proof of (cNUMBER Xn)
% 22.33/22.52 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 22.33/22.52 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 22.33/22.52 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 22.33/22.52 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 22.33/22.52 Found (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 22.33/22.52 Found (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 22.33/22.52 Found (and_rect30 (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 22.33/22.52 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 22.33/22.52 Found (((fun (P:Type) (x5:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x5) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 23.08/23.27 Found (((fun (P:Type) (x5:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x5) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 23.08/23.27 Found (x3 (((fun (P:Type) (x5:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x5) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 23.08/23.27 Found (x3 (((fun (P:Type) (x5:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x5) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 23.08/23.27 Found x30:(cNUMBER Xn0)
% 23.08/23.27 Instantiate: Xn0:=Xn:fofType
% 23.08/23.27 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 23.08/23.27 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 23.08/23.27 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 23.08/23.27 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 23.08/23.27 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 23.08/23.27 Found (x5 x40) as proof of (cNUMBER Xn)
% 23.08/23.27 Found (x5 x40) as proof of (cNUMBER Xn)
% 23.08/23.27 Found (fun (x7:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 23.08/23.27 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 23.08/23.27 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x40)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 23.08/23.27 Found x30:=(x3 x20):(cNUMBER Xn0)
% 23.08/23.27 Instantiate: Xn0:=Xn:fofType
% 23.08/23.27 Found (x3 x20) as proof of (cNUMBER Xn)
% 23.08/23.27 Found (fun (x7:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 23.08/23.27 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 23.08/23.27 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 23.08/23.27 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 23.08/23.27 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 23.08/23.27 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 23.83/24.02 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 23.83/24.02 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20)))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 23.83/24.02 Found x30:=(x3 x20):(cNUMBER Xn0)
% 23.83/24.02 Instantiate: Xn0:=Xn:fofType
% 23.83/24.02 Found (x3 x20) as proof of (cNUMBER Xn)
% 23.83/24.02 Found (fun (x7:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 23.83/24.02 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 23.83/24.02 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 23.83/24.02 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 23.83/24.02 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 23.83/24.02 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 23.83/24.02 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 23.83/24.02 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20)))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 25.73/25.96 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20)))) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 25.73/25.96 Found x30:=(x3 x21):(cNUMBER Xn0)
% 25.73/25.96 Instantiate: Xn0:=Xn:fofType
% 25.73/25.96 Found (x3 x21) as proof of (cNUMBER Xn)
% 25.73/25.96 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 25.73/25.96 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x21)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 25.73/25.96 Found x50:(cNUMBER Xn0)
% 25.73/25.96 Instantiate: Xn0:=Xn:fofType
% 25.73/25.96 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 25.73/25.96 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 25.73/25.96 Found x30:=(x3 x20):(cNUMBER Xn0)
% 25.73/25.96 Instantiate: Xn0:=Xn:fofType
% 25.73/25.96 Found (x3 x20) as proof of (cNUMBER Xn)
% 25.73/25.96 Found (x3 x20) as proof of (cNUMBER Xn)
% 25.73/25.96 Found x50:=(x5 x40):(cNUMBER Xn0)
% 25.73/25.96 Instantiate: Xn0:=Xn:fofType
% 25.73/25.96 Found (x5 x40) as proof of (cNUMBER Xn)
% 25.73/25.96 Found (fun (x7:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 25.73/25.96 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 25.73/25.96 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x40)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 25.73/25.96 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 25.73/25.96 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 25.73/25.96 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 25.73/25.96 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 25.73/25.96 Found x90:(cNUMBER Xn0)
% 25.73/25.96 Instantiate: Xn0:=Xn:fofType
% 25.73/25.96 Found x90 as proof of (cNUMBER Xn)
% 25.73/25.96 Found x7:(cODD (cS c0))
% 25.73/25.96 Instantiate: Xn0:=(cS c0):fofType
% 25.73/25.96 Found x7 as proof of (cODD Xn0)
% 25.73/25.96 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 25.73/25.96 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 25.73/25.96 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 26.93/27.16 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 26.93/27.16 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 26.93/27.16 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 26.93/27.16 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 26.93/27.16 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 26.93/27.16 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 26.93/27.16 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 26.93/27.16 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 26.93/27.16 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 26.93/27.16 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 26.93/27.16 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 26.93/27.16 Found (x3 (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 26.93/27.16 Found (x3 (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 26.93/27.16 Found x70:(cNUMBER Xn0)
% 26.93/27.16 Instantiate: Xn0:=Xn:fofType
% 26.93/27.16 Found x70 as proof of (cNUMBER Xn)
% 26.93/27.16 Found x50:(cNUMBER Xn0)
% 26.93/27.16 Instantiate: Xn0:=Xn:fofType
% 26.93/27.16 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 26.93/27.16 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 26.93/27.16 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 29.03/29.21 Found x30:=(x3 x20):(cNUMBER Xn0)
% 29.03/29.21 Instantiate: Xn0:=Xn:fofType
% 29.03/29.21 Found (x3 x20) as proof of (cNUMBER Xn)
% 29.03/29.21 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 29.03/29.21 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 29.03/29.21 Found x50:=(x5 x40):(cNUMBER Xn0)
% 29.03/29.21 Instantiate: Xn0:=Xn:fofType
% 29.03/29.21 Found (x5 x40) as proof of (cNUMBER Xn)
% 29.03/29.21 Found (fun (x7:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 29.03/29.21 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 29.03/29.21 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x40)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 29.03/29.21 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 29.03/29.21 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 29.03/29.21 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 29.03/29.21 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x40)))) as proof of (cNUMBER Xn)
% 29.03/29.21 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x40)))) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 29.03/29.21 Found x70:(cNUMBER Xn0)
% 29.03/29.21 Instantiate: Xn0:=Xn:fofType
% 29.03/29.21 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of (cNUMBER Xn)
% 29.03/29.21 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 29.03/29.21 Found x5:(cODD (cS c0))
% 29.03/29.21 Instantiate: Xn0:=(cS c0):fofType
% 29.03/29.21 Found x5 as proof of (cODD Xn0)
% 29.03/29.21 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 29.03/29.21 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 29.03/29.21 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 29.03/29.21 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 29.03/29.21 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 29.03/29.21 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 29.03/29.21 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 29.03/29.21 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 29.03/29.22 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 29.03/29.22 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 29.03/29.22 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 29.03/29.22 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 29.03/29.22 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 29.03/29.22 Found (fun (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 29.03/29.22 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 29.03/29.22 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 29.03/29.22 Found (and_rect20 (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 29.59/29.78 Found ((and_rect2 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 29.59/29.78 Found (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 29.59/29.78 Found (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 29.59/29.78 Found x50:=(x5 x40):(cNUMBER Xn0)
% 29.59/29.78 Instantiate: Xn0:=Xn:fofType
% 29.59/29.78 Found (x5 x40) as proof of (cNUMBER Xn)
% 29.59/29.78 Found (x5 x40) as proof of (cNUMBER Xn)
% 29.59/29.78 Found x30:=(x3 x20):(cNUMBER Xn0)
% 29.59/29.78 Instantiate: Xn0:=Xn:fofType
% 29.59/29.78 Found (x3 x20) as proof of (cNUMBER Xn)
% 29.59/29.78 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 29.59/29.78 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 29.59/29.78 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 30.99/31.24 Found x7:(cODD (cS c0))
% 30.99/31.24 Instantiate: Xn0:=(cS c0):fofType
% 30.99/31.24 Found x7 as proof of (cODD Xn0)
% 30.99/31.24 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 30.99/31.24 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 30.99/31.24 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 30.99/31.24 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 30.99/31.24 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 30.99/31.24 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 30.99/31.24 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 30.99/31.24 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 30.99/31.24 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 30.99/31.24 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 30.99/31.24 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 30.99/31.24 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 30.99/31.24 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 30.99/31.24 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 30.99/31.24 Found (x5 (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 30.99/31.24 Found (x5 (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 30.99/31.24 Found x30:=(x3 x20):(cNUMBER Xn0)
% 30.99/31.24 Found (x3 x20) as proof of (cNUMBER Xn)
% 35.20/35.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 35.20/35.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 35.20/35.44 Found x30:=(x3 x21):(cNUMBER Xn0)
% 35.20/35.44 Found (x3 x21) as proof of (cNUMBER Xn)
% 35.20/35.44 Found (x3 x21) as proof of (cNUMBER Xn)
% 35.20/35.44 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 35.20/35.44 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x21)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 35.20/35.44 Found x70:(cNUMBER Xn0)
% 35.20/35.44 Instantiate: Xn0:=Xn:fofType
% 35.20/35.44 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of (cNUMBER Xn)
% 35.20/35.44 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 35.20/35.44 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 35.20/35.44 Found x50:=(x5 x40):(cNUMBER Xn0)
% 35.20/35.44 Instantiate: Xn0:=Xn:fofType
% 35.20/35.44 Found (x5 x40) as proof of (cNUMBER Xn)
% 35.20/35.44 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 35.20/35.44 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 35.20/35.44 Found x90:=(x9 x80):(cNUMBER Xn0)
% 35.20/35.44 Instantiate: Xn0:=Xn:fofType
% 35.20/35.44 Found (x9 x80) as proof of (cNUMBER Xn)
% 35.20/35.44 Found (x9 x80) as proof of (cNUMBER Xn)
% 35.20/35.44 Found x30:=(x3 x20):(cNUMBER Xn0)
% 35.20/35.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 35.20/35.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 35.20/35.44 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 35.20/35.44 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 35.20/35.44 Found x70:=(x7 x60):(cNUMBER Xn0)
% 35.20/35.44 Instantiate: Xn0:=Xn:fofType
% 35.20/35.44 Found (x7 x60) as proof of (cNUMBER Xn)
% 35.20/35.44 Found (x7 x60) as proof of (cNUMBER Xn)
% 35.20/35.44 Found x50:=(x5 x40):(cNUMBER Xn0)
% 35.20/35.44 Instantiate: Xn0:=Xn:fofType
% 35.20/35.44 Found (x5 x40) as proof of (cNUMBER Xn)
% 35.20/35.44 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 35.20/35.44 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 35.20/35.44 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 35.20/35.44 Found x90:=(x9 x80):(cNUMBER Xn0)
% 35.20/35.44 Instantiate: Xn0:=Xn:fofType
% 35.20/35.44 Found (x9 x80) as proof of (cNUMBER Xn)
% 35.20/35.44 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 35.20/35.44 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 35.20/35.44 Found x50:=(x5 x40):(cNUMBER Xn0)
% 35.20/35.44 Found (x5 x40) as proof of (cNUMBER Xn)
% 35.20/35.44 Found (x5 x40) as proof of (cNUMBER Xn)
% 35.20/35.44 Found (x5 x40) as proof of (cNUMBER Xn)
% 35.20/35.44 Found x30:=(x3 x20):(cNUMBER Xn0)
% 35.20/35.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 35.20/35.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 35.20/35.44 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 35.20/35.44 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 35.20/35.44 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 35.20/35.44 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 35.20/35.44 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 35.20/35.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 37.44/37.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 37.44/37.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 37.44/37.65 Found x30:=(x3 x20):(cNUMBER Xn0)
% 37.44/37.65 Found (x3 x20) as proof of (cNUMBER Xn0)
% 37.44/37.65 Found (x3 x20) as proof of (cNUMBER Xn0)
% 37.44/37.65 Found x70:=(x7 x60):(cNUMBER Xn0)
% 37.44/37.65 Instantiate: Xn0:=Xn:fofType
% 37.44/37.65 Found (x7 x60) as proof of (cNUMBER Xn)
% 37.44/37.65 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 37.44/37.65 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 37.44/37.65 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 37.44/37.65 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 37.44/37.65 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 37.44/37.65 Found x31:(cNUMBER Xn0)
% 37.44/37.65 Instantiate: Xn0:=Xn:fofType
% 37.44/37.65 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 37.44/37.65 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 37.44/37.65 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 37.44/37.65 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 37.44/37.65 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 37.44/37.65 Found (x3 x21) as proof of (cNUMBER Xn)
% 37.44/37.65 Found (x3 x21) as proof of (cNUMBER Xn)
% 37.44/37.65 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 37.44/37.65 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x21)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 37.44/37.65 Found x31:(cNUMBER Xn0)
% 37.44/37.65 Instantiate: Xn0:=Xn:fofType
% 37.44/37.65 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 37.44/37.65 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 37.44/37.65 Found x7:(cODD (cS c0))
% 37.44/37.65 Instantiate: Xn0:=(cS c0):fofType
% 37.44/37.65 Found x7 as proof of (cODD Xn0)
% 37.44/37.65 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 37.44/37.65 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 37.44/37.65 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 37.44/37.65 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 37.44/37.65 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 37.44/37.65 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 37.44/37.65 Found x50:=(x5 x40):(cNUMBER Xn0)
% 37.44/37.65 Found (x5 x40) as proof of (cNUMBER Xn)
% 37.44/37.65 Found (x5 x40) as proof of (cNUMBER Xn)
% 37.44/37.65 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 37.44/37.65 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 37.44/37.65 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 37.44/37.65 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 37.44/37.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 37.44/37.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 37.44/37.65 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 37.44/37.65 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 37.44/37.65 Found x90:=(x9 x80):(cNUMBER Xn0)
% 37.44/37.65 Found (x9 x80) as proof of (cNUMBER Xn)
% 37.44/37.65 Found (x9 x80) as proof of (cNUMBER Xn)
% 37.44/37.65 Found (x9 x80) as proof of (cNUMBER Xn)
% 37.44/37.65 Found x30:=(x3 x21):(cNUMBER Xn0)
% 37.44/37.65 Instantiate: Xn0:=Xn:fofType
% 37.44/37.65 Found (x3 x21) as proof of (cNUMBER Xn)
% 37.44/37.65 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 39.84/40.02 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 39.84/40.02 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 39.84/40.02 Found x30:=(x3 x20):(cNUMBER Xn0)
% 39.84/40.02 Found (x3 x20) as proof of (cNUMBER Xn0)
% 39.84/40.02 Found (x3 x20) as proof of (cNUMBER Xn0)
% 39.84/40.02 Found x30:=(x3 x21):(cNUMBER Xn0)
% 39.84/40.02 Instantiate: Xn0:=Xn:fofType
% 39.84/40.02 Found (x3 x21) as proof of (cNUMBER Xn)
% 39.84/40.02 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 39.84/40.02 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 39.84/40.02 Found x70:=(x7 x60):(cNUMBER Xn0)
% 39.84/40.02 Instantiate: Xn0:=Xn:fofType
% 39.84/40.02 Found (x7 x60) as proof of (cNUMBER Xn)
% 39.84/40.02 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 39.84/40.02 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 39.84/40.02 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 39.84/40.02 Found x50:(cNUMBER Xn00)
% 39.84/40.02 Instantiate: Xn00:=Xn:fofType
% 39.84/40.02 Found x50 as proof of (cNUMBER Xn)
% 39.84/40.02 Found x30:(cNUMBER Xn0)
% 39.84/40.02 Instantiate: Xn0:=Xn:fofType
% 39.84/40.02 Found x30 as proof of (cNUMBER Xn)
% 39.84/40.02 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 39.84/40.02 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 39.84/40.02 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 39.84/40.02 Found x70:=(x7 x60):(cNUMBER Xn0)
% 39.84/40.02 Found (x7 x60) as proof of (cNUMBER Xn)
% 39.84/40.02 Found (x7 x60) as proof of (cNUMBER Xn)
% 39.84/40.02 Found (x7 x60) as proof of (cNUMBER Xn)
% 39.84/40.02 Found x31:(cNUMBER Xn0)
% 39.84/40.02 Instantiate: Xn0:=Xn:fofType
% 39.84/40.02 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 39.84/40.02 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 39.84/40.02 Found x50:=(x5 x40):(cNUMBER Xn0)
% 39.84/40.02 Found (x5 x40) as proof of (cNUMBER Xn0)
% 39.84/40.02 Found (x5 x40) as proof of (cNUMBER Xn0)
% 39.84/40.02 Found x50:=(x5 x41):(cNUMBER Xn0)
% 39.84/40.02 Instantiate: Xn0:=Xn:fofType
% 39.84/40.02 Found (x5 x41) as proof of (cNUMBER Xn)
% 39.84/40.02 Found (x5 x41) as proof of (cNUMBER Xn)
% 39.84/40.02 Found x50:=(x5 x40):(cNUMBER Xn0)
% 39.84/40.02 Found (x5 x40) as proof of (cNUMBER Xn)
% 39.84/40.02 Found (x5 x40) as proof of (cNUMBER Xn)
% 39.84/40.02 Found (x5 x40) as proof of (cNUMBER Xn)
% 39.84/40.02 Found x50:=(x5 x40):(cNUMBER Xn0)
% 39.84/40.02 Found (x5 x40) as proof of (cNUMBER Xn)
% 39.84/40.02 Found (x5 x40) as proof of (cNUMBER Xn)
% 39.84/40.02 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 39.84/40.02 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 39.84/40.02 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 39.84/40.02 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 39.84/40.02 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 39.84/40.02 Found (x5 x40) as proof of (cNUMBER Xn)
% 39.84/40.02 Found (x5 x40) as proof of (cNUMBER Xn)
% 39.84/40.02 Found (x5 x40) as proof of (cNUMBER Xn)
% 39.84/40.02 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 40.73/40.97 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 40.73/40.97 Found (x3 x20) as proof of (cNUMBER Xn)
% 40.73/40.97 Found (x3 x20) as proof of (cNUMBER Xn)
% 40.73/40.97 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 40.73/40.97 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 40.73/40.97 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 40.73/40.97 Found x5:(cODD (cS c0))
% 40.73/40.97 Instantiate: Xn0:=(cS c0):fofType
% 40.73/40.97 Found x5 as proof of (cODD Xn0)
% 40.73/40.97 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 40.73/40.97 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 40.73/40.97 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 40.73/40.97 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 40.73/40.97 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of (cNUMBER Xn0)
% 40.73/40.97 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of (cNUMBER Xn0)
% 40.73/40.97 Found x90:=(x9 x80):(cNUMBER Xn0)
% 40.73/40.97 Found (x9 x80) as proof of (cNUMBER Xn)
% 40.73/40.97 Found (x9 x80) as proof of (cNUMBER Xn)
% 40.73/40.97 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 40.73/40.97 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 40.73/40.97 Found x30:=(x3 x20):(cNUMBER Xn0)
% 40.73/40.97 Found (x3 x20) as proof of (cNUMBER Xn)
% 40.73/40.97 Found (x3 x20) as proof of (cNUMBER Xn)
% 40.73/40.97 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 40.73/40.97 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 40.73/40.97 Found x30:(cNUMBER Xn0)
% 40.73/40.97 Instantiate: Xn0:=Xn:fofType
% 40.73/40.97 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 40.73/40.97 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 40.73/40.97 Found x30:=(x3 x20):(cNUMBER Xn0)
% 40.73/40.97 Found (x3 x20) as proof of (cNUMBER Xn0)
% 40.73/40.97 Found (x3 x20) as proof of (cNUMBER Xn0)
% 40.73/40.97 Found x30:=(x3 x21):(cNUMBER Xn0)
% 40.73/40.97 Instantiate: Xn0:=Xn:fofType
% 40.73/40.97 Found (x3 x21) as proof of (cNUMBER Xn)
% 40.73/40.97 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 40.73/40.97 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 40.73/40.97 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 40.73/40.97 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 40.73/40.97 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 40.73/40.97 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 40.73/40.97 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 40.73/40.97 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 40.73/40.97 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 40.73/40.97 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 40.73/40.98 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 40.73/40.98 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 40.73/40.98 Found (x3 (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (cNUMBER Xn0)
% 40.73/40.98 Found (fun (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of (cNUMBER Xn0)
% 40.73/40.98 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn0))
% 40.73/40.98 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn0)))
% 40.73/40.98 Found (and_rect20 (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 40.73/40.99 Found ((and_rect2 (cNUMBER Xn0)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 40.73/40.99 Found (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) (cNUMBER Xn0)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 40.73/40.99 Found (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) (cNUMBER Xn0)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 40.73/40.99 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 40.73/40.99 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 40.73/40.99 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 40.73/40.99 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 40.73/40.99 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 40.73/41.00 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 40.73/41.00 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 40.73/41.00 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 40.73/41.00 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 40.73/41.00 Found (fun (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 40.73/41.00 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 40.73/41.00 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 40.73/41.00 Found (and_rect20 (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 40.82/41.00 Found ((and_rect2 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 40.82/41.00 Found (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 40.82/41.00 Found (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 40.82/41.00 Found (x3 (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 41.42/41.64 Found (x3 (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))))))) as proof of (cNUMBER Xn0)
% 41.42/41.64 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 41.42/41.64 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 41.42/41.64 Found (x5 x40) as proof of (cNUMBER Xn)
% 41.42/41.64 Found (x5 x40) as proof of (cNUMBER Xn)
% 41.42/41.64 Found (x5 x40) as proof of (cNUMBER Xn)
% 41.42/41.64 Found x30:=(x3 x20):(cNUMBER Xn0)
% 41.42/41.64 Found (x3 x20) as proof of (cNUMBER Xn0)
% 41.42/41.64 Found (x3 x20) as proof of (cNUMBER Xn0)
% 41.42/41.64 Found x30:=(x3 x21):(cNUMBER Xn0)
% 41.42/41.64 Instantiate: Xn0:=Xn:fofType
% 41.42/41.64 Found (x3 x21) as proof of (cNUMBER Xn)
% 41.42/41.64 Found (x3 x21) as proof of (cNUMBER Xn)
% 41.42/41.64 Found x30:=(x3 x20):(cNUMBER Xn0)
% 41.42/41.64 Found (x3 x20) as proof of (cNUMBER Xn)
% 41.42/41.64 Found (x3 x20) as proof of (cNUMBER Xn)
% 41.42/41.64 Found (x3 x20) as proof of (cNUMBER Xn)
% 41.42/41.64 Found x30:(cNUMBER Xn0)
% 41.42/41.64 Instantiate: Xn0:=Xn:fofType
% 41.42/41.64 Found x30 as proof of (cNUMBER Xn)
% 41.42/41.64 Found x7:(cODD (cS c0))
% 41.42/41.64 Instantiate: Xn0:=(cS c0):fofType
% 41.42/41.64 Found x7 as proof of (cODD Xn0)
% 41.42/41.64 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 41.42/41.64 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 41.42/41.64 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 41.42/41.64 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 41.42/41.64 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 41.42/41.64 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 41.42/41.64 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 41.42/41.64 Found x30:=(x3 x20):(cNUMBER Xn0)
% 41.42/41.64 Instantiate: Xn0:=Xn:fofType
% 41.42/41.64 Found (x3 x20) as proof of (cNUMBER Xn)
% 41.42/41.64 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 41.42/41.64 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 41.42/41.64 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 41.42/41.64 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 41.42/41.64 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 41.42/41.64 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 41.42/41.64 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 41.42/41.66 Found x6:(cODD (cS c0))
% 41.42/41.66 Instantiate: Xn0:=(cS c0):fofType
% 41.42/41.66 Found (fun (x6:(cODD (cS c0)))=> x6) as proof of (cODD Xn0)
% 41.42/41.66 Found (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x6:(cODD (cS c0)))=> x6) as proof of ((cODD (cS c0))->(cODD Xn0))
% 41.42/41.66 Found (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x6:(cODD (cS c0)))=> x6) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cODD Xn0)))
% 41.42/41.66 Found (and_rect30 (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x6:(cODD (cS c0)))=> x6)) as proof of (cODD Xn0)
% 41.42/41.66 Found ((and_rect3 (cODD Xn0)) (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x6:(cODD (cS c0)))=> x6)) as proof of (cODD Xn0)
% 41.42/41.66 Found (((fun (P:Type) (x5:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x5) x4)) (cODD Xn0)) (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x6:(cODD (cS c0)))=> x6)) as proof of (cODD Xn0)
% 41.42/41.66 Found (((fun (P:Type) (x5:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x5) x4)) (cODD Xn0)) (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x6:(cODD (cS c0)))=> x6)) as proof of (cODD Xn0)
% 41.42/41.66 Found (or_intror00 (((fun (P:Type) (x5:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x5) x4)) (cODD Xn0)) (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x6:(cODD (cS c0)))=> x6))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 41.42/41.66 Found ((or_intror0 (cODD Xn0)) (((fun (P:Type) (x5:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x5) x4)) (cODD Xn0)) (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x6:(cODD (cS c0)))=> x6))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 41.42/41.66 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x5:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x5) x4)) (cODD Xn0)) (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x6:(cODD (cS c0)))=> x6))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 41.42/41.66 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x5:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x5) x4)) (cODD Xn0)) (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x6:(cODD (cS c0)))=> x6))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 41.65/41.85 Found x7:(cODD (cS c0))
% 41.65/41.85 Instantiate: Xn0:=(cS c0):fofType
% 41.65/41.85 Found x7 as proof of (cODD Xn0)
% 41.65/41.85 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 41.65/41.85 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 41.65/41.85 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 41.65/41.85 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 41.65/41.85 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 41.65/41.85 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 41.65/41.85 Found x70:=(x7 x60):(cNUMBER Xn0)
% 41.65/41.85 Found (x7 x60) as proof of (cNUMBER Xn)
% 41.65/41.85 Found (x7 x60) as proof of (cNUMBER Xn)
% 41.65/41.85 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 41.65/41.85 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 41.65/41.85 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 41.65/41.85 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 41.65/41.85 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 41.65/41.85 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 41.65/41.85 Found (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 41.65/41.85 Found (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0))))
% 41.65/41.85 Found (and_rect30 (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 41.65/41.85 Found ((and_rect3 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 41.65/41.85 Found (((fun (P:Type) (x5:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x5) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 41.65/41.85 Found (((fun (P:Type) (x5:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x5) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 41.65/41.85 Found (or_comm_i00 (((fun (P:Type) (x5:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x5) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 41.65/41.85 Found ((or_comm_i0 (cEVEN Xn0)) (((fun (P:Type) (x5:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x5) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 42.78/42.97 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x5:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x5) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 42.78/42.97 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x5:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x5) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 42.78/42.97 Found x50:=(x5 x40):(cNUMBER Xn0)
% 42.78/42.97 Found (x5 x40) as proof of (cNUMBER Xn0)
% 42.78/42.97 Found (x5 x40) as proof of (cNUMBER Xn0)
% 42.78/42.97 Found x50:=(x5 x41):(cNUMBER Xn0)
% 42.78/42.97 Instantiate: Xn0:=Xn:fofType
% 42.78/42.97 Found (x5 x41) as proof of (cNUMBER Xn)
% 42.78/42.97 Found (x5 x41) as proof of (cNUMBER Xn)
% 42.78/42.97 Found x50:=(x5 x40):(cNUMBER Xn0)
% 42.78/42.97 Found (x5 x40) as proof of (cNUMBER Xn)
% 42.78/42.97 Found (x5 x40) as proof of (cNUMBER Xn)
% 42.78/42.97 Found (x5 x40) as proof of (cNUMBER Xn)
% 42.78/42.97 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 42.78/42.97 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 42.78/42.97 Found (x5 x40) as proof of (cNUMBER Xn)
% 42.78/42.97 Found (x5 x40) as proof of (cNUMBER Xn)
% 42.78/42.97 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 42.78/42.97 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 42.78/42.97 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 42.78/42.97 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 42.78/42.97 Found (x3 x20) as proof of (cNUMBER Xn)
% 42.78/42.97 Found (x3 x20) as proof of (cNUMBER Xn)
% 42.78/42.97 Found (x3 x20) as proof of (cNUMBER Xn)
% 42.78/42.97 Found x80:((or (cEVEN Xn0)) (cODD Xn0))
% 42.78/42.97 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 42.78/42.97 Found (x9 x80) as proof of (cNUMBER Xn)
% 42.78/42.97 Found (x9 x80) as proof of (cNUMBER Xn)
% 42.78/42.97 Found (x9 x80) as proof of (cNUMBER Xn)
% 42.78/42.97 Found x30:=(x3 x20):(cNUMBER Xn0)
% 42.78/42.97 Found (x3 x20) as proof of (cNUMBER Xn)
% 42.78/42.97 Found (x3 x20) as proof of (cNUMBER Xn)
% 42.78/42.97 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 42.78/42.97 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 42.78/42.97 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 42.78/42.97 Found x30:=(x3 x20):(cNUMBER Xn0)
% 42.78/42.97 Found (x3 x20) as proof of (cNUMBER Xn)
% 42.78/42.97 Found (x3 x20) as proof of (cNUMBER Xn)
% 42.78/42.97 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 42.78/42.97 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 42.99/43.23 Found x30:(cNUMBER Xn0)
% 42.99/43.23 Instantiate: Xn0:=Xn:fofType
% 42.99/43.23 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 42.99/43.23 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 42.99/43.23 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 42.99/43.23 Found x30:(cNUMBER Xn0)
% 42.99/43.23 Instantiate: Xn0:=Xn:fofType
% 42.99/43.23 Found (fun (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 42.99/43.23 Found (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 42.99/43.23 Found (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((cEVEN Xn0)->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 42.99/43.23 Found x30:(cNUMBER Xn0)
% 42.99/43.23 Instantiate: Xn0:=Xn:fofType
% 42.99/43.23 Found (fun (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 42.99/43.23 Found (fun (x5:(cODD Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 42.99/43.23 Found (fun (x5:(cODD Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((cODD Xn0)->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 42.99/43.23 Found ((or_ind00 (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 42.99/43.23 Found (((or_ind0 ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 42.99/43.23 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) x20)) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 42.99/43.23 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x30))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 42.99/43.23 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x30))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 42.99/43.23 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 42.99/43.23 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 42.99/43.23 Found (x5 x40) as proof of (cNUMBER Xn)
% 42.99/43.23 Found (x5 x40) as proof of (cNUMBER Xn)
% 42.99/43.23 Found (x5 x40) as proof of (cNUMBER Xn)
% 44.64/44.84 Found x30:(cNUMBER Xn0)
% 44.64/44.84 Instantiate: Xn0:=Xn:fofType
% 44.64/44.84 Found (fun (x12:(cEVEN c0))=> x30) as proof of (cNUMBER Xn)
% 44.64/44.84 Found (fun (x12:(cEVEN c0))=> x30) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 44.64/44.84 Found x30:=(x3 x20):(cNUMBER Xn0)
% 44.64/44.84 Found (x3 x20) as proof of (cNUMBER Xn0)
% 44.64/44.84 Found (x3 x20) as proof of (cNUMBER Xn0)
% 44.64/44.84 Found x30:=(x3 x21):(cNUMBER Xn0)
% 44.64/44.84 Instantiate: Xn0:=Xn:fofType
% 44.64/44.84 Found (x3 x21) as proof of (cNUMBER Xn)
% 44.64/44.84 Found (x3 x21) as proof of (cNUMBER Xn)
% 44.64/44.84 Found x30:=(x3 x20):(cNUMBER Xn0)
% 44.64/44.84 Found (x3 x20) as proof of (cNUMBER Xn)
% 44.64/44.84 Found (x3 x20) as proof of (cNUMBER Xn)
% 44.64/44.84 Found (x3 x20) as proof of (cNUMBER Xn)
% 44.64/44.84 Found x30:=(x3 x20):(cNUMBER Xn0)
% 44.64/44.84 Instantiate: Xn0:=Xn:fofType
% 44.64/44.84 Found (x3 x20) as proof of (cNUMBER Xn)
% 44.64/44.84 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 44.64/44.84 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 44.64/44.84 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 44.64/44.84 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 44.64/44.84 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 44.64/44.84 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 44.64/44.84 Found (fun (x7:(cODD (cS c0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 44.64/44.84 Found (fun (x7:(cODD (cS c0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 44.64/44.84 Found x70:=(x7 x60):(cNUMBER Xn0)
% 44.64/44.84 Found (x7 x60) as proof of (cNUMBER Xn)
% 44.64/44.84 Found (x7 x60) as proof of (cNUMBER Xn)
% 44.64/44.84 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 44.64/44.84 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 44.64/44.84 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 44.64/44.84 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 44.64/44.84 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 44.64/44.84 Found (x7 x60) as proof of (cNUMBER Xn)
% 44.64/44.84 Found (x7 x60) as proof of (cNUMBER Xn)
% 44.64/44.84 Found (x7 x60) as proof of (cNUMBER Xn)
% 44.64/44.84 Found x50:=(x5 x41):(cNUMBER Xn0)
% 44.64/44.84 Instantiate: Xn0:=Xn:fofType
% 44.64/44.84 Found (x5 x41) as proof of (cNUMBER Xn)
% 44.64/44.84 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 44.64/44.84 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x41)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 44.64/44.84 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 44.73/44.93 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 44.73/44.93 Found (x5 x40) as proof of (cNUMBER Xn)
% 44.73/44.93 Found (x5 x40) as proof of (cNUMBER Xn)
% 44.73/44.93 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 44.73/44.93 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 44.73/44.93 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 44.73/44.93 Found x30:=(x3 x20):(cNUMBER Xn0)
% 44.73/44.93 Instantiate: Xn0:=Xn:fofType
% 44.73/44.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 44.73/44.93 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 44.73/44.93 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 44.73/44.93 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 44.73/44.93 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 44.73/44.93 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 44.73/44.93 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 44.73/44.93 Found (fun (x7:(cODD (cS c0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 44.73/44.93 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 44.73/44.93 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 44.73/44.93 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 44.73/44.93 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 44.73/44.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 44.73/44.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 44.73/44.93 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 44.73/44.93 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 46.68/46.87 Found x7:(cODD (cS c0))
% 46.68/46.87 Instantiate: Xn0:=(cS c0):fofType
% 46.68/46.87 Found x7 as proof of (cODD Xn0)
% 46.68/46.87 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 46.68/46.87 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 46.68/46.87 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 46.68/46.87 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 46.68/46.87 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 46.68/46.87 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 46.68/46.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 46.68/46.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 46.68/46.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 46.68/46.87 Found x30:=(x3 x20):(cNUMBER Xn0)
% 46.68/46.87 Instantiate: Xn0:=Xn:fofType
% 46.68/46.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 46.68/46.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 46.68/46.87 Found x50:=(x5 x40):(cNUMBER Xn00)
% 46.68/46.87 Instantiate: Xn00:=Xn:fofType
% 46.68/46.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 46.68/46.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 46.68/46.87 Found x80:((or (cEVEN Xn0)) (cODD Xn0))
% 46.68/46.87 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 46.68/46.87 Found (x9 x80) as proof of (cNUMBER Xn)
% 46.68/46.87 Found (x9 x80) as proof of (cNUMBER Xn)
% 46.68/46.87 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 46.68/46.87 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 46.68/46.87 Found x7:(cODD (cS c0))
% 46.68/46.87 Instantiate: Xn0:=(cS c0):fofType
% 46.68/46.87 Found x7 as proof of (cODD Xn0)
% 46.68/46.87 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 46.68/46.87 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 46.68/46.87 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 46.68/46.87 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 46.68/46.87 Found x50:(cNUMBER Xn0)
% 46.68/46.87 Instantiate: Xn0:=Xn:fofType
% 46.68/46.87 Found x50 as proof of (cNUMBER Xn)
% 46.68/46.87 Found x30:(cNUMBER Xn0)
% 46.68/46.87 Instantiate: Xn0:=Xn:fofType
% 46.68/46.87 Found (fun (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 46.68/46.87 Found (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 46.68/46.87 Found (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((cEVEN Xn0)->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 46.68/46.87 Found x30:(cNUMBER Xn0)
% 46.68/46.87 Instantiate: Xn0:=Xn:fofType
% 46.68/46.87 Found (fun (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 46.68/46.87 Found (fun (x5:(cODD Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 46.68/46.87 Found (fun (x5:(cODD Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((cODD Xn0)->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 46.68/46.87 Found ((or_ind00 (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 46.68/46.87 Found (((or_ind0 ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 46.68/46.87 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) x20)) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 46.68/46.87 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x30))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 46.74/46.99 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))))=> ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x30))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 46.74/46.99 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))))=> ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x30))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30))) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 46.74/46.99 Found x7:(cODD (cS c0))
% 46.74/46.99 Instantiate: Xn0:=(cS c0):fofType
% 46.74/46.99 Found (fun (x7:(cODD (cS c0)))=> x7) as proof of (cODD Xn0)
% 46.74/46.99 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7) as proof of ((cODD (cS c0))->(cODD Xn0))
% 46.74/46.99 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cODD Xn0)))
% 46.74/46.99 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7)) as proof of (cODD Xn0)
% 46.74/46.99 Found ((and_rect3 (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7)) as proof of (cODD Xn0)
% 46.74/46.99 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7)) as proof of (cODD Xn0)
% 46.74/46.99 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7)) as proof of (cODD Xn0)
% 46.74/46.99 Found (or_intror00 (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 46.81/47.04 Found ((or_intror0 (cODD Xn0)) (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 46.81/47.04 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 46.81/47.04 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 46.81/47.04 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 46.81/47.04 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 46.81/47.04 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 46.81/47.04 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 46.81/47.04 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 46.81/47.04 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0))))
% 46.81/47.04 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 46.81/47.04 Found ((and_rect3 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 46.81/47.04 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 46.81/47.04 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 46.81/47.04 Found (or_comm_i00 (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 47.12/47.32 Found ((or_comm_i0 (cEVEN Xn0)) (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 47.12/47.32 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 47.12/47.32 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 47.12/47.32 Found x30:=(x3 x20):(cNUMBER Xn0)
% 47.12/47.32 Found (x3 x20) as proof of (cNUMBER Xn0)
% 47.12/47.32 Found (x3 x20) as proof of (cNUMBER Xn0)
% 47.12/47.32 Found x30:=(x3 x21):(cNUMBER Xn0)
% 47.12/47.32 Instantiate: Xn0:=Xn:fofType
% 47.12/47.32 Found (x3 x21) as proof of (cNUMBER Xn)
% 47.12/47.32 Found (x3 x21) as proof of (cNUMBER Xn)
% 47.12/47.32 Found x30:=(x3 x20):(cNUMBER Xn0)
% 47.12/47.32 Found (x3 x20) as proof of (cNUMBER Xn)
% 47.12/47.32 Found (x3 x20) as proof of (cNUMBER Xn)
% 47.12/47.32 Found (x3 x20) as proof of (cNUMBER Xn)
% 47.12/47.32 Found x30:(cNUMBER Xn0)
% 47.12/47.32 Instantiate: Xn0:=Xn:fofType
% 47.12/47.32 Found (fun (x12:(cEVEN c0))=> x30) as proof of (cNUMBER Xn)
% 47.12/47.32 Found (fun (x11:cIND) (x12:(cEVEN c0))=> x30) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 47.12/47.32 Found (fun (x11:cIND) (x12:(cEVEN c0))=> x30) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 47.12/47.32 Found x50:=(x5 x40):(cNUMBER Xn0)
% 47.12/47.32 Instantiate: Xn0:=Xn:fofType
% 47.12/47.32 Found (x5 x40) as proof of (cNUMBER Xn)
% 47.12/47.32 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 47.12/47.32 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 47.12/47.32 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 47.12/47.32 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 47.12/47.32 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 47.12/47.32 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 47.12/47.32 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 48.80/48.98 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 48.80/48.98 Instantiate: Xn0:=Xn:fofType
% 48.80/48.98 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 48.80/48.98 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 48.80/48.98 Instantiate: Xn00:=Xn:fofType
% 48.80/48.98 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 48.80/48.98 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 48.80/48.98 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 48.80/48.98 Found (x7 x60) as proof of (cNUMBER Xn)
% 48.80/48.98 Found (x7 x60) as proof of (cNUMBER Xn)
% 48.80/48.98 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 48.80/48.98 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 48.80/48.98 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 48.80/48.98 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 48.80/48.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 48.80/48.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 48.80/48.98 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 48.80/48.98 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 48.80/48.98 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 48.80/48.98 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 48.80/48.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 48.80/48.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 48.80/48.98 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 48.80/48.98 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 48.80/48.98 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 48.80/48.98 Found x30:=(x3 x20):(cNUMBER Xn0)
% 48.80/48.98 Instantiate: Xn0:=Xn:fofType
% 48.80/48.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 48.80/48.98 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 48.80/48.98 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 48.80/48.98 Found x50:=(x5 x40):(cNUMBER Xn00)
% 48.80/48.98 Instantiate: Xn00:=Xn:fofType
% 48.80/48.98 Found (x5 x40) as proof of (cNUMBER Xn)
% 48.80/48.98 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 48.80/48.98 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 48.80/48.98 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 48.80/48.98 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 48.80/48.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 48.80/48.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 48.80/48.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 48.80/48.98 Found x30:(cNUMBER Xn0)
% 48.80/48.98 Instantiate: Xn0:=Xn:fofType
% 48.80/48.98 Found (fun (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 48.80/48.98 Found (fun (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 48.80/48.98 Found (fun (x4:(cODD Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 48.85/49.04 Found (fun (x4:(cODD Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((cODD Xn0)->(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))))
% 48.85/49.04 Found x30:(cNUMBER Xn0)
% 48.85/49.04 Instantiate: Xn0:=Xn:fofType
% 48.85/49.04 Found (fun (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 48.85/49.04 Found (fun (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 48.85/49.04 Found (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 48.85/49.04 Found (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((cEVEN Xn0)->(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))))
% 48.85/49.04 Found ((or_ind00 (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) (fun (x4:(cODD Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 48.85/49.04 Found (((or_ind0 (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))) (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) (fun (x4:(cODD Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 48.85/49.04 Found ((((fun (P:Prop) (x4:((cEVEN Xn0)->P)) (x5:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x4) x5) x20)) (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn)))) (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x4:(cODD Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 50.19/50.37 Found ((((fun (P:Prop) (x4:((cEVEN Xn0)->P)) (x5:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x4) x5) (x2 x30))) (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn)))) (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x4:(cODD Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 50.19/50.37 Found ((((fun (P:Prop) (x4:((cEVEN Xn0)->P)) (x5:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x4) x5) (x2 x30))) (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn)))) (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x4:(cODD Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 50.19/50.37 Found x50:(cNUMBER Xn0)
% 50.19/50.37 Instantiate: Xn0:=Xn:fofType
% 50.19/50.37 Found (fun (x12:(cEVEN c0))=> x50) as proof of (cNUMBER Xn)
% 50.19/50.37 Found (fun (x12:(cEVEN c0))=> x50) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 50.19/50.37 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 50.19/50.37 Instantiate: Xn00:=Xn:fofType
% 50.19/50.37 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 50.19/50.37 Found x50:=(x5 x40):(cNUMBER Xn0)
% 50.19/50.37 Instantiate: Xn0:=Xn:fofType
% 50.19/50.37 Found (x5 x40) as proof of (cNUMBER Xn)
% 50.19/50.37 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 50.19/50.37 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 50.19/50.37 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 50.19/50.37 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 50.19/50.37 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 50.19/50.37 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 50.19/50.37 Found (fun (x7:(cODD (cS c0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)))) as proof of (cNUMBER Xn)
% 51.33/51.54 Found (fun (x7:(cODD (cS c0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 51.33/51.54 Found x7:(cODD (cS c0))
% 51.33/51.54 Instantiate: Xn0:=(cS c0):fofType
% 51.33/51.54 Found x7 as proof of (cODD Xn0)
% 51.33/51.54 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 51.33/51.54 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 51.33/51.54 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 51.33/51.54 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 51.33/51.54 Found x30:=(x3 x20):(cNUMBER Xn0)
% 51.33/51.54 Instantiate: Xn0:=Xn:fofType
% 51.33/51.54 Found (x3 x20) as proof of (cNUMBER Xn)
% 51.33/51.54 Found (x3 x20) as proof of (cNUMBER Xn)
% 51.33/51.54 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 51.33/51.54 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 51.33/51.54 Found (x7 x60) as proof of (cNUMBER Xn)
% 51.33/51.54 Found (x7 x60) as proof of (cNUMBER Xn)
% 51.33/51.54 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 51.33/51.54 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 51.33/51.54 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 51.33/51.54 Found x50:=(x5 x40):(cNUMBER Xn0)
% 51.33/51.54 Instantiate: Xn0:=Xn:fofType
% 51.33/51.54 Found (x5 x40) as proof of (cNUMBER Xn)
% 51.33/51.54 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 51.33/51.54 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 51.33/51.54 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 51.33/51.54 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 51.33/51.54 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 51.33/51.54 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 51.33/51.54 Found (fun (x7:(cODD (cS c0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)))) as proof of (cNUMBER Xn)
% 51.33/51.54 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 52.15/52.39 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 52.15/52.39 Found x7:(cODD (cS c0))
% 52.15/52.39 Instantiate: Xn0:=(cS c0):fofType
% 52.15/52.39 Found x7 as proof of (cODD Xn0)
% 52.15/52.39 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 52.23/52.43 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 52.23/52.43 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 52.23/52.43 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 52.23/52.43 Found x6:(cODD (cS c0))
% 52.23/52.43 Instantiate: Xn0:=(cS c0):fofType
% 52.23/52.43 Found x6 as proof of (cODD Xn0)
% 52.23/52.43 Found (or_intror00 x6) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 52.23/52.43 Found ((or_intror0 (cODD Xn0)) x6) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 52.23/52.43 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x6) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 52.23/52.43 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x6) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 52.23/52.43 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x6)) as proof of (cNUMBER Xn0)
% 52.23/52.43 Found (fun (x6:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x6))) as proof of (cNUMBER Xn0)
% 52.23/52.43 Found (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x6:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x6))) as proof of ((cODD (cS c0))->(cNUMBER Xn0))
% 52.23/52.43 Found (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x6:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x6))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn0)))
% 52.23/52.43 Found (and_rect30 (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x6:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x6)))) as proof of (cNUMBER Xn0)
% 52.23/52.43 Found ((and_rect3 (cNUMBER Xn0)) (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x6:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x6)))) as proof of (cNUMBER Xn0)
% 52.23/52.43 Found (((fun (P:Type) (x5:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x5) x4)) (cNUMBER Xn0)) (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x6:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x6)))) as proof of (cNUMBER Xn0)
% 52.23/52.43 Found (((fun (P:Type) (x5:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x5) x4)) (cNUMBER Xn0)) (fun (x5:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x6:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x6)))) as proof of (cNUMBER Xn0)
% 52.23/52.43 Found x30:=(x3 x20):(cNUMBER Xn0)
% 52.23/52.43 Instantiate: Xn0:=Xn:fofType
% 52.23/52.43 Found (x3 x20) as proof of (cNUMBER Xn)
% 52.23/52.43 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 53.05/53.24 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 53.05/53.24 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 53.05/53.24 Found x50:=(x5 x40):(cNUMBER Xn00)
% 53.05/53.24 Found (x5 x40) as proof of (cNUMBER Xn)
% 53.05/53.24 Found (x5 x40) as proof of (cNUMBER Xn)
% 53.05/53.24 Found (x5 x40) as proof of (cNUMBER Xn)
% 53.05/53.24 Found x30:=(x3 x20):(cNUMBER Xn0)
% 53.05/53.24 Found (x3 x20) as proof of (cNUMBER Xn)
% 53.05/53.24 Found (x3 x20) as proof of (cNUMBER Xn)
% 53.05/53.24 Found (x3 x20) as proof of (cNUMBER Xn)
% 53.05/53.24 Found x70:(cNUMBER Xn0)
% 53.05/53.24 Instantiate: Xn0:=Xn:fofType
% 53.05/53.24 Found x70 as proof of (cNUMBER Xn)
% 53.05/53.24 Found x5:(cODD (cS c0))
% 53.05/53.24 Instantiate: Xn0:=(cS c0):fofType
% 53.05/53.24 Found x5 as proof of (cODD Xn0)
% 53.05/53.24 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 53.05/53.24 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 53.05/53.24 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 53.05/53.24 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 53.05/53.24 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 53.05/53.24 Instantiate: Xn00:=Xn:fofType
% 53.05/53.24 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 53.05/53.24 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x40) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->((or (cEVEN Xn0)) (cODD Xn0)))
% 53.05/53.24 Found x7:(cODD (cS c0))
% 53.05/53.24 Instantiate: Xn0:=(cS c0):fofType
% 53.05/53.24 Found (fun (x7:(cODD (cS c0)))=> x7) as proof of (cODD Xn0)
% 53.05/53.24 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7) as proof of ((cODD (cS c0))->(cODD Xn0))
% 53.05/53.24 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cODD Xn0)))
% 53.05/53.24 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7)) as proof of (cODD Xn0)
% 53.05/53.24 Found ((and_rect3 (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7)) as proof of (cODD Xn0)
% 53.05/53.24 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7)) as proof of (cODD Xn0)
% 53.05/53.24 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7)) as proof of (cODD Xn0)
% 53.05/53.24 Found (or_intror00 (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 53.05/53.24 Found ((or_intror0 (cODD Xn0)) (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x2)) (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 53.28/53.48 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x2)) (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 53.28/53.48 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x2)) (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 53.28/53.48 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 53.28/53.48 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 53.28/53.48 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 53.28/53.48 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 53.28/53.48 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 53.28/53.48 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0))))
% 53.28/53.48 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 53.28/53.48 Found ((and_rect3 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 53.28/53.48 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 53.28/53.48 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 53.28/53.48 Found (or_comm_i00 (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 54.70/54.89 Found ((or_comm_i0 (cEVEN Xn0)) (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x2)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 54.70/54.89 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x2)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 54.70/54.89 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x2)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 54.70/54.89 Found x70:=(x7 x60):(cNUMBER Xn0)
% 54.70/54.89 Instantiate: Xn0:=Xn:fofType
% 54.70/54.89 Found (x7 x60) as proof of (cNUMBER Xn)
% 54.70/54.89 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 54.70/54.89 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 54.70/54.89 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 54.70/54.89 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 54.70/54.89 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 54.70/54.89 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 54.70/54.89 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 54.70/54.89 Found x50:(cNUMBER Xn0)
% 54.70/54.89 Instantiate: Xn0:=Xn:fofType
% 54.70/54.89 Found (fun (x12:(cEVEN c0))=> x50) as proof of (cNUMBER Xn)
% 54.70/54.89 Found (fun (x11:cIND) (x12:(cEVEN c0))=> x50) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 54.70/54.89 Found (fun (x11:cIND) (x12:(cEVEN c0))=> x50) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 54.70/54.89 Found x30:=(x3 x20):(cNUMBER Xn0)
% 54.70/54.89 Instantiate: Xn0:=Xn:fofType
% 54.70/54.89 Found (x3 x20) as proof of (cNUMBER Xn)
% 54.70/54.89 Found (fun (x12:(cEVEN c0))=> (x3 x20)) as proof of (cNUMBER Xn)
% 54.70/54.89 Found (fun (x12:(cEVEN c0))=> (x3 x20)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 56.42/56.67 Found x50:=(x5 x40):(cNUMBER Xn0)
% 56.42/56.67 Found (x5 x40) as proof of (cNUMBER Xn)
% 56.42/56.67 Found (x5 x40) as proof of (cNUMBER Xn)
% 56.42/56.67 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 56.42/56.67 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 56.42/56.67 Found x30:=(x3 x20):(cNUMBER Xn0)
% 56.42/56.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 56.42/56.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 56.42/56.67 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 56.42/56.67 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 56.42/56.67 Found x30:=(x3 x21):(cNUMBER Xn0)
% 56.42/56.67 Instantiate: Xn0:=Xn:fofType
% 56.42/56.67 Found (x3 x21) as proof of (cNUMBER Xn)
% 56.42/56.67 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 56.42/56.67 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 56.42/56.67 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 56.42/56.67 Found (and_rect20 (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 56.42/56.67 Found ((and_rect2 (cNUMBER Xn)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 56.42/56.67 Found (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 56.42/56.67 Found (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 56.42/56.67 Found x50:=(x5 x40):(cNUMBER Xn00)
% 56.42/56.67 Found (x5 x40) as proof of (cNUMBER Xn)
% 56.42/56.67 Found (x5 x40) as proof of (cNUMBER Xn)
% 56.42/56.67 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 56.42/56.67 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 56.42/56.67 Found x70:(cNUMBER Xn0)
% 56.42/56.67 Instantiate: Xn0:=Xn:fofType
% 56.42/56.67 Found (fun (x12:(cEVEN c0))=> x70) as proof of (cNUMBER Xn)
% 56.42/56.67 Found (fun (x12:(cEVEN c0))=> x70) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 57.80/58.00 Found x70:=(x7 x60):(cNUMBER Xn0)
% 57.80/58.00 Instantiate: Xn0:=Xn:fofType
% 57.80/58.00 Found (x7 x60) as proof of (cNUMBER Xn)
% 57.80/58.00 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 57.80/58.00 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 57.80/58.00 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 57.80/58.00 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 57.80/58.00 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 57.80/58.00 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 57.80/58.00 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)))) as proof of (cNUMBER Xn)
% 57.80/58.00 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)))) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 57.80/58.00 Found x7:(cODD (cS c0))
% 57.80/58.00 Instantiate: Xn0:=(cS c0):fofType
% 57.80/58.00 Found x7 as proof of (cODD Xn0)
% 57.80/58.00 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 57.80/58.00 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 57.80/58.00 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 57.80/58.00 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 57.80/58.00 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 57.80/58.00 Instantiate: Xn00:=Xn:fofType
% 57.80/58.00 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 57.80/58.00 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 57.80/58.00 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 57.80/58.00 Instantiate: Xn0:=Xn:fofType
% 57.80/58.00 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 57.80/58.00 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 57.80/58.00 Found x7:(cODD (cS c0))
% 57.80/58.00 Instantiate: Xn0:=(cS c0):fofType
% 57.80/58.00 Found x7 as proof of (cODD Xn0)
% 57.80/58.00 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 57.80/58.00 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 57.80/58.00 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 57.80/58.00 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 57.80/58.00 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 57.80/58.00 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 57.80/58.00 Found x120:(cNUMBER Xn0)
% 57.80/58.00 Instantiate: Xn0:=Xn:fofType
% 57.80/58.00 Found x120 as proof of (cNUMBER Xn)
% 57.80/58.00 Found or_introl00:=(or_introl0 (cODD Xn0)):((cEVEN c0)->((or (cEVEN c0)) (cODD Xn0)))
% 57.80/58.00 Found (or_introl0 (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 57.80/58.00 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 57.80/58.00 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 58.89/59.13 Found (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 58.89/59.13 Found (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of (cIND->((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0))))
% 58.89/59.13 Found (and_rect50 (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 58.89/59.13 Found ((and_rect5 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 58.89/59.13 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 58.89/59.13 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 58.89/59.13 Found x50:=(x5 x40):(cNUMBER Xn0)
% 58.89/59.13 Instantiate: Xn0:=Xn:fofType
% 58.89/59.13 Found (x5 x40) as proof of (cNUMBER Xn)
% 58.89/59.13 Found (x5 x40) as proof of (cNUMBER Xn)
% 58.89/59.13 Found x30:=(x3 x20):(cNUMBER Xn0)
% 58.89/59.13 Instantiate: Xn0:=Xn:fofType
% 58.89/59.13 Found (x3 x20) as proof of (cNUMBER Xn)
% 58.89/59.13 Found (fun (x12:(cEVEN c0))=> (x3 x20)) as proof of (cNUMBER Xn)
% 58.89/59.13 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 58.89/59.13 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20)) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 58.89/59.13 Found x5:(cODD (cS c0))
% 58.89/59.13 Instantiate: Xn0:=(cS c0):fofType
% 58.89/59.13 Found x5 as proof of (cODD Xn0)
% 58.89/59.13 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 58.89/59.13 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 58.89/59.13 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 58.89/59.13 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 58.89/59.13 Found x7:(cODD (cS c0))
% 58.89/59.13 Instantiate: Xn0:=(cS c0):fofType
% 58.89/59.13 Found x7 as proof of (cODD Xn0)
% 58.89/59.13 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 58.89/59.13 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 58.89/59.13 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 58.89/59.13 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 58.89/59.13 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 58.89/59.13 Found (fun (x7:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of (cNUMBER Xn0)
% 58.89/59.13 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of ((cODD (cS c0))->(cNUMBER Xn0))
% 58.89/59.13 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn0)))
% 58.89/59.13 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 58.89/59.13 Found ((and_rect3 (cNUMBER Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 58.89/59.13 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 58.89/59.13 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 60.51/60.70 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 60.51/60.70 Instantiate: Xn00:=Xn:fofType
% 60.51/60.70 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 60.51/60.70 Found (x3 x40) as proof of (cNUMBER Xn)
% 60.51/60.70 Found (x3 x40) as proof of (cNUMBER Xn)
% 60.51/60.70 Found (x3 x40) as proof of (cNUMBER Xn)
% 60.51/60.70 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 60.51/60.70 Instantiate: Xn0:=Xn:fofType
% 60.51/60.70 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 60.51/60.70 Found (x5 x20) as proof of (cNUMBER Xn)
% 60.51/60.70 Found (x5 x20) as proof of (cNUMBER Xn)
% 60.51/60.70 Found (x5 x20) as proof of (cNUMBER Xn)
% 60.51/60.70 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 60.51/60.70 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 60.51/60.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 60.51/60.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 60.51/60.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 60.51/60.70 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 60.51/60.70 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 60.51/60.70 Found (x5 x40) as proof of (cNUMBER Xn)
% 60.51/60.70 Found (x5 x40) as proof of (cNUMBER Xn)
% 60.51/60.70 Found (x5 x40) as proof of (cNUMBER Xn)
% 60.51/60.70 Found x30:=(x3 x20):(cNUMBER Xn0)
% 60.51/60.70 Found (x3 x20) as proof of (cNUMBER Xn0)
% 60.51/60.70 Found (x3 x20) as proof of (cNUMBER Xn0)
% 60.51/60.70 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 60.51/60.70 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 60.51/60.70 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 60.51/60.70 Found x31:(cNUMBER Xn0)
% 60.51/60.70 Instantiate: Xn0:=Xn:fofType
% 60.51/60.70 Found (fun (x7:(cODD (cS c0)))=> x31) as proof of (cNUMBER Xn)
% 60.51/60.70 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> x31) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 60.51/60.70 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> x31) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 60.51/60.70 Found x30:=(x3 x20):(cNUMBER Xn0)
% 60.51/60.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 60.51/60.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 60.51/60.70 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 60.51/60.70 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 60.51/60.70 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 60.51/60.70 Found x30:=(x3 x21):(cNUMBER Xn0)
% 60.51/60.70 Instantiate: Xn0:=Xn:fofType
% 60.51/60.70 Found (x3 x21) as proof of (cNUMBER Xn)
% 60.51/60.70 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 60.51/60.70 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 60.51/60.70 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 60.51/60.70 Found (and_rect20 (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 60.51/60.70 Found ((and_rect2 (cNUMBER Xn)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 62.73/62.92 Found (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 62.73/62.92 Found (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 62.73/62.92 Found x90:(cNUMBER Xn0)
% 62.73/62.92 Instantiate: Xn0:=Xn:fofType
% 62.73/62.92 Found x90 as proof of (cNUMBER Xn)
% 62.73/62.92 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 62.73/62.92 Instantiate: Xn00:=Xn:fofType
% 62.73/62.92 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 62.73/62.92 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 62.73/62.92 Found x70:(cNUMBER Xn0)
% 62.73/62.92 Instantiate: Xn0:=Xn:fofType
% 62.73/62.92 Found (fun (x12:(cEVEN c0))=> x70) as proof of (cNUMBER Xn)
% 62.73/62.92 Found (fun (x11:cIND) (x12:(cEVEN c0))=> x70) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 62.73/62.92 Found (fun (x11:cIND) (x12:(cEVEN c0))=> x70) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 62.73/62.92 Found x30:=(x3 x20):(cNUMBER Xn0)
% 62.73/62.92 Found (x3 x20) as proof of (cNUMBER Xn)
% 62.73/62.92 Found (x3 x20) as proof of (cNUMBER Xn)
% 62.73/62.92 Found (x3 x20) as proof of (cNUMBER Xn)
% 62.73/62.92 Found x50:=(x5 x40):(cNUMBER Xn0)
% 62.73/62.92 Instantiate: Xn0:=Xn:fofType
% 62.73/62.92 Found (x5 x40) as proof of (cNUMBER Xn)
% 62.73/62.92 Found (fun (x12:(cEVEN c0))=> (x5 x40)) as proof of (cNUMBER Xn)
% 62.73/62.92 Found (fun (x12:(cEVEN c0))=> (x5 x40)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 62.73/62.92 Found x31:(cNUMBER Xn0)
% 62.73/62.92 Instantiate: Xn0:=Xn:fofType
% 62.73/62.92 Found (fun (x7:(cODD (cS c0)))=> x31) as proof of (cNUMBER Xn)
% 62.73/62.92 Found (fun (x7:(cODD (cS c0)))=> x31) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 62.73/62.92 Found x7:(cODD (cS c0))
% 62.73/62.92 Instantiate: Xn0:=(cS c0):fofType
% 62.73/62.92 Found x7 as proof of (cODD Xn0)
% 62.73/62.92 Found (or_introl00 x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 62.73/62.92 Found ((or_introl0 (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 62.73/62.92 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 62.73/62.92 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 62.73/62.92 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 62.73/62.92 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 62.73/62.92 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 62.73/62.92 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 62.73/62.92 Found x5:(cODD (cS c0))
% 62.73/62.92 Instantiate: Xn0:=(cS c0):fofType
% 62.73/62.92 Found x5 as proof of (cODD Xn0)
% 62.73/62.92 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 62.73/62.92 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 62.73/62.92 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 62.73/62.92 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 62.73/62.92 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 62.73/62.92 Instantiate: Xn0:=Xn:fofType
% 62.73/62.92 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 65.20/65.46 Found (x5 x20) as proof of (cNUMBER Xn)
% 65.20/65.46 Found (x5 x20) as proof of (cNUMBER Xn)
% 65.20/65.46 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x20)) as proof of (cNUMBER Xn)
% 65.20/65.46 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 65.20/65.46 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 65.20/65.46 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 65.20/65.46 Found (x3 x20) as proof of (cNUMBER Xn)
% 65.20/65.46 Found (x3 x20) as proof of (cNUMBER Xn)
% 65.20/65.46 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 65.20/65.46 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 65.20/65.46 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 65.20/65.46 Instantiate: Xn00:=Xn:fofType
% 65.20/65.46 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 65.20/65.46 Found (x3 x40) as proof of (cNUMBER Xn)
% 65.20/65.46 Found (x3 x40) as proof of (cNUMBER Xn)
% 65.20/65.46 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x40)) as proof of (cNUMBER Xn)
% 65.20/65.46 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 65.20/65.46 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 65.20/65.46 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 65.20/65.46 Found (x5 x40) as proof of (cNUMBER Xn)
% 65.20/65.46 Found (x5 x40) as proof of (cNUMBER Xn)
% 65.20/65.46 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 65.20/65.46 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 65.20/65.46 Found x7:(cODD (cS c0))
% 65.20/65.46 Instantiate: Xn0:=(cS c0):fofType
% 65.20/65.46 Found x7 as proof of (cODD Xn0)
% 65.20/65.46 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 65.20/65.46 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 65.20/65.46 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 65.20/65.46 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 65.20/65.46 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 65.20/65.46 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 65.20/65.46 Found x30:=(x3 x20):(cNUMBER Xn0)
% 65.20/65.46 Found (x3 x20) as proof of (cNUMBER Xn0)
% 65.20/65.46 Found (x3 x20) as proof of (cNUMBER Xn0)
% 65.20/65.46 Found x30:=(x3 x21):(cNUMBER Xn0)
% 65.20/65.46 Instantiate: Xn0:=Xn:fofType
% 65.20/65.46 Found (x3 x21) as proof of (cNUMBER Xn)
% 65.20/65.46 Found (fun (x7:(cODD (cS c0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 65.20/65.46 Found (fun (x7:(cODD (cS c0)))=> (x3 x21)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 65.20/65.46 Found x90:(cNUMBER Xn0)
% 65.20/65.46 Instantiate: Xn0:=Xn:fofType
% 65.20/65.46 Found (fun (x12:(cEVEN c0))=> x90) as proof of (cNUMBER Xn)
% 65.20/65.46 Found (fun (x12:(cEVEN c0))=> x90) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 65.20/65.46 Found x30:=(x3 x21):(cNUMBER Xn0)
% 65.20/65.46 Instantiate: Xn0:=Xn:fofType
% 65.20/65.46 Found (x3 x21) as proof of (cNUMBER Xn)
% 65.20/65.46 Found (fun (x7:(cODD (cS c0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 65.20/65.46 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 65.20/65.46 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 65.20/65.46 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 65.20/65.46 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 65.20/65.46 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 65.20/65.46 Found x5:(cODD (cS c0))
% 65.20/65.46 Instantiate: Xn0:=(cS c0):fofType
% 65.20/65.46 Found x5 as proof of (cODD Xn0)
% 65.20/65.46 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 65.20/65.46 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 65.20/65.46 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 65.20/65.46 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 65.20/65.46 Found x30:=(x3 x20):(cNUMBER Xn0)
% 65.20/65.46 Found (x3 x20) as proof of (cNUMBER Xn)
% 66.79/66.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 66.79/66.98 Found (fun (x12:(cEVEN c0))=> (x3 x20)) as proof of (cNUMBER Xn)
% 66.79/66.98 Found (fun (x12:(cEVEN c0))=> (x3 x20)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 66.79/66.98 Found x7:(cODD (cS c0))
% 66.79/66.98 Instantiate: Xn0:=(cS c0):fofType
% 66.79/66.98 Found x7 as proof of (cODD Xn0)
% 66.79/66.98 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 66.79/66.98 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 66.79/66.98 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 66.79/66.98 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 66.79/66.98 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 66.79/66.98 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 66.79/66.98 Found or_introl00:=(or_introl0 (cODD Xn0)):((cEVEN c0)->((or (cEVEN c0)) (cODD Xn0)))
% 66.79/66.98 Found (or_introl0 (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 66.79/66.98 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 66.79/66.98 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 66.79/66.98 Found (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 66.79/66.98 Found (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of (cIND->((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0))))
% 66.79/66.98 Found (and_rect50 (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 66.79/66.98 Found ((and_rect5 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 66.79/66.98 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 66.79/66.98 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 66.79/66.98 Found x70:=(x7 x60):(cNUMBER Xn0)
% 66.79/66.98 Instantiate: Xn0:=Xn:fofType
% 66.79/66.98 Found (x7 x60) as proof of (cNUMBER Xn)
% 66.79/66.98 Found (x7 x60) as proof of (cNUMBER Xn)
% 66.79/66.98 Found or_introl00:=(or_introl0 (cODD Xn0)):((cEVEN c0)->((or (cEVEN c0)) (cODD Xn0)))
% 66.79/66.98 Found (or_introl0 (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 66.79/66.98 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 66.79/66.98 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 66.79/66.98 Found (fun (x11:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 66.79/66.98 Found (fun (x11:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of (cIND->((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0))))
% 66.79/66.98 Found (and_rect50 (fun (x11:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 66.79/66.98 Found ((and_rect5 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x11:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 66.79/66.98 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x11:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 66.79/66.98 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x11:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 66.79/66.98 Found x50:=(x5 x40):(cNUMBER Xn0)
% 66.79/66.98 Instantiate: Xn0:=Xn:fofType
% 66.79/66.98 Found (x5 x40) as proof of (cNUMBER Xn)
% 66.79/66.98 Found (fun (x12:(cEVEN c0))=> (x5 x40)) as proof of (cNUMBER Xn)
% 66.79/66.98 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 66.79/66.98 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40)) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 66.79/66.98 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 66.79/66.98 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 66.79/66.98 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 67.00/67.21 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 67.00/67.21 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 67.00/67.21 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 67.00/67.21 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 67.00/67.21 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 67.00/67.21 Found x7:(cODD (cS c0))
% 67.00/67.21 Instantiate: Xn0:=(cS c0):fofType
% 67.00/67.21 Found x7 as proof of (cODD Xn0)
% 67.00/67.21 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 67.00/67.21 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 67.00/67.21 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 67.00/67.21 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 67.00/67.21 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 67.00/67.21 Found (fun (x7:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of (cNUMBER Xn0)
% 67.00/67.21 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of ((cODD (cS c0))->(cNUMBER Xn0))
% 67.00/67.21 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn0)))
% 67.00/67.21 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 67.00/67.21 Found ((and_rect3 (cNUMBER Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 67.00/67.21 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) (cNUMBER Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 67.00/67.21 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) (cNUMBER Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 67.00/67.21 Found x31:(cNUMBER Xn0)
% 67.00/67.21 Instantiate: Xn0:=Xn:fofType
% 67.00/67.21 Found (fun (x7:(cODD (cS c0)))=> x31) as proof of (cNUMBER Xn)
% 67.00/67.21 Found (fun (x7:(cODD (cS c0)))=> x31) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 67.00/67.21 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 67.00/67.21 Instantiate: Xn0:=Xn:fofType
% 67.00/67.21 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 67.00/67.21 Found (x5 x20) as proof of (cNUMBER Xn)
% 67.00/67.21 Found (x5 x20) as proof of (cNUMBER Xn)
% 67.00/67.21 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x20)) as proof of (cNUMBER Xn)
% 67.00/67.21 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 67.00/67.21 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x20)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 67.00/67.21 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 67.00/67.21 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 67.00/67.21 Found (x3 x20) as proof of (cNUMBER Xn)
% 67.00/67.21 Found (x3 x20) as proof of (cNUMBER Xn)
% 67.00/67.21 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 69.50/69.70 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 69.50/69.70 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 69.50/69.70 Found x50:=(x5 x40):(cNUMBER Xn0)
% 69.50/69.70 Found (x5 x40) as proof of (cNUMBER Xn0)
% 69.50/69.70 Found (x5 x40) as proof of (cNUMBER Xn0)
% 69.50/69.70 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 69.50/69.70 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 69.50/69.70 Found (x5 x40) as proof of (cNUMBER Xn)
% 69.50/69.70 Found (x5 x40) as proof of (cNUMBER Xn)
% 69.50/69.70 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 69.50/69.70 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x40)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 69.50/69.70 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 69.50/69.70 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 69.50/69.70 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 69.50/69.70 Found x51:(cNUMBER Xn0)
% 69.50/69.70 Instantiate: Xn0:=Xn:fofType
% 69.50/69.70 Found (fun (x7:(cODD (cS c0)))=> x51) as proof of (cNUMBER Xn)
% 69.50/69.70 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> x51) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 69.50/69.70 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> x51) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 69.50/69.70 Found x5:(cODD (cS c0))
% 69.50/69.70 Instantiate: Xn0:=(cS c0):fofType
% 69.50/69.70 Found x5 as proof of (cODD Xn0)
% 69.50/69.70 Found (or_introl00 x5) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 69.50/69.70 Found ((or_introl0 (cEVEN Xn0)) x5) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 69.50/69.70 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 69.50/69.70 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 69.50/69.70 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 69.50/69.70 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 69.50/69.70 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 69.50/69.70 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 69.50/69.70 Found x30:=(x3 x20):(cNUMBER Xn0)
% 69.50/69.70 Found (x3 x20) as proof of (cNUMBER Xn0)
% 69.50/69.70 Found (x3 x20) as proof of (cNUMBER Xn0)
% 69.50/69.70 Found x30:=(x3 x21):(cNUMBER Xn0)
% 69.50/69.70 Instantiate: Xn0:=Xn:fofType
% 69.50/69.70 Found (x3 x21) as proof of (cNUMBER Xn)
% 69.50/69.70 Found (fun (x7:(cODD (cS c0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 69.50/69.70 Found (fun (x7:(cODD (cS c0)))=> (x3 x21)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 69.50/69.70 Found x90:(cNUMBER Xn0)
% 69.50/69.70 Instantiate: Xn0:=Xn:fofType
% 69.50/69.70 Found (fun (x12:(cEVEN c0))=> x90) as proof of (cNUMBER Xn)
% 69.50/69.70 Found (fun (x11:cIND) (x12:(cEVEN c0))=> x90) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 69.50/69.70 Found (fun (x11:cIND) (x12:(cEVEN c0))=> x90) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 69.50/69.70 Found x50:=(x5 x40):(cNUMBER Xn0)
% 69.50/69.70 Found (x5 x40) as proof of (cNUMBER Xn)
% 69.50/69.70 Found (x5 x40) as proof of (cNUMBER Xn)
% 69.50/69.70 Found (x5 x40) as proof of (cNUMBER Xn)
% 69.50/69.70 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 69.50/69.70 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 69.50/69.70 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 69.50/69.70 Found x30:=(x3 x20):(cNUMBER Xn0)
% 69.50/69.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 69.50/69.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 69.50/69.70 Found (fun (x12:(cEVEN c0))=> (x3 x20)) as proof of (cNUMBER Xn)
% 69.50/69.70 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 69.50/69.70 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20)) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 69.50/69.70 Found x70:=(x7 x60):(cNUMBER Xn0)
% 69.50/69.70 Instantiate: Xn0:=Xn:fofType
% 70.29/70.52 Found (x7 x60) as proof of (cNUMBER Xn)
% 70.29/70.52 Found (fun (x12:(cEVEN c0))=> (x7 x60)) as proof of (cNUMBER Xn)
% 70.29/70.52 Found (fun (x12:(cEVEN c0))=> (x7 x60)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 70.29/70.52 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 70.29/70.52 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.29/70.52 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.29/70.52 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.29/70.52 Found x51:(cNUMBER Xn0)
% 70.29/70.52 Instantiate: Xn0:=Xn:fofType
% 70.29/70.52 Found (fun (x7:(cODD (cS c0)))=> x51) as proof of (cNUMBER Xn)
% 70.29/70.52 Found (fun (x7:(cODD (cS c0)))=> x51) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 70.29/70.52 Found x30:=(x3 x20):(cNUMBER Xn0)
% 70.29/70.52 Found (x3 x20) as proof of (cNUMBER Xn0)
% 70.29/70.52 Found (x3 x20) as proof of (cNUMBER Xn0)
% 70.29/70.52 Found x30:=(x3 x21):(cNUMBER Xn0)
% 70.29/70.52 Instantiate: Xn0:=Xn:fofType
% 70.29/70.52 Found (x3 x21) as proof of (cNUMBER Xn)
% 70.29/70.52 Found (x3 x21) as proof of (cNUMBER Xn)
% 70.29/70.52 Found x30:=(x3 x20):(cNUMBER Xn0)
% 70.29/70.52 Found (x3 x20) as proof of (cNUMBER Xn)
% 70.29/70.52 Found (x3 x20) as proof of (cNUMBER Xn)
% 70.29/70.52 Found (x3 x20) as proof of (cNUMBER Xn)
% 70.29/70.52 Found x30:=(x3 x20):(cNUMBER Xn0)
% 70.29/70.52 Found (x3 x20) as proof of (cNUMBER Xn)
% 70.29/70.52 Found (x3 x20) as proof of (cNUMBER Xn)
% 70.29/70.52 Found (fun (x7:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 70.29/70.52 Found (fun (x7:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 70.29/70.52 Found x7:(cODD (cS c0))
% 70.29/70.52 Instantiate: Xn0:=(cS c0):fofType
% 70.29/70.52 Found x7 as proof of (cODD Xn0)
% 70.29/70.52 Found (or_introl00 x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 70.29/70.52 Found ((or_introl0 (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 70.29/70.52 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 70.29/70.52 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 70.29/70.52 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.29/70.52 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.29/70.52 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.29/70.52 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.29/70.52 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 70.29/70.52 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.29/70.52 Found (x3 x20) as proof of (cNUMBER Xn)
% 70.29/70.52 Found (x3 x20) as proof of (cNUMBER Xn)
% 70.29/70.52 Found (x3 x20) as proof of (cNUMBER Xn)
% 70.29/70.52 Found x7:(cODD (cS c0))
% 70.29/70.52 Instantiate: Xn0:=(cS c0):fofType
% 70.29/70.52 Found (fun (x7:(cODD (cS c0)))=> x7) as proof of (cODD Xn0)
% 70.29/70.52 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7) as proof of ((cODD (cS c0))->(cODD Xn0))
% 70.29/70.52 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cODD Xn0)))
% 70.29/70.52 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7)) as proof of (cODD Xn0)
% 70.29/70.52 Found ((and_rect3 (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7)) as proof of (cODD Xn0)
% 70.29/70.52 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7)) as proof of (cODD Xn0)
% 70.29/70.52 Found (fun (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7))) as proof of (cODD Xn0)
% 70.29/70.53 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cODD Xn0))
% 70.29/70.53 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7))) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cODD Xn0)))
% 70.29/70.53 Found (and_rect20 (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7)))) as proof of (cODD Xn0)
% 70.29/70.53 Found ((and_rect2 (cODD Xn0)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7)))) as proof of (cODD Xn0)
% 70.29/70.53 Found (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) (cODD Xn0)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7)))) as proof of (cODD Xn0)
% 70.29/70.54 Found (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) (cODD Xn0)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7)))) as proof of (cODD Xn0)
% 70.29/70.54 Found (or_intror00 (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) (cODD Xn0)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.29/70.54 Found ((or_intror0 (cODD Xn0)) (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x4) x0)) (cODD Xn0)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.29/70.54 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x4) x0)) (cODD Xn0)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.74/71.00 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x4) x0)) (cODD Xn0)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) (cODD Xn0)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x7:(cODD (cS c0)))=> x7))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.74/71.00 Found x7:(cODD (cS c0))
% 70.74/71.00 Instantiate: Xn0:=(cS c0):fofType
% 70.74/71.00 Found x7 as proof of (cODD Xn0)
% 70.74/71.00 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.74/71.00 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.74/71.00 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.74/71.00 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.74/71.00 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 70.74/71.00 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 70.74/71.00 Found x120:=(x12 x110):(cNUMBER Xn0)
% 70.74/71.00 Instantiate: Xn0:=Xn:fofType
% 70.74/71.00 Found (x12 x110) as proof of (cNUMBER Xn)
% 70.74/71.00 Found (x12 x110) as proof of (cNUMBER Xn)
% 70.74/71.00 Found or_introl00:=(or_introl0 (cEVEN Xn0)):((cODD (cS c0))->((or (cODD (cS c0))) (cEVEN Xn0)))
% 70.74/71.00 Found (or_introl0 (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 70.74/71.00 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 70.74/71.00 Found ((or_introl (cODD (cS c0))) (cEVEN Xn0)) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 70.74/71.00 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of ((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0)))
% 70.74/71.00 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cODD Xn0)) (cEVEN Xn0))))
% 70.74/71.00 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 70.74/71.00 Found ((and_rect3 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 70.74/71.00 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 70.74/71.00 Found (fun (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 70.74/71.00 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cODD Xn0)) (cEVEN Xn0)))
% 70.74/71.00 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cODD Xn0)) (cEVEN Xn0))))
% 70.74/71.00 Found (and_rect20 (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 70.74/71.00 Found ((and_rect2 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 70.74/71.00 Found (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 70.82/71.01 Found (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0)))))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 70.82/71.01 Found (or_comm_i00 (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 70.82/71.01 Found ((or_comm_i0 (cEVEN Xn0)) (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x4) x0)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 71.94/72.18 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x4) x0)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 71.94/72.18 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))) P) x4) x0)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x5:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0))) P) x6) x4)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_introl (cODD (cS c0))) (cEVEN Xn0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 71.94/72.18 Found x7:(cODD (cS c0))
% 71.94/72.18 Instantiate: Xn0:=(cS c0):fofType
% 71.94/72.18 Found x7 as proof of (cODD Xn0)
% 71.94/72.18 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 71.94/72.18 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 71.94/72.18 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 71.94/72.18 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 71.94/72.18 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 71.94/72.18 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 71.94/72.18 Found x50:=(x5 x40):(cNUMBER Xn0)
% 71.94/72.18 Found (x5 x40) as proof of (cNUMBER Xn0)
% 71.94/72.18 Found (x5 x40) as proof of (cNUMBER Xn0)
% 71.94/72.18 Found x50:=(x5 x41):(cNUMBER Xn0)
% 71.94/72.18 Instantiate: Xn0:=Xn:fofType
% 71.94/72.18 Found (x5 x41) as proof of (cNUMBER Xn)
% 71.94/72.18 Found (fun (x7:(cODD (cS c0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 71.94/72.18 Found (fun (x7:(cODD (cS c0)))=> (x5 x41)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 71.94/72.18 Found x50:=(x5 x41):(cNUMBER Xn0)
% 71.94/72.18 Instantiate: Xn0:=Xn:fofType
% 71.94/72.18 Found (x5 x41) as proof of (cNUMBER Xn)
% 71.94/72.18 Found (fun (x7:(cODD (cS c0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 71.94/72.18 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x41)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 71.94/72.18 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x41)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 73.29/73.47 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 73.29/73.47 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 73.29/73.47 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 73.29/73.47 Found x50:=(x5 x40):(cNUMBER Xn0)
% 73.29/73.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 73.29/73.47 Found (x5 x40) as proof of (cNUMBER Xn)
% 73.29/73.47 Found (fun (x12:(cEVEN c0))=> (x5 x40)) as proof of (cNUMBER Xn)
% 73.29/73.47 Found (fun (x12:(cEVEN c0))=> (x5 x40)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 73.29/73.47 Found x5:(cODD (cS c0))
% 73.29/73.47 Instantiate: Xn0:=(cS c0):fofType
% 73.29/73.47 Found x5 as proof of (cODD Xn0)
% 73.29/73.47 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 73.29/73.47 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 73.29/73.47 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 73.29/73.47 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 73.29/73.47 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of (cNUMBER Xn0)
% 73.29/73.47 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of (cNUMBER Xn0)
% 73.29/73.47 Found or_introl00:=(or_introl0 (cODD Xn0)):((cEVEN c0)->((or (cEVEN c0)) (cODD Xn0)))
% 73.29/73.47 Found (or_introl0 (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 73.29/73.47 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 73.29/73.47 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 73.29/73.47 Found (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 73.29/73.47 Found (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of (cIND->((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0))))
% 73.29/73.47 Found (and_rect50 (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 73.29/73.47 Found ((and_rect5 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 73.29/73.47 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 73.29/73.47 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 73.29/73.47 Found x90:=(x9 x80):(cNUMBER Xn0)
% 73.29/73.47 Instantiate: Xn0:=Xn:fofType
% 73.29/73.47 Found (x9 x80) as proof of (cNUMBER Xn)
% 73.29/73.47 Found (x9 x80) as proof of (cNUMBER Xn)
% 73.29/73.47 Found x50:(cNUMBER Xn00)
% 73.29/73.47 Found x50 as proof of (cNUMBER Xn00)
% 73.29/73.47 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 73.29/73.47 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 73.29/73.47 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 73.29/73.47 Found x30:(cNUMBER Xn0)
% 73.29/73.47 Found x30 as proof of (cNUMBER Xn0)
% 73.29/73.47 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 73.29/73.47 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 73.29/73.47 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 73.29/73.47 Found or_introl00:=(or_introl0 (cODD Xn0)):((cEVEN c0)->((or (cEVEN c0)) (cODD Xn0)))
% 73.29/73.47 Found (or_introl0 (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 73.29/73.47 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 73.29/73.47 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 73.29/73.47 Found (fun (x11:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 73.29/73.47 Found (fun (x11:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of (cIND->((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0))))
% 73.29/73.47 Found (and_rect50 (fun (x11:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 73.29/73.47 Found ((and_rect5 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x11:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 73.29/73.47 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x11:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 76.82/77.04 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x11:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 76.82/77.04 Found x70:=(x7 x60):(cNUMBER Xn0)
% 76.82/77.04 Instantiate: Xn0:=Xn:fofType
% 76.82/77.04 Found (x7 x60) as proof of (cNUMBER Xn)
% 76.82/77.04 Found (fun (x12:(cEVEN c0))=> (x7 x60)) as proof of (cNUMBER Xn)
% 76.82/77.04 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 76.82/77.04 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60)) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 76.82/77.04 Found x30:=(x3 x20):(cNUMBER Xn0)
% 76.82/77.04 Found (x3 x20) as proof of (cNUMBER Xn0)
% 76.82/77.04 Found (x3 x20) as proof of (cNUMBER Xn0)
% 76.82/77.04 Found x30:=(x3 x21):(cNUMBER Xn0)
% 76.82/77.04 Instantiate: Xn0:=Xn:fofType
% 76.82/77.04 Found (x3 x21) as proof of (cNUMBER Xn)
% 76.82/77.04 Found (x3 x21) as proof of (cNUMBER Xn)
% 76.82/77.04 Found x30:=(x3 x20):(cNUMBER Xn0)
% 76.82/77.04 Found (x3 x20) as proof of (cNUMBER Xn)
% 76.82/77.04 Found (x3 x20) as proof of (cNUMBER Xn)
% 76.82/77.04 Found (x3 x20) as proof of (cNUMBER Xn)
% 76.82/77.04 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 76.82/77.04 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 76.82/77.04 Found (x3 x20) as proof of (cNUMBER Xn)
% 76.82/77.04 Found (x3 x20) as proof of (cNUMBER Xn)
% 76.82/77.04 Found (x3 x20) as proof of (cNUMBER Xn)
% 76.82/77.04 Found x30:=(x3 x20):(cNUMBER Xn0)
% 76.82/77.04 Found (x3 x20) as proof of (cNUMBER Xn)
% 76.82/77.04 Found (x3 x20) as proof of (cNUMBER Xn)
% 76.82/77.04 Found (fun (x7:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 76.82/77.04 Found (fun (x7:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 76.82/77.04 Found x51:(cNUMBER Xn0)
% 76.82/77.04 Instantiate: Xn0:=Xn:fofType
% 76.82/77.04 Found (fun (x7:(cODD (cS c0)))=> x51) as proof of (cNUMBER Xn)
% 76.82/77.04 Found (fun (x7:(cODD (cS c0)))=> x51) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 76.82/77.04 Found x30:=(x3 x20):(cNUMBER Xn0)
% 76.82/77.04 Found (x3 x20) as proof of (cNUMBER Xn)
% 76.82/77.04 Found (x3 x20) as proof of (cNUMBER Xn)
% 76.82/77.04 Found (fun (x7:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 76.82/77.04 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 76.82/77.04 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 76.82/77.04 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 76.82/77.04 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 76.82/77.04 Found (x3 x20) as proof of (cNUMBER Xn)
% 76.82/77.04 Found (x3 x20) as proof of (cNUMBER Xn)
% 76.82/77.04 Found (fun (x12:(cEVEN c0))=> (x3 x20)) as proof of (cNUMBER Xn)
% 76.82/77.04 Found (fun (x12:(cEVEN c0))=> (x3 x20)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 76.82/77.04 Found x120:=(x12 x110):(cNUMBER Xn0)
% 76.82/77.04 Instantiate: Xn0:=Xn:fofType
% 76.82/77.04 Found (x12 x110) as proof of (cNUMBER Xn)
% 76.82/77.04 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x110)) as proof of (cNUMBER Xn)
% 76.82/77.04 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x110)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 76.82/77.04 Found x70:=(x7 x60):(cNUMBER Xn0)
% 76.82/77.04 Found (x7 x60) as proof of (cNUMBER Xn0)
% 76.82/77.04 Found (x7 x60) as proof of (cNUMBER Xn0)
% 76.82/77.04 Found x70:=(x7 x61):(cNUMBER Xn0)
% 76.82/77.04 Instantiate: Xn0:=Xn:fofType
% 76.82/77.04 Found (x7 x61) as proof of (cNUMBER Xn)
% 76.82/77.04 Found (x7 x61) as proof of (cNUMBER Xn)
% 76.82/77.04 Found x70:=(x7 x60):(cNUMBER Xn0)
% 76.82/77.04 Found (x7 x60) as proof of (cNUMBER Xn)
% 76.82/77.04 Found (x7 x60) as proof of (cNUMBER Xn)
% 76.82/77.04 Found (x7 x60) as proof of (cNUMBER Xn)
% 76.82/77.04 Found x50:=(x5 x40):(cNUMBER Xn0)
% 76.82/77.04 Found (x5 x40) as proof of (cNUMBER Xn0)
% 76.82/77.04 Found (x5 x40) as proof of (cNUMBER Xn0)
% 76.82/77.04 Found x50:=(x5 x41):(cNUMBER Xn0)
% 76.82/77.04 Instantiate: Xn0:=Xn:fofType
% 76.82/77.04 Found (x5 x41) as proof of (cNUMBER Xn)
% 76.82/77.04 Found (fun (x7:(cODD (cS c0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 76.82/77.04 Found (fun (x7:(cODD (cS c0)))=> (x5 x41)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 76.82/77.04 Found x30:=(x3 x20):(cNUMBER Xn0)
% 76.82/77.04 Instantiate: Xn0:=Xn:fofType
% 76.82/77.04 Found (x3 x20) as proof of (cNUMBER Xn)
% 76.82/77.04 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 78.40/78.62 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 78.40/78.62 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 78.40/78.62 Found (and_rect20 (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 78.40/78.62 Found ((and_rect2 (cNUMBER Xn)) (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 78.40/78.62 Found (((fun (P:Type) (x4:(((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->P)))=> (((((and_rect ((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))) P) x4) x11)) (cNUMBER Xn)) (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 78.40/78.62 Found x70:=(x7 x60):(cNUMBER Xn0)
% 78.40/78.62 Found (x7 x60) as proof of (cNUMBER Xn)
% 78.40/78.62 Found (x7 x60) as proof of (cNUMBER Xn)
% 78.40/78.62 Found (x7 x60) as proof of (cNUMBER Xn)
% 78.40/78.62 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 78.40/78.62 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 78.40/78.62 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 78.40/78.62 Found x50:(cNUMBER Xn00)
% 78.40/78.62 Found x50 as proof of (cNUMBER Xn00)
% 78.40/78.62 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 78.40/78.62 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 78.40/78.62 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 78.40/78.62 Found x50:=(x5 x40):(cNUMBER Xn0)
% 78.40/78.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 78.40/78.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 78.40/78.62 Found (fun (x12:(cEVEN c0))=> (x5 x40)) as proof of (cNUMBER Xn)
% 78.40/78.62 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 78.40/78.62 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40)) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 78.40/78.62 Found x90:=(x9 x80):(cNUMBER Xn0)
% 78.40/78.62 Instantiate: Xn0:=Xn:fofType
% 78.40/78.62 Found (x9 x80) as proof of (cNUMBER Xn)
% 78.40/78.62 Found (fun (x12:(cEVEN c0))=> (x9 x80)) as proof of (cNUMBER Xn)
% 78.40/78.62 Found (fun (x12:(cEVEN c0))=> (x9 x80)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 78.40/78.62 Found x50:=(x5 x40):(cNUMBER Xn0)
% 78.40/78.62 Found (x5 x40) as proof of (cNUMBER Xn0)
% 78.40/78.62 Found (x5 x40) as proof of (cNUMBER Xn0)
% 78.40/78.62 Found x50:=(x5 x41):(cNUMBER Xn0)
% 78.40/78.62 Instantiate: Xn0:=Xn:fofType
% 78.40/78.62 Found (x5 x41) as proof of (cNUMBER Xn)
% 78.40/78.62 Found (x5 x41) as proof of (cNUMBER Xn)
% 78.40/78.62 Found x50:=(x5 x41):(cNUMBER Xn0)
% 78.40/78.62 Found (x5 x41) as proof of (cNUMBER Xn)
% 78.40/78.62 Found (x5 x41) as proof of (cNUMBER Xn)
% 78.40/78.62 Found (x5 x41) as proof of (cNUMBER Xn)
% 78.40/78.62 Found x50:=(x5 x41):(cNUMBER Xn0)
% 78.40/78.62 Found (x5 x41) as proof of (cNUMBER Xn)
% 78.40/78.62 Found (x5 x41) as proof of (cNUMBER Xn)
% 78.40/78.62 Found (fun (x7:(cODD (cS c0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 78.40/78.62 Found (fun (x7:(cODD (cS c0)))=> (x5 x41)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 78.40/78.62 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 78.40/78.62 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 78.40/78.62 Found (x3 x20) as proof of (cNUMBER Xn)
% 78.40/78.62 Found (x3 x20) as proof of (cNUMBER Xn)
% 78.40/78.62 Found (fun (x7:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 78.40/78.62 Found (fun (x7:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 78.40/78.62 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 78.40/78.62 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 78.40/78.62 Found (x3 x20) as proof of (cNUMBER Xn)
% 78.40/78.62 Found (x3 x20) as proof of (cNUMBER Xn)
% 78.40/78.62 Found (x3 x20) as proof of (cNUMBER Xn)
% 78.40/78.62 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 78.40/78.62 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 78.40/78.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 78.40/78.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 78.40/78.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 78.40/78.62 Found x30:=(x3 x20):(cNUMBER Xn0)
% 78.40/78.62 Found (x3 x20) as proof of (cNUMBER Xn0)
% 78.40/78.62 Found (x3 x20) as proof of (cNUMBER Xn0)
% 78.40/78.62 Found x30:=(x3 x21):(cNUMBER Xn0)
% 78.40/78.62 Instantiate: Xn0:=Xn:fofType
% 78.40/78.62 Found (x3 x21) as proof of (cNUMBER Xn)
% 79.59/79.84 Found (x3 x21) as proof of (cNUMBER Xn)
% 79.59/79.84 Found x30:=(x3 x20):(cNUMBER Xn0)
% 79.59/79.84 Found (x3 x20) as proof of (cNUMBER Xn)
% 79.59/79.84 Found (x3 x20) as proof of (cNUMBER Xn)
% 79.59/79.84 Found (x3 x20) as proof of (cNUMBER Xn)
% 79.59/79.84 Found x7:(cODD (cS c0))
% 79.59/79.84 Instantiate: Xn0:=(cS c0):fofType
% 79.59/79.84 Found x7 as proof of (cODD Xn0)
% 79.59/79.84 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.59/79.84 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.59/79.84 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.59/79.84 Found (fun (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.59/79.84 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 79.59/79.84 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 79.59/79.84 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.59/79.84 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.59/79.84 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.59/79.84 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.59/79.84 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 79.59/79.84 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.59/79.84 Found (x3 x20) as proof of (cNUMBER Xn)
% 79.59/79.84 Found (x3 x20) as proof of (cNUMBER Xn)
% 79.59/79.84 Found (fun (x12:(cEVEN c0))=> (x3 x20)) as proof of (cNUMBER Xn)
% 79.59/79.84 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 79.59/79.84 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20)) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 79.59/79.84 Found x7:(cODD (cS c0))
% 79.59/79.84 Instantiate: Xn0:=(cS c0):fofType
% 79.59/79.84 Found x7 as proof of (cODD Xn0)
% 79.59/79.84 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.59/79.84 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.59/79.84 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.59/79.84 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 79.59/79.84 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 79.59/79.84 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 79.59/79.84 Found x70:=(x7 x60):(cNUMBER Xn0)
% 79.59/79.84 Found (x7 x60) as proof of (cNUMBER Xn0)
% 79.59/79.84 Found (x7 x60) as proof of (cNUMBER Xn0)
% 79.59/79.84 Found x70:=(x7 x61):(cNUMBER Xn0)
% 79.59/79.84 Instantiate: Xn0:=Xn:fofType
% 79.59/79.84 Found (x7 x61) as proof of (cNUMBER Xn)
% 79.59/79.84 Found (x7 x61) as proof of (cNUMBER Xn)
% 79.59/79.84 Found x70:=(x7 x60):(cNUMBER Xn0)
% 79.59/79.84 Found (x7 x60) as proof of (cNUMBER Xn)
% 79.59/79.84 Found (x7 x60) as proof of (cNUMBER Xn)
% 79.59/79.84 Found (x7 x60) as proof of (cNUMBER Xn)
% 79.59/79.84 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 79.59/79.84 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 81.93/82.16 Found (x7 x60) as proof of (cNUMBER Xn)
% 81.93/82.16 Found (x7 x60) as proof of (cNUMBER Xn)
% 81.93/82.16 Found (x7 x60) as proof of (cNUMBER Xn)
% 81.93/82.16 Found x30:=(x3 x20):(cNUMBER Xn0)
% 81.93/82.16 Instantiate: Xn0:=Xn:fofType
% 81.93/82.16 Found (x3 x20) as proof of (cNUMBER Xn)
% 81.93/82.16 Found (fun (x12:(cEVEN c0))=> (x3 x20)) as proof of (cNUMBER Xn)
% 81.93/82.16 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 81.93/82.16 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20)) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 81.93/82.16 Found (and_rect50 (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20))) as proof of (cNUMBER Xn)
% 81.93/82.16 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20))) as proof of (cNUMBER Xn)
% 81.93/82.16 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20))) as proof of (cNUMBER Xn)
% 81.93/82.16 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20))) as proof of (cNUMBER Xn)
% 81.93/82.16 Found x7:(cODD (cS c0))
% 81.93/82.16 Instantiate: Xn0:=(cS c0):fofType
% 81.93/82.16 Found x7 as proof of (cODD Xn0)
% 81.93/82.16 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 81.93/82.16 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 81.93/82.16 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 81.93/82.16 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 81.93/82.16 Found x5:(cODD (cS c0))
% 81.93/82.16 Instantiate: Xn0:=(cS c0):fofType
% 81.93/82.16 Found x5 as proof of (cODD Xn0)
% 81.93/82.16 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 81.93/82.16 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 81.93/82.16 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 81.93/82.16 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 81.93/82.16 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of (cNUMBER Xn0)
% 81.93/82.16 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of (cNUMBER Xn0)
% 81.93/82.16 Found x70:(cNUMBER Xn00)
% 81.93/82.16 Instantiate: Xn00:=Xn:fofType
% 81.93/82.16 Found x70 as proof of (cNUMBER Xn)
% 81.93/82.16 Found x50:(cNUMBER Xn0)
% 81.93/82.16 Instantiate: Xn0:=Xn:fofType
% 81.93/82.16 Found x50 as proof of (cNUMBER Xn)
% 81.93/82.16 Found x30:=(x3 x20):(cNUMBER Xn0)
% 81.93/82.16 Instantiate: Xn0:=Xn:fofType
% 81.93/82.16 Found (x3 x20) as proof of (cNUMBER Xn)
% 81.93/82.16 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 81.93/82.16 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 81.93/82.16 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 81.93/82.16 Found (and_rect20 (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 81.93/82.16 Found ((and_rect2 (cNUMBER Xn)) (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 81.93/82.16 Found (((fun (P:Type) (x4:(((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->P)))=> (((((and_rect ((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))) P) x4) x11)) (cNUMBER Xn)) (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 81.93/82.16 Found x70:=(x7 x60):(cNUMBER Xn0)
% 81.93/82.16 Found (x7 x60) as proof of (cNUMBER Xn)
% 81.93/82.16 Found (x7 x60) as proof of (cNUMBER Xn)
% 81.93/82.16 Found (fun (x12:(cEVEN c0))=> (x7 x60)) as proof of (cNUMBER Xn)
% 81.93/82.16 Found (fun (x12:(cEVEN c0))=> (x7 x60)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 81.93/82.16 Found x30:=(x3 x21):(cNUMBER Xn0)
% 81.93/82.16 Found (x3 x21) as proof of (cNUMBER Xn0)
% 81.93/82.16 Found (x3 x21) as proof of (cNUMBER Xn0)
% 81.93/82.16 Found x30:=(x3 x22):(cNUMBER Xn0)
% 83.01/83.21 Instantiate: Xn0:=Xn:fofType
% 83.01/83.21 Found (x3 x22) as proof of (cNUMBER Xn)
% 83.01/83.21 Found (x3 x22) as proof of (cNUMBER Xn)
% 83.01/83.21 Found x30:=(x3 x22):(cNUMBER Xn0)
% 83.01/83.21 Found (x3 x22) as proof of (cNUMBER Xn)
% 83.01/83.21 Found (x3 x22) as proof of (cNUMBER Xn)
% 83.01/83.21 Found (x3 x22) as proof of (cNUMBER Xn)
% 83.01/83.21 Found or_introl00:=(or_introl0 (cODD Xn0)):((cEVEN c0)->((or (cEVEN c0)) (cODD Xn0)))
% 83.01/83.21 Found (or_introl0 (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 83.01/83.21 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 83.01/83.21 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 83.01/83.21 Found (fun (x11:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 83.01/83.21 Found (fun (x11:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of (cIND->((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0))))
% 83.01/83.21 Found (and_rect50 (fun (x11:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 83.01/83.21 Found ((and_rect5 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x11:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 83.01/83.21 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x11:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 83.01/83.21 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x11:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 83.01/83.21 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 83.01/83.21 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 83.01/83.21 Found (x5 x41) as proof of (cNUMBER Xn)
% 83.01/83.21 Found (x5 x41) as proof of (cNUMBER Xn)
% 83.01/83.21 Found (x5 x41) as proof of (cNUMBER Xn)
% 83.01/83.21 Found x50:=(x5 x40):(cNUMBER Xn0)
% 83.01/83.21 Found (x5 x40) as proof of (cNUMBER Xn0)
% 83.01/83.21 Found (x5 x40) as proof of (cNUMBER Xn0)
% 83.01/83.21 Found x50:=(x5 x41):(cNUMBER Xn0)
% 83.01/83.21 Instantiate: Xn0:=Xn:fofType
% 83.01/83.21 Found (x5 x41) as proof of (cNUMBER Xn)
% 83.01/83.21 Found (x5 x41) as proof of (cNUMBER Xn)
% 83.01/83.21 Found x50:=(x5 x41):(cNUMBER Xn0)
% 83.01/83.21 Found (x5 x41) as proof of (cNUMBER Xn)
% 83.01/83.21 Found (x5 x41) as proof of (cNUMBER Xn)
% 83.01/83.21 Found (x5 x41) as proof of (cNUMBER Xn)
% 83.01/83.21 Found x90:=(x9 x80):(cNUMBER Xn0)
% 83.01/83.21 Instantiate: Xn0:=Xn:fofType
% 83.01/83.21 Found (x9 x80) as proof of (cNUMBER Xn)
% 83.01/83.21 Found (fun (x12:(cEVEN c0))=> (x9 x80)) as proof of (cNUMBER Xn)
% 83.01/83.21 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x9 x80)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 83.01/83.21 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x9 x80)) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 83.01/83.21 Found x50:=(x5 x41):(cNUMBER Xn0)
% 83.01/83.21 Found (x5 x41) as proof of (cNUMBER Xn)
% 83.01/83.21 Found (x5 x41) as proof of (cNUMBER Xn)
% 83.01/83.21 Found (fun (x7:(cODD (cS c0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 83.01/83.21 Found (fun (x7:(cODD (cS c0)))=> (x5 x41)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 83.01/83.21 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 83.01/83.21 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 83.01/83.21 Found (x3 x20) as proof of (cNUMBER Xn)
% 83.01/83.21 Found (x3 x20) as proof of (cNUMBER Xn)
% 83.01/83.21 Found (fun (x7:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 83.01/83.21 Found (fun (x7:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 83.01/83.21 Found x120:=(x12 x110):(cNUMBER Xn0)
% 83.01/83.21 Found (x12 x110) as proof of (cNUMBER Xn)
% 83.01/83.21 Found (x12 x110) as proof of (cNUMBER Xn)
% 83.01/83.21 Found (x12 x110) as proof of (cNUMBER Xn)
% 83.01/83.21 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 83.01/83.21 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 83.01/83.21 Found (x3 x20) as proof of (cNUMBER Xn)
% 83.01/83.21 Found (x3 x20) as proof of (cNUMBER Xn)
% 83.01/83.21 Found (fun (x7:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 83.01/83.21 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 83.01/83.21 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x20)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 83.01/83.21 Found x50:=(x5 x41):(cNUMBER Xn0)
% 83.01/83.21 Found (x5 x41) as proof of (cNUMBER Xn)
% 85.23/85.42 Found (x5 x41) as proof of (cNUMBER Xn)
% 85.23/85.42 Found (fun (x7:(cODD (cS c0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 85.23/85.42 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x41)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 85.23/85.42 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x41)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 85.23/85.42 Found x22:((or (cEVEN Xn0)) (cODD Xn0))
% 85.23/85.42 Found x22 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 85.23/85.42 Found (x3 x22) as proof of (cNUMBER Xn)
% 85.23/85.42 Found (x3 x22) as proof of (cNUMBER Xn)
% 85.23/85.42 Found (x3 x22) as proof of (cNUMBER Xn)
% 85.23/85.42 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 85.23/85.42 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 85.23/85.42 Found (x5 x40) as proof of (cNUMBER Xn)
% 85.23/85.42 Found (x5 x40) as proof of (cNUMBER Xn)
% 85.23/85.42 Found (fun (x12:(cEVEN c0))=> (x5 x40)) as proof of (cNUMBER Xn)
% 85.23/85.42 Found (fun (x12:(cEVEN c0))=> (x5 x40)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 85.23/85.42 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 85.23/85.42 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 85.23/85.42 Found (x3 x20) as proof of (cNUMBER Xn)
% 85.23/85.42 Found (x3 x20) as proof of (cNUMBER Xn)
% 85.23/85.42 Found (x3 x20) as proof of (cNUMBER Xn)
% 85.23/85.42 Found x70:(cNUMBER Xn00)
% 85.23/85.42 Instantiate: Xn00:=Xn:fofType
% 85.23/85.42 Found x70 as proof of (cNUMBER Xn)
% 85.23/85.42 Found x30:(cNUMBER Xn0)
% 85.23/85.42 Instantiate: Xn0:=Xn:fofType
% 85.23/85.42 Found x30 as proof of (cNUMBER Xn)
% 85.23/85.42 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 85.23/85.42 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 85.23/85.42 Found (x7 x60) as proof of (cNUMBER Xn)
% 85.23/85.42 Found (x7 x60) as proof of (cNUMBER Xn)
% 85.23/85.42 Found (x7 x60) as proof of (cNUMBER Xn)
% 85.23/85.42 Found x30:=(x3 x20):(cNUMBER Xn0)
% 85.23/85.42 Instantiate: Xn0:=Xn:fofType
% 85.23/85.42 Found (x3 x20) as proof of (cNUMBER Xn)
% 85.23/85.42 Found (fun (x12:(cEVEN c0))=> (x3 x20)) as proof of (cNUMBER Xn)
% 85.23/85.42 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 85.23/85.42 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20)) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 85.23/85.42 Found (and_rect50 (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20))) as proof of (cNUMBER Xn)
% 85.23/85.42 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20))) as proof of (cNUMBER Xn)
% 85.23/85.42 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20))) as proof of (cNUMBER Xn)
% 85.23/85.42 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 85.23/85.42 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20)))) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 85.23/85.42 Found x70:=(x7 x61):(cNUMBER Xn0)
% 85.23/85.42 Instantiate: Xn0:=Xn:fofType
% 85.23/85.42 Found (x7 x61) as proof of (cNUMBER Xn)
% 85.23/85.42 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x61)) as proof of (cNUMBER Xn)
% 85.23/85.42 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x61)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 85.23/85.42 Found x5:(cODD (cS c0))
% 85.23/85.42 Instantiate: Xn0:=(cS c0):fofType
% 85.23/85.42 Found x5 as proof of (cODD Xn0)
% 85.23/85.42 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 85.23/85.42 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 85.23/85.42 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 85.23/85.42 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 85.23/85.42 Found (x9 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of (cNUMBER Xn0)
% 85.23/85.42 Found (x9 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of (cNUMBER Xn0)
% 85.23/85.42 Found x50:(cNUMBER Xn0)
% 85.23/85.42 Instantiate: Xn0:=Xn:fofType
% 85.23/85.42 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of (cNUMBER Xn)
% 85.53/85.73 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 85.53/85.73 Found or_introl00:=(or_introl0 (cODD Xn0)):((cEVEN c0)->((or (cEVEN c0)) (cODD Xn0)))
% 85.53/85.73 Found (or_introl0 (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 85.53/85.73 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 85.53/85.73 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 85.53/85.73 Found (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 85.53/85.73 Found (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of (cIND->((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0))))
% 85.53/85.73 Found (and_rect50 (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 85.53/85.73 Found ((and_rect5 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 85.53/85.73 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 85.53/85.73 Found (fun (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 85.53/85.73 Found (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 85.53/85.73 Found (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))) as proof of (((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 85.53/85.73 Found (and_rect40 (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 85.53/85.73 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 85.53/85.73 Found (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 85.53/85.73 Found (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 86.41/86.65 Found x90:=(x9 x80):(cNUMBER Xn0)
% 86.41/86.65 Found (x9 x80) as proof of (cNUMBER Xn)
% 86.41/86.65 Found (x9 x80) as proof of (cNUMBER Xn)
% 86.41/86.65 Found (x9 x80) as proof of (cNUMBER Xn)
% 86.41/86.65 Found x30:=(x3 x20):(cNUMBER Xn0)
% 86.41/86.65 Instantiate: Xn0:=Xn:fofType
% 86.41/86.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 86.41/86.65 Found (fun (x12:(cEVEN c0))=> (x3 x20)) as proof of (cNUMBER Xn)
% 86.41/86.65 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 86.41/86.65 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20)) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 86.41/86.65 Found (and_rect50 (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20))) as proof of (cNUMBER Xn)
% 86.41/86.65 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20))) as proof of (cNUMBER Xn)
% 86.41/86.65 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20))) as proof of (cNUMBER Xn)
% 86.41/86.65 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 86.41/86.65 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20)))) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 86.41/86.65 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x20)))) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 86.41/86.65 Found x30:=(x3 x21):(cNUMBER Xn0)
% 86.41/86.65 Found (x3 x21) as proof of (cNUMBER Xn0)
% 86.41/86.65 Found (x3 x21) as proof of (cNUMBER Xn0)
% 86.41/86.65 Found x30:=(x3 x22):(cNUMBER Xn0)
% 86.41/86.65 Instantiate: Xn0:=Xn:fofType
% 86.41/86.65 Found (x3 x22) as proof of (cNUMBER Xn)
% 86.41/86.65 Found (x3 x22) as proof of (cNUMBER Xn)
% 86.41/86.65 Found x30:=(x3 x22):(cNUMBER Xn0)
% 86.41/86.65 Found (x3 x22) as proof of (cNUMBER Xn)
% 86.41/86.65 Found (x3 x22) as proof of (cNUMBER Xn)
% 86.41/86.65 Found (x3 x22) as proof of (cNUMBER Xn)
% 86.41/86.65 Found x30:(cNUMBER Xn0)
% 86.41/86.65 Instantiate: Xn0:=Xn:fofType
% 86.41/86.65 Found (fun (x8:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 86.41/86.65 Found (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 86.41/86.65 Found (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x30) as proof of ((cODD Xn0)->((cODD (cS c0))->(cNUMBER Xn)))
% 86.41/86.65 Found x30:(cNUMBER Xn0)
% 86.41/86.65 Instantiate: Xn0:=Xn:fofType
% 86.41/86.65 Found (fun (x8:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 86.41/86.65 Found (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 86.41/86.65 Found (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x30) as proof of ((cEVEN Xn0)->((cODD (cS c0))->(cNUMBER Xn)))
% 86.41/86.65 Found ((or_ind00 (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x30)) (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x30)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 86.41/86.65 Found (((or_ind0 ((cODD (cS c0))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x30)) (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x30)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 86.41/86.65 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) x20)) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x30)) (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x30)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 86.41/86.65 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x2 x30))) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x30)) (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x30)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 86.41/86.65 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x2 x30))) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x30)) (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x30)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 87.84/88.06 Found x70:=(x7 x60):(cNUMBER Xn0)
% 87.84/88.06 Found (x7 x60) as proof of (cNUMBER Xn)
% 87.84/88.06 Found (x7 x60) as proof of (cNUMBER Xn)
% 87.84/88.06 Found (fun (x12:(cEVEN c0))=> (x7 x60)) as proof of (cNUMBER Xn)
% 87.84/88.06 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 87.84/88.06 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60)) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 87.84/88.06 Found x50:(cNUMBER Xn00)
% 87.84/88.06 Instantiate: Xn00:=Xn:fofType
% 87.84/88.06 Found x50 as proof of (cNUMBER Xn)
% 87.84/88.06 Found x30:(cNUMBER Xn0)
% 87.84/88.06 Instantiate: Xn0:=Xn:fofType
% 87.84/88.06 Found x30 as proof of (cNUMBER Xn)
% 87.84/88.06 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 87.84/88.06 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 87.84/88.06 Found (x5 x41) as proof of (cNUMBER Xn)
% 87.84/88.06 Found (x5 x41) as proof of (cNUMBER Xn)
% 87.84/88.06 Found (fun (x7:(cODD (cS c0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 87.84/88.06 Found (fun (x7:(cODD (cS c0)))=> (x5 x41)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 87.84/88.06 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 87.84/88.06 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 87.84/88.06 Found (x5 x41) as proof of (cNUMBER Xn)
% 87.84/88.06 Found (x5 x41) as proof of (cNUMBER Xn)
% 87.84/88.06 Found (x5 x41) as proof of (cNUMBER Xn)
% 87.84/88.06 Found x50:=(x5 x40):(cNUMBER Xn0)
% 87.84/88.06 Found (x5 x40) as proof of (cNUMBER Xn0)
% 87.84/88.06 Found (x5 x40) as proof of (cNUMBER Xn0)
% 87.84/88.06 Found x50:=(x5 x41):(cNUMBER Xn0)
% 87.84/88.06 Instantiate: Xn0:=Xn:fofType
% 87.84/88.06 Found (x5 x41) as proof of (cNUMBER Xn)
% 87.84/88.06 Found (x5 x41) as proof of (cNUMBER Xn)
% 87.84/88.06 Found x50:=(x5 x41):(cNUMBER Xn0)
% 87.84/88.06 Found (x5 x41) as proof of (cNUMBER Xn)
% 87.84/88.06 Found (x5 x41) as proof of (cNUMBER Xn)
% 87.84/88.06 Found (x5 x41) as proof of (cNUMBER Xn)
% 87.84/88.06 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 87.84/88.06 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 87.84/88.06 Found (x7 x60) as proof of (cNUMBER Xn)
% 87.84/88.06 Found (x7 x60) as proof of (cNUMBER Xn)
% 87.84/88.06 Found (x7 x60) as proof of (cNUMBER Xn)
% 87.84/88.06 Found x22:((or (cEVEN Xn0)) (cODD Xn0))
% 87.84/88.06 Found x22 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 87.84/88.06 Found (x3 x22) as proof of (cNUMBER Xn)
% 87.84/88.06 Found (x3 x22) as proof of (cNUMBER Xn)
% 87.84/88.06 Found (x3 x22) as proof of (cNUMBER Xn)
% 87.84/88.06 Found x120:=(x12 x110):(cNUMBER Xn0)
% 87.84/88.06 Found (x12 x110) as proof of (cNUMBER Xn)
% 87.84/88.06 Found (x12 x110) as proof of (cNUMBER Xn)
% 87.84/88.06 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x110)) as proof of (cNUMBER Xn)
% 87.84/88.06 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x110)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 87.84/88.06 Found x7:(cODD (cS c0))
% 87.84/88.06 Instantiate: Xn0:=(cS c0):fofType
% 87.84/88.06 Found x7 as proof of (cODD Xn0)
% 87.84/88.06 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 87.84/88.06 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 87.84/88.06 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 87.84/88.06 Found (fun (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 87.84/88.06 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 87.84/88.06 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 87.84/88.06 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 87.84/88.06 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 87.84/88.06 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 90.39/90.61 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 90.39/90.61 Found x5:(cODD (cS c0))
% 90.39/90.61 Instantiate: Xn0:=(cS c0):fofType
% 90.39/90.61 Found x5 as proof of (cODD Xn0)
% 90.39/90.61 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 90.39/90.61 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 90.39/90.61 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 90.39/90.61 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 90.39/90.61 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of (cNUMBER Xn0)
% 90.39/90.61 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of (cNUMBER Xn0)
% 90.39/90.61 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 90.39/90.61 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 90.39/90.61 Found (x5 x40) as proof of (cNUMBER Xn)
% 90.39/90.61 Found (x5 x40) as proof of (cNUMBER Xn)
% 90.39/90.61 Found (fun (x12:(cEVEN c0))=> (x5 x40)) as proof of (cNUMBER Xn)
% 90.39/90.61 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 90.39/90.61 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40)) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 90.39/90.61 Found x7:(cODD (cS c0))
% 90.39/90.61 Instantiate: Xn0:=(cS c0):fofType
% 90.39/90.61 Found x7 as proof of (cODD Xn0)
% 90.39/90.61 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 90.39/90.61 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 90.39/90.61 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 90.39/90.61 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 90.39/90.61 Found x30:(cNUMBER Xn0)
% 90.39/90.61 Instantiate: Xn0:=Xn:fofType
% 90.39/90.61 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 90.39/90.61 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 90.39/90.61 Found x50:=(x5 x40):(cNUMBER Xn0)
% 90.39/90.61 Instantiate: Xn0:=Xn:fofType
% 90.39/90.61 Found (x5 x40) as proof of (cNUMBER Xn)
% 90.39/90.61 Found (fun (x12:(cEVEN c0))=> (x5 x40)) as proof of (cNUMBER Xn)
% 90.39/90.61 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 90.39/90.61 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40)) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 90.39/90.61 Found (and_rect50 (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40))) as proof of (cNUMBER Xn)
% 90.39/90.61 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40))) as proof of (cNUMBER Xn)
% 90.39/90.61 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40))) as proof of (cNUMBER Xn)
% 90.39/90.61 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40))) as proof of (cNUMBER Xn)
% 90.39/90.61 Found x7:(cODD (cS c0))
% 90.39/90.61 Instantiate: Xn0:=(cS c0):fofType
% 90.39/90.61 Found x7 as proof of (cODD Xn0)
% 90.39/90.61 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 90.39/90.61 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 90.39/90.61 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 90.39/90.61 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 90.39/90.61 Found x50:(cNUMBER Xn0)
% 90.39/90.61 Instantiate: Xn0:=Xn:fofType
% 90.39/90.61 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of (cNUMBER Xn)
% 90.39/90.61 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 92.65/92.88 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 92.65/92.88 Found x90:=(x9 x80):(cNUMBER Xn0)
% 92.65/92.88 Found (x9 x80) as proof of (cNUMBER Xn)
% 92.65/92.88 Found (x9 x80) as proof of (cNUMBER Xn)
% 92.65/92.88 Found (fun (x12:(cEVEN c0))=> (x9 x80)) as proof of (cNUMBER Xn)
% 92.65/92.88 Found (fun (x12:(cEVEN c0))=> (x9 x80)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 92.65/92.88 Found x30:=(x3 x21):(cNUMBER Xn0)
% 92.65/92.88 Instantiate: Xn0:=Xn:fofType
% 92.65/92.88 Found (x3 x21) as proof of (cNUMBER Xn)
% 92.65/92.88 Found (fun (x7:(cODD (cS c0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 92.65/92.88 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 92.65/92.88 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 92.65/92.88 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 92.65/92.88 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 92.65/92.88 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 92.65/92.88 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 92.65/92.88 Found x50:(cNUMBER Xn00)
% 92.65/92.88 Instantiate: Xn00:=Xn:fofType
% 92.65/92.88 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 92.65/92.88 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 92.65/92.88 Found x30:(cNUMBER Xn0)
% 92.65/92.88 Instantiate: Xn0:=Xn:fofType
% 92.65/92.88 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 92.65/92.88 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 92.65/92.88 Found x30:(cNUMBER Xn0)
% 92.65/92.88 Instantiate: Xn0:=Xn:fofType
% 92.65/92.88 Found (fun (x8:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 92.65/92.88 Found (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 92.65/92.88 Found (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x30) as proof of ((cEVEN Xn0)->((cODD (cS c0))->(cNUMBER Xn)))
% 92.65/92.88 Found x30:(cNUMBER Xn0)
% 92.65/92.88 Instantiate: Xn0:=Xn:fofType
% 92.65/92.88 Found (fun (x8:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 92.65/92.88 Found (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 92.65/92.88 Found (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x30) as proof of ((cODD Xn0)->((cODD (cS c0))->(cNUMBER Xn)))
% 92.65/92.88 Found ((or_ind00 (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x30)) (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x30)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 92.65/92.88 Found (((or_ind0 ((cODD (cS c0))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x30)) (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x30)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 93.19/93.46 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) x20)) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x30)) (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x30)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 93.19/93.46 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x2 x30))) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x30)) (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x30)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 93.19/93.46 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))))=> ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x2 x30))) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x30)) (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x30))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 93.19/93.46 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))))=> ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x2 x30))) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x30)) (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x30))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 93.19/93.46 Found or_introl00:=(or_introl0 (cODD Xn0)):((cEVEN c0)->((or (cEVEN c0)) (cODD Xn0)))
% 93.19/93.46 Found (or_introl0 (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 93.19/93.46 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 93.19/93.46 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 93.19/93.46 Found (fun (x11:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 93.19/93.46 Found (fun (x11:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of (cIND->((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0))))
% 93.19/93.46 Found (and_rect50 (fun (x11:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 93.19/93.46 Found ((and_rect5 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x11:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 93.19/93.46 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x11:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 93.19/93.46 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x11:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 93.19/93.46 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 93.19/93.46 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 93.19/93.46 Found (x5 x41) as proof of (cNUMBER Xn)
% 93.19/93.46 Found (x5 x41) as proof of (cNUMBER Xn)
% 93.19/93.46 Found (fun (x7:(cODD (cS c0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 93.19/93.46 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x41)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 93.19/93.46 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x41)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 93.19/93.46 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 93.19/93.46 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 93.19/93.46 Found (x5 x41) as proof of (cNUMBER Xn)
% 93.19/93.46 Found (x5 x41) as proof of (cNUMBER Xn)
% 93.19/93.46 Found (fun (x7:(cODD (cS c0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 93.19/93.46 Found (fun (x7:(cODD (cS c0)))=> (x5 x41)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 93.19/93.46 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 94.93/95.15 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.93/95.15 Found (x7 x60) as proof of (cNUMBER Xn)
% 94.93/95.15 Found (x7 x60) as proof of (cNUMBER Xn)
% 94.93/95.15 Found (fun (x12:(cEVEN c0))=> (x7 x60)) as proof of (cNUMBER Xn)
% 94.93/95.15 Found (fun (x12:(cEVEN c0))=> (x7 x60)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 94.93/95.15 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 94.93/95.15 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 94.93/95.15 Found (x5 x41) as proof of (cNUMBER Xn)
% 94.93/95.15 Found (x5 x41) as proof of (cNUMBER Xn)
% 94.93/95.15 Found (x5 x41) as proof of (cNUMBER Xn)
% 94.93/95.15 Found x30:(cNUMBER Xn0)
% 94.93/95.15 Instantiate: Xn0:=Xn:fofType
% 94.93/95.15 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 94.93/95.15 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 94.93/95.15 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 94.93/95.15 Found x30:=(x3 x21):(cNUMBER Xn0)
% 94.93/95.15 Instantiate: Xn0:=Xn:fofType
% 94.93/95.15 Found (x3 x21) as proof of (cNUMBER Xn)
% 94.93/95.15 Found (fun (x7:(cODD (cS c0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 94.93/95.15 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 94.93/95.15 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 94.93/95.15 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 94.93/95.15 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 94.93/95.15 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 94.93/95.15 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21)))) as proof of (cNUMBER Xn)
% 94.93/95.15 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21)))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 94.93/95.15 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21)))) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 95.43/95.62 Found x50:=(x5 x40):(cNUMBER Xn0)
% 95.43/95.62 Instantiate: Xn0:=Xn:fofType
% 95.43/95.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 95.43/95.62 Found (fun (x12:(cEVEN c0))=> (x5 x40)) as proof of (cNUMBER Xn)
% 95.43/95.62 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 95.43/95.62 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40)) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 95.43/95.62 Found (and_rect50 (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40))) as proof of (cNUMBER Xn)
% 95.43/95.62 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40))) as proof of (cNUMBER Xn)
% 95.43/95.62 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40))) as proof of (cNUMBER Xn)
% 95.43/95.62 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40)))) as proof of (cNUMBER Xn)
% 95.43/95.62 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40)))) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 95.43/95.62 Found x7:(cODD (cS c0))
% 95.43/95.62 Instantiate: Xn0:=(cS c0):fofType
% 95.43/95.62 Found x7 as proof of (cODD Xn0)
% 95.43/95.62 Found (or_introl00 x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 95.43/95.62 Found ((or_introl0 (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 95.43/95.62 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 95.43/95.62 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 95.43/95.62 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 95.43/95.62 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 95.43/95.62 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 95.43/95.62 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 95.43/95.62 Found x110:((or (cEVEN Xn0)) (cODD Xn0))
% 95.43/95.62 Found x110 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 95.43/95.62 Found (x12 x110) as proof of (cNUMBER Xn)
% 95.43/95.62 Found (x12 x110) as proof of (cNUMBER Xn)
% 95.43/95.62 Found (x12 x110) as proof of (cNUMBER Xn)
% 95.43/95.62 Found x30:=(x3 x21):(cNUMBER Xn0)
% 95.43/95.62 Instantiate: Xn0:=Xn:fofType
% 95.43/95.62 Found (x3 x21) as proof of (cNUMBER Xn)
% 95.43/95.62 Found (fun (x4:(cEVEN Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 95.43/95.62 Found (fun (x4:(cEVEN Xn0))=> (x3 x21)) as proof of ((cEVEN Xn0)->(cNUMBER Xn))
% 95.43/95.62 Found x30:=(x3 x21):(cNUMBER Xn0)
% 95.43/95.62 Instantiate: Xn0:=Xn:fofType
% 95.43/95.62 Found (x3 x21) as proof of (cNUMBER Xn)
% 95.43/95.62 Found (fun (x4:(cODD Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 95.43/95.62 Found (fun (x4:(cODD Xn0))=> (x3 x21)) as proof of ((cODD Xn0)->(cNUMBER Xn))
% 95.43/95.62 Found ((or_ind00 (fun (x4:(cEVEN Xn0))=> (x3 x21))) (fun (x4:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 95.43/95.62 Found (((or_ind0 (cNUMBER Xn)) (fun (x4:(cEVEN Xn0))=> (x3 x21))) (fun (x4:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 95.43/95.62 Found ((((fun (P:Prop) (x4:((cEVEN Xn0)->P)) (x5:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x4) x5) x20)) (cNUMBER Xn)) (fun (x4:(cEVEN Xn0))=> (x3 x21))) (fun (x4:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 95.43/95.62 Found ((((fun (P:Prop) (x4:((cEVEN Xn0)->P)) (x5:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x4) x5) x20)) (cNUMBER Xn)) (fun (x4:(cEVEN Xn0))=> (x3 x21))) (fun (x4:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 96.01/96.20 Found or_introl00:=(or_introl0 (cODD Xn0)):((cEVEN c0)->((or (cEVEN c0)) (cODD Xn0)))
% 96.01/96.20 Found (or_introl0 (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 96.01/96.20 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 96.01/96.20 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 96.01/96.20 Found (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 96.01/96.20 Found (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of (cIND->((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0))))
% 96.01/96.20 Found (and_rect50 (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 96.01/96.20 Found ((and_rect5 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 96.01/96.20 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 96.01/96.20 Found (fun (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 96.01/96.20 Found (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 96.01/96.20 Found (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))) as proof of (((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 96.01/96.20 Found (and_rect40 (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 96.01/96.20 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 96.01/96.20 Found (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 96.01/96.20 Found (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 96.49/96.71 Found x30:(cNUMBER Xn0)
% 96.49/96.71 Instantiate: Xn0:=Xn:fofType
% 96.49/96.71 Found (fun (x8:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 96.49/96.71 Found (fun (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x8:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 96.49/96.71 Found (fun (x6:(cEVEN Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x8:(cODD (cS c0)))=> x30) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 96.49/96.71 Found (fun (x6:(cEVEN Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x8:(cODD (cS c0)))=> x30) as proof of ((cEVEN Xn0)->(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn))))
% 96.49/96.71 Found x30:(cNUMBER Xn0)
% 96.49/96.71 Instantiate: Xn0:=Xn:fofType
% 96.49/96.71 Found (fun (x8:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 96.49/96.71 Found (fun (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x8:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 96.49/96.71 Found (fun (x6:(cODD Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x8:(cODD (cS c0)))=> x30) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 96.49/96.71 Found (fun (x6:(cODD Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x8:(cODD (cS c0)))=> x30) as proof of ((cODD Xn0)->(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn))))
% 96.49/96.71 Found ((or_ind00 (fun (x6:(cEVEN Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x8:(cODD (cS c0)))=> x30)) (fun (x6:(cODD Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x8:(cODD (cS c0)))=> x30)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 96.49/96.71 Found (((or_ind0 (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))) (fun (x6:(cEVEN Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x8:(cODD (cS c0)))=> x30)) (fun (x6:(cODD Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x8:(cODD (cS c0)))=> x30)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 96.49/96.71 Found ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) x20)) (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn)))) (fun (x6:(cEVEN Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x30)) (fun (x6:(cODD Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x30)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 96.49/96.71 Found ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) (x2 x30))) (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn)))) (fun (x6:(cEVEN Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x30)) (fun (x6:(cODD Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x30)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 97.01/97.22 Found ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) (x2 x30))) (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn)))) (fun (x6:(cEVEN Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x30)) (fun (x6:(cODD Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x30)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 97.01/97.22 Found x50:=(x5 x40):(cNUMBER Xn0)
% 97.01/97.22 Instantiate: Xn0:=Xn:fofType
% 97.01/97.22 Found (x5 x40) as proof of (cNUMBER Xn)
% 97.01/97.22 Found (fun (x12:(cEVEN c0))=> (x5 x40)) as proof of (cNUMBER Xn)
% 97.01/97.22 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 97.01/97.22 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40)) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 97.01/97.22 Found (and_rect50 (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40))) as proof of (cNUMBER Xn)
% 97.01/97.22 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40))) as proof of (cNUMBER Xn)
% 97.01/97.22 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40))) as proof of (cNUMBER Xn)
% 97.01/97.22 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40)))) as proof of (cNUMBER Xn)
% 97.01/97.22 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40)))) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 97.01/97.22 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x40)))) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 97.01/97.22 Found x70:=(x7 x60):(cNUMBER Xn00)
% 97.01/97.22 Instantiate: Xn00:=Xn:fofType
% 97.01/97.22 Found (x7 x60) as proof of (cNUMBER Xn)
% 97.01/97.22 Found (x7 x60) as proof of (cNUMBER Xn)
% 97.01/97.22 Found x50:=(x5 x40):(cNUMBER Xn0)
% 97.01/97.22 Instantiate: Xn0:=Xn:fofType
% 97.01/97.22 Found (x5 x40) as proof of (cNUMBER Xn)
% 97.01/97.22 Found (x5 x40) as proof of (cNUMBER Xn)
% 97.01/97.22 Found x50:(cNUMBER Xn0)
% 97.01/97.22 Instantiate: Xn0:=Xn:fofType
% 97.01/97.22 Found (fun (x8:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 97.01/97.22 Found (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 97.01/97.22 Found (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x50) as proof of ((cODD Xn0)->((cODD (cS c0))->(cNUMBER Xn)))
% 97.01/97.22 Found x50:(cNUMBER Xn0)
% 97.01/97.22 Instantiate: Xn0:=Xn:fofType
% 97.01/97.22 Found (fun (x8:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 97.01/97.22 Found (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 97.01/97.22 Found (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x50) as proof of ((cEVEN Xn0)->((cODD (cS c0))->(cNUMBER Xn)))
% 97.01/97.22 Found ((or_ind00 (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x50)) (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x50)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 97.01/97.22 Found (((or_ind0 ((cODD (cS c0))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x50)) (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x50)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 97.01/97.22 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) x40)) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x50)) (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x50)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 97.43/97.65 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x4 x50))) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x50)) (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x50)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 97.43/97.65 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x4 x50))) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x50)) (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x50)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 97.43/97.65 Found x30:=(x3 x21):(cNUMBER Xn0)
% 97.43/97.65 Instantiate: Xn0:=Xn:fofType
% 97.43/97.65 Found (x3 x21) as proof of (cNUMBER Xn)
% 97.43/97.65 Found (fun (x7:(cODD (cS c0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 97.43/97.65 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 97.43/97.65 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 97.43/97.65 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 97.43/97.65 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 97.43/97.65 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 97.43/97.65 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21)))) as proof of (cNUMBER Xn)
% 97.43/97.65 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21)))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 97.43/97.65 Found x90:=(x9 x80):(cNUMBER Xn0)
% 97.43/97.65 Found (x9 x80) as proof of (cNUMBER Xn)
% 97.43/97.65 Found (x9 x80) as proof of (cNUMBER Xn)
% 97.43/97.65 Found (fun (x12:(cEVEN c0))=> (x9 x80)) as proof of (cNUMBER Xn)
% 97.43/97.65 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x9 x80)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 97.43/97.65 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x9 x80)) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 97.43/97.65 Found x30:=(x3 x21):(cNUMBER Xn0)
% 97.43/97.65 Instantiate: Xn0:=Xn:fofType
% 97.43/97.65 Found (x3 x21) as proof of (cNUMBER Xn)
% 97.43/97.65 Found (fun (x7:(cODD (cS c0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 97.43/97.65 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 97.43/97.65 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 98.70/98.91 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 98.70/98.91 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 98.70/98.91 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 98.70/98.91 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 98.70/98.91 Found x30:(cNUMBER Xn0)
% 98.70/98.91 Instantiate: Xn0:=Xn:fofType
% 98.70/98.91 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 98.70/98.91 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 98.70/98.91 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 98.70/98.91 Found x50:(cNUMBER Xn00)
% 98.70/98.91 Instantiate: Xn00:=Xn:fofType
% 98.70/98.91 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 98.70/98.91 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 98.70/98.91 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x50) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 98.70/98.91 Found x7:(cODD (cS c0))
% 98.70/98.91 Instantiate: Xn0:=(cS c0):fofType
% 98.70/98.91 Found x7 as proof of (cODD Xn0)
% 98.70/98.91 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.70/98.91 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.70/98.91 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.70/98.91 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.70/98.91 Found x12:(cEVEN c0)
% 98.70/98.91 Instantiate: Xn0:=c0:fofType
% 98.70/98.91 Found x12 as proof of (cEVEN Xn0)
% 98.70/98.91 Found (or_introl00 x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.70/98.91 Found ((or_introl0 (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.70/98.91 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.70/98.91 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 98.70/98.91 Found x80:((or (cEVEN Xn0)) (cODD Xn0))
% 98.70/98.91 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 99.15/99.35 Found (x9 x80) as proof of (cNUMBER Xn)
% 99.15/99.35 Found (x9 x80) as proof of (cNUMBER Xn)
% 99.15/99.35 Found (x9 x80) as proof of (cNUMBER Xn)
% 99.15/99.35 Found x5:(cODD (cS c0))
% 99.15/99.35 Instantiate: Xn0:=(cS c0):fofType
% 99.15/99.35 Found x5 as proof of (cODD Xn0)
% 99.15/99.35 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 99.15/99.35 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 99.15/99.35 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 99.15/99.35 Found (fun (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 99.15/99.35 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 99.15/99.35 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 99.15/99.35 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 99.15/99.35 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 99.15/99.35 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 99.15/99.35 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 99.15/99.35 Found x30:=(x3 x21):(cNUMBER Xn0)
% 99.15/99.35 Instantiate: Xn0:=Xn:fofType
% 99.15/99.35 Found (x3 x21) as proof of (cNUMBER Xn)
% 99.15/99.35 Found (fun (x7:(cODD (cS c0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 99.15/99.35 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 99.15/99.35 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 99.15/99.35 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 99.15/99.35 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 99.15/99.35 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 99.15/99.35 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21)))) as proof of (cNUMBER Xn)
% 101.00/101.26 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21)))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 101.00/101.26 Found x7:(cODD (cS c0))
% 101.00/101.26 Instantiate: Xn0:=(cS c0):fofType
% 101.00/101.26 Found x7 as proof of (cODD Xn0)
% 101.00/101.26 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 101.00/101.26 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 101.00/101.26 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 101.00/101.26 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 101.00/101.26 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 101.00/101.26 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 101.00/101.26 Found (x7 x60) as proof of (cNUMBER Xn)
% 101.00/101.26 Found (x7 x60) as proof of (cNUMBER Xn)
% 101.00/101.26 Found (fun (x12:(cEVEN c0))=> (x7 x60)) as proof of (cNUMBER Xn)
% 101.00/101.26 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 101.00/101.26 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60)) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 101.00/101.26 Found x30:=(x3 x21):(cNUMBER Xn0)
% 101.00/101.26 Instantiate: Xn0:=Xn:fofType
% 101.00/101.26 Found (x3 x21) as proof of (cNUMBER Xn)
% 101.00/101.26 Found (fun (x7:(cODD (cS c0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 101.00/101.26 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 101.00/101.26 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 101.00/101.26 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 101.00/101.26 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 101.00/101.26 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 101.00/101.26 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x21))) as proof of (cNUMBER Xn)
% 101.00/101.26 Found x70:=(x7 x60):(cNUMBER Xn0)
% 101.00/101.26 Instantiate: Xn0:=Xn:fofType
% 101.00/101.26 Found (x7 x60) as proof of (cNUMBER Xn)
% 101.00/101.26 Found (fun (x12:(cEVEN c0))=> (x7 x60)) as proof of (cNUMBER Xn)
% 101.00/101.26 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 101.00/101.26 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60)) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 103.15/103.35 Found (and_rect50 (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60))) as proof of (cNUMBER Xn)
% 103.15/103.35 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60))) as proof of (cNUMBER Xn)
% 103.15/103.35 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60))) as proof of (cNUMBER Xn)
% 103.15/103.35 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60))) as proof of (cNUMBER Xn)
% 103.15/103.35 Found x30:=(x3 x20):(cNUMBER Xn0)
% 103.15/103.35 Instantiate: Xn0:=Xn:fofType
% 103.15/103.35 Found (x3 x20) as proof of (cNUMBER Xn)
% 103.15/103.35 Found (x3 x20) as proof of (cNUMBER Xn)
% 103.15/103.35 Found x70:=(x7 x60):(cNUMBER Xn00)
% 103.15/103.35 Instantiate: Xn00:=Xn:fofType
% 103.15/103.35 Found (x7 x60) as proof of (cNUMBER Xn)
% 103.15/103.35 Found (x7 x60) as proof of (cNUMBER Xn)
% 103.15/103.35 Found x5:(cODD (cS c0))
% 103.15/103.35 Instantiate: Xn0:=(cS c0):fofType
% 103.15/103.35 Found x5 as proof of (cODD Xn0)
% 103.15/103.35 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.15/103.35 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.15/103.35 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.15/103.35 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.15/103.35 Found x110:((or (cEVEN Xn0)) (cODD Xn0))
% 103.15/103.35 Found x110 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.15/103.35 Found (x12 x110) as proof of (cNUMBER Xn)
% 103.15/103.35 Found (x12 x110) as proof of (cNUMBER Xn)
% 103.15/103.35 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x110)) as proof of (cNUMBER Xn)
% 103.15/103.35 Found (fun (x12:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x12 x110)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 103.15/103.35 Found x30:=(x3 x21):(cNUMBER Xn0)
% 103.15/103.35 Instantiate: Xn0:=Xn:fofType
% 103.15/103.35 Found (x3 x21) as proof of (cNUMBER Xn)
% 103.15/103.35 Found (fun (x4:(cEVEN Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 103.15/103.35 Found (fun (x4:(cEVEN Xn0))=> (x3 x21)) as proof of ((cEVEN Xn0)->(cNUMBER Xn))
% 103.15/103.35 Found x30:=(x3 x21):(cNUMBER Xn0)
% 103.15/103.35 Instantiate: Xn0:=Xn:fofType
% 103.15/103.35 Found (x3 x21) as proof of (cNUMBER Xn)
% 103.15/103.35 Found (fun (x4:(cODD Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 103.15/103.35 Found (fun (x4:(cODD Xn0))=> (x3 x21)) as proof of ((cODD Xn0)->(cNUMBER Xn))
% 103.15/103.35 Found ((or_ind00 (fun (x4:(cEVEN Xn0))=> (x3 x21))) (fun (x4:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 103.15/103.35 Found (((or_ind0 (cNUMBER Xn)) (fun (x4:(cEVEN Xn0))=> (x3 x21))) (fun (x4:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 103.15/103.35 Found ((((fun (P:Prop) (x4:((cEVEN Xn0)->P)) (x5:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x4) x5) x20)) (cNUMBER Xn)) (fun (x4:(cEVEN Xn0))=> (x3 x21))) (fun (x4:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 103.15/103.35 Found ((((fun (P:Prop) (x4:((cEVEN Xn0)->P)) (x5:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x4) x5) x20)) (cNUMBER Xn)) (fun (x4:(cEVEN Xn0))=> (x3 x21))) (fun (x4:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 103.15/103.35 Found x30:=(x3 x20):(cNUMBER Xn0)
% 103.15/103.35 Found (x3 x20) as proof of (cNUMBER Xn0)
% 103.15/103.35 Found (x3 x20) as proof of (cNUMBER Xn0)
% 103.15/103.35 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 103.15/103.35 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.15/103.35 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 103.15/103.35 Found x31:(cNUMBER Xn0)
% 103.15/103.35 Instantiate: Xn0:=Xn:fofType
% 103.15/103.35 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 103.15/103.35 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 103.15/103.35 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x31) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 103.15/103.35 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 103.15/103.35 Instantiate: Xn0:=Xn:fofType
% 103.15/103.35 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 103.15/103.35 Found x50:=(x5 x40):(cNUMBER Xn0)
% 103.15/103.35 Instantiate: Xn0:=Xn:fofType
% 103.15/103.35 Found (x5 x40) as proof of (cNUMBER Xn)
% 103.15/103.35 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 104.83/105.05 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 104.83/105.05 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 104.83/105.05 Instantiate: Xn00:=Xn:fofType
% 104.83/105.05 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 104.83/105.05 Found x70:=(x7 x60):(cNUMBER Xn00)
% 104.83/105.05 Instantiate: Xn00:=Xn:fofType
% 104.83/105.05 Found (x7 x60) as proof of (cNUMBER Xn)
% 104.83/105.05 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 104.83/105.05 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 104.83/105.05 Found x50:=(x5 x41):(cNUMBER Xn0)
% 104.83/105.05 Instantiate: Xn0:=Xn:fofType
% 104.83/105.05 Found (x5 x41) as proof of (cNUMBER Xn)
% 104.83/105.05 Found (fun (x7:(cODD (cS c0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 104.83/105.05 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x41)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 104.83/105.05 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x41)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 104.83/105.05 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x41))) as proof of (cNUMBER Xn)
% 104.83/105.05 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x41))) as proof of (cNUMBER Xn)
% 104.83/105.05 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x41))) as proof of (cNUMBER Xn)
% 104.83/105.05 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x41))) as proof of (cNUMBER Xn)
% 104.83/105.05 Found x50:(cNUMBER Xn0)
% 104.83/105.05 Instantiate: Xn0:=Xn:fofType
% 104.83/105.05 Found (fun (x8:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 104.83/105.05 Found (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 104.83/105.05 Found (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x50) as proof of ((cEVEN Xn0)->((cODD (cS c0))->(cNUMBER Xn)))
% 104.83/105.05 Found x50:(cNUMBER Xn0)
% 104.83/105.05 Instantiate: Xn0:=Xn:fofType
% 104.83/105.05 Found (fun (x8:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 104.83/105.05 Found (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 104.83/105.05 Found (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x50) as proof of ((cODD Xn0)->((cODD (cS c0))->(cNUMBER Xn)))
% 104.83/105.05 Found ((or_ind00 (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x50)) (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x50)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 104.83/105.05 Found (((or_ind0 ((cODD (cS c0))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x50)) (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x50)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 104.83/105.05 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) x40)) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x50)) (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x50)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 104.83/105.05 Found ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x4 x50))) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x50)) (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x50)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 107.93/108.18 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))))=> ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x4 x50))) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x50)) (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x50))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 107.93/108.18 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))))=> ((((fun (P:Prop) (x7:((cEVEN Xn0)->P)) (x8:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x7) x8) (x4 x50))) ((cODD (cS c0))->(cNUMBER Xn))) (fun (x7:(cEVEN Xn0)) (x8:(cODD (cS c0)))=> x50)) (fun (x7:(cODD Xn0)) (x8:(cODD (cS c0)))=> x50))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 107.93/108.18 Found x70:=(x7 x60):(cNUMBER Xn0)
% 107.93/108.18 Found (x7 x60) as proof of (cNUMBER Xn)
% 107.93/108.18 Found (x7 x60) as proof of (cNUMBER Xn)
% 107.93/108.18 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 107.93/108.18 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 107.93/108.18 Found x30:=(x3 x20):(cNUMBER Xn0)
% 107.93/108.18 Instantiate: Xn0:=Xn:fofType
% 107.93/108.18 Found (x3 x20) as proof of (cNUMBER Xn)
% 107.93/108.18 Found (x3 x20) as proof of (cNUMBER Xn)
% 107.93/108.18 Found x50:=(x5 x40):(cNUMBER Xn00)
% 107.93/108.18 Instantiate: Xn00:=Xn:fofType
% 107.93/108.18 Found (x5 x40) as proof of (cNUMBER Xn)
% 107.93/108.18 Found (x5 x40) as proof of (cNUMBER Xn)
% 107.93/108.18 Found x80:((or (cEVEN Xn0)) (cODD Xn0))
% 107.93/108.18 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 107.93/108.18 Found (x9 x80) as proof of (cNUMBER Xn)
% 107.93/108.18 Found (x9 x80) as proof of (cNUMBER Xn)
% 107.93/108.18 Found (fun (x12:(cEVEN c0))=> (x9 x80)) as proof of (cNUMBER Xn)
% 107.93/108.18 Found (fun (x12:(cEVEN c0))=> (x9 x80)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 107.93/108.18 Found x7:(cODD (cS c0))
% 107.93/108.18 Instantiate: Xn0:=(cS c0):fofType
% 107.93/108.18 Found x7 as proof of (cODD Xn0)
% 107.93/108.18 Found (or_introl00 x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 107.93/108.18 Found ((or_introl0 (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 107.93/108.18 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 107.93/108.18 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 107.93/108.18 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 107.93/108.18 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 107.93/108.18 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 107.93/108.18 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 107.93/108.18 Found x30:=(x3 x20):(cNUMBER Xn0)
% 107.93/108.18 Instantiate: Xn0:=Xn:fofType
% 107.93/108.18 Found (x3 x20) as proof of (cNUMBER Xn)
% 107.93/108.18 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 107.93/108.18 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 107.93/108.18 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 107.93/108.18 Instantiate: Xn0:=Xn:fofType
% 107.93/108.18 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 107.93/108.18 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 107.93/108.18 Instantiate: Xn00:=Xn:fofType
% 107.93/108.18 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 107.93/108.18 Found x70:=(x7 x60):(cNUMBER Xn00)
% 107.93/108.18 Instantiate: Xn00:=Xn:fofType
% 107.93/108.18 Found (x7 x60) as proof of (cNUMBER Xn)
% 107.93/108.18 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 107.93/108.18 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 107.93/108.18 Found x7:(cODD (cS c0))
% 107.93/108.18 Instantiate: Xn0:=(cS c0):fofType
% 107.93/108.18 Found x7 as proof of (cODD Xn0)
% 107.93/108.18 Found (or_introl00 x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 107.93/108.18 Found ((or_introl0 (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 107.93/108.18 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 109.13/109.37 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 109.13/109.37 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 109.13/109.37 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 109.13/109.37 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 109.13/109.37 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 109.13/109.37 Found x70:=(x7 x60):(cNUMBER Xn0)
% 109.13/109.37 Instantiate: Xn0:=Xn:fofType
% 109.13/109.37 Found (x7 x60) as proof of (cNUMBER Xn)
% 109.13/109.37 Found (fun (x12:(cEVEN c0))=> (x7 x60)) as proof of (cNUMBER Xn)
% 109.13/109.37 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 109.13/109.37 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60)) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 109.13/109.37 Found (and_rect50 (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60))) as proof of (cNUMBER Xn)
% 109.13/109.37 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60))) as proof of (cNUMBER Xn)
% 109.13/109.37 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60))) as proof of (cNUMBER Xn)
% 109.13/109.37 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60)))) as proof of (cNUMBER Xn)
% 109.13/109.37 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60)))) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 109.13/109.37 Found x7:(cODD (cS c0))
% 109.13/109.37 Instantiate: Xn0:=(cS c0):fofType
% 109.13/109.37 Found x7 as proof of (cODD Xn0)
% 109.13/109.37 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 109.13/109.37 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 109.13/109.37 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 109.13/109.37 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 109.13/109.37 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 109.13/109.37 Found (fun (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of (cNUMBER Xn0)
% 109.13/109.37 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn0))
% 109.13/109.37 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of (((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn0)))
% 109.13/109.37 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 109.13/109.37 Found ((and_rect4 (cNUMBER Xn0)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 109.13/109.37 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn0)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 109.13/109.37 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn0)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 110.88/111.07 Found x31:(cNUMBER Xn0)
% 110.88/111.07 Instantiate: Xn0:=Xn:fofType
% 110.88/111.07 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 110.88/111.07 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 110.88/111.07 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 110.88/111.07 Instantiate: Xn00:=Xn:fofType
% 110.88/111.07 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 110.88/111.07 Found x50:(cNUMBER Xn0)
% 110.88/111.07 Instantiate: Xn0:=Xn:fofType
% 110.88/111.07 Found (fun (x8:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 110.88/111.07 Found (fun (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x8:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 110.88/111.07 Found (fun (x6:(cODD Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x8:(cODD (cS c0)))=> x50) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 110.88/111.07 Found (fun (x6:(cODD Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x8:(cODD (cS c0)))=> x50) as proof of ((cODD Xn0)->(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn))))
% 110.88/111.07 Found x50:(cNUMBER Xn0)
% 110.88/111.07 Instantiate: Xn0:=Xn:fofType
% 110.88/111.07 Found (fun (x8:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 110.88/111.07 Found (fun (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x8:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 110.88/111.07 Found (fun (x6:(cEVEN Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x8:(cODD (cS c0)))=> x50) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 110.88/111.07 Found (fun (x6:(cEVEN Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x8:(cODD (cS c0)))=> x50) as proof of ((cEVEN Xn0)->(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn))))
% 110.88/111.07 Found ((or_ind00 (fun (x6:(cEVEN Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x8:(cODD (cS c0)))=> x50)) (fun (x6:(cODD Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x8:(cODD (cS c0)))=> x50)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 110.88/111.07 Found (((or_ind0 (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))) (fun (x6:(cEVEN Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x8:(cODD (cS c0)))=> x50)) (fun (x6:(cODD Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x8:(cODD (cS c0)))=> x50)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 110.88/111.07 Found ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) x40)) (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn)))) (fun (x6:(cEVEN Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x50)) (fun (x6:(cODD Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x50)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 111.84/112.06 Found ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) (x4 x50))) (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn)))) (fun (x6:(cEVEN Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x50)) (fun (x6:(cODD Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x50)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 111.84/112.06 Found ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) (x4 x50))) (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->(cNUMBER Xn)))) (fun (x6:(cEVEN Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x50)) (fun (x6:(cODD Xn0)) (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x8:(cODD (cS c0)))=> x50)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 111.84/112.06 Found x70:=(x7 x60):(cNUMBER Xn0)
% 111.84/112.06 Instantiate: Xn0:=Xn:fofType
% 111.84/112.06 Found (x7 x60) as proof of (cNUMBER Xn)
% 111.84/112.06 Found (fun (x12:(cEVEN c0))=> (x7 x60)) as proof of (cNUMBER Xn)
% 111.84/112.06 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 111.84/112.06 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60)) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 111.84/112.06 Found (and_rect50 (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60))) as proof of (cNUMBER Xn)
% 111.84/112.06 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60))) as proof of (cNUMBER Xn)
% 111.84/112.06 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60))) as proof of (cNUMBER Xn)
% 111.84/112.06 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60)))) as proof of (cNUMBER Xn)
% 111.84/112.06 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60)))) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 111.84/112.06 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x7 x60)))) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 111.84/112.06 Found x50:=(x5 x40):(cNUMBER Xn0)
% 111.84/112.06 Instantiate: Xn0:=Xn:fofType
% 111.84/112.06 Found (x5 x40) as proof of (cNUMBER Xn)
% 111.84/112.06 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 111.84/112.06 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 111.84/112.06 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 111.84/112.06 Found x50:=(x5 x41):(cNUMBER Xn0)
% 111.84/112.06 Instantiate: Xn0:=Xn:fofType
% 111.84/112.06 Found (x5 x41) as proof of (cNUMBER Xn)
% 111.84/112.06 Found (fun (x7:(cODD (cS c0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 113.30/113.51 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x41)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 113.30/113.51 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x41)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 113.30/113.51 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x41))) as proof of (cNUMBER Xn)
% 113.30/113.51 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x41))) as proof of (cNUMBER Xn)
% 113.30/113.51 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x41))) as proof of (cNUMBER Xn)
% 113.30/113.51 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x41))) as proof of (cNUMBER Xn)
% 113.30/113.51 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 113.30/113.51 Instantiate: Xn0:=Xn:fofType
% 113.30/113.51 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 113.30/113.51 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 113.30/113.51 Instantiate: Xn00:=Xn:fofType
% 113.30/113.51 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 113.30/113.51 Found x50:=(x5 x40):(cNUMBER Xn00)
% 113.30/113.51 Instantiate: Xn00:=Xn:fofType
% 113.30/113.51 Found (x5 x40) as proof of (cNUMBER Xn)
% 113.30/113.51 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 113.30/113.51 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 113.30/113.51 Found x30:=(x3 x20):(cNUMBER Xn0)
% 113.30/113.51 Instantiate: Xn0:=Xn:fofType
% 113.30/113.51 Found (x3 x20) as proof of (cNUMBER Xn)
% 113.30/113.51 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 113.30/113.51 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 113.30/113.51 Found x7:(cODD (cS c0))
% 113.30/113.51 Instantiate: Xn0:=(cS c0):fofType
% 113.30/113.51 Found x7 as proof of (cODD Xn0)
% 113.30/113.51 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 113.30/113.51 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 113.30/113.51 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 113.30/113.51 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 113.30/113.51 Found x12:(cEVEN c0)
% 113.30/113.51 Instantiate: Xn0:=c0:fofType
% 113.30/113.51 Found x12 as proof of (cEVEN Xn0)
% 113.30/113.51 Found (or_introl00 x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 113.30/113.51 Found ((or_introl0 (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 113.30/113.51 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 113.30/113.51 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 113.30/113.51 Found x30:=(x3 x20):(cNUMBER Xn0)
% 113.30/113.51 Found (x3 x20) as proof of (cNUMBER Xn0)
% 113.30/113.51 Found (x3 x20) as proof of (cNUMBER Xn0)
% 113.30/113.51 Found x30:=(x3 x21):(cNUMBER Xn0)
% 113.30/113.51 Instantiate: Xn0:=Xn:fofType
% 113.30/113.51 Found (x3 x21) as proof of (cNUMBER Xn)
% 113.30/113.51 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 113.30/113.51 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 116.92/117.15 Found x50:=(x5 x40):(cNUMBER Xn0)
% 116.92/117.15 Found (x5 x40) as proof of (cNUMBER Xn)
% 116.92/117.15 Found (x5 x40) as proof of (cNUMBER Xn)
% 116.92/117.15 Found (x5 x40) as proof of (cNUMBER Xn)
% 116.92/117.15 Found x70:=(x7 x60):(cNUMBER Xn00)
% 116.92/117.15 Found (x7 x60) as proof of (cNUMBER Xn)
% 116.92/117.15 Found (x7 x60) as proof of (cNUMBER Xn)
% 116.92/117.15 Found (x7 x60) as proof of (cNUMBER Xn)
% 116.92/117.15 Found x80:((or (cEVEN Xn0)) (cODD Xn0))
% 116.92/117.15 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.92/117.15 Found (x9 x80) as proof of (cNUMBER Xn)
% 116.92/117.15 Found (x9 x80) as proof of (cNUMBER Xn)
% 116.92/117.15 Found (fun (x12:(cEVEN c0))=> (x9 x80)) as proof of (cNUMBER Xn)
% 116.92/117.15 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x9 x80)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 116.92/117.15 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x9 x80)) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 116.92/117.15 Found x7:(cODD (cS c0))
% 116.92/117.15 Instantiate: Xn0:=(cS c0):fofType
% 116.92/117.15 Found x7 as proof of (cODD Xn0)
% 116.92/117.15 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.92/117.15 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.92/117.15 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.92/117.15 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.92/117.15 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 116.92/117.15 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 116.92/117.15 Found x5:(cODD (cS c0))
% 116.92/117.15 Instantiate: Xn0:=(cS c0):fofType
% 116.92/117.15 Found x5 as proof of (cODD Xn0)
% 116.92/117.15 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.92/117.15 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.92/117.15 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.92/117.15 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.92/117.15 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 116.92/117.15 Instantiate: Xn00:=Xn:fofType
% 116.92/117.15 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.92/117.15 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 116.92/117.15 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.92/117.15 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.92/117.15 Found x30:=(x3 x20):(cNUMBER Xn0)
% 116.92/117.15 Instantiate: Xn0:=Xn:fofType
% 116.92/117.15 Found (x3 x20) as proof of (cNUMBER Xn)
% 116.92/117.15 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 116.92/117.15 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 116.92/117.15 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 116.92/117.15 Found x90:=(x9 x80):(cNUMBER Xn0)
% 116.92/117.15 Instantiate: Xn0:=Xn:fofType
% 116.92/117.15 Found (x9 x80) as proof of (cNUMBER Xn)
% 116.92/117.15 Found (fun (x12:(cEVEN c0))=> (x9 x80)) as proof of (cNUMBER Xn)
% 116.92/117.15 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x9 x80)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 116.92/117.15 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x9 x80)) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 116.92/117.15 Found (and_rect50 (fun (x11:cIND) (x12:(cEVEN c0))=> (x9 x80))) as proof of (cNUMBER Xn)
% 116.92/117.15 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x9 x80))) as proof of (cNUMBER Xn)
% 116.92/117.15 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x6)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x9 x80))) as proof of (cNUMBER Xn)
% 116.92/117.15 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x6)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x9 x80))) as proof of (cNUMBER Xn)
% 116.92/117.15 Found x5:(cODD (cS c0))
% 116.92/117.15 Instantiate: Xn0:=(cS c0):fofType
% 116.92/117.15 Found x5 as proof of (cODD Xn0)
% 116.92/117.15 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.92/117.15 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.92/117.15 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.92/117.15 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 116.92/117.15 Found x30:=(x3 x21):(cNUMBER Xn0)
% 118.33/118.52 Instantiate: Xn0:=Xn:fofType
% 118.33/118.52 Found (x3 x21) as proof of (cNUMBER Xn)
% 118.33/118.52 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 118.33/118.52 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 118.33/118.52 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 118.33/118.52 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 118.33/118.52 Instantiate: Xn00:=Xn:fofType
% 118.33/118.52 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x60) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 118.33/118.52 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x60) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->((or (cEVEN Xn0)) (cODD Xn0)))
% 118.33/118.52 Found x50:=(x5 x40):(cNUMBER Xn0)
% 118.33/118.52 Found (x5 x40) as proof of (cNUMBER Xn0)
% 118.33/118.52 Found (x5 x40) as proof of (cNUMBER Xn0)
% 118.33/118.52 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 118.33/118.52 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 118.33/118.52 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 118.33/118.52 Found x51:(cNUMBER Xn0)
% 118.33/118.52 Instantiate: Xn0:=Xn:fofType
% 118.33/118.52 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x51) as proof of (cNUMBER Xn)
% 118.33/118.52 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x51) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 118.33/118.52 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x51) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 118.33/118.52 Found x31:(cNUMBER Xn0)
% 118.33/118.52 Instantiate: Xn0:=Xn:fofType
% 118.33/118.52 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 118.33/118.52 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 118.33/118.52 Found x30:=(x3 x21):(cNUMBER Xn0)
% 118.33/118.52 Instantiate: Xn0:=Xn:fofType
% 118.33/118.52 Found (x3 x21) as proof of (cNUMBER Xn)
% 118.33/118.52 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 118.33/118.52 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 118.33/118.52 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 118.33/118.52 Found (and_rect20 (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 118.33/118.52 Found ((and_rect2 (cNUMBER Xn)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 118.33/118.52 Found (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21))) as proof of (cNUMBER Xn)
% 121.62/121.86 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)))) as proof of (cNUMBER Xn)
% 121.62/121.86 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x21)))) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 121.62/121.86 Found x30:=(x3 x20):(cNUMBER Xn0)
% 121.62/121.86 Found (x3 x20) as proof of (cNUMBER Xn)
% 121.62/121.86 Found (x3 x20) as proof of (cNUMBER Xn)
% 121.62/121.86 Found (x3 x20) as proof of (cNUMBER Xn)
% 121.62/121.86 Found x70:=(x7 x60):(cNUMBER Xn00)
% 121.62/121.86 Found (x7 x60) as proof of (cNUMBER Xn)
% 121.62/121.86 Found (x7 x60) as proof of (cNUMBER Xn)
% 121.62/121.86 Found (x7 x60) as proof of (cNUMBER Xn)
% 121.62/121.86 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 121.62/121.86 Instantiate: Xn0:=Xn:fofType
% 121.62/121.86 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 121.62/121.86 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 121.62/121.86 Instantiate: Xn00:=Xn:fofType
% 121.62/121.86 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 121.62/121.86 Found x7:(cODD (cS c0))
% 121.62/121.86 Instantiate: Xn0:=(cS c0):fofType
% 121.62/121.86 Found x7 as proof of (cODD Xn0)
% 121.62/121.86 Found (or_introl00 x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 121.62/121.86 Found ((or_introl0 (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 121.62/121.86 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 121.62/121.86 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 121.62/121.86 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 121.62/121.86 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 121.62/121.86 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 121.62/121.86 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 121.62/121.86 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 121.62/121.86 Instantiate: Xn00:=Xn:fofType
% 121.62/121.86 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x60) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 121.62/121.86 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x60) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->((or (cEVEN Xn0)) (cODD Xn0)))
% 121.62/121.86 Found x50:=(x5 x40):(cNUMBER Xn00)
% 121.62/121.86 Instantiate: Xn00:=Xn:fofType
% 121.62/121.86 Found (x5 x40) as proof of (cNUMBER Xn)
% 121.62/121.86 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 121.62/121.86 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 121.62/121.86 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 123.64/123.85 Found x30:=(x3 x20):(cNUMBER Xn0)
% 123.64/123.85 Instantiate: Xn0:=Xn:fofType
% 123.64/123.85 Found (x3 x20) as proof of (cNUMBER Xn)
% 123.64/123.85 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 123.64/123.85 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 123.64/123.85 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 123.64/123.85 Found x50:=(x5 x40):(cNUMBER Xn0)
% 123.64/123.85 Found (x5 x40) as proof of (cNUMBER Xn)
% 123.64/123.85 Found (x5 x40) as proof of (cNUMBER Xn)
% 123.64/123.85 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 123.64/123.85 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 123.64/123.85 Found x70:=(x7 x60):(cNUMBER Xn00)
% 123.64/123.85 Found (x7 x60) as proof of (cNUMBER Xn)
% 123.64/123.85 Found (x7 x60) as proof of (cNUMBER Xn)
% 123.64/123.85 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 123.64/123.85 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 123.64/123.85 Found x7:(cODD (cS c0))
% 123.64/123.85 Instantiate: Xn0:=(cS c0):fofType
% 123.64/123.85 Found x7 as proof of (cODD Xn0)
% 123.64/123.85 Found (or_introl00 x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 123.64/123.85 Found ((or_introl0 (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 123.64/123.85 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 123.64/123.85 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 123.64/123.85 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 123.64/123.85 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 123.64/123.85 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 123.64/123.85 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 123.64/123.85 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 123.64/123.85 Instantiate: Xn00:=Xn:fofType
% 123.64/123.85 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 123.64/123.85 Found x30:=(x3 x20):(cNUMBER Xn0)
% 123.64/123.85 Found (x3 x20) as proof of (cNUMBER Xn0)
% 123.64/123.85 Found (x3 x20) as proof of (cNUMBER Xn0)
% 123.64/123.85 Found x30:=(x3 x21):(cNUMBER Xn0)
% 123.64/123.85 Instantiate: Xn0:=Xn:fofType
% 123.64/123.85 Found (x3 x21) as proof of (cNUMBER Xn)
% 123.64/123.85 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of (cNUMBER Xn)
% 123.64/123.85 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x21)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 123.64/123.85 Found x12:(cEVEN c0)
% 123.64/123.85 Found x12 as proof of (cEVEN c0)
% 123.64/123.85 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 123.64/123.85 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 123.64/123.85 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 123.64/123.85 Found x5:(cODD (cS c0))
% 123.64/123.85 Instantiate: Xn0:=(cS c0):fofType
% 123.64/123.85 Found x5 as proof of (cODD Xn0)
% 123.64/123.85 Found (or_introl00 x5) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 123.64/123.85 Found ((or_introl0 (cEVEN Xn0)) x5) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 123.64/123.85 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 123.64/123.85 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 124.64/124.85 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 124.64/124.85 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 124.64/124.85 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 124.64/124.85 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 124.64/124.85 Found x90:=(x9 x80):(cNUMBER Xn0)
% 124.64/124.85 Instantiate: Xn0:=Xn:fofType
% 124.64/124.85 Found (x9 x80) as proof of (cNUMBER Xn)
% 124.64/124.85 Found (fun (x12:(cEVEN c0))=> (x9 x80)) as proof of (cNUMBER Xn)
% 124.64/124.85 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x9 x80)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 124.64/124.85 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x9 x80)) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 124.64/124.85 Found (and_rect50 (fun (x11:cIND) (x12:(cEVEN c0))=> (x9 x80))) as proof of (cNUMBER Xn)
% 124.64/124.85 Found ((and_rect5 (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x9 x80))) as proof of (cNUMBER Xn)
% 124.64/124.85 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x6)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x9 x80))) as proof of (cNUMBER Xn)
% 124.64/124.85 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x6)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x9 x80)))) as proof of (cNUMBER Xn)
% 124.64/124.85 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x6)) (cNUMBER Xn)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x9 x80)))) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 124.64/124.85 Found x50:=(x5 x40):(cNUMBER Xn00)
% 124.64/124.85 Found (x5 x40) as proof of (cNUMBER Xn)
% 124.64/124.85 Found (x5 x40) as proof of (cNUMBER Xn)
% 124.64/124.85 Found (x5 x40) as proof of (cNUMBER Xn)
% 124.64/124.85 Found x30:=(x3 x20):(cNUMBER Xn0)
% 124.64/124.85 Found (x3 x20) as proof of (cNUMBER Xn)
% 124.64/124.85 Found (x3 x20) as proof of (cNUMBER Xn)
% 124.64/124.85 Found (x3 x20) as proof of (cNUMBER Xn)
% 124.64/124.85 Found x7:(cODD (cS c0))
% 124.64/124.85 Instantiate: Xn0:=(cS c0):fofType
% 124.64/124.85 Found x7 as proof of (cODD Xn0)
% 124.64/124.85 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 124.64/124.85 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 124.64/124.85 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 124.64/124.85 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 124.64/124.85 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 124.64/124.85 Found (fun (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of (cNUMBER Xn0)
% 124.64/124.85 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn0))
% 124.64/124.85 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of (((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn0)))
% 124.64/124.85 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 124.64/124.85 Found ((and_rect4 (cNUMBER Xn0)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 124.64/124.85 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn0)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 126.13/126.39 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn0)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 126.13/126.39 Found x51:(cNUMBER Xn0)
% 126.13/126.39 Instantiate: Xn0:=Xn:fofType
% 126.13/126.39 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x51) as proof of (cNUMBER Xn)
% 126.13/126.39 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x51) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 126.13/126.39 Found x30:=(x3 x20):(cNUMBER Xn0)
% 126.13/126.39 Found (x3 x20) as proof of (cNUMBER Xn)
% 126.13/126.39 Found (x3 x20) as proof of (cNUMBER Xn)
% 126.13/126.39 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 126.13/126.39 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 126.13/126.39 Found x12:(cEVEN c0)
% 126.13/126.39 Found x12 as proof of (cEVEN c0)
% 126.13/126.39 Found or_introl00:=(or_introl0 (cODD Xn0)):((cEVEN c0)->((or (cEVEN c0)) (cODD Xn0)))
% 126.13/126.39 Found (or_introl0 (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 126.13/126.39 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 126.13/126.39 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 126.13/126.39 Found (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 126.13/126.39 Found (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of (cIND->((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0))))
% 126.13/126.39 Found (and_rect50 (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 126.13/126.39 Found ((and_rect5 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 126.13/126.39 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 126.13/126.39 Found (fun (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 126.13/126.39 Found (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 126.13/126.39 Found (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))) as proof of (((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 126.13/126.39 Found (and_rect40 (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 126.13/126.39 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 126.22/126.43 Found (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 126.22/126.43 Found (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 126.22/126.43 Found (x3 (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))))) as proof of (cNUMBER Xn0)
% 126.22/126.43 Found (x3 (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))))) as proof of (cNUMBER Xn0)
% 126.22/126.43 Found or_introl00:=(or_introl0 (cODD Xn0)):((cEVEN c0)->((or (cEVEN c0)) (cODD Xn0)))
% 126.22/126.43 Found (or_introl0 (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 126.22/126.43 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 126.22/126.43 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 126.22/126.43 Found (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 126.22/126.43 Found (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of (cIND->((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0))))
% 126.22/126.43 Found (and_rect50 (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 126.22/126.43 Found ((and_rect5 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 126.22/126.43 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 126.22/126.43 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 126.22/126.43 Found (x3 (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))) as proof of (cNUMBER Xn0)
% 126.22/126.43 Found (fun (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))))) as proof of (cNUMBER Xn0)
% 127.19/127.42 Found (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))))) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn0))
% 127.19/127.42 Found (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))))) as proof of (((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn0)))
% 127.19/127.42 Found (and_rect40 (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))))) as proof of (cNUMBER Xn0)
% 127.19/127.42 Found ((and_rect4 (cNUMBER Xn0)) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))))) as proof of (cNUMBER Xn0)
% 127.19/127.42 Found (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) (cNUMBER Xn0)) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))))) as proof of (cNUMBER Xn0)
% 127.19/127.42 Found (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) (cNUMBER Xn0)) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x3 (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))))) as proof of (cNUMBER Xn0)
% 127.19/127.42 Found x70:=(x7 x60):(cNUMBER Xn00)
% 127.19/127.42 Found (x7 x60) as proof of (cNUMBER Xn)
% 127.19/127.42 Found (x7 x60) as proof of (cNUMBER Xn)
% 127.19/127.42 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 127.19/127.42 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 127.19/127.42 Found x30:=(x3 x20):(cNUMBER Xn0)
% 127.19/127.42 Found (x3 x20) as proof of (cNUMBER Xn0)
% 127.19/127.42 Found (x3 x20) as proof of (cNUMBER Xn0)
% 127.19/127.42 Found x30:=(x3 x21):(cNUMBER Xn0)
% 127.19/127.42 Instantiate: Xn0:=Xn:fofType
% 127.19/127.42 Found (x3 x21) as proof of (cNUMBER Xn)
% 127.19/127.42 Found (x3 x21) as proof of (cNUMBER Xn)
% 127.19/127.42 Found x30:=(x3 x20):(cNUMBER Xn0)
% 127.19/127.42 Found (x3 x20) as proof of (cNUMBER Xn)
% 127.19/127.42 Found (x3 x20) as proof of (cNUMBER Xn)
% 127.19/127.42 Found (x3 x20) as proof of (cNUMBER Xn)
% 127.19/127.42 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 127.19/127.42 Instantiate: Xn00:=Xn:fofType
% 127.19/127.42 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 127.19/127.42 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 127.19/127.42 Instantiate: Xn0:=Xn:fofType
% 127.19/127.42 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x20) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 127.19/127.42 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x20) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->((or (cEVEN Xn00)) (cODD Xn00)))
% 127.19/127.42 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 127.19/127.42 Instantiate: Xn00:=Xn:fofType
% 128.83/129.04 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.83/129.04 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x40) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 128.83/129.04 Found x12:(cEVEN c0)
% 128.83/129.04 Found x12 as proof of (cEVEN c0)
% 128.83/129.04 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 128.83/129.04 Instantiate: Xn00:=Xn:fofType
% 128.83/129.04 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.83/129.04 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.83/129.04 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 128.83/129.04 Instantiate: Xn0:=Xn:fofType
% 128.83/129.04 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 128.83/129.04 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 128.83/129.04 Found x30:=(x3 x20):(cNUMBER Xn0)
% 128.83/129.04 Found (x3 x20) as proof of (cNUMBER Xn)
% 128.83/129.04 Found (x3 x20) as proof of (cNUMBER Xn)
% 128.83/129.04 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 128.83/129.04 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 128.83/129.04 Found x12:(cEVEN c0)
% 128.83/129.04 Instantiate: Xn0:=c0:fofType
% 128.83/129.04 Found x12 as proof of (cEVEN Xn0)
% 128.83/129.04 Found (or_introl00 x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.83/129.04 Found ((or_introl0 (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.83/129.04 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.83/129.04 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.83/129.04 Found x5:(cODD (cS c0))
% 128.83/129.04 Instantiate: Xn0:=(cS c0):fofType
% 128.83/129.04 Found x5 as proof of (cODD Xn0)
% 128.83/129.04 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.83/129.04 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.83/129.04 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.83/129.04 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.83/129.04 Found x7:(cODD (cS c0))
% 128.83/129.04 Instantiate: Xn0:=(cS c0):fofType
% 128.83/129.04 Found x7 as proof of (cODD Xn0)
% 128.83/129.04 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.83/129.04 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.83/129.04 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.83/129.04 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.83/129.04 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 128.83/129.04 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 128.83/129.04 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 128.83/129.04 Instantiate: Xn0:=Xn:fofType
% 128.83/129.04 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 128.83/129.04 Found (x7 x40) as proof of (cNUMBER Xn)
% 128.83/129.04 Found (x7 x40) as proof of (cNUMBER Xn)
% 128.83/129.04 Found (x7 x40) as proof of (cNUMBER Xn)
% 128.83/129.04 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 128.83/129.04 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.83/129.04 Found (x5 x40) as proof of (cNUMBER Xn)
% 128.83/129.04 Found (x5 x40) as proof of (cNUMBER Xn)
% 128.83/129.04 Found (x5 x40) as proof of (cNUMBER Xn)
% 128.83/129.04 Found x50:=(x5 x40):(cNUMBER Xn0)
% 128.83/129.04 Found (x5 x40) as proof of (cNUMBER Xn0)
% 128.83/129.04 Found (x5 x40) as proof of (cNUMBER Xn0)
% 128.83/129.04 Found x50:=(x5 x41):(cNUMBER Xn0)
% 128.83/129.04 Instantiate: Xn0:=Xn:fofType
% 128.83/129.04 Found (x5 x41) as proof of (cNUMBER Xn)
% 128.83/129.04 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 128.83/129.04 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 128.83/129.04 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 128.83/129.04 Instantiate: Xn00:=Xn:fofType
% 128.83/129.04 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x60) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.83/129.04 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x60) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->((or (cEVEN Xn0)) (cODD Xn0)))
% 128.83/129.04 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 128.83/129.04 Instantiate: Xn00:=Xn:fofType
% 128.83/129.04 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 128.83/129.04 Found (x5 x60) as proof of (cNUMBER Xn)
% 128.83/129.04 Found (x5 x60) as proof of (cNUMBER Xn)
% 132.50/132.70 Found (x5 x60) as proof of (cNUMBER Xn)
% 132.50/132.70 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 132.50/132.70 Found x60 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 132.50/132.70 Found (x7 x60) as proof of (cNUMBER Xn)
% 132.50/132.70 Found (x7 x60) as proof of (cNUMBER Xn)
% 132.50/132.70 Found (x7 x60) as proof of (cNUMBER Xn)
% 132.50/132.70 Found x12:(cEVEN c0)
% 132.50/132.70 Found x12 as proof of (cEVEN c0)
% 132.50/132.70 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 132.50/132.70 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.50/132.70 Found (x7 x60) as proof of (cNUMBER Xn)
% 132.50/132.70 Found (x7 x60) as proof of (cNUMBER Xn)
% 132.50/132.70 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 132.50/132.70 Found (fun (x7:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x7 x60)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 132.50/132.70 Found x50:=(x5 x40):(cNUMBER Xn0)
% 132.50/132.70 Found (x5 x40) as proof of (cNUMBER Xn)
% 132.50/132.70 Found (x5 x40) as proof of (cNUMBER Xn)
% 132.50/132.70 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 132.50/132.70 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 132.50/132.70 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 132.50/132.70 Found x5:(cODD (cS c0))
% 132.50/132.70 Instantiate: Xn0:=(cS c0):fofType
% 132.50/132.70 Found x5 as proof of (cODD Xn0)
% 132.50/132.70 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.50/132.70 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.50/132.70 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.50/132.70 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.50/132.70 Found x7:(cODD (cS c0))
% 132.50/132.70 Instantiate: Xn0:=(cS c0):fofType
% 132.50/132.70 Found x7 as proof of (cODD Xn0)
% 132.50/132.70 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.50/132.70 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.50/132.70 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.50/132.70 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.50/132.70 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 132.50/132.70 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 132.50/132.70 Found x12:(cEVEN c0)
% 132.50/132.70 Found x12 as proof of (cEVEN c0)
% 132.50/132.70 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 132.50/132.70 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.50/132.70 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 132.50/132.70 Found x30:=(x3 x21):(cNUMBER Xn0)
% 132.50/132.70 Found (x3 x21) as proof of (cNUMBER Xn0)
% 132.50/132.70 Found (x3 x21) as proof of (cNUMBER Xn0)
% 132.50/132.70 Found x30:=(x3 x20):(cNUMBER Xn0)
% 132.50/132.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 132.50/132.70 Found (x3 x20) as proof of (cNUMBER Xn)
% 132.50/132.70 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 132.50/132.70 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 132.50/132.70 Found x50:=(x5 x40):(cNUMBER Xn00)
% 132.50/132.70 Found (x5 x40) as proof of (cNUMBER Xn)
% 132.50/132.70 Found (x5 x40) as proof of (cNUMBER Xn)
% 132.50/132.70 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 132.50/132.70 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 132.50/132.70 Found x50:=(x5 x41):(cNUMBER Xn0)
% 132.50/132.70 Instantiate: Xn0:=Xn:fofType
% 132.50/132.70 Found (x5 x41) as proof of (cNUMBER Xn)
% 132.50/132.70 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 132.50/132.70 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 132.50/132.70 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 134.29/134.53 Found x70:=(x7 x60):(cNUMBER Xn0)
% 134.29/134.53 Found (x7 x60) as proof of (cNUMBER Xn0)
% 134.29/134.53 Found (x7 x60) as proof of (cNUMBER Xn0)
% 134.29/134.53 Found x20:=(x2 x31):((or (cEVEN Xn0)) (cODD Xn0))
% 134.29/134.53 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.29/134.53 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.29/134.53 Found x32:(cNUMBER Xn0)
% 134.29/134.53 Instantiate: Xn0:=Xn:fofType
% 134.29/134.53 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x32) as proof of (cNUMBER Xn)
% 134.29/134.53 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x32) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 134.29/134.53 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x32) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 134.29/134.53 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 134.29/134.53 Instantiate: Xn00:=Xn:fofType
% 134.29/134.53 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.29/134.53 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.29/134.53 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 134.29/134.53 Instantiate: Xn0:=Xn:fofType
% 134.29/134.53 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 134.29/134.53 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 134.29/134.53 Found x30:=(x3 x21):(cNUMBER Xn0)
% 134.29/134.53 Found (x3 x21) as proof of (cNUMBER Xn0)
% 134.29/134.53 Found (x3 x21) as proof of (cNUMBER Xn0)
% 134.29/134.53 Found x30:=(x3 x22):(cNUMBER Xn0)
% 134.29/134.53 Instantiate: Xn0:=Xn:fofType
% 134.29/134.53 Found (x3 x22) as proof of (cNUMBER Xn)
% 134.29/134.53 Found (x3 x22) as proof of (cNUMBER Xn)
% 134.29/134.53 Found x30:=(x3 x22):(cNUMBER Xn0)
% 134.29/134.53 Found (x3 x22) as proof of (cNUMBER Xn)
% 134.29/134.53 Found (x3 x22) as proof of (cNUMBER Xn)
% 134.29/134.53 Found (x3 x22) as proof of (cNUMBER Xn)
% 134.29/134.53 Found x51:(cNUMBER Xn0)
% 134.29/134.53 Instantiate: Xn0:=Xn:fofType
% 134.29/134.53 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x51) as proof of (cNUMBER Xn)
% 134.29/134.53 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x51) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 134.29/134.53 Found x60:=(x6 x70):((or (cEVEN Xn0)) (cODD Xn0))
% 134.29/134.53 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.29/134.53 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.29/134.53 Found x71:(cNUMBER Xn0)
% 134.29/134.53 Instantiate: Xn0:=Xn:fofType
% 134.29/134.53 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x71) as proof of (cNUMBER Xn)
% 134.29/134.53 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x71) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 134.29/134.53 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x71) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 134.29/134.53 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 134.29/134.53 Instantiate: Xn0:=Xn:fofType
% 134.29/134.53 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 134.29/134.53 Found (x7 x20) as proof of (cNUMBER Xn)
% 134.29/134.53 Found (x7 x20) as proof of (cNUMBER Xn)
% 134.29/134.53 Found (x7 x20) as proof of (cNUMBER Xn)
% 134.29/134.53 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 134.29/134.53 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.29/134.53 Found (x3 x20) as proof of (cNUMBER Xn)
% 134.29/134.53 Found (x3 x20) as proof of (cNUMBER Xn)
% 134.29/134.53 Found (x3 x20) as proof of (cNUMBER Xn)
% 134.29/134.53 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 134.29/134.53 Instantiate: Xn00:=Xn:fofType
% 134.29/134.53 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 134.29/134.53 Found (x3 x60) as proof of (cNUMBER Xn)
% 134.29/134.53 Found (x3 x60) as proof of (cNUMBER Xn)
% 134.29/134.53 Found (x3 x60) as proof of (cNUMBER Xn)
% 134.29/134.53 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 134.29/134.53 Found x60 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 134.29/134.53 Found (x7 x60) as proof of (cNUMBER Xn)
% 134.29/134.53 Found (x7 x60) as proof of (cNUMBER Xn)
% 134.29/134.53 Found (x7 x60) as proof of (cNUMBER Xn)
% 134.29/134.53 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 136.30/136.50 Instantiate: Xn00:=Xn:fofType
% 136.30/136.50 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 136.30/136.50 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x40) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 136.30/136.50 Found x30:=(x3 x20):(cNUMBER Xn0)
% 136.30/136.50 Found (x3 x20) as proof of (cNUMBER Xn)
% 136.30/136.50 Found (x3 x20) as proof of (cNUMBER Xn)
% 136.30/136.50 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 136.30/136.50 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 136.30/136.50 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 136.30/136.50 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 136.30/136.50 Instantiate: Xn00:=Xn:fofType
% 136.30/136.50 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 136.30/136.50 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 136.30/136.50 Found x30:=(x3 x20):(cNUMBER Xn0)
% 136.30/136.50 Found (x3 x20) as proof of (cNUMBER Xn0)
% 136.30/136.50 Found (x3 x20) as proof of (cNUMBER Xn0)
% 136.30/136.50 Found x30:=(x3 x21):(cNUMBER Xn0)
% 136.30/136.50 Instantiate: Xn0:=Xn:fofType
% 136.30/136.50 Found (x3 x21) as proof of (cNUMBER Xn)
% 136.30/136.50 Found (x3 x21) as proof of (cNUMBER Xn)
% 136.30/136.50 Found x30:=(x3 x20):(cNUMBER Xn0)
% 136.30/136.50 Found (x3 x20) as proof of (cNUMBER Xn)
% 136.30/136.50 Found (x3 x20) as proof of (cNUMBER Xn)
% 136.30/136.50 Found (x3 x20) as proof of (cNUMBER Xn)
% 136.30/136.50 Found x12:(cEVEN c0)
% 136.30/136.50 Found x12 as proof of (cEVEN c0)
% 136.30/136.50 Found x7:(cODD (cS c0))
% 136.30/136.50 Instantiate: Xn0:=(cS c0):fofType
% 136.30/136.50 Found x7 as proof of (cODD Xn0)
% 136.30/136.50 Found (or_introl00 x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 136.30/136.50 Found ((or_introl0 (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 136.30/136.50 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 136.30/136.50 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 136.30/136.50 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 136.30/136.50 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 136.30/136.50 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 136.30/136.50 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 136.30/136.50 Found or_introl000:=(or_introl00 (cODD Xn0)):((or (cEVEN Xn0)) (cODD Xn0))
% 136.30/136.50 Found (or_introl00 (cODD Xn0)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 136.30/136.50 Found ((fun (B:Prop)=> ((or_introl0 B) x12)) (cODD Xn0)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 136.30/136.50 Found ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x12)) (cODD Xn0)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 136.30/136.50 Found ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x12)) (cODD Xn0)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 136.30/136.50 Found (x3 ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x12)) (cODD Xn0))) as proof of (cNUMBER c0)
% 136.30/136.50 Found (x3 ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x12)) (cODD Xn0))) as proof of (cNUMBER c0)
% 136.30/136.50 Found (x3 ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x12)) (cODD Xn0))) as proof of (cNUMBER c0)
% 136.30/136.50 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 136.30/136.50 Instantiate: Xn00:=Xn:fofType
% 136.30/136.50 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 136.30/136.50 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x40) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 136.30/136.50 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x40) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 137.62/137.81 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 137.62/137.81 Instantiate: Xn0:=Xn:fofType
% 137.62/137.81 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x20) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 137.62/137.81 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x20) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->((or (cEVEN Xn00)) (cODD Xn00)))
% 137.62/137.81 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x20) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->((or (cEVEN Xn00)) (cODD Xn00))))
% 137.62/137.81 Found x12:(cEVEN c0)
% 137.62/137.81 Found x12 as proof of (cEVEN c0)
% 137.62/137.81 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 137.62/137.81 Instantiate: Xn0:=Xn:fofType
% 137.62/137.81 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 137.62/137.81 Found (x7 x40) as proof of (cNUMBER Xn)
% 137.62/137.81 Found (x7 x40) as proof of (cNUMBER Xn)
% 137.62/137.81 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x40)) as proof of (cNUMBER Xn)
% 137.62/137.81 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 137.62/137.81 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 137.62/137.81 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 137.62/137.81 Found (x5 x40) as proof of (cNUMBER Xn)
% 137.62/137.81 Found (x5 x40) as proof of (cNUMBER Xn)
% 137.62/137.81 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 137.62/137.81 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 137.62/137.81 Found x32:(cNUMBER Xn0)
% 137.62/137.81 Instantiate: Xn0:=Xn:fofType
% 137.62/137.81 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x32) as proof of (cNUMBER Xn)
% 137.62/137.81 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x32) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 137.62/137.81 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 137.62/137.81 Instantiate: Xn00:=Xn:fofType
% 137.62/137.81 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 137.62/137.81 Found (x5 x60) as proof of (cNUMBER Xn)
% 137.62/137.81 Found (x5 x60) as proof of (cNUMBER Xn)
% 137.62/137.81 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x60)) as proof of (cNUMBER Xn)
% 137.62/137.81 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 137.62/137.81 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 137.62/137.81 Found x60 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 137.62/137.81 Found (x7 x60) as proof of (cNUMBER Xn)
% 137.62/137.81 Found (x7 x60) as proof of (cNUMBER Xn)
% 137.62/137.81 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 137.62/137.81 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 137.62/137.81 Found x12:(cEVEN c0)
% 137.62/137.81 Found x12 as proof of (cEVEN c0)
% 137.62/137.81 Found x30:=(x3 x20):(cNUMBER Xn0)
% 137.62/137.81 Found (x3 x20) as proof of (cNUMBER Xn)
% 137.62/137.81 Found (x3 x20) as proof of (cNUMBER Xn)
% 137.62/137.81 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 137.62/137.81 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 137.62/137.81 Found x5:(cODD (cS c0))
% 137.62/137.81 Instantiate: Xn0:=(cS c0):fofType
% 137.62/137.81 Found x5 as proof of (cODD Xn0)
% 137.62/137.81 Found (or_introl00 x5) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 137.62/137.81 Found ((or_introl0 (cEVEN Xn0)) x5) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 137.62/137.81 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 139.74/139.93 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 139.74/139.93 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 139.74/139.93 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 139.74/139.93 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 139.74/139.93 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 139.74/139.93 Found x30:=(x3 x20):(cNUMBER Xn0)
% 139.74/139.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 139.74/139.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 139.74/139.93 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 139.74/139.93 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 139.74/139.93 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 139.74/139.93 Found x12:(cEVEN c0)
% 139.74/139.93 Found x12 as proof of (cEVEN c0)
% 139.74/139.93 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 139.74/139.93 Instantiate: Xn00:=Xn:fofType
% 139.74/139.93 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 139.74/139.93 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 139.74/139.93 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 139.74/139.93 Instantiate: Xn0:=Xn:fofType
% 139.74/139.93 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 139.74/139.93 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 139.74/139.93 Found x50:=(x5 x40):(cNUMBER Xn0)
% 139.74/139.93 Found (x5 x40) as proof of (cNUMBER Xn0)
% 139.74/139.93 Found (x5 x40) as proof of (cNUMBER Xn0)
% 139.74/139.93 Found x50:=(x5 x41):(cNUMBER Xn0)
% 139.74/139.93 Instantiate: Xn0:=Xn:fofType
% 139.74/139.93 Found (x5 x41) as proof of (cNUMBER Xn)
% 139.74/139.93 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 139.74/139.93 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 139.74/139.93 Found x12:(cEVEN c0)
% 139.74/139.93 Found x12 as proof of (cEVEN c0)
% 139.74/139.93 Found x12:(cEVEN c0)
% 139.74/139.93 Found x12 as proof of (cEVEN c0)
% 139.74/139.93 Found x12:(cEVEN c0)
% 139.74/139.93 Found x12 as proof of (cEVEN c0)
% 139.74/139.93 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 139.74/139.93 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 139.74/139.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 139.74/139.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 139.74/139.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 139.74/139.93 Found or_comm_i100:=(or_comm_i10 x20):((or (cODD Xn0)) (cEVEN Xn0))
% 139.74/139.93 Found (or_comm_i10 x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 139.74/139.93 Found ((or_comm_i1 (cODD Xn0)) x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 139.74/139.93 Found (((or_comm_i (cEVEN Xn0)) (cODD Xn0)) x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 139.74/139.93 Found (((or_comm_i (cEVEN Xn0)) (cODD Xn0)) x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 139.74/139.93 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 139.74/139.93 Instantiate: Xn00:=Xn:fofType
% 139.74/139.93 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 139.74/139.93 Found (x3 x40) as proof of (cNUMBER Xn)
% 139.74/139.93 Found (x3 x40) as proof of (cNUMBER Xn)
% 139.74/139.93 Found (x3 x40) as proof of (cNUMBER Xn)
% 139.74/139.93 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 139.74/139.93 Instantiate: Xn0:=Xn:fofType
% 139.74/139.93 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 139.74/139.93 Found (x5 x20) as proof of (cNUMBER Xn)
% 139.74/139.93 Found (x5 x20) as proof of (cNUMBER Xn)
% 139.74/139.93 Found (x5 x20) as proof of (cNUMBER Xn)
% 139.74/139.93 Found x12:(cEVEN c0)
% 139.74/139.93 Found x12 as proof of (cEVEN c0)
% 139.74/139.93 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 139.74/139.93 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 139.74/139.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 139.74/139.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 139.74/139.93 Found (x3 x20) as proof of (cNUMBER Xn)
% 139.74/139.93 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 139.74/139.93 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 139.74/139.93 Found (x5 x40) as proof of (cNUMBER Xn)
% 139.74/139.93 Found (x5 x40) as proof of (cNUMBER Xn)
% 139.74/139.93 Found (x5 x40) as proof of (cNUMBER Xn)
% 139.74/139.93 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 139.74/139.93 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 139.74/139.93 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 141.09/141.31 Found x12:(cEVEN c0)
% 141.09/141.31 Found x12 as proof of (cEVEN c0)
% 141.09/141.31 Found x9:(cEVEN c0)
% 141.09/141.31 Instantiate: Xn0:=c0:fofType
% 141.09/141.31 Found x9 as proof of (cEVEN Xn0)
% 141.09/141.31 Found (or_introl00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 141.09/141.31 Found ((or_introl0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 141.09/141.31 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 141.09/141.31 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 141.09/141.31 Found x5:(cODD (cS c0))
% 141.09/141.31 Instantiate: Xn0:=(cS c0):fofType
% 141.09/141.31 Found x5 as proof of (cODD Xn0)
% 141.09/141.31 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 141.09/141.31 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 141.09/141.31 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 141.09/141.31 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 141.09/141.31 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 141.09/141.31 Instantiate: Xn00:=Xn:fofType
% 141.09/141.31 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 141.09/141.31 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 141.09/141.31 Found x30:=(x3 x20):(cNUMBER Xn0)
% 141.09/141.31 Found (x3 x20) as proof of (cNUMBER Xn)
% 141.09/141.31 Found (x3 x20) as proof of (cNUMBER Xn)
% 141.09/141.31 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 141.09/141.31 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 141.09/141.31 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 141.09/141.31 Found x50:=(x5 x40):(cNUMBER Xn00)
% 141.09/141.31 Found (x5 x40) as proof of (cNUMBER Xn)
% 141.09/141.31 Found (x5 x40) as proof of (cNUMBER Xn)
% 141.09/141.31 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 141.09/141.31 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 141.09/141.31 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 141.09/141.31 Found x12:(cEVEN c0)
% 141.09/141.31 Found x12 as proof of (cEVEN c0)
% 141.09/141.31 Found x5:(cODD (cS c0))
% 141.09/141.31 Instantiate: Xn0:=(cS c0):fofType
% 141.09/141.31 Found x5 as proof of (cODD Xn0)
% 141.09/141.31 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 141.09/141.31 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 141.09/141.31 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 141.09/141.31 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 141.09/141.31 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of (cNUMBER Xn0)
% 141.09/141.31 Found (fun (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5))) as proof of (cNUMBER Xn0)
% 141.09/141.31 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5))) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn0))
% 141.09/141.31 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5))) as proof of (((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn0)))
% 141.94/142.19 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)))) as proof of (cNUMBER Xn0)
% 141.94/142.19 Found ((and_rect4 (cNUMBER Xn0)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)))) as proof of (cNUMBER Xn0)
% 141.94/142.19 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x4)) (cNUMBER Xn0)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)))) as proof of (cNUMBER Xn0)
% 141.94/142.19 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x4)) (cNUMBER Xn0)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)))) as proof of (cNUMBER Xn0)
% 141.94/142.19 Found x71:(cNUMBER Xn0)
% 141.94/142.19 Instantiate: Xn0:=Xn:fofType
% 141.94/142.19 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x71) as proof of (cNUMBER Xn)
% 141.94/142.19 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x71) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 141.94/142.19 Found x30:=(x3 x22):(cNUMBER Xn0)
% 141.94/142.19 Instantiate: Xn0:=Xn:fofType
% 141.94/142.19 Found (x3 x22) as proof of (cNUMBER Xn)
% 141.94/142.19 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of (cNUMBER Xn)
% 141.94/142.19 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 141.94/142.19 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 141.94/142.19 Found x30:=(x3 x21):(cNUMBER Xn0)
% 141.94/142.19 Found (x3 x21) as proof of (cNUMBER Xn0)
% 141.94/142.19 Found (x3 x21) as proof of (cNUMBER Xn0)
% 141.94/142.19 Found x30:=(x3 x22):(cNUMBER Xn0)
% 141.94/142.19 Instantiate: Xn0:=Xn:fofType
% 141.94/142.19 Found (x3 x22) as proof of (cNUMBER Xn)
% 141.94/142.19 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of (cNUMBER Xn)
% 141.94/142.19 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 141.94/142.19 Found x12:(cEVEN c0)
% 141.94/142.19 Found x12 as proof of (cEVEN c0)
% 141.94/142.19 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 141.94/142.19 Instantiate: Xn0:=Xn:fofType
% 141.94/142.19 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 141.94/142.19 Found (x7 x20) as proof of (cNUMBER Xn)
% 141.94/142.19 Found (x7 x20) as proof of (cNUMBER Xn)
% 141.94/142.19 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x20)) as proof of (cNUMBER Xn)
% 141.94/142.19 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 141.94/142.19 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 141.94/142.19 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 141.94/142.19 Found (x3 x20) as proof of (cNUMBER Xn)
% 141.94/142.19 Found (x3 x20) as proof of (cNUMBER Xn)
% 141.94/142.19 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 141.94/142.19 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 141.94/142.19 Found x30:=(x3 x22):(cNUMBER Xn0)
% 142.81/142.99 Instantiate: Xn0:=Xn:fofType
% 142.81/142.99 Found (x3 x22) as proof of (cNUMBER Xn)
% 142.81/142.99 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x22)) as proof of (cNUMBER Xn)
% 142.81/142.99 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x22)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 142.81/142.99 Found x20:=(x2 x31):((or (cEVEN Xn0)) (cODD Xn0))
% 142.81/142.99 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 142.81/142.99 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 142.81/142.99 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 142.81/142.99 Instantiate: Xn00:=Xn:fofType
% 142.81/142.99 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 142.81/142.99 Found (x3 x60) as proof of (cNUMBER Xn)
% 142.81/142.99 Found (x3 x60) as proof of (cNUMBER Xn)
% 142.81/142.99 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x60)) as proof of (cNUMBER Xn)
% 142.81/142.99 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 142.81/142.99 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 142.81/142.99 Found x60 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 142.81/142.99 Found (x7 x60) as proof of (cNUMBER Xn)
% 142.81/142.99 Found (x7 x60) as proof of (cNUMBER Xn)
% 142.81/142.99 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 142.81/142.99 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 142.81/142.99 Found or_introl00:=(or_introl0 (cODD Xn0)):((cEVEN c0)->((or (cEVEN c0)) (cODD Xn0)))
% 142.81/142.99 Found (or_introl0 (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 142.81/142.99 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 142.81/142.99 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 142.81/142.99 Found (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 142.81/142.99 Found (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of (cIND->((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0))))
% 142.81/142.99 Found (and_rect50 (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 142.81/142.99 Found ((and_rect5 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 142.81/142.99 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 142.81/142.99 Found (fun (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 142.81/142.99 Found (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 142.81/142.99 Found (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))) as proof of (((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 142.81/142.99 Found (and_rect40 (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 142.81/142.99 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 142.82/143.01 Found (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 142.82/143.01 Found (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 142.82/143.01 Found (x5 (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))))) as proof of (cNUMBER Xn0)
% 142.82/143.01 Found (x5 (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))))) as proof of (cNUMBER Xn0)
% 142.82/143.01 Found or_introl00:=(or_introl0 (cODD Xn0)):((cEVEN c0)->((or (cEVEN c0)) (cODD Xn0)))
% 142.82/143.01 Found (or_introl0 (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 142.82/143.01 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 142.82/143.01 Found ((or_introl (cEVEN c0)) (cODD Xn0)) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 142.82/143.01 Found (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of ((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0)))
% 142.82/143.01 Found (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))) as proof of (cIND->((cEVEN c0)->((or (cEVEN Xn0)) (cODD Xn0))))
% 142.82/143.01 Found (and_rect50 (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 142.82/143.01 Found ((and_rect5 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 142.82/143.01 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 142.82/143.01 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 142.82/143.01 Found (x5 (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))) as proof of (cNUMBER Xn0)
% 143.30/143.57 Found (fun (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))))) as proof of (cNUMBER Xn0)
% 143.30/143.57 Found (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))))) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn0))
% 143.30/143.57 Found (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0)))))) as proof of (((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn0)))
% 143.30/143.57 Found (and_rect40 (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))))) as proof of (cNUMBER Xn0)
% 143.30/143.57 Found ((and_rect4 (cNUMBER Xn0)) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))))) as proof of (cNUMBER Xn0)
% 143.30/143.57 Found (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) (cNUMBER Xn0)) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))))) as proof of (cNUMBER Xn0)
% 143.30/143.57 Found (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) (cNUMBER Xn0)) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (x5 (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x9:cIND)=> ((or_introl (cEVEN c0)) (cODD Xn0))))))) as proof of (cNUMBER Xn0)
% 143.30/143.57 Found x50:=(x5 x40):(cNUMBER Xn0)
% 143.30/143.57 Found (x5 x40) as proof of (cNUMBER Xn0)
% 143.30/143.57 Found (x5 x40) as proof of (cNUMBER Xn0)
% 143.30/143.57 Found x50:=(x5 x41):(cNUMBER Xn0)
% 143.30/143.57 Instantiate: Xn0:=Xn:fofType
% 143.30/143.57 Found (x5 x41) as proof of (cNUMBER Xn)
% 143.30/143.57 Found (x5 x41) as proof of (cNUMBER Xn)
% 143.30/143.57 Found x50:=(x5 x41):(cNUMBER Xn0)
% 143.30/143.57 Found (x5 x41) as proof of (cNUMBER Xn)
% 143.30/143.57 Found (x5 x41) as proof of (cNUMBER Xn)
% 143.30/143.57 Found (x5 x41) as proof of (cNUMBER Xn)
% 143.30/143.57 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 143.30/143.57 Instantiate: Xn00:=Xn:fofType
% 143.30/143.57 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 143.30/143.57 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x40) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 143.30/143.57 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x40) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 146.20/146.38 Found x12:(cEVEN c0)
% 146.20/146.38 Found x12 as proof of (cEVEN c0)
% 146.20/146.38 Found x30:=(x3 x20):(cNUMBER Xn0)
% 146.20/146.38 Found (x3 x20) as proof of (cNUMBER Xn0)
% 146.20/146.38 Found (x3 x20) as proof of (cNUMBER Xn0)
% 146.20/146.38 Found x30:=(x3 x21):(cNUMBER Xn0)
% 146.20/146.38 Instantiate: Xn0:=Xn:fofType
% 146.20/146.38 Found (x3 x21) as proof of (cNUMBER Xn)
% 146.20/146.38 Found (x3 x21) as proof of (cNUMBER Xn)
% 146.20/146.38 Found x30:=(x3 x20):(cNUMBER Xn0)
% 146.20/146.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 146.20/146.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 146.20/146.38 Found (x3 x20) as proof of (cNUMBER Xn)
% 146.20/146.38 Found x50:=(x5 x41):(cNUMBER Xn0)
% 146.20/146.38 Found (x5 x41) as proof of (cNUMBER Xn)
% 146.20/146.38 Found (x5 x41) as proof of (cNUMBER Xn)
% 146.20/146.38 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 146.20/146.38 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 146.20/146.38 Found x12:(cEVEN c0)
% 146.20/146.38 Instantiate: Xn0:=c0:fofType
% 146.20/146.38 Found x12 as proof of (cEVEN Xn0)
% 146.20/146.38 Found (or_introl00 x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 146.20/146.38 Found ((or_introl0 (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 146.20/146.38 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 146.20/146.38 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 146.20/146.38 Found (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12)) as proof of (cNUMBER Xn0)
% 146.20/146.38 Found (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12)) as proof of (cNUMBER Xn0)
% 146.20/146.38 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 146.20/146.38 Instantiate: Xn0:=Xn:fofType
% 146.20/146.38 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 146.20/146.38 Found (x7 x40) as proof of (cNUMBER Xn)
% 146.20/146.38 Found (x7 x40) as proof of (cNUMBER Xn)
% 146.20/146.38 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x40)) as proof of (cNUMBER Xn)
% 146.20/146.38 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 146.20/146.38 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x40)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 146.20/146.38 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 146.20/146.38 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 146.20/146.38 Found (x5 x40) as proof of (cNUMBER Xn)
% 146.20/146.38 Found (x5 x40) as proof of (cNUMBER Xn)
% 146.20/146.38 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 146.20/146.38 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 146.20/146.38 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 146.20/146.38 Found x70:=(x7 x60):(cNUMBER Xn0)
% 146.20/146.38 Found (x7 x60) as proof of (cNUMBER Xn0)
% 146.20/146.38 Found (x7 x60) as proof of (cNUMBER Xn0)
% 146.20/146.38 Found x70:=(x7 x61):(cNUMBER Xn0)
% 146.20/146.38 Instantiate: Xn0:=Xn:fofType
% 146.20/146.38 Found (x7 x61) as proof of (cNUMBER Xn)
% 146.20/146.38 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x61)) as proof of (cNUMBER Xn)
% 146.20/146.38 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x61)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 146.20/146.38 Found x12:(cEVEN c0)
% 146.20/146.38 Found x12 as proof of (cEVEN c0)
% 146.20/146.38 Found x7:(cODD (cS c0))
% 146.20/146.38 Instantiate: Xn0:=(cS c0):fofType
% 146.20/146.38 Found x7 as proof of (cODD Xn0)
% 146.20/146.38 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 146.20/146.38 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 146.20/146.38 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 146.20/146.38 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 147.74/147.98 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 147.74/147.98 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 147.74/147.98 Found x12:(cEVEN c0)
% 147.74/147.98 Instantiate: Xn0:=c0:fofType
% 147.74/147.98 Found x12 as proof of (cEVEN Xn0)
% 147.74/147.98 Found (or_introl00 x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 147.74/147.98 Found ((or_introl0 (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 147.74/147.98 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 147.74/147.98 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 147.74/147.98 Found x5:(cODD (cS c0))
% 147.74/147.98 Instantiate: Xn0:=(cS c0):fofType
% 147.74/147.98 Found x5 as proof of (cODD Xn0)
% 147.74/147.98 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 147.74/147.98 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 147.74/147.98 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 147.74/147.98 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 147.74/147.98 Found x32:(cNUMBER Xn0)
% 147.74/147.98 Instantiate: Xn0:=Xn:fofType
% 147.74/147.98 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x32) as proof of (cNUMBER Xn)
% 147.74/147.98 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x32) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 147.74/147.98 Found x32:(cNUMBER Xn0)
% 147.74/147.98 Instantiate: Xn0:=Xn:fofType
% 147.74/147.98 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x32) as proof of (cNUMBER Xn)
% 147.74/147.98 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x32) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 147.74/147.98 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 147.74/147.98 Instantiate: Xn00:=Xn:fofType
% 147.74/147.98 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 147.74/147.98 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 147.74/147.98 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 147.74/147.98 Instantiate: Xn0:=Xn:fofType
% 147.74/147.98 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 147.74/147.98 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 147.74/147.98 Found x5:(cODD (cS c0))
% 147.74/147.98 Instantiate: Xn0:=(cS c0):fofType
% 147.74/147.98 Found x5 as proof of (cODD Xn0)
% 147.74/147.98 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 147.74/147.98 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 147.74/147.98 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 147.74/147.98 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 147.74/147.98 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of (cNUMBER Xn0)
% 147.74/147.98 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of (cNUMBER Xn0)
% 147.74/147.98 Found x12:(cEVEN c0)
% 147.74/147.98 Found x12 as proof of (cEVEN c0)
% 147.74/147.98 Found x60:=(x6 x70):((or (cEVEN Xn0)) (cODD Xn0))
% 147.74/147.98 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 147.74/147.98 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 147.74/147.98 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 147.74/147.98 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 147.74/147.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 147.74/147.98 Found (x3 x20) as proof of (cNUMBER Xn)
% 147.74/147.98 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 147.74/147.98 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 147.74/147.98 Found x5:(cODD (cS c0))
% 147.74/147.98 Instantiate: Xn0:=(cS c0):fofType
% 147.74/147.98 Found x5 as proof of (cODD Xn0)
% 147.74/147.98 Found (or_introl00 x5) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 147.74/147.98 Found ((or_introl0 (cEVEN Xn0)) x5) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 147.74/147.98 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 147.74/147.98 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 147.74/147.98 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 147.74/147.98 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 147.74/147.98 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 150.92/151.12 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 150.92/151.12 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 150.92/151.12 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 150.92/151.12 Found (x3 x20) as proof of (cNUMBER Xn)
% 150.92/151.12 Found (x3 x20) as proof of (cNUMBER Xn)
% 150.92/151.12 Found (x3 x20) as proof of (cNUMBER Xn)
% 150.92/151.12 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 150.92/151.12 Instantiate: Xn0:=Xn:fofType
% 150.92/151.12 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 150.92/151.12 Found (x5 x20) as proof of (cNUMBER Xn)
% 150.92/151.12 Found (x5 x20) as proof of (cNUMBER Xn)
% 150.92/151.12 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x20)) as proof of (cNUMBER Xn)
% 150.92/151.12 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 150.92/151.12 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 150.92/151.12 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 150.92/151.12 Found (x3 x20) as proof of (cNUMBER Xn)
% 150.92/151.12 Found (x3 x20) as proof of (cNUMBER Xn)
% 150.92/151.12 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 150.92/151.12 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 150.92/151.12 Found x50:=(x5 x41):(cNUMBER Xn0)
% 150.92/151.12 Found (x5 x41) as proof of (cNUMBER Xn0)
% 150.92/151.12 Found (x5 x41) as proof of (cNUMBER Xn0)
% 150.92/151.12 Found x50:=(x5 x42):(cNUMBER Xn0)
% 150.92/151.12 Instantiate: Xn0:=Xn:fofType
% 150.92/151.12 Found (x5 x42) as proof of (cNUMBER Xn)
% 150.92/151.12 Found (x5 x42) as proof of (cNUMBER Xn)
% 150.92/151.12 Found x50:=(x5 x41):(cNUMBER Xn0)
% 150.92/151.12 Found (x5 x41) as proof of (cNUMBER Xn)
% 150.92/151.12 Found (x5 x41) as proof of (cNUMBER Xn)
% 150.92/151.12 Found (x5 x41) as proof of (cNUMBER Xn)
% 150.92/151.12 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 150.92/151.12 Instantiate: Xn00:=Xn:fofType
% 150.92/151.12 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 150.92/151.12 Found (x3 x40) as proof of (cNUMBER Xn)
% 150.92/151.12 Found (x3 x40) as proof of (cNUMBER Xn)
% 150.92/151.12 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x40)) as proof of (cNUMBER Xn)
% 150.92/151.12 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x40)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 150.92/151.12 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 150.92/151.12 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 150.92/151.12 Found (x5 x40) as proof of (cNUMBER Xn)
% 150.92/151.12 Found (x5 x40) as proof of (cNUMBER Xn)
% 150.92/151.12 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 150.92/151.12 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 150.92/151.12 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 150.92/151.12 Instantiate: Xn00:=Xn:fofType
% 150.92/151.12 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 150.92/151.12 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 150.92/151.12 Found x70:=(x7 x61):(cNUMBER Xn0)
% 150.92/151.12 Instantiate: Xn0:=Xn:fofType
% 150.92/151.12 Found (x7 x61) as proof of (cNUMBER Xn)
% 150.92/151.12 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x61)) as proof of (cNUMBER Xn)
% 150.92/151.12 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x61)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 150.92/151.12 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x61)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 150.92/151.12 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 150.92/151.12 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 150.92/151.12 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 150.92/151.12 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 150.92/151.12 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 150.92/151.12 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 150.92/151.12 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 150.92/151.12 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 150.92/151.12 Found x11:(cEVEN c0)
% 150.92/151.12 Instantiate: Xn0:=c0:fofType
% 150.92/151.12 Found (fun (x11:(cEVEN c0))=> x11) as proof of (cEVEN Xn0)
% 150.92/151.12 Found (fun (x9:cIND) (x11:(cEVEN c0))=> x11) as proof of ((cEVEN c0)->(cEVEN Xn0))
% 151.99/152.19 Found (fun (x9:cIND) (x11:(cEVEN c0))=> x11) as proof of (cIND->((cEVEN c0)->(cEVEN Xn0)))
% 151.99/152.19 Found (and_rect50 (fun (x9:cIND) (x11:(cEVEN c0))=> x11)) as proof of (cEVEN Xn0)
% 151.99/152.19 Found ((and_rect5 (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11)) as proof of (cEVEN Xn0)
% 151.99/152.19 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11)) as proof of (cEVEN Xn0)
% 151.99/152.19 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11)) as proof of (cEVEN Xn0)
% 151.99/152.19 Found (or_introl00 (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 151.99/152.19 Found ((or_introl0 (cODD Xn0)) (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 151.99/152.19 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 151.99/152.19 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 151.99/152.19 Found x30:(cNUMBER Xn0)
% 151.99/152.19 Instantiate: Xn00:=Xn0:fofType
% 151.99/152.19 Found x30 as proof of (cNUMBER Xn00)
% 151.99/152.19 Found x71:(cNUMBER Xn0)
% 151.99/152.19 Instantiate: Xn0:=Xn:fofType
% 151.99/152.19 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x71) as proof of (cNUMBER Xn)
% 151.99/152.19 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x71) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 151.99/152.19 Found x30:=(x3 x21):(cNUMBER Xn0)
% 151.99/152.19 Found (x3 x21) as proof of (cNUMBER Xn0)
% 151.99/152.19 Found (x3 x21) as proof of (cNUMBER Xn0)
% 151.99/152.19 Found x30:=(x3 x22):(cNUMBER Xn0)
% 151.99/152.19 Instantiate: Xn0:=Xn:fofType
% 151.99/152.19 Found (x3 x22) as proof of (cNUMBER Xn)
% 151.99/152.19 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of (cNUMBER Xn)
% 151.99/152.19 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 151.99/152.19 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 151.99/152.19 Instantiate: Xn0:=Xn00:fofType
% 151.99/152.19 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 151.99/152.19 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 151.99/152.19 Instantiate: Xn0:=Xn:fofType
% 151.99/152.19 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 151.99/152.19 Found (x7 x20) as proof of (cNUMBER Xn)
% 151.99/152.19 Found (x7 x20) as proof of (cNUMBER Xn)
% 151.99/152.19 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x20)) as proof of (cNUMBER Xn)
% 151.99/152.19 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 151.99/152.19 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x20)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 151.99/152.19 Found x30:=(x3 x21):(cNUMBER Xn0)
% 151.99/152.19 Found (x3 x21) as proof of (cNUMBER Xn0)
% 151.99/152.19 Found (x3 x21) as proof of (cNUMBER Xn0)
% 151.99/152.19 Found x30:=(x3 x22):(cNUMBER Xn0)
% 151.99/152.19 Instantiate: Xn0:=Xn:fofType
% 151.99/152.19 Found (x3 x22) as proof of (cNUMBER Xn)
% 151.99/152.19 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of (cNUMBER Xn)
% 151.99/152.19 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 151.99/152.19 Found x30:(cNUMBER Xn0)
% 151.99/152.19 Instantiate: Xn00:=Xn0:fofType
% 151.99/152.19 Found x30 as proof of (cNUMBER Xn00)
% 151.99/152.19 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 151.99/152.19 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 151.99/152.19 Found (x3 x20) as proof of (cNUMBER Xn)
% 154.23/154.44 Found (x3 x20) as proof of (cNUMBER Xn)
% 154.23/154.44 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 154.23/154.44 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 154.23/154.44 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 154.23/154.44 Found x20:=(x2 x31):((or (cEVEN Xn0)) (cODD Xn0))
% 154.23/154.44 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.23/154.44 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.23/154.44 Found x30:=(x3 x22):(cNUMBER Xn0)
% 154.23/154.44 Found (x3 x22) as proof of (cNUMBER Xn)
% 154.23/154.44 Found (x3 x22) as proof of (cNUMBER Xn)
% 154.23/154.44 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of (cNUMBER Xn)
% 154.23/154.44 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 154.23/154.44 Found x20:=(x2 x31):((or (cEVEN Xn0)) (cODD Xn0))
% 154.23/154.44 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.23/154.44 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.23/154.44 Found x50:=(x5 x40):(cNUMBER Xn0)
% 154.23/154.44 Found (x5 x40) as proof of (cNUMBER Xn0)
% 154.23/154.44 Found (x5 x40) as proof of (cNUMBER Xn0)
% 154.23/154.44 Found x50:=(x5 x41):(cNUMBER Xn0)
% 154.23/154.44 Instantiate: Xn0:=Xn:fofType
% 154.23/154.44 Found (x5 x41) as proof of (cNUMBER Xn)
% 154.23/154.44 Found (x5 x41) as proof of (cNUMBER Xn)
% 154.23/154.44 Found x50:=(x5 x41):(cNUMBER Xn0)
% 154.23/154.44 Found (x5 x41) as proof of (cNUMBER Xn)
% 154.23/154.44 Found (x5 x41) as proof of (cNUMBER Xn)
% 154.23/154.44 Found (x5 x41) as proof of (cNUMBER Xn)
% 154.23/154.44 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 154.23/154.44 Instantiate: Xn0:=Xn00:fofType
% 154.23/154.44 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.23/154.44 Found or_introl000:=(or_introl00 (cODD Xn0)):((or (cEVEN Xn0)) (cODD Xn0))
% 154.23/154.44 Found (or_introl00 (cODD Xn0)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.23/154.44 Found ((fun (B:Prop)=> ((or_introl0 B) x12)) (cODD Xn0)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.23/154.44 Found ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x12)) (cODD Xn0)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.23/154.44 Found ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x12)) (cODD Xn0)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.23/154.44 Found (x5 ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x12)) (cODD Xn0))) as proof of (cNUMBER c0)
% 154.23/154.44 Found (x5 ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x12)) (cODD Xn0))) as proof of (cNUMBER c0)
% 154.23/154.44 Found (x5 ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x12)) (cODD Xn0))) as proof of (cNUMBER c0)
% 154.23/154.44 Found x5:(cODD (cS c0))
% 154.23/154.44 Instantiate: Xn0:=(cS c0):fofType
% 154.23/154.44 Found x5 as proof of (cODD Xn0)
% 154.23/154.44 Found (or_introl00 x5) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 154.23/154.44 Found ((or_introl0 (cEVEN Xn0)) x5) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 154.23/154.44 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 154.23/154.44 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 154.23/154.44 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.23/154.44 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.23/154.44 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.23/154.44 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 154.23/154.44 Found x30:=(x3 x21):(cNUMBER Xn0)
% 154.23/154.44 Found (x3 x21) as proof of (cNUMBER Xn0)
% 154.23/154.44 Found (x3 x21) as proof of (cNUMBER Xn0)
% 154.23/154.44 Found x30:=(x3 x22):(cNUMBER Xn0)
% 154.23/154.44 Instantiate: Xn0:=Xn:fofType
% 154.23/154.44 Found (x3 x22) as proof of (cNUMBER Xn)
% 154.23/154.44 Found (x3 x22) as proof of (cNUMBER Xn)
% 154.23/154.44 Found x30:=(x3 x22):(cNUMBER Xn0)
% 154.23/154.44 Found (x3 x22) as proof of (cNUMBER Xn)
% 154.23/154.44 Found (x3 x22) as proof of (cNUMBER Xn)
% 154.23/154.44 Found (x3 x22) as proof of (cNUMBER Xn)
% 154.23/154.44 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 154.23/154.44 Instantiate: Xn00:=Xn:fofType
% 154.23/154.44 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 156.30/156.56 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 156.30/156.56 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 156.30/156.56 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 156.30/156.56 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 156.30/156.56 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 156.30/156.56 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 156.30/156.56 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 156.30/156.56 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 156.30/156.56 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 156.30/156.56 Found x50:=(x5 x41):(cNUMBER Xn0)
% 156.30/156.56 Found (x5 x41) as proof of (cNUMBER Xn)
% 156.30/156.56 Found (x5 x41) as proof of (cNUMBER Xn)
% 156.30/156.56 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 156.30/156.56 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 156.30/156.56 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 156.30/156.56 Instantiate: Xn0:=Xn:fofType
% 156.30/156.56 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 156.30/156.56 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 156.30/156.56 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->((or (cEVEN Xn00)) (cODD Xn00)))
% 156.30/156.56 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 156.30/156.56 Instantiate: Xn00:=Xn:fofType
% 156.30/156.56 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 156.30/156.56 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 156.30/156.56 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 156.30/156.56 Found x90:=(x9 x80):(cNUMBER Xn0)
% 156.30/156.56 Found (x9 x80) as proof of (cNUMBER Xn0)
% 156.30/156.56 Found (x9 x80) as proof of (cNUMBER Xn0)
% 156.30/156.56 Found x90:=(x9 x81):(cNUMBER Xn0)
% 156.30/156.56 Instantiate: Xn0:=Xn:fofType
% 156.30/156.56 Found (x9 x81) as proof of (cNUMBER Xn)
% 156.30/156.56 Found (x9 x81) as proof of (cNUMBER Xn)
% 156.30/156.56 Found x90:=(x9 x80):(cNUMBER Xn0)
% 156.30/156.56 Found (x9 x80) as proof of (cNUMBER Xn)
% 156.30/156.56 Found (x9 x80) as proof of (cNUMBER Xn)
% 156.30/156.56 Found (x9 x80) as proof of (cNUMBER Xn)
% 156.30/156.56 Found x50:=(x5 x41):(cNUMBER Xn0)
% 156.30/156.56 Found (x5 x41) as proof of (cNUMBER Xn)
% 156.30/156.56 Found (x5 x41) as proof of (cNUMBER Xn)
% 156.30/156.56 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 156.30/156.56 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 156.30/156.56 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 156.30/156.56 Found x12:(cEVEN c0)
% 156.30/156.56 Found x12 as proof of (cEVEN c0)
% 156.30/156.56 Found x22:((or (cEVEN Xn0)) (cODD Xn0))
% 156.30/156.56 Found x22 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 156.30/156.56 Found (x3 x22) as proof of (cNUMBER Xn)
% 156.30/156.56 Found (x3 x22) as proof of (cNUMBER Xn)
% 156.30/156.56 Found (x3 x22) as proof of (cNUMBER Xn)
% 156.30/156.56 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 156.30/156.56 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 156.30/156.56 Found (x5 x41) as proof of (cNUMBER Xn)
% 156.30/156.56 Found (x5 x41) as proof of (cNUMBER Xn)
% 156.30/156.56 Found (x5 x41) as proof of (cNUMBER Xn)
% 156.30/156.56 Found x70:=(x7 x60):(cNUMBER Xn0)
% 156.30/156.56 Found (x7 x60) as proof of (cNUMBER Xn0)
% 156.30/156.56 Found (x7 x60) as proof of (cNUMBER Xn0)
% 156.30/156.56 Found x70:=(x7 x61):(cNUMBER Xn0)
% 156.30/156.56 Instantiate: Xn0:=Xn:fofType
% 156.30/156.56 Found (x7 x61) as proof of (cNUMBER Xn)
% 156.30/156.56 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x61)) as proof of (cNUMBER Xn)
% 156.30/156.56 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x61)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 156.30/156.56 Found x12:(cEVEN c0)
% 156.30/156.56 Found x12 as proof of (cEVEN c0)
% 156.30/156.56 Found x12:(cEVEN c0)
% 156.30/156.56 Found x12 as proof of (cEVEN c0)
% 156.30/156.56 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 157.42/157.67 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 157.42/157.67 Found (x5 x41) as proof of (cNUMBER Xn)
% 157.42/157.67 Found (x5 x41) as proof of (cNUMBER Xn)
% 157.42/157.67 Found (x5 x41) as proof of (cNUMBER Xn)
% 157.42/157.67 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 157.42/157.67 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 157.42/157.67 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 157.42/157.67 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 157.42/157.67 Found x50:=(x5 x41):(cNUMBER Xn0)
% 157.42/157.67 Found (x5 x41) as proof of (cNUMBER Xn0)
% 157.42/157.67 Found (x5 x41) as proof of (cNUMBER Xn0)
% 157.42/157.67 Found x50:=(x5 x42):(cNUMBER Xn0)
% 157.42/157.67 Instantiate: Xn0:=Xn:fofType
% 157.42/157.67 Found (x5 x42) as proof of (cNUMBER Xn)
% 157.42/157.67 Found (x5 x42) as proof of (cNUMBER Xn)
% 157.42/157.67 Found x50:=(x5 x41):(cNUMBER Xn0)
% 157.42/157.67 Found (x5 x41) as proof of (cNUMBER Xn)
% 157.42/157.67 Found (x5 x41) as proof of (cNUMBER Xn)
% 157.42/157.67 Found (x5 x41) as proof of (cNUMBER Xn)
% 157.42/157.67 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 157.42/157.67 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 157.42/157.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 157.42/157.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 157.42/157.67 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 157.42/157.67 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 157.42/157.67 Found x60:=(x6 x70):((or (cEVEN Xn0)) (cODD Xn0))
% 157.42/157.67 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 157.42/157.67 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 157.42/157.67 Found x12:(cEVEN c0)
% 157.42/157.67 Found x12 as proof of (cEVEN c0)
% 157.42/157.67 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 157.42/157.67 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 157.42/157.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 157.42/157.67 Found (x3 x20) as proof of (cNUMBER Xn)
% 157.42/157.67 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 157.42/157.67 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 157.42/157.67 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 157.42/157.67 Found x12:(cEVEN c0)
% 157.42/157.67 Found x12 as proof of (cEVEN c0)
% 157.42/157.67 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 157.42/157.67 Instantiate: Xn00:=Xn:fofType
% 157.42/157.67 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 157.42/157.67 Found (x3 x40) as proof of (cNUMBER Xn)
% 157.42/157.67 Found (x3 x40) as proof of (cNUMBER Xn)
% 157.42/157.67 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x40)) as proof of (cNUMBER Xn)
% 157.42/157.67 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x40)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 157.42/157.67 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x40)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 157.42/157.67 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 157.42/157.67 Instantiate: Xn0:=Xn:fofType
% 157.42/157.67 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 157.42/157.67 Found (x5 x20) as proof of (cNUMBER Xn)
% 157.42/157.67 Found (x5 x20) as proof of (cNUMBER Xn)
% 157.42/157.67 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x20)) as proof of (cNUMBER Xn)
% 157.42/157.67 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 157.42/157.67 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x20)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 161.13/161.36 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 161.13/161.36 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 161.13/161.36 Found (x3 x20) as proof of (cNUMBER Xn)
% 161.13/161.36 Found (x3 x20) as proof of (cNUMBER Xn)
% 161.13/161.36 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 161.13/161.36 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 161.13/161.36 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 161.13/161.36 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 161.13/161.36 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 161.13/161.36 Found (x5 x40) as proof of (cNUMBER Xn)
% 161.13/161.36 Found (x5 x40) as proof of (cNUMBER Xn)
% 161.13/161.36 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 161.13/161.36 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 161.13/161.36 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 161.13/161.36 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 161.13/161.36 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 161.13/161.36 Found (x3 x20) as proof of (cNUMBER Xn)
% 161.13/161.36 Found (x3 x20) as proof of (cNUMBER Xn)
% 161.13/161.36 Found (x3 x20) as proof of (cNUMBER Xn)
% 161.13/161.36 Found x12:(cEVEN c0)
% 161.13/161.36 Found x12 as proof of (cEVEN c0)
% 161.13/161.36 Found x50:(cNUMBER Xn00)
% 161.13/161.36 Instantiate: Xn00:=Xn:fofType
% 161.13/161.36 Found x50 as proof of (cNUMBER Xn)
% 161.13/161.36 Found x30:(cNUMBER Xn0)
% 161.13/161.36 Instantiate: Xn0:=Xn:fofType
% 161.13/161.36 Found x30 as proof of (cNUMBER Xn)
% 161.13/161.36 Found x12:(cEVEN c0)
% 161.13/161.36 Found x12 as proof of (cEVEN c0)
% 161.13/161.36 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 161.13/161.36 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 161.13/161.36 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 161.13/161.36 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 161.13/161.36 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 161.13/161.36 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 161.13/161.36 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 161.13/161.36 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 161.13/161.36 Found x70:=(x7 x60):(cNUMBER Xn0)
% 161.13/161.36 Found (x7 x60) as proof of (cNUMBER Xn0)
% 161.13/161.36 Found (x7 x60) as proof of (cNUMBER Xn0)
% 161.13/161.36 Found x70:=(x7 x61):(cNUMBER Xn0)
% 161.13/161.36 Instantiate: Xn0:=Xn:fofType
% 161.13/161.36 Found (x7 x61) as proof of (cNUMBER Xn)
% 161.13/161.36 Found (x7 x61) as proof of (cNUMBER Xn)
% 161.13/161.36 Found x70:=(x7 x60):(cNUMBER Xn0)
% 161.13/161.36 Found (x7 x60) as proof of (cNUMBER Xn)
% 161.13/161.36 Found (x7 x60) as proof of (cNUMBER Xn)
% 161.13/161.36 Found (x7 x60) as proof of (cNUMBER Xn)
% 161.13/161.36 Found x30:(cNUMBER Xn0)
% 161.13/161.36 Instantiate: Xn00:=Xn0:fofType
% 161.13/161.36 Found x30 as proof of (cNUMBER Xn00)
% 161.13/161.36 Found x22:((or (cEVEN Xn0)) (cODD Xn0))
% 161.13/161.36 Found x22 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 161.13/161.36 Found (x3 x22) as proof of (cNUMBER Xn)
% 161.13/161.36 Found (x3 x22) as proof of (cNUMBER Xn)
% 161.13/161.36 Found (x3 x22) as proof of (cNUMBER Xn)
% 161.13/161.36 Found x30:=(x3 x22):(cNUMBER Xn0)
% 161.13/161.36 Found (x3 x22) as proof of (cNUMBER Xn)
% 161.13/161.36 Found (x3 x22) as proof of (cNUMBER Xn)
% 161.13/161.36 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of (cNUMBER Xn)
% 162.82/163.03 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 162.82/163.03 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 162.82/163.03 Found x30:=(x3 x22):(cNUMBER Xn0)
% 162.82/163.03 Found (x3 x22) as proof of (cNUMBER Xn)
% 162.82/163.03 Found (x3 x22) as proof of (cNUMBER Xn)
% 162.82/163.03 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of (cNUMBER Xn)
% 162.82/163.03 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 162.82/163.03 Found x30:=(x3 x22):(cNUMBER Xn0)
% 162.82/163.03 Found (x3 x22) as proof of (cNUMBER Xn)
% 162.82/163.03 Found (x3 x22) as proof of (cNUMBER Xn)
% 162.82/163.03 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of (cNUMBER Xn)
% 162.82/163.03 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 162.82/163.03 Found x50:=(x5 x40):(cNUMBER Xn0)
% 162.82/163.03 Found (x5 x40) as proof of (cNUMBER Xn0)
% 162.82/163.03 Found (x5 x40) as proof of (cNUMBER Xn0)
% 162.82/163.03 Found x50:=(x5 x41):(cNUMBER Xn0)
% 162.82/163.03 Instantiate: Xn0:=Xn:fofType
% 162.82/163.03 Found (x5 x41) as proof of (cNUMBER Xn)
% 162.82/163.03 Found (x5 x41) as proof of (cNUMBER Xn)
% 162.82/163.03 Found x50:=(x5 x41):(cNUMBER Xn0)
% 162.82/163.03 Found (x5 x41) as proof of (cNUMBER Xn)
% 162.82/163.03 Found (x5 x41) as proof of (cNUMBER Xn)
% 162.82/163.03 Found (x5 x41) as proof of (cNUMBER Xn)
% 162.82/163.03 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 162.82/163.03 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 162.82/163.03 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 162.82/163.03 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 162.82/163.03 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 162.82/163.03 Instantiate: Xn00:=Xn:fofType
% 162.82/163.03 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 162.82/163.03 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 162.82/163.03 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 162.82/163.03 Found x30:=(x3 x21):(cNUMBER Xn0)
% 162.82/163.03 Found (x3 x21) as proof of (cNUMBER Xn0)
% 162.82/163.03 Found (x3 x21) as proof of (cNUMBER Xn0)
% 162.82/163.03 Found x30:=(x3 x22):(cNUMBER Xn0)
% 162.82/163.03 Instantiate: Xn0:=Xn:fofType
% 162.82/163.03 Found (x3 x22) as proof of (cNUMBER Xn)
% 162.82/163.03 Found (x3 x22) as proof of (cNUMBER Xn)
% 162.82/163.03 Found x30:=(x3 x22):(cNUMBER Xn0)
% 162.82/163.03 Found (x3 x22) as proof of (cNUMBER Xn)
% 162.82/163.03 Found (x3 x22) as proof of (cNUMBER Xn)
% 162.82/163.03 Found (x3 x22) as proof of (cNUMBER Xn)
% 162.82/163.03 Found x50:(cNUMBER Xn00)
% 162.82/163.03 Instantiate: Xn0:=Xn00:fofType
% 162.82/163.03 Found x50 as proof of (cNUMBER Xn0)
% 162.82/163.03 Found x30:(cNUMBER Xn0)
% 162.82/163.03 Instantiate: Xn00:=Xn0:fofType
% 162.82/163.03 Found x30 as proof of (cNUMBER Xn00)
% 162.82/163.03 Found x70:=(x7 x60):(cNUMBER Xn0)
% 162.82/163.03 Found (x7 x60) as proof of (cNUMBER Xn)
% 162.82/163.03 Found (x7 x60) as proof of (cNUMBER Xn)
% 162.82/163.03 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 162.82/163.03 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 162.82/163.03 Found x7:(cODD (cS c0))
% 162.82/163.03 Instantiate: Xn0:=(cS c0):fofType
% 162.82/163.03 Found x7 as proof of (cODD Xn0)
% 162.82/163.03 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 162.82/163.03 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 162.82/163.03 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 162.82/163.03 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 162.82/163.03 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 164.71/164.89 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 164.71/164.89 Found x30:=(x3 x21):(cNUMBER Xn0)
% 164.71/164.89 Found (x3 x21) as proof of (cNUMBER Xn0)
% 164.71/164.89 Found (x3 x21) as proof of (cNUMBER Xn0)
% 164.71/164.89 Found x30:=(x3 x22):(cNUMBER Xn0)
% 164.71/164.89 Instantiate: Xn0:=Xn:fofType
% 164.71/164.89 Found (x3 x22) as proof of (cNUMBER Xn)
% 164.71/164.89 Found (x3 x22) as proof of (cNUMBER Xn)
% 164.71/164.89 Found x30:=(x3 x22):(cNUMBER Xn0)
% 164.71/164.89 Found (x3 x22) as proof of (cNUMBER Xn)
% 164.71/164.89 Found (x3 x22) as proof of (cNUMBER Xn)
% 164.71/164.89 Found (x3 x22) as proof of (cNUMBER Xn)
% 164.71/164.89 Found x5:(cODD (cS c0))
% 164.71/164.89 Instantiate: Xn0:=(cS c0):fofType
% 164.71/164.89 Found x5 as proof of (cODD Xn0)
% 164.71/164.89 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 164.71/164.89 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 164.71/164.89 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 164.71/164.89 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 164.71/164.89 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of (cNUMBER Xn0)
% 164.71/164.89 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of (cNUMBER Xn0)
% 164.71/164.89 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 164.71/164.89 Instantiate: Xn0:=Xn00:fofType
% 164.71/164.89 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 164.71/164.89 Found x30:(cNUMBER Xn0)
% 164.71/164.89 Instantiate: Xn0:=Xn:fofType
% 164.71/164.89 Found x30 as proof of (cNUMBER Xn)
% 164.71/164.89 Found x12:(cEVEN c0)
% 164.71/164.89 Found x12 as proof of (cEVEN c0)
% 164.71/164.89 Found x50:(cNUMBER Xn00)
% 164.71/164.89 Instantiate: Xn00:=Xn:fofType
% 164.71/164.89 Found x50 as proof of (cNUMBER Xn)
% 164.71/164.89 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 164.71/164.89 Instantiate: Xn00:=Xn0:fofType
% 164.71/164.89 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 164.71/164.89 Found x90:=(x9 x80):(cNUMBER Xn0)
% 164.71/164.89 Found (x9 x80) as proof of (cNUMBER Xn0)
% 164.71/164.89 Found (x9 x80) as proof of (cNUMBER Xn0)
% 164.71/164.89 Found x90:=(x9 x81):(cNUMBER Xn0)
% 164.71/164.89 Instantiate: Xn0:=Xn:fofType
% 164.71/164.89 Found (x9 x81) as proof of (cNUMBER Xn)
% 164.71/164.89 Found (x9 x81) as proof of (cNUMBER Xn)
% 164.71/164.89 Found x90:=(x9 x80):(cNUMBER Xn0)
% 164.71/164.89 Found (x9 x80) as proof of (cNUMBER Xn)
% 164.71/164.89 Found (x9 x80) as proof of (cNUMBER Xn)
% 164.71/164.89 Found (x9 x80) as proof of (cNUMBER Xn)
% 164.71/164.89 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 164.71/164.89 Instantiate: Xn0:=Xn00:fofType
% 164.71/164.89 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 164.71/164.89 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 164.71/164.89 Instantiate: Xn00:=Xn0:fofType
% 164.71/164.89 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 164.71/164.89 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 164.71/164.89 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 164.71/164.89 Found (x5 x41) as proof of (cNUMBER Xn)
% 164.71/164.89 Found (x5 x41) as proof of (cNUMBER Xn)
% 164.71/164.89 Found (x5 x41) as proof of (cNUMBER Xn)
% 164.71/164.89 Found x5:(cODD (cS c0))
% 164.71/164.89 Instantiate: Xn0:=(cS c0):fofType
% 164.71/164.89 Found x5 as proof of (cODD Xn0)
% 164.71/164.89 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 164.71/164.89 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 164.71/164.89 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 164.71/164.89 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 164.71/164.89 Found (x9 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of (cNUMBER Xn0)
% 164.71/164.89 Found (x9 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of (cNUMBER Xn0)
% 164.71/164.89 Found x12:(cEVEN c0)
% 164.71/164.89 Found x12 as proof of (cEVEN c0)
% 164.71/164.89 Found x50:=(x5 x40):(cNUMBER Xn0)
% 164.71/164.89 Instantiate: Xn0:=Xn:fofType
% 164.71/164.89 Found (x5 x40) as proof of (cNUMBER Xn)
% 164.71/164.89 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 164.71/164.89 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 164.71/164.89 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 164.71/164.89 Found (and_rect30 (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 164.71/164.89 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 167.02/167.24 Found (((fun (P:Type) (x6:(((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->P)))=> (((((and_rect ((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))) P) x6) x11)) (cNUMBER Xn)) (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 167.02/167.24 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 167.02/167.24 Instantiate: Xn00:=Xn:fofType
% 167.02/167.24 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 167.02/167.24 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 167.02/167.24 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 167.02/167.24 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 167.02/167.24 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 167.02/167.24 Instantiate: Xn0:=Xn:fofType
% 167.02/167.24 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 167.02/167.24 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 167.02/167.24 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->((or (cEVEN Xn00)) (cODD Xn00)))
% 167.02/167.24 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->((or (cEVEN Xn00)) (cODD Xn00))))
% 167.02/167.24 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 167.02/167.24 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 167.02/167.24 Found (x5 x41) as proof of (cNUMBER Xn)
% 167.02/167.24 Found (x5 x41) as proof of (cNUMBER Xn)
% 167.02/167.24 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 167.02/167.24 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 167.02/167.24 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 167.02/167.24 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 167.02/167.24 Found (x5 x41) as proof of (cNUMBER Xn)
% 167.02/167.24 Found (x5 x41) as proof of (cNUMBER Xn)
% 167.02/167.24 Found (x5 x41) as proof of (cNUMBER Xn)
% 167.02/167.24 Found x30:=(x3 x20):(cNUMBER Xn0)
% 167.02/167.24 Instantiate: Xn0:=Xn:fofType
% 167.02/167.24 Found (x3 x20) as proof of (cNUMBER Xn)
% 167.02/167.24 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 167.02/167.24 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 167.02/167.24 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 167.02/167.24 Found (and_rect30 (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 167.02/167.25 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 167.02/167.25 Found (((fun (P:Type) (x6:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 167.02/167.25 Found (((fun (P:Type) (x6:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 167.02/167.25 Found x50:=(x5 x40):(cNUMBER Xn00)
% 167.02/167.25 Instantiate: Xn00:=Xn:fofType
% 167.02/167.25 Found (x5 x40) as proof of (cNUMBER Xn)
% 167.02/167.25 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 167.02/167.25 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 167.02/167.25 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 167.02/167.25 Found (and_rect30 (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 167.02/167.25 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 167.02/167.25 Found (((fun (P:Type) (x6:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 167.02/167.25 Found (((fun (P:Type) (x6:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 169.21/169.44 Found x70:(cNUMBER Xn00)
% 169.21/169.44 Found x70 as proof of (cNUMBER Xn00)
% 169.21/169.44 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 169.21/169.44 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 169.21/169.44 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 169.21/169.44 Found x50:(cNUMBER Xn0)
% 169.21/169.44 Found x50 as proof of (cNUMBER Xn0)
% 169.21/169.44 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 169.21/169.44 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 169.21/169.44 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 169.21/169.44 Found x50:(cNUMBER Xn00)
% 169.21/169.44 Instantiate: Xn00:=Xn:fofType
% 169.21/169.44 Found (fun (x9:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 169.21/169.44 Found (fun (x9:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 169.21/169.44 Found x30:(cNUMBER Xn0)
% 169.21/169.44 Instantiate: Xn0:=Xn:fofType
% 169.21/169.44 Found (fun (x9:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 169.21/169.44 Found (fun (x9:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 169.21/169.44 Found x9:(cEVEN c0)
% 169.21/169.44 Found x9 as proof of (cEVEN c0)
% 169.21/169.44 Found x22:((or (cEVEN Xn0)) (cODD Xn0))
% 169.21/169.44 Found x22 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 169.21/169.44 Found (x3 x22) as proof of (cNUMBER Xn)
% 169.21/169.44 Found (x3 x22) as proof of (cNUMBER Xn)
% 169.21/169.44 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of (cNUMBER Xn)
% 169.21/169.44 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 169.21/169.44 Found x11:(cEVEN c0)
% 169.21/169.44 Instantiate: Xn0:=c0:fofType
% 169.21/169.44 Found (fun (x11:(cEVEN c0))=> x11) as proof of (cEVEN Xn0)
% 169.21/169.44 Found (fun (x9:cIND) (x11:(cEVEN c0))=> x11) as proof of ((cEVEN c0)->(cEVEN Xn0))
% 169.21/169.44 Found (fun (x9:cIND) (x11:(cEVEN c0))=> x11) as proof of (cIND->((cEVEN c0)->(cEVEN Xn0)))
% 169.21/169.44 Found (and_rect50 (fun (x9:cIND) (x11:(cEVEN c0))=> x11)) as proof of (cEVEN Xn0)
% 169.21/169.44 Found ((and_rect5 (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11)) as proof of (cEVEN Xn0)
% 169.21/169.44 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11)) as proof of (cEVEN Xn0)
% 169.21/169.44 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11)) as proof of (cEVEN Xn0)
% 169.21/169.44 Found (or_introl00 (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 169.21/169.44 Found ((or_introl0 (cODD Xn0)) (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 169.21/169.44 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 169.21/169.44 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 169.21/169.44 Found x80:((or (cEVEN Xn0)) (cODD Xn0))
% 169.21/169.44 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 169.21/169.44 Found (x9 x80) as proof of (cNUMBER Xn)
% 169.21/169.44 Found (x9 x80) as proof of (cNUMBER Xn)
% 169.21/169.44 Found (x9 x80) as proof of (cNUMBER Xn)
% 169.21/169.44 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 169.21/169.44 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 169.21/169.44 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 169.21/169.44 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 169.21/169.44 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 169.21/169.44 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 169.21/169.44 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 170.21/170.41 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 170.21/170.41 Found x30:=(x3 x20):(cNUMBER Xn0)
% 170.21/170.41 Instantiate: Xn0:=Xn:fofType
% 170.21/170.41 Found (x3 x20) as proof of (cNUMBER Xn)
% 170.21/170.41 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 170.21/170.41 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 170.21/170.41 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 170.21/170.41 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 170.21/170.41 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 170.21/170.41 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 170.21/170.41 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 170.21/170.41 Found x22:((or (cEVEN Xn0)) (cODD Xn0))
% 170.21/170.41 Found x22 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 170.21/170.41 Found (x3 x22) as proof of (cNUMBER Xn)
% 170.21/170.41 Found (x3 x22) as proof of (cNUMBER Xn)
% 170.21/170.41 Found (x3 x22) as proof of (cNUMBER Xn)
% 170.21/170.41 Found x31:(cNUMBER Xn0)
% 170.21/170.41 Instantiate: Xn0:=Xn:fofType
% 170.21/170.41 Found (fun (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 170.21/170.41 Found (fun (x5:(cODD Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 170.21/170.41 Found (fun (x5:(cODD Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((cODD Xn0)->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 170.21/170.41 Found x31:(cNUMBER Xn0)
% 170.21/170.41 Instantiate: Xn0:=Xn:fofType
% 170.21/170.41 Found (fun (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 170.21/170.41 Found (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 170.21/170.41 Found (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((cEVEN Xn0)->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 170.21/170.41 Found ((or_ind00 (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 170.21/170.41 Found (((or_ind0 ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 170.21/170.41 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) x20)) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 172.13/172.40 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x31))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 172.13/172.40 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x31))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 172.13/172.40 Found x22:((or (cEVEN Xn0)) (cODD Xn0))
% 172.13/172.40 Found x22 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 172.13/172.40 Found (x3 x22) as proof of (cNUMBER Xn)
% 172.13/172.40 Found (x3 x22) as proof of (cNUMBER Xn)
% 172.13/172.40 Found (x3 x22) as proof of (cNUMBER Xn)
% 172.13/172.40 Found x70:=(x7 x60):(cNUMBER Xn0)
% 172.13/172.40 Found (x7 x60) as proof of (cNUMBER Xn0)
% 172.13/172.40 Found (x7 x60) as proof of (cNUMBER Xn0)
% 172.13/172.40 Found x70:=(x7 x61):(cNUMBER Xn0)
% 172.13/172.40 Instantiate: Xn0:=Xn:fofType
% 172.13/172.40 Found (x7 x61) as proof of (cNUMBER Xn)
% 172.13/172.40 Found (x7 x61) as proof of (cNUMBER Xn)
% 172.13/172.40 Found x70:=(x7 x60):(cNUMBER Xn0)
% 172.13/172.40 Found (x7 x60) as proof of (cNUMBER Xn)
% 172.13/172.40 Found (x7 x60) as proof of (cNUMBER Xn)
% 172.13/172.40 Found (x7 x60) as proof of (cNUMBER Xn)
% 172.13/172.40 Found x30:=(x3 x20):(cNUMBER Xn0)
% 172.13/172.40 Instantiate: Xn0:=Xn:fofType
% 172.13/172.40 Found (x3 x20) as proof of (cNUMBER Xn)
% 172.13/172.40 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 172.13/172.40 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 172.13/172.40 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 172.13/172.40 Found (and_rect30 (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 172.13/172.40 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 172.13/172.40 Found (((fun (P:Type) (x6:(((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->P)))=> (((((and_rect ((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))) P) x6) x11)) (cNUMBER Xn)) (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 172.13/172.40 Found x30:(cNUMBER Xn0)
% 172.13/172.40 Instantiate: Xn0:=Xn:fofType
% 172.13/172.40 Found x30 as proof of (cNUMBER Xn)
% 172.13/172.40 Found x90:(cNUMBER Xn00)
% 172.13/172.40 Instantiate: Xn00:=Xn:fofType
% 172.13/172.40 Found x90 as proof of (cNUMBER Xn)
% 172.13/172.40 Found x90:=(x9 c0):((cEVEN c0)->(cEVEN (cS (cS c0))))
% 172.13/172.40 Found (x9 c0) as proof of ((cEVEN c0)->(cEVEN Xn0))
% 172.13/172.40 Found (x9 c0) as proof of ((cEVEN c0)->(cEVEN Xn0))
% 172.13/172.40 Found (fun (x11:cIND)=> (x9 c0)) as proof of ((cEVEN c0)->(cEVEN Xn0))
% 172.13/172.40 Found (fun (x11:cIND)=> (x9 c0)) as proof of (cIND->((cEVEN c0)->(cEVEN Xn0)))
% 172.13/172.40 Found (and_rect50 (fun (x11:cIND)=> (x9 c0))) as proof of (cEVEN Xn0)
% 172.13/172.40 Found ((and_rect5 (cEVEN Xn0)) (fun (x11:cIND)=> (x9 c0))) as proof of (cEVEN Xn0)
% 172.13/172.40 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND)=> (x9 c0))) as proof of (cEVEN Xn0)
% 172.13/172.40 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND)=> (x9 c0))) as proof of (cEVEN Xn0)
% 174.03/174.26 Found (or_introl00 (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND)=> (x9 c0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 174.03/174.26 Found ((or_introl0 (cODD Xn0)) (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND)=> (x9 c0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 174.03/174.26 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND)=> (x9 c0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 174.03/174.26 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND)=> (x9 c0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 174.03/174.26 Found or_introl000:=(or_introl00 (cODD Xn0)):((or (cEVEN Xn0)) (cODD Xn0))
% 174.03/174.26 Found (or_introl00 (cODD Xn0)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 174.03/174.26 Found ((fun (B:Prop)=> ((or_introl0 B) x12)) (cODD Xn0)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 174.03/174.26 Found ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x12)) (cODD Xn0)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 174.03/174.26 Found ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x12)) (cODD Xn0)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 174.03/174.26 Found (x7 ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x12)) (cODD Xn0))) as proof of (cNUMBER c0)
% 174.03/174.26 Found (x7 ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x12)) (cODD Xn0))) as proof of (cNUMBER c0)
% 174.03/174.26 Found (x7 ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x12)) (cODD Xn0))) as proof of (cNUMBER c0)
% 174.03/174.26 Found x60:=(x6 x70):((or (cEVEN Xn00)) (cODD Xn00))
% 174.03/174.26 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 174.03/174.26 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 174.03/174.26 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 174.03/174.26 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 174.03/174.26 Instantiate: Xn00:=Xn0:fofType
% 174.03/174.26 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 174.03/174.26 Found x50:(cNUMBER Xn00)
% 174.03/174.26 Instantiate: Xn00:=Xn:fofType
% 174.03/174.26 Found x50 as proof of (cNUMBER Xn)
% 174.03/174.26 Found x30:(cNUMBER Xn0)
% 174.03/174.26 Instantiate: Xn0:=Xn:fofType
% 174.03/174.26 Found x30 as proof of (cNUMBER Xn)
% 174.03/174.26 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 174.03/174.26 Instantiate: Xn0:=Xn00:fofType
% 174.03/174.26 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 174.03/174.26 Found x30:=(x3 x21):(cNUMBER Xn0)
% 174.03/174.26 Found (x3 x21) as proof of (cNUMBER Xn0)
% 174.03/174.26 Found (x3 x21) as proof of (cNUMBER Xn0)
% 174.03/174.26 Found x30:=(x3 x22):(cNUMBER Xn0)
% 174.03/174.26 Instantiate: Xn0:=Xn:fofType
% 174.03/174.26 Found (x3 x22) as proof of (cNUMBER Xn)
% 174.03/174.26 Found (x3 x22) as proof of (cNUMBER Xn)
% 174.03/174.26 Found x30:=(x3 x22):(cNUMBER Xn0)
% 174.03/174.26 Found (x3 x22) as proof of (cNUMBER Xn)
% 174.03/174.26 Found (x3 x22) as proof of (cNUMBER Xn)
% 174.03/174.26 Found (x3 x22) as proof of (cNUMBER Xn)
% 174.03/174.26 Found x30:=(x3 x21):(cNUMBER Xn0)
% 174.03/174.26 Found (x3 x21) as proof of (cNUMBER Xn0)
% 174.03/174.26 Found (x3 x21) as proof of (cNUMBER Xn0)
% 174.03/174.26 Found x30:=(x3 x22):(cNUMBER Xn0)
% 174.03/174.26 Instantiate: Xn0:=Xn:fofType
% 174.03/174.26 Found (x3 x22) as proof of (cNUMBER Xn)
% 174.03/174.26 Found (x3 x22) as proof of (cNUMBER Xn)
% 174.03/174.26 Found x30:=(x3 x22):(cNUMBER Xn0)
% 174.03/174.26 Found (x3 x22) as proof of (cNUMBER Xn)
% 174.03/174.26 Found (x3 x22) as proof of (cNUMBER Xn)
% 174.03/174.26 Found (x3 x22) as proof of (cNUMBER Xn)
% 174.03/174.26 Found x30:=(x3 x21):(cNUMBER Xn0)
% 174.03/174.26 Found (x3 x21) as proof of (cNUMBER Xn0)
% 174.03/174.26 Found (x3 x21) as proof of (cNUMBER Xn0)
% 174.03/174.26 Found x30:=(x3 x22):(cNUMBER Xn0)
% 174.03/174.26 Instantiate: Xn0:=Xn:fofType
% 174.03/174.26 Found (x3 x22) as proof of (cNUMBER Xn)
% 174.03/174.26 Found (x3 x22) as proof of (cNUMBER Xn)
% 174.03/174.26 Found x30:=(x3 x22):(cNUMBER Xn0)
% 174.03/174.26 Found (x3 x22) as proof of (cNUMBER Xn)
% 174.03/174.26 Found (x3 x22) as proof of (cNUMBER Xn)
% 174.03/174.26 Found (x3 x22) as proof of (cNUMBER Xn)
% 174.03/174.26 Found x70:=(x7 x60):(cNUMBER Xn0)
% 174.03/174.26 Found (x7 x60) as proof of (cNUMBER Xn)
% 174.03/174.26 Found (x7 x60) as proof of (cNUMBER Xn)
% 174.03/174.26 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 174.03/174.26 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 174.03/174.26 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 175.09/175.37 Found x70:=(x7 x60):(cNUMBER Xn0)
% 175.09/175.37 Found (x7 x60) as proof of (cNUMBER Xn)
% 175.09/175.37 Found (x7 x60) as proof of (cNUMBER Xn)
% 175.09/175.37 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 175.09/175.37 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 175.09/175.37 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 175.09/175.37 Instantiate: Xn00:=Xn:fofType
% 175.09/175.37 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 175.09/175.37 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 175.09/175.37 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 175.09/175.37 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 175.09/175.37 Found x30:(cNUMBER Xn0)
% 175.09/175.37 Found x30 as proof of (cNUMBER Xn0)
% 175.09/175.37 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 175.09/175.37 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 175.09/175.37 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 175.09/175.37 Found x70:(cNUMBER Xn00)
% 175.09/175.37 Found x70 as proof of (cNUMBER Xn00)
% 175.09/175.37 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 175.09/175.37 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 175.09/175.37 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 175.09/175.37 Found x50:=(x5 x40):(cNUMBER Xn0)
% 175.09/175.37 Instantiate: Xn0:=Xn:fofType
% 175.09/175.37 Found (x5 x40) as proof of (cNUMBER Xn)
% 175.09/175.37 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 175.09/175.37 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 175.09/175.37 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 175.09/175.37 Found (and_rect30 (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 175.09/175.37 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 175.09/175.37 Found (((fun (P:Type) (x6:(((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->P)))=> (((((and_rect ((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))) P) x6) x11)) (cNUMBER Xn)) (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40))) as proof of (cNUMBER Xn)
% 175.09/175.37 Found x12:(cEVEN c0)
% 175.09/175.37 Found x12 as proof of (cEVEN c0)
% 175.09/175.37 Found x30:=(x3 x20):(cNUMBER Xn0)
% 175.09/175.37 Instantiate: Xn0:=Xn:fofType
% 175.09/175.37 Found (x3 x20) as proof of (cNUMBER Xn)
% 175.09/175.37 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 175.09/175.37 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 175.09/175.37 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 175.70/175.97 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 175.70/175.97 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 175.70/175.97 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 175.70/175.97 Found (fun (x7:(cODD (cS c0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 175.70/175.97 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 175.70/175.97 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 175.70/175.97 Found x90:=(x9 x81):(cNUMBER Xn0)
% 175.70/175.97 Instantiate: Xn0:=Xn:fofType
% 175.70/175.97 Found (x9 x81) as proof of (cNUMBER Xn)
% 175.70/175.97 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x81)) as proof of (cNUMBER Xn)
% 175.70/175.97 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x81)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 175.70/175.97 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 175.70/175.97 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 175.70/175.97 Found (x7 x60) as proof of (cNUMBER Xn)
% 175.70/175.97 Found (x7 x60) as proof of (cNUMBER Xn)
% 175.70/175.97 Found (x7 x60) as proof of (cNUMBER Xn)
% 175.70/175.97 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 175.70/175.97 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 175.70/175.97 Found (x5 x41) as proof of (cNUMBER Xn)
% 175.70/175.97 Found (x5 x41) as proof of (cNUMBER Xn)
% 175.70/175.97 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 175.70/175.97 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 175.70/175.97 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 175.70/175.97 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 175.70/175.97 Found (x5 x41) as proof of (cNUMBER Xn)
% 175.70/175.97 Found (x5 x41) as proof of (cNUMBER Xn)
% 175.70/175.97 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (cNUMBER Xn)
% 175.70/175.97 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 175.70/175.97 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x41)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 176.70/176.96 Found x70:(cNUMBER Xn00)
% 176.70/176.96 Found x70 as proof of (cNUMBER Xn00)
% 176.70/176.96 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 176.70/176.96 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 176.70/176.96 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 176.70/176.96 Found x12:(cEVEN c0)
% 176.70/176.96 Found x12 as proof of (cEVEN c0)
% 176.70/176.96 Found x30:=(x3 x20):(cNUMBER Xn0)
% 176.70/176.96 Found (x3 x20) as proof of (cNUMBER Xn0)
% 176.70/176.96 Found (x3 x20) as proof of (cNUMBER Xn0)
% 176.70/176.96 Found x41:((or (cEVEN Xn0)) (cODD Xn0))
% 176.70/176.96 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 176.70/176.96 Found (x5 x41) as proof of (cNUMBER Xn)
% 176.70/176.96 Found (x5 x41) as proof of (cNUMBER Xn)
% 176.70/176.96 Found (x5 x41) as proof of (cNUMBER Xn)
% 176.70/176.96 Found x30:=(x3 x20):(cNUMBER Xn0)
% 176.70/176.96 Instantiate: Xn0:=Xn:fofType
% 176.70/176.96 Found (x3 x20) as proof of (cNUMBER Xn)
% 176.70/176.96 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 176.70/176.96 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 176.70/176.96 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 176.70/176.96 Found (and_rect30 (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 176.70/176.96 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 176.70/176.96 Found (((fun (P:Type) (x6:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 176.70/176.96 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (((fun (P:Type) (x6:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 176.70/176.96 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (((fun (P:Type) (x6:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)))) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 178.71/178.90 Found x50:=(x5 x40):(cNUMBER Xn00)
% 178.71/178.90 Instantiate: Xn00:=Xn:fofType
% 178.71/178.90 Found (x5 x40) as proof of (cNUMBER Xn)
% 178.71/178.90 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 178.71/178.90 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 178.71/178.90 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 178.71/178.90 Found (and_rect30 (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 178.71/178.90 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 178.71/178.90 Found (((fun (P:Type) (x6:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 178.71/178.90 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (((fun (P:Type) (x6:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)))) as proof of (cNUMBER Xn)
% 178.71/178.90 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (((fun (P:Type) (x6:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x5 x40)))) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 178.71/178.90 Found x12:(cEVEN c0)
% 178.71/178.90 Found x12 as proof of (cEVEN c0)
% 178.71/178.90 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 178.71/178.90 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 178.71/178.90 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 178.71/178.90 Found x31:(cNUMBER Xn0)
% 178.71/178.90 Instantiate: Xn0:=Xn:fofType
% 180.82/181.01 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x31) as proof of (cNUMBER Xn)
% 180.82/181.01 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x31) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 180.82/181.01 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x31) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 180.82/181.01 Found x30:(cNUMBER Xn0)
% 180.82/181.01 Instantiate: Xn0:=Xn:fofType
% 180.82/181.01 Found x30 as proof of (cNUMBER Xn)
% 180.82/181.01 Found x70:(cNUMBER Xn00)
% 180.82/181.01 Instantiate: Xn00:=Xn:fofType
% 180.82/181.01 Found x70 as proof of (cNUMBER Xn)
% 180.82/181.01 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 180.82/181.01 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 180.82/181.01 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 180.82/181.01 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 180.82/181.01 Found x12:(cEVEN c0)
% 180.82/181.01 Found x12 as proof of (cEVEN c0)
% 180.82/181.01 Found x30:=(x3 x20):(cNUMBER Xn0)
% 180.82/181.01 Instantiate: Xn0:=Xn:fofType
% 180.82/181.01 Found (x3 x20) as proof of (cNUMBER Xn)
% 180.82/181.01 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 180.82/181.01 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 180.82/181.01 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 180.82/181.01 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 180.82/181.01 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 180.82/181.01 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 180.82/181.01 Found (fun (x7:(cODD (cS c0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 180.82/181.01 Found (fun (x7:(cODD (cS c0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 180.82/181.01 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 180.82/181.01 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 180.82/181.01 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 180.82/181.01 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 180.82/181.01 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 180.82/181.01 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 180.82/181.01 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 180.82/181.01 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 180.82/181.01 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 180.82/181.01 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->((or (cEVEN Xn00)) (cODD Xn00)))
% 181.52/181.77 Found x80:((or (cEVEN Xn0)) (cODD Xn0))
% 181.52/181.77 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 181.52/181.77 Found (x9 x80) as proof of (cNUMBER Xn)
% 181.52/181.77 Found (x9 x80) as proof of (cNUMBER Xn)
% 181.52/181.77 Found (x9 x80) as proof of (cNUMBER Xn)
% 181.52/181.77 Found x50:(cNUMBER Xn00)
% 181.52/181.77 Instantiate: Xn00:=Xn:fofType
% 181.52/181.77 Found (fun (x9:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 181.52/181.77 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 181.52/181.77 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x50) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 181.52/181.77 Found x30:(cNUMBER Xn0)
% 181.52/181.77 Instantiate: Xn0:=Xn:fofType
% 181.52/181.77 Found (fun (x9:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 181.52/181.77 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 181.52/181.77 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x30) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 181.52/181.77 Found x22:((or (cEVEN Xn0)) (cODD Xn0))
% 181.52/181.77 Found x22 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 181.52/181.77 Found (x3 x22) as proof of (cNUMBER Xn)
% 181.52/181.77 Found (x3 x22) as proof of (cNUMBER Xn)
% 181.52/181.77 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of (cNUMBER Xn)
% 181.52/181.77 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 181.52/181.77 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 181.52/181.77 Found x30:=(x3 x20):(cNUMBER Xn0)
% 181.52/181.77 Instantiate: Xn0:=Xn:fofType
% 181.52/181.77 Found (x3 x20) as proof of (cNUMBER Xn)
% 181.52/181.77 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 181.52/181.77 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 181.52/181.77 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 181.52/181.77 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 181.52/181.77 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 181.52/181.77 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 181.52/181.77 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 183.93/184.13 Found x22:((or (cEVEN Xn0)) (cODD Xn0))
% 183.93/184.13 Found x22 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 183.93/184.13 Found (x3 x22) as proof of (cNUMBER Xn)
% 183.93/184.13 Found (x3 x22) as proof of (cNUMBER Xn)
% 183.93/184.13 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of (cNUMBER Xn)
% 183.93/184.13 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 183.93/184.13 Found x22:((or (cEVEN Xn0)) (cODD Xn0))
% 183.93/184.13 Found x22 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 183.93/184.13 Found (x3 x22) as proof of (cNUMBER Xn)
% 183.93/184.13 Found (x3 x22) as proof of (cNUMBER Xn)
% 183.93/184.13 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of (cNUMBER Xn)
% 183.93/184.13 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x22)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 183.93/184.13 Found x50:(cNUMBER Xn00)
% 183.93/184.13 Found x50 as proof of (cNUMBER Xn00)
% 183.93/184.13 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 183.93/184.13 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 183.93/184.13 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 183.93/184.13 Found x30:(cNUMBER Xn0)
% 183.93/184.13 Found x30 as proof of (cNUMBER Xn0)
% 183.93/184.13 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 183.93/184.13 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 183.93/184.13 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 183.93/184.13 Found x22:((or (cEVEN Xn0)) (cODD Xn0))
% 183.93/184.13 Found x22 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 183.93/184.13 Found (x3 x22) as proof of (cNUMBER Xn)
% 183.93/184.13 Found (x3 x22) as proof of (cNUMBER Xn)
% 183.93/184.13 Found (x3 x22) as proof of (cNUMBER Xn)
% 183.93/184.13 Found x22:((or (cEVEN Xn0)) (cODD Xn0))
% 183.93/184.13 Found x22 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 183.93/184.13 Found (x3 x22) as proof of (cNUMBER Xn)
% 183.93/184.13 Found (x3 x22) as proof of (cNUMBER Xn)
% 183.93/184.13 Found (x3 x22) as proof of (cNUMBER Xn)
% 183.93/184.13 Found x30:=(x3 x20):(cNUMBER Xn0)
% 183.93/184.13 Instantiate: Xn0:=Xn:fofType
% 183.93/184.13 Found (x3 x20) as proof of (cNUMBER Xn)
% 183.93/184.13 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 183.93/184.13 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 183.93/184.13 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 183.93/184.13 Found (and_rect30 (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 183.93/184.13 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 183.93/184.13 Found (((fun (P:Type) (x6:(((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->P)))=> (((((and_rect ((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))) P) x6) x11)) (cNUMBER Xn)) (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 183.93/184.13 Found x22:((or (cEVEN Xn0)) (cODD Xn0))
% 183.93/184.13 Found x22 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 183.93/184.13 Found (x3 x22) as proof of (cNUMBER Xn)
% 183.93/184.13 Found (x3 x22) as proof of (cNUMBER Xn)
% 183.93/184.13 Found (x3 x22) as proof of (cNUMBER Xn)
% 183.93/184.13 Found x30:(cNUMBER Xn0)
% 183.93/184.13 Instantiate: Xn0:=Xn:fofType
% 183.93/184.13 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 183.93/184.13 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 183.93/184.13 Found x31:(cNUMBER Xn0)
% 183.93/184.13 Instantiate: Xn0:=Xn:fofType
% 183.93/184.13 Found (fun (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 184.21/184.39 Found (fun (x5:(cODD Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 184.21/184.39 Found (fun (x5:(cODD Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((cODD Xn0)->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 184.21/184.39 Found x31:(cNUMBER Xn0)
% 184.21/184.39 Instantiate: Xn0:=Xn:fofType
% 184.21/184.39 Found (fun (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 184.21/184.39 Found (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 184.21/184.39 Found (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((cEVEN Xn0)->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 184.21/184.39 Found ((or_ind00 (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 184.21/184.39 Found (((or_ind0 ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 184.21/184.39 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) x20)) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 184.21/184.39 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x31))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 184.21/184.39 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x31))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 184.21/184.39 Found x31:(cNUMBER Xn0)
% 184.21/184.39 Instantiate: Xn0:=Xn:fofType
% 184.21/184.39 Found (fun (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 184.21/184.39 Found (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 184.21/184.39 Found (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((cEVEN Xn0)->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 184.21/184.39 Found x31:(cNUMBER Xn0)
% 184.21/184.39 Instantiate: Xn0:=Xn:fofType
% 184.21/184.39 Found (fun (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of (cNUMBER Xn)
% 184.21/184.39 Found (fun (x5:(cODD Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 184.21/184.39 Found (fun (x5:(cODD Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31) as proof of ((cODD Xn0)->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 185.39/185.58 Found ((or_ind00 (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 185.39/185.58 Found (((or_ind0 ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 185.39/185.58 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) x20)) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 185.39/185.58 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x31))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 185.39/185.58 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))))=> ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x31))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 185.39/185.58 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))))=> ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x31))) ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31)) (fun (x5:(cODD Xn0)) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x31))) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 185.39/185.58 Found x70:=(x7 x60):(cNUMBER Xn0)
% 185.39/185.58 Found (x7 x60) as proof of (cNUMBER Xn0)
% 185.39/185.58 Found (x7 x60) as proof of (cNUMBER Xn0)
% 185.39/185.58 Found x70:=(x7 x61):(cNUMBER Xn0)
% 185.39/185.58 Instantiate: Xn0:=Xn:fofType
% 185.39/185.58 Found (x7 x61) as proof of (cNUMBER Xn)
% 185.39/185.58 Found (x7 x61) as proof of (cNUMBER Xn)
% 185.39/185.58 Found x70:=(x7 x60):(cNUMBER Xn0)
% 185.39/185.58 Found (x7 x60) as proof of (cNUMBER Xn)
% 185.39/185.58 Found (x7 x60) as proof of (cNUMBER Xn)
% 185.39/185.58 Found (x7 x60) as proof of (cNUMBER Xn)
% 185.39/185.58 Found x30:=(x3 x22):(cNUMBER Xn0)
% 185.39/185.58 Found (x3 x22) as proof of (cNUMBER Xn)
% 185.39/185.58 Found (x3 x22) as proof of (cNUMBER Xn)
% 185.39/185.58 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x22)) as proof of (cNUMBER Xn)
% 185.39/185.58 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x22)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 185.39/185.58 Found x30:=(x3 x20):(cNUMBER Xn0)
% 185.39/185.58 Instantiate: Xn0:=Xn:fofType
% 185.39/185.58 Found (x3 x20) as proof of (cNUMBER Xn)
% 185.39/185.58 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 185.39/185.58 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 186.03/186.26 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 186.03/186.26 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 186.03/186.26 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 186.03/186.26 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 186.03/186.26 Found (fun (x7:(cODD (cS c0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 186.03/186.26 Found (fun (x7:(cODD (cS c0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 186.03/186.26 Found x5:(cODD (cS c0))
% 186.03/186.26 Instantiate: Xn0:=(cS c0):fofType
% 186.03/186.26 Found x5 as proof of (cODD Xn0)
% 186.03/186.26 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 186.03/186.26 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 186.03/186.26 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 186.03/186.26 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 186.03/186.26 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of (cNUMBER Xn0)
% 186.03/186.26 Found (x7 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of (cNUMBER Xn0)
% 186.03/186.26 Found x70:(cNUMBER Xn00)
% 186.03/186.26 Found x70 as proof of (cNUMBER Xn00)
% 186.03/186.26 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 186.03/186.26 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 186.03/186.26 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 186.03/186.26 Found x5:(cODD (cS c0))
% 186.03/186.26 Instantiate: Xn0:=(cS c0):fofType
% 186.03/186.26 Found x5 as proof of (cODD Xn0)
% 186.03/186.26 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 186.03/186.26 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 186.03/186.26 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 186.03/186.26 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 186.03/186.26 Found (x9 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of (cNUMBER Xn0)
% 186.03/186.26 Found (x9 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of (cNUMBER Xn0)
% 186.03/186.26 Found x50:(cNUMBER Xn00)
% 186.03/186.26 Instantiate: Xn00:=Xn:fofType
% 186.03/186.26 Found x50 as proof of (cNUMBER Xn)
% 186.03/186.26 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 186.03/186.26 Instantiate: Xn00:=Xn0:fofType
% 186.03/186.26 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 186.03/186.26 Found x30:=(x3 x20):(cNUMBER Xn0)
% 186.03/186.26 Instantiate: Xn0:=Xn:fofType
% 186.03/186.26 Found (x3 x20) as proof of (cNUMBER Xn)
% 186.03/186.26 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 186.03/186.26 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 186.03/186.26 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 192.63/192.86 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 192.63/192.86 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 192.63/192.86 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 192.63/192.86 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 192.63/192.86 Found x31:(cNUMBER Xn0)
% 192.63/192.86 Instantiate: Xn0:=Xn:fofType
% 192.63/192.86 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x31) as proof of (cNUMBER Xn)
% 192.63/192.86 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x31) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 192.63/192.86 Found x30:(cNUMBER Xn0)
% 192.63/192.86 Instantiate: Xn0:=Xn:fofType
% 192.63/192.86 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 192.63/192.86 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 192.63/192.86 Found x30:(cNUMBER Xn0)
% 192.63/192.86 Instantiate: Xn0:=Xn:fofType
% 192.63/192.86 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 192.63/192.86 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 192.63/192.86 Found x12:(cEVEN c0)
% 192.63/192.86 Found x12 as proof of (cEVEN c0)
% 192.63/192.86 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 192.63/192.86 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 192.63/192.86 Found (x7 x60) as proof of (cNUMBER Xn)
% 192.63/192.86 Found (x7 x60) as proof of (cNUMBER Xn)
% 192.63/192.86 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 192.63/192.86 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 192.63/192.86 Found x70:(cNUMBER Xn0)
% 192.63/192.86 Instantiate: Xn0:=Xn:fofType
% 192.63/192.86 Found x70 as proof of (cNUMBER Xn)
% 192.63/192.86 Found x90:(cNUMBER Xn00)
% 192.63/192.86 Instantiate: Xn00:=Xn:fofType
% 192.63/192.86 Found x90 as proof of (cNUMBER Xn)
% 192.63/192.86 Found or_introl000:=(or_introl00 (cODD Xn0)):((or (cEVEN Xn0)) (cODD Xn0))
% 192.63/192.86 Found (or_introl00 (cODD Xn0)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 192.63/192.86 Found ((fun (B:Prop)=> ((or_introl0 B) x9)) (cODD Xn0)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 192.63/192.86 Found ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x9)) (cODD Xn0)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 192.63/192.86 Found ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x9)) (cODD Xn0)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 192.63/192.86 Found (x12 ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x9)) (cODD Xn0))) as proof of (cNUMBER c0)
% 192.63/192.86 Found (x12 ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x9)) (cODD Xn0))) as proof of (cNUMBER c0)
% 192.63/192.86 Found (x12 ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x9)) (cODD Xn0))) as proof of (cNUMBER c0)
% 192.63/192.86 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 192.63/192.86 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 192.63/192.86 Found (x7 x60) as proof of (cNUMBER Xn)
% 192.63/192.86 Found (x7 x60) as proof of (cNUMBER Xn)
% 192.63/192.86 Found (x7 x60) as proof of (cNUMBER Xn)
% 192.63/192.86 Found x30:=(x3 x20):(cNUMBER Xn0)
% 192.63/192.86 Instantiate: Xn0:=Xn:fofType
% 192.63/192.86 Found (x3 x20) as proof of (cNUMBER Xn)
% 192.63/192.86 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 192.63/192.86 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 192.63/192.87 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 192.63/192.87 Found (and_rect30 (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 192.63/192.87 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 192.63/192.87 Found (((fun (P:Type) (x6:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 192.63/192.87 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (((fun (P:Type) (x6:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)))) as proof of (cNUMBER Xn)
% 192.63/192.87 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (((fun (P:Type) (x6:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)))) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 192.63/192.87 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (((fun (P:Type) (x6:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x0)) (cNUMBER Xn)) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)))) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 194.52/194.71 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 194.52/194.71 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 194.52/194.71 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 194.52/194.71 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 194.52/194.71 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 194.52/194.71 Found x30:(cNUMBER Xn0)
% 194.52/194.71 Instantiate: Xn0:=Xn:fofType
% 194.52/194.71 Found (fun (x9:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 194.52/194.71 Found (fun (x9:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 194.52/194.71 Found x70:(cNUMBER Xn00)
% 194.52/194.71 Instantiate: Xn00:=Xn:fofType
% 194.52/194.71 Found (fun (x9:(cODD (cS c0)))=> x70) as proof of (cNUMBER Xn)
% 194.52/194.71 Found (fun (x9:(cODD (cS c0)))=> x70) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 194.52/194.71 Found x30:=(x3 x21):(cNUMBER Xn0)
% 194.52/194.71 Instantiate: Xn0:=Xn:fofType
% 194.52/194.71 Found (x3 x21) as proof of (cNUMBER Xn)
% 194.52/194.71 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 194.52/194.71 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 194.52/194.71 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 194.52/194.71 Found x30:(cNUMBER Xn0)
% 194.52/194.71 Instantiate: Xn0:=Xn:fofType
% 194.52/194.71 Found (fun (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 194.52/194.71 Found (fun (x9:(cODD Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 194.52/194.71 Found (fun (x9:(cODD Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of ((cODD Xn0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 194.52/194.71 Found x30:(cNUMBER Xn0)
% 194.52/194.71 Instantiate: Xn0:=Xn:fofType
% 194.52/194.71 Found (fun (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 194.52/194.71 Found (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 194.52/194.71 Found (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of ((cEVEN Xn0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 194.52/194.71 Found ((or_ind00 (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 194.52/194.71 Found (((or_ind0 ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 194.52/194.71 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) x20)) ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x30)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 194.52/194.71 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x2 x30))) ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x30)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 194.90/195.14 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x2 x30))) ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x30)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 194.90/195.14 Found x30:=(x3 x20):(cNUMBER Xn0)
% 194.90/195.14 Found (x3 x20) as proof of (cNUMBER Xn0)
% 194.90/195.14 Found (x3 x20) as proof of (cNUMBER Xn0)
% 194.90/195.14 Found x30:=(x3 x21):(cNUMBER Xn0)
% 194.90/195.14 Instantiate: Xn0:=Xn:fofType
% 194.90/195.14 Found (x3 x21) as proof of (cNUMBER Xn)
% 194.90/195.14 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 194.90/195.14 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 194.90/195.14 Found x11:(cEVEN c0)
% 194.90/195.14 Instantiate: Xn0:=c0:fofType
% 194.90/195.14 Found (fun (x11:(cEVEN c0))=> x11) as proof of (cEVEN Xn0)
% 194.90/195.14 Found (fun (x9:cIND) (x11:(cEVEN c0))=> x11) as proof of ((cEVEN c0)->(cEVEN Xn0))
% 194.90/195.14 Found (fun (x9:cIND) (x11:(cEVEN c0))=> x11) as proof of (cIND->((cEVEN c0)->(cEVEN Xn0)))
% 194.90/195.14 Found (and_rect50 (fun (x9:cIND) (x11:(cEVEN c0))=> x11)) as proof of (cEVEN Xn0)
% 194.90/195.14 Found ((and_rect5 (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11)) as proof of (cEVEN Xn0)
% 194.90/195.14 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11)) as proof of (cEVEN Xn0)
% 194.90/195.14 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11)) as proof of (cEVEN Xn0)
% 194.90/195.14 Found (or_introl00 (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 194.90/195.14 Found ((or_introl0 (cODD Xn0)) (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 194.90/195.14 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 194.90/195.14 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 194.90/195.14 Found x30:=(x3 x20):(cNUMBER Xn0)
% 194.90/195.14 Instantiate: Xn00:=Xn0:fofType
% 194.90/195.14 Found (x3 x20) as proof of (cNUMBER Xn00)
% 194.90/195.14 Found (x3 x20) as proof of (cNUMBER Xn00)
% 194.90/195.14 Found x30:(cNUMBER Xn0)
% 194.90/195.14 Instantiate: Xn0:=Xn:fofType
% 194.90/195.14 Found (fun (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 194.90/195.14 Found (fun (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 194.90/195.14 Found (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 194.90/195.14 Found (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((cEVEN Xn0)->(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))))
% 195.00/195.20 Found x30:(cNUMBER Xn0)
% 195.00/195.20 Instantiate: Xn0:=Xn:fofType
% 195.00/195.20 Found (fun (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 195.00/195.20 Found (fun (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 195.00/195.20 Found (fun (x4:(cODD Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 195.00/195.20 Found (fun (x4:(cODD Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30) as proof of ((cODD Xn0)->(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))))
% 195.00/195.20 Found ((or_ind00 (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) (fun (x4:(cODD Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 195.00/195.20 Found (((or_ind0 (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))) (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) (fun (x4:(cODD Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x6:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> x30)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 195.00/195.20 Found ((((fun (P:Prop) (x4:((cEVEN Xn0)->P)) (x5:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x4) x5) x20)) (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn)))) (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x4:(cODD Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 195.03/195.27 Found ((((fun (P:Prop) (x4:((cEVEN Xn0)->P)) (x5:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x4) x5) (x2 x31))) (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn)))) (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x4:(cODD Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 195.03/195.27 Found ((((fun (P:Prop) (x4:((cEVEN Xn0)->P)) (x5:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x4) x5) (x2 x31))) (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->(cNUMBER Xn)))) (fun (x4:(cEVEN Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) (fun (x4:(cODD Xn0)) (x5:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x6:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> x30)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 195.03/195.27 Found x30:=(x3 x21):(cNUMBER Xn0)
% 195.03/195.27 Instantiate: Xn0:=Xn:fofType
% 195.03/195.27 Found (x3 x21) as proof of (cNUMBER Xn)
% 195.03/195.27 Found (fun (x4:(cODD Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 195.03/195.27 Found (fun (x4:(cODD Xn0))=> (x3 x21)) as proof of ((cODD Xn0)->(cNUMBER Xn))
% 195.03/195.27 Found x30:=(x3 x21):(cNUMBER Xn0)
% 195.03/195.27 Instantiate: Xn0:=Xn:fofType
% 195.03/195.27 Found (x3 x21) as proof of (cNUMBER Xn)
% 195.03/195.27 Found (fun (x4:(cEVEN Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 195.03/195.27 Found (fun (x4:(cEVEN Xn0))=> (x3 x21)) as proof of ((cEVEN Xn0)->(cNUMBER Xn))
% 195.03/195.27 Found ((or_ind00 (fun (x4:(cEVEN Xn0))=> (x3 x21))) (fun (x4:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 195.03/195.27 Found (((or_ind0 (cNUMBER Xn)) (fun (x4:(cEVEN Xn0))=> (x3 x21))) (fun (x4:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 195.03/195.27 Found ((((fun (P:Prop) (x4:((cEVEN Xn0)->P)) (x5:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x4) x5) x20)) (cNUMBER Xn)) (fun (x4:(cEVEN Xn0))=> (x3 x21))) (fun (x4:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 195.03/195.27 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> ((((fun (P:Prop) (x4:((cEVEN Xn0)->P)) (x5:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x4) x5) x20)) (cNUMBER Xn)) (fun (x4:(cEVEN Xn0))=> (x3 x21))) (fun (x4:(cODD Xn0))=> (x3 x21)))) as proof of (cNUMBER Xn)
% 195.03/195.27 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> ((((fun (P:Prop) (x4:((cEVEN Xn0)->P)) (x5:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x4) x5) x20)) (cNUMBER Xn)) (fun (x4:(cEVEN Xn0))=> (x3 x21))) (fun (x4:(cODD Xn0))=> (x3 x21)))) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 195.03/195.27 Found x50:=(x5 x40):(cNUMBER Xn0)
% 195.03/195.27 Instantiate: Xn0:=Xn:fofType
% 195.03/195.27 Found (x5 x40) as proof of (cNUMBER Xn)
% 195.03/195.27 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 195.03/195.27 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 195.03/195.27 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 196.82/197.03 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 196.82/197.03 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 196.82/197.03 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 196.82/197.03 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 196.82/197.03 Found x30:=(x3 x20):(cNUMBER Xn0)
% 196.82/197.03 Instantiate: Xn00:=Xn0:fofType
% 196.82/197.03 Found (x3 x20) as proof of (cNUMBER Xn00)
% 196.82/197.03 Found (x3 x20) as proof of (cNUMBER Xn00)
% 196.82/197.03 Found x30:(cNUMBER Xn0)
% 196.82/197.03 Found x30 as proof of (cNUMBER Xn0)
% 196.82/197.03 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 196.82/197.03 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 196.82/197.03 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 196.82/197.03 Found x50:(cNUMBER Xn00)
% 196.82/197.03 Found x50 as proof of (cNUMBER Xn00)
% 196.82/197.03 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 196.82/197.03 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 196.82/197.03 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 196.82/197.03 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 196.82/197.03 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 196.82/197.03 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 196.82/197.03 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 196.82/197.03 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->((or (cEVEN Xn00)) (cODD Xn00)))
% 196.82/197.03 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->((or (cEVEN Xn00)) (cODD Xn00))))
% 196.82/197.03 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 196.82/197.03 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 196.82/197.03 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 196.82/197.03 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 196.82/197.03 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 196.82/197.03 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 196.82/197.03 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 196.82/197.03 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 199.43/199.64 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 199.43/199.64 Found x50:=(x5 x40):(cNUMBER Xn00)
% 199.43/199.64 Instantiate: Xn00:=Xn:fofType
% 199.43/199.64 Found (x5 x40) as proof of (cNUMBER Xn)
% 199.43/199.64 Found (x5 x40) as proof of (cNUMBER Xn)
% 199.43/199.64 Found x50:(cNUMBER Xn0)
% 199.43/199.64 Instantiate: Xn0:=Xn:fofType
% 199.43/199.64 Found x50 as proof of (cNUMBER Xn)
% 199.43/199.64 Found x30:=(x3 x20):(cNUMBER Xn0)
% 199.43/199.64 Instantiate: Xn0:=Xn:fofType
% 199.43/199.64 Found (x3 x20) as proof of (cNUMBER Xn)
% 199.43/199.64 Found (x3 x20) as proof of (cNUMBER Xn)
% 199.43/199.64 Found x90:(cNUMBER Xn00)
% 199.43/199.64 Instantiate: Xn00:=Xn:fofType
% 199.43/199.64 Found x90 as proof of (cNUMBER Xn)
% 199.43/199.64 Found x30:(cNUMBER Xn0)
% 199.43/199.64 Instantiate: Xn0:=(cS Xx):fofType
% 199.43/199.64 Found x30 as proof of (cNUMBER (cS Xx))
% 199.43/199.64 Found x12:(cEVEN c0)
% 199.43/199.64 Instantiate: Xn0:=c0:fofType
% 199.43/199.64 Found (fun (x12:(cEVEN c0))=> x12) as proof of (cEVEN Xn0)
% 199.43/199.64 Found (fun (x11:cIND) (x12:(cEVEN c0))=> x12) as proof of ((cEVEN c0)->(cEVEN Xn0))
% 199.43/199.64 Found (fun (x11:cIND) (x12:(cEVEN c0))=> x12) as proof of (cIND->((cEVEN c0)->(cEVEN Xn0)))
% 199.43/199.64 Found (and_rect50 (fun (x11:cIND) (x12:(cEVEN c0))=> x12)) as proof of (cEVEN Xn0)
% 199.43/199.64 Found ((and_rect5 (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12)) as proof of (cEVEN Xn0)
% 199.43/199.64 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12)) as proof of (cEVEN Xn0)
% 199.43/199.64 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12)) as proof of (cEVEN Xn0)
% 199.43/199.64 Found (or_introl00 (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 199.43/199.64 Found ((or_introl0 (cODD Xn0)) (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 199.43/199.64 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 199.43/199.64 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 199.43/199.64 Found x13:(cNUMBER Xx)
% 199.43/199.64 Instantiate: Xn0:=Xx:fofType
% 199.43/199.64 Found x13 as proof of (cNUMBER Xn0)
% 199.43/199.64 Found or_introl000:=(or_introl00 (cODD Xn0)):((or (cEVEN Xn0)) (cODD Xn0))
% 199.43/199.64 Found (or_introl00 (cODD Xn0)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 199.43/199.64 Found ((fun (B:Prop)=> ((or_introl0 B) x12)) (cODD Xn0)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 199.43/199.64 Found ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x12)) (cODD Xn0)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 199.43/199.64 Found ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x12)) (cODD Xn0)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 199.43/199.64 Found (x9 ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x12)) (cODD Xn0))) as proof of (cNUMBER c0)
% 199.43/199.64 Found (x9 ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x12)) (cODD Xn0))) as proof of (cNUMBER c0)
% 199.43/199.64 Found (x9 ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x12)) (cODD Xn0))) as proof of (cNUMBER c0)
% 199.43/199.64 Found x30:(cNUMBER Xn0)
% 199.43/199.64 Instantiate: Xn0:=Xn:fofType
% 199.43/199.64 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 199.43/199.64 Found (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 199.43/199.64 Found (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 199.43/199.64 Found x30:=(x3 x20):(cNUMBER Xn0)
% 199.43/199.64 Instantiate: Xn0:=Xn:fofType
% 199.43/199.64 Found (x3 x20) as proof of (cNUMBER Xn)
% 199.43/199.64 Found (fun (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 199.43/199.64 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 202.71/202.92 Found (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 202.71/202.92 Found (and_rect30 (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 202.71/202.92 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 202.71/202.92 Found (((fun (P:Type) (x6:(((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->P)))=> (((((and_rect ((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))) P) x6) x11)) (cNUMBER Xn)) (fun (x6:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x7:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20))) as proof of (cNUMBER Xn)
% 202.71/202.92 Found x70:(cNUMBER Xn00)
% 202.71/202.92 Found x70 as proof of (cNUMBER Xn00)
% 202.71/202.92 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 202.71/202.92 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 202.71/202.92 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 202.71/202.92 Found x11:(cEVEN c0)
% 202.71/202.92 Instantiate: Xn0:=c0:fofType
% 202.71/202.92 Found x11 as proof of (cEVEN Xn0)
% 202.71/202.92 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 202.71/202.92 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 202.71/202.92 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 202.71/202.92 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 202.71/202.92 Found (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)) as proof of (cNUMBER Xn0)
% 202.71/202.92 Found (fun (x11:(cEVEN c0))=> (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11))) as proof of (cNUMBER Xn0)
% 202.71/202.92 Found (fun (x9:cIND) (x11:(cEVEN c0))=> (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11))) as proof of ((cEVEN c0)->(cNUMBER Xn0))
% 202.71/202.92 Found (fun (x9:cIND) (x11:(cEVEN c0))=> (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11))) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn0)))
% 202.71/202.92 Found (and_rect50 (fun (x9:cIND) (x11:(cEVEN c0))=> (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)))) as proof of (cNUMBER Xn0)
% 202.71/202.92 Found ((and_rect5 (cNUMBER Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)))) as proof of (cNUMBER Xn0)
% 202.71/202.92 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) (cNUMBER Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)))) as proof of (cNUMBER Xn0)
% 202.71/202.92 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) (cNUMBER Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> (x3 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)))) as proof of (cNUMBER Xn0)
% 202.71/202.92 Found x30:(cNUMBER Xn0)
% 202.71/202.92 Instantiate: Xn0:=Xn:fofType
% 202.71/202.92 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 202.71/202.92 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 202.71/202.92 Found x31:(cNUMBER Xn0)
% 202.71/202.92 Instantiate: Xn0:=Xn:fofType
% 202.71/202.92 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x31) as proof of (cNUMBER Xn)
% 202.71/202.92 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x31) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 202.71/202.92 Found x50:=(x5 x40):(cNUMBER Xn0)
% 202.71/202.92 Instantiate: Xn0:=Xn:fofType
% 202.71/202.92 Found (x5 x40) as proof of (cNUMBER Xn)
% 202.71/202.92 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 202.71/202.92 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 202.71/202.92 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 203.62/203.80 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 203.62/203.80 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 203.62/203.80 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 203.62/203.80 Found (fun (x7:(cODD (cS c0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)))) as proof of (cNUMBER Xn)
% 203.62/203.80 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 203.62/203.80 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 203.62/203.80 Found x70:(cNUMBER Xn0)
% 203.62/203.80 Instantiate: Xn0:=Xn:fofType
% 203.62/203.80 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x70) as proof of (cNUMBER Xn)
% 203.62/203.80 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x70) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 203.62/203.80 Found x30:=(x3 x20):(cNUMBER Xn0)
% 203.62/203.80 Found (x3 x20) as proof of (cNUMBER Xn0)
% 203.62/203.80 Found (x3 x20) as proof of (cNUMBER Xn0)
% 203.62/203.80 Found x7:(cODD (cS c0))
% 203.62/203.80 Instantiate: Xn0:=(cS c0):fofType
% 203.62/203.80 Found x7 as proof of (cODD Xn0)
% 203.62/203.80 Found (or_introl00 x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 203.62/203.80 Found ((or_introl0 (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 203.62/203.80 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 203.62/203.80 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 203.62/203.80 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 203.62/203.80 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 203.62/203.80 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 203.62/203.80 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 203.62/203.80 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 203.62/203.80 Instantiate: Xn0:=Xn00:fofType
% 203.62/203.80 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 203.62/203.80 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 203.62/203.80 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 203.62/203.80 Found (x7 x60) as proof of (cNUMBER Xn)
% 203.62/203.80 Found (x7 x60) as proof of (cNUMBER Xn)
% 203.62/203.80 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 208.03/208.29 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 208.03/208.29 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 208.03/208.29 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 208.03/208.29 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 208.03/208.29 Found (x7 x60) as proof of (cNUMBER Xn)
% 208.03/208.29 Found (x7 x60) as proof of (cNUMBER Xn)
% 208.03/208.29 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 208.03/208.29 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 208.03/208.29 Found x9:(cEVEN c0)
% 208.03/208.29 Instantiate: Xn0:=c0:fofType
% 208.03/208.29 Found x9 as proof of (cEVEN Xn0)
% 208.03/208.29 Found (or_introl00 x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 208.03/208.29 Found ((or_introl0 (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 208.03/208.29 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 208.03/208.29 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 208.03/208.29 Found (x12 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 208.03/208.29 Found (x12 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x9)) as proof of (cNUMBER Xn0)
% 208.03/208.29 Found x7:(cODD (cS c0))
% 208.03/208.29 Instantiate: Xn0:=(cS c0):fofType
% 208.03/208.29 Found x7 as proof of (cODD Xn0)
% 208.03/208.29 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 208.03/208.29 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 208.03/208.29 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 208.03/208.29 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 208.03/208.29 Found x12:(cEVEN c0)
% 208.03/208.29 Instantiate: Xn0:=c0:fofType
% 208.03/208.29 Found x12 as proof of (cEVEN Xn0)
% 208.03/208.29 Found (or_introl00 x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 208.03/208.29 Found ((or_introl0 (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 208.03/208.29 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 208.03/208.29 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 208.03/208.29 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 208.03/208.29 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 208.03/208.29 Found (x7 x60) as proof of (cNUMBER Xn)
% 208.03/208.29 Found (x7 x60) as proof of (cNUMBER Xn)
% 208.03/208.29 Found (x7 x60) as proof of (cNUMBER Xn)
% 208.03/208.29 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 208.03/208.29 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 208.03/208.29 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 208.03/208.29 Found x31:(cNUMBER Xn0)
% 208.03/208.29 Instantiate: Xn0:=Xn:fofType
% 208.03/208.29 Found (fun (x12:(cEVEN c0))=> x31) as proof of (cNUMBER Xn)
% 208.03/208.29 Found (fun (x11:cIND) (x12:(cEVEN c0))=> x31) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 208.03/208.29 Found (fun (x11:cIND) (x12:(cEVEN c0))=> x31) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 208.03/208.29 Found x70:(cNUMBER Xn00)
% 208.03/208.29 Instantiate: Xn00:=Xn:fofType
% 208.03/208.29 Found x70 as proof of (cNUMBER Xn)
% 208.03/208.29 Found x50:(cNUMBER Xn0)
% 208.03/208.29 Instantiate: Xn0:=Xn:fofType
% 208.03/208.29 Found x50 as proof of (cNUMBER Xn)
% 208.03/208.29 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 208.03/208.29 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 208.03/208.29 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 208.03/208.29 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 208.03/208.29 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 208.03/208.29 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 209.31/209.57 Found x50:=(x5 x40):(cNUMBER Xn0)
% 209.31/209.57 Instantiate: Xn0:=Xn:fofType
% 209.31/209.57 Found (x5 x40) as proof of (cNUMBER Xn)
% 209.31/209.57 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 209.31/209.57 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 209.31/209.57 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 209.31/209.57 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 209.31/209.57 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 209.31/209.57 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 209.31/209.57 Found (fun (x7:(cODD (cS c0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)))) as proof of (cNUMBER Xn)
% 209.31/209.57 Found (fun (x7:(cODD (cS c0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 209.31/209.57 Found x12:(cEVEN c0)
% 209.31/209.57 Found x12 as proof of (cEVEN c0)
% 209.31/209.57 Found x50:(cNUMBER Xn00)
% 209.31/209.57 Found x50 as proof of (cNUMBER Xn00)
% 209.31/209.57 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 209.31/209.57 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 209.31/209.57 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 209.31/209.57 Found x30:(cNUMBER Xn0)
% 209.31/209.57 Instantiate: Xn0:=Xn:fofType
% 209.31/209.57 Found (fun (x9:(cODD (cS c0)))=> x30) as proof of (cNUMBER Xn)
% 209.31/209.57 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x30) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 209.31/209.57 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x30) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 209.31/209.57 Found x70:(cNUMBER Xn00)
% 209.31/209.57 Instantiate: Xn00:=Xn:fofType
% 209.31/209.57 Found (fun (x9:(cODD (cS c0)))=> x70) as proof of (cNUMBER Xn)
% 209.31/209.57 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x70) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 209.31/209.57 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x70) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 209.31/209.57 Found x30:=(x3 x20):(cNUMBER Xn0)
% 209.31/209.57 Found (x3 x20) as proof of (cNUMBER Xn0)
% 209.31/209.57 Found (x3 x20) as proof of (cNUMBER Xn0)
% 209.31/209.57 Found x30:=(x3 x21):(cNUMBER Xn0)
% 209.31/209.57 Instantiate: Xn0:=Xn:fofType
% 209.31/209.57 Found (x3 x21) as proof of (cNUMBER Xn)
% 209.31/209.57 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 210.42/210.62 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 210.42/210.62 Found or_introl000:=(or_introl00 (cODD Xn0)):((or (cEVEN Xn0)) (cODD Xn0))
% 210.42/210.62 Found (or_introl00 (cODD Xn0)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 210.42/210.62 Found ((fun (B:Prop)=> ((or_introl0 B) x9)) (cODD Xn0)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 210.42/210.62 Found ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x9)) (cODD Xn0)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 210.42/210.62 Found ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x9)) (cODD Xn0)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 210.42/210.62 Found (x12 ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x9)) (cODD Xn0))) as proof of (cNUMBER c0)
% 210.42/210.62 Found (x12 ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x9)) (cODD Xn0))) as proof of (cNUMBER c0)
% 210.42/210.62 Found (x12 ((fun (B:Prop)=> (((or_introl (cEVEN Xn0)) B) x9)) (cODD Xn0))) as proof of (cNUMBER c0)
% 210.42/210.62 Found x30:=(x3 x20):(cNUMBER Xn0)
% 210.42/210.62 Instantiate: Xn00:=Xn0:fofType
% 210.42/210.62 Found (x3 x20) as proof of (cNUMBER Xn00)
% 210.42/210.62 Found (x3 x20) as proof of (cNUMBER Xn00)
% 210.42/210.62 Found x50:(cNUMBER Xn00)
% 210.42/210.62 Found x50 as proof of (cNUMBER Xn00)
% 210.42/210.62 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 210.42/210.62 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 210.42/210.62 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 210.42/210.62 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 210.42/210.62 Found x50:=(x5 x40):(cNUMBER Xn0)
% 210.42/210.62 Instantiate: Xn0:=Xn:fofType
% 210.42/210.62 Found (x5 x40) as proof of (cNUMBER Xn)
% 210.42/210.62 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 210.42/210.62 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 210.42/210.62 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 210.42/210.62 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 210.42/210.62 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 210.42/210.62 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 210.42/210.62 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 210.42/210.62 Found x30:(cNUMBER Xn0)
% 210.42/210.62 Found x30 as proof of (cNUMBER Xn0)
% 210.42/210.62 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 210.42/210.62 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 210.42/210.62 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 210.42/210.62 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->((or (cEVEN Xn00)) (cODD Xn00)))
% 210.42/210.62 Found x30:(cNUMBER Xn0)
% 210.42/210.62 Instantiate: Xn0:=Xn:fofType
% 210.42/210.62 Found (fun (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 210.42/210.62 Found (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 213.32/213.55 Found (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of ((cEVEN Xn0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 213.32/213.55 Found x30:(cNUMBER Xn0)
% 213.32/213.55 Instantiate: Xn0:=Xn:fofType
% 213.32/213.55 Found (fun (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 213.32/213.55 Found (fun (x9:(cODD Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 213.32/213.55 Found (fun (x9:(cODD Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of ((cODD Xn0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 213.32/213.55 Found ((or_ind00 (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 213.32/213.55 Found (((or_ind0 ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 213.32/213.55 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) x20)) ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x30)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 213.32/213.55 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x2 x30))) ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x30)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x30)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 213.32/213.55 Found (fun (x8:((and cIND) (cEVEN c0)))=> ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x2 x30))) ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x30)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x30))) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 213.32/213.55 Found (fun (x8:((and cIND) (cEVEN c0)))=> ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x2 x30))) ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x30)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x30))) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 213.32/213.55 Found x30:=(x3 x21):(cNUMBER Xn0)
% 213.32/213.55 Found (x3 x21) as proof of (cNUMBER Xn)
% 213.32/213.55 Found (x3 x21) as proof of (cNUMBER Xn)
% 213.32/213.55 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 213.32/213.55 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 213.32/213.55 Found x50:(cNUMBER Xn0)
% 215.88/216.15 Instantiate: Xn0:=Xn:fofType
% 215.88/216.15 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of (cNUMBER Xn)
% 215.88/216.15 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 215.88/216.15 Found x30:=(x3 x20):(cNUMBER Xn0)
% 215.88/216.15 Instantiate: Xn0:=Xn:fofType
% 215.88/216.15 Found (x3 x20) as proof of (cNUMBER Xn)
% 215.88/216.15 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 215.88/216.15 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 215.88/216.15 Found x50:=(x5 x40):(cNUMBER Xn00)
% 215.88/216.15 Instantiate: Xn00:=Xn:fofType
% 215.88/216.15 Found (x5 x40) as proof of (cNUMBER Xn)
% 215.88/216.15 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 215.88/216.15 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 215.88/216.15 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 215.88/216.15 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 215.88/216.15 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 215.88/216.15 Found x50:=(x5 x40):(cNUMBER Xn0)
% 215.88/216.15 Instantiate: Xn0:=Xn:fofType
% 215.88/216.15 Found (x5 x40) as proof of (cNUMBER Xn)
% 215.88/216.15 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 215.88/216.15 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 215.88/216.15 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 215.88/216.15 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 215.88/216.15 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 215.88/216.15 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 215.88/216.15 Found (fun (x7:(cODD (cS c0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)))) as proof of (cNUMBER Xn)
% 215.88/216.15 Found (fun (x7:(cODD (cS c0)))=> (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)))) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 215.88/216.15 Found x5:(cODD (cS c0))
% 215.88/216.15 Instantiate: Xn0:=(cS c0):fofType
% 215.88/216.15 Found x5 as proof of (cODD Xn0)
% 215.88/216.15 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 215.88/216.15 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 215.88/216.15 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 215.88/216.15 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 215.88/216.15 Found (x9 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of (cNUMBER Xn0)
% 215.88/216.15 Found (x9 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5)) as proof of (cNUMBER Xn0)
% 215.88/216.15 Found x30:(cNUMBER Xn0)
% 215.88/216.15 Instantiate: Xn0:=(cS Xx):fofType
% 215.88/216.15 Found (fun (x13:(cNUMBER Xx))=> x30) as proof of (cNUMBER (cS Xx))
% 215.88/216.15 Found (fun (x13:(cNUMBER Xx))=> x30) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 215.88/216.15 Found x50:=(x5 x40):(cNUMBER Xn0)
% 215.88/216.15 Instantiate: Xn0:=Xn:fofType
% 215.88/216.15 Found (x5 x40) as proof of (cNUMBER Xn)
% 215.88/216.15 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (cNUMBER Xn)
% 220.42/220.61 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 220.42/220.61 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 220.42/220.61 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 220.42/220.61 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 220.42/220.61 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 220.42/220.61 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x5 x40))) as proof of (cNUMBER Xn)
% 220.42/220.61 Found x50:=(x5 x40):(cNUMBER Xn00)
% 220.42/220.61 Instantiate: Xn0:=Xn00:fofType
% 220.42/220.61 Found (x5 x40) as proof of (cNUMBER Xn0)
% 220.42/220.61 Found (x5 x40) as proof of (cNUMBER Xn0)
% 220.42/220.61 Found x30:=(x3 x20):(cNUMBER Xn0)
% 220.42/220.61 Instantiate: Xn00:=Xn0:fofType
% 220.42/220.61 Found (x3 x20) as proof of (cNUMBER Xn00)
% 220.42/220.61 Found (x3 x20) as proof of (cNUMBER Xn00)
% 220.42/220.61 Found x50:=(x5 x40):(cNUMBER Xn00)
% 220.42/220.61 Instantiate: Xn0:=Xn00:fofType
% 220.42/220.61 Found (x5 x40) as proof of (cNUMBER Xn0)
% 220.42/220.61 Found (x5 x40) as proof of (cNUMBER Xn0)
% 220.42/220.61 Found x30:=(x3 x20):(cNUMBER Xn0)
% 220.42/220.61 Instantiate: Xn00:=Xn0:fofType
% 220.42/220.61 Found (x3 x20) as proof of (cNUMBER Xn00)
% 220.42/220.61 Found (x3 x20) as proof of (cNUMBER Xn00)
% 220.42/220.61 Found x30:=(x3 x20):(cNUMBER Xn0)
% 220.42/220.61 Found (x3 x20) as proof of (cNUMBER Xn0)
% 220.42/220.61 Found (x3 x20) as proof of (cNUMBER Xn0)
% 220.42/220.61 Found x30:=(x3 x21):(cNUMBER Xn0)
% 220.42/220.61 Instantiate: Xn0:=Xn:fofType
% 220.42/220.61 Found (x3 x21) as proof of (cNUMBER Xn)
% 220.42/220.61 Found (x3 x21) as proof of (cNUMBER Xn)
% 220.42/220.61 Found x30:=(x3 x21):(cNUMBER Xn0)
% 220.42/220.61 Found (x3 x21) as proof of (cNUMBER Xn)
% 220.42/220.61 Found (x3 x21) as proof of (cNUMBER Xn)
% 220.42/220.61 Found (x3 x21) as proof of (cNUMBER Xn)
% 220.42/220.61 Found x50:=(x5 x41):(cNUMBER Xn00)
% 220.42/220.61 Instantiate: Xn00:=Xn:fofType
% 220.42/220.61 Found (x5 x41) as proof of (cNUMBER Xn)
% 220.42/220.61 Found (x5 x41) as proof of (cNUMBER Xn)
% 220.42/220.61 Found x50:=(x5 x40):(cNUMBER Xn00)
% 220.42/220.61 Found (x5 x40) as proof of (cNUMBER Xn00)
% 220.42/220.61 Found (x5 x40) as proof of (cNUMBER Xn00)
% 220.42/220.61 Found x50:=(x5 x41):(cNUMBER Xn00)
% 220.42/220.61 Found (x5 x41) as proof of (cNUMBER Xn)
% 220.42/220.61 Found (x5 x41) as proof of (cNUMBER Xn)
% 220.42/220.61 Found (x5 x41) as proof of (cNUMBER Xn)
% 220.42/220.61 Found x50:=(x5 x40):(cNUMBER Xn00)
% 220.42/220.61 Instantiate: Xn00:=Xn:fofType
% 220.42/220.61 Found (x5 x40) as proof of (cNUMBER Xn)
% 220.42/220.61 Found (x5 x40) as proof of (cNUMBER Xn)
% 220.42/220.61 Found x30:=(x3 x20):(cNUMBER Xn0)
% 220.42/220.61 Instantiate: Xn0:=Xn:fofType
% 220.42/220.61 Found (x3 x20) as proof of (cNUMBER Xn)
% 220.42/220.61 Found (x3 x20) as proof of (cNUMBER Xn)
% 220.42/220.61 Found x50:=(x5 x40):(cNUMBER Xn00)
% 220.42/220.61 Instantiate: Xn00:=Xn:fofType
% 220.42/220.61 Found (x5 x40) as proof of (cNUMBER Xn)
% 220.42/220.61 Found (x5 x40) as proof of (cNUMBER Xn)
% 220.42/220.61 Found x30:=(x3 x20):(cNUMBER Xn0)
% 220.42/220.61 Instantiate: Xn0:=Xn:fofType
% 220.42/220.61 Found (x3 x20) as proof of (cNUMBER Xn)
% 220.42/220.61 Found (x3 x20) as proof of (cNUMBER Xn)
% 220.42/220.61 Found x30:=(x3 x20):(cNUMBER Xn0)
% 220.42/220.61 Instantiate: Xn0:=Xn:fofType
% 220.42/220.61 Found (x3 x20) as proof of (cNUMBER Xn)
% 220.42/220.61 Found (x3 x20) as proof of (cNUMBER Xn)
% 220.42/220.61 Found x90:=(x9 x80):(cNUMBER Xn00)
% 220.42/220.61 Instantiate: Xn00:=Xn:fofType
% 220.42/220.61 Found (x9 x80) as proof of (cNUMBER Xn)
% 220.42/220.61 Found (x9 x80) as proof of (cNUMBER Xn)
% 220.42/220.61 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 220.42/220.61 Instantiate: Xn00:=Xn:fofType
% 220.42/220.61 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 220.42/220.61 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 220.42/220.61 Instantiate: Xn0:=Xn:fofType
% 223.72/223.94 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 223.72/223.94 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 223.72/223.94 Instantiate: Xn0:=Xn00:fofType
% 223.72/223.94 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 223.72/223.94 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 223.72/223.94 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 223.72/223.94 Instantiate: Xn00:=Xn0:fofType
% 223.72/223.94 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 223.72/223.94 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 223.72/223.94 Found x70:(cNUMBER Xn0)
% 223.72/223.94 Instantiate: Xn0:=Xn:fofType
% 223.72/223.94 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x70) as proof of (cNUMBER Xn)
% 223.72/223.94 Found (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x70) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 223.72/223.94 Found (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x70) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 223.72/223.94 Found x30:(cNUMBER Xn0)
% 223.72/223.94 Instantiate: Xn0:=Xn:fofType
% 223.72/223.94 Found (fun (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 223.72/223.94 Found (fun (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 223.72/223.94 Found (fun (x8:(cEVEN Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 223.72/223.94 Found (fun (x8:(cEVEN Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of ((cEVEN Xn0)->(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))))
% 223.72/223.94 Found x30:(cNUMBER Xn0)
% 223.72/223.94 Instantiate: Xn0:=Xn:fofType
% 223.72/223.94 Found (fun (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of (cNUMBER Xn)
% 223.72/223.94 Found (fun (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 223.72/223.94 Found (fun (x8:(cODD Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 223.72/223.94 Found (fun (x8:(cODD Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30) as proof of ((cODD Xn0)->(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))))
% 223.72/223.94 Found ((or_ind00 (fun (x8:(cEVEN Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30)) (fun (x8:(cODD Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 223.72/223.94 Found (((or_ind0 (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))) (fun (x8:(cEVEN Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30)) (fun (x8:(cODD Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x30)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 223.72/223.94 Found ((((fun (P:Prop) (x8:((cEVEN Xn0)->P)) (x9:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x8) x9) x20)) (((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn)))) (fun (x8:(cEVEN Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x30)) (fun (x8:(cODD Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x30)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 225.34/225.60 Found ((((fun (P:Prop) (x8:((cEVEN Xn0)->P)) (x9:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x8) x9) (x2 x30))) (((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn)))) (fun (x8:(cEVEN Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x30)) (fun (x8:(cODD Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x30)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 225.34/225.60 Found ((((fun (P:Prop) (x8:((cEVEN Xn0)->P)) (x9:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x8) x9) (x2 x30))) (((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn)))) (fun (x8:(cEVEN Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x30)) (fun (x8:(cODD Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x30)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 225.34/225.60 Found x31:(cNUMBER Xn0)
% 225.34/225.60 Instantiate: Xn0:=Xn:fofType
% 225.34/225.60 Found (fun (x12:(cEVEN c0))=> x31) as proof of (cNUMBER Xn)
% 225.34/225.60 Found (fun (x12:(cEVEN c0))=> x31) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 225.34/225.60 Found x50:(cNUMBER Xn0)
% 225.34/225.60 Instantiate: Xn0:=Xn:fofType
% 225.34/225.60 Found (fun (x9:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 225.34/225.60 Found (fun (x9:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 225.34/225.60 Found x70:(cNUMBER Xn00)
% 225.34/225.60 Instantiate: Xn00:=Xn:fofType
% 225.34/225.60 Found (fun (x9:(cODD (cS c0)))=> x70) as proof of (cNUMBER Xn)
% 225.34/225.60 Found (fun (x9:(cODD (cS c0)))=> x70) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 225.34/225.60 Found x50:(cNUMBER Xn0)
% 225.34/225.60 Instantiate: Xn0:=Xn:fofType
% 225.34/225.60 Found (fun (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 225.34/225.60 Found (fun (x9:(cODD Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 225.34/225.60 Found (fun (x9:(cODD Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of ((cODD Xn0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 225.34/225.60 Found x50:(cNUMBER Xn0)
% 225.34/225.60 Instantiate: Xn0:=Xn:fofType
% 225.34/225.60 Found (fun (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 225.34/225.60 Found (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 225.34/225.60 Found (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of ((cEVEN Xn0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 225.34/225.60 Found ((or_ind00 (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 225.34/225.60 Found (((or_ind0 ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 225.34/225.60 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) x40)) ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x50)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 226.83/227.08 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x4 x50))) ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x50)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 226.83/227.08 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x4 x50))) ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x50)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 226.83/227.08 Found x50:(cNUMBER Xn00)
% 226.83/227.08 Found x50 as proof of (cNUMBER Xn00)
% 226.83/227.08 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 226.83/227.08 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 226.83/227.08 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 226.83/227.08 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 226.83/227.08 Found x30:=(x3 x20):(cNUMBER Xn0)
% 226.83/227.08 Instantiate: Xn0:=Xn:fofType
% 226.83/227.08 Found (x3 x20) as proof of (cNUMBER Xn)
% 226.83/227.08 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 226.83/227.08 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 226.83/227.08 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 226.83/227.08 Found (and_rect20 (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 226.83/227.08 Found ((and_rect2 (cNUMBER Xn)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 226.83/227.08 Found (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 226.83/227.08 Found (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 230.33/230.52 Found x70:=(x7 x60):(cNUMBER Xn0)
% 230.33/230.52 Instantiate: Xn0:=Xn:fofType
% 230.33/230.52 Found (x7 x60) as proof of (cNUMBER Xn)
% 230.33/230.52 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 230.33/230.52 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 230.33/230.52 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 230.33/230.52 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 230.33/230.52 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 230.33/230.52 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 230.33/230.52 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 230.33/230.52 Found x41:((or (cEVEN Xn00)) (cODD Xn00))
% 230.33/230.52 Instantiate: Xn00:=Xn:fofType
% 230.33/230.52 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 230.33/230.52 Found (x3 x41) as proof of (cNUMBER Xn)
% 230.33/230.52 Found (x3 x41) as proof of (cNUMBER Xn)
% 230.33/230.52 Found (x3 x41) as proof of (cNUMBER Xn)
% 230.33/230.52 Found x41:((or (cEVEN Xn00)) (cODD Xn00))
% 230.33/230.52 Found x41 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 230.33/230.52 Found (x5 x41) as proof of (cNUMBER Xn)
% 230.33/230.52 Found (x5 x41) as proof of (cNUMBER Xn)
% 230.33/230.52 Found (x5 x41) as proof of (cNUMBER Xn)
% 230.33/230.52 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 230.33/230.52 Instantiate: Xn0:=Xn:fofType
% 230.33/230.52 Found x21 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 230.33/230.52 Found (x5 x21) as proof of (cNUMBER Xn)
% 230.33/230.52 Found (x5 x21) as proof of (cNUMBER Xn)
% 230.33/230.52 Found (x5 x21) as proof of (cNUMBER Xn)
% 230.33/230.52 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 230.33/230.52 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 230.33/230.52 Found (x3 x21) as proof of (cNUMBER Xn)
% 230.33/230.52 Found (x3 x21) as proof of (cNUMBER Xn)
% 230.33/230.52 Found (x3 x21) as proof of (cNUMBER Xn)
% 230.33/230.52 Found x50:(cNUMBER Xn00)
% 230.33/230.52 Instantiate: Xn0:=Xn00:fofType
% 230.33/230.52 Found x50 as proof of (cNUMBER Xn0)
% 230.33/230.52 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 230.33/230.52 Instantiate: Xn0:=Xn00:fofType
% 230.33/230.52 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 230.33/230.52 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 230.33/230.52 Instantiate: Xn00:=Xn0:fofType
% 230.33/230.52 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 230.33/230.52 Found x30:(cNUMBER Xn0)
% 230.33/230.52 Instantiate: Xn00:=Xn0:fofType
% 230.33/230.52 Found x30 as proof of (cNUMBER Xn00)
% 230.33/230.52 Found x30:=(x3 x21):(cNUMBER Xn0)
% 230.33/230.52 Found (x3 x21) as proof of (cNUMBER Xn)
% 230.33/230.52 Found (x3 x21) as proof of (cNUMBER Xn)
% 230.33/230.52 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 230.33/230.52 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 230.33/230.52 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 231.31/231.55 Found x30:(cNUMBER Xn0)
% 231.31/231.55 Found x30 as proof of (cNUMBER Xn0)
% 231.31/231.55 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 231.31/231.55 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 231.31/231.55 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 231.31/231.55 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->((or (cEVEN Xn00)) (cODD Xn00)))
% 231.31/231.55 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->((or (cEVEN Xn00)) (cODD Xn00))))
% 231.31/231.55 Found x50:(cNUMBER Xn00)
% 231.31/231.55 Found x50 as proof of (cNUMBER Xn00)
% 231.31/231.55 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 231.31/231.55 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 231.31/231.55 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 231.31/231.55 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 231.31/231.55 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 231.31/231.55 Found x30:=(x3 x21):(cNUMBER Xn0)
% 231.31/231.55 Found (x3 x21) as proof of (cNUMBER Xn)
% 231.31/231.55 Found (x3 x21) as proof of (cNUMBER Xn)
% 231.31/231.55 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 231.31/231.55 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 231.31/231.55 Found x70:=(x7 x60):(cNUMBER Xn00)
% 231.31/231.55 Instantiate: Xn00:=Xn:fofType
% 231.31/231.55 Found (x7 x60) as proof of (cNUMBER Xn)
% 231.31/231.55 Found (x7 x60) as proof of (cNUMBER Xn)
% 231.31/231.55 Found x30:=(x3 x20):(cNUMBER Xn0)
% 231.31/231.55 Instantiate: Xn0:=Xn:fofType
% 231.31/231.55 Found (x3 x20) as proof of (cNUMBER Xn)
% 231.31/231.55 Found (x3 x20) as proof of (cNUMBER Xn)
% 231.31/231.55 Found x30:=(x3 x21):(cNUMBER Xn0)
% 231.31/231.55 Found (x3 x21) as proof of (cNUMBER Xn0)
% 231.31/231.55 Found (x3 x21) as proof of (cNUMBER Xn0)
% 231.31/231.55 Found x90:=(x9 c0):((cEVEN c0)->(cEVEN (cS (cS c0))))
% 231.31/231.55 Found (x9 c0) as proof of ((cEVEN c0)->(cEVEN Xn0))
% 231.31/231.55 Found (x9 c0) as proof of ((cEVEN c0)->(cEVEN Xn0))
% 231.31/231.55 Found (fun (x11:cIND)=> (x9 c0)) as proof of ((cEVEN c0)->(cEVEN Xn0))
% 231.31/231.55 Found (fun (x11:cIND)=> (x9 c0)) as proof of (cIND->((cEVEN c0)->(cEVEN Xn0)))
% 231.31/231.55 Found (and_rect50 (fun (x11:cIND)=> (x9 c0))) as proof of (cEVEN Xn0)
% 231.31/231.55 Found ((and_rect5 (cEVEN Xn0)) (fun (x11:cIND)=> (x9 c0))) as proof of (cEVEN Xn0)
% 231.31/231.55 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND)=> (x9 c0))) as proof of (cEVEN Xn0)
% 231.31/231.55 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND)=> (x9 c0))) as proof of (cEVEN Xn0)
% 231.31/231.55 Found (or_introl00 (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND)=> (x9 c0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 231.31/231.55 Found ((or_introl0 (cODD Xn0)) (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND)=> (x9 c0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 232.13/232.32 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND)=> (x9 c0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 232.13/232.32 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND)=> (x9 c0)))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 232.13/232.32 Found x50:(cNUMBER Xn0)
% 232.13/232.32 Instantiate: Xn0:=(cS Xx):fofType
% 232.13/232.32 Found x50 as proof of (cNUMBER (cS Xx))
% 232.13/232.32 Found x13:(cNUMBER Xx)
% 232.13/232.32 Instantiate: Xn0:=Xx:fofType
% 232.13/232.32 Found x13 as proof of (cNUMBER Xn0)
% 232.13/232.32 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 232.13/232.32 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 232.13/232.32 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 232.13/232.32 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 232.13/232.32 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 232.13/232.32 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 232.13/232.32 Found (and_rect40 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 232.13/232.32 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 232.13/232.32 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 232.13/232.32 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 232.13/232.32 Found x50:=(x5 x40):(cNUMBER Xn00)
% 232.13/232.32 Instantiate: Xn00:=Xn:fofType
% 232.13/232.32 Found (x5 x40) as proof of (cNUMBER Xn)
% 232.13/232.32 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 232.13/232.32 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 232.13/232.32 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 232.13/232.32 Found x30:=(x3 x20):(cNUMBER Xn0)
% 232.13/232.32 Instantiate: Xn0:=Xn:fofType
% 232.13/232.32 Found (x3 x20) as proof of (cNUMBER Xn)
% 232.13/232.32 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 232.13/232.32 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 232.13/232.32 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 232.89/233.10 Found x50:(cNUMBER Xn0)
% 232.89/233.10 Instantiate: Xn0:=Xn:fofType
% 232.89/233.10 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of (cNUMBER Xn)
% 232.89/233.10 Found (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 232.89/233.10 Found (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x50) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 232.89/233.10 Found x20:=(x2 x31):((or (cEVEN Xn0)) (cODD Xn0))
% 232.89/233.10 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 232.89/233.10 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 232.89/233.10 Found x32:(cNUMBER Xn0)
% 232.89/233.10 Instantiate: Xn0:=Xn:fofType
% 232.89/233.10 Found (fun (x7:(cODD (cS c0)))=> x32) as proof of (cNUMBER Xn)
% 232.89/233.10 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> x32) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 232.89/233.10 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> x32) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 232.89/233.10 Found x7:(cODD (cS c0))
% 232.89/233.10 Instantiate: Xn0:=(cS c0):fofType
% 232.89/233.10 Found x7 as proof of (cODD Xn0)
% 232.89/233.10 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 232.89/233.10 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 232.89/233.10 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 232.89/233.10 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 232.89/233.10 Found (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 232.89/233.10 Found (fun (x11:(cEVEN c0))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of (cNUMBER Xn0)
% 232.89/233.10 Found (fun (x9:cIND) (x11:(cEVEN c0))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of ((cEVEN c0)->(cNUMBER Xn0))
% 232.89/233.10 Found (fun (x9:cIND) (x11:(cEVEN c0))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn0)))
% 232.89/233.10 Found (and_rect50 (fun (x9:cIND) (x11:(cEVEN c0))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 232.89/233.10 Found ((and_rect5 (cNUMBER Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 232.89/233.10 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) (cNUMBER Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 232.89/233.10 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) (cNUMBER Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> (x5 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 232.89/233.10 Found x30:=(x3 x20):(cNUMBER Xn0)
% 232.89/233.10 Found (x3 x20) as proof of (cNUMBER Xn0)
% 232.89/233.10 Found (x3 x20) as proof of (cNUMBER Xn0)
% 232.89/233.10 Found x30:=(x3 x21):(cNUMBER Xn0)
% 232.89/233.10 Instantiate: Xn0:=Xn:fofType
% 232.89/233.10 Found (x3 x21) as proof of (cNUMBER Xn)
% 232.89/233.10 Found (fun (x12:(cEVEN c0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 232.89/233.10 Found (fun (x12:(cEVEN c0))=> (x3 x21)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 232.89/233.10 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn00)) (cODD (cS c0))))
% 232.89/233.10 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn00)) (cODD Xn00)))
% 232.89/233.10 Found ((or_intror (cEVEN Xn00)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn00)) (cODD Xn00)))
% 232.89/233.10 Found ((or_intror (cEVEN Xn00)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn00)) (cODD Xn00)))
% 232.89/233.10 Found (fun (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))))=> ((or_intror (cEVEN Xn00)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn00)) (cODD Xn00)))
% 232.89/233.15 Found (fun (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))))=> ((or_intror (cEVEN Xn00)) (cODD (cS c0)))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->((or (cEVEN Xn00)) (cODD Xn00))))
% 232.89/233.15 Found (and_rect40 (fun (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))))=> ((or_intror (cEVEN Xn00)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 232.89/233.15 Found ((and_rect4 ((or (cEVEN Xn00)) (cODD Xn00))) (fun (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))))=> ((or_intror (cEVEN Xn00)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 232.89/233.15 Found (((fun (P:Type) (x7:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn00)) (cODD Xn00))) (fun (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))))=> ((or_intror (cEVEN Xn00)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 232.89/233.15 Found (((fun (P:Type) (x7:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn00)) (cODD Xn00))) (fun (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))))=> ((or_intror (cEVEN Xn00)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 232.89/233.15 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 232.89/233.15 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 232.89/233.15 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 232.89/233.15 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 232.89/233.15 Found (fun (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 232.89/233.15 Found (fun (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 232.89/233.15 Found (and_rect40 (fun (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 232.89/233.15 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 232.89/233.15 Found (((fun (P:Type) (x7:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 232.89/233.15 Found (((fun (P:Type) (x7:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 235.62/235.87 Found x30:=(x3 x20):(cNUMBER Xn0)
% 235.62/235.87 Instantiate: Xn00:=Xn0:fofType
% 235.62/235.87 Found (x3 x20) as proof of (cNUMBER Xn00)
% 235.62/235.87 Found (x3 x20) as proof of (cNUMBER Xn00)
% 235.62/235.87 Found x50:=(x5 x40):(cNUMBER Xn00)
% 235.62/235.87 Instantiate: Xn0:=Xn00:fofType
% 235.62/235.87 Found (x5 x40) as proof of (cNUMBER Xn0)
% 235.62/235.87 Found (x5 x40) as proof of (cNUMBER Xn0)
% 235.62/235.87 Found x30:=(x3 x20):(cNUMBER Xn0)
% 235.62/235.87 Found (x3 x20) as proof of (cNUMBER Xn0)
% 235.62/235.87 Found (x3 x20) as proof of (cNUMBER Xn0)
% 235.62/235.87 Found x30:=(x3 x21):(cNUMBER Xn0)
% 235.62/235.87 Instantiate: Xn0:=Xn:fofType
% 235.62/235.87 Found (x3 x21) as proof of (cNUMBER Xn)
% 235.62/235.87 Found (x3 x21) as proof of (cNUMBER Xn)
% 235.62/235.87 Found x30:=(x3 x21):(cNUMBER Xn0)
% 235.62/235.87 Found (x3 x21) as proof of (cNUMBER Xn)
% 235.62/235.87 Found (x3 x21) as proof of (cNUMBER Xn)
% 235.62/235.87 Found (x3 x21) as proof of (cNUMBER Xn)
% 235.62/235.87 Found x90:=(x9 x80):(cNUMBER Xn0)
% 235.62/235.87 Found (x9 x80) as proof of (cNUMBER Xn)
% 235.62/235.87 Found (x9 x80) as proof of (cNUMBER Xn)
% 235.62/235.87 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 235.62/235.87 Found (fun (x9:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x9 x80)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 235.62/235.87 Found x50:=(x5 x40):(cNUMBER Xn00)
% 235.62/235.87 Found (x5 x40) as proof of (cNUMBER Xn00)
% 235.62/235.87 Found (x5 x40) as proof of (cNUMBER Xn00)
% 235.62/235.87 Found x50:=(x5 x41):(cNUMBER Xn00)
% 235.62/235.87 Instantiate: Xn00:=Xn:fofType
% 235.62/235.87 Found (x5 x41) as proof of (cNUMBER Xn)
% 235.62/235.87 Found (x5 x41) as proof of (cNUMBER Xn)
% 235.62/235.87 Found x50:=(x5 x41):(cNUMBER Xn00)
% 235.62/235.87 Found (x5 x41) as proof of (cNUMBER Xn)
% 235.62/235.87 Found (x5 x41) as proof of (cNUMBER Xn)
% 235.62/235.87 Found (x5 x41) as proof of (cNUMBER Xn)
% 235.62/235.87 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 235.62/235.87 Instantiate: Xn0:=Xn:fofType
% 235.62/235.87 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 235.62/235.87 Found x50:=(x5 x40):(cNUMBER Xn00)
% 235.62/235.87 Instantiate: Xn00:=Xn:fofType
% 235.62/235.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 235.62/235.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 235.62/235.87 Found x30:=(x3 x20):(cNUMBER Xn0)
% 235.62/235.87 Instantiate: Xn0:=Xn:fofType
% 235.62/235.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 235.62/235.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 235.62/235.87 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 235.62/235.87 Instantiate: Xn00:=Xn:fofType
% 235.62/235.87 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 235.62/235.87 Found x50:=(x5 x40):(cNUMBER Xn00)
% 235.62/235.87 Instantiate: Xn00:=Xn:fofType
% 235.62/235.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 235.62/235.87 Found (x5 x40) as proof of (cNUMBER Xn)
% 235.62/235.87 Found x30:=(x3 x20):(cNUMBER Xn0)
% 235.62/235.87 Instantiate: Xn0:=Xn:fofType
% 235.62/235.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 235.62/235.87 Found (x3 x20) as proof of (cNUMBER Xn)
% 235.62/235.87 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 235.62/235.87 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 235.62/235.87 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 235.62/235.87 Found x50:=(x5 x41):(cNUMBER Xn0)
% 235.62/235.87 Instantiate: Xn0:=Xn:fofType
% 235.62/235.87 Found (x5 x41) as proof of (cNUMBER Xn)
% 235.62/235.87 Found (fun (x7:(cODD (cS c0)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 235.62/235.87 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x41)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 235.62/235.87 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x41)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 235.62/235.87 Found (and_rect30 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x41))) as proof of (cNUMBER Xn)
% 235.62/235.87 Found ((and_rect3 (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x41))) as proof of (cNUMBER Xn)
% 235.62/235.87 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x41))) as proof of (cNUMBER Xn)
% 238.80/239.06 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x41)))) as proof of (cNUMBER Xn)
% 238.80/239.06 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) (cNUMBER Xn)) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x5 x41)))) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 238.80/239.06 Found x7:(cODD (cS c0))
% 238.80/239.06 Instantiate: Xn0:=(cS c0):fofType
% 238.80/239.06 Found x7 as proof of (cODD Xn0)
% 238.80/239.06 Found (or_introl00 x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 238.80/239.06 Found ((or_introl0 (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 238.80/239.06 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 238.80/239.06 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 238.80/239.06 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 238.80/239.06 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 238.80/239.06 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 238.80/239.06 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 238.80/239.06 Found x30:=(x3 x20):(cNUMBER Xn0)
% 238.80/239.06 Instantiate: Xn0:=Xn:fofType
% 238.80/239.06 Found (x3 x20) as proof of (cNUMBER Xn)
% 238.80/239.06 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 238.80/239.06 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 238.80/239.06 Found x90:=(x9 x80):(cNUMBER Xn00)
% 238.80/239.06 Instantiate: Xn00:=Xn:fofType
% 238.80/239.06 Found (x9 x80) as proof of (cNUMBER Xn)
% 238.80/239.06 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 238.80/239.06 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 238.80/239.06 Found x7:(cODD (cS c0))
% 238.80/239.06 Instantiate: Xn0:=(cS c0):fofType
% 238.80/239.06 Found x7 as proof of (cODD Xn0)
% 238.80/239.06 Found (or_introl00 x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 238.80/239.06 Found ((or_introl0 (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 238.80/239.06 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 238.80/239.06 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 238.80/239.06 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 238.80/239.06 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 238.80/239.06 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 238.80/239.06 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 238.80/239.06 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 238.80/239.06 Instantiate: Xn00:=Xn:fofType
% 238.80/239.06 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 238.80/239.06 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 238.80/239.06 Instantiate: Xn0:=Xn:fofType
% 238.80/239.06 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 238.80/239.06 Found x50:=(x5 x40):(cNUMBER Xn0)
% 238.80/239.06 Found (x5 x40) as proof of (cNUMBER Xn0)
% 238.80/239.06 Found (x5 x40) as proof of (cNUMBER Xn0)
% 238.80/239.06 Found x30:(cNUMBER Xn0)
% 238.80/239.06 Instantiate: Xn0:=Xn:fofType
% 238.80/239.06 Found (fun (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 239.31/239.52 Found (fun (x5:(cEVEN Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 239.31/239.52 Found (fun (x5:(cEVEN Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((cEVEN Xn0)->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 239.31/239.52 Found x30:(cNUMBER Xn0)
% 239.31/239.52 Instantiate: Xn0:=Xn:fofType
% 239.31/239.52 Found (fun (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 239.31/239.52 Found (fun (x5:(cODD Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 239.31/239.52 Found (fun (x5:(cODD Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((cODD Xn0)->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 239.31/239.52 Found ((or_ind00 (fun (x5:(cEVEN Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) (fun (x5:(cODD Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 239.31/239.52 Found (((or_ind0 ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) (fun (x5:(cODD Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 239.31/239.52 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) x20)) ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) (fun (x5:(cODD Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 239.31/239.52 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x30))) ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) (fun (x5:(cODD Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 239.31/239.52 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x30))) ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) (fun (x5:(cODD Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 239.31/239.52 Found x11:(cEVEN c0)
% 239.31/239.52 Instantiate: Xn0:=c0:fofType
% 239.31/239.52 Found (fun (x11:(cEVEN c0))=> x11) as proof of (cEVEN Xn0)
% 239.31/239.52 Found (fun (x9:cIND) (x11:(cEVEN c0))=> x11) as proof of ((cEVEN c0)->(cEVEN Xn0))
% 239.31/239.52 Found (fun (x9:cIND) (x11:(cEVEN c0))=> x11) as proof of (cIND->((cEVEN c0)->(cEVEN Xn0)))
% 239.31/239.52 Found (and_rect50 (fun (x9:cIND) (x11:(cEVEN c0))=> x11)) as proof of (cEVEN Xn0)
% 239.31/239.52 Found ((and_rect5 (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11)) as proof of (cEVEN Xn0)
% 239.31/239.52 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11)) as proof of (cEVEN Xn0)
% 239.31/239.52 Found (fun (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))) as proof of (cEVEN Xn0)
% 239.31/239.52 Found (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0))
% 239.31/239.52 Found (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))) as proof of (((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0)))
% 239.31/239.53 Found (and_rect40 (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11)))) as proof of (cEVEN Xn0)
% 239.31/239.53 Found ((and_rect4 (cEVEN Xn0)) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11)))) as proof of (cEVEN Xn0)
% 239.31/239.53 Found (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) (cEVEN Xn0)) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11)))) as proof of (cEVEN Xn0)
% 239.31/239.53 Found (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) (cEVEN Xn0)) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11)))) as proof of (cEVEN Xn0)
% 239.31/239.53 Found (or_introl00 (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) (cEVEN Xn0)) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 239.31/239.53 Found ((or_introl0 (cODD Xn0)) (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x7) x6)) (cEVEN Xn0)) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 239.31/239.53 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x7) x6)) (cEVEN Xn0)) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 239.31/239.53 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x7) x6)) (cEVEN Xn0)) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 241.12/241.38 Found x7:(cODD (cS c0))
% 241.12/241.38 Instantiate: Xn0:=(cS c0):fofType
% 241.12/241.38 Found x7 as proof of (cODD Xn0)
% 241.12/241.38 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 241.12/241.38 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 241.12/241.38 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 241.12/241.38 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 241.12/241.38 Found (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)) as proof of (cNUMBER Xn0)
% 241.12/241.38 Found (fun (x12:(cEVEN c0))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of (cNUMBER Xn0)
% 241.12/241.38 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of ((cEVEN c0)->(cNUMBER Xn0))
% 241.12/241.38 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7))) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn0)))
% 241.12/241.38 Found (and_rect50 (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 241.21/241.42 Found ((and_rect5 (cNUMBER Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 241.21/241.42 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 241.21/241.42 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7)))) as proof of (cNUMBER Xn0)
% 241.21/241.42 Found x12:(cEVEN c0)
% 241.21/241.42 Instantiate: Xn0:=c0:fofType
% 241.21/241.42 Found x12 as proof of (cEVEN Xn0)
% 241.21/241.42 Found (or_introl00 x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.42 Found ((or_introl0 (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.42 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.42 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.42 Found x7:(cODD (cS c0))
% 241.21/241.42 Instantiate: Xn0:=(cS c0):fofType
% 241.21/241.42 Found x7 as proof of (cODD Xn0)
% 241.21/241.42 Found (or_intror00 x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.42 Found ((or_intror0 (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.42 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.42 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x7) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.42 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.42 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.42 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.42 Found x51:(cNUMBER Xn0)
% 241.21/241.42 Instantiate: Xn0:=Xn:fofType
% 241.21/241.42 Found (fun (x12:(cEVEN c0))=> x51) as proof of (cNUMBER Xn)
% 241.21/241.42 Found (fun (x11:cIND) (x12:(cEVEN c0))=> x51) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 241.21/241.42 Found (fun (x11:cIND) (x12:(cEVEN c0))=> x51) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 241.21/241.42 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 241.21/241.42 Instantiate: Xn0:=Xn00:fofType
% 241.21/241.42 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.42 Found (x3 x40) as proof of (cNUMBER Xn0)
% 241.21/241.42 Found (x3 x40) as proof of (cNUMBER Xn0)
% 241.21/241.42 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 241.21/241.42 Instantiate: Xn0:=Xn00:fofType
% 241.21/241.42 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.42 Found (x3 x40) as proof of (cNUMBER Xn0)
% 241.21/241.42 Found (x3 x40) as proof of (cNUMBER Xn0)
% 241.21/241.42 Found or_intror00:=(or_intror0 (cEVEN c0)):((cEVEN c0)->((or (cODD Xn0)) (cEVEN c0)))
% 241.21/241.42 Found (or_intror0 (cEVEN c0)) as proof of ((cEVEN c0)->((or (cODD Xn0)) (cEVEN Xn0)))
% 241.21/241.42 Found ((or_intror (cODD Xn0)) (cEVEN c0)) as proof of ((cEVEN c0)->((or (cODD Xn0)) (cEVEN Xn0)))
% 241.21/241.42 Found ((or_intror (cODD Xn0)) (cEVEN c0)) as proof of ((cEVEN c0)->((or (cODD Xn0)) (cEVEN Xn0)))
% 241.21/241.42 Found (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0))) as proof of ((cEVEN c0)->((or (cODD Xn0)) (cEVEN Xn0)))
% 241.21/241.42 Found (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0))) as proof of (cIND->((cEVEN c0)->((or (cODD Xn0)) (cEVEN Xn0))))
% 241.21/241.42 Found (and_rect50 (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 241.21/241.42 Found ((and_rect5 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 241.21/241.42 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 241.21/241.42 Found (fun (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0))))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 241.21/241.42 Found (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0))))) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cODD Xn0)) (cEVEN Xn0)))
% 241.21/241.42 Found (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0))))) as proof of (((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cODD Xn0)) (cEVEN Xn0))))
% 241.21/241.42 Found (and_rect40 (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0)))))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 241.21/241.42 Found ((and_rect4 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0)))))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 241.21/241.42 Found (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0)))))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 241.21/241.42 Found (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0)))))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 241.21/241.42 Found (or_comm_i00 (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 241.21/241.42 Found ((or_comm_i0 (cEVEN Xn0)) (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 243.83/244.04 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 243.83/244.04 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 243.83/244.04 Found x30:=(x3 x20):(cNUMBER Xn0)
% 243.83/244.04 Found (x3 x20) as proof of (cNUMBER Xn)
% 243.83/244.04 Found (x3 x20) as proof of (cNUMBER Xn)
% 243.83/244.04 Found (x3 x20) as proof of (cNUMBER Xn)
% 243.83/244.04 Found x50:=(x5 x40):(cNUMBER Xn00)
% 243.83/244.04 Found (x5 x40) as proof of (cNUMBER Xn)
% 243.83/244.04 Found (x5 x40) as proof of (cNUMBER Xn)
% 243.83/244.04 Found (x5 x40) as proof of (cNUMBER Xn)
% 243.83/244.04 Found x70:=(x7 x60):(cNUMBER Xn0)
% 243.83/244.04 Instantiate: Xn0:=Xn:fofType
% 243.83/244.04 Found (x7 x60) as proof of (cNUMBER Xn)
% 243.83/244.04 Found (x7 x60) as proof of (cNUMBER Xn)
% 243.83/244.04 Found x90:=(x9 x80):(cNUMBER Xn00)
% 243.83/244.04 Instantiate: Xn00:=Xn:fofType
% 243.83/244.04 Found (x9 x80) as proof of (cNUMBER Xn)
% 243.83/244.04 Found (x9 x80) as proof of (cNUMBER Xn)
% 243.83/244.04 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 243.83/244.04 Instantiate: Xn0:=Xn:fofType
% 243.83/244.04 Found x21 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 243.83/244.04 Found (x5 x21) as proof of (cNUMBER Xn)
% 243.83/244.04 Found (x5 x21) as proof of (cNUMBER Xn)
% 243.83/244.04 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x21)) as proof of (cNUMBER Xn)
% 243.83/244.04 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x21)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 243.83/244.04 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 243.83/244.04 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 243.83/244.04 Found (x3 x21) as proof of (cNUMBER Xn)
% 243.83/244.04 Found (x3 x21) as proof of (cNUMBER Xn)
% 243.83/244.04 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 243.83/244.04 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 243.83/244.04 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 243.83/244.04 Instantiate: Xn00:=Xn:fofType
% 243.83/244.04 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 243.83/244.04 Found x30:=(x3 x20):(cNUMBER Xn0)
% 243.83/244.04 Instantiate: Xn0:=Xn:fofType
% 243.83/244.04 Found (x3 x20) as proof of (cNUMBER Xn)
% 243.83/244.04 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (cNUMBER Xn)
% 243.83/244.04 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 243.83/244.04 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 244.52/244.79 Found (and_rect20 (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 244.52/244.79 Found ((and_rect2 (cNUMBER Xn)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 244.52/244.79 Found (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 244.52/244.79 Found (((fun (P:Type) (x4:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x4) x0)) (cNUMBER Xn)) (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x3 x20))) as proof of (cNUMBER Xn)
% 244.52/244.79 Found x31:(cNUMBER Xn0)
% 244.52/244.79 Instantiate: Xn0:=Xn:fofType
% 244.52/244.79 Found (fun (x12:(cEVEN c0))=> x31) as proof of (cNUMBER Xn)
% 244.52/244.79 Found (fun (x12:(cEVEN c0))=> x31) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 244.52/244.79 Found x30:=(x3 x21):(cNUMBER Xn0)
% 244.52/244.79 Instantiate: Xn0:=Xn:fofType
% 244.52/244.79 Found (x3 x21) as proof of (cNUMBER Xn)
% 244.52/244.79 Found (fun (x6:(cEVEN Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 244.52/244.79 Found (fun (x6:(cEVEN Xn0))=> (x3 x21)) as proof of ((cEVEN Xn0)->(cNUMBER Xn))
% 244.52/244.79 Found x30:=(x3 x21):(cNUMBER Xn0)
% 244.52/244.79 Instantiate: Xn0:=Xn:fofType
% 244.52/244.79 Found (x3 x21) as proof of (cNUMBER Xn)
% 244.52/244.79 Found (fun (x6:(cODD Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 244.52/244.79 Found (fun (x6:(cODD Xn0))=> (x3 x21)) as proof of ((cODD Xn0)->(cNUMBER Xn))
% 244.52/244.79 Found ((or_ind00 (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 244.52/244.79 Found (((or_ind0 (cNUMBER Xn)) (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 244.52/244.79 Found ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) x20)) (cNUMBER Xn)) (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 244.52/244.79 Found ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) x20)) (cNUMBER Xn)) (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 244.52/244.79 Found x30:=(x3 x21):(cNUMBER Xn0)
% 244.52/244.79 Instantiate: Xn0:=Xn:fofType
% 244.52/244.79 Found (x3 x21) as proof of (cNUMBER Xn)
% 244.52/244.79 Found (fun (x12:(cEVEN c0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 244.52/244.79 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x21)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 244.52/244.79 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x3 x21)) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 244.52/244.79 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 244.52/244.79 Instantiate: Xn0:=Xn:fofType
% 244.52/244.79 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 244.52/244.79 Found x70:(cNUMBER Xn00)
% 244.52/244.79 Instantiate: Xn00:=Xn:fofType
% 244.52/244.79 Found (fun (x9:(cODD (cS c0)))=> x70) as proof of (cNUMBER Xn)
% 244.52/244.79 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x70) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 245.00/245.24 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x70) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 245.00/245.24 Found x50:(cNUMBER Xn0)
% 245.00/245.24 Instantiate: Xn0:=Xn:fofType
% 245.00/245.24 Found (fun (x9:(cODD (cS c0)))=> x50) as proof of (cNUMBER Xn)
% 245.00/245.24 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x50) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 245.00/245.24 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x50) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 245.00/245.24 Found x30:(cNUMBER Xn0)
% 245.00/245.24 Instantiate: Xn0:=c0:fofType
% 245.00/245.24 Found x30 as proof of (cNUMBER c0)
% 245.00/245.24 Found x50:(cNUMBER Xn0)
% 245.00/245.24 Instantiate: Xn0:=Xn:fofType
% 245.00/245.24 Found (fun (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 245.00/245.24 Found (fun (x9:(cODD Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 245.00/245.24 Found (fun (x9:(cODD Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of ((cODD Xn0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 245.00/245.24 Found x50:(cNUMBER Xn0)
% 245.00/245.24 Instantiate: Xn0:=Xn:fofType
% 245.00/245.24 Found (fun (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 245.00/245.24 Found (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 245.00/245.24 Found (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of ((cEVEN Xn0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 245.00/245.24 Found ((or_ind00 (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 245.00/245.24 Found (((or_ind0 ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 245.00/245.24 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) x40)) ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x50)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 245.00/245.24 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x4 x50))) ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x50)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x50)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 245.00/245.24 Found (fun (x8:((and cIND) (cEVEN c0)))=> ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x4 x50))) ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x50)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x50))) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 245.69/245.89 Found (fun (x8:((and cIND) (cEVEN c0)))=> ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x4 x50))) ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x50)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x50))) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 245.69/245.89 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 245.69/245.89 Instantiate: Xn0:=Xn:fofType
% 245.69/245.89 Found x21 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 245.69/245.89 Found (x5 x21) as proof of (cNUMBER Xn)
% 245.69/245.89 Found (x5 x21) as proof of (cNUMBER Xn)
% 245.69/245.89 Found (x5 x21) as proof of (cNUMBER Xn)
% 245.69/245.89 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 245.69/245.89 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 245.69/245.89 Found (x3 x21) as proof of (cNUMBER Xn)
% 245.69/245.89 Found (x3 x21) as proof of (cNUMBER Xn)
% 245.69/245.89 Found (x3 x21) as proof of (cNUMBER Xn)
% 245.69/245.89 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 245.69/245.89 Instantiate: Xn0:=Xn:fofType
% 245.69/245.89 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 245.69/245.89 Found (fun (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 245.69/245.89 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->((or (cEVEN Xn00)) (cODD Xn00)))
% 245.69/245.89 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->((or (cEVEN Xn00)) (cODD Xn00))))
% 245.69/245.89 Found (and_rect30 (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30))) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 245.69/245.89 Found ((and_rect3 ((or (cEVEN Xn00)) (cODD Xn00))) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30))) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 245.69/245.89 Found (((fun (P:Type) (x6:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x0)) ((or (cEVEN Xn00)) (cODD Xn00))) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30))) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 245.69/245.89 Found (((fun (P:Type) (x6:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x0)) ((or (cEVEN Xn00)) (cODD Xn00))) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x7:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> (x2 x30))) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 245.82/246.03 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 245.82/246.03 Instantiate: Xn00:=Xn:fofType
% 245.82/246.03 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 245.82/246.03 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 245.82/246.03 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 245.82/246.03 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 245.82/246.03 Found (and_rect30 (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 245.82/246.03 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 245.82/246.03 Found (((fun (P:Type) (x6:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 245.82/246.03 Found (((fun (P:Type) (x6:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 245.82/246.03 Found x70:=(x7 x60):(cNUMBER Xn0)
% 245.82/246.03 Instantiate: Xn0:=Xn:fofType
% 245.82/246.03 Found (x7 x60) as proof of (cNUMBER Xn)
% 245.82/246.03 Found (fun (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (cNUMBER Xn)
% 245.82/246.03 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 245.82/246.03 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 245.82/246.03 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 245.82/246.03 Found ((and_rect4 (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 250.62/250.81 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 250.62/250.81 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x4)) (cNUMBER Xn)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> (x7 x60))) as proof of (cNUMBER Xn)
% 250.62/250.81 Found x32:(cNUMBER Xn0)
% 250.62/250.81 Instantiate: Xn0:=Xn:fofType
% 250.62/250.81 Found (fun (x7:(cODD (cS c0)))=> x32) as proof of (cNUMBER Xn)
% 250.62/250.81 Found (fun (x7:(cODD (cS c0)))=> x32) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 250.62/250.81 Found x50:(cNUMBER Xn00)
% 250.62/250.81 Found x50 as proof of (cNUMBER Xn00)
% 250.62/250.81 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 250.62/250.81 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 250.62/250.81 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 250.62/250.81 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 250.62/250.81 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 250.62/250.81 Found x41:((or (cEVEN Xn00)) (cODD Xn00))
% 250.62/250.81 Instantiate: Xn00:=Xn:fofType
% 250.62/250.81 Found x41 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 250.62/250.81 Found (x3 x41) as proof of (cNUMBER Xn)
% 250.62/250.81 Found (x3 x41) as proof of (cNUMBER Xn)
% 250.62/250.81 Found (x3 x41) as proof of (cNUMBER Xn)
% 250.62/250.81 Found x41:((or (cEVEN Xn00)) (cODD Xn00))
% 250.62/250.81 Found x41 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 250.62/250.81 Found (x5 x41) as proof of (cNUMBER Xn)
% 250.62/250.81 Found (x5 x41) as proof of (cNUMBER Xn)
% 250.62/250.81 Found (x5 x41) as proof of (cNUMBER Xn)
% 250.62/250.81 Found x30:=(x3 x20):(cNUMBER Xn0)
% 250.62/250.81 Instantiate: Xn0:=Xn:fofType
% 250.62/250.81 Found (x3 x20) as proof of (cNUMBER Xn)
% 250.62/250.81 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 250.62/250.81 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 250.62/250.81 Found x70:=(x7 x60):(cNUMBER Xn00)
% 250.62/250.81 Instantiate: Xn00:=Xn:fofType
% 250.62/250.81 Found (x7 x60) as proof of (cNUMBER Xn)
% 250.62/250.81 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 250.62/250.81 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 250.62/250.81 Found x22:((or (cEVEN Xn0)) (cODD Xn0))
% 250.62/250.81 Found x22 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 250.62/250.81 Found (x3 x22) as proof of (cNUMBER Xn)
% 250.62/250.81 Found (x3 x22) as proof of (cNUMBER Xn)
% 250.62/250.81 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x22)) as proof of (cNUMBER Xn)
% 250.62/250.81 Found (fun (x3:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x3 x22)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 250.62/250.81 Found x30:=(x3 x20):(cNUMBER Xn0)
% 250.62/250.81 Found (x3 x20) as proof of (cNUMBER Xn00)
% 250.62/250.81 Found (x3 x20) as proof of (cNUMBER Xn00)
% 250.62/250.81 Found (x3 x20) as proof of (cNUMBER Xn00)
% 250.62/250.81 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 250.62/250.81 Instantiate: Xn00:=Xn:fofType
% 250.62/250.81 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 250.62/250.81 Found x30:=(x3 x20):(cNUMBER Xn0)
% 250.62/250.81 Found (x3 x20) as proof of (cNUMBER Xn0)
% 250.62/250.81 Found (x3 x20) as proof of (cNUMBER Xn0)
% 250.62/250.81 Found x30:=(x3 x40):(cNUMBER Xn0)
% 250.62/250.81 Found (x3 x40) as proof of (cNUMBER Xn00)
% 250.62/250.81 Found (x3 x40) as proof of (cNUMBER Xn00)
% 250.62/250.81 Found (x3 x40) as proof of (cNUMBER Xn00)
% 254.41/254.65 Found x30:=(x3 x20):(cNUMBER Xn0)
% 254.41/254.65 Found (x3 x20) as proof of (cNUMBER Xn00)
% 254.41/254.65 Found (x3 x20) as proof of (cNUMBER Xn00)
% 254.41/254.65 Found (x3 x20) as proof of (cNUMBER Xn00)
% 254.41/254.65 Found x50:(cNUMBER Xn0)
% 254.41/254.65 Instantiate: Xn0:=(cS Xx):fofType
% 254.41/254.65 Found (fun (x13:(cNUMBER Xx))=> x50) as proof of (cNUMBER (cS Xx))
% 254.41/254.65 Found (fun (x13:(cNUMBER Xx))=> x50) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 254.41/254.65 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 254.41/254.65 Instantiate: Xn0:=Xn:fofType
% 254.41/254.65 Found (fun (x9:(cODD (cS c0)))=> x20) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 254.41/254.65 Found (fun (x9:(cODD (cS c0)))=> x20) as proof of ((cODD (cS c0))->((or (cEVEN Xn00)) (cODD Xn00)))
% 254.41/254.65 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 254.41/254.65 Instantiate: Xn00:=Xn:fofType
% 254.41/254.65 Found (fun (x9:(cODD (cS c0)))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 254.41/254.65 Found (fun (x9:(cODD (cS c0)))=> x40) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 254.41/254.65 Found x30:=(x3 x20):(cNUMBER Xn0)
% 254.41/254.65 Instantiate: Xn00:=Xn0:fofType
% 254.41/254.65 Found (x3 x20) as proof of (cNUMBER Xn00)
% 254.41/254.65 Found (x3 x20) as proof of (cNUMBER Xn00)
% 254.41/254.65 Found x30:=(x3 x20):(cNUMBER Xn0)
% 254.41/254.65 Instantiate: Xn0:=Xn:fofType
% 254.41/254.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 254.41/254.65 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 254.41/254.65 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 254.41/254.65 Found x30:=(x3 x20):(cNUMBER Xn0)
% 254.41/254.65 Found (x3 x20) as proof of (cNUMBER Xn0)
% 254.41/254.65 Found (x3 x20) as proof of (cNUMBER Xn0)
% 254.41/254.65 Found x30:=(x3 x21):(cNUMBER Xn0)
% 254.41/254.65 Instantiate: Xn0:=Xn:fofType
% 254.41/254.65 Found (x3 x21) as proof of (cNUMBER Xn)
% 254.41/254.65 Found (x3 x21) as proof of (cNUMBER Xn)
% 254.41/254.65 Found x30:=(x3 x21):(cNUMBER Xn0)
% 254.41/254.65 Found (x3 x21) as proof of (cNUMBER Xn)
% 254.41/254.65 Found (x3 x21) as proof of (cNUMBER Xn)
% 254.41/254.65 Found (x3 x21) as proof of (cNUMBER Xn)
% 254.41/254.65 Found x50:=(x5 x41):(cNUMBER Xn0)
% 254.41/254.65 Found (x5 x41) as proof of (cNUMBER Xn0)
% 254.41/254.65 Found (x5 x41) as proof of (cNUMBER Xn0)
% 254.41/254.65 Found x50:=(x5 x42):(cNUMBER Xn0)
% 254.41/254.65 Instantiate: Xn0:=Xn:fofType
% 254.41/254.65 Found (x5 x42) as proof of (cNUMBER Xn)
% 254.41/254.65 Found (x5 x42) as proof of (cNUMBER Xn)
% 254.41/254.65 Found x50:=(x5 x40):(cNUMBER Xn00)
% 254.41/254.65 Instantiate: Xn00:=Xn:fofType
% 254.41/254.65 Found (x5 x40) as proof of (cNUMBER Xn)
% 254.41/254.65 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 254.41/254.65 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 254.41/254.65 Found x50:=(x5 x40):(cNUMBER Xn00)
% 254.41/254.65 Instantiate: Xn00:=Xn:fofType
% 254.41/254.65 Found (x5 x40) as proof of (cNUMBER Xn)
% 254.41/254.65 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 254.41/254.65 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 254.41/254.65 Found x30:=(x3 x20):(cNUMBER Xn0)
% 254.41/254.65 Instantiate: Xn0:=Xn:fofType
% 254.41/254.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 254.41/254.65 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 254.41/254.65 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 254.41/254.65 Found x30:=(x3 x20):(cNUMBER Xn0)
% 254.41/254.65 Instantiate: Xn0:=Xn:fofType
% 254.41/254.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 254.41/254.65 Found (x3 x20) as proof of (cNUMBER Xn)
% 254.41/254.65 Found x30:=(x3 x20):(cNUMBER Xn0)
% 254.41/254.65 Found (x3 x20) as proof of (cNUMBER Xn0)
% 254.41/254.65 Found (x3 x20) as proof of (cNUMBER Xn0)
% 254.41/254.65 Found x30:=(x3 x21):(cNUMBER Xn0)
% 254.41/254.65 Instantiate: Xn0:=Xn:fofType
% 254.41/254.65 Found (x3 x21) as proof of (cNUMBER Xn)
% 254.41/254.65 Found (fun (x12:(cEVEN c0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 254.41/254.65 Found (fun (x12:(cEVEN c0))=> (x3 x21)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 254.41/254.65 Found x50:=(x5 x40):(cNUMBER Xn00)
% 254.41/254.65 Instantiate: Xn00:=Xn:fofType
% 254.41/254.65 Found (x5 x40) as proof of (cNUMBER Xn)
% 254.41/254.65 Found (x5 x40) as proof of (cNUMBER Xn)
% 254.41/254.65 Found x50:=(x5 x41):(cNUMBER Xn0)
% 254.41/254.65 Found (x5 x41) as proof of (cNUMBER Xn)
% 254.41/254.65 Found (x5 x41) as proof of (cNUMBER Xn)
% 254.41/254.65 Found (x5 x41) as proof of (cNUMBER Xn)
% 254.41/254.65 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 254.41/254.65 Instantiate: Xn00:=Xn:fofType
% 254.41/254.65 Found (fun (x9:(cODD (cS c0)))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 258.22/258.48 Found (fun (x9:(cODD (cS c0)))=> x40) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 258.22/258.48 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 258.22/258.48 Instantiate: Xn0:=Xn:fofType
% 258.22/258.48 Found (fun (x9:(cODD (cS c0)))=> x20) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 258.22/258.48 Found (fun (x9:(cODD (cS c0)))=> x20) as proof of ((cODD (cS c0))->((or (cEVEN Xn00)) (cODD Xn00)))
% 258.22/258.48 Found x50:=(x5 x41):(cNUMBER Xn00)
% 258.22/258.48 Instantiate: Xn00:=Xn:fofType
% 258.22/258.48 Found (x5 x41) as proof of (cNUMBER Xn)
% 258.22/258.48 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x41)) as proof of (cNUMBER Xn)
% 258.22/258.48 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x41)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 258.22/258.48 Found x90:=(x9 x80):(cNUMBER Xn00)
% 258.22/258.48 Instantiate: Xn00:=Xn:fofType
% 258.22/258.48 Found (x9 x80) as proof of (cNUMBER Xn)
% 258.22/258.48 Found (x9 x80) as proof of (cNUMBER Xn)
% 258.22/258.48 Found x50:=(x5 x40):(cNUMBER Xn0)
% 258.22/258.48 Instantiate: Xn0:=Xn:fofType
% 258.22/258.48 Found (x5 x40) as proof of (cNUMBER Xn)
% 258.22/258.48 Found (x5 x40) as proof of (cNUMBER Xn)
% 258.22/258.48 Found x30:=(x3 x20):(cNUMBER Xn0)
% 258.22/258.48 Instantiate: Xn0:=Xn:fofType
% 258.22/258.48 Found (x3 x20) as proof of (cNUMBER Xn)
% 258.22/258.48 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 258.22/258.48 Found (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 258.22/258.48 Found (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 258.22/258.48 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 258.22/258.48 Instantiate: Xn00:=Xn:fofType
% 258.22/258.48 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 258.22/258.48 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 258.22/258.48 Instantiate: Xn0:=Xn:fofType
% 258.22/258.48 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 258.22/258.48 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 258.22/258.48 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 258.22/258.48 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 258.22/258.48 Found x30:=(x3 x21):(cNUMBER Xn0)
% 258.22/258.48 Found (x3 x21) as proof of (cNUMBER Xn0)
% 258.22/258.48 Found (x3 x21) as proof of (cNUMBER Xn0)
% 258.22/258.48 Found x30:=(x3 x22):(cNUMBER Xn0)
% 258.22/258.48 Instantiate: Xn0:=Xn:fofType
% 258.22/258.48 Found (x3 x22) as proof of (cNUMBER Xn)
% 258.22/258.48 Found (fun (x7:(cODD (cS c0)))=> (x3 x22)) as proof of (cNUMBER Xn)
% 258.22/258.48 Found (fun (x7:(cODD (cS c0)))=> (x3 x22)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 258.22/258.48 Found x41:((or (cEVEN Xn00)) (cODD Xn00))
% 258.22/258.48 Instantiate: Xn00:=Xn:fofType
% 258.22/258.48 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x41) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 258.22/258.48 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x41) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->((or (cEVEN Xn0)) (cODD Xn0)))
% 258.22/258.48 Found x20:=(x2 x31):((or (cEVEN Xn0)) (cODD Xn0))
% 258.22/258.48 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 258.22/258.48 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 258.22/258.48 Found x30:(cNUMBER Xn0)
% 258.22/258.48 Instantiate: Xn0:=Xn:fofType
% 258.22/258.48 Found (fun (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 258.22/258.48 Found (fun (x5:(cODD Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 258.22/258.48 Found (fun (x5:(cODD Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((cODD Xn0)->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 258.22/258.48 Found x30:(cNUMBER Xn0)
% 258.22/258.48 Instantiate: Xn0:=Xn:fofType
% 258.22/258.48 Found (fun (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 258.22/258.48 Found (fun (x5:(cEVEN Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 258.22/258.48 Found (fun (x5:(cEVEN Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((cEVEN Xn0)->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 258.22/258.48 Found ((or_ind00 (fun (x5:(cEVEN Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) (fun (x5:(cODD Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 259.53/259.73 Found (((or_ind0 ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) (fun (x5:(cODD Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 259.53/259.73 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) x20)) ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) (fun (x5:(cODD Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 259.53/259.73 Found ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x30))) ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) (fun (x5:(cODD Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 259.53/259.73 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00))))=> ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x30))) ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) (fun (x5:(cODD Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30))) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 259.53/259.73 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00))))=> ((((fun (P:Prop) (x5:((cEVEN Xn0)->P)) (x6:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x5) x6) (x2 x30))) ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))) (fun (x5:(cEVEN Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) (fun (x5:(cODD Xn0)) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30))) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 259.53/259.73 Found x50:(cNUMBER Xn0)
% 259.53/259.73 Instantiate: Xn0:=Xn:fofType
% 259.53/259.73 Found (fun (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 259.53/259.73 Found (fun (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 259.53/259.73 Found (fun (x8:(cEVEN Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 259.53/259.73 Found (fun (x8:(cEVEN Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of ((cEVEN Xn0)->(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))))
% 259.53/259.73 Found x50:(cNUMBER Xn0)
% 259.53/259.73 Instantiate: Xn0:=Xn:fofType
% 259.53/259.73 Found (fun (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of (cNUMBER Xn)
% 259.53/259.73 Found (fun (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 259.53/259.73 Found (fun (x8:(cODD Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 259.53/259.73 Found (fun (x8:(cODD Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50) as proof of ((cODD Xn0)->(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))))
% 260.40/260.61 Found ((or_ind00 (fun (x8:(cEVEN Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50)) (fun (x8:(cODD Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 260.40/260.61 Found (((or_ind0 (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))) (fun (x8:(cEVEN Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50)) (fun (x8:(cODD Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x50)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 260.40/260.61 Found ((((fun (P:Prop) (x8:((cEVEN Xn0)->P)) (x9:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x8) x9) x40)) (((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn)))) (fun (x8:(cEVEN Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x50)) (fun (x8:(cODD Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x50)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 260.40/260.61 Found ((((fun (P:Prop) (x8:((cEVEN Xn0)->P)) (x9:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x8) x9) (x4 x50))) (((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn)))) (fun (x8:(cEVEN Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x50)) (fun (x8:(cODD Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x50)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 260.40/260.61 Found ((((fun (P:Prop) (x8:((cEVEN Xn0)->P)) (x9:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x8) x9) (x4 x50))) (((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn)))) (fun (x8:(cEVEN Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x50)) (fun (x8:(cODD Xn0)) (x9:((and cIND) (cEVEN c0))) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x50)) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 260.40/260.61 Found x30:=(x3 x22):(cNUMBER Xn0)
% 260.40/260.61 Instantiate: Xn0:=Xn:fofType
% 260.40/260.61 Found (x3 x22) as proof of (cNUMBER Xn)
% 260.40/260.61 Found (fun (x7:(cODD (cS c0)))=> (x3 x22)) as proof of (cNUMBER Xn)
% 260.40/260.61 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x22)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 260.40/260.61 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> (x3 x22)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 260.40/260.61 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 260.40/260.61 Instantiate: Xn00:=Xn:fofType
% 260.40/260.61 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 260.40/260.61 Found x50:=(x5 x40):(cNUMBER Xn00)
% 260.40/260.61 Found (x5 x40) as proof of (cNUMBER Xn)
% 260.40/260.61 Found (x5 x40) as proof of (cNUMBER Xn)
% 260.40/260.61 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 260.40/260.61 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 260.40/260.61 Found x30:=(x3 x20):(cNUMBER Xn0)
% 260.40/260.61 Found (x3 x20) as proof of (cNUMBER Xn)
% 260.40/260.61 Found (x3 x20) as proof of (cNUMBER Xn)
% 260.40/260.61 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 260.40/260.61 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 260.40/260.61 Found x51:(cNUMBER Xn0)
% 261.31/261.54 Instantiate: Xn0:=Xn:fofType
% 261.31/261.54 Found (fun (x12:(cEVEN c0))=> x51) as proof of (cNUMBER Xn)
% 261.31/261.54 Found (fun (x12:(cEVEN c0))=> x51) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 261.31/261.54 Found x70:=(x7 x60):(cNUMBER Xn0)
% 261.31/261.54 Instantiate: Xn0:=Xn:fofType
% 261.31/261.54 Found (x7 x60) as proof of (cNUMBER Xn)
% 261.31/261.54 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 261.31/261.54 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 261.31/261.54 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 261.31/261.54 Instantiate: Xn00:=Xn:fofType
% 261.31/261.54 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 261.31/261.54 Found (fun (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 261.31/261.54 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of ((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0)))
% 261.31/261.54 Found (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50)) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))->((forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00)))))->((or (cEVEN Xn0)) (cODD Xn0))))
% 261.31/261.54 Found (and_rect30 (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 261.31/261.54 Found ((and_rect3 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 261.31/261.54 Found (((fun (P:Type) (x6:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 261.31/261.54 Found (((fun (P:Type) (x6:(((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->P)))=> (((((and_rect ((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))) P) x6) x0)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (cODD (cS c0)))) (x7:(forall (Xn00:fofType), ((cODD Xn00)->(cODD (cS (cS Xn00))))))=> (x4 x50))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 261.31/261.54 Found x70:(cNUMBER Xn0)
% 261.31/261.54 Instantiate: Xn0:=Xn:fofType
% 261.31/261.54 Found (fun (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of (cNUMBER Xn)
% 261.31/261.54 Found (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 261.31/261.54 Found (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of ((cEVEN Xn0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 261.31/261.54 Found x70:(cNUMBER Xn0)
% 261.71/261.97 Instantiate: Xn0:=Xn:fofType
% 261.71/261.97 Found (fun (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of (cNUMBER Xn)
% 261.71/261.97 Found (fun (x9:(cODD Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 261.71/261.97 Found (fun (x9:(cODD Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of ((cODD Xn0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 261.71/261.97 Found ((or_ind00 (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 261.71/261.97 Found (((or_ind0 ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 261.71/261.97 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) x60)) ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x70)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x70)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 261.71/261.97 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x6 x70))) ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x70)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x70)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 261.71/261.97 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x6 x70))) ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x70)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x70)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 261.71/261.97 Found x90:=(x9 x80):(cNUMBER Xn00)
% 261.71/261.97 Instantiate: Xn00:=Xn:fofType
% 261.71/261.97 Found (x9 x80) as proof of (cNUMBER Xn)
% 261.71/261.97 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 261.71/261.97 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 261.71/261.97 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 261.71/261.97 Instantiate: Xn0:=Xn:fofType
% 261.71/261.97 Found x21 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 261.71/261.97 Found (x5 x21) as proof of (cNUMBER Xn)
% 261.71/261.97 Found (x5 x21) as proof of (cNUMBER Xn)
% 261.71/261.97 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x21)) as proof of (cNUMBER Xn)
% 261.71/261.97 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x21)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 261.71/261.97 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x21)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 261.71/261.97 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 261.71/261.97 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 261.71/261.97 Found (x3 x21) as proof of (cNUMBER Xn)
% 261.71/261.97 Found (x3 x21) as proof of (cNUMBER Xn)
% 261.71/261.97 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 263.00/263.24 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 263.00/263.24 Found (fun (x4:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 263.00/263.24 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 263.00/263.24 Instantiate: Xn0:=Xn:fofType
% 263.00/263.24 Found x21 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 263.00/263.24 Found (x5 x21) as proof of (cNUMBER Xn)
% 263.00/263.24 Found (x5 x21) as proof of (cNUMBER Xn)
% 263.00/263.24 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x21)) as proof of (cNUMBER Xn)
% 263.00/263.24 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x21)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 263.00/263.24 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 263.00/263.24 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 263.00/263.24 Found (x3 x21) as proof of (cNUMBER Xn)
% 263.00/263.24 Found (x3 x21) as proof of (cNUMBER Xn)
% 263.00/263.24 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 263.00/263.24 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x21)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 263.00/263.24 Found or_comm_i100:=(or_comm_i10 x20):((or (cODD Xn0)) (cEVEN Xn0))
% 263.00/263.24 Found (or_comm_i10 x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 263.00/263.24 Found ((or_comm_i1 (cODD Xn0)) x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 263.00/263.24 Found (((or_comm_i (cEVEN Xn0)) (cODD Xn0)) x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 263.00/263.24 Found (((or_comm_i (cEVEN Xn0)) (cODD Xn0)) x20) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 263.00/263.24 Found x30:=(x3 x21):(cNUMBER Xn0)
% 263.00/263.24 Instantiate: Xn0:=Xn:fofType
% 263.00/263.24 Found (x3 x21) as proof of (cNUMBER Xn)
% 263.00/263.24 Found (fun (x6:(cEVEN Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 263.00/263.24 Found (fun (x6:(cEVEN Xn0))=> (x3 x21)) as proof of ((cEVEN Xn0)->(cNUMBER Xn))
% 263.00/263.24 Found x30:=(x3 x21):(cNUMBER Xn0)
% 263.00/263.24 Instantiate: Xn0:=Xn:fofType
% 263.00/263.24 Found (x3 x21) as proof of (cNUMBER Xn)
% 263.00/263.24 Found (fun (x6:(cODD Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 263.00/263.24 Found (fun (x6:(cODD Xn0))=> (x3 x21)) as proof of ((cODD Xn0)->(cNUMBER Xn))
% 263.00/263.24 Found ((or_ind00 (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 263.00/263.24 Found (((or_ind0 (cNUMBER Xn)) (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 263.00/263.24 Found ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) x20)) (cNUMBER Xn)) (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 263.00/263.24 Found (fun (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) x20)) (cNUMBER Xn)) (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21)))) as proof of (cNUMBER Xn)
% 263.00/263.24 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) x20)) (cNUMBER Xn)) (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21)))) as proof of ((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn))
% 263.00/263.24 Found (fun (x4:((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))) (x5:(forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0))))))=> ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) x20)) (cNUMBER Xn)) (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21)))) as proof of (((and ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0)))->((forall (Xn0:fofType), ((cODD Xn0)->(cODD (cS (cS Xn0)))))->(cNUMBER Xn)))
% 267.30/267.57 Found x30:=(x3 x20):(cNUMBER Xn0)
% 267.30/267.57 Instantiate: Xn0:=(cS Xx):fofType
% 267.30/267.57 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 267.30/267.57 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 267.30/267.57 Found x30:=(x3 x21):(cNUMBER Xn0)
% 267.30/267.57 Instantiate: Xn0:=Xn:fofType
% 267.30/267.57 Found (x3 x21) as proof of (cNUMBER Xn)
% 267.30/267.57 Found (fun (x6:(cODD Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 267.30/267.57 Found (fun (x6:(cODD Xn0))=> (x3 x21)) as proof of ((cODD Xn0)->(cNUMBER Xn))
% 267.30/267.57 Found x30:=(x3 x21):(cNUMBER Xn0)
% 267.30/267.57 Instantiate: Xn0:=Xn:fofType
% 267.30/267.57 Found (x3 x21) as proof of (cNUMBER Xn)
% 267.30/267.57 Found (fun (x6:(cEVEN Xn0))=> (x3 x21)) as proof of (cNUMBER Xn)
% 267.30/267.57 Found (fun (x6:(cEVEN Xn0))=> (x3 x21)) as proof of ((cEVEN Xn0)->(cNUMBER Xn))
% 267.30/267.57 Found ((or_ind00 (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 267.30/267.57 Found (((or_ind0 (cNUMBER Xn)) (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 267.30/267.57 Found ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) x20)) (cNUMBER Xn)) (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 267.30/267.57 Found ((((fun (P:Prop) (x6:((cEVEN Xn0)->P)) (x7:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x6) x7) x20)) (cNUMBER Xn)) (fun (x6:(cEVEN Xn0))=> (x3 x21))) (fun (x6:(cODD Xn0))=> (x3 x21))) as proof of (cNUMBER Xn)
% 267.30/267.57 Found x40:(cNUMBER Xn00)
% 267.30/267.57 Instantiate: Xn0:=Xn00:fofType
% 267.30/267.57 Found x40 as proof of (cNUMBER Xn0)
% 267.30/267.57 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 267.30/267.57 Instantiate: Xn0:=Xn:fofType
% 267.30/267.57 Found x21 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 267.30/267.57 Found (x5 x21) as proof of (cNUMBER Xn)
% 267.30/267.57 Found (x5 x21) as proof of (cNUMBER Xn)
% 267.30/267.57 Found (x5 x21) as proof of (cNUMBER Xn)
% 267.30/267.57 Found x21:((or (cEVEN Xn0)) (cODD Xn0))
% 267.30/267.57 Found x21 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 267.30/267.57 Found (x3 x21) as proof of (cNUMBER Xn)
% 267.30/267.57 Found (x3 x21) as proof of (cNUMBER Xn)
% 267.30/267.57 Found (x3 x21) as proof of (cNUMBER Xn)
% 267.30/267.57 Found x32:(cNUMBER Xn0)
% 267.30/267.57 Instantiate: Xn0:=Xn:fofType
% 267.30/267.57 Found (fun (x7:(cODD (cS c0)))=> x32) as proof of (cNUMBER Xn)
% 267.30/267.57 Found (fun (x7:(cODD (cS c0)))=> x32) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 267.30/267.57 Found x32:(cNUMBER Xn0)
% 267.30/267.57 Instantiate: Xn0:=Xn:fofType
% 267.30/267.57 Found (fun (x7:(cODD (cS c0)))=> x32) as proof of (cNUMBER Xn)
% 267.30/267.57 Found (fun (x7:(cODD (cS c0)))=> x32) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 267.30/267.57 Found x90:=(x9 x80):(cNUMBER Xn00)
% 267.30/267.57 Found (x9 x80) as proof of (cNUMBER Xn)
% 267.30/267.57 Found (x9 x80) as proof of (cNUMBER Xn)
% 267.30/267.57 Found (x9 x80) as proof of (cNUMBER Xn)
% 267.30/267.57 Found x30:=(x3 x20):(cNUMBER Xn0)
% 267.30/267.57 Found (x3 x20) as proof of (cNUMBER Xn)
% 267.30/267.57 Found (x3 x20) as proof of (cNUMBER Xn)
% 267.30/267.57 Found (x3 x20) as proof of (cNUMBER Xn)
% 267.30/267.57 Found x50:=(x5 x40):(cNUMBER Xn0)
% 267.30/267.57 Instantiate: Xn0:=Xn:fofType
% 267.30/267.57 Found (x5 x40) as proof of (cNUMBER Xn)
% 267.30/267.57 Found (x5 x40) as proof of (cNUMBER Xn)
% 267.30/267.57 Found x70:=(x7 x60):(cNUMBER Xn00)
% 267.30/267.57 Instantiate: Xn00:=Xn:fofType
% 267.30/267.57 Found (x7 x60) as proof of (cNUMBER Xn)
% 267.30/267.57 Found (x7 x60) as proof of (cNUMBER Xn)
% 267.30/267.57 Found x50:=(x5 x41):(cNUMBER Xn0)
% 267.30/267.57 Found (x5 x41) as proof of (cNUMBER Xn0)
% 267.30/267.57 Found (x5 x41) as proof of (cNUMBER Xn0)
% 267.30/267.57 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 267.30/267.57 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 267.30/267.57 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 267.30/267.57 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 267.30/267.57 Found (fun (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 267.30/267.57 Found (fun (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 267.30/267.57 Found (and_rect40 (fun (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 268.08/268.28 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 268.08/268.28 Found (((fun (P:Type) (x7:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 268.08/268.28 Found (((fun (P:Type) (x7:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x7) x4)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x7:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 268.08/268.28 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 268.08/268.28 Instantiate: Xn00:=Xn:fofType
% 268.08/268.28 Found (fun (x9:(cODD (cS c0)))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 268.08/268.28 Found (fun (x9:(cODD (cS c0)))=> x40) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 268.08/268.28 Found x13:(cNUMBER Xx)
% 268.08/268.28 Instantiate: Xn0:=Xx:fofType
% 268.08/268.28 Found x13 as proof of (cNUMBER Xn0)
% 268.08/268.28 Found x70:(cNUMBER Xn0)
% 268.08/268.28 Instantiate: Xn0:=(cS Xx):fofType
% 268.08/268.28 Found x70 as proof of (cNUMBER (cS Xx))
% 268.08/268.28 Found x12:(cEVEN c0)
% 268.08/268.28 Instantiate: Xn0:=c0:fofType
% 268.08/268.28 Found (fun (x12:(cEVEN c0))=> x12) as proof of (cEVEN Xn0)
% 268.08/268.28 Found (fun (x11:cIND) (x12:(cEVEN c0))=> x12) as proof of ((cEVEN c0)->(cEVEN Xn0))
% 268.08/268.28 Found (fun (x11:cIND) (x12:(cEVEN c0))=> x12) as proof of (cIND->((cEVEN c0)->(cEVEN Xn0)))
% 268.08/268.28 Found (and_rect50 (fun (x11:cIND) (x12:(cEVEN c0))=> x12)) as proof of (cEVEN Xn0)
% 268.08/268.28 Found ((and_rect5 (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12)) as proof of (cEVEN Xn0)
% 268.08/268.28 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x6)) (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12)) as proof of (cEVEN Xn0)
% 268.08/268.28 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x6)) (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12)) as proof of (cEVEN Xn0)
% 268.08/268.28 Found (or_introl00 (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x6)) (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 268.08/268.28 Found ((or_introl0 (cODD Xn0)) (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x6)) (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 268.08/268.28 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x6)) (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 268.08/268.28 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x6)) (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 268.08/268.28 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 268.08/268.28 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 268.08/268.28 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 268.08/268.28 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 268.08/268.28 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 269.39/269.61 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 269.39/269.61 Found (and_rect40 (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 269.39/269.61 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 269.39/269.61 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 269.39/269.61 Found (((fun (P:Type) (x6:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x6) x2)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 269.39/269.61 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 269.39/269.61 Instantiate: Xn0:=Xn00:fofType
% 269.39/269.61 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 269.39/269.61 Found (x3 x40) as proof of (cNUMBER Xn0)
% 269.39/269.61 Found (x3 x40) as proof of (cNUMBER Xn0)
% 269.39/269.61 Found x70:=(x7 x60):(cNUMBER Xn00)
% 269.39/269.61 Instantiate: Xn00:=Xn:fofType
% 269.39/269.61 Found (x7 x60) as proof of (cNUMBER Xn)
% 269.39/269.61 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 269.39/269.61 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 269.39/269.61 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 269.39/269.61 Found x30:=(x3 x20):(cNUMBER Xn0)
% 269.39/269.61 Instantiate: Xn0:=Xn:fofType
% 269.39/269.61 Found (x3 x20) as proof of (cNUMBER Xn)
% 269.39/269.61 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 269.39/269.61 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 269.39/269.61 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 269.39/269.61 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 269.39/269.61 Instantiate: Xn00:=Xn0:fofType
% 269.39/269.61 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 269.39/269.61 Found (x5 x20) as proof of (cNUMBER Xn00)
% 269.39/269.61 Found (x5 x20) as proof of (cNUMBER Xn00)
% 269.39/269.61 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 269.39/269.61 Instantiate: Xn0:=Xn00:fofType
% 269.39/269.61 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 269.39/269.61 Found (x3 x40) as proof of (cNUMBER Xn0)
% 269.39/269.61 Found (x3 x40) as proof of (cNUMBER Xn0)
% 269.39/269.61 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 269.39/269.61 Instantiate: Xn00:=Xn0:fofType
% 269.39/269.61 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 269.39/269.61 Found (x5 x20) as proof of (cNUMBER Xn00)
% 269.39/269.61 Found (x5 x20) as proof of (cNUMBER Xn00)
% 269.39/269.61 Found x30:=(x3 x20):(cNUMBER Xn0)
% 269.39/269.61 Found (x3 x20) as proof of (cNUMBER Xn0)
% 269.39/269.61 Found (x3 x20) as proof of (cNUMBER Xn0)
% 269.39/269.61 Found x30:=(x3 x21):(cNUMBER Xn0)
% 269.39/269.61 Instantiate: Xn0:=Xn:fofType
% 270.60/270.83 Found (x3 x21) as proof of (cNUMBER Xn)
% 270.60/270.83 Found (x3 x21) as proof of (cNUMBER Xn)
% 270.60/270.83 Found x30:=(x3 x20):(cNUMBER Xn0)
% 270.60/270.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 270.60/270.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 270.60/270.83 Found (x3 x20) as proof of (cNUMBER Xn)
% 270.60/270.83 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 270.60/270.83 Instantiate: Xn00:=Xn:fofType
% 270.60/270.83 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 270.60/270.83 Found x60:((or (cEVEN Xn0)) (cODD Xn0))
% 270.60/270.83 Instantiate: Xn0:=Xn:fofType
% 270.60/270.83 Found x60 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 270.60/270.83 Found x40:=(x4 x51):((or (cEVEN Xn0)) (cODD Xn0))
% 270.60/270.83 Found (x4 x51) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 270.60/270.83 Found (x4 x51) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 270.60/270.83 Found x52:(cNUMBER Xn0)
% 270.60/270.83 Instantiate: Xn0:=Xn:fofType
% 270.60/270.83 Found (fun (x7:(cODD (cS c0)))=> x52) as proof of (cNUMBER Xn)
% 270.60/270.83 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> x52) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 270.60/270.83 Found (fun (x6:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x7:(cODD (cS c0)))=> x52) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 270.60/270.83 Found x11:(cEVEN c0)
% 270.60/270.83 Instantiate: Xn0:=c0:fofType
% 270.60/270.83 Found x11 as proof of (cEVEN Xn0)
% 270.60/270.83 Found (or_introl00 x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 270.60/270.83 Found ((or_introl0 (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 270.60/270.83 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 270.60/270.83 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 270.60/270.83 Found (x7 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)) as proof of (cNUMBER Xn0)
% 270.60/270.83 Found (fun (x11:(cEVEN c0))=> (x7 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11))) as proof of (cNUMBER Xn0)
% 270.60/270.83 Found (fun (x9:cIND) (x11:(cEVEN c0))=> (x7 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11))) as proof of ((cEVEN c0)->(cNUMBER Xn0))
% 270.60/270.83 Found (fun (x9:cIND) (x11:(cEVEN c0))=> (x7 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11))) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn0)))
% 270.60/270.83 Found (and_rect50 (fun (x9:cIND) (x11:(cEVEN c0))=> (x7 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)))) as proof of (cNUMBER Xn0)
% 270.60/270.83 Found ((and_rect5 (cNUMBER Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> (x7 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)))) as proof of (cNUMBER Xn0)
% 270.60/270.83 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) (cNUMBER Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> (x7 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)))) as proof of (cNUMBER Xn0)
% 270.60/270.83 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x8)) (cNUMBER Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> (x7 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x11)))) as proof of (cNUMBER Xn0)
% 270.60/270.83 Found x50:=(x5 x40):(cNUMBER Xn0)
% 270.60/270.83 Found (x5 x40) as proof of (cNUMBER Xn0)
% 270.60/270.83 Found (x5 x40) as proof of (cNUMBER Xn0)
% 270.60/270.83 Found x50:=(x5 x41):(cNUMBER Xn0)
% 270.60/270.83 Instantiate: Xn0:=Xn:fofType
% 270.60/270.83 Found (x5 x41) as proof of (cNUMBER Xn)
% 270.60/270.83 Found (fun (x12:(cEVEN c0))=> (x5 x41)) as proof of (cNUMBER Xn)
% 270.60/270.83 Found (fun (x12:(cEVEN c0))=> (x5 x41)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 270.60/270.83 Found x30:=(x3 x20):(cNUMBER Xn0)
% 270.60/270.83 Found (x3 x20) as proof of (cNUMBER Xn00)
% 270.60/270.83 Found (x3 x20) as proof of (cNUMBER Xn00)
% 270.60/270.83 Found (x3 x20) as proof of (cNUMBER Xn00)
% 270.60/270.83 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn00)) (cODD (cS c0))))
% 270.60/270.83 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn00)) (cODD Xn00)))
% 270.60/270.83 Found ((or_intror (cEVEN Xn00)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn00)) (cODD Xn00)))
% 270.60/270.83 Found ((or_intror (cEVEN Xn00)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn00)) (cODD Xn00)))
% 270.60/270.83 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))))=> ((or_intror (cEVEN Xn00)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn00)) (cODD Xn00)))
% 270.60/270.83 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))))=> ((or_intror (cEVEN Xn00)) (cODD (cS c0)))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->((or (cEVEN Xn00)) (cODD Xn00))))
% 271.39/271.67 Found (and_rect40 (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))))=> ((or_intror (cEVEN Xn00)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 271.39/271.67 Found ((and_rect4 ((or (cEVEN Xn00)) (cODD Xn00))) (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))))=> ((or_intror (cEVEN Xn00)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 271.39/271.67 Found (((fun (P:Type) (x8:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn00)) (cODD Xn00))) (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))))=> ((or_intror (cEVEN Xn00)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 271.39/271.67 Found (((fun (P:Type) (x8:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn00)) (cODD Xn00))) (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))))=> ((or_intror (cEVEN Xn00)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 271.39/271.67 Found or_intror00:=(or_intror0 (cODD (cS c0))):((cODD (cS c0))->((or (cEVEN Xn0)) (cODD (cS c0))))
% 271.39/271.67 Found (or_intror0 (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 271.39/271.67 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 271.39/271.67 Found ((or_intror (cEVEN Xn0)) (cODD (cS c0))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 271.39/271.67 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 271.39/271.67 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0)))) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 271.39/271.67 Found (and_rect40 (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 271.39/271.67 Found ((and_rect4 ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 271.39/271.67 Found (((fun (P:Type) (x8:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 271.39/271.67 Found (((fun (P:Type) (x8:(((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->P)))=> (((((and_rect ((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (cODD (cS c0))) P) x8) x6)) ((or (cEVEN Xn0)) (cODD Xn0))) (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))))=> ((or_intror (cEVEN Xn0)) (cODD (cS c0))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 271.39/271.67 Found x30:(cNUMBER Xn0)
% 271.39/271.67 Instantiate: Xn0:=Xn:fofType
% 271.51/271.72 Found (fun (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 271.51/271.72 Found (fun (x5:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 271.51/271.72 Found (fun (x4:(cEVEN Xn0)) (x5:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 271.51/271.72 Found (fun (x4:(cEVEN Xn0)) (x5:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((cEVEN Xn0)->(((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))))
% 271.51/271.72 Found x30:(cNUMBER Xn0)
% 271.51/271.72 Instantiate: Xn0:=Xn:fofType
% 271.51/271.72 Found (fun (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (cNUMBER Xn)
% 271.51/271.72 Found (fun (x5:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 271.51/271.72 Found (fun (x4:(cODD Xn0)) (x5:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 271.51/271.72 Found (fun (x4:(cODD Xn0)) (x5:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30) as proof of ((cODD Xn0)->(((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))))
% 271.51/271.72 Found ((or_ind00 (fun (x4:(cEVEN Xn0)) (x5:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) (fun (x4:(cODD Xn0)) (x5:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 271.51/271.72 Found (((or_ind0 (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))) (fun (x4:(cEVEN Xn0)) (x5:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) (fun (x4:(cODD Xn0)) (x5:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 271.51/271.72 Found ((((fun (P:Prop) (x4:((cEVEN Xn0)->P)) (x5:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x4) x5) x20)) (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))) (fun (x4:(cEVEN Xn0)) (x5:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) (fun (x4:(cODD Xn0)) (x5:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 271.51/271.72 Found ((((fun (P:Prop) (x4:((cEVEN Xn0)->P)) (x5:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x4) x5) (x2 x30))) (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))) (fun (x4:(cEVEN Xn0)) (x5:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) (fun (x4:(cODD Xn0)) (x5:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 271.51/271.72 Found ((((fun (P:Prop) (x4:((cEVEN Xn0)->P)) (x5:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x4) x5) (x2 x30))) (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))) (fun (x4:(cEVEN Xn0)) (x5:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) (fun (x4:(cODD Xn0)) (x5:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x6:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x30)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 272.67/272.94 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 272.67/272.94 Instantiate: Xn0:=Xn:fofType
% 272.67/272.94 Found (fun (x9:(cODD (cS c0)))=> x20) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 272.67/272.94 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x20) as proof of ((cODD (cS c0))->((or (cEVEN Xn00)) (cODD Xn00)))
% 272.67/272.94 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x20) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->((or (cEVEN Xn00)) (cODD Xn00))))
% 272.67/272.94 Found x40:=(x4 x50):((or (cEVEN Xn0)) (cODD Xn0))
% 272.67/272.94 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 272.67/272.94 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 272.67/272.94 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 272.67/272.94 Instantiate: Xn00:=Xn:fofType
% 272.67/272.94 Found (fun (x9:(cODD (cS c0)))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 272.67/272.94 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x40) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 272.67/272.94 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x40) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 272.67/272.94 Found x7:(cODD (cS c0))
% 272.67/272.94 Instantiate: Xn0:=(cS c0):fofType
% 272.67/272.94 Found x7 as proof of (cODD Xn0)
% 272.67/272.94 Found (or_introl00 x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 272.67/272.94 Found ((or_introl0 (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 272.67/272.94 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 272.67/272.94 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 272.67/272.94 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 272.67/272.94 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 272.67/272.94 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 272.67/272.94 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 272.67/272.94 Found x50:=(x5 x40):(cNUMBER Xn0)
% 272.67/272.94 Instantiate: Xn0:=Xn:fofType
% 272.67/272.94 Found (x5 x40) as proof of (cNUMBER Xn)
% 272.67/272.94 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 272.67/272.94 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 272.67/272.94 Found x50:(cNUMBER Xn00)
% 272.67/272.94 Instantiate: Xn0:=Xn00:fofType
% 272.67/272.94 Found x50 as proof of (cNUMBER Xn0)
% 272.67/272.94 Found (x2 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 272.67/272.94 Found (x2 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 272.67/272.94 Found x7:(cODD (cS c0))
% 272.67/272.94 Instantiate: Xn0:=(cS c0):fofType
% 272.67/272.94 Found x7 as proof of (cODD Xn0)
% 272.67/272.94 Found (or_introl00 x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 272.67/272.94 Found ((or_introl0 (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 272.67/272.94 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 272.67/272.94 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 272.67/272.94 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 272.67/272.94 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 275.00/275.28 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 275.00/275.28 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x7)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 275.00/275.28 Found x30:(cNUMBER Xn0)
% 275.00/275.28 Instantiate: Xn00:=Xn0:fofType
% 275.00/275.28 Found x30 as proof of (cNUMBER Xn00)
% 275.00/275.28 Found (x4 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 275.00/275.28 Found (x4 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 275.00/275.28 Found x50:=(x5 x40):(cNUMBER Xn00)
% 275.00/275.28 Instantiate: Xn00:=Xn:fofType
% 275.00/275.28 Found (x5 x40) as proof of (cNUMBER Xn)
% 275.00/275.28 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 275.00/275.28 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 275.00/275.28 Found x30:=(x3 x20):(cNUMBER Xn0)
% 275.00/275.28 Instantiate: Xn0:=Xn:fofType
% 275.00/275.28 Found (x3 x20) as proof of (cNUMBER Xn)
% 275.00/275.28 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 275.00/275.28 Found (fun (x5:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 275.00/275.28 Found x90:=(x9 x80):(cNUMBER Xn00)
% 275.00/275.28 Instantiate: Xn00:=Xn:fofType
% 275.00/275.28 Found (x9 x80) as proof of (cNUMBER Xn)
% 275.00/275.28 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 275.00/275.28 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 275.00/275.28 Found x12:(cEVEN c0)
% 275.00/275.28 Found x12 as proof of (cEVEN c0)
% 275.00/275.28 Found x50:=(x5 x42):(cNUMBER Xn0)
% 275.00/275.28 Instantiate: Xn0:=Xn:fofType
% 275.00/275.28 Found (x5 x42) as proof of (cNUMBER Xn)
% 275.00/275.28 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x42)) as proof of (cNUMBER Xn)
% 275.00/275.28 Found (fun (x5:(((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0)))=> (x5 x42)) as proof of ((((or (cEVEN Xn0)) (cODD Xn0))->(cNUMBER Xn0))->(cNUMBER Xn))
% 275.00/275.28 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 275.00/275.28 Instantiate: Xn0:=Xn:fofType
% 275.00/275.28 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 275.00/275.28 Found x70:=(x7 x60):(cNUMBER Xn0)
% 275.00/275.28 Found (x7 x60) as proof of (cNUMBER Xn0)
% 275.00/275.28 Found (x7 x60) as proof of (cNUMBER Xn0)
% 275.00/275.28 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 275.00/275.28 Instantiate: Xn00:=Xn:fofType
% 275.00/275.28 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 275.00/275.28 Found x5:(cODD (cS c0))
% 275.00/275.28 Instantiate: Xn0:=(cS c0):fofType
% 275.00/275.28 Found x5 as proof of (cODD Xn0)
% 275.00/275.28 Found (or_introl00 x5) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 275.00/275.28 Found ((or_introl0 (cEVEN Xn0)) x5) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 275.00/275.28 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 275.00/275.28 Found (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 275.00/275.28 Found (or_comm_i00 (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 275.00/275.28 Found ((or_comm_i0 (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 275.00/275.28 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 275.00/275.28 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((or_introl (cODD Xn0)) (cEVEN Xn0)) x5)) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 275.00/275.28 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 275.00/275.28 Instantiate: Xn00:=Xn:fofType
% 275.00/275.28 Found (fun (x9:(cODD (cS c0)))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 275.00/275.28 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x40) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 275.00/275.28 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x40) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 275.00/275.28 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 275.00/275.28 Instantiate: Xn0:=Xn:fofType
% 275.00/275.28 Found (fun (x9:(cODD (cS c0)))=> x20) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 278.27/278.49 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x20) as proof of ((cODD (cS c0))->((or (cEVEN Xn00)) (cODD Xn00)))
% 278.27/278.49 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> x20) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->((or (cEVEN Xn00)) (cODD Xn00))))
% 278.27/278.49 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 278.27/278.49 Instantiate: Xn00:=Xn:fofType
% 278.27/278.49 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.27/278.49 Found x12:(cEVEN c0)
% 278.27/278.49 Instantiate: Xn0:=c0:fofType
% 278.27/278.49 Found x12 as proof of (cEVEN Xn0)
% 278.27/278.49 Found (or_introl00 x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.27/278.49 Found ((or_introl0 (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.27/278.49 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.27/278.49 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.27/278.49 Found (x5 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12)) as proof of (cNUMBER Xn0)
% 278.27/278.49 Found (fun (x12:(cEVEN c0))=> (x5 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12))) as proof of (cNUMBER Xn0)
% 278.27/278.49 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12))) as proof of ((cEVEN c0)->(cNUMBER Xn0))
% 278.27/278.49 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12))) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn0)))
% 278.27/278.49 Found (and_rect50 (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12)))) as proof of (cNUMBER Xn0)
% 278.27/278.49 Found ((and_rect5 (cNUMBER Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12)))) as proof of (cNUMBER Xn0)
% 278.27/278.49 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12)))) as proof of (cNUMBER Xn0)
% 278.27/278.49 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cNUMBER Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12)))) as proof of (cNUMBER Xn0)
% 278.27/278.49 Found x30:=(x3 x21):(cNUMBER Xn0)
% 278.27/278.49 Found (x3 x21) as proof of (cNUMBER Xn0)
% 278.27/278.49 Found (x3 x21) as proof of (cNUMBER Xn0)
% 278.27/278.49 Found x30:=(x3 x22):(cNUMBER Xn0)
% 278.27/278.49 Instantiate: Xn0:=Xn:fofType
% 278.27/278.49 Found (x3 x22) as proof of (cNUMBER Xn)
% 278.27/278.49 Found (fun (x7:(cODD (cS c0)))=> (x3 x22)) as proof of (cNUMBER Xn)
% 278.27/278.49 Found (fun (x7:(cODD (cS c0)))=> (x3 x22)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 278.27/278.49 Found x11:(cEVEN c0)
% 278.27/278.49 Instantiate: Xn0:=c0:fofType
% 278.27/278.49 Found (fun (x11:(cEVEN c0))=> x11) as proof of (cEVEN Xn0)
% 278.27/278.49 Found (fun (x9:cIND) (x11:(cEVEN c0))=> x11) as proof of ((cEVEN c0)->(cEVEN Xn0))
% 278.27/278.49 Found (fun (x9:cIND) (x11:(cEVEN c0))=> x11) as proof of (cIND->((cEVEN c0)->(cEVEN Xn0)))
% 278.27/278.49 Found (and_rect50 (fun (x9:cIND) (x11:(cEVEN c0))=> x11)) as proof of (cEVEN Xn0)
% 278.27/278.49 Found ((and_rect5 (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11)) as proof of (cEVEN Xn0)
% 278.27/278.49 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11)) as proof of (cEVEN Xn0)
% 278.27/278.49 Found (fun (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))) as proof of (cEVEN Xn0)
% 278.27/278.49 Found (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0))
% 278.27/278.49 Found (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))) as proof of (((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0)))
% 278.41/278.61 Found (and_rect40 (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11)))) as proof of (cEVEN Xn0)
% 278.41/278.61 Found ((and_rect4 (cEVEN Xn0)) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11)))) as proof of (cEVEN Xn0)
% 278.41/278.61 Found (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) (cEVEN Xn0)) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11)))) as proof of (cEVEN Xn0)
% 278.41/278.61 Found (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) (cEVEN Xn0)) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11)))) as proof of (cEVEN Xn0)
% 278.41/278.61 Found (or_introl00 (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) (cEVEN Xn0)) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.41/278.61 Found ((or_introl0 (cODD Xn0)) (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x7) x6)) (cEVEN Xn0)) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.41/278.61 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x7) x6)) (cEVEN Xn0)) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.41/278.61 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x7) x6)) (cEVEN Xn0)) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) (cEVEN Xn0)) (fun (x9:cIND) (x11:(cEVEN c0))=> x11))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 278.41/278.61 Found x5:(cODD (cS c0))
% 278.41/278.61 Instantiate: Xn0:=(cS c0):fofType
% 280.52/280.80 Found x5 as proof of (cODD Xn0)
% 280.52/280.80 Found (or_intror00 x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 280.52/280.80 Found ((or_intror0 (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 280.52/280.80 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 280.52/280.80 Found (((or_intror (cEVEN Xn0)) (cODD Xn0)) x5) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 280.52/280.80 Found x12:(cEVEN c0)
% 280.52/280.80 Instantiate: Xn0:=c0:fofType
% 280.52/280.80 Found x12 as proof of (cEVEN Xn0)
% 280.52/280.80 Found (or_introl00 x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 280.52/280.80 Found ((or_introl0 (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 280.52/280.80 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 280.52/280.80 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) x12) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 280.52/280.80 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 280.52/280.80 Instantiate: Xn00:=Xn:fofType
% 280.52/280.80 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x80) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 280.52/280.80 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x80) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->((or (cEVEN Xn0)) (cODD Xn0)))
% 280.52/280.80 Found x30:=(x3 x21):(cNUMBER Xn0)
% 280.52/280.80 Found (x3 x21) as proof of (cNUMBER Xn0)
% 280.52/280.80 Found (x3 x21) as proof of (cNUMBER Xn0)
% 280.52/280.80 Found x30:=(x3 x22):(cNUMBER Xn0)
% 280.52/280.80 Instantiate: Xn0:=Xn:fofType
% 280.52/280.80 Found (x3 x22) as proof of (cNUMBER Xn)
% 280.52/280.80 Found (fun (x7:(cODD (cS c0)))=> (x3 x22)) as proof of (cNUMBER Xn)
% 280.52/280.80 Found (fun (x7:(cODD (cS c0)))=> (x3 x22)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 280.52/280.80 Found x50:=(x5 x40):(cNUMBER Xn00)
% 280.52/280.80 Found (x5 x40) as proof of (cNUMBER Xn0)
% 280.52/280.80 Found (x5 x40) as proof of (cNUMBER Xn0)
% 280.52/280.80 Found (x5 x40) as proof of (cNUMBER Xn0)
% 280.52/280.80 Found x60:=(x6 x70):((or (cEVEN Xn0)) (cODD Xn0))
% 280.52/280.80 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 280.52/280.80 Found (x6 x70) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 280.52/280.80 Found x71:(cNUMBER Xn0)
% 280.52/280.80 Instantiate: Xn0:=Xn:fofType
% 280.52/280.80 Found (fun (x12:(cEVEN c0))=> x71) as proof of (cNUMBER Xn)
% 280.52/280.80 Found (fun (x11:cIND) (x12:(cEVEN c0))=> x71) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 280.52/280.80 Found (fun (x11:cIND) (x12:(cEVEN c0))=> x71) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 280.52/280.80 Found x30:=(x3 x20):(cNUMBER Xn0)
% 280.52/280.80 Found (x3 x20) as proof of (cNUMBER Xn00)
% 280.52/280.80 Found (x3 x20) as proof of (cNUMBER Xn00)
% 280.52/280.80 Found (x3 x20) as proof of (cNUMBER Xn00)
% 280.52/280.80 Found x50:=(x5 x40):(cNUMBER Xn00)
% 280.52/280.80 Found (x5 x40) as proof of (cNUMBER Xn0)
% 280.52/280.80 Found (x5 x40) as proof of (cNUMBER Xn0)
% 280.52/280.80 Found (x5 x40) as proof of (cNUMBER Xn0)
% 280.52/280.80 Found x30:=(x3 x20):(cNUMBER Xn0)
% 280.52/280.80 Found (x3 x20) as proof of (cNUMBER Xn)
% 280.52/280.80 Found (x3 x20) as proof of (cNUMBER Xn)
% 280.52/280.80 Found (fun (x12:(cEVEN c0))=> (x3 x20)) as proof of (cNUMBER Xn)
% 280.52/280.80 Found (fun (x12:(cEVEN c0))=> (x3 x20)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 280.52/280.80 Found x30:=(x3 x20):(cNUMBER Xn0)
% 280.52/280.80 Found (x3 x20) as proof of (cNUMBER Xn00)
% 280.52/280.80 Found (x3 x20) as proof of (cNUMBER Xn00)
% 280.52/280.80 Found (x3 x20) as proof of (cNUMBER Xn00)
% 280.52/280.80 Found or_intror00:=(or_intror0 (cEVEN c0)):((cEVEN c0)->((or (cODD Xn0)) (cEVEN c0)))
% 280.52/280.80 Found (or_intror0 (cEVEN c0)) as proof of ((cEVEN c0)->((or (cODD Xn0)) (cEVEN Xn0)))
% 280.52/280.80 Found ((or_intror (cODD Xn0)) (cEVEN c0)) as proof of ((cEVEN c0)->((or (cODD Xn0)) (cEVEN Xn0)))
% 280.52/280.80 Found ((or_intror (cODD Xn0)) (cEVEN c0)) as proof of ((cEVEN c0)->((or (cODD Xn0)) (cEVEN Xn0)))
% 280.52/280.80 Found (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0))) as proof of ((cEVEN c0)->((or (cODD Xn0)) (cEVEN Xn0)))
% 280.52/280.80 Found (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0))) as proof of (cIND->((cEVEN c0)->((or (cODD Xn0)) (cEVEN Xn0))))
% 280.52/280.80 Found (and_rect50 (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 280.52/280.80 Found ((and_rect5 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 280.52/280.80 Found (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0)))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 280.52/280.80 Found (fun (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0))))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 280.52/280.82 Found (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0))))) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cODD Xn0)) (cEVEN Xn0)))
% 280.52/280.82 Found (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0))))) as proof of (((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->((or (cODD Xn0)) (cEVEN Xn0))))
% 280.52/280.82 Found (and_rect40 (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0)))))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 280.52/280.82 Found ((and_rect4 ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0)))))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 280.52/280.82 Found (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0)))))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 280.52/280.82 Found (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0)))))) as proof of ((or (cODD Xn0)) (cEVEN Xn0))
% 280.52/280.82 Found (or_comm_i00 (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 280.52/280.82 Found ((or_comm_i0 (cEVEN Xn0)) (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 282.38/282.61 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 282.38/282.61 Found (((or_comm_i (cODD Xn0)) (cEVEN Xn0)) (((fun (P:Type) (x7:(((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x7) x6)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x7:((and cIND) (cEVEN c0))) (x8:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x9:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x9) x7)) ((or (cODD Xn0)) (cEVEN Xn0))) (fun (x9:cIND)=> ((or_intror (cODD Xn0)) (cEVEN c0))))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 282.38/282.61 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 282.38/282.61 Instantiate: Xn00:=Xn:fofType
% 282.38/282.61 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 282.38/282.61 Found x20:=(x2 x31):((or (cEVEN Xn0)) (cODD Xn0))
% 282.38/282.61 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 282.38/282.61 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 282.38/282.61 Found x30:=(x3 x20):(cNUMBER Xn0)
% 282.38/282.61 Found (x3 x20) as proof of (cNUMBER Xn)
% 282.38/282.61 Found (x3 x20) as proof of (cNUMBER Xn)
% 282.38/282.61 Found (x3 x20) as proof of (cNUMBER Xn)
% 282.38/282.61 Found x20:=(x2 x31):((or (cEVEN Xn0)) (cODD Xn0))
% 282.38/282.61 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 282.38/282.61 Found (x2 x31) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 282.38/282.61 Found x70:=(x7 x60):(cNUMBER Xn00)
% 282.38/282.61 Found (x7 x60) as proof of (cNUMBER Xn)
% 282.38/282.61 Found (x7 x60) as proof of (cNUMBER Xn)
% 282.38/282.61 Found (x7 x60) as proof of (cNUMBER Xn)
% 282.38/282.61 Found x50:=(x5 x40):(cNUMBER Xn00)
% 282.38/282.61 Found (x5 x40) as proof of (cNUMBER Xn)
% 282.38/282.61 Found (x5 x40) as proof of (cNUMBER Xn)
% 282.38/282.61 Found (x5 x40) as proof of (cNUMBER Xn)
% 282.38/282.61 Found x12:(cEVEN c0)
% 282.38/282.61 Instantiate: Xn0:=c0:fofType
% 282.38/282.61 Found (fun (x12:(cEVEN c0))=> x12) as proof of (cEVEN Xn0)
% 282.38/282.61 Found (fun (x11:cIND) (x12:(cEVEN c0))=> x12) as proof of ((cEVEN c0)->(cEVEN Xn0))
% 282.38/282.61 Found (fun (x11:cIND) (x12:(cEVEN c0))=> x12) as proof of (cIND->((cEVEN c0)->(cEVEN Xn0)))
% 282.38/282.61 Found (and_rect50 (fun (x11:cIND) (x12:(cEVEN c0))=> x12)) as proof of (cEVEN Xn0)
% 282.38/282.61 Found ((and_rect5 (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12)) as proof of (cEVEN Xn0)
% 282.38/282.61 Found (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12)) as proof of (cEVEN Xn0)
% 282.38/282.61 Found (fun (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12))) as proof of (cEVEN Xn0)
% 282.38/282.61 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12))) as proof of ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0))
% 282.38/282.61 Found (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12))) as proof of (((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cEVEN Xn0)))
% 282.38/282.61 Found (and_rect40 (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12)))) as proof of (cEVEN Xn0)
% 282.71/282.95 Found ((and_rect4 (cEVEN Xn0)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12)))) as proof of (cEVEN Xn0)
% 282.71/282.95 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12)))) as proof of (cEVEN Xn0)
% 282.71/282.95 Found (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12)))) as proof of (cEVEN Xn0)
% 282.71/282.95 Found (or_introl00 (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 282.71/282.95 Found ((or_introl0 (cODD Xn0)) (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 282.71/282.95 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 282.71/282.95 Found (((or_introl (cEVEN Xn0)) (cODD Xn0)) (((fun (P:Type) (x8:(((and cIND) (cEVEN c0))->((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->P)))=> (((((and_rect ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))) P) x8) x6)) (cEVEN Xn0)) (fun (x8:((and cIND) (cEVEN c0))) (x9:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> (((fun (P:Type) (x11:(cIND->((cEVEN c0)->P)))=> (((((and_rect cIND) (cEVEN c0)) P) x11) x8)) (cEVEN Xn0)) (fun (x11:cIND) (x12:(cEVEN c0))=> x12))))) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 282.71/282.95 Found x50:=(x5 x40):(cNUMBER Xn00)
% 282.71/282.95 Found (x5 x40) as proof of (cNUMBER Xn)
% 282.71/282.95 Found (x5 x40) as proof of (cNUMBER Xn)
% 282.71/282.95 Found (x5 x40) as proof of (cNUMBER Xn)
% 282.71/282.95 Found x30:=(x3 x20):(cNUMBER Xn0)
% 282.71/282.95 Found (x3 x20) as proof of (cNUMBER Xn)
% 282.71/282.95 Found (x3 x20) as proof of (cNUMBER Xn)
% 282.71/282.95 Found (x3 x20) as proof of (cNUMBER Xn)
% 282.71/282.95 Found x30:=(x3 x20):(cNUMBER Xn0)
% 282.71/282.95 Found (x3 x20) as proof of (cNUMBER Xn)
% 282.71/282.95 Found (x3 x20) as proof of (cNUMBER Xn)
% 285.29/285.51 Found (x3 x20) as proof of (cNUMBER Xn)
% 285.29/285.51 Found x70:=(x7 x60):(cNUMBER Xn0)
% 285.29/285.51 Instantiate: Xn0:=Xn:fofType
% 285.29/285.51 Found (x7 x60) as proof of (cNUMBER Xn)
% 285.29/285.51 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 285.29/285.51 Found (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 285.29/285.51 Found (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x7 x60)) as proof of (((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))->((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn)))
% 285.29/285.51 Found x50:=(x5 x40):(cNUMBER Xn00)
% 285.29/285.51 Found (x5 x40) as proof of (cNUMBER Xn)
% 285.29/285.51 Found (x5 x40) as proof of (cNUMBER Xn)
% 285.29/285.51 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 285.29/285.51 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 285.29/285.51 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 285.29/285.51 Found x30:=(x3 x20):(cNUMBER Xn0)
% 285.29/285.51 Found (x3 x20) as proof of (cNUMBER Xn)
% 285.29/285.51 Found (x3 x20) as proof of (cNUMBER Xn)
% 285.29/285.51 Found (fun (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 285.29/285.51 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 285.29/285.51 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))) (x9:(cODD (cS c0)))=> (x3 x20)) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))->((cODD (cS c0))->(cNUMBER Xn)))
% 285.29/285.51 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 285.29/285.51 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 285.29/285.51 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 285.29/285.51 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 285.29/285.51 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 285.29/285.51 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 285.29/285.51 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 285.29/285.51 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 285.29/285.51 Found x51:(cNUMBER Xn0)
% 285.29/285.51 Instantiate: Xn0:=Xn:fofType
% 285.29/285.51 Found (fun (x12:(cEVEN c0))=> x51) as proof of (cNUMBER Xn)
% 285.29/285.51 Found (fun (x12:(cEVEN c0))=> x51) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 285.29/285.51 Found x40:((or (cEVEN Xn0)) (cODD Xn0))
% 285.29/285.51 Instantiate: Xn0:=Xn:fofType
% 285.29/285.51 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 285.29/285.51 Found x50:=(x5 x41):(cNUMBER Xn0)
% 285.29/285.51 Instantiate: Xn0:=Xn:fofType
% 285.29/285.51 Found (x5 x41) as proof of (cNUMBER Xn)
% 285.29/285.51 Found (fun (x12:(cEVEN c0))=> (x5 x41)) as proof of (cNUMBER Xn)
% 285.29/285.51 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x41)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 285.29/285.51 Found (fun (x11:cIND) (x12:(cEVEN c0))=> (x5 x41)) as proof of (cIND->((cEVEN c0)->(cNUMBER Xn)))
% 285.29/285.51 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 285.29/285.51 Instantiate: Xn00:=Xn:fofType
% 285.29/285.51 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 285.29/285.51 Found x50:(cNUMBER Xn0)
% 285.29/285.51 Instantiate: Xn0:=c0:fofType
% 285.29/285.51 Found x50 as proof of (cNUMBER c0)
% 285.29/285.51 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 285.29/285.51 Instantiate: Xn0:=Xn:fofType
% 285.29/285.51 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 285.29/285.51 Found (x5 x20) as proof of (cNUMBER Xn)
% 285.29/285.51 Found (x5 x20) as proof of (cNUMBER Xn)
% 285.29/285.51 Found (x5 x20) as proof of (cNUMBER Xn)
% 285.29/285.51 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 285.29/285.51 Found x20 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 285.29/285.51 Found (x3 x20) as proof of (cNUMBER Xn)
% 285.29/285.51 Found (x3 x20) as proof of (cNUMBER Xn)
% 285.29/285.51 Found (x3 x20) as proof of (cNUMBER Xn)
% 285.29/285.51 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 285.29/285.51 Instantiate: Xn00:=Xn:fofType
% 285.29/285.51 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 285.29/285.51 Found (x3 x40) as proof of (cNUMBER Xn)
% 285.29/285.51 Found (x3 x40) as proof of (cNUMBER Xn)
% 285.29/285.51 Found (x3 x40) as proof of (cNUMBER Xn)
% 285.29/285.51 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 285.90/286.15 Found x40 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 285.90/286.15 Found (x5 x40) as proof of (cNUMBER Xn)
% 285.90/286.15 Found (x5 x40) as proof of (cNUMBER Xn)
% 285.90/286.15 Found (x5 x40) as proof of (cNUMBER Xn)
% 285.90/286.15 Found x70:(cNUMBER Xn0)
% 285.90/286.15 Instantiate: Xn0:=Xn:fofType
% 285.90/286.15 Found (fun (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of (cNUMBER Xn)
% 285.90/286.15 Found (fun (x9:(cODD Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 285.90/286.15 Found (fun (x9:(cODD Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of ((cODD Xn0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 285.90/286.15 Found x70:(cNUMBER Xn0)
% 285.90/286.15 Instantiate: Xn0:=Xn:fofType
% 285.90/286.15 Found (fun (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of (cNUMBER Xn)
% 285.90/286.15 Found (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 285.90/286.15 Found (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70) as proof of ((cEVEN Xn0)->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 285.90/286.15 Found ((or_ind00 (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 285.90/286.15 Found (((or_ind0 ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0))))))=> x70)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 285.90/286.15 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) x60)) ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x70)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x70)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 285.90/286.15 Found ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x6 x70))) ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x70)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x70)) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 285.90/286.15 Found (fun (x8:((and cIND) (cEVEN c0)))=> ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x6 x70))) ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x70)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x70))) as proof of ((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn))
% 285.90/286.15 Found (fun (x8:((and cIND) (cEVEN c0)))=> ((((fun (P:Prop) (x9:((cEVEN Xn0)->P)) (x11:((cODD Xn0)->P))=> ((((((or_ind (cEVEN Xn0)) (cODD Xn0)) P) x9) x11) (x6 x70))) ((forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00)))))->(cNUMBER Xn))) (fun (x9:(cEVEN Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x70)) (fun (x9:(cODD Xn0)) (x11:(forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))=> x70))) as proof of (((and cIND) (cEVEN c0))->((forall (Xn0:fofType), ((cEVEN Xn0)->(cEVEN (cS (cS Xn0)))))->(cNUMBER Xn)))
% 285.90/286.15 Found x52:(cNUMBER Xn0)
% 289.76/289.99 Instantiate: Xn0:=Xn:fofType
% 289.76/289.99 Found (fun (x7:(cODD (cS c0)))=> x52) as proof of (cNUMBER Xn)
% 289.76/289.99 Found (fun (x7:(cODD (cS c0)))=> x52) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 289.76/289.99 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 289.76/289.99 Instantiate: Xn00:=Xn:fofType
% 289.76/289.99 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 289.76/289.99 Found (x4 x50) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 289.76/289.99 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 289.76/289.99 Instantiate: Xn0:=Xn:fofType
% 289.76/289.99 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 289.76/289.99 Found (x2 x30) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 289.76/289.99 Found x12:(cEVEN c0)
% 289.76/289.99 Found x12 as proof of (cEVEN c0)
% 289.76/289.99 Found x30:=(x3 x20):(cNUMBER Xn0)
% 289.76/289.99 Instantiate: Xn0:=(cS Xx):fofType
% 289.76/289.99 Found (x3 x20) as proof of (cNUMBER (cS Xx))
% 289.76/289.99 Found (fun (x13:(cNUMBER Xx))=> (x3 x20)) as proof of (cNUMBER (cS Xx))
% 289.76/289.99 Found (fun (x13:(cNUMBER Xx))=> (x3 x20)) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 289.76/289.99 Found x30:=(x3 x20):(cNUMBER Xn0)
% 289.76/289.99 Found (x3 x20) as proof of (cNUMBER Xn)
% 289.76/289.99 Found (x3 x20) as proof of (cNUMBER Xn)
% 289.76/289.99 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of (cNUMBER Xn)
% 289.76/289.99 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x3 x20)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 289.76/289.99 Found x70:=(x7 x60):(cNUMBER Xn00)
% 289.76/289.99 Instantiate: Xn00:=Xn:fofType
% 289.76/289.99 Found (x7 x60) as proof of (cNUMBER Xn)
% 289.76/289.99 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of (cNUMBER Xn)
% 289.76/289.99 Found (fun (x9:(cODD (cS c0)))=> (x7 x60)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 289.76/289.99 Found x50:=(x5 x40):(cNUMBER Xn0)
% 289.76/289.99 Instantiate: Xn0:=Xn:fofType
% 289.76/289.99 Found (x5 x40) as proof of (cNUMBER Xn)
% 289.76/289.99 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 289.76/289.99 Found (fun (x9:(cODD (cS c0)))=> (x5 x40)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 289.76/289.99 Found x90:=(x9 x80):(cNUMBER Xn00)
% 289.76/289.99 Found (x9 x80) as proof of (cNUMBER Xn)
% 289.76/289.99 Found (x9 x80) as proof of (cNUMBER Xn)
% 289.76/289.99 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of (cNUMBER Xn)
% 289.76/289.99 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x9 x80)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 289.76/289.99 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 289.76/289.99 Instantiate: Xn00:=Xn:fofType
% 289.76/289.99 Found x80 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 289.76/289.99 Found x20:=(x2 x31):((or (cEVEN Xn0)) (cODD Xn0))
% 289.76/289.99 Instantiate: Xn0:=Xn:fofType
% 289.76/289.99 Found (x2 x31) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 289.76/289.99 Found (x2 x31) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 289.76/289.99 Found x20:=(x2 x30):((or (cEVEN Xn0)) (cODD Xn0))
% 289.76/289.99 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 289.76/289.99 Found (x2 x30) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 289.76/289.99 Found x20:=(x2 x31):((or (cEVEN Xn0)) (cODD Xn0))
% 289.76/289.99 Found (x2 x31) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 289.76/289.99 Found (x2 x31) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 289.76/289.99 Found (x2 x31) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 289.76/289.99 Found x40:=(x4 x50):((or (cEVEN Xn00)) (cODD Xn00))
% 289.76/289.99 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 289.76/289.99 Found (x4 x50) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 289.76/289.99 Found x40:=(x4 x51):((or (cEVEN Xn00)) (cODD Xn00))
% 289.76/289.99 Instantiate: Xn00:=Xn:fofType
% 289.76/289.99 Found (x4 x51) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 289.76/289.99 Found (x4 x51) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 289.76/289.99 Found x40:=(x4 x51):((or (cEVEN Xn00)) (cODD Xn00))
% 289.76/289.99 Found (x4 x51) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 289.76/289.99 Found (x4 x51) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 289.76/289.99 Found (x4 x51) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 289.76/289.99 Found x12:(cEVEN c0)
% 289.76/289.99 Found x12 as proof of (cEVEN c0)
% 289.76/289.99 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 289.76/289.99 Instantiate: Xn00:=Xn0:fofType
% 289.76/289.99 Found x20 as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 289.76/289.99 Found (x5 x20) as proof of (cNUMBER Xn00)
% 289.76/289.99 Found (x5 x20) as proof of (cNUMBER Xn00)
% 289.76/289.99 Found x30:=(x3 x21):(cNUMBER Xn0)
% 289.76/289.99 Found (x3 x21) as proof of (cNUMBER Xn0)
% 289.76/289.99 Found (x3 x21) as proof of (cNUMBER Xn0)
% 289.76/289.99 Found x30:=(x3 x22):(cNUMBER Xn0)
% 289.76/289.99 Instantiate: Xn0:=Xn:fofType
% 289.76/289.99 Found (x3 x22) as proof of (cNUMBER Xn)
% 289.76/289.99 Found (x3 x22) as proof of (cNUMBER Xn)
% 289.76/289.99 Found x30:=(x3 x21):(cNUMBER Xn0)
% 289.76/289.99 Found (x3 x21) as proof of (cNUMBER Xn)
% 289.76/289.99 Found (x3 x21) as proof of (cNUMBER Xn)
% 289.76/289.99 Found (x3 x21) as proof of (cNUMBER Xn)
% 294.98/295.19 Found x30:=(x3 x21):(cNUMBER Xn0)
% 294.98/295.19 Found (x3 x21) as proof of (cNUMBER Xn)
% 294.98/295.19 Found (x3 x21) as proof of (cNUMBER Xn)
% 294.98/295.19 Found (fun (x7:(cODD (cS c0)))=> (x3 x21)) as proof of (cNUMBER Xn)
% 294.98/295.19 Found (fun (x7:(cODD (cS c0)))=> (x3 x21)) as proof of ((cODD (cS c0))->(cNUMBER Xn))
% 294.98/295.19 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 294.98/295.19 Instantiate: Xn0:=Xn00:fofType
% 294.98/295.19 Found x40 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 294.98/295.19 Found (x3 x40) as proof of (cNUMBER Xn0)
% 294.98/295.19 Found (x3 x40) as proof of (cNUMBER Xn0)
% 294.98/295.19 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 294.98/295.19 Instantiate: Xn00:=Xn:fofType
% 294.98/295.19 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 294.98/295.19 Found x70:(cNUMBER Xn0)
% 294.98/295.19 Instantiate: Xn0:=(cS Xx):fofType
% 294.98/295.19 Found (fun (x13:(cNUMBER Xx))=> x70) as proof of (cNUMBER (cS Xx))
% 294.98/295.19 Found (fun (x13:(cNUMBER Xx))=> x70) as proof of ((cNUMBER Xx)->(cNUMBER (cS Xx)))
% 294.98/295.19 Found x40:((or (cEVEN Xn00)) (cODD Xn00))
% 294.98/295.19 Instantiate: Xn00:=Xn:fofType
% 294.98/295.19 Found (fun (x9:(cODD (cS c0)))=> x40) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 294.98/295.19 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x40) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 295.00/295.21 Found (fun (x8:((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))) (x9:(cODD (cS c0)))=> x40) as proof of (((and ((and cIND) (cEVEN c0))) (forall (Xn00:fofType), ((cEVEN Xn00)->(cEVEN (cS (cS Xn00))))))->((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0))))
% 295.00/295.21 Found x30:=(x3 x20):(cNUMBER Xn0)
% 295.00/295.21 Found (x3 x20) as proof of (cNUMBER Xn0)
% 295.00/295.21 Found (x3 x20) as proof of (cNUMBER Xn0)
% 295.00/295.21 Found x30:=(x3 x21):(cNUMBER Xn0)
% 295.00/295.21 Instantiate: Xn0:=Xn:fofType
% 295.00/295.21 Found (x3 x21) as proof of (cNUMBER Xn)
% 295.00/295.21 Found (x3 x21) as proof of (cNUMBER Xn)
% 295.00/295.21 Found x30:=(x3 x20):(cNUMBER Xn0)
% 295.00/295.21 Found (x3 x20) as proof of (cNUMBER Xn)
% 295.00/295.21 Found (x3 x20) as proof of (cNUMBER Xn)
% 295.00/295.21 Found (x3 x20) as proof of (cNUMBER Xn)
% 295.00/295.21 Found x12:(cEVEN c0)
% 295.00/295.21 Found x12 as proof of (cEVEN c0)
% 295.00/295.21 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 295.00/295.21 Instantiate: Xn00:=Xn:fofType
% 295.00/295.21 Found x60 as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 295.00/295.21 Found x50:=(x5 x40):(cNUMBER Xn0)
% 295.00/295.21 Found (x5 x40) as proof of (cNUMBER Xn0)
% 295.00/295.21 Found (x5 x40) as proof of (cNUMBER Xn0)
% 295.00/295.21 Found x50:=(x5 x41):(cNUMBER Xn0)
% 295.00/295.21 Instantiate: Xn0:=Xn:fofType
% 295.00/295.21 Found (x5 x41) as proof of (cNUMBER Xn)
% 295.00/295.21 Found (fun (x12:(cEVEN c0))=> (x5 x41)) as proof of (cNUMBER Xn)
% 295.00/295.21 Found (fun (x12:(cEVEN c0))=> (x5 x41)) as proof of ((cEVEN c0)->(cNUMBER Xn))
% 295.00/295.21 Found x20:((or (cEVEN Xn0)) (cODD Xn0))
% 295.00/295.21 Instantiate: Xn0:=Xn:fofType
% 295.00/295.21 Found (fun (x9:(cODD (cS c0)))=> x20) as proof of ((or (cEVEN Xn00)) (cODD Xn00))
% 295.00/295.21 Found (fun (x9:(cODD (cS c0)))=> x20) as proof of ((cODD (cS c0))->((or (cEVEN Xn00)) (cODD Xn00)))
% 295.00/295.21 Found x60:((or (cEVEN Xn00)) (cODD Xn00))
% 295.00/295.21 Instantiate: Xn00:=Xn:fofType
% 295.00/295.21 Found (fun (x9:(cODD (cS c0)))=> x60) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 295.00/295.21 Found (fun (x9:(cODD (cS c0)))=> x60) as proof of ((cODD (cS c0))->((or (cEVEN Xn0)) (cODD Xn0)))
% 295.00/295.21 Found x12:(cEVEN c0)
% 295.00/295.21 Found x12 as proof of (cEVEN c0)
% 295.00/295.21 Found x80:((or (cEVEN Xn00)) (cODD Xn00))
% 295.00/295.21 Instantiate: Xn00:=Xn:fofType
% 295.00/295.21 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x80) as proof of ((or (cEVEN Xn0)) (cODD Xn0))
% 295.00/295.21 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> x80) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->((or (cEVEN Xn0)) (cODD Xn0)))
% 295.00/295.21 Found x70:=(x7 x60):(cNUMBER Xn0)
% 295.00/295.21 Found (x7 x60) as proof of (cNUMBER Xn)
% 295.00/295.21 Found (x7 x60) as proof of (cNUMBER Xn)
% 295.00/295.21 Found (x7 x60) as proof of (cNUMBER Xn)
% 295.00/295.21 Found x90:=(x9 x80):(cNUMBER Xn00)
% 295.00/295.21 Found (x9 x80) as proof of (cNUMBER Xn)
% 295.00/295.21 Found (x9 x80) as proof of (cNUMBER Xn)
% 295.00/295.21 Found (x9 x80) as proof of (cNUMBER Xn)
% 295.00/295.21 Found x50:=(x5 x40):(cNUMBER Xn0)
% 295.00/295.21 Instantiate: Xn0:=Xn:fofType
% 295.00/295.21 Found (x5 x40) as proof of (cNUMBER Xn)
% 295.00/295.21 Found (fun (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of (cNUMBER Xn)
% 295.00/295.21 Found (fun (x8:((cNUMBER Xn00)->((or (cEVEN Xn00)) (cODD Xn00)))) (x9:(((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00)))=> (x5 x40)) as proof of ((((or (cEVEN Xn00)) (cODD Xn00))->(cNUMBER Xn00))->(cNUMBER Xn))
% 295.00/295.21 Found (fun
%------------------------------------------------------------------------------